[
    {
        "image_filename": "designv10_12_0002777_iceeot.2016.7754868-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002777_iceeot.2016.7754868-Figure2-1.png",
        "caption": "Fig. 2 free body diagram of a quadrotor",
        "texts": [
            " STRUCTURE OF QUADROTOR The quadrotor is assumed to be symmetric with respect to the x and y axes. A general structure is presented in fig.1. The model analyzed in this paper assumes the following: \u2022 The structure is rigid. \u2022 The structure is symmetrical. \u2022 The center of gravity and the body fixed frame origin coincident. \u2022 The propellers are rigid. \u2022 Thrust and drag are proportional to the square of propeller\u2019s speed. III. QUADROTOR DYNAMICS The orientation of quadrotor is determined by roll angle (\u03c6), pitch angle ( ) and yaw angle ( ).The angles are depicted in the fig.2 The control inputs for guiding and stabilizing the quadrotor are mapped from the four independent motor thrusts to one force and three torques: the total thrust force, roll torque, pitch torque, and yaw torque. The rotors generate thrust force which are perpendicular to x - y plane. Each rotor produces a lift force and moment. The two pairs of rotors, i.e., rotors (1,3) and rotors (2,4), rotate in opposite directions so as to cancel the moment produced by the other pair. To make a roll angle (\u03c6), along the x-axis of the body frame, one can increase the angular velocity of rotor (2) and decrease the angular velocity of rotor (4) while keeping the whole thrust constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001270_mnl.2012.0533-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001270_mnl.2012.0533-Figure7-1.png",
        "caption": "Figure 7 Photographs of the developed portable electrochemical system and the microsensor chip",
        "texts": [
            " Then, 1000 mmol/l nitrate was measured in the presence of 1000 mmol/l of each kind of interfering ions, which can indicate whether the interfering ions will affect the normal nitrate analytic signal to be determined. The experiment results are summarised in Fig. 6. It was found that the interference was negligible for most ions, while nitrite caused the biggest signal distortion of 10%, which was also reasonably small. 3.5. Nitrate determination in real samples: Based on the modified microsensor, a portable electrochemical system was developed for nitrate determination in real samples, as shown in Fig. 7. The determination procedure mainly contains three steps: first, three standard nitrate samples with the concentrations of 0, 5 and 10 mg/l were detected to measure and store the corresponding amperometric values at 2510 mV (against Ref). Secondly, the fitted relation between nitrate concentration and amperometric response was calculated by the software embedded in the portable device automatically. Finally, the amperometric response of the calibrated Micro & Nano Letters, 2012, Vol. 7, Iss. 12, pp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.7-1.png",
        "caption": "Fig. 9.7 Chinese southpointing chariot",
        "texts": [
            "6b the angular velocity diagram is shown. End of example. Subject of this section is an engineering problem. In Needham [7] it is reported that in China possibly as early as 3000 years ago and with certainty at about 200 a.C. during imperial processions two-wheel chariots were displayed on which a rotating wooden statue pointed its arm due south independent of driving maneuvers. In a rather detailed description dated 1107 a gear train connecting the wheels of the chariot to the vertical axis of the statue is described. In Fig. 9.7 the essential elements of a modern reconstruction by Lanchester [6] are shown. In the chariot (body 1 ) wheels 6 and 7 are rotating about vertical axes. These wheels are driven by wheel pairs 2 , 4 and 3 , 5 , respectively. Together with the two wheels 8 wheels 6 and 7 constitute a bevel differential2. The statue 9 is rotated by the wheels 8 . The system has only three parameters, namely, the width of the track, the radius r of the chariot wheels 2 and 3 and the angular velocity ratio 2 In spite of its elaborate character the description of the year 1107 is not detailed enough",
            " Finally, \u03c991 and \u03c989 are determined from the vector equation \u03c991 + \u03c918 + \u03c989 = 0 . The angular velocity diagram reveals the relationship 9.8 Acceleration Distribution. Instantaneous Center of Acceleration 309 \u03c991 = \u03c961 \u2212 1 2 \u03c967 = \u03c961 \u2212 1 2 (\u03c961 \u2212 \u03c971) = 1 2 (\u03c961 + \u03c971) . (9.77) Hence with (9.76) \u03c991 = i 2 (\u03c921 \u2212 \u03c931) . (9.78) Equations (9.74) and (9.75) yield \u03c991 = r (\u03c921 \u2212 \u03c931) . (9.79) The identity of these two expressions is the condition to be satisfied by the system parameters: i = 2r . (9.80) The wheels shown in Fig. 9.7 do not satisfy this condition. Note: Precise functioning of the chariot requires a perfectly even terrain. The instantaneous acceleration distribution in a rigid body is determined by (9.14). It depends on the vectors aA , \u03c9 and \u03c9\u0307 : a = aA + \u03c9\u0307 \u00d7 + \u03c9 \u00d7 (\u03c9 \u00d7 ) . (9.81) If \u03c9 and \u03c9\u0307 are not collinear, there exists a single body-fixed point G which instantaneously has zero acceleration. This point is called instantaneous center of acceleration. It is located on the so-called inflection curve. This is the geometric locus of all points characterized instantaneously by collinearity of acceleration a and velocity v "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.5-1.png",
        "caption": "Fig. 17.5 Three double-rockers of second kind with different distributions of the link lengths (4, 5, 6, 8). No link is fully rotating",
        "texts": [
            " For a single input angle the two existing positions of the four-bar are shown (one of them with dashed lines). In these two positions the output link is located on one and the same side of the base line. In Figs. 17.4a , b and c reflection of every possible position in the base line is another possible position. Four-Bars not Satisfying Grashof\u2019s Condition For demonstration the link lengths (4, 5, 6, 8) are used which do not satisfy Grashof\u2019s condition (4+8 > 5+6) . Not a single link is fully rotating relative to the fixed link. These four-bars are referred to as double-rockers of second kind. Figure 17.5a shows the limit positions of both rockers. The angular range of each rocker is a single sector which is symmetrical to the base line. For a single input angle the two existing positions of the four-bar are shown (one of them with dashed lines). In Figs. 17.5a,b,c the four given lengths are given to different links of the four-bar. It is seen that depending on this distribution the fixed link is inside the angular range of either both rockers (Fig. 17.5a) or of a single rocker (Fig. 17.5b) or of no rocker (Fig. 17.5c). Foldable Four-Bars Satisfying Grashof\u2019s Equality Condition min + max = \u2032 + \u2032\u2032 . 572 17 Planar Four-Bar Mechanism For demonstration the link lengths (1, 3, 4, 6) are used which satisfy the condition that 1 + 6 = 3 + 4 . Depending on whether the shortest link is the fixed link or the input link or the coupler the four-bar is either a double-crank or a crank-rocker or a double-rocker of first kind, respectively (compare Figs. 17.4a, b, c). In this respect there is no difference to the general case of fourbars satisfying the inequality condition min + max < \u2032 + \u2032\u2032 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003106_aris50834.2020.9205794-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003106_aris50834.2020.9205794-Figure20-1.png",
        "caption": "Figure 20. Underwater robot. (Left) CAD drawing; (Right) Actual.",
        "texts": [],
        "surrounding_texts": [
            "The most critical part of this concept is that UAV can accurately and autonomously land on the ground mobile robot. The fuzzy-neural network and image-based servo control were implemented to complete the landing [11]."
        ]
    },
    {
        "image_filename": "designv10_12_0001702_rpj-10-2013-0101-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001702_rpj-10-2013-0101-Figure3-1.png",
        "caption": "Figure 3 Geometry of a scaffold fabricated by SLM and a magnified image of a pore of which the structure is built, with its nominal dimensions",
        "texts": [
            " Material hardness within the struts was measured with using a Zwick-Roell ZH -A hardness tester and the equivalent modulus of elasticity was determined during a static compression test on a static materials testing machine (Instron 3384). During the first stage of the test, the minimum regular pore size of the mesh structure that was possible to obtain with the use of the SLM technology was determined. The structure designed for that purpose was composed of cubic cells with boundaries in the form of cylindrical bars (struts) (Figure 3). To speed up calculations and simplify the computer models of such structure (recorded in the form of a net of triangles), the cylindrical bars were replaced with hexagonal struts of equivalent cross section, which is of little importance when such small details are represented geometrically. By gradually reducing both the \u201cdiameter\u201d of struts from original \u00d8250 m and the distance between the strut axes (pore size) from 1,000 m, as well as changing the scanning strategy and orientation of the built-up struts, the correct shape of pores was obtained in the built-up specimens and it was possible to remove loose powder from the inside"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure7-1.png",
        "caption": "Fig. 7. Three-drive hybrid limbs: (a) R 2 R M R M (b) R 2 R N R M (c) R 2 R N R N (d) PR N R N .",
        "texts": [
            " Similarly, the serial limb R 2 R 2 R 2 can also be converted into three-drive hybrid limbs. When the five-bar mechanism actuates the second passive joint, the third revolute joint can also be driven by another planar mechanism. Therefore, the R 2 R M R M , R 2 R N R M and R 2 R N R N hybrid limbs can be derived. Because the corresponding kinematic joints of the serial limbs are located on one plane, the PR 2 P a R 2 limb and the PR 2 R 2 limb can also be transformed into the PR N P a R 2 limb and the PR N R N limb, respectively. The diagrams are as drawn in Fig. 7 . According to this design philosophy, the planar four-bar linkages are expanded to spherical closed-loop kinematic linkages. If the first three kinematic joints of the serial limb R 3 R 3 R 3 are found on a spherical surface, the spherical multi-drive hybrid limbs can also be derived. Then the two-drive R 3 R P hybrid limb and the three-drive R 3 R P R P hybrid limb are obtained. In summary, the serial limb with planar kinematic chains R 2 R 2 , PR 2 , R 4 R 4 or PR 4 connected to the links can be trans- formed into the two-drive R 2 R M , R 2 R N , PR N , R 4 R M , R 4 R N , or PR N hybrid limbs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.22-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.22-1.png",
        "caption": "Fig. 17.22 Proof that double points of the coupler curve lie on the circle of singular foci",
        "texts": [
            "2 on the existence of three cognate four-bars generating one and the same coupler curve. The three centers A0 , B0 and C0 are referred to as singular foci, and the circle itself is called circle of singular foci. Since \u0394 equals zero on the circle, cos\u03b1 and sin\u03b1 are indeterminate if the coupler point is located on the circle. Indeterminate means that at least two different positions of the four-bar generate one and the same point of the coupler curve. In other words: The coupler curve intersects the circle at this point at least twice. Figure 17.22 proves the inverse statement: If the coupler point C is at one and the same point in two (or more) positions of the four-bar, this multiple point lies on the circle. The coupler triangle is (A1,B1,C) in one position 17.8 Coupler Curves 599 and (A2,B2,C) in the other. It must be shown that (A0,C,B0) equals the angle \u03b2 in the coupler triangle. The dashed lines A0C and B0C bisect the auxiliary angles \u03b3 and \u03b4 . With \u03c8 as auxiliary angle \u03b2 = \u03b3 + \u03c8 = \u03b4 + \u03c8 and, consequently, \u03b4 = \u03b3 . Hence (A0,C,B0)= \u03b3/2 + \u03c8 + \u03b4/2 = \u03b2 ",
            " Thus, the equation \u0394 = 0 has the alternative form S4C7y \u2212 C4S7 + S7z(S4x+ C4z) = 0 . (18.32) This equation defines a surface in the x, y, z-system. The curve \u03c4 is the intersection of the surface with the unit sphere. Indeterminacy of sin\u03b1 and cos\u03b1 means that a position of the coupler point C on \u03c4 is produced by (at least) two positions of the four-bar with different angles \u03b1 . This means that a point C on \u03c4 is a multiple point of the coupler curve. For comparison: In the case of the planar four-bar, the condition \u0394 = 0 defines the circle of singular foci with Eq.(17.87). Figure 17.22 was used for proving that the inverse statement is true: If the coupler point C is at one and the same point in two (or more) different positions of the four-bar, this multiple point lies on the circle. Following Dobrovolski [2] the same Fig. 17.22 is now used for proving that this statement holds true for spherical four-bars if the word circle is replaced by curve \u03c4 . The straight lines in the figure are interpreted as arcs of great circles on the unit sphere and the angle \u03b2 in the coupler triangle has the new name \u03b17 . Repeating the old arguments it is shown that the angle (A0CB0) equals the angle \u03b17 of the coupler triangle. In other words this means: The curve \u03c4 described by (18.31) and (18.32) is the geometric locus of all points on the sphere from which the base A0B0 is seen under the angle \u03b17 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000942_i2012-12098-5-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000942_i2012-12098-5-Figure4-1.png",
        "caption": "Fig. 4. (Colour on-line) Sketch of the splay and bend deformation when the colloidal particle is dragged along different directions. Panels (a) and (b) refer to dragging in a contractile and extensile fluid, respectively. Blue arrows refer to the active forces, while the red one represents the external force. The sketch is further discussed in the text.",
        "texts": [
            " More strikingly, our results show that, as soon as \u03b6 = 0, a completely different behaviour is observed regarding the dependence of \u03b7eff on R: Stokes\u2019 law is no longer valid when activity is turned on. Let us focus on fig. 3(a) first: here \u03b7eff rapidly increases with R when the particle is dragged along the director. When an extensile active fluid is considered (fig. 3(b)) instead, \u03b7eff decreases with R, the effect being more visible when the particle is dragged normal to the far-field director. We qualitatively explain these results with the following heuristic argument, sketched in fig. 4 (and summarised previously in [17]). If the particle were not moving, the deformations in the director field due to the anchoring condi- tion would be perfectly symmetric, and forces on the probe due to the active stress would cancel. On the other hand, we expect that, when the particle is dragged through the active nematic fluid some asymmetries will show up in the director profile. In particular, in the case of planar anchoring, when the particle is dragged along the director, the splay in front of the particle should be greater than the one at the back (see fig. 4(a)). This generates a net force that opposes the external one, if the fluid is contractile, and that favours it, in the extensile case. That the effect is more important in contractile fluids can probably be ascribed to the fact that they tend to splay more easily than their passive counterparts, while extensile ones are more stable in resisting splay [36]. An R dependence may then be expected as the splayed region depends on probe size. On the other hand, the director field bends, both down and upstream of the particle, when the external force is applied perpendicular to the far-field director (see fig. 4(b)). When pulling upwards along that direction, again one expects the bending deformation on the top to be larger than the one at the bottom of the particle. These contributions combine to give a force opposing motion in contractile fluids and favouring it in extensile ones. Similarly to the case sketched in fig. 4(a), the effect is now larger for extensile fluids, as they tend to bend more easily than their passive counterpart, while contractile nematics are more resistant to bending [36]. This argument explains qualitatively our results on planar anchoring in fig. 3. It further suggests that the orientation of the director field at the particle surface should play a key role in determining the microrheological drag of the particles. We therefore now investigate this aspect more in depth. We present in what follows both the cases of normal and of no imposed anchoring (W = 0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002277_s00773-018-0550-6-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002277_s00773-018-0550-6-Figure1-1.png",
        "caption": "Fig. 1 The coordinate frames to describe ship motions",
        "texts": [
            " A disturbance observer (DO) is adopted to estimate the lumped disturbance, and an MPC RRS controller with feed-forward compensation mechanism is proposed to reject the lumped disturbance. Simulations are carried out to test the performance of the proposed controller. Simulation results show that the proposed controller is able to avoid control phase lag induced by rudder rate saturation, and possesses a better performance compared to the LQR controller under the variation of environmental disturbances. Conventionally, the formulation of ship\u2019s motion is described in two coordinate frames, the earth frame O0 and the bodyfixed frame O, as indicated in Fig.\u00a01. The earth frame is fixed to the Earth, it is an inertial frame. The body-fixed frame is commonly located at the midship, it is not an inertial frame. The coordinate system and notations of motions adopted in this paper accord with the ITTC convention. To simplify the problem and to get a linear model, we assume that the ship sails at a constant speed, so surge motion will not be considered. Sway, roll, and yaw motions are taken into account in the design of the RRS controller. The 3-degrees of freedom nonlinear ship model about sway, yaw and roll obtained using Newton\u2019s laws is where m is the mass of the ship, zG and xG are positions of the center of gravity in the body fixed frame, v is the sway velocity, p is the angular velocity of roll, r is the angular velocity of yaw, Iz and Ix are rotational inertia about z and x axis, is the density of the sea water, g is the gravity constant, \u2207 is the displacement of the ship, is the roll angle, GZ(\u22c5 ) is the length of the righting arm, Y is the force along y axis, N and K are moments about z and x axis, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002469_s10659-017-9635-4-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002469_s10659-017-9635-4-Figure1-1.png",
        "caption": "Fig. 1 The isotropic bilayer",
        "texts": [
            " (4) and Theorems 2 (the general case) and 3 (a more explicit version for materials with isotropic Hooke\u2019s law). We begin with a few examples of rods with misfit. Several of the experiments mentioned in this section deal with ribbons rather than rods, but find results that are present in rod theory. See Sect. 5.1 for some comments on the distinction between ribbons and rods. THE ISOTROPIC BILAYER: We start with a well-known example. Consider a rod made of two different layers, bonded as shown in Fig. 1. Both layers prefer to expand isotropically when heated, but by different amounts. The two layers cannot assume their stress-free deformation because they must meet on the boundary, but one layer can expand more than the other if the rod bends. Of course, each cross section will deform slightly, and that there can be boundary effects. It is well known, both theoretically and experimentally, that the rod bends. Motivated by the application to bimetallic thermometers, Timoshenko calculated the preferred curvature of the isotropic bilayer using linear elasticity [35]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000521_epc.2008.4763350-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000521_epc.2008.4763350-Figure2-1.png",
        "caption": "Fig. 2. Misplaced Hall sensors in a prototype BLDC motor.",
        "texts": [
            " Jatskevich are with the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (e-mail: p_alaei@ece.ubc.ca, sinach@ece.ubc.ca, jurij@ece.ubc.ca) The theory and modeling of Hall-sensor-driven BLDC motors have been well investigated in the literature [1], [4], [5], [6]. Most of the publications on BLDC assume that Hall sensors are positioned exactly 120 electrical degrees apart. This assumption may not be true for many low-cost and lowprecision motors that are mass-produced on the market. Fig. 2, shows a prototype BLDC motor with misplaced Hall sensors. Dashed axes represent ideal position of the sensors while solid axes represent the actual position of the sensors. As can be seen, the Hall sensors H1, H2 and H3 are mounted on a PC board placed outside the motor case. These sensors react to the magnetic field produced by a permanent magnet tablet that is attached to motor shaft and revolves with the rotor. This tablet is magnetized in a way to have the same magnetization characteristics as that of the rotor. In Fig. 2, the misplacement angles in mechanical degrees are denoted by mA\u03c6 , mB\u03c6 and mC\u03c6 for H1, H2 and H3, respectively. Although the actual mechanical misplacements may appear small (on the order of few degrees), for the motors with large number of magnetic poles these values translate into an even greater errors in electrical degrees as mxx P \u03c6\u03c6 2 = . (1) Evaluating Misalignment of Hall Sensors in Brushless DC Motors Pooya Alaeinovin, Student member, IEEE, Sina Chiniforoosh, Student member, IEEE, and Juri Jatskevich, Member IEEE B 2008 IEEE Electrical Power & Energy Conference 978-1-4244-2895-3/08/$25"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure8.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure8.1-1.png",
        "caption": "Fig. 8.1 Test stand of the gyroscope with the counterweight",
        "texts": [],
        "surrounding_texts": [
            "of the equations for gyroscopemotions around axes. The compensation of the inertial torques cannot be accepted by the rules of physics but accepted by rules of abstract mathematics. The practical tests of the gyroscope motions around two axes demonstrate the deactivation of inertial torques when its precession motion around one axis is blocked. At this condition, the gyroscope demonstrates several new properties represented by the mathematical models and validated by the practical tests. The physical phenomena of the deactivation of inertial torques contradict known principles of classical mechanics and need deep analytical and practical analysis. The tests of the deactivation of gyroscopic inertial torques are conducted on the stand assembled with the high precession gyroscope and the counterweight. The test stand with Super Precision Gyroscope \u201cBrightfusion LTD\u201d is demonstrated in Figs. 8.1 and 8.2, and the technical data are represented in Table 8.1. The mass of the counterweight is selected with the aim to have the slow gyroscope turn around axis ox and to have the ability to record the time of motions. The location of the centre mass is near the centre o of the coordinate system oxyz, and the difference between masses left and right sides is small. The gyroscope with one side support connected with the counterweight G by the axle s. The axle s is fixed on the centre beam b with the ability to free rotation around axis ox. The spherical journals B and D of the centre beam are located on the supports of conical surfaces on the vertical arms of the frame. The centre beam is assembled with the frame that contains two arms mounted on the horizontal bar bs. This assembled construction presents the gyroscope gimbal. The gimbal has the ability to free rotation about the fixed pivot C (vertical axis oy) on the platform. Table 8.1 contains the following symbols: Jx\u00b7W = Jy\u00b7W = (MR2 c/4) + Ml2 is the mass moment of the movable gyroscope component inertia around axes ox and oy,"
        ]
    },
    {
        "image_filename": "designv10_12_0001460_tmag.2013.2239271-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001460_tmag.2013.2239271-Figure1-1.png",
        "caption": "Fig. 1. Magnetic-geared motor in this study (initial position).",
        "texts": [
            " The N-T curves with and without current limiting are computed by using finite element method (FEM) under vector control. Manuscript received November 01, 2012; revised January 07, 2013; accepted January 08, 2013. Date of current version May 07, 2013. Corresponding author: N. Niguchi (e-mail: noboru.niguchi@ams.eng.osaka-u.ac.jp). Digital Object Identifier 10.1109/TMAG.2013.2239271 The magnetic-geared motor in this study consists of a highspeed rotor, a low-speed rotor, and a stator, as shown in Fig. 1. The high-speed rotor consists of a yokemade of carbon steel and 8 segment-type permanent magnets of T. The lowspeed rotor consists of 20 steel pole pieces formed by 50A400 laminated silicon steel sheets, which are joined to each other by a thin bridge. The 12-slot stator has three-phase concentrated windings, with the diameter of the wire and the number of turns per coil being 0.5 mm and 100, respectively. The 3-phase coils mounted onto the 12-slot stator produce a 4-pole-pair magnetomotive force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002241_we.2150-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002241_we.2150-Figure6-1.png",
        "caption": "FIGURE 6 High\u2010speed shaft and bearing roller loads at 100% power calculated using theTransmission3D model. The contact areas on the rollers are highlighted [Colour figure can be viewed at wileyonlinelibrary.com]",
        "texts": [
            "20 In this section, the bearing load models are first compared with the measured, steady\u2010state load data for validation. Then the effects of torque, rotor moments, and generator misalignment are examined. Finally, bearing loads and predicted contact stress during a braking event and a grid loss event are examined for their potential contribution to WEC generation. The measured TRB loads are compared with the predicted Transmission3D load zone in 3 different pure\u2010torque conditions, as shown in Figure 5. For reference, the TRB and CRB roller loads predicted by the Transmission3D model are shown in Figure 6 for the full\u2010power condition. The TRB pair was designed with very little preload, provided only by small springs that force apart the bearing outer races, to allow for thermal expansion during operation. The gear mesh forces the shaft upwind in operation, resulting in an axial load that is almost entirely supported by the downwind TRB. As shown in Figure 5 (left), the downwind TRB has a nearly symmetric load zone that simply increases in size with drivetrain power and torque, while its oval shape is a result of shaft tilting in the vertical direction because of clearance in the CRB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.30-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.30-1.png",
        "caption": "Fig. 3.30 Robert Bosch Corporation ESP system [ROMANO 2000].",
        "texts": [
            "29 is shown an actual implementation of the EMB AWD DBW dispulsion mechatronic control system with the single-sense of a direction vector redundant ring structure that contains the following components and/or responsibilities [CADENCE 2003]: Two travel sensors and one force sensor to determine driver intent (each sensor connected to a different wheel node); Sensor values communicated over the network \u2192 consistency checks; Wheel node calculates the actuation commands for all four wheels; Commands communicated by means of network \u2192 each of the four wheel nodes compares its own actuation commands with those calculated by the other wheel nodes; Voting mechanism in the network layer of each wheel node can then disable the power to individual actuators in the case of a fault; If a node needs to be shut down, the brake force is redistributed to prevent the ehicle from yawing; The advanced brake functions (ABS) are executed in two front-wheel nodes; If the front-wheel nodes do not calculate the same output commands for these advanced brake functions, the function may be deactivated; this provides fail-safe operation; redundant power supply. Automotive Mechatronics 486 In Figure 3.30, as an example solution, a Robert Bosch Corporation ESP system is shown [ROMANO 2000]. In Figure 3.31 the components in the Robert Bosch Corporation ESP system are presented. They include (A) active wheel angular velocity (speed) sensors; (B) steering angle sensor; (C) combined yaw rate sensor/lateral accelerometer; (D) attached ECU; (E) E-M motor; (F) pressure sensor, and (G) fluidical (hydraulical) unit. Some ESP system use ride height sensors [ROMANO 2000]. [Robert Bosh Corporation; ROMANO 2000]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001525_j.mechmachtheory.2013.04.001-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001525_j.mechmachtheory.2013.04.001-Figure2-1.png",
        "caption": "Fig. 2. Coordinate systems in enveloping process.",
        "texts": [
            " 001 Nomenclature a Center distance of the worm drive, (mm) Z1, Z2 Number of the crown worm threads and the planar internal gear teeth, respectively rb Radius of the main basic circle, (mm) r1 Reference radius of the crown worm at its umbilicus, (mm) mt Transverse module, (mm) l Effective length of the crown worm, (mm) b Width of the planar internal gear, (mm) \u03b4 Axes crossing angle between the planar internal gear and the crown worm, (\u00b0) \u03b2 Inclination angle of the generating plane, (\u00b0) i12 Gearing ratio of the worm drive, here i12 = Z2/Z1 \u03c31,\u03c32 Fixed coordinate systems \u03c3w,\u03c3g Movable coordinate systems \u03c3a Auxiliary coordinate system \u03c9g,\u03c9w,\u03c9b Angular velocity vectors of the planar internal gear, the crown worm and the workbench, respectively, (rad/s) \u03c9p,\u03c9f Angular velocity vectors of the planar grinding wheel and the finger milling cutter, respectively, (rad/s) \u03c9gw Relative angular velocity vector between the planar internal gear and the crown worm, (rad/s) \u03c9xa gw,\u03c9ya gw,\u03c9za gw Component of the relative angular velocity vector \u03c9gw in \u03c3a about xa, ya and za directions, respectively, (rad/s) vX,vY Translational velocity vectors of the workbench along X and Y, respectively, (mm/s) vxg,vyg Translational velocity vectors of the finger milling cutter along xg and ya, respectively, (mm/s) vgw Relative velocity vector between planar internal gear and crown worm, (mm/s) vxa gw,vyagw,vzagw Component of the relative velocity vector vgw in \u03c3a about xa, ya and za directions, respectively, (mm/s) \u03c6g,\u03c6w Rotating angles of the planar internal gear and the crown worm, respectively, (\u00b0) \u03c6g2 Intermittent rotating angles of the planar internal gear, (\u00b0) \u03a3g,\u03a3w Tooth surface of the planar internal gear and the crown worm, respectively rg,rw Position vector of \u03a3g and \u03a3w, respectively xn m,ynm,znm Coordinate value of the planar internal gear (m = g) or the crown worm (m = w) in \u03c3n(n = 1, 2, a, g, w) ng Unit normal vector of \u03a3g nxa g ,nyag ,nzag Component of the unit normal vector ng in \u03c3a about xa, ya and za directions, respectively \u03a6,\u03a6t,\u03a8 Function of meshing, meshing limit and undercutting limit, respectively Mmn Matrix for coordinate transformation from \u03c3m(m = 1, 2, a, g, w) to \u03c3n(n = 1, 2, a, g, w) an Normal vector of the contact line on meshing point in \u03c3a k\u03c1 Induced principal curvature, (mm\u22121) \u03b8v Sliding angle, (\u00b0) fc Undercutting function on the crown worm tooth surface, (mm) Considering the assembly interference and physical constraint, the planar internal gear single-enveloping crown worm drive in the case of non-orthogonal (Fig. 1) is discussed. Because of the symmetry of two sides of the tooth surfaces, here, only one side of the tooth surfaces is considered in the theoretical calculation. The crown worm surface is considered as a conjugate surface, which is generated as an enveloping about a series of planar internal gear surfaces. The coordinate systems in the enveloping process are shown in Fig. 2. The fixed coordinate systems \u03c31(o1 : x1, y1, z1) and \u03c32(o2 : x2, y2, z2) indicate the initial position of the crown worm and the planar internal gear, respectively. The movable coordinate system \u03c3w(ow : xw, yw, zw) is rigidly connected to the crown worm, while \u03c3g(og : xg, yg, zg) is rigidly connected to the planar internal gear. The crown worm and the planar internal gear rotate about axes z1 and z2 with the angular velocity vectors \u03c9w and\u03c9g, respectively. The rotating angles are \u03c6w and \u03c6g at some instant. The shortest distance between axes z1 and z2 is a, while the crossing angle is \u03b4. The generating plane xaoaza is in the auxiliary coordinate system \u03c3a(oa : xa, ya, za). The origin of the auxiliary coordinate system is always on the main basic circle, and the radius of the main basic circle is rb. The crossing angle between axes xg and za is \u03b2, which is also the inclination angle of the generating plane. The directions of rotation correspond to the right-hand worm drive. As shown in Fig. 2, the planar internal gear surface\u03a3g is the generating plane xaoaza. The vector equation of rg can be represented in coordinate system \u03c3g as follows: where rg u; v\u00f0 \u00de \u00bc xgg ygg zgg h iT \u00bc rb\u2212v sin \u03b2 \u2212u v cos \u03b2\u00bd T \u00f01\u00de u and v are the surface parameters of \u03a3g. Without losing generality, it is possible to assume that the crown worm rotates with angular velocity \u03c9w = 1 rad/s, and then the planar internal gear rotates with angular velocity \u03c9g = 1/i12 rad/s. According to the known tooth surface \u03a3g, the relative velocity vector vgw and relative angular velocity vector \u03c9gw at the conjugate point can be represented in coordinate system \u03c3a as follows: where vgw \u03c6g \u00bc vgwxa vgwya vgwza h iT \u00bc rb sin \u03b4\u2212a sin \u03b4 sin\u03c6g\u2212v sin \u03b2 sin \u03b4\u2212v cos \u03b2 cos \u03b4 cos\u03c6g \u00fe rb\u2212v sin \u03b2\u00f0 \u00de=i12 rb cos \u03b2 cos \u03b4 sin\u03c6g \u00fe a sin \u03b2 sin \u03b4 cos\u03c6g\u2212a cos \u03b2 cos \u03b4\u00fe u sin \u03b2 sin \u03b4\u00fe u cos \u03b2 cos \u03b4 cos \u03c6g \u00fe u sin \u03b2\u00f0 \u00de=i12 \u2212rb sin \u03b2 cos \u03b4 sin\u03c6g \u00fe a cos \u03b2 sin \u03b4 cos\u03c6g \u00fe a sin \u03b2 cos \u03b4\u00fe u cos \u03b2 sin \u03b4\u2212 u sin \u03b2 cos \u03b4 cos\u03c6g \u00fe v cos \u03b4 sin\u03c6g \u00fe u cos \u03b2\u00f0 \u00de=i12 2 66664 3 77775 \u00f02\u00de \u03c9gw \u03c6g \u00bc \u03c9gw xa \u03c9gw ya \u03c9gw za h iT \u00bc cos \u03b4 sin\u03c6g sin \u03b2 cos \u03b4 cos\u03c6g\u2212 cos \u03b2 sin \u03b4\u2212 cos \u03b2=i12 cos \u03b2 cos \u03b4 cos\u03c6g \u00fe sin \u03b2 sin \u03b4\u00fe sin \u03b2=i12 2 4 3 5: \u00f03\u00de Because the known tooth surface \u03a3g is a plane, the unit normal vector of it can be represented in coordinate system \u03c3a as following: ng \u00bc ng xa ng ya ng za h iT \u00bc 0 0 1\u00bd T: \u00f04\u00de According to the gear meshing theory [2], for conjugated action, tooth surfaces \u03a3g and \u03a3w are in tangency during the meshing process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003709_tec.2021.3052365-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003709_tec.2021.3052365-Figure2-1.png",
        "caption": "Fig. 2. Cross-section of SCIM model.",
        "texts": [
            " These harmonics are then synthesized by the equivalent current layers in the airgap and are substituted into the 2D FEA loss models in Section III. At last, prototype tests and 3D FEA model are conducted to verify the accuracy of the proposed model in Section IV. II. ANALYSIS OF AIRGAP MAGNETIC FIELD SPACE HARMONICS The airgap magnetic flux density space harmonics of IM s are the leading causes of stray load loss [21]. Therefore, it is essential to accurately calculate the airgap magnetic flux density space harmonics for stray load loss calculation. The cross-section of the SCIM is shown in Fig. 2. The main quantities of the motor are listed in Table I. The material of the silicon steel sheet is N23-50. And the material of the rotor bar is aluminum. A. Magnetizing MMF calculation based on the GAFMT In GAFMT, the equivalent airgap model is proposed and an electrical machine is considered as a cascade of three elementary parts, i.e., the source magnetizing MMF (source), the short-circuited coil (SCC)/salient pole reluctance (SPR)/flux guide (modulator) and the armature winding (filter). 1) Source magnetizing MMF A series of Fourier decomposition functions of the source magnetizing MMF induced by the stator winding based on winding function can be expressed as [23]: ( )\u2211 = = 3 1m mmf iWF \u03c6 ( )tpIkN fw t \u03c9\u03c6 \u03c0 \u2212\u22c5\u22c5= cos2 2 3 2 4 (1)            \u22c5= 2 sin/ 2 sin) 2 (cos \u03b1\u03b1\u03b2 ff f w pqqp p k (2) Authorized licensed use limited to: California State University Fresno"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003254_s11431-020-1588-5-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003254_s11431-020-1588-5-Figure6-1.png",
        "caption": "Figure 6 (Color online) The cylinder interference model and the definition in leg interference evaluation.",
        "texts": [
            " The leg interference is the other effect factor which determines the gait topology of the six-legged robot. Shin interferences are very common when the six-legged robot walks on continuous-nondifferentiable terrains. The 2-DOF leg of Hexa-XIII robot lack the abduction-adduction DOF, so that the six-legged robot is more likely to encounter the shin and knee interference than legged robots with 3-DOF legs. Therefore, we use the interference criteria to evaluated leg interference and switch gait topologies. The interference criteria are modelled by the cylinder model (see Figure 6). The cylinder elements are utilized to replace the leg components and terrain features. Robots always perceive the environment by vision sensors which can acquire terrain point clouds. In the proposed interference model, a series of terrain cylinder elements are generated centered at the point cloud at a specific resolution to express the terrain feature. We calculate the distance from the terrain cylinder element axis to the leg cylinder axis as the distance margin of interference (see Figure 6(b)). Therefore, the nonlinear shin-terrain interference problem could be calculated in a liner solution. In HCS, the terrain cylinder elements ei are generated with the axis alone the z-axis. The six-legged robot evaluates the interference margin with the range from the tolerable radius rt in touchdown neighbourhood to the radius rc to ensure the collision prevention of legs. The interference distance margin D is the minimum distance from terrain cylinders center to the leg. According to the resolution of the point cloud \u03be, the index ic range of terrain cylinder elements can be got by eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001782_1.4031792-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001782_1.4031792-Figure13-1.png",
        "caption": "Fig. 13 Edge detection: (a) original image and (b) detail edge detection",
        "texts": [
            "org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use object in a binary image directly. For that reason, it obtains the results significantly faster (by a factor of 100) than the star operator and is therefore the utilized algorithm for analyzing bearing cage movement analysis in this paper. The developed algorithms described in this paper are applied to images of a spindle bearing (designation HCB 7014) taken on the test rig that was shown in Fig. 2. First, the original image of the bearing (Fig. 13(a)) is contrast standardized and edge detection is performed. With the identified outer edge pixels of the cage (compare detail view of the bearing in Fig. 13(b)), it is possible to determine the center of the cage for each image using the Zhou or star operator. In this example, the rotational speed of the shaft, respectively, the inner ring is 3000 rpm and the bearing cage is stable. Figure 14 shows the plot of the cage centers, in other words, the cage whirl, for 625 images or five revolutions of the cage in 2D and three-dimensional (3D); in the latter, the z-axis shows the image number continuously. It can be seen that the cage center moves on two circular paths with different radii in an alternating fashion around the bearing center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure8-1.png",
        "caption": "Fig. 8 Thermal FE analysis results for two hot rollers (one on each cone assembly) (heating scenario 7 in Table 2)",
        "texts": [
            " To further investigate the effect of hot rollers on the temperature of the bearing cup, which is the surface scanned by the infrared wayside HBDs, several hypothetical heating scenarios were explored; three of which are discussed hereafter. The question posed earlier in this paper as to whether it is possible for certain rollers to heat to temperatures above 232 C (450 F) within the bearing and go undetected by the HBDs can be answered by looking at the results of simulations 7\u201310. Simulation 7 in Table 2, shown in Fig. 8, models the case in which two rollers, one on each cone assembly, are operating abnormally. The 031002-8 / Vol. 4, SEPTEMBER 2012 Transactions of the ASME Downloaded From: http://thermalscienceapplication.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use motivation behind this simulation is to determine the roller temperature and heat rate associated with a bearing cup temperature of 90 C, which is still about 40 C below the hot-box alarm threshold assuming an ambient temperature of 25 C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003040_taes.2020.2988170-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003040_taes.2020.2988170-Figure3-1.png",
        "caption": "Fig. 3: Diagram of the relative positions of satellite P and satellite E",
        "texts": [
            " \u02d9\u0302 Df = \u03b31 \u2225\u2225vreT\u2225\u2225 \u02d9\u0302 D\u03c4 = \u03b32 \u2225\u2225\u03c9reT\u2225\u2225 \u02d9\u0302m = \u03b33vre Tu1 \u02d9\u0302 Jc = \u03b34\u03c9reu2 T \u02d9\u0302\u03c7t = \u03b35\u2016\u03c9t\u20162 (\u2225\u2225vreT\u2225\u2225 \u2016pt\u2016+ \u2225\u2225\u03c9reT\u2225\u2225) \u02d9\u0302\u03c7c = \u03b36 \u2225\u2225\u03c9reT\u2225\u2225 \u2016\u03c9c\u20162 (17) The derivation process of the updated rule and the proof of the closed-loop system\u2019s stability are presented in Appendix A. This section focuses on the tracking of a mobile target. Because the target is maneuverable, the tracking mission is actually a pursuing and escaping scenario. Let P and E denote the pursuing and escaping satellites, respectively. Satellite P aims to track satellite E, while satellite E escapes from satellite P . The reference orbit frame, Fo, is established, where the origin point o is located near the two satellites. The relations are drawn in Fig. 3. The position of satellite P in Fo is xP = [xP , yP , zP ] T, while the position of satellite E is xE = [xE , yE , zE ] T. The orbital dynamics are Authorized licensed use limited to: University of Exeter. Downloaded on June 15,2020 at 12:55:34 UTC from IEEE Xplore. Restrictions apply. 0018-9251 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. x\u0308i (t) = 2 \u00b5\u2295 r3 (t) xi (t) + 2\u03c9 (t) y\u0307i (t) + \u03c9\u0307 (t) yi (t) + \u03c92 (t)xi (t) + Tiu x i (t) y\u0308i (t) = \u2212 \u00b5\u2295 r3 (t) yi (t)\u2212 2\u03c9 (t) x\u0307i (t)\u2212 \u03c9\u0307 (t)xi (t) + \u03c92 (t) yi (t) + Tiu y i (t) z\u0308i (t) = \u2212\u03c92 (t) zi (t) + Tiu z i (t) (18) where \u03c9 (t) represents the instantaneous angular velocity of the reference orbit; r (t) represents the instantaneous radius of orbit; \u00b5\u2295 represents the Earth\u2019s gravitational constant; Ti represents the maximum unit mass thrust of the satellite; ui = [uxi , u y i , u z i ] T represents the control variables, and i \u2208 {P,E}",
            " Yushan Zhao majored general mechanics for his bachelor degree in Northwestern Polytechnical University between February, 1978 and January, 1982, and then got his master degree in 1985 and Ph.D degree in 1995. During 1998 and 1999, he engaged in advanced studies in Samara University of Aeronautics and Astronautics in Russia. He taught in Northwestern Polytechnical University from February, 1982 to June, 2002, and then worked in Beihang University since 2002, where he was awarded the excellent teacher of Beihang University. Figure Captions: Fig. 1: Diagram of relative position between chaser and target Fig. 2: Diagram of the feature point on disabled satellite Fig. 3: Diagram of the relative positions of satellite P and satellite E Fig. 4: Schematic diagram of learning logic in x-channel Fig. 5: The critic fuzzy inference system in x-channel Fig. 6: The expected hovering position to the feature point on the target Fig. 7: Membership functions Fig. 8: Time histories of the relative states by using the PSTC Fig. 9: Contrast of control acceleration under adaptive controller and PSTC(a) Fig. 10: Contrast of control acceleration under adaptive controller and PSTC(b) Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003167_pi-c.1959.0034-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003167_pi-c.1959.0034-Figure10-1.png",
        "caption": "Fig. 10 shows the electric field surrounding a single-phase line consisting of a bundle of two conductors. The solid lines are obtained from theoretical calculations by the method outlined in the paper, and the small circles indicate experimental points. The closeness between the experimental results and the theoretical calculations can be clearly seen. A similar result has been obtained for n = 3 and n = A.",
        "texts": [],
        "surrounding_texts": [
            "The electric field surrounding bundle conductors can be determined by replacing each conductor of the bundle by one of negligible radius displaced slightly from the centre of the original conductor. This is based on the feet that equipotential surfaces near such a thin conductor are nearly cylindrical, so that an actual conductor may be so placed as to take up the position of one of the equipotentials. The accuracy of the method depends on the ratio, Did, between the diameter of the bundle circle and that of each conductor; the greater the ratio, the more accurate is the method. With the ratios usually found in highvoltage transmission lines, the deviation of the equipotential surface from a true cylinder is small, and it can be arranged that the deviation is zero at the point of maximum surface gradient. Maximum deviation from the surface of a cylinder occurs somewhere between points of maximum and minimum gradients. For example, with a bundle of two conductors and Did =10 , this maximum deviation does not exceed 0-5%; with Did = 20 it is about 0-1 %. The analysis deals with single-phase lines with a bundle of 2, 3 or 4 conductors, but it can be extended to cover any number of conductors in a bundle. For 3-phase lines the resultant field can be found by the principle of superposition when the fields due to the two other phases are taken into consideration. In the latter case, the electric charge per metre of each phase is to be determined with all the three phases and their images involved. Formulae giving the potential gradient at any point on a conductor surface are developed and compared with those given by Cahen.1 The method is checked by experimental field mapping using a circular double-layer electrolytic tank."
        ]
    },
    {
        "image_filename": "designv10_12_0001796_s12541-015-0346-0-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001796_s12541-015-0346-0-Figure5-1.png",
        "caption": "Fig. 5 Motion of roller and inner race",
        "texts": [
            " \u03b4k is defined as , (3) where \u03b40 and \u03b2 \u00d7 lk are the contact compressions due to the translation motion and relative angular misalignment \u03b2 between the roller and inner race, respectively, and hk and drk are the crown drops due to the modified roller profile and the out-of-roundness of the inner race, respectively. drk can be easily determined from Fig. 4 with the radius difference defined as , (4) where R and r are the nominal and instantaneous inner raceway radii, respectively, at an arbitrary position along the contact line. . (5) The time-varying angle \u03d5(t) depends on the instantaneous orbital position angles \u03d5r(t) and \u03d5s(t) of the roller and the rotating race, as demonstrated in Fig. 5. These angles are defined as (6) (7) , (8) where \u03a9 and \u03a9m are the angular speed of the inner race and the orbital speed of roller, respectively. The contact force and moment between the roller and nonrotating outer race can be calculated in a manner similar to the inner race with the quantity \u03d5s(t) omitted from Eq. (6). The roller-flange contact force Qf is determined according to the classical Hertzian point contact theory for a flat flange and a spherical roller end as , (9) where cf is the contact constant depending on the material and geometry at the contact point and \u03b4f is the contact compression between the roller and flange"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001290_s11581-014-1290-1-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001290_s11581-014-1290-1-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the formation of BH-Ag/Pt NPs at different stages of galvanic replacement process",
        "texts": [
            " Then, 5 \u03bcL of BH-Ag/ Pt NPs and CH-mixed solution was poured on the surface of the pretreated Au electrode. It was then left to dry under ambient condition for 3 h at 4 \u00b0C. Ultimately, the Au electrode modified with BH-Ag/Pt NPs was rinsed twice with doubledistilled water and dried in the air. The electrode was stored at 4 \u00b0C, when it was not in use. Mechanism of galvanic replacement reaction between AgNPs and PtCl6 2\u2212 The schematic of the galvanic replacement reaction between Ag NPs and PtCl6 2\u2212 ions is shown in Fig. 1. The formation process of the BH-Ag/Pt NPs via an in situ replacement reaction between the Ag atoms and PtCl6 2\u2212 ions without any additional reducing agent can be explained as follows. As the PtCl6 2\u2212 ions approach the surface of Ag NPs, they are directly reduced to Pt due to the difference in reduction potential relative to that of the Ag atoms. Pt is simultaneously deposited onto the surface of Ag NPs. Meanwhile, the Ag atoms are oxidized to Ag+. The chemical transformation initially takes place from the core of the Ag NPs leading to a continuous consumption of Ag in the core region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000254_j.jmatprotec.2008.03.067-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000254_j.jmatprotec.2008.03.067-Figure6-1.png",
        "caption": "Fig. 6 \u2013 The schematic of the fi",
        "texts": [
            " he heat transfer equation (Shinoda and Li, 1999) is 1c1 \u2202T \u2202t = 1 r \u2202 \u2202r ( r 1 \u2202T \u2202r ) + \u2202 \u2202x ( 1 \u2202T \u2202x ) + qv (15) The boundary conditions exhibit heat convection between he outer surface and the surrounding atmosphere, and heat adiation and heat import at the friction interface. The heat onvection coefficient and radiation coefficient can then be eplaced by synthetical heat transfer coefficient h. The heat ransfer coefficient h increases as temperature increases. To nsure accurate results, while calculating for the tempera- Fig. 6 is the schematic for finite difference grid and notations. The integral of controlled volume dv = r r x is calculated from time t to t + t, from s to n in the direction of r, and from w to e in the direction of x. The following explicit discrete equation is constructed: apTp = aeT0 e + awT0 w + anT0 n + asT0 s + a0 pT0 p + b (16) where ap = cprp r x t , ae = erp r (\u0131x)e , aw = wrp r (\u0131x)w , as = srs x (\u0131r)s , an = nrn x (\u0131r)n , a0 p = ap \u2212 ae \u2212 aw \u2212 an \u2212 as, b = qvrp r x 4.2. Boundary conditions (1) Temperature of consumable-rod\u2019s bottom center Here the temperature of the consumable-rod\u2019s center is considered to be equivalent to that of the nearest difference point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000928_j.mechmachtheory.2012.10.007-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000928_j.mechmachtheory.2012.10.007-Figure9-1.png",
        "caption": "Fig. 9. Free body diagram for tangential tooth load calculations.",
        "texts": [
            " The mesh loads due to the torque transfer of the Pericyclic Transmission System gears are assumed to be localized at the mean pitch diameter (Dmp) of the gears as a point load. In Fig. 7-b, the mesh loads Ft, Fr, Fa refer to tangential, radial and axial loads, respectively. As shown in this figure, Ft, Fr, Fa are parallel to x, y, z coordinates of the tooth, respectively. The tangential tooth loads at eachmesh are derived as a function of gear radius and the transmitted torque based on the free body diagram presented in Fig. 9-a and -b for the single PMC design [4,5]. Here, Rr, Rpr, Rpo and Ro are gear radii of RCM, PMCmeshing with RCM, PMCmeshingwith output and output gears, respectively. The tangential force (Ft) at each meshing teeth is calculated from the total transferred driving force (\u03a3Ft) as shown in Fig. 9-b. The total transmitted driving force on the output gear is formulated as \u03a3Fto=\u2212Tout/Ro where Tout is the output gear torque. The reaction force on the PMC gear meshing with output has the same magnitude and opposite direction to \u03a3Fto. In Fig. 9, positive \u03a3Fto is shown in positive-x direction which points on the out of page direction. The tangential force at one tooth of the meshing face-gear at the output side is derived from driving force as: Fto \u00bc \u03a3Fto\u22c5 5 N4 \u22c51 k \u00f011\u00de This equation contains 5/N4 term to calculate the tangential load per tooth, since one fifth of the total number of teeth of the PMT gears are in contact. Here, N4 is the number of teeth on the output gear. Split-torque factor (k) takes the value 1 or 2 depending on single PMC or split torque twin-PMC design, respectively. The tangential mesh load at the RCM side is calculated from the equilibrium of moments about the carrier axis and formulated as: Tin \u00fe \u03a3Fto\u22c5Rpo \u00fe \u03a3Ftr\u22c5Rpr \u00bc 0 \u00f012\u00de Here, Tin is the input torque transmitted from the carrier. RCM side mesh tangential load (\u03a3Ftr) is calculated by rearranging Eq. (12) as: \u03a3Ftr \u00bc Tout\u22c5Rpo=Ro \u2212Tin =Rpr \u00f013\u00de \u03a3Ftr on the PMC is in the same direction with \u03a3Fto as presented in Fig. 9. The tangential force at one tooth of the meshing face-gear at the RCM side is: Ftr \u00bc \u03a3Ftr\u22c5 5 N1 \u22c51 k \u00f014\u00de Similar to the RCM side the tooth contact ratio is included in Eq. (14) with the term 5/N1 to calculate the load per tooth. Here, N1 is the number of teeth on the RCM gear and k is the split-torque factor. In this paper, only twin PMC split torque design is investigated (k=2). The radial and axial loads are presented as a function of tangential load, pressure angle (\u03b1) at the mean pitch diameter and pitch cone angle of the gear of interest (\u03b2i) in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000846_0954405411407997-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000846_0954405411407997-Figure3-1.png",
        "caption": "Fig. 3 Surface requiring support within joint clearance",
        "texts": [
            " However, because of the staircase effect, the surface roughness deteriorates with decreasing tilt angle when the layer thickness is constant, which indicates that the friction coefficient would increase, and the surface would be easily worn. Therefore the thickness of layers seems more important, since it affects the quality of the tilting surface. In practice not all joints can be adjusted to a suitable configuration; even if the joint is displayed at a suitable configuration, the surface within the clearance of the joint may still need support structures. As shown in Fig. 3, the critical angle of fabrication is represented by u; the hole surface between A and B and the pin surface between C and D need support structures. As discussed above, increasing the scanning speed decreases the transferred heat, and thus avoids a deep laser penetration effect, but the motion of the joint may be still affected by trapped powder clumps, or even by sticking of the vertical surfaces, since the clearance is often very small. Thus the supports influence not only the surface quality but also the joint mobility"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001278_j.engfailanal.2013.02.030-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001278_j.engfailanal.2013.02.030-Figure1-1.png",
        "caption": "Fig. 1. External loads on a large roller slewing bearing assembly (a), components of a large three-row roller slewing bearing (b).",
        "texts": [
            " Numerically determined contact stresses then serve as a basis for fatigue analyses, where the bearing\u2019s service life of the bearing is determined by using the stress-life approach, considering typical material parameters of the bearing\u2019s raceway. 2013 Elsevier Ltd. All rights reserved. Slewing bearings are machine parts of large dimensions with diameters up to several meters and are used in different applications (i.e. cranes, turning tables, excavators, wind turbines, etc.). They connect two main structural parts and enable controlled relative rotation and transmission of external loads between them. As shown in Fig. 1a, slewing bearing assemblies are connected to the rest of the structure (mounting supports) with pre-stressed bolted joint connections and are usually exposed to axial force (Fa), radial force (Frad) and overturning (tilting) moment (MT). Due to a wide variety of applications, slewing bearings are manufactured in different sizes and configurations [1]. This paper deals with three-row roller slewing bearings (Fig. 1b) which have cylindrical rolling elements (rollers) in three rows; two axial rows (carrying and supporting row) for transmission of the axial force and the overturning moment, and one radial row for transmission of the radial force. There are some well-established industry standards for calculation of both static [2] and dynamic [3] load ratings of common rolling-element bearings. These standardized calculation procedures are based on different bearing life prediction theories which are fully described in [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000444_s12206-008-0110-9-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000444_s12206-008-0110-9-Figure5-1.png",
        "caption": "Fig. 5. Electromagnetic analysis using 2D FEM ; (a) Flux line, (b) Flux density.",
        "texts": [
            " Electromagnetic sources are divided into local and global forces. The local force is affected by the magneto-motive force and the airgap permeance. For a 3- phase BLDC motor, frequency components of local forces such as normal and tangential forces, and global forces such as torque ripple and cogging torque, can be expressed as in (1-3)[13]. 60lf Nf n p= (1) 6 2 60tr p Nf n= (2) 60ct Nf n lcm= (3) Frequency decomposition of the global and local forces, calculated by 2D FEM and the Maxwell method, is performed to analyze the force harmonics. Fig. 5 shows the electromagnetic analysis results which display flux lines and flux density distribution of the test motor at different rotor position. The local forces at A and B are analyzed with respect to the rotor angular position as shown in Fig. 7. It can be seen in Fig. 6 and 7 that the 32nd and the 96th harmonic orders are local force and global forces, respectively. However, the noise characteristics shown in Fig. 8 indicate that the noise emission near 650 Hz is not much affected by the electromagnetic forces since the frequency components of electromagnetic forces are proportional to the motor RPM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.38-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.38-1.png",
        "caption": "Fig. 17.38 Tschebyschev\u2019s straight-line approximation. Solid lines: Crank-rocker with r = .4 , a = 1.3 . Approximation of the line y0 \u2248 2, 19 . Measures of quality L/ \u2248 1.44 , |B/L| \u2248 .00020 . In dashed lines the cognate four-bar generating the same coupler curve. For P1 and P2 see the text following (17.100)",
        "texts": [
            " With y = 0 the following equation is obtained for these points which is of third order in x and in \u03b7 : 604 17 Planar Four-Bar Mechanism (\u03b7 \u2212 a)(x\u2212 )(x2 + \u03b72 \u2212 r21)\u2212 \u03b7x[(x\u2212 )2 + (\u03b7 \u2212 a)2 \u2212 r22] = 0 . (17.100) For given parameters the equation has either one or three real roots x . For this reason one does not expect coupler curves which do not intersect the x -axis. Such coupler curves do exist, however. Example: If \u03b7 = 2a and r2 = a , the equation has the roots x1 = and x2,3 = \u00b1 \u221a 4a2 + 2 \u2212 r21 . For the parameter values = 1 , a = 1.3 and r1 = 0.4 the three roots are real. Yet, the coupler curve does not intersect the x -axis. In Fig. 17.38 the branch of this curve above the x -axis is shown. The three real roots are marked B0 , P1 and P2 . They represent singular points of the coupler curve. In order to understand this phenomenon (17.80) and (17.81) must be formulated for the special case b1 = \u03b7 , b2 = \u03b7 \u2212 a , \u03b2 = 0 , y = 0 : x2 + \u03b72 \u2212 2x\u03b7 sin\u03b1 = r21 , (x\u2212 )2 +(\u03b7\u2212 a)2 \u2212 2(x\u2212 )(\u03b7\u2212 a) sin\u03b1 = r22 . (17.101) Each equation expresses the cosine law for one of the triangles of Fig. 17.13 . The elimination of sin\u03b1 is possible without imposing the constraint equation cos2 \u03b1 + sin2 \u03b1 = 1 ",
            " The diagram in Fig. 17.37 shows as functions of the ratios L/ and |B/L| characterizing the quality of the straight-line approximation. The former should be large and the latter very small. These goals are achieved with values of close to 1/3 . Example: With = r/ = .4 (17.171), (17.173), (17.176) and (17.174), determine the coupler length a = 1.3 , the length y0 \u2248 2.19 and the measures of quality L/ \u2248 1.44 and |B/L| \u2248 .00020 . This is an excellent straight-line approximation. The entire coupler curve is shown in Fig. 17.38 . The four-bar is drawn in solid lines. Dashed lines show the cognate fourbar generating the same coupler curve. For the significance of the points B0 , P1 and P2 see the comment following (17.100). For comparison: The straight-line approximations by Watt / Evans (Fig. 17.34a,b ) and by Roberts (Fig. 17.35) are not nearly as good. The measures of quality for Roberts\u2019 approximation are L/ \u2248 1 and |B/L| \u2248 .0068 . From Fig. 17.37 it is seen that with increasing the measure of quality L/ improves while the essential measure of quality |B/L| deteriorates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure6.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure6.6-1.png",
        "caption": "Fig. 6.6 View of the swing shown in Fig. 6.1 at eight selected times, showing the positions of the bat, the four arm segments, the batter\u2019s head and shoulders, and his stationary left foot. LF Left forearm, RF Right forearm",
        "texts": [
            "6, and it allows us to determine the forces and torques acting on the bat, at least in the horizontal plane. Batters normally swing a bat in a plane that is inclined to the horizontal, given that the tip of the bat starts at a point above the shoulders and drops to about waist level when the bat collides with the ball. To obtain the results in Figs. 6.1, 6.5, and 6.6, the batter was asked to swing in a horizontal plane, although he started off with the bat near shoulder height, a bit closer to the camera. That is why the bat in Fig. 6.6 appears to be a bit longer at the start of the swing than later on. Ideally, several cameras should be used to get a full three-dimensional view of the swing, but that would have complicated the experiment considerably. Alternatively, a single camera could be used, viewing in a direction perpendicular to the swing plane, as is sometimes done to view the swing action of a golfer. By plotting the x and y coordinates of the bat CM as a function of time, the velocity Vx in the x direction and the velocity Vy in the y direction were determined to calculate the speed V D ",
            "7 Rotation of the Bat 97 Towards the end of the swing, the centripetal force is much larger than the other component, so the batter pulls on the handle in a direction almost parallel to the dashed lines shown in Fig. 6.5. The motion of the bat can be regarded as consisting of two separate motions. One is the motion of the bat CM, which follows a spiral path, starting from a point near the batter\u2019s right shoulder, and ending in front of the batter when the batter makes contact with the ball. On top of that motion is a rotation of the whole bat around an axis through the bat CM. In Fig. 6.6, the whole bat rotates through an angle of about 180\u0131 from t D 0 to t D 340 ms, and almost 360\u0131 from t D 0 to t D 420 ms. The object of the exercise, assuming the batter wants to hit the ball at high speed, is to allow the bat to line up almost at right angles to the path of the incoming ball at a time when the impact point on the barrel is traveling at maximum speed. The forces shown in Figs. 6.7 and 6.8 are not the only forces acting on the bat. In addition, the batter exerts a torque on the bat to make it rotate",
            " That is why, in Fig. 6.9, a negative couple of almost 60 Nm was applied by the batter 6.8 Wrist Torque 99 near the end of the swing. Without that couple, the bat would rotate much too fast and the bat might end up pointing straight at the pitcher rather than at right angles to the path of the incoming ball. The large negative couple near the end of the swing arises naturally, without the batter doing anything special to the bat, apart from hanging onto the handle firmly. The situation shown in Fig. 6.6 at 300 or 340 ms indicates that if the bat were allowed to rotate at high speed then the handle would push firmly on the batter\u2019s left hand and pull out of his right hand. To prevent this happening, the batter pushes on the handle with his left hand and pulls with his right hand, thereby generating the large negative couple required to counteract the large positive torque arising from the centripetal force on the bat. The batter simultaneously pulls the bat towards his chest to provide that centripetal force",
            " Much has been written, especially in relation to the golf swing, about the action of the wrists. When swinging a bat or a club, the wrists are used at the beginning of the swing to hold the bat or club at an angle of about 90\u0131 to the forearms. By locking the wrists in this manner, the bat or club, as well as the forearms, can swing around like a solid, rigid object. As the bat speeds up, the wrists relax. By the time the bat collides with the ball, the wrists have allowed the bat to line up with the forearms, as indicated at the end of the swing in Fig. 6.6. It might appear that the wrists are actively causing the bat to rotate, but it is primarily the centripetal force that causes the bat to rotate. The wrists are not strong enough to generate rapid rotation of the bat, nor are they strong enough to prevent the rotation. The bat, therefore, causes the hands to rotate about an axis through the wrist, not the other way around. The strength of the wrists can be measured by holding a bat in a horizontal position with one hand and by hanging a weight at the far end",
            " A person can easily hold the bat by itself in this manner, but when a weight is added to the barrel end, it becomes more difficult to hold the bat in a horizontal position. The wrist torque needed to support a 0.9 kg bat in a horizontal position, when the bat center of mass is 0.45 m from the wrist, is 4 Nm. If a person can support an additional 2.2 lb (1 kg) weight located 0.7 m from the wrist, then the additional torque exerted by the wrist is 6.9 Nm, giving a total torque of 10.9 Nm. With two wrists, a batter can exert a maximum wrist torque of about 22 Nm on the bat. In Fig. 6.6, the maximum couple exerted on the bat is about 60 Nm. That couple is too large to be provided by wrist action alone, and must be supplied by the equal and opposite forces exerted on the handle by each arm. Consequently, the wrists play only a small role at the end of the swing, although they are often used by batters when they roll one wrist over the top of the other during the follow-through. 100 6 Swinging a Bat The rotation axis of a bat is not as easily identified as one might expect. The rotation axis of the bat is shown in Fig. 6.6 at several different times during the swing. At the start of the swing, the bat rotates about an axis in the handle near the batter\u2019s right shoulder. That axis can also be identified in Fig. 6.5 by the intersection point of images of the bat at times t D 0, 180 and 200 ms. At later times, the bat axis moves to a point outside the bat, above the batter\u2019s head (see Fig. 6.6). In the latter case, the bat axis is not defined as the intersection point of sequential images of the bat. Rather, every point in the bat rotates about the axis in a circular orbit, although the radius of the orbit is different for different points. You can see how this arises if you rotate the letter L about an axis through the bottom, right hand corner of the letter. The axis is not at the intersection of subsequent images of the vertical part of the letter. The axis would correspond to the intersection of subsequent images of the vertical part of the letter only if the actual axis was located somewhere along the vertical part of the letter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.9-1.png",
        "caption": "Figure 5.9. Schema for the mutual gravitational attraction of two particles.",
        "texts": [
            " Our objective is to show that in all cases the gravitational force acting on a material object is equal to the product of its mass and the gravitational field strength it experiences. Afterwards, Newton's theory of gravitation is illustrated in a few examples. The gravitational attraction by an ideal planet is determined, and subsequently the definition of the weight of a body is introduced. We begin with a pair of particles PI, P2 having mass m I , m2, respectively, and denote by F 12 the force exerted on PI by P2 , as shown in Fig. 5.9. Let e be a unit vector directed from P2, the source of the action, toward PI; and write r = IX2 - XII for the distance between PI and P2, wherein XI and X2 are the respective distinct position vectors of PI and P2 in any reference frame <I> = {F ; Id .Clearly, only the relative position vector r == re of PI from P2 is important, so a reference frame is needed only for the solution of particular problems. These terms are used to state the following law of nature. Newton's lawof gravitation: Between any two particles in the world, there exists a mutual gravitational force that is directly proportional to the product of their masses, inversely proportional to the square of their distance ofseparation, and directed in the sense ofmutual attraction along their common line, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000038_12.654906-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000038_12.654906-Figure3-1.png",
        "caption": "Figure 3: Calibration coordinates system, adapted from [5]",
        "texts": [
            "aspx z y x tzyxoffsetr tzyxoffsetr tzyxoffsetr \u2212=\u22c5\u2212\u22c5+\u22c5+\u22c5 \u2212=\u22c5+\u22c5\u2212\u22c5+\u22c5 \u2212=\u22c5+\u22c5+\u22c5\u2212\u22c5 00022 00012 00002 100 010 001 (2) These equations can then be written as: EzDyCxBoffsetA =+++ 000 **** (3) In equation (3), A, B, C, D and E are the column coefficient vectors, which can then be re-written as: N z y x offset M = \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 \u22c5 0 0 0 (4) Since M is not a square matrix, the unknowns can be found using the singular value decomposition (SVD) or MoorePenrose inverse: ( ) NMMM z y x offset TT \u22c5\u22c5\u22c5= \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 \u22121 0 0 0 (5) Additionally, the RMS error can be computed as: [ ] numNzyxoffsetMrms T 2 000 \u2212\u22c5= (6) where num is the number of samples. To set up the experiment, we placed the ultrasound probe into a container of water. After the probe and the field generator were fixed at several different positions, the tracked needle was dipped into the water and moved to determine the exact position where the tip intersected with the imaging plane. The transformation relationship of the calibration system is shown in Figure 3. The position of the needle tip, Ptip, can be determined by its pixel location in the ultrasound image, Pus, the calibration matrix, Tc, and the reference tracker\u2019s transformation matrix, Tref, using the following equation: Proc. of SPIE Vol. 6141 61412M-4 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/15/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx uscreftip PTTP \u22c5\u22c5= (7) where ( )Tus vuP 1,0,,= , and u and v are the column and row indices of the pixel in the acquired image"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003202_j.semcdb.2020.03.007-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003202_j.semcdb.2020.03.007-Figure3-1.png",
        "caption": "Fig. 3. Sub-volume averaging of outer doublet microtubules generated with 96-nm repeats in mouse respiratory cilia. (a) Surface-rendering model of the outer doublet microtubules in a cross-sectional view from the proximal end of the axoneme. (b) Most of the outer doublet microtubules have seven inner-arm dyneins, (c) while two inner-arm dyneins are missing in the one or two outer doublet microtubules in the axoneme.",
        "texts": [
            " The details of the stacking structure at the center of the cartwheel, referred to as the hub, and the connection of each triplet microtubule, called the A\u2013C linker, have been elucidated, as shown in Fig. 2(b and c). The three-dimensional structures of cilia and flagella have been analyzed by cryoelectron tomography and image processing in sea urchin sperm and Chlamydomonas flagella [10\u201312]. More detailed ciliary structures have been reported in mammalian cells, such as mouse and human respiratory cilia [13,14]. We also reported the axonemal structure of mouse respiratory cilia by cryoelectron tomography, as shown in Fig. 3(a). We found an asymmetric arrangement of inner dynein arms in the nine outer doublet microtubules of the respiratory cilia, as shown in Fig. 3(b and c). The asymmetrical ciliary motion is likely produced by asymmetric dynein arrangements [13]. The asymmetric alignment of the inner dynein arms in Chlamydomonas flagella has also been repoted [15]. Dynein is a large ring-like molecule that can be divided into the head, stalk, buttress/strut, and tail domains. Cytoplasmic dynein plays a role in the transport of proteins, nucleotides, and organelles from the plus end to the minus end of microtubules, while ciliary/flagellar dynein produces a periodic waveform in cilia and flagella"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure5.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure5.3-1.png",
        "caption": "Fig. 5.3 Cross-sectional view of a brushed separately excited DC machine with compensation windings (left) and interpoles (right)",
        "texts": [
            "30 Simulation results for speed and reference torque versus time without and with anti-windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Fig. 5.1 Cross-sectional view of a brushed separately excited and permanent magnet DC machine [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Fig. 5.2 Vector diagram for brushed DC machine with constant armature current ia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Fig. 5.3 Cross-sectional view of a brushed separately excited DC machine with compensation windings (left) and interpoles (right) 131 Fig. 5.4 Vector diagram for brushed DC machine with current commutation in the neutral zone. (a) Rotated commutator and brush assembly. (b) Compensation windings or interpoles . . . 131 Fig. 5.5 Symbolic field-oriented model: quadrature axis configuration . . . 132 Fig. 5.6 Voltage source model of the brushed DC machine . . . . . . . . . . . . . . . . 133 Fig. 5.7 Generic model of a brushed DC machine, connected to a voltage source ua ",
            " The flux generated by the compensation windings will be such that it compensates the armature reaction flux \u03c8ar in which case the neutral zone remains aligned with the geometrical \u03b2 axis. The displacement angle now is \u03c1 = 0 and the armature flux is \u03c8a = \u03c8f. Note that the compensation winding is magnetically coupled with the armature. Due to this mutual coupling the resulting inductance La reduces to a leakage inductance. However, adding such compensation windings in the poles is expensive and therefore only used for larger machines and servo machines, i.e., machines that are exposed to fast changing load conditions. Such a machine is shown in Fig. 5.3 (left) and the resulting vector diagram is shown in Fig. 5.4b. \u2022 A set of so -called interpoles [1], in effect similar to compensation windings, may be introduced to improve the commutation process. Interpoles are additional poles with windings that also carry the armature current ia. These poles are positioned on the \u03b2 axis of the machine and also serve to compensate the armature reaction flux \u03c8ar. The cross-section of such a machine is shown in Fig. 5.3 (right). The task of developing a set of representative models of the DC machine with either a field winding or permanent magnets is undertaken with the aid of Fig. 5.4. The underlying assumption in this case is that the machine has sufficient commutator 5.1 Modeling of Brushed DC Machines 131 segments to ensure that the current vector ia remains stationary and stays aligned with the neutral zone of the machine. Under these circumstances the scalar voltage/current variables are simply equal to ia = { ia } , ua = { ua} and ea = { ea = j\u03c9m \u03c8a } "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure3-1.png",
        "caption": "Fig. 3 Solid model of the bearing-axle assembly showing how the boundary conditions (BCs) were applied for the FE analyses conducted for this study. Note: (1) heat flux was applied to the circumferential surface of the rollers only, (2) bearing overall heat transfer coefficient was applied to the bearing external surfaces (i.e., bearing cup external surface and side walls, and bearing cone side walls), and (3) axle heat transfer coefficient and radiation were applied to all exposed surfaces of the axle.",
        "texts": [
            "32 W K 1 for the bearing cup, which takes into account forced convection generated by a 5 m s 1 airstream and radiation to an ambient at a temperature of 25 C. However, since the software used for the FE simulations requires convection coefficients to be entered in units of W m 2 K 1, the external surface area of the bearing cup Acup\u00bc 0.1262 m2 was used to obtain the heat transfer coefficient in the appropriate units (ho\u00bc 65.9 W m 2 K 1). The latter overall heat transfer coefficient was applied to the external (exposed) surface of the bearing only, as illustrated in Fig. 3. For the axle, the cylinder-in-cross-flow correlation, Eq. (1), and the flow over a flat surface correlation, Eq. (2), given in Incropera et al. [34] (Chap. 7, p. 427 and 410, respectively), were utilized to calculate the convection heat transfer coefficient from the circumferential surface and the two ends of the axle, respectively. Both correlations yielded a convection coefficient value of haxle\u00bc 25 W m 2 K 1 corresponding to a 6 m s 1 airstream and a 25 C ambient temperature. Nu \u00bc 0:3\u00fe 0:62Re1=2Pr1=3 1\u00fe 0:4=Pr\u00f0 \u00de2=3 h i 1=4 1\u00fe Re 282; 000 5=8 \" #4=5 \u00bc hLc k ; Pe 0:2 (1) Nu \u00bc 2 0:3387 Re 1=2Pr 1=3 1\u00fe 0:0468=Pr\u00f0 \u00de2=3 h i1=4 8>< >: 9>= >; \u00bc hLc k ; Pe 100 (2) where Re \u00bc VLc v ; Pe \u00bc Re Pr (3) In Eqs",
            " The only parameter needed to calculate radiation from the axle to the ambient was emissivity, and it was measured to be about 0.96 from previous experimentation (Tarawneh et al. [24]). Again, a sensitivity analysis was performed on the emissivity value used in this study, which revealed that the results differed by less than 1% when the emissivity value was lowered by 20%. Finally, to simulate heat generation within the bearing assembly, heat flux was applied to the circumferential surface of the rollers, as depicted in Fig. 3. The appropriate heat flux value was determined through a trial-and-error process starting with an overall heat input of 11.5 W per roller (normal operation conditions) and increasing this input until the desired external cup temperature was achieved. The acquired heat input per roller was then divided by the surface area of the roller to obtain the heat flux value. Here, it is assumed that the rollers are the source of heat within the bearing which is justified considering the mass of the roller (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.146-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.146-1.png",
        "caption": "Fig. 2.146 Indispensable components of the Toyota Prius drivetrain or powertrain [http://www.cleangreencar.co.nz; WALKER 2006].",
        "texts": [
            " Application of regenerative braking improves stopping power and, incorporated with a BBW AWB dispulsion mechatronic control system, provides a better brake pedal for the driver. As an example, in Figures 2.146 and 2.147, are shown indispensable components of the Toyota Prius are shown, including the drivetrain or powertrain as well as its DC-AC/AC-DC macrocommutators and CH-E/E-CH storage battery, respectively [WALKER 2006]. Automotive Mechatronics 340 The Toyota Prius powertrain and drivetrain (see Fig. 2.146) contains three basic components, namely: 1.500 cm3 petrol ICE, 56 kW: Atkinson thermodynamic cycle (vs. Otto); 34 % efficient at 10 kW (13.5 hp). Two DC-AC/AC-DC macrocommuator IPM motors/generators: MG1, 18 kW; MG2, 30 kW. A planetary gear that allows a continuously variable drive ratio. The Toyota Prius DC-AC/AC-DC macrocommutators and CH-E/ E-CH storage battery (see Fig. 2.147) contains two basic components, namely: Two DC-AC/AC-DC macrocommutators (DC-AC inverters/AC-DC rectifiers) matched to E-M/M-E motors/generators: 50 kW total at 500 VDC; Liquid cooled under bonnet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure11-1.png",
        "caption": "Fig. 11 a The flat Miura-ori unit cell: a = b = 0.02, a = 60 ; his are fold angles at the creases. b The Miura-ori with 5 9 5 unit cells and b = 118.27 . c The kirigami obtained by cutting away 32 facets from the Miura-ori",
        "texts": [
            " Table 3 Displacement loading conditions for the pop-up kirigami, see Fig. 8 Nodes A3, B3, C3, D3 B0, C0 A5, B5, C5, D5 Prescribed W 0 0.06 0.1 Fig. 9 Crane. a The crease pattern where the valley folds (hrest[ 0) and mountain folds (hrest\\ 0) are indicated by chained and solid lines, respectively. b A paper model of the folded form 5.4 Compressing the Miura-ori and the derived Kirigami This example considers the folding of a Miura-ori and its derived kirigami under displacement compression (Liu and Paulino 2017). Figure 11a shows the flat Miura unit cell which is made up of four identical parallelograms with a = b = 0.02 and a = 60 . The Miura-ori consists of 5 9 5-unit cells. In the flat configuration, b = 120 , L = Lflat = 0.1H3 & 0.173 and W = Wflat = 0.2. To avoid the buckling instability under the compressive loading, the initial configuration in Fig. 11b is taken to be nearly flat (b = 118.27 ) but not perfectly flat. On the supporting conditions, node O is fixed; the nodes at X = 0 are on the same vertical plane and their X-displacements are fixed. The nodes at the other end of X (& 0.172) are on Table 4 Displacement loading conditions for the crane Nodes A5, A6 A10 A1 A9 A7, A8 Prescribed W 10.5 9 10-3 22.0 9 10-3 22.5 9 10-3 26.3 9 10-3 40.5 9 10-3 Fig. 10 Crane under displacement loading (a) and (b): a isometric view of the final configuration and the Z-displacement plot, b top view of the final configuration and the maximum principal membrane strain plot. c and d are the predictions under rest angle loading another vertical plane and their X-displacements are prescribed to be - 0.16 under the compressive loading. For nodes on the X\u2013Y-plane at the two ends, their Z-displacements are fixed. The kirigami in Fig. 11c is obtained by cutting away 32 facets from the Miura-ori. Here, the paperboard is still adopted as the facet material. For the structures to behave like a mechanism with rigid panels connected by hinges, the ratio k/D should be small (Liu and Paulino 2017). To benchmark the predictions with the analytical solution based on the rigid facet assumption, the fold stiffness is reduced to k = 10\u20134. With the setting, the kirigami experiences convergence problem. In this light, its initial time increment is set to be 0",
            "55 are shown in Fig. 12b, c. Figure 13a, b show the histories of the crease energy and the reaction force (X-component) at the compressed end, respectively. They are essentially identical to the analytical solutions. Since the stiffness of the crease is much smaller than that of the facet, the deformation is confined to crease folding whilst the membrane and bending energies are negligible. Based on the rigid facet assumption, it is known that h3 = -h1 (minor folds) and h4 = h2 (major folds), see Fig. 11a for the labels, during the folding process (Lang and Howell 2018). The Miura-ori has 90 minor and major folds whilst this number decreases to 26 for the kirigami. Thus, Uc for the Miura-ori: Uc for the kirigami = 90: 26. The numerical predictions are in good agreement with this ratio, see Fig. 13a. The same ratio also holds for the magnitude of the reaction force which is shown in Fig. 13b. The animation videoes for Miura-ori and the derived kirigami are given in Online Resources 9 and 10, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000714_1.3157159-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000714_1.3157159-Figure3-1.png",
        "caption": "Fig. 3. The pinhole camera model shows how a real world point X is projected as X on the camera image plane uv, through the optical center C of the lens. Also note how the camera frame x y z is fixed to the optical center of the lens.",
        "texts": [
            " The camera calibration toolbox from the Computational Vision Group at Caltech was used in conjunction with MATLAB to calibrate the camera; for a detailed description of the procedure, see Ref. 16. The MATLAB toolbox also incorporates an extrinsic calibration element. The extrinsic calibration procedure enables metric measurements to be made from the values given in terms of pixels. This procedure provides the translation and rotation matrices that relate the real world coordinate system to the image plane see Fig. 3 . The equation for the transformation between a point in the world frame xyz to its corresponding image point in the camera fame x y z is x =Rc x+Tc, where Rc and Tc are the rotation and translation matrices, respectively.17 A real world coordinate system was selected such that it was fixed to the snooker table so that two of its axes lie along the two perpendicular edges of the table and both x and y lie on the imaginary plane that is created by the ball centers see Fig. 2 b , which is 26.2 mm above the table surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001654_s00170-017-1048-9-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001654_s00170-017-1048-9-Figure14-1.png",
        "caption": "Fig. 14 Interaction of feed rate and annealing temperature on average roughness (a, b) and mean roughness depth (c, d) using ANN and Poisson statistical analyses",
        "texts": [
            " This tends to increase the value of the surface roughness for both average roughness and mean roughness depth [54]. h\u2248 D2 c 8R0 ; h \u00bc R\u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4R2 0\u2212D 2 c q 2 \u00f021\u00de Figure 13a\u2013d shows that increasing the value of surface roughness can be associated with the stronger effect of the explained phenomenon versus reduction in cutting forces. The slope of the contour colors is small and shows the variations in finishing allowance which has a small effect on increasing the surface roughness [55]. Figure 14 illustrates that by increasing heat treatment temperature, both surface roughness parameters decreased, which is related to change in the microstructure, strain, stress and hardness. For as-built samples due to high working temperature and cooling rate \u03b1, martensite and high tensile strength (1.35 Gpa) with low elongation (3%) were observed in agreement with the literature [56, 57]. In stress relieving and mill annealing due to low cooling rate in furnace cooling, primary alpha is retained and a small portion of secondary alpha is grown so grain size increases slightly",
            " Ftotal \u00bc WDc ftoothNtooth Khard \u00f022\u00de where ftooth is the feed per tooth, Ftotal is a vector sum of the force component, W is the width of the chip, Ntooth is the number of the tooth and Khard is the metal removal factor that is inversely related to the hardness of the workpiece. Decreasing the value of hardness in higher annealing temperature results in increasing the value of Khard so the cutting force decreases and Fr (z, \u03b8) in Eq. 9AA increases. This trend leads to generation of lower cutting force and vibration. Also, ductility increased by increasing annealing temperature and bigger chips were observed after machining, hence cutting pressure decreased. Finally, surface roughness decreased and a better surface was obtained which is shown in Fig. 14a\u2013d with approximately 40% reduction in the average roughness and mean roughness depth after \u03b2 annealing in both ANN and Poisson analyses. Figure 15 shows EBSD images of as-built and \u03b2 heat-treated samples. In this work, spherical components were designed and printed by an SLM machine. In order to modify surface quality, postprocessing by annealing and machining has been carried out. Two surface parameters, average roughness and mean roughness depth, were measured using an optical profilometer, and surface parameters in four cross-validations were modelled by Taguchi, Poisson and ANN methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000918_j.fss.2011.06.001-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000918_j.fss.2011.06.001-Figure3-1.png",
        "caption": "Fig. 3. Double-inverted pendulums connected by a torsional spring.",
        "texts": [
            "36 \u00d7 103. The feedback and observer gain vectors are selected as Kc = [ 144 0 24 0 0 144 0 24 ]T and Ko = [ 80 0 900 0 0 60 0 900 ], respectively. The filter L\u22121 i (s) is selected as L\u22121 i (s) = 1/(s + 2). The membership functions for all inputs are given as A1 j ( \u02c6\u0304e) = 1 (1 + exp(5 \u00d7 ( \u02c6\u0304e + 1.5))) A2 j ( \u02c6\u0304e) = exp(\u2212( \u02c6\u0304e)2) A3 j ( \u02c6\u0304e) = 1 (1 + exp(\u22125 \u00d7 ( \u02c6\u0304e \u2212 1.5))) Example 1. We consider the following problem of balancing double-inverted pendulums connected by a torsional spring shown in Fig. 3. Each pendulum may be positioned by a torque input ui applied by a servomotor at its base. Here, it is assumed that the torque disturbances d1 and d2 are values randomly in the interval [\u22120.05, 0.05]. The equations of motion of the pendulums are defined by Eq. (31), where 1 = x11 and 2 = x21 are the angular displacements of the pendulums from the vertical reference, the end masses of the pendulums are m1 = 2 kg and m2 = 25 kg, the moments of inertia are J1 = 2 kg and J2 = 25 kg, the constant of the connecting torsional spring is k = 2 N m/rad, the pendulum height is r = 1 m, the gravitational acceleration is g = 981 m/s2, and the torsional spring is relaxed when the pendulums are all in the upright position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure6.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure6.11-1.png",
        "caption": "Fig. 6.11 Four pole, interior permanent magnet synchronous machine, showing two-layer stator winding and rotor saliency",
        "texts": [
            "6 Generic current based rotor-oriented non-salient synchronous machine model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Fig. 6.7 Load angle definition (\u03c1m) in phasor diagram . . . . . . . . . . . . . . . . . . . . . 160 Fig. 6.8 Non-salient synchronous, phasor based machine model . . . . . . . . . . 160 Fig. 6.9 Blondel diagram of a non-salient synchronous machine . . . . . . . . . . 161 Fig. 6.10 Output power versus load angle curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Fig. 6.11 Four pole, interior permanent magnet synchronous machine, showing two-layer stator winding and rotor saliency . . . 164 Fig. 6.12 Synchronous machine, with a salient rotor . . . . . . . . . . . . . . . . . . . . . . . . . 164 Fig. 6.13 Generic synchronous machine model, with a salient rotor . . . . . . . . 166 Fig. 6.14 Vector diagram with direct and quadrature axis for salient machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ",
            " The parameters deployed here are identical to those used for Fig. 6.9. Also, the same operating points are shown in Fig. 6.10 for comparative purposes. A tutorial example which demonstrates the use of the Blondel diagram is given in Sect. 6.3.2. Salient synchronous machines have a reluctance that is rotor position dependent. A common type of salient synchronous machines is the interior permanent magnet machine which carries magnets within the rotor lamination. A cross section of an interior magnet machine with four poles is shown in Fig. 6.11. In the direction of the x-axis, the magnets are in the flux path, increasing the effective air-gap due to their low permeability. In the direction of the y-axis, the magnets have no effect and thus the effective air-gap is unchanged [3]. Consequently, the magnetizing inductances Lmx and Lmy related to the x- and y-axes are different. In the example given, Lmy is larger than Lmx. This is typical for interior magnet machines and contrary to salient pole machines with field windings where Lmy is usually smaller than Lmx",
            " The generic model of the salient synchronous machine follows directly from the non-salient model, according to Fig. 6.3. For the salient model, the gain module 1/Ls shown in Fig. 6.3 must be replaced by a gain 1/Lsd, 1/Lsq as illustrated in Fig. 6.13. The input and output vectors for this gain module are unchanged, while the gain variables are defined by equation set (6.15). As with the non-salient case, the field flux linkage \u03c8f may be supplied by an excitation winding which carries a current if or by permanent magnets, as shown in Fig. 6.11. The coordinate transformation process for deriving a symbolic and generic representation of the rotor-oriented model of the salient machine is similar to that undertaken for the non-salient case in Sect. 6.1.3. The process is initiated with 166 6 Synchronous Machine Modeling Concepts the aid of Eqs. (6.14a) and (6.15). For a rotor flux based model the synchronous reference frame with the direct and quadrature axis is linked to the field flux linkage vector \u03c8f, as shown in Fig. 6.14. The equation set for the salient rotor flux based model can be written as udq s = Rs idq s + d \u03c8dq s dt + j\u03c9s \u03c8dq s (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002856_ab3c3a-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002856_ab3c3a-Figure7-1.png",
        "caption": "Fig. 7. Vibration modes of the transducer. (a) Anti-symmetric vibration mode. (b) Symmetric vibration mode.",
        "texts": [],
        "surrounding_texts": [
            "2.1 Configuration of the proposed robotic finger The proposed robotic finger consists of three phalanges, two joints, and some tension springs. The robotic finger belongs to a serial manipulator. Using two tension springs, the three phalanges and the two joints are connected with each other alternately to form the finger, as shown in Fig. 1. Joints Phalanx A Phalanx B Phalanx C Tension springs Fig. 1. Configuration of the proposed robotic finger. Each phalanx is mainly composed of a bonded-type piezoelectric transducer, a pair of rectangular connecting beams, two bolts, and two studs with steps, as shown in Fig. 2(a). The bonded-type piezoelectric transducer with a simple symmetrical structure contains four pieces of piezoelectric ceramic (PZT) plates and a metal substrate. Two parallel beams, two driving feet, and a holder form the metal substrate. The holder located at the geometric center of the metal substrate adopts cross frame construction to fix the transducer, as shown in Fig. 2(b). Two PZT plates with opposite polarization directions, which are polarized along their thickness directions and bonded on the upper and lower surfaces of the same beam, form a group, as illustrated in Fig. 2(c). Two rectangular grooves are distributed at both ends of the connecting beam. Two location holes and a convex platform in the middle of the connecting beam are used to install the holder of the transducer by two bolts. There are many adjustment holes along the length direction of the connecting beam to mount two studs with steps, as shown in Fig. 2(d). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an us cr ip t 5 Connecting beam Bolt Stud with steps o z y x Bonded-type piezoelectric transducer (a) PZT plates o z y x Beam Foot-1 Holder Foot-2 (b) o z y x Group B & Polarization direction Group A (c) Location holes Adjustment holes Convex platform Groove (d) Fig. 2. Configuration of the phalanx. (a) Explosive view of the phalanx. (b) Configuration of the bonded-type piezoelectric transducer. (c) Polarizations and arrangements of the PZT plates. (d) Three-dimensional model of the two connecting beams. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an us cr ip t 6 Each joint is composed of two rotors and two shafts, as shown in Fig. 3. There are two limit blocks located in the rotor, determining the rotational angle of the rotor. The two rotors are assembled vertically, and then the shaft passes through the center hole of the rotor. Two grooves on the side of the shaft are fitted into the rectangular grooves at one end of two connecting beams. The shaft connects with the stud with steps of the phalanx by two tension springs, and the rotor is pressed against the driving foot of the transducer. Rotor ShaftLimit block Grooves Center hole Fig. 3. Assembly of the joint. The preloading force between the rotor and the transducer is imposed by two tension springs, and most importantly the direction of the preloading force is always along the length direction of the connecting beam. Selecting the appropriate adjustment holes or replacing tension springs with different stiffness can adjust the preloading force. There is no chamber in the proposed bonded-type piezoelectric transducer, and the proposed robotic finger is designed as an open configuration, eliminating the limitation of water pressure on the working depth of the robotic finger. 2.2 Operating principle To drive the two rotors to rotate in opposite directions, elliptical trajectories of the surface points of the two driving feet must be reversed. If two groups PZT plates are supplied with two electrical signals with a temporal phase difference of \u03c0, respectively, the piezoelectric transducer is excited to vibrate at an anti-symmetric vibration mode, leading to the surface points of the two driving feet moving with the same vibration direction along the x direction, as shown in Fig. 4(a). When an electrical signal is simultaneously applied to the two groups of PZT plates, the piezoelectric transducer is stimulated to vibrate at a symmetric vibration mode, resulting in the opposite vibration movement along the y direction for the surface points of the two driving feet, as shown in Fig. 4(b). To simultaneously generate the anti-symmetric and symmetric vibration modes of the piezoelectric transducer, two electrical signals with a temporal phase difference of \u03c0/2 are applied to the two groups of PZT plates, respectively. The surface points of the two driving feet move in opposite elliptical motions. As two rotors contact the surface of the two driving feet under a certain preloading force, the frictional force is produced to push the rotor, as shown in Fig. 5. The motion directions of two rotors can be reversed as the temporal phase difference of two excitation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te M an us cr ip t 7 signals is switched to -\u03c0/2. To validate the elliptical trajectory, point P is selected to indicate the center point on the surface of the driving foot, as shown in Fig. 4. When the anti-symmetric and symmetric vibration modes of the transducer are excited, the vibration characteristics of the point P in the x and y directions can be given in Eqs. (1) and (2), respectively. 1sin( )x xU A t = + (1) 2sin( )y yU A t = + (2) where Ux and Uy are the vibration displacements of the point P in the x and y directions, respectively. Ax and Ay are the maximum vibration amplitude of the point P in the x and y directions, respectively.  donates the angular frequency, \u03c61 and \u03c62 are the initial phases of the anti-symmetric and symmetric vibration modes, and t is time. The vibration trajectory of the point P can be expressed in Eq. (3) when the anti-symmetric and symmetric vibration modes of the transducer are simultaneously excited in the transducer. 22 2 1 2 1 2 2 cos( ) sin ( ) y x yx x y x y U U UU A A A A        + \u2212 \u2212 = \u2212         (3) In addition, Eq. (3) can be simplified as Eq. (4) when the phase difference (\u03c61-\u03c62) is \u03c0/2 or -\u03c0/2. 22 1 yx x y UU A A    + =         (4) It is obvious that the point P moves in elliptical motion in the xoy plane. P P2 A x yo x (a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an us cr ip t 8 yo x2Ay P P (b) Fig. 4. Generation mechanism of the elliptical motion. (a) Anti-symmetric vibration mode of the bonded-type piezoelectric transducer. (b) Symmetric vibration mode of the bonded-type piezoelectric transducer. o x y Rotation directionElliptical trajectoryPreloading fore Fig. 5. Operating principle of the proposed robotic finger. 3. Finite element analysis 3.1 Modal analysis To confirm the vibration shapes of the anti-symmetric and symmetric vibration modes, and to tune their resonant frequencies together, the modal analysis was conducted by the commercial software ANSYS/Workbench 15.0. The material of the PZT plates is PZT-8 (Haiying Company, Wuxi, China), and the metal substrate is made of aluminum alloy. Their material parameters are listed in Table 1. During the modal analysis, the free boundary condition was considered for the piezoelectric transducer. The geometrical parameters of the proposed transducer are shown in Fig. 6, and they can be adjusted to minimize the resonant frequency difference between two operating vibration modes. After adjustments, the sizes of the PZT plates are 24 mm in length, 6.7 mm in 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an us cr ip t 9 width, and 1 mm in thickness, and the optimized geometrical parameters of the metal substrate are listed in Table 2. The expected anti-symmetric and symmetric vibration modes are calculated, as shown in Figs. 7(a) and (b), and their resonant frequencies are 68.742 kHz and 68.760 kHz, respectively. The resonant frequency difference between the two operating vibration modes is 18 Hz, meeting the design requirement. And other adjacent modes are separated from the two operating vibration modes in a frequency difference of more than 2.5 kHz. The nodes of the two operating modes are coincident, which is beneficial to set the holder of the transducer. Table 1 Materials used in the transducer. Materials Young's modulus (GPa) Piezoelectric constant (C/m2) Poisson's ratio Density (kg/m3) Aluminum alloy 71 / 0.33 2810 PZT-8 120.6 53.5 51.5 0 0 0 53.5 120.6 51.5 0 0 0 51.5 51.5 104.5 0 0 0 0 0 0 31.3 0 0 0 0 0 0 31.3 0 0 0 0 0 0 34.6                    0 0 5.2 0 0 5.2 0 0 15.1 0 12.7 0 12.7 0 0 0 0 0 \u2212    \u2212               0.30 7650 R1 L1 L2 L3 L4 L5 B 1 B 2 B 3 B 4 Fig. 6. Main geometrical parameters of the transducer. Table 2 Optimized structural parameters of the transducer (unit: mm). Parameter R1 R2 B1 B2 B3 B4 L1 L2 L3 L4 L5 Thickness Value 3 15 2 3.4 6.4 19.9 1.5 8 24 28 38 5.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an us cr ip t 10 3.2 Harmonic response analysis In order to investigate the vibration displacements of the points at the two driving feet, the harmonic response analysis was computed under the condition with the damping coefficient of 0.3%. Based on the modal analysis results, the sine and cosine signals, with a peak voltage of 20 V and a frequency of 68.751 kHz, were applied to the two groups of PZT plates, respectively. Points P and Q distributed on the surfaces of the two driving feet were selected, and their motion trajectories in one working period were calculated as plotted in Fig. 8. It can be found that points P and Q moved elliptically. These results confirmed the operating principle of the proposed piezoelectric transducer. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep t d M 11 Q P P Q Ux (\u03bcm) U y (\u03bc m ) Fig. 8. Motion trajectories of points P and Q in one working period at 20 Vpp."
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.8-1.png",
        "caption": "Figure 10.8. Plane motion of a slender rigid link,",
        "texts": [
            "77e) of our accounting for the drag torque, i.e. the load, on the system. 0 Exercise 10.4. A horizontal force P = - Pi is applied at d = 3/4 ft above the center of the log who se motion at an instant of interest is described in Example 10.2, page 421. Model the log as a homogeneous circular cylinder, and thu s determine all of the forces that act on the log at that instant. 0 442 10.12.3. Application to the Plane Motion of a Rigid Link Chapter 10 Example 10.8. A homogeneous slender link of length eshown in Fig. 10.8 is constrained to move in lubricated slots A and B. The link starts from rest at an angle eo in the vertical plane . Find the forces that act on the link as functions of the angle e. Model the link as a uniform thin rod. Solution. The free body diagram inFig. I0.8(a) shows the equipollent normal reaction forces N = - NI and R = RJ exerted on the link by the smooth slots, and the weight W = - WJ = mg ofthe homogeneous link acting at its center of gravity, which coincides with the center of mass. Other resultant contact forces A = AK and B = BK perpendicular to the plane of motion are represented by heavy dots at A and B",
            "131) to derive the equation for the small angu lar motion 8(t ) of the rod from its horizontal equ ilibrium state, in terms of the assigned parameters. (b) Characterize the lightly damped , free vibrational motion of the rod for the initial data 8(0) = 0, 8(0) = WO, and determine its frequen cy. (c) Describe the corresponding undamped moti on and find its period. 10.64. A homogeneous, slender, curved rigid link of mas s m and lengt h I is hinged at its end s A and B to slider blocks that are con strain ed to move in smooth perpend icular slots in the horizontal plane similar to the device in Fig. 10.8, page 442 . The center of mass is at the midpoint on the line of length 2d joining A and B. The link is moving in a viscous medium that exert s a drag force per unit length s along the link in accordance with Stoke s's law. (a) Apply Euler's laws to derive the differential equation (10.151) for the moti on 8( t) of the link . Find the angular motion 8( t) of a link whose initial angular veloci ty is Wo at 80 . (b) What can be said about the physical nature of the slot reaction forces? Use the mechanical power rule (10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.10-1.png",
        "caption": "Fig. 9.10 Freely flying body with accelerometers mounted at body-fixed points P1, . . . ,P6",
        "texts": [
            "119) has the desired symmetrical form \u03c9\u0307 = 1 n2 n \u00b7 3\u2211 i=1 (ai \u2212 \u03c9 \u00d7 vi)(rj \u2212 rk) (i, j, k = 1, 2, 3 cyclic) . (9.123) 9.9 Angular Acceleration of a Body in Terms of Positions, Velocities.... 317 318 9 Angular Velocity. Angular Acceleration Special case : If P3 is fixed, r3 = 0 (arbitrarily) and v3 = 0 , a3 = 0 . Equations (9.113) and (9.123) are \u03c9\u0307 = \u23a7\u23aa\u23a8 \u23aa\u23a9 \u2212 (a1 \u2212 \u03c9 \u00d7 v1)\u00d7 (a2 \u2212 \u03c9 \u00d7 v2) r1 \u00b7 (a2 \u2212 \u03c9 \u00d7 v2) (denominator = 0) , \u2212 r1 \u00d7 r2 (r1 \u00d7 r2) 2 \u00b7 [a1r2 \u2212 a2r1 \u2212 \u03c9 \u00d7 (v1r2 \u2212 v2r1)] (else) . (9.124) The body shown in Fig. 9.10 stands for an aircraft. In an inertial reference basis e1 the body-fixed point A has the position vector r(t) . The points Pi (i = 1, . . . , 6) are six body-fixed points with position vectors i = \u2212\u2212\u2192 APi . Let ai be the acceleration of Pi relative to e1 . An accelerometer positioned at Pi measures as function of time the component \u03b1i(t) of this acceleration ai in a body-fixed direction specified by the unit vector ni : \u03b1i(t) = ai \u00b7ni (i = 1, . . . , 6). To be determined are, as functions of time, the position r(t) and the direction cosine matrix A12(t) relating e1 to a body-fixed basis e2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003384_s12555-019-0904-9-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003384_s12555-019-0904-9-Figure8-1.png",
        "caption": "Fig. 8. The model of the PVA.",
        "texts": [
            " When the following switch condition S2 is satisfied, S2:=  \u2223\u2223q1\u2212qd 1 \u2223\u2223\u2264 e1, |q\u03071| \u2264 e2, |q2\u2212 q\u0303m 2 | \u2264 e1, |q\u03072| \u2264 e2, |q3| \u2264 e1, |q\u03073| \u2264 e2, (56) the stable control of the PVP is realized using the controller (28). So far, the target angle of the FAL has been achieved and the planar APA system has been stabilized with all links\u2019 angular velocities being zero, which means the planar APA system is reduced to the PVA. 4. CONTROLLER DESIGN FOR PVA In this section, we realize the control objective of PVA. That is, we control the TAL to its target value, also bringing the SUL to its. 4.1. Modeling for PVA Fig. 8 shows a model of PVA. Because the initial value of this stage is the termination value of the previous stage, at this stage, we let the initial states of the PVA be[ \u03b8 0 p q0 3 0 0 ] , where q0 3 = 0. The \u03b8 0 p is also expressed as{ \u03b8 0 p = qd 1 +qm 2 , qm 2 = q\u0303m 2 . (57) The dynamic equation of PVA is M\u0302 (q\u0302) \u00a8\u0302q+ H\u0302 ( q\u0302, \u02d9\u0302q ) = \u03c4\u0302, (58) where M\u0302 (q\u0302) = [ M\u030222 M\u030223 M\u030232 M\u030233 ] , H\u0302 ( q\u0302, \u02d9\u0302q ) = [ H\u03021 ( q\u0302, \u02d9\u0302q ) H\u03022 ( q\u0302, \u02d9\u0302q )] , (59) q\u0302 = [\u03b8p q3] T , \u03c4\u0302 = [0 \u03c4\u03023] T , (60) M\u030222 = c1 + c2 +2c3cosq3, M\u030223 = M\u030232 = c2 + c3cosq3, M\u030233 = c2, H\u03021 =\u2212c3 ( 2\u03b8\u0307pq\u03073 +(q\u03073) 2 ) sinq3, H\u03022 = c3 ( \u03b8\u0307p )2sinq3, (61)  c1 = m2Lc2 2 +m3L2 2 + J\u03021, c2 = m3Lc3 2 + J\u03022, c3 = m3L2Lc3",
            " In other words, when the TAL is controlled to its target states, the PVA is stabilized at the target position. 4.2. Solution of target angles In this subsection, the target angles of two links of PVA are solved according to the following constraint relationships by using PSO algorithm: (i) the geometric constraint relationship between the angles of all links; (ii) the reachable area of the FAL, which is selected as a suitable value; (iii) the states of the SUL satisfying S1b; (iv) the angle constraint of the PVA, which is given by (65). From Fig. 8, we get{ x =\u2212sinqd 1L1\u2212 sin\u03b8pL2\u2212 sin(\u03b8p +q3)L3, y = cosqd 1L1 + cos\u03b8pL2 + cos(\u03b8p +q3)L3. (67) According to (3), we can obtain the reachable area of the FAL. The angle of the FAL is adjusted to qd 1 , which can guarantee the end-point reaches to its target position. Considering the above constraint relationships, the PSO algorithm is introduced to calculate the middle angle of SUL qm 2 and the target angle of the TAL qd 3 . The iterative rule is as follows: s\u03b4 k (t +1) = s\u03b4 k (t)+ v\u03b4 k (t +1), v\u03b4 k (t +1) = \u03c9v\u03b4 k (t)+w1\u00b51 ( g\u03b4 k \u2212 s\u03b4 k (t) ) +w2\u00b52 ( b\u03b4 \u2212 s\u03b4 k (t) ) , (68) where \u03b4 = 1, 2, \u00b7 \u00b7 \u00b7 , S; k = 1, 2, \u00b7 \u00b7 \u00b7 , N; t is the distance traveled by each particle; s\u03b4 k and v\u03b4 k are the location and velocity of the kth particle, respectively; g\u03b4 k and b\u03b4 are the best location and global best location, respectively; \u03c9 is the inertia weight; \u00b51, \u00b52 \u2208 [0,1]; w1 and w2 are the weighting factors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001832_icict.2015.7469486-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001832_icict.2015.7469486-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor",
        "texts": [
            " The quadrotor and its non-linear dynamic model are discussed in section II. Section III presents the discrete PID control of quadrotor. Section IV presents the discrete time model of quadrotor and its parameters identification. Model predictive control strategy is presented in section V. Simulation results of MPC are shown in section VI. Robustness to noise of proposed schemes is shown in section VII. The paper is concluded in section VIII. II. QUADROTOR DYNAMICS Quadrotor is a MIMO non-linear system with complex dynamics. As shown in Fig. 1 [18], Quadrotor has four lift generating propellers. Two propellers rotate clockwise and the other two rotates counter-clockwise. Quadrotor control is achieved by varying the propellers angular speed i (i = 1, 2, 3, 4). Let (a) the rotation angles of quadrotor are roll angle ( ), pitch angle ( ) and yaw angle ( ) and (b) the translationalvector movement of quadrotor centre of mass is [x, y, z]. The mathematical model of quadrotor [19] is: (1) Where M is the mass of the system, g is the acceleration due to gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000813_j.bios.2011.04.057-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000813_j.bios.2011.04.057-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of n-alkylamine-stabilized PdNPs-based glucose biosensor (not in scale).",
        "texts": [],
        "surrounding_texts": [
            "S A e\nZ M a b c\na\nA R R A A\nK P A G\n1\nb n s g m r o e d e l o p e s p w\n0 d\nBiosensors and Bioelectronics 26 (2011) 4619\u2013 4623\nContents lists available at ScienceDirect\nBiosensors and Bioelectronics\nj our na l ho me page: www.elsev ier .com/ locate /b ios\nhort communication\npplication of hydrophobic palladium nanoparticles for the development of lectrochemical glucose biosensor\nhongping Lia, Xu Wanga, Guangming Wenb, Shaomin Shuangb, Chuan Donga,\u2217, an Chin Paauc, Martin M.F. Choic,\u2217\u2217\nResearch Center of Environmental Science and Engineering, Shanxi University, Taiyuan 030006, PR China School of Chemistry and Chemical Engineering, Shanxi University, Taiyuan 030006, PR China Department of Chemistry, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, PR China\nr t i c l e i n f o\nrticle history: eceived 6 February 2011 eceived in revised form 15 April 2011 ccepted 28 April 2011 vailable online 6 May 2011\neywords:\na b s t r a c t\nAn amperometric glucose biosensor based on an n-alkylamine-stabilized palladium nanoparticles (PdNPs)-glucose oxidase (GOx) modified glassy carbon (GC) electrode has been successfully fabricated. PdNPs were initially synthesized by a biphase mixture of water and toluene method using n-alkylamines (dodecylamine, C12-NH2 and octadecylamine, C18-NH2) as stabilizing ligands. The performance of the PdNPs-GOx/GC biosensor was studied by cyclic voltammetry. The optimum working potential for amperometric measurement of glucose in pH 7.0 phosphate buffer solution is \u22120.02 V (vs. Ag/AgCl). The\nalladium nanoparticles mperometry lucose\nanalytical performance of the biosensor prepared from C18-PdNPs-GOx is better than that of C12-PdNPsGOx. The C18-PdNPs-GOx/GC biosensor exhibits a fast response time of ca. 3 s, a detection limit of 3.0 M (S/N = 3) and a linear range of 3.0 M\u20138.0 mM. The linear dependence of current density with glucose concentration is 70.8 A cm\u22122 mM\u22121. The biosensor shows good stability, repeatability and reproducibility. It has been successfully applied to determine the glucose content in human blood serum samples.\n. Introduction\nIt is well recognized that amperometric enzyme electrodes ased on glucose oxidase (GOx) play a leading role for the determiation of glucose, attributing to their high sensitivity, repeatability, tability and simple operation. Since the first development of lucose biosensor, strategy striving to improve the response perforance of enzyme electrodes has been the main focus in biosensor esearch (Dong et al., 2010; Wei et al., 2010). The key issue in develping a successful amperometric biosensor mainly relies on the ffectiveness and stability of the immobilized enzymes such as oxiase or dehydrogenase on the electrode surface. Among the various nzyme immobilization approaches, the enzyme monomolecularevel modification of the electrode surface has become a method f choice since this method can retain the biological recognition roperties and stability of the immobilized enzymes. Immobilized nzymes have many operational advantages over free enzymes uch as possibility of continuous operation, modulation of catalytic roperties, lower cost of operation, reusability, good stability and ider working concentration range of analytes (Song et al., 2010).\n\u2217 Corresponding author. Tel.: +86 351 7018613; fax: +86 351 7018613. \u2217\u2217 Corresponding author. Tel.: +852 34117839; fax: +852 34117348.\nE-mail addresses: dc@sxu.edu.cn (C. Dong), mfchoi@hkbu.edu.hk (M.M.F. Choi).\n956-5663/$ \u2013 see front matter \u00a9 2011 Elsevier B.V. All rights reserved. oi:10.1016/j.bios.2011.04.057\n\u00a9 2011 Elsevier B.V. All rights reserved.\nIn the past decade, nanostructured materials have been used as substrates or platforms for immobilizing enzymes because of their favorable intriguing properties such as large surface-to-volume ratio, high catalytic efficiency, and high surface reaction activity (Deng et al., 2010; Pandey and Singh, 2008; Rosi and Mirkin, 2005; Katz and Willner, 2004). Direct electron transfer of redox biomolecule to nanoparticles (NPs) is thought to occur when nanomaterial is used to modify the surfaces of working electrodes. Many kinds of nanomaterials have been used in biosensor fabrication (Zheng et al., 2010, 2011; Wang et al., 2010; Zhang et al., 2010; Rakhi et al., 2009; Shan et al., 2009). However, most of these nanomaterials require cross-linking reagents or Nafion film to prevent enzyme leaching from electrode surface (Kausaite-Minkstimiene et al., 2010; Wu et al., 2007). Moreover, electrochemical sensors using nano-metal materials for non-enzymatic glucose detection are prone to chloride ion interference which is abundant in nature, particularly in physiological fluids (Chen et al., 2009; Taylor et al., 1997; Lei et al., 1995). Chloride ion can completely suppress glucose adsorption, resulting in total loss of enzyme activity. As such, the search for new nanomaterials and methods for immobilizing enzymes is still an important subject in developing more sensitive and stable biosensors.\nPalladium (Pd) is the preferred metal for electrocatalysis because of its various advantageous properties. Different methodologies have been attempted to incorporate Pd particles into",
            "4 oelectronics 26 (2011) 4619\u2013 4623\np e s g e ( p ( o t s o c o\n2\n2\nl A d f A o b u j S a S p a\n2\np e ( N b d o a p G e d C a a o t t F e\n2\ni 1 t\n620 Z. Li et al. / Biosensors and Bi\nolymer matrices for fabrication of Pd modified electrodes (Willner t al., 2007). In this work, we explore the use of n-alkylaminetabilized PdNPs for immobilizing GOx and its application in lucose biosensing. The biosensing mechanism is based on the nzymatic oxidation of glucose to produce hydrogen peroxide H2O2) which can subsequently enhance the reduction current of alladium(II) oxide (PdO) on a PdNPs-GOx modified glassy carbon GC) electrode (vide infra). To our knowledge, this is the first report n using hydrophobic nanomaterial membrane to immobilize GOx o achieve higher enzyme activity, better detection sensitivity and tability. The effect of pH, loading of GOx and PdNPs on the response f the glucose biosensor was studied in detail. Our proposed gluose biosensor has been successfully applied for the determination f glucose in human serum samples.\n. Experimental\n.1. Materials and reagents\nn-Dodecylamine, d(+)-glucose (99.5%), n-octadecylamine, paladium(II) chloride and sodium borohydride were obtained from ldrich (Milwaukee, WI, USA). Sodium dihydrogen phosphate dihyrate and disodium hydrogen orthophosphate dihydrate were rom Fluka (Buchs, Switzerland). Glucose oxidase (EC 1.1.3.4. from spergillus niger) with a specific activity of 235 units per milligram f solid was from Sigma (St. Louis, MO, USA). Acetaminophen, ascoric acid (AA), glutamate (GA), H2O2 solution (30 wt% aqueous) and ric acid (UA) were from Beijing Chemical Reagent Company (Beiing, China). Blood serum samples were kindly provided by the hanxi University Hospital (Taiyuan, China). All other reagents of nalytical-reagent grade were used without further purification. tandard glucose solutions were prepared in 0.10 M pH 7.0 phoshate buffer solution (PBS) and were allowed to mutarotate for 24 h t room temperature before use.\n.2. Immobilization of PdNPs-GOx on GC electrode\nThe synthesis of n-alkylamine-stabilized PdNPs is based on our revious work using a biphase mixture of water and toluene (Li t al., 2010). Two types of PdNPs stabilized with n-dodecylamine C12-NH2) and n-octadecylamine (C18-NH2) ligands, i.e., C12H2-PdNPs and C18-NH2-PdNPs, were used to prepare glucose iosensors. First, a 0.40% (w/v) enzyme solution was prepared by issolving 4.0 mg GOx in 1.0 mL PBS. Second, a known quantity f C18-NH2-PdNPs (or C12-NH2-PdNPs) was dissolved in toluene nd various volumes of this PdNPs solution were used to preare the C18-NH2-PdNPs-GOx (or C12-NH2-PdNPs-GOx) modified C electrodes. The diameter and surface area of the GC working lectrode were 3.0 mm and 0.07065 cm2, respectively. The proceure followed the layer-by-layer deposition method. In a typical 18-NH2-PdNPs-GOx modified GC electrode preparation, a 4.0- L liquot of 0.40% (w/v) GOx solution was dropped onto the surface of\nGC electrode, left for 5 min at room temperature, and then 6.0 L f a 0.10% (w/v) C18-NH2-PdNPs toluene solution was added onto he GC electrode. The whole C18-NH2-PdNPs-GOx modified GC elecrode was left overnight in ambient conditions to complete dryness. ig. 1 illustrates the structure of a Cn-NH2-PdNPs-GOx/GC modified lectrode, where n = 12 or 18.\n.3. Instrumentation\nAll electrochemical studies were conducted on an Electrochemcal Workstation CHI 660B (CH Instruments, Austin, TX, USA). A 5-mL electrolytic cell, an Ag/AgCl (saturated KCl) reference elecrode, a platinum foil auxiliary electrode, and a Cn-NH2-PdNPs-GOx\nmodified GC working electrode were used for electrochemical measurements. Before glucose analysis, the background response of the Cn-NH2-PdNPs-GOx modified GC working electrode was allowed to decay to a steady state with stirring.\nAll pH measurements were taken by a combined glass electrode and a pHS-3C digital pH-meter (Shanghai Lei Ci Device Works, Shanghai, China). A JEOL JEM-1010 transmission electron microscope (Tokyo, Japan) operating at an accelerating voltage of 100 kV in bright field mode was used to observe the appearance and morphology of Cn-NH2-PdNPs and Cn-NH2-PdNPs-GOx samples. The sample was prepared by casting and evaporating an aqueous suspension of Cn-NH2-PdNPs or Cn-NH2-PdNPs-GOx droplet onto a carbon-coated copper grid (400 mesh). Purified water from a MilliQ-RO4 water purification system (Millipore, Bedford, MA, USA) with a resistivity higher than 18 M cm was used to prepare all solutions.\nTEM technique is a powerful technique to determine the morphology, size and dispersity of metal NPs. Fig. S1 depicts the TEM images of Cn-NH2-PdNPs and Cn-NH2-PdNPs-GOx. It is clearly observed that small spherical Cn-NH2-PdNPs were evenly dispersed on the carbon-coated copper grids. Particle analysis revealed that the average sizes of C18-NH2-PdNPs (Fig. S1A) and C12-NH2-PdNPs (Fig. S1B) were 5.6 \u00b1 0.8 and 6.8 \u00b1 0.8 nm, respectively. Fig. S1C and D shows the TEM images of C18-NH2PdNPs-GOx and C12-NH2-PdNPs-GOx, respectively. Some light grey patches of enzyme GOx on the carbon-coated copper grids are observed. Black dots of spherical Cn-NH2-PdNPs are densely adhered to the enzyme patches. The sizes of the enzyme immobilized Cn-NH2-PdNPs are more or less the same as the free Cn-NH2-PdNPs (Fig. S1A and B), indicating no aggregation of Cn-NH2-PdNPs in Cn-NH2-PdNPs-GOx hybrid material. It is interesting to note that all the Cn-NH2-PdNPs were readily attached to the enzyme molecules. This can be explained by the fact that the enzyme molecule consisting of amino acids such as aspartic acid, glutamic acid and serine residues (O\u2019Malley and Weaver, 1972) can bind to the Cn-NH2-PdNPs via the linkage of \u2013COHRN :\u2192 Pd (Li et al., 2010). Excess C18-NH2-PdNPs or C12NH2-PdNPs will form a thin hydrophobic layer on the enzyme, resulting in a stable nanohybrid material of Cn-NH2-PdNPs-GOx, ready to be employed for biosensing in our subsequent work. Collectively, the TEM results demonstrate that the spherical CnNH2-PdNPs were successfully adhered to the enzyme molecules and retained their morphology without aggregation. It is also observed that a clear thin Cn-NH2-PdNPs film was formed on the GC electrode which could keep the enzyme molecules on",
            "Z. Li et al. / Biosensors and Bioelect\nt t\n3\nP i a B fi w t p a a f a t O c s\n18-NH2-PdNPs-GOx modified GC electrodes in various concentrations of glucose BS solutions (0.10 M, pH 7.0): (a) 0.00, (b) 0.050, (c) 0.20, (d) 0.50, (e) 1.00, and (f) .50 mM. The scan rate is 20 mV/s.\nhe electrode surface; thus preventing their leakage to the soluion.\n.2. Response mechanisms of glucose\nFig. 2 displays the cyclic voltammograms (CVs) of (A) C12-NH2dNPs-GOx and (B) C18-NH2-PdNPs-GOx modified GC electrodes n 0.10 M pH 7.0 PBS containing various concentrations of glucose t a scan rate of 20 mV/s. In the absence of glucose (Fig. 2A(a) and (a)), both C12-NH2-PdNPs-GOx and C18-NH2-PdNPs-GOx modied GC electrodes exhibit CVs with well defined reversible redox aves in both forward and reverse scans at ca. +0.2\u20130.6 and \u22120.05 o 0.0 V (vs. Ag/AgCl) respectively (see also Fig. S2A and B of Suplementary data). In the forward scan, the current starts to rise at\npotential of ca. +0.2 V due to the oxidation of Pd to form Pd\u2013OH nd then rapidly increases at above +0.4 V corresponding to the ormation of Pd oxides (i.e., Pd \u2192 Pd2+ + 2e\u2212). In the reverse scan,\nlarge cathodic peak at \u22120.03 to 0.00 V appeared which is related 2+ \u2212\no the reduction of Pd oxides (i.e., Pd + 2e \u2192 Pd) (Jia et al., 2009). n the addition of glucose to the PBS, both anodic and cathodic urrents increase with the increase in glucose concentration as hown in Fig. 2A(b\u2013f) and B(b\u2013f). It is well known that glucose is\nronics 26 (2011) 4619\u2013 4623 4621\nenzymatically oxidized to gluconic acid with a concomitant release of H2O2:\nD-Glucose + O2 + H2O GOx\u2212\u2192D-Gluconic acid + H2O2 (1)\nThe generated H2O2 can be oxidized on the C12-NH2-PdNPs and C18-NH2-PdNPs modified GC electrodes as depicted in Fig. S2 (Supplementary data), producing high anodic current. Thus, the anodic peaks are broad attributing to the electro-oxidation of both H2O2 and PdNPs on the C12-NH2-PdNPs-GOx and C18-NH2-PdNPs-GOx modified GC electrodes. However, the oxidation potentials for H2O2 and PdNPs are so close that they cannot be resolved or identified accurately.\nOn the reverse scan, the PdO is electrochemically reduced back to PdNPs as follows:\nPdO + 2e\u2212 + 2H+ \u2192 Pd + H2O (2)\nIt has been reported that the cathodic current of a PdNPs/GC modified electrode is enhanced in the presence of H2O2, attributing to the electrocatalytic effect of PdNPs on H2O2 at the GC electrode (Liu et al., 2010). In this work, the cathodic peak is enhanced possibly due to the presence of residual H2O2. To compare and verify the effect of H2O2, a set of experiments was performed to determine the electrochemical response of the Cn-NH2-PdNPs/GC modified electrode in 0.10 M PBS (pH 7.0) with and without H2O2 as depicted in Fig. S2 (Supplementary data). It was found that H2O2 is very effective in enhancing the cathodic and anodic currents of C12-NH2PdNPs and C18-NH2-PdNPs modified GC electrodes.\nIn essence, well-defined and larger cathodic and broad anodic glucose responses were obtained at the C18-NH2-PdNPs-GOx biosensor at potentials of +0.45 and \u22120.02 V, respectively (Fig. 2B). Unfortunately, it is found that the C18-NH2-PdNPs-GOx biosensor also responds to acetaminophen, AA and UA at the working potential of +0.45 V since these interferents are also electrochemically oxidized. A lower operating potential should greatly reduce this problem (Lin et al., 2004). As such, we chose the operating potential of \u22120.02 V to minimize interferences from easily oxidizable species such as AA and UA (vide infra). In essence, the detection of glucose by our C18-NH2-PdNPs-GOx/GC electrode can be realized at a very low working potential (\u22120.02 V vs. Ag/AgCl) and the resulting current should be proportional to the level of glucose in sample solutions.\nPdNPs and GOx play important roles in the response of PdNPs-GOx modified GC electrode to glucose. In this work, C18NH2-PdNPs-GOx modified GC electrode was chosen to optimize the fabrication condition of PdNPs-GOx in order that more stable and higher sensitive glucose biosensor can be produced. The effect of enzyme concentration (1.0\u20136.0 mg/mL) in the PdNPs-GOx on the current response of C18-NH2-PdNPs-GOx/GC electrode at \u22120.02 V to 1.0 mM glucose in PBS (pH 7.0) was investigated and depicted in Fig. S3A. The current increases with the increase in enzyme loading until its maximum at 4.0 mg/mL. It is obvious that increasing the amount of GOx will increase the sensitivity of glucose detection. However, the current drops slightly after 4.0 mg/mL attributing to the thicker enzyme layer of excess GOx. As such, 4.0 mg/mL of GOx was chosen as the optimal enzyme concentration for preparing the C18-NH2-PdNPs-GOx modified GC electrode in the subsequent work.\nThe influence of the amount of C18-NH2-PdNPs on the response of C18-NH2-PdNPs-GOx modified GC to glucose was investigated (Fig. S3B). When the amount of C18-NH2-PdNPs is insufficient to cover and bind with the enzyme molecules, the enzyme will leach."
        ]
    },
    {
        "image_filename": "designv10_12_0001255_978-3-642-31988-4_17-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001255_978-3-642-31988-4_17-Figure1-1.png",
        "caption": "Fig. 1 A cable-driven parallel robot with 4 cables: a geometric model; b static model",
        "texts": [
            " The following issues, which are classic challenges in robot analysis [35], are specifically dealt with: 1. determination of the number of solutions in the (zero-dimensional) algebraic variety defined by the problem polynomial equations; 2. reduction of the problem to a single equation in one unknown; 3. numerical computation of the solution set; 4. identification of a specific geometry providing the maximal number of distinct real-valued solutions. In all numerical examples presented in the text, measures are given in SI units. A mobile platform is connected to a fixed base by 4 cables (Fig. 1). The i th cable exits from the base at point Ai and it is connected to the mobile platform at point Bi . The cable length is \u03c1i , with \u03c1i > 0. Oxyz is a Cartesian coordinate frame fixed to the base, with i, j and k being unit vectors along the coordinate axes and k being oriented along the downward vertical. Gx \u2032y\u2032z\u2032 is a Cartesian frame attached to the end-effector, with i\u2032, j\u2032 and k\u2032 being the corresponding unit vectors along the coordinate axes. Without loss of generality, O is chosen to coincide with A1 and G is assumed to be the platform center of mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001153_1077546312474679-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001153_1077546312474679-Figure4-1.png",
        "caption": "Figure 4. Sketch of a rotor rolling bearing system: 1 coupling, 2 front of axis, 3 bearing 1, 4 disk, 5 bearing 2.",
        "texts": [
            " To keep the same descend rate of f X\u00f0 \u00de as that of the step, Equation (22) is used to determine whether Xk\u00fe1 is the descend point of f X\u00f0 \u00de or not: f \u00f0Xk\u00fe1\u00de f \u00f0Xk\u00de \u00fe \"rf Xk\u00fe1 Xk\u00f0 \u00de \u00f023\u00de where \" is a very small positive number. The continuation-shooting method improves the efficiency of solving the periodic solution of nonautonomous consumedly. The state transition matrix of the periodic solution can be obtained during iteration, and eigenvalues are called Floquet multipliers. A rotor ball bearing system is shown in Figure 4. The shaft is supported symmetrically by two identical angular contact ball bearings 7005/HQ1P4A, and the rigid disk is located at the mid-span of the shaft. Unbalance can be set in the disk by screws. The parameters of the bearings are shown in Table 1. The elastic modulus of balls of the bearing is 3.1 1011Pa: others are 2.04 1011Pa. Poisson\u2019s ratio is 0.3. Loads acting on the bearings are f500N, 1000N, 1000N, 0, 0g. The damping factor of the bearings is 200N s/m. The shaft is modeled as four finite element beams, and the rotor system is modeled as five nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000739_iros.2010.5651324-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000739_iros.2010.5651324-Figure2-1.png",
        "caption": "Fig. 2. Segment of centipede-like multi-legged robot",
        "texts": [
            " This paper is organized as follows: Section II introduces a multi-legged robot composed of N -segments. Sections III and IV cover control modes of each leg and the transition conditions of the control modes. Section V explains a method to allocate a new contact point of the first leg and adjust the stroke speed. Section VI reviews simulation results verifying the feasibility of our proposal and section VII presents conclusions. First of all, we define a segment consisting of a trunk and a pair of legs. The leg is composed of three links (Fig. 2). Each segment is connected serially with fore and/or rear segments 978-1-4244-6676-4/10/$25.00 \u00a92010 IEEE 5341 through revolute passive joints, intersegment joints, of pitch and yaw angles. We hereinafter consider a multi-legged robot composed of N(\u2265 3) segments (Fig. 3). Left (l) and right (r) legs of segment i \u2208 {1, \u00b7 \u00b7 \u00b7 , N} have coordinate systems Cs i = (xsi , y s i , z s i ), s \u2208 {l, r} respectively, and the origin is assigned to the beginning point of each leg (Link 1). Each leg has a movable area Ms i in which the leg tip can reach anywhere"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000972_978-3-642-22164-4_2-Figure2.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000972_978-3-642-22164-4_2-Figure2.8-1.png",
        "caption": "Fig. 2.8 Variable parameter L. The input signal and its derivatives (a), convergence of the differentiator (b)",
        "texts": [
            " Differentiation with Variable Parameter L. Consider a differential equation y(4) + ... y + y\u0308+ y\u0307 = (cos0.5t + 0.5sint + 0.5)( ... y \u22122y\u0307+ y) with initial values y(0) = 55, y\u0307(0) =\u2212100, y\u0308(0) =\u221225, ... y (0) = 1000. The measured output is y(t), the parametric function L(t) = 3(y2 + y\u03072 + y\u03082 + ... y 2 + 36)1/2 is taken. The third order differentiator (2.10) is taken with \u03bb0 = 1.1,\u03bb1 = 1.5,\u03bb2 = 2,\u03bb3 = 3. The initial values of the differentiator are z0(0) = 10,z1(0) = z2(0) = z3(0) = 0. The graphs of y, y\u0307, y\u0308, ... y are shown in Fig. 2.8a. It is seen that the functions tend to infinity fast. In particular they are \u201cmeasured\u201d in millions, and y(4) is about 7.5 \u00b7 106 at t = 10. The accuracies |z0 \u2212 y| \u2264 6.0 \u00b7 10\u22126, |z1 \u2212 y\u0307| \u2264 1.1 \u00b7 10\u22124, |z2 \u2212 y\u0308| \u2264 0.97, |z3 \u2212 ... y | \u2264 4.4 \u00b7 103 are obtained with \u03c4 = 10\u22124. In the graph scale of Fig. 2.8a the estimations z0,z1,z2,z3 cannot be distinguished respectively from y, y\u0307, y\u0308, ... y . Convergence of the differentiator outputs during the first 2 time units is demonstrated in Fig. 2.8b. Note that also here the graph of z0 cannot be distinguished from the graph of y. The normalized coordinates \u03c30(t) = (z0(t)\u2212 y(t))/L(t),\u03c31(t) = (z1(t)\u2212 y\u0307(t))/L(t),\u03c32(t) = (z2(t)\u2212 y\u0308(t))/L(t),\u03c33(t) = (z3(t)\u2212 ... y (t))/L(t) get the accuracies |\u03c30| \u2264 6.9 \u00b7 10\u221216, |\u03c31| \u2264 1.2 \u00b7 10\u221211, |\u03c32| \u2264 1.0 \u00b710\u22127, |\u03c33| \u2264 4.6 \u00b710\u22124 with \u03c4 = 10\u22124. With \u03c4 = 10\u22123 the accuracies change to |\u03c30| \u2264 2.0 \u00b710\u221212, |\u03c31| \u2264 5.0 \u00b710\u22129, |\u03c32| \u2264 5.2 \u00b710\u22126, |\u03c33| \u2264 2.4 \u00b710\u22123. A gray image is represented in computers as a noisy function given on a planar grid, which takes integer values in the range 0 - 255"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000716_b822966j-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000716_b822966j-Figure7-1.png",
        "caption": "Fig. 7 A polymeric artificial phosphodiesterase for the amperometric detection and quantification of ATP.",
        "texts": [
            ", opposite electrostatic charges), allows the formation of composite materials that exhibit three-dimensional structures and original properties to act, for instance, as membranes.21 Following this concept, Haruyama et al. designed and synthesized an artificial enzyme through the self-assembly of a cationic polyhistidine polymer, an anionic polystyrene sulfonate polymer and Cu(II) ions, leading to the formation within the composite material of multiple nanocavities that displayed phosphodiesterase activity towards biologicallyrelevant phosphates such as ATP, ADP and AMP (Fig. 7).22 The release of phosphate anions could be monitored either amperometrically23 or potentiometrically.24 The authors showed that the hydrolytic activity significantly increased from AMP to ATP, and that the selectivity of the sensor was attributed to the easier penetration of the longer phosphate residues into the nanocavities (i.e., the active sites of the artificial enzyme). One potential application of such an artificial enzyme-based biosensor is in the field of biosurveillance, since ATP is a molecule found in every biological system and, as a consequence, is a good marker of microbial contamination by microorganisms during the preparation and processing of food"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003437_j.ymssp.2020.107158-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003437_j.ymssp.2020.107158-Figure1-1.png",
        "caption": "Fig. 1. The physical structure of the mechatronics system of the industrial-grade parallel tool head.",
        "texts": [
            " Finally, a typical application about tracking performance prediction and compensation is further given based on the mechatronics modeling. The rest parts of the paper are organized as follows: Section 2 performs the physics-based mechatronics modeling of the parallel tool head; Section 3 carries out the friction torque identification experiment and gives the verification results; Section 4 presents a related application based on the mechatronics modeling; Section 5 states the conclusion. As shown in Fig. 1, it is the physical structure of the mechatronics system of the industrial-grade parallel tool head studied in this paper. The mechanical part is composed of a moving platform and three identical links, and each link consists of a slider, a parallelogram structure and a spherical joint. The slider is actuated by a servo motor via a ball screw system, and the moving platform can achieve the motion with two rotational degrees of freedom and one translational degree of freedom (2R1T). Because of the characteristics of the parallelogram structure, the link of the parallel tool head could be equivalent as a PRS mechanism [15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.15-1.png",
        "caption": "Fig. 13.15 Homokinetic shaft coupling with balls in torus-shaped tracks",
        "texts": [
            "14 has two balls-in-tracks in parallel to a spherical joint S . The tracks are symmetrically located cylinders. In order to keep the centers of the balls in the bisecting plane \u03a3 the balls are also constrained to move along the cylindrical pin 3 which is rigidly attached to the sphere of the joint S . This implies that the sphere of the joint S cannot be rigidly connected to any of the two shafts. Details of design not shown in the figure allow the shaft coupling to be assembled under prestress in such a way that its elements are firmly held together. Figure 13.15 shows the essential elements of a shaft coupling without central spherical joint and with balls in torus-shaped tracks in the particular position when the circular lines of contact between ball and both tori (indi- 406 13 Shaft Couplings 13.4 Homokinetic Shaft Couplings 407 cated by the dashed circles) are in the plane of the drawing4. Let this be the position \u03d5 = 0 of the shafts. The radii r1 and r2 of these circles satisfy the condition r2 \u2212 r1 = 2\u03c1 where \u03c1 is the radius of the balls. This has the effect that the trajectory of the center C of the ball relative to shaft 1 is the circle of radius r = r1 + \u03c1 about 01 and that the trajectory of C relative to shaft 2 is the circle of the same radius r about 02 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001523_tmag.2014.2364264-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001523_tmag.2014.2364264-Figure2-1.png",
        "caption": "Fig. 2. Topologies of single-tooth VFRMs with Nr = Ns \u00b1 1.",
        "texts": [
            " For all the stator and rotor pole combinations, their coil connections of the armature winding are determined by the conventional coil-EMF vector method, in which electrical degree \u03b1e between two adjacent coil-EMF vectors [17] can be calculated from the mechanical degree \u03b1m and Nr as, = (3) B. Conditions for Symmetrical Bipolar Phase Back-EMF Among all the combinations for single-tooth VFRMs, symmetrical bipolar phase flux-linkage and back-EMF waveforms can be obtained when Nr = Ns \u00b1 1 with 6-pole stator [7]. It is due to that individual coils in the same phase are connected in series with 180 electrical degrees shifting (opposite polarity) as shown in Fig. 2. Thus, all the even order harmonics in a single coil which cause the back-EMF waveform asymmetric and slant to right or left in half electrical cycle are cancelled completely in the phase winding, Fig. 3 and Fig. 4. For multi-tooth VFRMs, the flux linkage and back-EMF waveforms of a single coil may also be asymmetric in half electrical cycle. In order to obtain symmetrical bipolar phase flux-linkage and back-EMF waveforms by 180 electrical degrees phase shifting between the coils, two conditions should be satisfied",
            " 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. In VFRM having 6-pole stator, the magnetic circuit models having all or only one DC coil excited are illustrated in Fig. 7. Based on (3), the winding configurations of 6-pole stator single- and multi-tooth VFRMs which stator and rotor pole combinations satisfying (6) are same as the example shown in Fig. 2. Hence, according to the result in section C, the MMFs of coils A1 and A2 by adopting the superposition method and considering the direction of flux can be expressed as (12) and (13) ( , ~ ) = \u2219 \u2211 (12) ( , ~ ) = \u2212 \u2219 \u2211 (13) Meanwhile, based on the waveforms of phase- and coil-flux linkages shown in Fig. 3, the peak value of open-circuit phase flux \u03c6PA (or phase flux linkage, \u03c8PA) can be obtained by the sum of the coil fluxes \u03c6CA1 and \u03c6CA2 (or coil flux linkages, \u03c8CA1, \u03c8CA2) at aligned position (\u03b8osr=0) as = + (14) = (15) where \u03c6 is flux, F is MMF and P is permeance",
            " In the following subsections, in order to further analyse the influence of Ns, Nr and n, the electromagnetic performance of single- and 4-tooth VFRMs with Nr=nNs+1 are selected for comparison since the 6/7 stator/rotor pole VFRM exhibits the highest average torque among the 6-stator pole single-tooth VFRMs as shown in Fig. 8 [20]. All the machines are globally optimized with maximum average torque under the same rated copper loss and stator outer radius. Their main parameters are detailed in Table I. For all the combinations, the winding configurations can be obtained based on the method mentioned in section II. (The winding configuration of 6/25 stator/rotor pole 4-tooth VFRM is same as that of 6/7 stator/rotor pole single-tooth VFRM which shown in Fig. 2(b)) B. Open-Circuit Field Distribution Fig. 9 shows the open circuit equipotential and flux density distributions of single- and 4-tooth VFRMs at the aligned position under the rated DC field current (pf = 15W for both machines). It can be seen that when stator and rotor pole combination is determined by Nr=nNs+1, both machines have short flux path and the coils belong to the same phase have completely independent flux loop. The open-circuit air-gap flux density waveforms of two VFRMs at the aligned position are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000208_j.arcontrol.2008.08.003-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000208_j.arcontrol.2008.08.003-Figure9-1.png",
        "caption": "Fig. 9. Diagram of the aircraft body axes system.",
        "texts": [
            " We consider the problem of controlling a rigid-body aircraft so that it follows a predefined path in space with desired speed and attitude. The control actuation is assumed to be represented by three surface deflection angles (corresponding to ailerons, elevators and rudder) and the thrust. The variables that are assumed to be measurable are position, velocity, Euler angles and angular rates. The mathematical model used in the design is that of a six-degrees-of-freedom rigid body of constant mass, whose attitude is expressed in standard Euler angles (roll, pitch and yaw) based on a conventional body axes system, depicted in Fig. 9. The proposed control scheme consists of the following modules. 1. A n adaptive attitude controller that achieves asymptotic tracking of the roll, pitch and yaw angles, in the presence of aerodynamic moments with unknown coefficients. 2. A n adaptive airspeed controller that achieves asymptotic regulation of the airspeed, in the presence of unknown drag and lift coefficients. 3. A trajectory tracking controller that produces the required references for the roll, pitch and yaw, in order to asymptotically follow a predefined geometric path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003447_s11665-020-05061-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003447_s11665-020-05061-9-Figure2-1.png",
        "caption": "Fig. 2 Schematic representations of (a) cube and (b) bar samples",
        "texts": [
            " The samples were built with a prototype LP-DED system equipped with an Yb laser (YLS 3000, IPG Laser) on a threeaxis CNC unit to control the movement of the X\u2013Y deposition table. A multi-nozzle (4 ways) is used to deliver the powder into the melt pool. All the samples were performed at fixed parameters of laser power, laser spot diameter, hatching distance, travel speed and layer thickness which lead to porosity values lower than 0.3%. Two types of samples were built for these experimental activities, namely cubes, having 20 mm side, and bars, having the following dimensions 12 9 12 9 93 mm3 (Fig. 2a and b). A total of 12 cubes and 6 bars were built. Cubes were used for microstructural and stress analyses, and bars instead were used for tensile tests. Two deposition strategies, characterized by a different rotation angle between the layers (60 and 90 ), were used for the deposition process (Fig. 3a and b). Finally, some samples underwent heat treatments at 600 and 800 C for 2 h followed by air cooling. These temperatures were selected in order to avoid the recrystallization of the microstructure and the consequent reduction in mechanical properties",
            " The samples were identified using a three-field code based on the following criteria: \u2022 The first field represents the shape of the sample; in this work, cubic and bars samples were produced, and thus, the shape was identified by the letters C and B; \u2022 The second field identified the deposition strategy, and the numbers 0060 and 0090 identified the 0 -60 and the 0 - 90 deposition strategy, respectively; \u2022 The third field identified the heat treatment adopted; AB means that the sample was analyzed in the as-built condition, and 600 and 800 represent the temperatures used in the heat treatment. Table 1 summarizes the identification of samples and the process parameters used for the production. Journal of Materials Engineering and Performance The samples were wire electrical discharge machining (WEDM) cut along the Z direction into two parts, as represented in Fig. 2(a). Part I was used for microstructure and hardness analysis, whereas part II was used for residual stress evaluation. Previous studies showed that wire EDM method is recognized as a suitable process for sample cutting due to the very small area influenced and modified by the cutting process (Ref 20, 21). After cutting operation, half of each sample was ground with 600-1200-2000 and 4000 grit SiC paper and polished using 3 and 1 lm diamond pastes. The polished surfaces were then observed by means of a Leica DMI 5000 optical microscope (Leica microsystems, Germany)",
            " Vickers microhardness values were evaluated on the XZ cross section by means of a Leica VMHT indenter (UHL Technische Mikroskopie GmbH, Germany). The hardness trend along the Z direction was evaluated by performing the indentations with 300 g and 15 s. Indentations were performed in the sample s center every 1 mm in order to evaluate the hardness mean values and standard deviations. Finally, tensile samples were tested using a Zwick Z100 tensile machine using 8 9 10 3 s 1 as strain rate. The samples were machined based on the ASTM-E8 standard (Ref 27) from the AB and HT bars as represented in Fig. 2(b). Four samples per condition were tested. In the following paragraphs, the results obtained on the AB and HT samples are described. Firstly, the results in terms of microstructure and the hardness are presented. Then, the residual stress distribution with respect to the depth is described. Porosity of C-0090-AB and C-0060-AB samples was measured to be 0.28 \u00b1 0.11 and 0.23 \u00b1 0.08%, respectively, showing that in both cases high density values could be achieved and that the deposition strategy does not have a significant effect on the consolidation of these samples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003190_j.ijheatmasstransfer.2020.119536-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003190_j.ijheatmasstransfer.2020.119536-Figure1-1.png",
        "caption": "Fig. 1. Deposition principle and experimental setup of the laser assisted UHF induction deposition method: (a) deposition principle and (b) experimental setup .",
        "texts": [
            " By sing a self-designed deposition platform, experiments with dif- erent processing parameters are conducted to validate the proess feasibility of the proposed deposition method and the estabished numerical model. The performance of the deposited layers ith different processing parameters is also investigated, and the ariation in performance is discussed in view of the control of the hermal process. . Description of the experimental approach The principle and experimental setup of the laser assisted UHF nduction deposition method are illustrated in Fig. 1 . During de- osition, a metal wire with a diameter of 2 mm is transferred to he induction coil by the wire feeder. With the eddy current genrated by the induction coil, the metal wire is rapidly melted and eposited onto the substrate, which is placed on a moving platorm. Pure argon as shielding gas is used to protect metal maerials from oxidation. Meanwhile, an auxiliary laser beam irradites the surface area in front of the deposited molten metal. The urrent that flows through the induction coil is supplied by UHF nduction power"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002071_s12206-014-1032-3-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002071_s12206-014-1032-3-Figure1-1.png",
        "caption": "Fig. 1. Fatigue analysis: (a) simulation; (b) experiment.",
        "texts": [
            " In the hybrid PSO algorithm, PSO is the main optimizer and SQP serves as a tuner for refining the solution of PSO, as follows: Step 1: Initialize swarm population with random positions and velocities (set t = 1). Step 2: If the maximum iterations or convergence criteria are not satisfied, then For i = 1 to NOP (number of particle). Calculate fitness value; Update velocity and position according to Eq. (8); Calculate pBesti(t); If pBesti(t) < pBesti(t-1) then Run SQP with ( )i tp as the initial point; Fig. 1(a) displays the finite element analysis (FEA) model of a truck cab using the commercial FEA code MSC.NASTRAN. The panels are modeled with CQUAD and CTRIA surface element, and their material property is assigned linear elastic material model MAT1. The cab is subjected to a torsional cyclic load at the rear body mounts when the front body mounts are fixed. As shown in Fig. 1(a), the forces F1, F2 form the torsional moment, and its amplitude and frequency of two load cases are listed in Table 2 according to our previous studies [25]. This in-house manufacturer\u2019s specification provides a simple and empirical guide for the rapid development of cab assembly, which can be applied even when chassis and other assemblies are not available. In this procedural guideline, the torsional load is considered as a critical load case to fatigue durability [26]. Loading data on the typical tracks of the predecessor trucks with the similar configuration was collected and analyzed to determine the amplitudes and frequencies of the sinusoidal torsional moments in a realistic way",
            " (10) were thus calculated from the uniform material law: ' fs = 534MPa, b = -0.087, ' fe = 1.182, c = -0.58. In order to validate the FE model, the modal and static stiffness experiments were conducted as shown in Figs. 2 and 3 prior to the fatigue test. The corresponding simulations were performed under the same conditions and the correlation results were list in Table 3. It can be noted that the simulation models had satisfactory accuracies by correlating to the physical experiments. In the fatigue experiment (Fig. 1(b)), we checked every 30 minutes for the first load case and every 10 minutes for the second load case if there were visible cracks on the surface of sheets. The fatigue life was the cumulative number of load cycles when the first crack was detected. Note that as a large engineering structure, the cab can probably continue to mostly or partially fulfill its function even after some small cracks appear. Nevertheless, it is difficult to quantify this ability. As a result, visible crack might be a good choice to assess the fatigue life"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.138-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.138-1.png",
        "caption": "Fig. 2.138 Layout of the series/parallel hybrid-electric vehicle (HEV) [DRIESEN 2006].",
        "texts": [
            " As a result, mechanical energy from the axle acts on the E-M motor, turning it in effect into a M-E generator such that the torque directly from the ICE to the axle is re-circulated, thereby lowering transmission energy conversion efficiency in that range. Changing the operating range of the ICE to high speed and low load for the equivalent power output enables recirculation to be avoided, but it also reduces the ICE\u2019s energy efficiency. An exemplary series/parallel HEV layout with an ICE and two electrical machines is shown in Figure 2.138 [DRIESEN 2006]. In Figure 2.139 is shown the HEV driving circumstances during starting when the ICE remains off to save liquid fuel and the E-M motor drives the series/parallel HEV. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 336 In Figure 2.140 HEV driving circumstances are shown during normal driving when the ICE starts and may drive the series/parallel HEV and produce electrical energy for the E-M motor or is charging the CH-E/E-CH storage battery. In Figure 2.141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001557_s12206-014-0804-0-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001557_s12206-014-0804-0-Figure2-1.png",
        "caption": "Fig. 2. Rolling speeds and velocities.",
        "texts": [
            " \u2022 The bearings operate under isothermal conditions. \u2022 The shape of the pulse generated by impact at the defect as shown in Fig. 8 models the defect. bearing Ball bearings are used to support various kinds of loads while permitting rotational motion of a shaft. The expressions for rolling bearing internal rotational speeds are developed by Harris [2]. When a bearing mounted on a shaft rotates at some speed, the rolling elements orbit the bearing axis and simultaneously revolve about their own axes (refer Fig. 2). The rotational speed of the cage is given by . (1) The angular velocity of the cage is . (2) Angular velocity of balls is defined by the following rela- tion: . (3) Bearing load distribution (refer to Fig. 3) with respect to angular position of ball is calculated by Eq. (4): (4) where In general, the deflection of the ith ball located at any angle q is calculated by following expression (refer to Fig. 4): . (5a) x and y are the deflections along X and Y direction respectively and g is the internal radial clearance which is the clearance between an imaginary circle, which circumscribes the balls and the outer race"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001619_s11666-017-0554-5-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001619_s11666-017-0554-5-Figure4-1.png",
        "caption": "Fig. 4 Schema of the meshed geometry for deposited wall and substrate",
        "texts": [
            " Although powder particles experience phases of acceleration and deceleration in the flowing process many times, they ultimately reach the surface of the substrate as converged powder stream of optimized parameters of carrier gas and shielding gas (shown in Fig. 1). The process of acceleration and deceleration for powder particles and their peak flowing velocity are in agreement with that in Ref 17 and 19. The computation domain is composed of a thin wall and a substrate, both are in solid phases. The substrate in the simulations used in this paper is 60 9 20 9 2 mm3 in X, Y, and Z direction, where a vertical thin wall with 3D-size of 40 9 1 9 3 mm3 is built (shown in Fig. 4). At the start of calculation, there is only the substrate, the clad track will be formed on the substrate surface once deposition begins. Two deposition patterns are used to fabricate the thin wall. They are uniform deposition pattern and back and forth pattern, respectively. To accurately calculate the strong liquid motion, free surface motion, and local high temperature gradient as well as to reduce calculation time, an average mesh size (medium mesh) of 200 lm is overlaid on the laser and powder interaction zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001235_tro.2012.2228132-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001235_tro.2012.2228132-Figure4-1.png",
        "caption": "Fig. 4. Rotation that satisfies the constraint b1 + Cb2 = 0, where w = b 1 \u00d7b 2",
        "texts": [
            " (6) If we define a scalar a := \u2212vT 1p3 , then it is easy to see that (6) and (2) have identical structure. C. Rotation Matrix Determination We have shown that for both Systems 1 and 2, in order to determine the rotation matrix C, we need to solve the following system of equations: b1 + Cb2 = 0 (7) vT C2p4 + a = 0. (8) The key idea behind our approach is to first exploit the geometric properties of (7) which will allow us to determine 2 DOF in rotation. The remaining unknown DOF can subsequently be computed using (8). We start by first showing the following lemma (see Fig. 4). Lemma 2: A particular solution to (7) is C\u2217 = C(w, \u03b2), where w = b1 \u00d7b2 \u2016b1 \u00d7b2 \u2016 , and \u03b2 = Atan2(\u2016b1 \u00d7 b2\u2016,\u2212bT 1 b2). Proof: Using the Rodrigues rotation formula, we have C(w, \u03b2) = c\u03b2I + s\u03b2 w\u00d7 + (1 \u2212 c\u03b2)wwT (9) where w\u00d7 is the skew-symmetric matrix of w so that w\u00d7 b2 = w \u00d7 b2 . Substituting C(w, \u03b2) into (7), we have \u2212b1 = (c\u03b2I + s\u03b2 w\u00d7 + (1 \u2212 c\u03b2)wwT )b2 (10) \u21d2 \u2212b1 = c\u03b2b2 + s\u03b2 w\u00d7 b2 . (11) Projecting (11) on b2 yields c\u03b2 = \u2212bT 1 b2 . (12) Premultiplying both sides of (11) with b2 \u00d7 yields \u2212 b2 \u00d7 b1 = s\u03b2 b2 \u00d7 w\u00d7 b2 \u21d2 w\u2016b1 \u00d7 b2\u2016 = \u2212s\u03b2 b2 \u00d7 b2 \u00d7 w \u21d2 w\u2016b1 \u00d7 b2\u2016 = \u2212s\u03b2(\u2212I + b2bT 2 )w \u21d2 w\u2016b1 \u00d7 b2\u2016 = s\u03b2w \u21d2 s\u03b2 = \u2016b1 \u00d7 b2\u2016"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001610_s11071-017-3369-5-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001610_s11071-017-3369-5-Figure9-1.png",
        "caption": "Fig. 9 A separately excited DC motor",
        "texts": [
            " This shows that the system is GUUB. And it is clear from (55) that max {\u2016\u03b6(t)\u20162} = \u221a 1 \u03bbmin(\u0393 ) ( V (0) + \u03b2 \u03b1 ) , (57) that is, \u03b6(t) exponentially converges to a bounded region W = {\u03b6(t) : 0 < \u2016\u03b6(t)\u20162 \u2264\u221a 1 \u03bbmin(\u0393 ) ( V (0) + \u03b2 \u03b1 )} . An upper bound on the steady-state compensation error is now given. A simple calculation gives D\u0303(s) D(s) = B+LC[s I \u2212 A + LC]\u22121B T s + B+LC[s I \u2212 A + LC]\u22121B . (58) Thus, D(s) = D(s) \u2212 D\u0303(s) = T s T s + B+LC[s I \u2212 A + LC]\u22121B D(s). This gives (38). Consider a separately excited DC motor (Fig. 9). It has a dead zone due to static friction and a backlash due to the magnet characteristic of a field core. For simplicity, we take the dead zone and the backlash as input nonlinearities. And we employ the above described method to compensate for those nonlinearities. Note that the EID approach can compensate for nonlinearities in the state. This will be discussed in detail in a separate report. The state-space equation of the system is\u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 [ i\u0307a(t) w\u0307(t) ] = [ \u2212 Ra La \u2212 Kb La K J \u2212\u03bc J ][ ia(t) w(t) ] + [ 1 La 0 ] Ea(t), y(t) = [ 0 1 ] [ ia(t) w(t) ] , (59) where Ea(t) is the electric voltage, ia(t) is the electric current, Ra is the electric resistance, La is the electric inductance, \u03bc is the damping ratio of the mechanical system, J is the moment of inertia of the rotor, Kb is the electromotive force constant, and K is the motor torque constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002513_s00339-017-1313-7-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002513_s00339-017-1313-7-Figure3-1.png",
        "caption": "Fig. 3 Morphology of single-layer, three-layer and five-layer scanned tracks",
        "texts": [
            " Nanohardness measurements of the polished specimens were carried out on an Agilent Technologies G200 tester equipped with continuous stiffness measurement (CSM). It offers a direct measure of hardness, and elastic modulus during the loading portion of an indentation test. A three-sided pyramid diamond Berkovich indenter with a radius of 20\u00a0nm and normal angle of 65.3\u00b0 between the tip axis and the faces of triangular pyramid was used. The vertical resolution of the instrument is better than 1\u00a0nm and the force resolution is about 250 mN. Figure\u00a03 shows the cross-section of the three samples; the width is about 125\u00a0\u03bcm, and the heights are about 60, 200 and 270\u00a0\u03bcm, respectively. There are no distinct voids in the cross-section, indicating that the process parameters is capable of fabricating high-density parts. Points P1\u2013P3 were arranged at the cores of the 1st layers of scanned tracks, while points P4 and P5 were arranged at the cores of the 3rd and 5th layers of five-layer scanned track. Points P1, P2 and P3 (located at height about 30\u00a0\u03bcm from the bottom) were selected as comparison group 1, which was used to study the tempering effect of subsequent layers on the microstructure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003024_s00202-020-00955-2-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003024_s00202-020-00955-2-Figure4-1.png",
        "caption": "Fig. 4 Mesh region of the proposed motor",
        "texts": [
            " Initial dimension and design parameters are identified using a standard induction motor design procedure [18]. Based on the design parameters, motor is modeled and optimized in 2D time-stepping FEA software [19, 20]. To identify the losses and performances accurately, the properties of magnet, copper, aluminum andM43-29G are adjusted in FEA simulation software. To get accurate results, it is essential to design the motor in accordance with stator overhang and rotor end ring. A complete model is split into n number for fine triangular mesh element as shown in Fig. 4, and all the mash elements are solved by a Maxwell\u2019s equation. The sizing of the magnet is crucial in designing a motor, which involves the selection of rotor configuration, various magnetic materials, grade, operating temperature, ambient, starting capability and steady-state performance. By considering the application requirement, the initial magnet size is determined by standard design formulas [21]. The optimumdimension of themagnet is identified fromOptimetrics, which is in-built in FEA software"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure1.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure1.2-1.png",
        "caption": "Fig. 1.2 Mechanical gyroscope and its components",
        "texts": [
            " Amechanical gyroscope presents a system containing a heavy metal disc or rotor, universally mounted with three degrees of freedom: spinning freedom at about an axis perpendicular to its centre; tilting freedom at about a horizontal axis at right angles to the spin axis and veering freedom around a vertical axis perpendicular to both other axes. The three degrees of freedom are obtained by mounting the rotor in two concentrically pivoted rings called inner and outer rings or gimbals. The laboratory gyroscope presents this construction in Fig. 1.2. The whole assembly is known as the gimbal system of a free or space gyroscope. The gimbal system is mounted in a frame with supports and base so that it is in its normal operating position. All axes of a gyroscope are at right angles to one another and intersect at the centre of the rotor\u2019s gravity. Such a gyroscope is called static or balanced, whereas, on the contrary case, it is called heavy. The rotor\u2019s centre of gravity can be in a fixed position or may be offset from an axis of oscillation",
            " The action of the system of inertial torques represents the rotational motions around axes is called the gyroscopic effects. The system will not exhibit any gyroscopic effects unless the rotor is spinning. If the rotor ismade to rotate at high-speed and displaced at about its axis, then the rotor torques manifest valid gyroscope properties that possess essential fundamental functions. The gyroscopic device orientation remains nearly fixed, regardless of the mounting platformmotion. The permanent orientation of a gyroscope in space is made manifest when the following conditions are met (Fig. 1.2): external torque is applied to the gyroscope\u2019s spinning rotor, and gyroscope\u2019s axis of rotation must be capable of changing its orientation in space. If the gyroscope is subjected to an external torque tending to rotate around some axis, the external torque generates several inertial torques of the spinning rotor. These conditions demonstrate the following properties: \u2022 The rotor\u2019s axis oz of the gyroscope starts to rotate (precession) in a right angle direction to the external torque. \u2022 Simultaneously, the gyroscope, as well as its gimbals, starts to turn around axes ox and oy but with different angular velocities and minor accelerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.14-1.png",
        "caption": "Fig. 13.14 Devos coupling with balls in cylindrical tracks",
        "texts": [
            " joint. Homokinetic shaft couplings with ball-in-track joints have many advantages such as small size, small dynamic unbalance and distribution of contact forces among a large number of balls. However, there are disadvantages, too. Problems arise from the fact that the motion of balls in crossing tracks is not rolling, but sliding and boring with the possibility of jamming due to friction. This aspect of kinematics see in Phillips/Winter [14]. The so-called Devos coupling shown schematically in Fig. 13.14 has two balls-in-tracks in parallel to a spherical joint S . The tracks are symmetrically located cylinders. In order to keep the centers of the balls in the bisecting plane \u03a3 the balls are also constrained to move along the cylindrical pin 3 which is rigidly attached to the sphere of the joint S . This implies that the sphere of the joint S cannot be rigidly connected to any of the two shafts. Details of design not shown in the figure allow the shaft coupling to be assembled under prestress in such a way that its elements are firmly held together"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.22-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.22-1.png",
        "caption": "Fig. 14.22 Pole curve for the poles of Fig. 14.18 with significant points and lines",
        "texts": [
            " These lines create the pole quadrilateral (Pij , \u03a0j ,Pk , \u03a0ik) in which \u03a0j and \u03a0ik are opposite poles. The six \u03a0-points constitute three pairs of opposite poles. Consequently, they represent the poles belonging to four positions of the plane with which the same pole curve p is associated. The \u03a0-points of these poles are poles again etc. Starting from the six original poles this procedure produces an infinite sequence of six-tuples of poles all lying on p . On a computer screen a graph of p is most easily generated by calculating a sufficiently large number of six-tuples of poles. In Fig. 14.22 the pole curve for the six poles of Fig. 14.18 is shown together with its focus and its asymptote. The point of intersection of the asymptote with p is called cardinal point H of p . Next, Eq.(14.53) of the pole curve p is considered again. New coordinates \u03be, \u03b7 are defined through the transformation equations x = \u03bc(\u03be \u2212 \u03be0) + \u03bb(\u03b7 \u2212 \u03b70)\u221a \u03bb2 + \u03bc2 , y = \u2212\u03bb(\u03be \u2212 \u03be0) + \u03bc(\u03b7 \u2212 \u03b70)\u221a \u03bb2 + \u03bc2 (14.55) where \u03be0 and \u03b70 are as yet unspecified constants. This transformation has the effect that the \u03be-axis is parallel to the asymptote of p ",
            " The points Pij , P i , \u03a0ik on ki have the coordinates ( 0, 0 ), (a4, b4) and ( a\u22172, 0 ), and the points Pij , \u03a0j , Pjk on kj have the coordinates ( 0, 0 ), (a\u22174, b \u2217 4) and ( a2, 0 ) with a\u22172 = a4 \u2212 b4 a3 \u2212 a4 b3 \u2212 b4 , a\u22174 = a4a2b3 b3a4 \u2212 b4(a3 \u2212 a2) , b\u22174 = b4 a4 a\u22174 . (14.61) With these coordinates the equations of ki and kj are \u2212(x2 + y2) + xa\u22172 +y [ a4 b4 (a4 \u2212 a\u22172) + b4 ] = 0 , \u2212(x2 + y2) + xa2 +y [ a4 b4 (a\u22174 \u2212 a2) + b\u22174 ] = 0 . \u23ab\u23ac \u23ad (14.62) Both equations are, indeed, satisfied with (14.58) in combination with (14.54). End of proof. Resolution of (14.59) for \u03b7 \u2212 a yields an expression which tends to zero for \u03be \u2192 \u00b1\u221e . Consequently, the asymptote of p in the \u03be, \u03b7-system has the equation \u03b7 = a . Its intersection with p , i.e., the cardinal point H in Fig. 14.22 , has the coordinates \u03b7H = a and \u03beH = \u2212ae/d . The midline of all three pole quadrilaterals has the equation \u03b7 = a/2 . This follows from previous comments on Fig. 14.20 . Further properties of the pole curve are revealed by introducing in (14.59) for \u03be2 + \u03b72 the abbreviation r2 and by resolving the equation for \u03b7 . This results in the equations \u03be2 + \u03b72 = r2, \u03b7 = a r2 \u2212 \u03bed/a r2 + e = \u03b7H r2 + e \u03be/\u03beH r2 + e . (14.63) They are parameter equations with parameter r of a family of concentric circles centered at \u03a6 and of a family of lines passing through the cardinal point H ",
            " The resulting equation is quadratic in x : x2(y \u2212 \u03b7D) + 2xy\u03beD + y2(y + \u03b7D) = 0 . (14.66) It is satisfied by x = y = 0 . The Taylor formula for the solutions in the neighborhood of the origin is x1,2 = y\u03be\u20321,2 with the expressions (14.65). End of proof. The equation e = a2 4 \u2212 d2 a2 (14.67) resulting from (14.64) is a necessary condition for the existence of a double point. Because of the squaring of a and d it is not a sufficient condition. A pole curve without double point is either bicursal (Fig. 14.22) or unicursal (the solid line in Fig. 14.23). Of which type it is can be seen directly from Fig. 14.18. An arbitrarily chosen quadrilateral (Pij ,Pjk,Pk ,P i) 14.6 Tilings 441 (i, j, k, = 1, 2, 3, 4 different) is interpreted as mobile four-bar with two arbitrarily chosen neighboring poles, say Pij and Pjk , serving as frame (Fig. 14.24). Following a rotation \u03d5 of the left crank (or rocker) the coupler P iPk is either in the position AB or in the position AB\u2032 . The midnormal of P iA is intersected by the midnormal of Pk B at Q0 and by the midnormal of Pk B \u2032 at Q\u2032 0 ",
            " The center point Q0 is the infinitely distant point on the asymptote of the pole curve. The straight line is orthogonal to the asymptote. Since it is passing through the orthocenters, of all four pole triangles (see Fig. 14.14) collinearity of these orthocenters is proved. Likewise, there is only a single solution with circle points Q1, Q2, Q3, Q4 at infinity. From Fig.14.15 it is known that the center point Q0 is located on the circumcircles of all four pole triangles. These circles have a single point of intersection U (Fig. 14.22). As in the case of three positions, the directions Q0Qi (i = 1, 2, 3, 4) toward the infinitely distant circle points are determined from pole triangles (Fig. 14.15). A center point Q0 on p close to U is associated with a very long crank with very distant circle points. Circle point curves: The geometric locus of the circle point Qi is called circle point curve ki ( i = 1, 2, 3, 4 ). If a single circle point curve, say k1 , is known, the other three curves are obtained by rotating k1 about poles",
            " A crank-rocker is producing four prescribed positions in the prescribed order 1 , 2 , 3 , 4 if the circle points on the crank circle are arranged in the order Q1 , Q2 , Q3 , Q4 either clockwise or counterclockwise. For this to be the case, the three triangles of circle points (Q1,Q2,Q3), (Q2,Q3,Q4) and (Q3,Q4,Q1 ) must have one and the same sense. For the definition of sense of a triangle see Fig. 14.16 and the accompanying text. The sense is determined by the location of the center point Q0 relative to the three lines of the corresponding pole triangle. Four pole triangles have altogether twelve lines dividing the infinite plane into domains. From Fig. 14.22 the following properties of the center point curve are known. The curve is intersected by lines at the six poles Pij , at the six points \u03a0ij (i, j = 1, 2, 3, 4 different) and at no other point. From this and from Fig. 14.16 the following conclusions are drawn. When Q0 travels on p through a pole Pij (i, j = 1, 2, 3, 4 different), two lines belonging to one and the same pole triangle are crossed. This crossing has no effect on the sense of any triangle of circle points. In contrast, when Q0 travels through a point \u03a0ij (i, j = 1, 2, 3, 4 different), two lines belonging to different pole triangles are crossed",
            " This has the consequence that two triangles of circle points change sense. The six points \u03a0ij (i, j = 1, 2, 3, 4 different) divide the curve into seven sections (no matter whether the curve is unicursal or bicursal). The senses of circle point triangles do not change as long as Q0 stays in one and the same section of the curve. Identical senses of all three circle point triangles are achieved with a set of points Q0 which is either a single section or the union of several nonneighboring sections. In what follows, the set is denoted \u03c3c. Example: In Fig. 14.22 the sense of the three circle point triangles is clockwise for points Q0 in the unbounded section to the right of \u03a012 and in the section \u03a014-\u03a6-\u03a034 . It is counterclockwise in the unbounded section to the left of \u03a023 . Thus, the set \u03c3c of admissible crank centers is the union of these three sections. From Fig. 17.4b the following properties of crank-rockers are known. A four-bar is a crank-rocker if (a) Grashof\u2019s inequality condition min + max \u2264 \u2032 + \u2032\u2032 is satisfied and if, in addition, (b) the crank has the minimal length min "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure8.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure8.5-1.png",
        "caption": "Fig. 8.5 Schematic of measurement value of the precession torque",
        "texts": [
            " The blocking of the gyroscope rotation around axis oy deactivates all inertial torques generated by the rotatingmass elements of the spinning rotor. However, this blocking does not lead to the deactivation of the precession torque of the change in the angular momentumacting around axisoy. The validation of the action of the precession torque and the measure of its value is conducted on the stand that represented in Fig. 8.4. The gyroscope stand additionally equipped with the angular rocker that transfers the action of the precession torque to the digital scale. The sketch of the stand is represented in Fig. 8.5. The bar of the gimbal is contacted with the angular rocker that presses the platform of the digital scale of Model TS-SF 400A with division one gr. The digital scale has demonstrated the value of the force generated by the precession torque. The practical result is compared with the theoretical value of the force of the precession torque computed for the horizontal location of the running gyroscope. The torque and forces acting on the gyroscope stand are represented in Fig. 8.5. The basic geometrical parameters of the stand are represented in Table 8.1, Fig. 8.2 and in Sect. 8.1. The value of the velocity is changed with the change in the angle of the gyroscope turn and time of motion. The force of the precession torque is varied with the change of the angular velocity and the time of the motion of the gyroscope. The expression of the precession torque for the horizontal location (\u03b3 = 0\u00b0) of the gyroscope is represented by substituting \u03c9x (Eq. 6) into T am = J\u03c9\u03c9x: Tam = J\u03c9 \u00d7 (3.086464199 cos 0\u25e6 \u2212 2.595701613) ( 1 \u2212 e\u22121.050580906t) = 0.490762586J\u03c9 ( 1 \u2212 e\u22121.050580906t ) (8.42) where all parameters are as specified above. The precession torque produces the reactive forcesFs of the digital scale (Fig. 8.5) that represented by the following equation: Fslh = Tamlv lb/2 \u2212 Tam(dr/2) fr lb/2 or Fs = 2Tam lhlb ( lv \u2212 dr fr 2 ) (8.43) where lh = 90.0 mm, lv = 80.0 mm and lb = 115.5 mm is the length of the rocker\u2019s horizontal and vertical arm and the bar of the gimbal, respectively; dr = 4.0 mm is the diameter of the rocker\u2019s pivot; f r = 0.5 is the friction coefficient in the rocker\u2019s pivot (wood-steel) [21]; other parameters are as specified above. Substituting Eqs. (8.42) into Eq. (8.43) and transformation yield the following equation: Fs = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001366_1.4745081-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001366_1.4745081-Figure7-1.png",
        "caption": "FIG. 7. High pressure compressor (HPC) BLISK (Rolls-Royce Deutschland, Ltd. & Co. KG).",
        "texts": [
            " A BLISK (BLade Integrated DiSK\u00bc a compressor This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 23:38:17 disk of a jet engine with integrated blades) that features an approximately 30% smaller weight compared to a former component is conventionally manufactured by 5-axis-milling or linear friction welding of pre-milled blades onto a preturned disk (Fig. 7). This conventional manufacturing chain covers many process steps including NDT and is especially time and material consuming: e.g., the net machining time can be over 100 h, resulting in material losses of more than 80%\u201390%. Assuming that the same static and dynamic mechanical properties can be achieved by LMD, would it not be a much more cost effective alternative to manufacture such a part additively and to \u201cgrow\u201d the 76 blades layer-by-layer onto the pre-turned disk and to finish machine those in a subsequent 5-axis-milling step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001209_imece2012-86513-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001209_imece2012-86513-Figure4-1.png",
        "caption": "FIGURE 4. SECTION VIEW OF GEAR MOUNTED IN THE TESTING MACHINE.",
        "texts": [
            " During the test, a sinusoidal load is applied at about 35 Hz. Even if the load acting on a gear tooth during actual meshing is pulsating from zero, the tests have been performed with a fatigue ratio R = 0.1, as usually done, since it is not possible to apply a zero load in this kind of tests. The load is applied along the normal to the tooth flank surface (i.e. the common normal to 1One tooth if the pair of teeth is not symmetrically loaded, otherwise two. tooth flank and to anvil contact planes ((1) in Figure 4)); hence, the load acts along a line tangent to the base circle of the gear. The position of the center of the gear being tested is determined by the supporting structure. Since the load line ((2) in Figure 4) is tangent to base circle and it is normal to anvil contact planes, its position is completely defined. Let assume that there are k\u22122 teeth between the two loaded teeth. If the horizontal distance (X) between the plane of the left anvil and the gear centre is exactly equal to an half of the span measurement over k teeth2 the two teeth are loaded symmetrically, hence the load is applied at the same radius. On the contrary, if this distance is different, the position of the load applied on the two teeth will be different"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.30-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.30-1.png",
        "caption": "Fig. 17.30 Planar parallel robot. Four-bar A0ABB0 with coupler curve generated by C . The rate of change r\u03073 of the leg length r3 causes the platform to rotate with angular velocity \u03c93 = r\u03073/( 3 cos\u03b13) about P3",
        "texts": [
            "118) This equation is formally identical with Eq.(17.87) for the four-bar. Both a and denote the length of the fixed link. The definitions of \u03b2 are different, 17.10 Planar Parallel Robot 609 however. The maximum number of double points and of cusps of coupler curves on the circle is three. It can be shown that the third singular focus coincides with the singular focus A0 . This has the consequence that there are no cognate inverted slider-crank mechanisms. The triangular platform (A,B,C) of the planar parallel robot in Fig. 17.30 is positioned by means of three telescopic arms with controllable lengths ri ( i = 1, 2, 3 ) which are pivoted at A0 , B0 , C0 . The platform serves as carrier of tools or of work pieces7. The characterization as parallel points to the fact that the platform is positioned by arms in a parallel arrangement in contrast to a serial robot where it is positioned by a single arm with a series of links and joints (see Sect. 5.7). Parallel robots are able to manipulate heavier loads than serial robots, and they position them with higher accuracy and with greater stiffness",
            " These are three quantities specifying the triangle (A,B,C), the arm lengths ri ( i = 1, 2, 3 ) and, in the x, y -system shown, the x -coordinate of B0 and the x, y -coordinates of C0 . To be determined are all possible positions of the triangle (A,B,C). Solution: Imagine that joint C connecting the platform with arm 3 is eliminated. Point C is located on the coupler curve generated by C fixed to the four-bar A0ABB0 and also on the circle k of radius r3 about C0 . The four-bar and the coupler curve in Fig. 17.30 are copied from Fig. 17.23. The circle k intersects the coupler curve at six points. This is the maximum possible number of points. How to calculate these points was explained following (17.85). Each point determines a possible position of the robot. This concludes the position analysis. Next, the velocity state is analyzed. Imagine that the telescopic joint in arm 3 is a passive joint so that this arm adapts itself freely to motions of the four-bar A0ABB0 with fixed lengths r1 and r2 . The platform (A,B,C) has relative to the base the instantaneous center P3 at the intersection of arms 1 and 2 ",
            " Conversely, if r\u03073 is prescribed, \u03c93 = r\u03073/( 3 cos\u03b13) . This angular velocity and the instantaneous center P3 determine the velocities of A , B and C . The formula for \u03c93 shows that r\u03073 = 0 is possible only if in the position under investigation the coupler curve and the circle k are not in tangential contact. The quantities 3 and cos\u03b13 are calculated from the triangle (C0,P3,C) . Similar statements are valid when in the position under investigation arm 1 only or arm 2 only experiences a rate of change of length r\u03071 or r\u03072 , respectively. In Fig. 17.30 also the instantaneous centers P1 , P2 together with the associated quantities 1 , \u03b11 and 2 , \u03b12 are shown. When the three rates of change r\u03071 , r\u03072 , r\u03073 occur simultaneously, the superposition principle yields the resultant angular velocity \u03c9 = 3\u2211 i=1 r\u0307i i cos\u03b1i . (17.119) The velocity of each of the points A , B , C is the sum of three velocities two of which are collinear. The instantaneous center of the platform is the intersection point of the normals of the velocities of A , B and C . 17"
        ],
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    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.24-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.24-1.png",
        "caption": "Fig. 17.24 Four different fourbars A0ABB0 in positions in which the coupler point C coincides with the instantaneous center of rotation of the coupler thereby passing through a cusp of its coupler curve",
        "texts": [
            " From this it follows that also cusps lie on the circle (17.87), and that the maximum number of cusps is three. The condition for a cusp to exist is that the coupler point C is located on the moving centrode of the coupler. In the course of rolling of the moving centrode on the fixed centrode the point C generates the cusp when it is the point of contact, i.e., the instantaneous center of rotation of the coupler and, hence, the intersection point of the input and the output link of the four-bar. 17.8 Coupler Curves 601 Figure 17.24 demonstrates that this may happen in altogether four different configurations. The common feature is that the segments of lengths (r1, b1) and (r2, b2) are pairwise collinear. In any such configuration the base A0B0 is seen from C either under the angle \u03b2 or under the angle \u03c0 \u2212 \u03b2 . This proves again that cusps lie on the circle (17.87). In the four-bar A0ABB0 drawn with thick lines the cosine law applied to the triangles (A0,B0,C) and (A,B,C) yields the equations 2 = (r1 + b1) 2 + (r2 + b2) 2 \u2212 2(r1 + b1)(r2 + b2) cos\u03b2 , a2 = b21 + b22 \u2212 2b1b2 cos\u03b2 . } (17.93) Elimination of cos\u03b2 results in a condition for the existence of cusps: b1b2[(r1+b1) 2+(r2+b2) 2\u2212 2]\u2212(r1+b1)(r2+b2)(b 2 1+b22\u2212a2) = 0 . (17.94) With reference to Fig. 17.24 (b1, b2) can be replaced by (\u2212b1, b2) , (b1,\u2212b2) and (\u2212b1,\u2212b2) . Example: To be determined are parameters of coupler curves of foldable four-bars of the kind +r1 = a+r2 which have not only the singular double point, but also a cusp on the circle of singular foci. Solution: The parameters must satisfy (17.92) as well as (17.94). Substitution of the expressions (17.92) into (17.94) results in (\u03bc1 + \u03bc2 \u2212 1)[\u03bc1(1 + \u03bc1)r1 \u2212 \u03bc2(1 + \u03bc2)r2] 2 = 0 , i.e., 602 17 Planar Four-Bar Mechanism either \u03bc2 = 1\u2212 \u03bc1 (\u03bc1 , r1 , r2 arbitrary) (a) or r2 = \u03bc1(1 + \u03bc1) \u03bc2(1 + \u03bc2) r1 (\u03bc1 , \u03bc2, r1 arbitrary) (b) ",
            " Condition (b) is a special case. Substitution of this expression for r2 and of b1 = \u03bc1r1 , b2 = \u03bc2r2 into the second Eq.(17.93) shows that cos\u03b2 = 1 . This means that the generating point of the coupler curve lies on the coupler. End of example. Figure 17.25 is proof of the existence of coupler curves with three cusps. A coupler curve has three cusps if in one of the three positions both A and B are located on the circle with the diameter A0\u2013B0 (Cayley [6] v.9:551\u2013580 , Mayer [27]). Let the position drawn in thick lines in Fig. 17.24 be modified so as to satisfy this condition. The angles in the coupler triangle are denoted \u03b2 , (CBA) = \u03b1 and (CAB) = \u03b3 . Proposition: The triangles (C,A0,B0) and (C,A,B) are congruent with (CA0B0) = \u03b1 and (CB0A0) = \u03b3 . Proof: It suffices to prove the first identity. This is done in three steps. 1. (CA0B) = \u03c0/2\u2212 \u03b2 (right-angled triangle). 2. The center 0 of the said circle is the apex of the three isosceles triangles (A0,0,A) , (A,0,B) and (B,0,B0) . The second triangle has the apex angle (A0B) = \u03c0 \u2212 2\u03b2 (twice the angle subtended by A\u2013B )",
            " It shows in stereographic projection the coupler curve and the curve \u03c4 for the set of parameters \u03b11 = 85\u25e6 , \u03b12 = 82\u25e6 , \u03b13 = 100\u25e6 , \u03b14 = 90\u25e6 , \u03b15 = \u03b16 = 50\u25e6 (\u03b12 , \u03b15 and \u03b16 determine \u03b17 \u2248 117.8\u25e6 ). Note: In this figure the central point of the stereographic projection is the north pole (the point y = 1 ). This has the advantage that the projection of the curve \u03c4 is symmetric4. As is known from the planar four-bar double points may degenerate into cusps. Conditions for the occurrence of cusps are developed as follows (compare with the formulation of condition (17.94) for the planar four-bar and with Fig. 17.24). The coupler point C is located in a cusp when the coupler is momentarily rotating about the axis 0C . Then A0 , A and C lie on a great circle, and B0 , B and C lie on another great circle. This can happen in altogether four different configurations. The common feature is that the 4 Equation (18.33) is the principal-axes equation of \u03c4 . The pertinent transformation equations are x\u0304 = 4\u03be \u03be2+\u03b62+4 , y = \u03be2+\u03b62\u22124 \u03be2+\u03b62+4 , z\u0304 = 4\u03b6 \u03be2+\u03b62+4 . This projection produces the principal-axes equation of the curve shown in Fig. 18.5: (\u03be2 + \u03b62)2 sin(\u03b14 \u2212 \u03b17)\u2212 8(\u03be2 \u2212 \u03b62) sin\u03b17 \u2212 16 sin(\u03b14 + \u03b17) = 0 18.3 Coupler Curves 655 great-circle arcs of lengths \u03b11 , \u03b15 and of \u03b13 , \u03b16 are pairwise co-tangent. In any such configuration the base A0B0 is seen from C either under the angle \u03b17 or under the angle \u03c0\u2212\u03b17 . This proves again that cusps lie on the curve \u03c4 . The four configurations are shown by Fig. 17.24 if the straight lines are interpreted as great-circle arcs and if the notations are changed according to Fig. 18.3. The cosine law applied to the spherical triangles (A0,B0,C) and (A,B,C) yields the equations C4 = cos(\u03b11 + \u03b15) cos(\u03b13 + \u03b16) + sin(\u03b11 + \u03b15) sin(\u03b13 + \u03b16)C7 , C2 = C5C6 + S5S6C7 . } (18.47) Elimination of C7 = cos\u03b17 results in a condition for the existence of cusps. With the help of addition theorems it can be given the form C1S3S5(C5 \u2212 C2C6) + S1C3S6(C6 \u2212 C2C5) + S1S3(C 2 5 + C2 6 \u2212 C2C5C6 \u2212 1) + S5S6(C4 \u2212 C1C2C3) = 0 . (18.48) With reference to Fig. 17.24 the combination (S1, S3) can be replaced by any of the combinations (\u2212S1, S3) , (S1,\u2212S3) and (\u2212S1,\u2212S3) . In Primrose/Freudenstein [7] the numerical example is given: \u03b11 = \u03b13 = \u03b14 = 90\u25e6 , \u03b15 = \u03b16 = 30\u25e6 , \u03b12 = cos\u22121 2 3 . With these parameters both the four-bar and the coupler triangle are symmetric. Condition (18.48) is satisfied with all four combinations (S1, S3) , (\u2212S1, S3) , (S1,\u2212S3) and (\u2212S1,\u2212S3) . Equation (18.47) yields C7 = \u22121/3 . The coupler curve with these parameters is bicursal with two cusps in each branch"
        ],
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    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure4.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure4.8-1.png",
        "caption": "Fig. 4.8 Spatial closed chain with six bodies and six revolute joints",
        "texts": [
            "2 Illustrative Examples 149 \u03d5\u03082 = \u03d5\u03081 cos\u03d51 (1\u2212 sin\u03d51) \u221a 1\u2212 2 sin\u03d51 + \u03d5\u03072 1 2\u2212 2 sin\u03d51 \u2212 sin2 \u03d51 (1\u2212 sin\u03d51)(1\u2212 2 sin\u03d51)3/2 . (4.25) The mechanism is highly special. A mechanism having two trihedrals of permanently intersecting axes need not be plane-symmetric, and a planesymmetric mechanism need not be trihedral. Bricard [1] discovered a fiveparametric family of trihedral mechanisms and an eight-parametric family of plane-symmetric mechanisms. These mechanisms are analyzed in Sects. 6.4.2 and 6.4.3 . The mechanism shown in Fig. 4.8 is another spatial closed chain with six bodies (fixed body 0 and bodies 1, . . . , 5) and with six revolute joints 1, . . . , 6 (thick lines). The two joint axes of each body are mutually orthogonal and intersecting. In the position shown the axes are edges of a cube (dashed lines). The name of the mechanism points to the fact that the six joint axes are pairwise symmetric with respect to a line (pairs 1 and 4 , 2 and 5 , 3 and 6 ). In the cube configuration the line of symmetry is identified as follows",
            " Franke: Vom Aufbau der Getriebe, v.2 (1951) Deutscher-IngenieurVerlag Du\u0308sseldorf shows, without kinematics analysis, a line-symmetric mechanism in which the joint axes on the bodies are skew. 150 4 Degree of Freedom of a Mechanism Equation (4.1) yields F = d . Hence a degree of freedom F > 0 exists only if at least one constraint is dependent. Constraint equations are formulated by a method similar to the one used in the previous section. On each body i (i = 0, . . . , 5) a body-fixed basis ei is defined. In Fig. 4.8 only basis e0 is shown. In the position shown in this figure all body-fixed bases are aligned parallel. Three of the five constraint equations express the fact that, independent of rotation angles in the joints, the chain of vectors leading from the point P on body 0 along body edges to the coincident point P on body 5 is closed. This is the constraint equation e01 + e13 \u2212 e21 \u2212 e32 \u2212 e43 + e52 = 0 . (4.26) Let Ai be the transformation matrix in the relationship ei = Aie i\u22121 (i = 0, . . . , 5 cyclic)",
            " Only if \u03d51 is in the interval between these bounds, the angle \u03d52 is real. At the bounds the solution is c2 = \u221a 3\u22121 . This determines the angles \u03d52 \u2248 \u00b142, 9\u25e6 . In the diagram in Fig. 4.9 \u03d52k and \u03d53k (k = 1, 2) are shown as functions of \u03d51 . The mechanism can be assembled in two configurations. The change from one configuration to the other is achieved by opening and re-closing a single joint in such a way that body-fixed vectors along the opened joint axis have equal directions after if they have equal directions before. In Fig. 4.8 the first configuration is shown for the variable \u03d51 = 0 with \u03d52 = . . . = \u03d55 = 0 . In the second configuration \u03d51 = 0 is associated with \u03d53 = \u2212\u03c0/2 , \u03d54 = 0 , \u03d52 = \u03d55 = \u03d56 = \u03c0/2 . This configuration is shown in Fig. 4.10a . It is possible to open and to re-close a single joint in such a way that the said body-fixed vectors along the joint axis reverse their relative orientation. However, this re-closing is possible in a single position only in which the system is then rigid. This position is shown in Fig"
        ],
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    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-FigureD.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-FigureD.4-1.png",
        "caption": "Figure D.4. Thin conical shell.",
        "texts": [],
        "surrounding_texts": [
            "1. GREENWOOD, D. T., Principles of Dynamics , Prentice-Hall, EnglewoodCliffs, NewJersey, 1965. Cast at an intermediate level comparable to thepresent text, thisbookprovides anexcellentresource for collateral study. Lagrange's equations, including a thorough discussion of constraints and the method of virtual work, are discussed in Chapter 6. The theoryof vibrations, including discussion of degenerate systems, is treated in Chapter 9. 2. HOUSNER, G. w.,and HUDSON, D. E.,Applied Mechanics: Dynamics, 2ndEdition, Van-Nostrand, Princeton, NewJersey, 1959. Lagrange's equations applied to the\u00b7theoryof small, free, and forced vibrations are studied in Chapter 9. The authors provide good preparation throughout for the student's subsequent study of advanced topics in dynamics. Some examples and problems in the current chapter are modeledafter those presented in this book. 3. LAGRANGE,1.L.,Analytical Mechanics, translated from theMecanique analytique novelle edition of 1811, editors A. Boissonnadeand V.V. Vagliente, Kluwer, Dordrecht, The Netherlands, 1997. Theoriginalofth isenduringclassical workoften is unavailablefor study, so thisEnglish translation is a most helpful substitute. The translators' \"Introduction\" provides an interesting sketch of the life and times of Lagrange. Lagrange's treatise, based on the methodof virtual work, beginswith principlesof statics in Part I; the greater emphasis is on the variousprinciples of dynamics in Part II. 4. LANCZOS, C; The Variat ional Principles of Mechanics, University of Toronto Press. Toronto, Canada, 1949. A beautifully written text highly recommended for advanced study. The focus, however, ismainlyon the theoretical aspects of Lagrange's differential equations of motionand the Hamilton-Jacobi canonical theoryof equations. There are very few, thoughwell chosen examples throughout.The method of undeterminedmultipliers is applied in the formulationof Lagrange's equations for systems with constraints. Our discussion of nonholonomic constraints mirrors that presented in this text. 5. LONG, R. R.,Engineering Science Mechanics, Prentice-Hall, EnglewoodCliffs,NewJersey, 1963. Vector and Cartesian tensor methods are integrated in this treatment of topics on engineering mechanics. Hamilton's principleand Lagrange's equations are introducedin Chapter3. The latter, however, are not uniformly applied throughoutthe text,which otherwise provides a good resource for collateral reading and for additional problems and examples. 6. MARION, J. B., Classical Dynamics of Particles and Rigid Bodies, Academic, New York, 1965. In Chapter 9, Lagrange's equations are derived from Hamilton's principle, and the method of undetermined multipliers to characterize constraints on a system is introduced. Muitidegree of freedom systems are studied in Chapter 14. Applications of Euler's equations and the energy principle for rigid bodies, including the spinning top problem, are studied in Chapter 13. See also MARION, J. B., and THORNTON, S. T.,Classical Dynamics ofParticles and Rigid Bodies,Harcourt Brace, NewYork, 1995. 7. PARS, L. A., A Treatise on Analytical Dynamics, Ox BowPress,Woodbridge, Connecticut, 1965. This text provides many examples for advanced readers. 8. ROSENBERG, R. M., Analytical Dynamics of Discrete Systems . Plenum. New York, 1977. This is a carefully written, thorough treatment of analytical dynamics based on the geometry of the configurationspace of generalizedcoordinates, including a precise presentation of the geometry of constraints and virtual displacements, and their relation to constrained systems. Chapter 9 is a clear analysis and description of D'Alembert's principle that leads in subsequent chapters to Lagrange's equations for arbitrary systems. There are manyworkedexamples throughout. Int roduction to Advanced Dynamics 561 9. SYNGE, 1. L., and GRIFFITH , B. A., Principles of Mechanics, 3rd Edition, McGraw-Hill, New York, 1959. Chapter 14 treats the general problem of the spinning top and the gyroscope by Euler's equations and the energy method, and Chapter 15 deals with Lagrange's equations with several examples, including the top problem. 10. TRUESDELL, C., Essays in the History ofMechanics, Springer-Verlag, Berlin, Heidelberg, New York, 1968. The author argues in Chapters 2 and 5 that Euler's laws are more general than Lagrange's equations, pointing specifically to the significance of Euler's principle of moment of momentum and noting that it is nevermentioned or used by Lagrange. II. WHITTAKER, E.T., ATreatise on the Analytical Dynamics of Pan icles and Rigid Bodies, 3rd Edition, Cambridge University Press, Cambridge, 1927. This classical volume, highly recommended to advanced readers, remains one of the best mathematical treatments of analytical dynamics. The treatise focuses entirely on the Lagrangian and Hamiltonian theories and includes many worked examples throughout. The reader may find the problems rather challenging, however. The theory of vibrations, includingdegenerate systems, is analyzed thoroughly inChapter VII; nonholonomic systems are studied in Chapter VIII, and extension of Hamilton's principle to conservative and nonconservative, nonholonomic systems follows in Chapter IX. 12. YEH, H., and ABRAMS, 1. I., Principles of Mechanics of Solids and Fluids, Vol. 1, Panicle and Rigid Body MechanicsMcGraw-Hill,New York, 1960. Lagrange's equations and someexamples, including application to the vibrations of a structure, are discussed in Chapters 13. Problems 11.1. Introduce C, = - A I C and C2 = - B IC , in which A = A(q\" qi , q3), B = Btq\u00ab, qi , q3), and C = C(qI, q2, q3), so that the differential constraint (11.5) becomes Adq, + Bdq -. + Cdq, = O. Show that the test condition (11.6) may be rewritten in the form ( aB ac ) ( ac aA ) ( aA aB )A - - - +B --- + C -- - - 0 aq3 aq2 aq, aq3 aq2 aq, - . (P I 1.1) Notice that this is satisfied identically when the terms in parentheses vanish. In this case, the constraint is integrable and hence holonomic. If these terms do not vanish, but (PI 1.1) vanishes identically, the constraint is holonomic, otherwise not. In either case, however, the integral of the differential constraint is not revealed (See Rosenberg, p. 46.), and it may be quite difficult to determine. If (P11.1) yields a relation qs = q3(q , , q2) that satisfies the conditions aq31aq , = C, and aq31aq2= C2, then q3= q3(q l , q2) is the holonomic constraint corresponding to (P I 1.1). Apply this method to decide the nature of the differential constraint relation in Exercise 11.1, page 499. 11.2. A particle P moves on a space curve with path variable s( t) .Apply Lagrange's method to derive the intrinsic equation of motion of P. 11.3. Introduce spherical coordinates in Example 7.15, page 260, for the spherical pendulum. Apply Lagrange's equations to derive the equations of motion, and determine their first integrals. 11.4. A small mass m is attached to a weightless, inextensible string that passes through a tiny, smooth hole in a horizontal plate. The specified time variable force P(t ) shown in the figure controls the cord length \u00a3(1) as a function of time so that the mass moves in the vertical plane. (a) Howmany degreesoffr eedomdoes this system have? (b) Apply Lagrange's equations to derive equations to determine B(t) and \u00a3(1). (c) What results follow from the moment of momentum principle? (d) Derive the same equations from Newton's law. 562 P(t) J 9 Problem 11.4. Chapter 11 11.5. A particle of mass m moves on the smooth inner surface of a thin paraboloid al shell of revolution defined by r 2 = az in cylindrical coordinates (r, e,z), where a is a constant. The particle, with weight W = -mgk : encounters air resistance described by a Stokes drag force Fd = - cv. Apply Lagrange 's equations to derive the equations of motion. Find the generalized forces (a) by the method of virtual work, (b) by application of (11.14), and (c) by use of (11.20). 11.6. Consider the motion of the slider block 5 in Problem 6.54. Identify the rheonomic constraint. Let R denote the force exerted on the slider by the smooth rod. Show that Q\\ = R \u00b7 (Jx /(J r = 0, where x is the position vector of 5 from F at the center of the table. Use Lagrange 's equations to derive the equation of motion of 5 for the generalized coordinate q, == ret). Find the motion of the slider when reO) = 0 and ; (0) = Vo initially. 11.7. The slider 5 described in Problem 6.55 is released from rest at 0 , relative to the table. Apply Lagrange 's method to derive the equation of motion for 5, and find its relative motion ret) for all constant values of the angular speed to, Refer all quantities to the rod frame If! = {O; ik } shown in Problem 6.54. 11.8. Identify any rheonomic constraints and apply Lagrange's method to derive the equation of motion of the slider block described in Problem 6.51. 11.9. Consider the system described in Problem 6.56. (a) Identify the rheonomic constraint and derive the equation of motion for the mass m by application of Lagrange's method. (b) Relax the constraint, obtain a second equation of motion involving the constraint reaction force R exerted by the rod on the slider, and thereby determine R in the case when to = WO, a constant. (c) Suppose the slider is released from rest at x = a to oscillate along the smooth rod. Find R as a function of x . 11.10. Determine the generalized forces and derive the Lagrange equations of motion for the pendulum bob described in Example 6.14, page 150. Show how the bob constraining force may be found. 11.11. A particle of mass m with cylindrical coordinate s (r ,e,z) moves in a gravitational field g = - gk on a smooth, concave upward surface of revolution defined by r = r(z) with reO) = O. Use Lagrange 's equations to derive the equation of motion for z(t), and outline how the angular placement e(t) may be found . 11.12. Apply Lagrange 's equations (11.15) to find the applied forces required to control the uniform motion of the particle relative to the rotating frame in Example 5.9, page 71. Identify the physical nature of the pseudoforces described by - (JT / (Jqk. 11.13. Apply Lagrange's equations to derive the equation s of motion for the system described in Problem 8.16. 11.14. Use Lagrange 's equations to investigate Problem 8.29. 11.15. Derive Lagrange's equations for small amplitude oscillations of the system shown in Problem 10.14. Introduction to Advanced Dynamics 563 11.16. A uniform rod of mass m and leng th 2e moves on a smooth horizontal plane with angular veloc ity w =wk. Its center C has a ve locity v' = ui + vj referred to a body frame cp = {C ; ikl with i directed along the rod . Apply Lagrange 's method to find the impulsive force P = Pxi+ Pvj applied at a point B distant b from C in order to bring poi nt B instan taneously to rest. Expre ss the result in term s of the ass igned parameters. 11.17. Identify the generalized coordinates and the number ofdegrees offreedom of the log in Problem 10.58. Use Lagrange's method to dedu ce the equations of motion and thus determine the frequency of the vertical oscilla tions of the log. 11.18. The wire and bob assembly of the rotating simple pendu lum shown in the diagram for Problem 6.47 is repl aced by a thin rigid rod of length I and mass m. The rod is hinged in a smooth beari ng at 0 and is free to slide on the smooth horizon tal table. (a) Identi fy the rheonomic constrai nt and apply Lagrange' s equations to der ive the equ ation for finite amplitude osc illations of the rod relat ive to the table. (b) Relax the constraint, determine the genera lized forces that act on the rod at its hinge bearing, and thus find the constraint reac tion force as an exact function of the finite angular placement fJ for initia l data fJ(O)= fJo and ~(O) = O. 11.19. Derive Lagrange 's equation of motion for the rolling cylinder in Problem 10.43. 11.20. A homogeneous circular cylindrical segment of radiu s R, length L, height h, and mass m perform s rocking osc illa tions without slipping on a rough hori zontal surface. The center of mass is at r from the center O. The segment is released from rest at the placement 9(0) = 90 \u2022 (a) Derive the different ial equation for the finite angular mot ion 9(1) by (i) applica tion of Lagrange's equations, and (ii) by use of the Newton- Euler equations. (b) Determine the first integral of the equation of motion. (c) Der ive an equation for the period of the large amplitude oscilla tions. (d) Find the circ ular frequency for small oscilla tions. o Problem 11.20. 11.21. A uniform, thin rigid rod shown in Probl em 10.37 slides in the vertica l plane with its ends on a smoo th circle of radius rand subtending a central angle of 1200 \u2022 (a) Derive the equation of motion by use of (i) Euler's laws, (ii) Lagrange' s method, and (ii i) the work--energy principle . (b) What is the first integral of the equation of motion ? (c) Discu ss briefly the exact solution for the motion 9(1) of the rod . (d) Find as functions of 9 alone the contact forces acting on the rod . (e) What are the major differences among the thre e methods used in (a)? (f) What is the length e,expressed in term s of r , of an equivalent simple pendulum having the same frequency? 11.22. Suppose the thin rod in the previous problem has its ends set in smooth bearings that slide along a circular hoop of radius r and negligible mass. The hoop rotates about its vertical centra l ax is with a cons tant angular speed Q . Th e rod is released from rest relative to the hoop at an angle 90 = 9(0). (a) Use Lagrange 's method to der ive the equations of mot ion of the rod . Are there any surprising fea tures of these results? (b) Derive the equations of motion by use of Euler 's laws. (c) Find the bea ring reaction forces exerted on the rod. (d) In what manner would the mass M of the hoop affec t the results? 564 Chapter 11 11.23. A nonhomogeneous circular cylinder has its center of mass C at a distance a from its geometrical cente r 0 , and its circular cross sectional plane through 0 is a plane of symmetry . The cylinder is released from rest when 0 = 0 and rolls without slipping on the horizontal surface . (a) Apply Lagrange's equations to determine the angular velocity wand angular accelerationw of the cylinder as functions of O. (b) Deduce the same results starting from the energy principle. (c) Find the surface reaction forces at D in terms of 0, co, andw. (d) Use Euler 's equation s to derive the equation of motion for the cylinder. (e) Discuss the principal difference between the methods of Euler and Lagrange . Problem 11.23. 11.24. Use Lagrange's equations to formulate the equations of motion of the spring and pulley system described in Problem 7.49, about its static equilibrium state. The pulley has radius a, mass m, and rolls without slipping on its inextensible belt. How many degrees of freedom does this system have? 11.25. Use Lagrange 's method to set up the equation for the finite motion of the system described in Problem 10.39 for a thin hoop whose mass m is the same as that of the thin rod. (a) Find the first integral of the equation of motion. (b) Derive an equation from which the exact period of the finite rocking oscillation is determ ined. (c) What is the circular frequency of small amplitude oscillat ions? (d) What is the length of a simple pendulum having the same small amplitude frequency as that of this system? 11.26. A smooth rigid rod shown in the figure for Problem 6.56 is attached to a table T that rotates in the horizontal plane about a smooth bearing at F . The table has mass M , radiu s of gyration K about F , and its variable angular speed due to an applied driving torque I1F(t) = I1F(t)k about F is wet ) = e(t ) . The mass of the rod is negligible. A slider block of mass m, supported symmetrically by identical springs of stiffness k, is released from rest relative to the rod at a distance a from the unstretched state at O . (a) Derive the equations of motion for the system (i) by use of Lagrange 's equation s, and (ii) by use of the Newton-Euler laws. (b) Find the torque I1F(t) required to sustain a stable motion of the system with a constant angular speed. 11.27. Apply Lagrange's method to derive the equations of motion for the system described in Problem 8.30. Solve these for the given initial conditions, and determine the small amplitude vertical and rotational frequencies of the motion . 11.28. Use Lagrange's equations to solve Problem 8.18. 11.29. Two uniform rigid rods, each of mass m and length 2\u00a3, are connected end-to-end by a smooth hinge and placed in a straight line along the y-axis on a smooth horizontal table in the xy-plane . The end of one rod is struck suddenly by a force P = Pi. Find the subsequent instantaneous generali zed velocit ies of the system. What is the increase of the total energy of the system due to the impulse ? Introduction to AdvancedDynamics 565 11.30. Consider the systemdescribed in Problem6.57, but nowsuppose that the rigid rod is homogeneous with mass M. (i) Determine by integration the moment of inertia of the rod about the point O. (ii) LetBdenote the small angularplacementfrom thehorizontalequilibrium position. Derive the equations of motion and find the vibrational frequency of the system by use of (a) Euler's equations, (b) the energymethod, and (c) Lagrange's equations.Which is the simplest, most direct method?(iii) Determinethe dynamicpart of the support reaction force as a functionof B for the case b = 2a.Does this dependon mass? 11.31. A pendulumdevice consists of a thin rod of mass m and lengthesupported in the vertical plane by a smooth hinge H attached at the rim of a thin circular disk of radius Rand massM .The disk turns in the verticalplanewith a steadyangularspeed to about a smoothfixed axle at its center. Use Lagrange's methodto derive the equationsof motion. 11.32. Formulate Lagrange's equations for small vibrations of the system described in Problem 10.56. 11.33. DeriveLagrange's equationsfor small amplitudeoscillationsof the systemin Problem 10.57. 11.34. Applythe theoryof smallvibrationsto derivetheequationsofmotionfor thependula shown in the figure, and solve these for the angular motions Bj(t) and B2(t) . Determine the eigenfrequencies, find the normal mode motions, and characterize these physically when the pendula are appropriately displacedand released from rest initially. Problem 11.34. 11.35. (a)DeriveLagrange's equationsof motionfor the finiteamplitudeoscillationsofthe double pendulumdescribed in Problem8.32. Deducefrom these results the equations for small amplitudeoscillations. (b) Apply the theory of small vibrationsto derive the latter equationsof motion. 11.36. (a) Derive the equation for the finite amplitudemotion of the system described in Problem 8.33. Then linearize the result to obtain the equation for small amplitudeoscillations. (b) Apply the theoryof small vibrationsto derive the equationof motion. 11.37. Suppose that the system of pendula in Problem 11.34moves in a Stokes medium, whichmight be the surroundingair for example.Find the Rayleighdissipation function for the system of particles, and derive the equations for its small oscillations. Show that when k =0, the coupled equations of motion reduce to those for the small damped oscillations of simple pendula. AppendixC Internal Potential Energy of a System ofParticles The internal potential energy of a particle P j due to the mutual internal force b j k exerted on P j by Pk is defined by {Jjk = 1fr(Xj, Xk), a scalar-valued function that depends only on the positions of both particles. By application of the principle of material frame indifference in Section 8.9.2, page 325, it is shown that for a conservative internal force , the mutual internal potential energy 1fr(xi - Xk) for an arbitrary pair of interacting particles is a function of only the distance between the particles, namely, 1fr(Xj , Xk) = 1fr(lrj k I), where r j k == Xj - Xk is the vector joining the two particles. This led to (8.75), namely, {Jjk = 1fr(lrj k I).This important result, however, may be derived without use of frame indifference.Rather, it can be shown* that, given the third law (8.3), 1fr(xi - Xk) is a function ofonly the distance between the particles, if and only if the mutual internal forces act along their common line. We first show that {Jjk = 1fr(xi- xd is a function of only the vector r j k == Xj - Xk joining the two particles . To see this, fix j and k =1= i . and introduce the two vectors (C.I) With (C. I) in mind, introducing 1fr(Xj , Xk) = If(u, r) and noting that for any vector v, avlav = 1, the identity tensor, we find alf alf au alf ar alf alf alf alf -=---+---=-1+-1=-+- (C.2) a Xj au aXj ar aXj au ar au ar ' alf alf au alf ar alf alf alf alf - = -- + -- = -1- -1 = - - - . (C.3) a Xk au aXk ar aXk au ar au ar * Thedevelopmenthere is similarto thatduetoG.M.Kapoulitsas,Thebehaviorof theinternalpotential energy of a system of particles in a noninertial frame, Ingenieur-Archiv 57, 393-9 (1987), wherein it is also shown that the result holds in all reference frames, inertial or not. 567 568 Appendix C From Newton 's third law (S.3) for fixed j and k =1= j, and with the aid of (S.73) and f3kj = 1jJ (Xb Xj ) = 'if; (u , -r), it can be shown that af3j k af3kj = = aXj aXk (C.4) Therefore, it follows from (e.2) and (C.3) that a'if; / au = 0, that is, 'if; = 'if;(r) is independent of u. Consequently, by the second relation in (C;l ), we have (e. S) ExerciseC.l. (a) Introduce the Cartesian components up = xt + x;, rp =xt -x; of the vectors u and r , and show that V j(up,rp) = (ip , ip ) and Vk(u p, rp) = (i p , -ip ) . Now consider 1jJ (Xj, Xk) = 'if;(up, rp), recall (S.73 ), and thus derive (C.2) and (C.3) in vector notation, wherein a/au == L~=l( a/aup)ip, for example. (b) Derive (e.4) as described above. D We next show that the dependence in (C .S) is reflected onl y in the distance Ir jk Ibetween the particles. The result follows from the assumption that the internal forces act along their mutual line so that the internal force exerted on Pj by Pk may be written as b == bj k = - Ibj k[e., where e, is the unit vector directed from Pk toward Pj .Recall (S.73) so that b = - V j 'if;(rjk) in accordance with (e. S).The reader will find that in spherical coordinates, the gradient operator (7.48) may be written as a 1 a 1 a V = er ar + eo-; ae + e\u00a2r sin ea\u00a2, (C.6) in which the spherical basis vectors (e. , eo' e\u00a2) may be referred to a Cartesian frame <I> = {F;Id in Fig . 4.21, page 277 of Volume 1. Because b is assumed parallel to er(e,\u00a2 ) in <1> , it follows from (Cxi) that a'if; /ae = a'if; /a\u00a2 = 0, and hence 'if; (r j k) = 1jJ(r) depends on r alone , where (e.7) Thus, in our original notation, the mutual internal potential energy for an arbitrary pair of interacting particles may be written as (e.S) Conversely, it follows from (C.S) that the mutual force (S.73) is directed along the line connecting the particles. See Exercise S.S, page 325. Because the results use only the position vectors of the particles and ultimately only the vector connecting them, the result doe s not depend on use of any particular reference frame, inertial or not. The result (CS) is the same as (S.7S). The important difference in comparison with the frame indifference point of view discussed in Chapter 5, however, is that Internal Potential Energy of a System of Particles 569 here it is assumed that (i) the internal forces act along their mutual line and (ii) these satisfy Newton 's third law. These assumptions follow as theorems in Noll's proof in Chapter 5. Exe rcise C.2. Derive the gradient operator (C.6) for spherical coordinates. o AppendixD Properties ofHomogeneous Rigid Bodies D.I. Nomenclature The following representative nomenclature of symbols is used in the table of properties of various homogeneous simple rigid bodies provided in Section D.3: q; = {O ; ik } : body reference frame at 0 q;* = {C; iZ} : body reference frame at the center of mass V : material volume of the body A : surface area of a thin-walled body e:length measure of a lineal body m : total mass of the body x* : position vector of the center of mass C from point 0 in q; 10 : moment of inertia tensor relative to point 0 in q; Ie : moment of inertia tensor relative to C in q;* i jk == i j 0 ik : tensor product basis associated with q; ijk == i j 0 iZ: tensor product basis associated with q;* . It is expected, of course, that the reader will adjust to the use of diverse but similar notation for various corresponding entitie s encountered throughout the text, such as M for mass , lj;{Q;ek} for a body or fixed reference frame at the point Q at which the moment of inertia tensor is IQ = Irsers, e., == e, 0 e, for the tensor product basi s, and many other parallel notational variations. D.2. A Wordof Caution In a great many other dynamics texts , the products of inertia, as emphasized in (9.16), are defined as the negatives of those used in this book . Therefore, the reader 571 572 AppendixD must exercise caution when consulting other sources for special formulae, tables of properties, or supplementary reading. The moment of inertia tensor components defined in (9.14) and (9.15) are used throughout the text and in the table below. In every case illustrated in the table, however, both <p and <p* are principal frames of reference with respect to which the products of inertia vanish . This generally will not be the case for an arbitrary frame orientation or for a shift of origin point of either reference frame . D.3. Tableof Properties Center of mass, volume/area, moment Body of inertia Figure D.l. Rectangular solid/cube. .L Figure D.2. Right rectangular pyramid. 1 h Rectangular parallelepiped V = Euih, I = ~[(w2 + h2)i* + W+ \u00a32)i*e 12 II 22 + (\u00a32+ 11/)i33]. Cube: \u00a3 = w = h = a V =aJ , m Ie = 6a21. I V = v\": 10 = ;[(b2 + 2h2)ill + (a2 + 2h2)h 2 +(a2 + b2 )i33 ]\u2022 Properties of Homogeneous Rigid Bodies 573 v = nabt , 574 Table D.3. (continued) Body Figure D.6. Solid right cylinder. Appendix D Center of mass. volume/area . moment of inertia Ellipt ical cylinder , e, x = 2 13. 1 m [ (b2 e 2 ) ., ( 2 e 2 ) \"e = \"4 + 3\" I II + a + 3\" 122 +(a2 +b2)ij3] ' Circular cylinder: a =b = R , e. V R2ex = 2 13 . = n . m ( 2 e2 ) . , \" mR2 . ,Ie =\"4 R + 3\" (I II + 122) + - 2-133' Properties of Homogeneous RigidBodies 575 576 Table 0.3. (continued) Body AppcndixD Center of mass, volume/area , moment of inertia 1 m [ b2 2 \u2022 ( 2 2)'o = 5 ( +C )111+ a +c 122 +(a2 +b2)b J]. Hemisphere : a = b = c = R \u2022 3R . 2 1 X =glJ , V = \"31rR-, Semiellipsoid \u2022 3c. x = 813 , 2 V = \"31rabc , Answers to Selected Problems Chapter 5 5.1. (a) IOx*(tl,O) = 8i - 6j + 17k m, (b) p(tl , 0) = 7i - 6j - 16k kg -m/sec. 5.3. de = a/2 . 5.5. x*(9i3) = ~hk from the apex, M = lrpr2h /3 . 5.7. p(9i3, 2) = 3600i gm ern/sec, hA(99, 2) = 43, 200k gm-cm2tsec. 5.9. ho = m[w(e2 + a2) - ev]k. 5.11. hF = 30i+ 23j - 6k kg 'm2tsec, ho = -2(4i + 16j+ k) kg 'm2tsec. 5.13. w = 2Wa/(a + g). 5.15. F = -2/.LGM /lrb 2i. 2GMX (I I)5.17. g(X) = --2--2 - k. R2-R1 J X2+ Rf J X2 + Ri 5.21. g(Q) = mG2 k hemispherical shell, g(Q) = 0 closed spherical shell. 2R 5.23. F(Rt> = _ mMG log [(C+ b)(a + J (c - w+ a2)] j. 2ab (c - b)(a + J (c+W + a2) 5.25. gm = 5.18 ft/sec? = 1.58 m/sec- ; Wm = 0.161We \"\"We/6 . ( 2+ /.Ltan8) vW25.27. (a) P =/.LW1 , (b)T= . ' I + /.L tan 8 cos 8 + v sm 8 5.31. (a) W* = 60j Ib;W* = 260j lb; a = 32j It/sec\", 5.33. F = 0.3gi - 150J3w2j + 1.5J3wk N. 5.35. (b) yes, (c) Any pair of the planes x - 9y - 4 = 0, 2y - z+ I = 0, 2x - 9z+ I = 0, (e) Xo= ~(-3i - 29j+ 28k) m. Chapter 6 6.1. T = 12i+ 16jN, N = -16j N, f= -4i N. 6.3. (b) FA=0.02IN, FB =0.352JN. 6.5. v = J 2gd(/.L cos 8 - sin 8) . 6.7. w = J /.Lg / r . 6.9. N = 76J2n Ib, T = -8i lb. 577 578 Answers to Selected Problems 6.11. (a) N = 7n lb, T = 2J2j Ib, (b) N = IOn Ib, T = 5(t - n) Ib, f = -3t lb. 6.13. N = 3.56 X 10-5 N. 6.15. Fe = -34i-36j +47k lb. 6.17. (b) s(3) = 50 ft/sec, (c) x*(5) = 118.5i+ 216j ft. 6.19. T=Wsec,B . 6.21. (a) Emax = Wd fqh , (b) eE = 12i, (c) y = ax, a == g cos el (eE - g sin e). 6.23. S = vol k. 6.25. x(2) = -4.54i - 0.76j +49.87k ft, v(2) = 3.46i - 0.49j +44.05k ft/sec. 6.27. (a) v(h) = vooVI - e- 2vh , (b) vet) = Voo tanhtrZr ), with v, T constant. 6.33. XC?, t) == x - gl p2 = Xmax cos(pt - 4\u00bb , X(Q , t) == x + gl p2 = Xmin cosh(pt + 1Jr), _~22 '\" _ q . X _~22 h,1< _ q _ VoXmax - o+q ,tan'l'--' min- o-q , tan 'I' --, q=- . Xo Xo P 6.35. (a) a = gin , (c) x(t) = g2 (cos pt - I) , (e) all are equivalent. p 6.37. u = (ffi13)cos(pt + 4\u00bb with tan 4> = i \u00b7 6.39. XA = 1.25 em, f = 14/Jr Hz. 6.41. (a) k = 24 N/cm, (b) T = 2Jrj7 sec, (c) x(2) = 0.684 em. 6.43. (a) T = 2JrVm l(k1 +k2), (c) X = XA cos(pt - 4\u00bb, tan4> = -volxop. 6.45. (b)p = JAElw2, (c) ke=2JrAElr. 6.47. co = 8Jr rad/sec, T = 0.128Jr2n N at ,Bo . 6.49. (a) R = mw2(2vx2 - a2 - h), (b) xeS, t) = a cosh cot i. 6.51. (a) Rod reaction force components and the motion xes, t) (b) xes , t) = A(cosh(w+Q)t - cos ox) , A == aQ2/(w2+ (w+Q)2). 6.53. (a) Stable forw < vklm , (b) k* = k - mw2. 6.55. (a) rs = -g sina/( ~ - w2cos?a) ; (b) ret) = vot - ~gt2 sino for the case m kim = w2 cos2a; (c) rs < 0 stable, rs ~ 0 unstable . a 6.57. f = -vkl m. Tnb 2k (b)26.59. The motion is simple harmonic with frequency f = - ~ + - - . 2Jr a m a rq2 w 6.61. (b) e(t) = eocos pt + e(l _ q2) (sinwt - q sin pt), q == p. 6.65. W\u00ab kglw 2 = 9.79 lb. 6.67. Resonant frequency : Q* = Q l /2= 600 rpm. 6.69. (a)(fJ+2v<iJ + p2 sin4> = (Folmr)cos4>sinQt with 2v = elm, p2 = str. (b) T = (2J21p) ft'(cos 4> - cos4>0)-1/2d4>, T = 2Jr..ji]g . 6.71. R = -2aQpsinAsinpti - (g + 2aQpcosA sin pt)k. 6.75. x - w2x - 2wy = -2Q[zsinwtcos A- (y +wx) sinAJ, y - w2y+2wx = -2Q[z coswt COSA + (x - wy) sin A] , z= -g +2Q cos A[(Y+wx)coswt + (x - wy) sinwt]. Chapter 7 7.3. 7.5. (a) dv 2 +2vv2 = -2gr(sin4> + v cos 4\u00bb, (d) .iT= (m +M)v2vgr4>0i. d4> ab (a) (i) 11/= 19/6 , (iii) 11/= 10/3 , No, (b) 11/= 55 (lOb2 + 33). Answers to Selected Problems 7.7. (b) 11/= 2./2P and (c) Ii = 25/4J PIm are solutions for the line. 7.9. (a) f!>. {lJ = 2(e4t - I) , (b) x =~ue2t , a straight line. 7.11. 0 = 7.5 em. 7.13. (a) Pi\" = mv(g - vv), (b) 1//= ~mv~(l - e- vt)2. ( g Ik) (g 9k)7.15. vB=L 2 -+-- , vc=L 2 -+-- . L 4m L 32 m 7.17. (3= (I + ~) J2gd(sina + vcosa)i. 7.19. (a) 11/= 0, (b) No. 7.21. V(x) = Vo - tan\"! (~) with r f. O. 7.23. V(x) = Vo+ 5zcosx - y(x + Zyz), 11/=12. t: 7.25. COS02 = -- COSOI , 01 > O2\u2022t: - tl 7.27. n = wL /(L - R). 7.29. v = 8./3 ft/sec. 7.31. Vo = 25,145 mph. 733 .. Vo~ \u2022\u2022 Xm = --Vvo - vI\u00b7 01 7.35. (a) d = 7.5 in, (b) r = 0.71 sec. y mw2 7.37. (a) V*(y) = Vo - mgy + mw2[(1 - 4k2A2)2k + 2y2], (b) N(y) = \"2kJI + 4ky . 7.39. (a) N = 216n N, (b) vQ = 3 m1sec, (c) h = 25/16 m. 7.41. (a) Vc = 8.26 ft/sec, (b) n lw = 3. 7.43. 0 = 40.4 cm. 7.45. (b) Xs = ~ ft, p = 8 rad/sec, (c) XA = ~ ft. n 7.47. (a) d = 6r , (b) N( 2\") = 7W. .. 2 5mg 4 7.49. (a) z + p z = g, z, = 4k' (b) k, = sk, (d) one degree offreedom. 7.51. curlT = - ~W sin Ok f. 0 everywhere. M (gD2 )1/27.53. (b) a = {3 - - - + 2vgd , (VO)max = J2vgd . m 2H _ t _ I t/J dt/J t _ k 7.57. (a) v - J4g(i , (b) - - - fo J ' a > I, - - -K(k). ~ ~a I_~~t/J ~ ~ 7.59. (a) r\" = 2.36 sec, (b) t = 0.281 sec. 7.61. (i) p=~, (ii) p =.;ag. 7.63. f = 0.073J81(i at \u00a2o = 1.564rr rad, f = 0.033J81(i at \u00a2o = 7.5lh rad. 7.65. s = is!n2) sin y, a cycloid. 7.67. (a) y = a, (b) s = 2a./2. 7.69. L = 2.622a. Chapter 8 8.1. (b) p* = 16i - lOj +5kkg \u00b7m1sec, (c) hF = 19i + 8j - 48k kg\u00b7m2/sec, (d) ho = -6i - 30j - 44k kg -m2/sec. 8.3. st. = en. 579 580 Answers to Selected Problems VB m A8.5. (a) - = - cosB(tanB - tan</i) . VA m B 8.7. (a) Q = w/4, (b) unchanged. a2 + b2 a - b 8.9. v = 2(a2+ ab + b2)VO, W = 2(a2+ ab + b2)vok. m21 \u2022 ( , m21 )8.11. (a)x'(t)=---I+ -2gt2+---wot j,B(t)=wot , m,+m2 m,+m2 m,m212 (b) he = ---wok, ho = m21(-gt + lwo)k m, +m2 \u2022 I F 2 . ' ~8.13. x (I) = 4m t + xo' </i =V-;;;[ sm</i . 8.15. (a) A(t)= B(t)+4mg = -!.... (cos (~t2) i + sin (~t2) k) for t ::: 2 sec,2 8mr 8mr F (c)w(2)=-. 2mr 8.17. A = 805k lb, B = -400j-773k lb. 8.19. (a) 5m\u00a32(j + 4kB - 2mg\u00a3 sinB = 0, (b) B(t) = Bo cos pt , (c) Stability of equilibrium states Be requires k - kc cosBe > O. In particular, Be = 0 is stable fork > k, == m~\u00a3 . Other stableequilibriumstates exist.Considerthe case k] kc = 2/Jr, for example. m2 m, I m,m2 28.21. v, = ----v, v2 = ---v, K = ----v . . m, +m2 m, +m2 2m, +m2 8.23. K = mg2t2+ mw2d2sin2 t/> . 8.25. (a) p' = -80i+ 2k kg\u00b7 m/sec, (b) Ke = 229N \u00b7m, (c) K = 1830N \u00b7m, (d) ho = 4i80j + 175k kg \u00b7 m2/sec, (e) hro = -80j + 175k kg \u00b7 m2/sec, (g) hre = 15k kg \u00b7 m2/sec. 8.27. omax = 1.5 ft,.q; = 201.5j slug\u00b7 ft/sec. 8.29. (a) Stability of Be = 4mg/ k\u00a3 requires 1 - 2Be/5 > 0, (b) B(t) = Bo cos pt . 8.31. m I XI + (k l + k2)XI - k2X2 = mig, m2x2+ k2X2 - k2XI = m-g , 8.33. (c) !(M\u00a32 + 4mr2)4>2+ Mg\u00a3(cost/>o - cos t/\u00bb + mgr(cos 2t/>0 - cos 2t/\u00bb = 0, 1 Mge +4mgr (d) f = 2Jr Me2+ 4mr2 . J 2PbB 4gb Jgb8.35. (a) v(B) = -- + -(B + cosB - I), (c) v(B) = 2 -(B + cosB - I). M it it V \u2022 \u2022 9 28.37. (a) v\u00b7 = 4(21+ J + 3k), (b)!'>.K = -4mv . m V M-m v T (M_m)28.39. (a)w=---k,(b)w=----k,-= -- M+mr M+mr ~ M+m Chapter 9 9.3. 9.5. 9.7. See AppendixD for solutions. \u2022 2 sinBR~+RoRi+Rl.x=--- I\" 3 B Ro + R, m 2 2 sin2B . sin2B . . mL2 \u2022 \u2022 10 = \"4(Ro + Rj)[(1 - 2B)11' + (I + 2B)122 + 21331 + 12(111 + 122)' See AppendixD. Answers to Selected Problems 581 9.9. See Appendix D. 9.11. See Appendix D. 9.13. m (~ ) = 12.78 slug, Rz = 1.42 ft. 9.15. See Appendix D. 9.17. See Appendix D. 3m 3mr2 3mr2(r2+ 6h2) 9.19. I - _(r 2 + 4h2 )(i + i )+ - - i [ Q - ----=-::-:-'-;;--~....:..Q - 20 11 21 10 33, nn - 20(r2+ h2) I mR 2 [5\" st 7\" ~(\" ' / )] ' ,f,9.21. C = -4- 4111 + In + 4133+ 4 113 + 131 III v - 9.23. The centroid of the plane triangle at (1,1,1). y z - 12 9.25. x = - = - - . 6 -20 9.27. Nearest point is at (1/2 ,1 /2 ,0); and dmin = -/6/6. 9.29. Vma, = 9 at (I , -2,2); 7//= - 8 units. 9.31. Al = 5 ~ el = ~(e l - e2); A2 = -3 ~ e2 = .;;(e, + e2); A3 = I ~ e3 = e3. No, T cannot be a moment of inertia tensor, A2 < O. ma2 9.33. (a) 10 = 6 [8ill + 2h2+ lOi33 - 3(i12+ hd1. ma2 \u2022 \u2022 (c) 10 = 6 [(5+ 3./2)ell + (5 - 3./2)en + lOe331 \u00b7 9.35. (a)?X2+ 592+ 222 = I, (b) Possible plane body ellipsoid. 9.37. (a)Al = A - B ~ e l = ';; (11+ 12); A2 = A + B ; A3 = 2A ~ e3 = 13; m (c) I Q = 12 [(a 2 + b2)ell + (7a 2 + b2) en + 2(4a2 + b2)e331. 9.39. (b) IQ = a [2ell + lOe22+ 8e33 - 3(e13 + e31)], a = ~ma2 , (c) AI = a(5 + 3./2), A2 = lOa , A3 = a(5 - 3./2). 1/2 3 M I9.41. T = 2: (ell + e22)+ v 3e33 - 2: (e12 + e21)' tr:\u00bb, (A+B. (zif. 9.43. (a) GQ = V-----;;;-- ell +V-----;;;-- en +V-;;e33. Chapter 10 10.3. F = - 920i N with v = vi. 10.5. hA = 1mR2w]i+mWz( ~R2 +d2)j ,MB = -1mR2wlw2k . W P W P 1f .1f 10.7. (a) A = ( - + - )j , B = ( - - -)j , (b) P =-Wi,x = - gt2i. 2 n 2 tt 2 4 dW dW 10.9. h - - < H < h + - .P - - P 10.11. (a) f = ~ rI,(b) 8 = 80 cos pt , (c) Show that Jl = 21fmhe2f 2[a\". 1feY; 10.13. RH = {i2 ft, T = 21f fITsec.'13 v3i 582 Answers to Selected Problems I {Wi irr 10.15. (a) 1 = 2rrY?e ' (c) Ro = 3'1 z\u00b7 10.17. A = - 19, 839k Ib, B = - 64, OOOj + 20, 161k lb. 10 19 M I Z Z \u2022 2 N Me. . e = gmr W SID ex, =U . jdZ+ RZ RZ10.21. (a) r = 2rr e, (b) d = Re , (c) b = .-S.- . gd d 3../2 * F*10.23 . w=-F*k , v = -. 2ma m 10.25. n = w /7 . bZ/ Aw aWA 10.29. WA = Z Z , WB=-. b /A+ a /B b ND 2 1 ND10.33. - - < - < 2 Ns 1+ 3 sinzex ' 2 Ns . W sinex 3g sin2ex 10.35. T = 1+ 3cosz ex (cos a i - sin a j) ,W = e .1+ 3 cosza k. 10.37. NI = W(- ~ + cos e + Y; sine )(-i + J3j), Nz = W(~ - cos e + Y; sin e)(i + J3j,) referred to a body frame at C. mi mi 10.39. (a) N = W + Z(wsin e +wZcos e ), 1 = Z[w(2 - cos e )+wZsine], 6 . ~ ~w= - ml [N sID e + 1 (2 - cos e )], (b) Wo = - 8i = - \"4' (d) e = eo cos pt . pZ 2M 10041. XI + p f (5xI - xz) = 0, XZ + pi (x z - XI) = 0, -i = - . pz 3m .. Z Z 2g I ( eo ) 2r10043. (a)e + p sin e = O, p =3h (b)e = 2 sin- sinzsnpt ,r* =-;- K (k ), (c) N = tmg (7 cos e - 4cos eo) , 1 = tmg sine. 10 47 () dur i I\u00b7 ' * 2vg. . a urlDg s IpplDg: v = vg t ,W = - - t + WO , r 2rwz (b) VD = 3vg t - rwo (c) e(r) = _ _0 . . 9vg 10.49\u00b71 = 2~ : i Z (ka Z + ~ Wi). 10.51. r = 2rrJ7i . 109 M J2(m + M )gi10.53. f3 = (I + - )i ( I - cos eo) . m /0 \u00b7z _ 3g cose-coseo _ 4 rOo 4- 3 cos e . z _ 10.55. o -e \u00b7 4- 3 cos e , r - -;; )O 2(cose -coseo)de ,p = 3g12\u00a3\u00b7 mi z \u00b7z \u00b7 \u00b7 \u00b7z m i Z[ (k 3g) Z g z]10.57 . K = 6 (4e l + 3elez + ez ), v = 4 ;;; + e e1 + eez . I~ 10.59. e(t) = Acospt + B sin p t , p = 4'1 b +;;. Answers to Selected Problems 583 10.61. 10.63. 10.65. 10.67. ~ I'd '(a) Wtube = V~' (b) so 1 wins. .. 3c . 3k wo I J3k 3c2(a) e + -e + -e = 0, (b) e(t) = _e-vt sinwdt , 1=- -(1- -), m 4m Wd 271\" 4m k (c) r = 271\" f\u00a5i. .. . . 2c (a) e + f3e = 0, (b) the nonviscous forces are workless, K + - K = 0, (J (c) N = W, 1= awoe-fJt(271\"ca - mf3). r r 2T Wo (a) w(t) = fi+ (wo - fi)e- fJt, r == mR2 ' (b) e = eo+ -;g(l - e- fJ1). Chapter 11 ILL 11.3. ll .5. 11.7. 11.9. 11.11. 11.13. 11.15. 11.17. 11.19. 11.21. 11.23. 11.25. 11.27. Constraint is holonomic with z = sirr' y + e2x - e' sin y . 2 2.. Yt/J cosf g . _'2 Yt/J 2g _ ._ e-~-3-+-Sllle-o, e + 2 --cose-Eo,Yt/J-constant. m e sin e e m2e4 sin e e d [( r 2)] ri . r ( r 2) - mi 1+4- -4m--mre2+2mg-=-cf 1+4- , dt a2 a2 a a2 ~ (mr 2ti )= - cr 2ti . dt Three familiar type solutions evolve from, + (~ - w2 cos?a ) r = - g sin a . (a)i + (2~ -W2)X = 0,(c) R = mp2 (r \u00b12:0 Ja2 -X2) . ~2 r' (l + (r l)2)z + r'r \"z2 - ~ 3\" + g = 0, Ye = constant. m r (m, + m2)' - mlr<b2 + m-ig = 0, mlr2<b = h , constant. .. 2 2 ke+pe=o,p =3- . m .. 8k 2g .. 8k 2g I /lfke+ -e = - , or z+-z = - ;1= - - . One degree of freedom. ~ ~ ~ 3 71\" ~ .. 2 ' f2ie+ p sille = 0, p = V3ft . .. 2 2 g . 2 2 (a) e + p sine = 0, p = -, (b) e -2p cos e = e, constant, r J3 mr J3 mr (d) Ni = mg(2cose + 6\" sine) + T e, N2 = mg(2cose - 6\" sine) + T e. 2 2mga sine (a) W = ( ) 'Ic+m a2+R2-2aRsine (c) I = m[w(R - asine) -aw2cosej, N = W +m(-wacose +aw2 sine). fJi l eo 10 - 3 cos eo 14 (b) r = 4 - de , (d) L = -l. 3g 0 cose-coseo 3Iffx = xe(l - cos Pxt) , e= eocos Pet, I, = 21e = - - . 271\" m 584 Answers to Selected Problems P . 3P . 9P 7p2 11.29. i = - -,.5' = 0, 01 = --,02 = - ; !:IT = - . m 4ml 4m l 4m .. 3R 2 3g 11.31. \u00a2 -ew sin(wt -\u00a2)+2lsin\u00a2 =0. .. .. (k 3g ) .. .. 3g11.33. 801+ 302+ 3 - + - 01 = 0, 301+ 202+ - 02 = O. m l l 11.35. (a) 2ml 2(fi +ml 2(j cos(O - \u00a2) - ml 2e2sin(O - \u00a2) + 2mg l sin\u00a2 = 0, ml 2(j +ml 2(fi cos(O - \u00a2 ) +ml 2rb2sin(O - \u00a2) +mgt.sin0 = 0, (b) 2(fi + (j + 2: \u00a2 = 0, (j + (fi + fo =O. 11.37. D = ~cl 2 (e~ +\u00ab\u00bb Index Abrams, J.I., 86, 198,396,480 ,555 ,560 Accelerationof gravity, 46, 77 apparent for Earth, 75--6 Action integral, 527, seeHamilton's principle conservative system, 528-9 nonconservativesystem, 531-2, 534 Aczel, A.D., 182, 196 Amontons,G., 51, 83 AnalyticalMechanics, Lagrange, 560 Angularmomentum, seeMoment of momentum Arago, E, 182-3, 196 Astronomical frame, see Inertial frame Axiomof continuity of matter, 408 Axis of symmetry, axisymmetric body, cross section, 362 Balanceof a rotor, 438-9 Bartlett, A.A., 64, 83 Beatty, M.E, 88,1 96,477-8,480 Bell, J.E, 132 Berlinski, D., 83 Billiardball motion, 456--60 Binet, M., 183, 196 Biot, M.A., seeHubbertand Rubey, 84 Bixby, VV.,4, 83,405 Blanco, V.M., 284, 342 Body of revolution, 363 Boissonnade, A., 560 Bona, J.L., seeBeatty, 196 Boulanger, Ph., 403 Boundedconstraints, 497-8 Bowden, EP., 52, 83 Bowen, R.M., 396 Brahe, T., 278 Buck, R.C., 396 Burton, R., 196 Byrd, P.E, 266, 297 Cajori, E, 83, 284, 340, 342 Carroll,M.M., 478 Catenary, 131 Cauchy's inertia ellipsoid, 387-90 Center of force, 18 Centerof gravity, 48, 50 Center of mass, see AppendixD body, II homogeneous bodies, various, 571--6 rigid body, 355 center of mass particle,object, 9, II particlemoments of inertia, 372 composite body, 356-7 Lagrange's lemma, theorem,87-8 momentumand velocity of, 9,14 properties of, 7-8 , 11-12 system of particles, 7 Center of oscillation, 485 Center of percussion, 486 Center of symmetry, 362 Centroid, volume, 12,50 Chandrasekhar, S., 83 Change of reference frame, 79 Clairaut, A., 183,seeDugas, 196 Coefficient of restitution, 340--1 Cohen, H., 479 Composite body, 356 mass, 356 center of mass, 356-7 momentof inertia tensor, 368, 374-5 Conservation laws electriccharge, 105 energy, 253, 257, 324, 328,471 Lagrangian form, 521 scleronomic system, 507 general conservationtheorem, 248-9 generalized momentum, 519-20 585 586 Conservation laws (cont.) instantaneous moment of momentum, 228-9, 311,430 instant aneous momentum, 226, 305, 419 mass, 6, 10, 27 moment of momentum, 250-1 , 311, 430 momentum, linear , 249, 302- 3, 4 19 Conservative Force, see Force Conservative system, 230, 240-6, 324-8, 507, 519-20 Con straints, see Kinematical constraints Continuity of matter , axiom , 408 Cooper, L., III , 196 Coriolis, G.G. de, 183 Coulomb, C , 50 Coulomb's laws friction, 4, 50, 54-5, 83 electrostatic, 82, 104 Couple, 20, 413, 416 Critical damping coefficient, 157 Curl of a vector cylindrical coordinates, 296 rectan gular coordinates, 244 Curve, simple, closed, 240 D'Alembert, J., 495, 559-60 Da Vinci, L., 1,50-1, see Hart . 84, Truesdell , 85 Dafermos, C., see Beatty. 196 Damp ing, drag force, see Force Damping exponent. ratio, 151-3 Dashpot, viscous damper, 151 Degenerate systems, 552 Degree s of freedom, 496, 498 Delta function, 225, see Chapter I, 50 Deresiewicz, H.\u2022 51, 83 Dillon , a.w., 98 Dimen sional units , see Physical dimensions Dissipative systems, Stokes type , 556-7 free fall , III , 510, 557 generalized damping coeffcients, 556 generalized Stoke s force, 556 Lagrange's equations , 556-7 mechanica l power expended, 556 Rayleigh dissipation function, 556 Drag , damping coeffcient, 119, 153,556 Dugas, R., 183, 196,478 Durell . C v; 83 Dynamic viscos ity, 121 Dynamic s, defined , 3 Earth apparent acceleration of gravit y, 75-7 average radiu s, mass density, 45-6. 74, 76-7 Index Earth frame , seeMotion relative to Earth International ellip soid formula, 77 International gravity formul a. 77 variable rad ius formula , 76-7 Easthope, CE., 196 Einstein, A., 33, 83 relativistic energy, 240 Electric charge. measure unit. 104, 125 Elect ric field strength, 104-5 Electrostatic constant; value, 104 Electro static force; Coulomb 's law, 82, 104 Ellipsoid of inerti a, 387- 90 Elliptic functions, see Jacobi an elliptic functions Elliptic integral first kind , 266, 268, 469, 538, 542 comp lete , 266, 268, 538 series approximation, 270 handbook and tables, 266, 297 second kind, 267, 283 complete, 267, 283 third kind, 267, 542 Energy criterion, stability, 549-50 Equations of motion conservative sys tem, particle s, 328, 527-9 cylindrical reference frame, 96. 504 dissipative systems, Stokes force, 557 Euler 's equations: rigid body, 418, 433-4 Euler's laws. 29. 409 free vibrations, 152-8 forced, driven vibrations, 152, 158-69 general nonline ar force , 169 intrin sic referen ce frame, 96 Lagrang e's equations, 502. 507- 9 Newton 's laws. 24 noncon servative system, 329. 531-2. 534 noninerti al reference frame . 69-71 noninertial Earth frame. 73. 78 rectangular Cartesian frame . 96 relative to Earth , 77-8 . 177-8 relativistic particle. 103 scalar equations, 97 spherical refere nce frame . 97 system of particles. 28, 302. 314 work-energy. 236. 256, 318-21. 329 Equilibrium, 27 body principle of determinism, 412 rigid body, 30, 434-5 relative equilibrium states. 125, 146-7 , 172 infinitesima l stability of, 172-6 ,21 3-14,218. 347,349,447-50,545-7 stability criterion , 175,549-50 vibrations about, 152- 8 Index Equilibrium (cont.) relative to Earth, 74-5 relative to a moving frame, 70-1 system of particles, 31 Equipollent force systems, 18 center of force, 18 distributed over a lineal body, 474-5 equipollent to zero, 20, 30, 434 frictional, normal, tangential, 51-3 gravitational, 42, 47 workless, 475 Ericksen, J.L., seeBeatty, 196 Espinasse, M., 132 Euler, L., 4, 405-6 , 414, 495, 559, seeTruesdell, 85,479,561 Euler angles, 539 Euler's equations: rigid body, 418, 433-4 Euler's identity, 123 Euler's laws, 4, 405-9, 412-1 4, seeTruesdell, 85, 479,561 first law, 29, 406, 409 first law, center of mass, 414, 418 second law, 29,406, 409, 430 arbitrary moving point, 426--8 first form, 426--7 second form, 427-8 relative to center of mass, 427-8, 430 referred to a moving frame, 428, 433 rigid body, 418 classical vector form, 433 referred to principal body frame, 434 special moving reference points, 430 Falkland Islands, battle, 192- 5, 197-8 Fernandez-Chapou, J.L., 284 Fernie, J.D., 33, 83-4 Flory, P.1 ., 88 Force apparent force, weight, 70, 77 average value, 222 body force, 4, 25 central force, 251 centrifugal force, 70 components of, 96--7 conservative force, 230, 240-6 , 507 criterion for, 244 theorem on, 242 constant force, 110 contact force, 4, 25, 51-3 Coriolis force, 70, 78, 177-89 damping force, lSI disturbing, driving force, 152, 158 Force (cont.) drag, Stokes type, 119, 152,473,556 drag, viscous friction, 55, 151- 2 electromagnetic, Lorentz force, 106 electrostatic, electric force, 82, 104-5 external force, 25, 30I frictional force, 52-4 generalized force, 502, 504, 507, 509 generalized Stokes force, 556 gravitational force, 34-8, 76--7, 81-2 impulsive force, 221-5, 305, 419 inertial force, 70, 519 internal force, 25, 301 Lagrange forces, 519 magnetic force, 105 nonconservative force, 230, 255- 7, 509 nonlinear force, 169 normal force, 51- 2, 54 pseudoforces, 70, 519 shear force, 51 spring force, 133 time varying force, 109-10 velocity dependent force, 118- 20, 122 weight, 45, 77 Foucault, L., 181-4, 196--8, seePendulum Fox, E.A., 478 Frame indifference, 79,85, 104,213,567,569 objective transformation, seeChapter 4 principle of, 5, 80-5 Frank, P., 84 Free body, diagram, 31, 55-6 , 58 French, A.P., see Reich, 197 Friction, see Coulomb's laws Amontons' discovery, 51 coeffcients of, static, dynamic, 54 da Vinci's law, 50-I ideal smooth surface, 53 molecular theories, 52, 84 rolling, 55 sliding, 52 static, dynamic, 53-5 viscous, 55 Friedman, M.D., 266, 297 Galileo, 83-4, Ill , 196 Galileo's principle, III General energy principle conservative holonomic system, 508 nonconservative scleronomic system, 522 particle, center of mass object, 256--7 rigid body, 471 system of particles, 328- 9 Generalized coordinates, velocities, 496, 500 587 588 Generalized forces, 502, 504 conservative, 507 force-motion gradient relation, 502, 5 I3 force-velocity relation, 504 nonconservative,509 Stokes force, 556 Goodstein, D., 124, seeMillikan, 197 Gradient operator rectangular coordinates, 24 I spherical coordinates, 568 Gravitational attraction ideal planet, 42-5 Newton's law, 32 particle and body, 36, 38-9 particle and systemof particles, 35 two bodies, 37,40-2 two particles, 32-4 Gravitational constant; value, 33, 46 Gravitational field, 34 apparent strength, 75-6 of a body, 36 of a particle, 34 of a system of particles, 35 Gray, A., 547 Greenwood, D.T., 396, 478, 542, 555, 560 Griffth, B.A., 85, 198, 284, 479, 542, 56 I Gunther, R.T., 132 Gyration tensor, 402 Gyrocompass, 450-3 effect of Earth's rotation undamped, damped motion, 453 Lagrange formulation, 538-9 Gyroscopic moment, 453 Gyroscopic pendulum, 543, 545 Hamilton's principle, 528, 560 conservative system, 528-9 nonconservativesystem, 531-2 Hamilton, WR., 528, 559 Hart, LB., 5 I, 84 Hayes, M.A., 403-4 Heiskanen, WA ., 74, 76, 84 Hertz, H., 3, 84 frequency measure unit, 135 Holonomic constraints, 497-9, 597, 599, 561 Homogeneous bodies, properties, see Appendix D, 571-6 Hooke's law anagram, 132 elasticity, 2I0 invariance,80, 2I3 linear spring, 132 Index Hooke, R., 80, 83, 132 Housner,G.W, 197,342,560 Howarth, D., 192, 196 Hubbert, M.K., 60, 84 Hudson, D.E., 197,342,560 Huygens,c.,277 isochronousclock, 277-8 Hyperbolic functions, defined, 130 properties, graphs, 130-1 Ignorable coordinates, 5 I8-21 Impact, see Impulse, instantaneous; Law of restitution head-on collision, 34I instantaneousmoment of momentum, 228-9, 311,430 loss of kinetic energy, 342 perfectly elastic, inelastic, 34 I types, colliding bodies, 340 Impulse force, 221-2, 305 generalized force, 524 instantaneous, 223--6,305, 4I9,430, 524 work done, 230 torque, instantaneous, 227-8, 3 I 1,430 Impulse-momentumprinciple, 221-2 body, 419 Lagrangian form, 524 systemof particles, 305 Inertia ellipsoid, see Cauchy's inertia ellipsoid Inertia tensor, seeMoment of inertia tensor Inertial frame, 26, 68-7 I Inertial forces, 70, 5 I9 Infinitesimalstability, 172-6 asymptotic stability, 173, 175 equilibrium, energy criterion, 549 motionof top, 545-7 neutral stability, 173, 175 relative equilibrium, 172,449-50 torque-free rotation, 454-5, 490-I Ink jet printer, I16-18 , see Beatty, 196 Integral action, 527, 531 derivativeof (Leibniz's formula), 206 line, path, work, 229 Isochronous pendulum, clock, 272-8 Jacobian elliptic functions, 268-9,456,469, 493, 538,542 derivativesof, 297 properties of, 268-9, 296-7 Jardin, L., 132 Index Kane, T.R., 84, 396 Kaplan, I., seeMillikan, 197 Kapoulitsas, G.M., 567 Karelitz, M.B., 60, see Hubbert and Rubey, 84 Kepler's laws first law, 281 second law, 251- 2 third law, 28 1-2 third law, two body correction, 304 Kepler, J., 278 Kinderlehrer, D., see Beatty, 196 Kinematical constraints differential scleronomic type, integrability, 499 , 56 1 holonomic, 497 rheonomic, 497, 510-12, 536, 538, 548, 562-3 scleronomic, 497, 499, 502, 505-8, 510, 513, 521- 2, 548-9,551 ,556-7 virtual displacements, 502 nonholonomic, nonintegrable, 498-9, 561 Kinematics of a particle, see Chapter 1 Kinematics of rigid body motion, see Chapter 2 Kinetic energy arbitrary body, 460 center of mass, 317, 460 generalized momenta, 519-20, 523~ generalized velocities, 505-6 Lagrangian notation, function, 50 I, 507, 513 particle, 235 quadratic function of generalized velocities, 505, 550 relative to an arbitrary point, 46 1 relative to center of mass, 317, 460-1 relativistic, 240 rigid body, 461-3 referred to principal body axes, 462 relative to arbitrary base point , 46 1 relative to center of mass, 461 scleronomic system, 505 system of particles, 317- 18, 513 of center of mass, 317 relative to center of mass, 317 total for system, 318 total, center of mass relation arbitrary body, 460-1 rigid body, 462 King, w.w.,479 Klein, E , 547 Knowles, J.K ., 171, 197 KrIDge,L.G., 197, 284, 343, 479 Krim, J., 52, 84 589 Lagrange , J.L., 86, 495, 558, 560, see Truesdell, 479, 561 Lagrange forces, 519 Lagrange multiplier method , 379-80, 403, 529 Lagrange' s equations, 495, 500-2, 508-9, 512, 557, 560 conserva tion of energy, 507, 521 conservation of generali zed momenta, 520 conservative holonomic system, 508, 52 1, 527-9 constraints, 496-9, 505- 13, 521- 3, 536-8 dissipative scleronomic systems, Stokes type, 556-7 first fundamental form, 502 first integrals, 517-23 generalized coordinates, 496 , 500, 513 generalized forces, 502-5, 513 generalized impulse-momentum principle, 523~ generali zed momenta, 519- 21 conservative system, 519 nonconservative system, 519 generalized Stokes force, 556 generalized velocities, 500, 513 Hamilton's principle conservative systems, 527-9 nonconservative systems, 53 1-2, 534 ignorable (absentee) coordinates, 518- 521 nonconservative holonomic systems, 509-12, 53 1-3 rule for interchange of derivatives, 501 rule of cancellation of dots, 501 second fundamental form, 509 system of particles, 512-14 theory of small vibrations, 549-51 Lamb, H., 284 Lanczos , c.,529, 559, 560 Lass, H., 245, 284 Law of mutual action, 24, 30-1, 81- 2, 302, 325-6, 414-18 Law of restitution, 339~0 Leibniz's formula, derivative of integral, 206 Lind, N.C., see Truesdell, 86 Lindberg, c, 117 Line integral, seeWork Lineal body, 473, see Rigid body motion Linear momentum, seeMomentum Linear spring, elasticity, see Hooke's law Ling, EE, see Deresiewicz, 83 Long, R.R., 84, 197, 479, 560 Lorentz force, see Force, electromagnetic MacMillan, W.D., 479 Magnetic field strength, 105 590 Marion, J.B., 194, 197,342,542,560 Mass body, 10 composite body, 356-7 conservation, see Conservation laws mass density, 10 particle , 6 reduced, 304 relativistic, 102 rest, invariant, 102 system of particles, 6 Material universe, 25,408 Mathieu's equation , 216 Matrix algebra, elements , see Appendix B Measure units, 86 McCuskey, S.w., 284, 342 McGill , D.1., 479 MecaniqueAnalytique, 495, 560 Mechanical power, 236, 465, 468-9 dissipative scleronomic systems, Stokes type, 556 lineal body, Stokes drag force, 475 rigid body, 465, 467 scleronomic systems , 506 system of particles, 319, 321 translational , rotational , 465-6, 469 Meinesz, FAY., 74, 76,84 Meirovitch , L., 177, 197 Meriam , J.L., 197,284,343,479 Millikan, R.A., 124, 197 oil drop experiment, 123--6, 197 Moment of a vector, 15 point transformation rule, 16 Moment of force, torque, 16, 413 couple , 20 distributed force , 17 equipollent to zero, 20 point transformation rule, 17 system of forces, 16-18, 20 Moment of inertia tensor, 358, see Appendix D about an axis, 360 axisymmetric body, 362, 386-7 Cartesian component form, 358-9 Cartesian transformation law, 376, 451 Cauchy 's inertia ellipsoid , 387-90 center of mass particle, 372 characteristic equation, 383 components for a lamina, 360 composite body, 368, 374-5 constraint equation, 378, 383 extremal values, see principal values geometrical properties , Cauchy's ellipsoid , 387-90 Index Moment of inertia (cont.) gyration tensor, 402 homogeneous bodies , 571-6 annular plate, 366 circular cylinder solid, 366, 574 tube, 366, 573 cube,377,572 rectangular parallelepiped, 364, 572 rectangular plate, 365 sphere , 367, 575 symmetric body, planes, axis of symmetry, 361-3 thin circular disk, 367 thin rod, 365--6, 574 method of Lagrange multipliers , 379-80 normal components, 359-61 parallel axis theorem, 372-3 point transformation rule, 371 principal axes theorem, 384 principal directions (basis) and invariants, 383 principal frame, basis, 378 principal moments of inertia, 384 principal values problem, directions , 375, 378, 382-4 principal vector equation , 383 products of inertia , 359 radius of gyration , 360 scalar components, 358 second moment vector, 396, see Kane, 396 symmetric tensor property, 358 trace of, 359 Moment of momentum about an axis, 250 conservation of, see Conservation laws instantaneous torque-impulse, 228 of a general body, 22 of a particle, 21 of a rigid body, 431-2 of a system of particles, 21-2, 307-10 of center of mass, 309,423 point transformation rule, system, body, 309, 422 referred to a principal body frame, 432 relative to moving point, 307-8, 312, 423-4 relative to center of mass, 307-8, 424 velocity transformation rule, particle, system, body,21 ,309,423-4 Moment of momentum principle, see Euler 's Laws, second law body,409,4l3,427-8,430 moving reference point, 426-8, 430 referred to moving frame, 428 rigid body, 418, 433-4 Index Moment of momentum (cont.) particle , 148 moving reference point, 149 system of particles , 310-14 moving reference point center of mass, 314 first form, 312-13 second form, 313-14 referred to moving frame, 314 Momenta l ellipsoid, 387-90 Momentum conservation of, see Conservati on laws generalized momenta, 519 in an impulse , 222, 224, 305, 419, 524 of a body, rigid body, 10, 14 of a particle , 6 of a system of particles , 6-7 of center of mass (object) rigid body, 14 system of particles, 9 relative to the center of mass rigid body, 14-15 system of particles , 9 relativi stic, 102 Moody, E.A., see Hart, 84 Morison, Adm. S.E., 64, 84 Motion, see Chapter I freefall , 111, with air resistance, 120-2 ,510,557 function of generalized coordinates, 500 particle , 26 Newton 's first law (principle of determini sm), 24, 408,411-12 plane motion with resistance , 122-3 relativistic, 102-3, 105-6, 112 simple harmonic , 134 uniform , 10, 26, 408, 411-1 2 Motion of a top, 539-47 apparent potential energy, 541 equations of motion, 539-41 Euler angles, 539-40 geometric al, physical descriptio ns, 542-4 Lagrangian formulation, 539-41 nutation , 543 precession , steady, 543-7 equation s, fast, slow, 545 infinitesima l stability of, 545-6 sleeping top, 546 total angular velocity, 539 total energy, 541 turning points, 542 Motion referred to moving frame, see Chapter 4 591 Motion relative to Earth, 77-8 , 177-8 constant force; vector form, 189-90 Falkland Islands, battle, 192-5 Foucault pendulum general equations , 184 small oscillations, 185-9 free fall equations, deflection, 179-81 genera l equations , 178 gyrocompass, 450-3 , 538-9 projectile motion , 190-2 Reich's experiment, 181 Murphy, D., 64, 85 Mutua l action , see Law of mutual action Neutral stability, 173, 175, 549 Newton's laws, 3-4 , 24-31 , 83-4 , 86 equilibrium , 27 first law, 24, 408, 412 first law, standard form, 26 gravitation, 4, 32, 81-2 law of restitution , 340 logical structure of, see Frank, P., 84 Mach's principle , see Long, 84 noninert ial reference frame, 69-71 planetary motion , 278 relative to Earth frame, 70, 72-3, 78, 177-8 second law, 24, 95, 504 classica l form, 27-8 component form, 96-7 system of particles, 28, 302 statics , 27, 30-1 third law, 24, 30-1, 81-2,414-18,567 Newton, 1., 3, 83, 86, 284, 342,405,495, 559 see Truesdell, 479, 561 Newton-Euler laws, 5, 95, 408-9 Lagrange form, 519 vector component forms, 96-7 Newtonian frame, see Inertial frame Noble, B., 60, seeHubbert and Rubey, 84 Noll, w.,80-2, 85-6 , 104,414 ,479,569 Nonconservative system, 230, 256, 324, 329, 509 Nonholonomic constraints, 498-9, 561 Orbital motion, 278-83, see Kepler's laws equation of motion, 27, 509, 518 geometry analytical terminology, 279-80 aphelion, perihelio n, 282 apocenter, pericenter, 281-2 apogee, perigee , 282 circumference, 283 orbit equation , 279 Lagrangian formulation, 509, 518 592 Orbital motion (cont.) path, cylindrical coordinates, 279 periodic time, 281-2, 304 trajectories, eccentricity, 279-80 two body problem, 303--4 Pao, C.H.T., see Deresiewicz, 83 Parallel axis theorem, seeMoment of inertia tensor Pars, L.A., 529, 559-60 Pearson , K., 132 Peck, E.R. , 197 Pendulum , see Chapters 6 and 7: Reference s ballistic pendulum , 226, 229, 236, 285-6, 491 cyeloidal pendulum finite motion , 274-5, 338 uniqueness property, 276-7 double pendulum, 350--1,492, 552, 565 driven pendulum, 150, 532-3 Foucault pendulum, 181-9, 196-8 ,284 gyroscopic pendulum, 543, 545 Huygens's cyeloidal elock, 277-8 isochronous pendulum, 272-7 motion on concave path, 273--4 physical pendulum , 467, 471, 552 simple pendulum, 137-9, 149 frequency, period, 139 infinitesimal stability, 176 moving support, 150,209-11 ,215-18,298, 536-8 simple pendulum, exact solution, 264-72 elliptic integral , 266, 538 finite motion , 265, 277, 536, 538 Jacobian elliptic functions , 269, 538 Lagrang ian formulation , 508, 536-8 nonoscillatory, whirling , 271-2 period ,rrequency, 266-7,538 rotating support , 536-8 small amplitude motion, 269-71 small motion, error analysis , 270, 297 suspension tension , 138,265, 296 sleeping gyroscopic pendulum, 547 small oscillation on concave path, 274 spherical pendulum , 260--1, 521, 561 Phase plane, 261-2 Phase plane diagram, graph, 135, 140 constant energy curves , 261-2 linear spring, 264 Physical dimensions acceleration of gravity, 45 damping exponent, coeffcient, 153 dynamic viscosity, 121 electric charge , 104 electrostatic constant, 104 Index Physical dimensions (cont.) force, 26 frequency, circular frequency, 135 generalized forces, 504 gravitational constant, 33 impulse , 222 kinetic energy, 235 Lagrange forces , 519 mass, 6 mechanical power, 236 moment offorce, torque, 16 moment of inertia, 358 moment of momentum, 21 momentum, linear momentum , 6 period of oscillation, 135 potential energy, 243 spring constant, 132 torque-impulse, 228 work,229 Poisson, S.D., 183 Pollard, H., 284 Potential energy, 240-6 distributed force, 469-70 elastic , linear spring, 248 gravitational, 246-7, 470 Lagrangian function , 507 mutual internal , pair of particles, 567-8 quadratic function of generalized coordinates, 550 rigid body, 470 system of partieles external, 324 internal , 325, 567-8 Lagrange 's equations, 513 rigid system, 328 total,327 time varying, 255-6 Power, seeMechanical power Preferred, preferential frame, 24, see Inertial frame Primitive concepts : force, length, mass, particle , time, torque, 407-8; see Chapter 1, 4-6 Principal axes theorem , seeMoment of inertia tensor Principia,3, 83, 86, 284, 342, 405, 495 Principle of determinism, 408, 411-12, 435 equilibrium of a body, 412 Euler 's laws, 408 Newton's first law, 24, 26 Principle of frame indifference, 567, see Frame indifference Products of inertia, seeMoment of inertia tensor Index Projectilemotion, 258-9 elements, without friction, 112-15 escape velocity, 290 ink jet printer, 116-18 range, trajectory, 191, 259 relative to Earth, 190-5 trajectories, elliptic property, 259, 284 with air resistance, 122-3 Pseudoforces centrifugal, Coriolis, seeForces in Lagrange's equations, 519 Quadratic form invariance, orthogonal transformation, 550 theory of small vibrations kinetic energy, 550 Lagrangianfunction, 550 potential energy, 550 Rayleigh dissipation function, 556, 558 stability of equilibrium, 549-50 Radius of gyration, seeMomentof inertia tensor Ramsey, A.S., 74, 85 Rayleighdissipation function,556, 558 Referenceframe change of frame, 79 astronomical, inertial,Newtonian, preferred, 26, 68-71 principal frame, 378, 383 Reich, E, 181, 197 Relativeequilibrium, 70, 146, 172,449 Relativemotion. seeChapter 4 Restitution, coeffcient of, 340-1 Retardation time, 121 Rheonomic constraint, 497, 510-12, 536-8 Rigid body motion balance of a rotor, 438-9, 447 ballistic pendulum, 491 bearing reaction forces, 444-7 belt driven machine, 440 billiard ball motion on rough surface, 457-9, 490-1 on smooth surface, 457 centers of oscillation and percussion, 485-6 connecting rod experiment, 489 Euler's equations, 433-4 Euler's laws, 409, 413, 418, 433-4 flywheel and clutch engagement, 437 flywheel control, 441 flywheel , design analysis, 534-5 force, momentof force, 413 gyrocompass, 450-3, 538-9 593 Rigid body motion (cont .) lineal body general equations with Stokes force, 473-5 universal energyequation, 476 universal motions,476-7 momentof momentum, 22, 431-2 momentum, 10, 14 motion of a top, 539-47 moving base point, connecting rod, 424, 428, 432-3,462-3 kinetic energy, 461-2 physical pendulum, 467-9, 471 driven, 532-4 planemotion, 438 rigid link, 442- 3 rotation about fixedbody axis, 436 spinning thin rod bearing reaction torque, 447-8 energy method, 472 infinitesimal stability, 449-50 system, two bodies, 530-1 torque-free, steady rotation about a principal axis, 454-5 axisymmetricbody, 463-4 general discussion, 456 infinitesimal stabilityanalysis, 454-5 infinitesimal stabilityexperiment,455 infinitesimal stability theorem, 455 stabilityof tennis racket,490-1 torque impulse, 430, 437 uniform motion, 408 work-energy principle,467, 471 Rollingwithout slip, 488 Romer,R.H., see Reich, 197 Roscoe, T., 64, 67, 85 Rosenberg,R.M., 396, 529, 542, 559-61 Routh, EJ., 197,284 Rubey, W.w., 60,84 Salas-Brito, A.L.. 284 Scleronomicconstraints. 497 Second moment vector, see Kane, 396 Shames,I.H., 197.284,343,396,479 Simple harmonicoscillator amplitude, 134, 140 general model, 139-41 on concave path, 274 period, frequency, 134-5, 139 phase angle, 140 phase plane diagram, 135, 140 simple pendulum, 137-9 spring/mass system, 134 Simply connected region, 240 594 Single-valuedfunction, 241 Snyder, G.S., 65, 85 Sommerfeld, A., 197,284,547 Spafford, Maj. R.N., 192, 194, 198 Spring constant elasticity, modulus,stiffness, 132 Stability, see Infinitesimal stability Stapp, Col. J.P., 98 Statics, 27, 30-1 Stiffnesscoefficients, 549-50 Stokes's curl theorem,245, 289, 291 Stokes's law, 119, 124,473,510,556 Surfacearea, thin homogeneous bodies,Appendix D,571-6 Symmetric tensors Cauchy's ellipsoid,388, 394 characteristicequation, 391 multiciplicity of principalvalues, 392-4 orthogonalshear components, 403 orthogonalityof principalvectors, 392-3 positivesquare root, 402 principalvalues, directions, invariants, 391 realityof principalvalues, 392 spectral representation, 394 Synge, J.L., 85,198,284,479,542,560 Systemof particles,6-10, see Chapter8 Tabor,D., 83 Tensor, see Chapter3 Cartesiantransformation law, 376-7 identity, 358 inertia, momentof inertia,358 notation,operations, see Chapter3 spherical,367, 377 symmetric, propertiesof, 358, 390-5, 402-3 Terminal speed, velocity, 121, 123, 125 Theoryof small vibrations, 549-51 characteristicequation, frequencies , 552 degeneratesystems,552 dissipative systems,557-8 equationsof motion, 551, 558 inertiacoefficients, 550 Lagrangian function,550 stiffnesscoefficients, 549 Thornton,S.T., 342, 560 Timoshenko, S., 198,284,343 Tobin,w., 182, 184, 198,284 Todhunter, I., 132 Torque, 16, 407, seeMomentof force averagevalue,228 body, contact, 410 generalizedcouples,413 gravitational,36-7, 41-2 internal, external, 410 Index Torque(cont.) momentof force, 413 primitiveconcept, 407-8 Torque-free rotation, 454-6, 463-5 Torque-impulse, principle,227-9, 430-1 , 437 Torsional spring, stiffness, 482 Truesdell, c.,3, 80, 85-6, 406, 416, 478-9, 495, 561 Twobody problem, 303-5, 318 Uniformmotionof body,408, 411-12, 480 Unit step function, 62, 225, see Chapter I, 48-9 Unit slope function, 63, seeChapter I, 51-2 Units, in mechanics,86 Engineering, English, International (SI) Systems, 86-7 Vagliente, v.v.,560 Vargas, C.A., 284 Variation of a definiteintegral, 528 of a function, 526-7 of coordinates,526, 596 Vectorcalculus, elements,seeAppendixA Velocity, averagevalue,224 Verrier, U.J.J. Le, 33, see Fernie, 83 Vibrations amplitude, 134, 140 coupledsystem characteristicequation,frequencies, 516 eigenfrequencies, normalmode, natural frequencies, 516. 552 normalcoordinates,modes,517 two-degreesof freedom, 329-33, 514-17 uncouplednormalequations,517 critical dampingcoeffcient, 157 dampingexponent, coeffcient, 153 forced,driven, 152, 158 damped, transmissibility, transmission factor, 168-9 forceamplitude, 158 forcing, driving frequency, 158 steady-state, 158 transient, 158-9 , 165 undamped, 160-1 free, 152 criticallydamped, 156-8 damped, 151-8 damped, logarithmic decrement, 155 heavilydamped, 156-7 lightlydamped, 153-5, 157 lightlydamped, frequency, period. 154 infinitesimal stability, 172-7 Index Vibrations (cont.) free (cont.) linear systems , 133-7 with viscous damping , 151-69 frequency, circular frequency, 134 natural frequency, 159 period, 134 nonlinear, 169- 72 resonance phenomenon, 162, 167 simple harmonic motion, 134 small vibrat ions, 547-51 , see Theory of inertia coeffcients , 550 stiffness coeffcients, 549 with damping , 556-8 steady-state, 158 amplitude, magnification factors, 162, 165-7 damped motion, 165 response graphs, 163-5 undamped motion , 158-65 viscous damping ratio, 153 Virtual displacement vector, 502 Virtual work, 502-5 by impulsive generalized forces, 524 by Stokes force, 556 Volume moments of inertia , 359 Volume, homogeneous bodies, see Appendix D, 571-6 Weight, 45, 77 apparent relative to Earth, 75, 77 particle, system of particles, body, 45-6 relative, relative to Earth, 45, 77 Whittaker, E.T., 529, 542, 555, 558-60 Wilms, E.V., 477-80 Work, 229-33, 318-21 , see Potential energy by constant force, 233 by Coulomb frictiona l force, 234 by generalized forces , 505, 507 by gravity, 233 by instantaneous impulse, 230 by linear force , 234 by spring force, elastic, 235 conservative system of particles , 327 line, path integral, 229-31 nonconserv ative system, 256, 328-9 rigid body, translational, rotat ional, 465 system of particles , 318-21 center of mass relation , 319 relative to center of mass, 320 total for system, 320--1 theorem on potential energy, 241, 507 virtual work, 502, 505 Work-energy principle, 235, 257 rigid body, 466-7 general motion, 467, 471 translational, rotationa l motion , 466 with fixed point, 467 scleronomic systems , 506, 513, 522 system of particles , 320--2, 329 for center of mass, 319 relative to center of mass, 320 rigid system, 321-2 total,320 Yeh,H., 86, 198,396,480,555,560 Young, D.H., 343 595"
        ]
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.72-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.72-1.png",
        "caption": "Fig. 2.72 Torque converter (TC) [HOWSTUFFWORKS.COM 2003].",
        "texts": [
            " When driving with manual shift, the transmission\u2019s computer betters the driver if she/he tries to shift in a less suitable situation. The computer may make the shift as soon as the situation is considered suitable. In Figure 2.71, as an example of this development, a mechatronically controlled four-speed automatic transmission with driver-selected operating modes is shown. This automatic transmission uses a torque converter (TC) that allows the ECE or ICE to spin somewhat independently of the transmission. The torque converter (TC) with its connections to the ECE or ICE and the transmission is shown in Figure 2.72. The M-F pump inside a TC is a type of centrifugal M-F pump. As fluid is flung to the outside, a vacuum is created that draws more fluid in at the centre. The fluid then enters the blades of the turbine, which is connected to the transmission. The fluid exits the turbine at the centre, moving in a different direction than when it entered. If the fluid was allowed to hit the M-F pump, it would slow the ECE or ICE down, wasting power which is the reason for the stator. Automotive Mechatronics 226 The stator resides at the very centre of the torque converter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure12-1.png",
        "caption": "Fig. 12. (a) 3-D robot with four land-fixed winches and three UAVs. (b) SAW of the moving platform in point [X,Y,Z] = [\u221250, 50, 100]m with rAW = 205.7N in the UAVs\u2019 collision-free optimal arrangement [\u03c8\u2032\u2217 1 , \u03c8 \u2032\u2217 2 , \u03c8 \u2032\u2217 3 , \u03bb \u2032\u2217 1 , \u03bb \u2032\u2217 2 , \u03bb \u2032\u2217 3 ] = [95.1\u25e6, 132.6\u25e6, 240.1\u25e6, 3.3\u25e6, 64.2\u25e6, 51.5\u25e6].",
        "texts": [
            " Regarding the fact that r\u2217AW,i is limited by a tangent plane to its corresponding sphere, the orientation of the UAV with maximum effects on all border planes is obtained and among them, the border plane with maximum\u0394rAW,i, which provides a zonotope that surrounds the corresponding sphere, is selected as the result of such step. By following this approach inn steps, the optimal orientations of the UAVs are obtained. Based on the definition of rAW and SW, one can conclude that selecting the optimal configuration of UAVs in all points of the space provides the maximum size of SW for any robot where the set of all points with rAW = 0 forms the SW\u2019s boundary. In order to show the application of the proposed approach, this section presents an example. Fig. 12(a) illustrates a 3-D robot with four land-fixed winches located at A1 = [\u221250,\u221250, 0]T m, A2 = [\u221250, 50, 0]T m, A3 = [50, 50, 0]T m, and A4 = [50,\u221250, 0]T m, and three UAVs that are connected to 3m length cables to hold a 15-kg moving platform. Each winch is able to provide \u03c4max = 1000N, where the length density of the connected cables is considered as \u03b7 = 0.01kg/m. The mass and the maximum thrust force of UAVs are 15kg and tmax = 450N, where the dimensions of virtual cage around them are considered as dv = 0",
            " By finding rAW for different points of a 400 \u00d7 400 \u00d7 200 m space, SW of the 3-D CDPR is obtained. In order to show SW, rAW distribution over one quarter of the the selected volume is illustrated in Fig. 13. In this figure, the radius of the circular marker in each point of SW is proportional to the magnitude of rAW in such point. Regarding the symmetric arrangement of land-fixed winches, rAW distribution is symmetric with respect to X \u2212 Y and X \u2212 Z planes. Accordingly, by considering Fig. 13, rAW distribution over the selected 3-D space can be imagined. In order to provide more details, Fig. 12(b) illustrates SAW of the moving platform in an arbitrary point [X,Y,Z] = [\u221250, 50, 100]m as an example, where rAW = 205.7N is obtained in the UAVs\u2019 collision-free optimal arrangement [\u03c8\u2032\u2217 1 , \u03c8 \u2032\u2217 2 , \u03c8 \u2032\u2217 3 , \u03bb \u2032\u2217 1 , \u03bb \u2032\u2217 2 , \u03bb \u2032\u2217 3 ] = [95.1\u25e6, 132.6\u25e6, 240.1\u25e6, 3.3\u25e6, 64.2\u25e6, 51.5\u25e6]. In order to show the variation of rAW and UAVs\u2019 optimal angles over the selected 3-D space, two arbitrary planes of the 3-D workspace are selected and such results are presented for them. As the first case, rAW distribution over an area of 400 \u00d7 200 m in the vertical planeX = 0 is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure1-1.png",
        "caption": "Figure 1. Temperature field based on RTM measurement from a 1,6 l GTDI > 90kW/l [2]. Left: Spray cooled piston, Right: Salt core channel cooled.",
        "texts": [
            " The latter has been dismissed for small engines due to the increased complexity of integrating a cooling gallery into the connecting rod. Internal cooling galleries have been traditionally implemented within pistons for diesel engines where several manufacturing techniques for both steel and aluminum pistons have been applied (forged, casting, composite welded or friction welding [1]). However, only aluminum piston with salt-core cooling gallery has been previously designed for gasoline applications. Figure 1 demonstrates the temperature reduction resulting from introducing a cooling gallery within a commercial gasoline piston. Temperature reductions above 25\u00b0C are observed for the piston top land, but it is also observed in that figure a better temperature distribution between the piston thrust side (TS) and anti-thrust side (ATS). In Figure 2 taken from reference [1] the heat transfer ratio rejected from each piston component is depicted. As can be observed, the temperature reduction and heat flow ratios are more significant when a cooling gallery is introduced within a piston design where half of the heat transmitted to the piston top land can be removed by means of the internal cooling gallery"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure3-1.png",
        "caption": "Fig. 3. The 4/8/4 type platform structure sensor with isometric legs.",
        "texts": [
            " [24] proposed a fully pre-stressed parallel structure which possesses better performances and distributes the pre-stress equally on the different legs by a modified pre-tightening method without exceeding certain limits. As a result, the 4/8/4 type platform structure sensor with isometric legs is proposed. The 8/4-4 structure is a parallel structure with its legs being placed on one platform and divided into two sets. If the axes of either set are lengthened in the direction along the upper platform, the result is the 4/8/4 type platform structure sensor with isometric legs. The latter case is shown in Fig. 3. Still, this type possesses a half-symmetric structure and all the legs are equal in length. Therefore, it is similar to the 8/4-4 type which is shown in Fig. 2. Besides, three platforms includes the upper one used for pre-stress, themiddle one used formeasurement and the lower one used for fixation. This structural distribution realizes full pre-stress on all themeasuring legs and results in better mechanical characteristics. The configuration is determined by the following parameters: Rs, Rw, r, Hs, \u03b11, \u03b12, \u03b21 and\u03b22"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003749_s00170-021-07105-3-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003749_s00170-021-07105-3-Figure3-1.png",
        "caption": "Fig. 3 Simulation domain used to perform a 250-\u03bcm-long single-track simulation",
        "texts": [
            " The optical microscope is used to observe the melt pool boundary, and the width and depth of the single tracks are measured. The shape of the melt pool boundary is used to separate between the conduction mode and keyhole mode melting. FLOW-3D commercial software is used to develop a powder scale numerical model. An open source discrete element method (DEM) package is used to simulate the spreading of the IN625 powder layer and the powder layer is imported to the FLOW-3D software to perform the thermo-fluid simulation [18]. Figure 3 shows the simulation domain used in this study. The dimension of the solid substrate is 500 \u03bcm \u00d7 300 \u03bcm\u00d7 250 \u03bcm, and a layer of powder is defined on top of the solid substrate. The short scan length simulation is performed to analyze the variation in temperature distribution Table 1 LEDs (J/mm) with different laser power and scan speed Constant parameter Variable parameter (LED, J/mm) 195 W 200 mm/s (0.98) 400 mm/s (0.49) 600 mm/s (0.33) 800 mm/s (0.24) 1000 mm/s (0.20) 1200 mm/s (0.16) 200 mm/s 105 W (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003228_j.procir.2020.03.003-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003228_j.procir.2020.03.003-Figure5-1.png",
        "caption": "Fig. 5. The FEM model created to calculate the stress distribution within the C-ring. Example in the case of 700N.",
        "texts": [
            " Surface topographies of the examined specimens and characteristic profiles. To help estimating the stresses developed and their distribution within the specimen, finite element analysis was performed through a static elastic explicit solver employing ANSYS software package. The modelled geometry of the CRing was meshed using hexahedral elements. The meshing algorithm generated about 21x103 elements by defining an element size of 0.4 mm, which was determined after applying an element size convergence study. The fine mesh produced is shown at the top of Figure 5. Boundary conditions where 2 Michailidis / Procedia CIRP 00 (2019) 000\u2013000 Maraging steel 18Ni-C300 with its high strength, hardness and good corrosion resistance, featuring also sufficient dimensional stability during aging treatment, is suitable for demanding applications such as aerospace components and mould and tooling systems [6,7]. Fatigue strength properties of metallic materials rely on their microstructure, hence inherent processing characteristics in AM, e.g. surface roughness as well as material defects show a major impact on the integrity of the fabricated parts",
            " This is because of the higher corrosion rates caused by the emergence of local stress due to multiple melt cavities, harder dendritic structure and roughness, resulting in increased anodic behavior in these areas. To help estimating the stresses developed and their distribution within the specimen, finite element analysis was performed through a static elastic explicit solver employing ANSYS software package. The modelled geometry of the CRing was meshed using hexahedral elements. The meshing algorithm generated about 21x103 elements by defining an element size of 0.4 mm, which was determined after applying an element size convergence study. The fine mesh produced is shown at the top of Figure 5. Boundary conditions where 2 Michailidis / Procedia CIRP 00 (2019) 000\u2013000 Maraging steel 18Ni-C300 with its high strength, hardness and good corrosion resistance, featuring also sufficient dimensional stability during aging treatment, is suitable for demanding applications such as aerospace components and mould and tooling systems [6,7]. Fatigue strength properties of metallic materials rely on their microstructure, hence inherent processing characteristics in AM, e.g. surface roughness as well as material defects show a major impact on the integrity of the fabricated parts",
            " Additionally, the nodes of the upper hole where defined to follow a prescribed movement towards to the minus Z direction to the extent that the resulting reaction force matches the experimental one (700 N in the presented example), whereas the nodes of the bottom hole where fixed. The rotations for all nodes where set free. A simple linear structural model was defined with a Young\u2019s modulus of 190 GPa and a Poisson ratio of 0.3. The example presented at the bottom of the figure, corresponds to a maximum loading of the C-ring at 700 N, which yields to a maximum von Mises stress of 875 MPa, developing at the outer face of the specimen. There is a highly stressed area along the specimen, which is likely to cause fracture, indicated as critical zone in Figure 5. The different surface-initiated fracture modes during pure fatigue and corrosion-fatigue of the specimens can be visualized from the selection of characteristic fractographs taken by stereo microscope (Leica MS5 equipped with Leica DFC490 digital camera) and presented in Figure 6. A clear outcome of this investigation is that the specimens tested in a corrosion environment are more susceptible to brittle failure, judging from the crack propagation shown in low magnification images (left column of micrographs",
            " Multiple smaller and bigger cracks are present, and the crack path is more fluctuating than in the case of corrosion-free specimens. A further outcome yielding from the comparison of the wrought with SLM specimens is that the presence of high roughness at the SLM samples is the cause for the multiple crack initiation sites. Some of the crack initiation points are marked with red arrows. In extreme cases, the crack elevates at sites different than the ones where the maximum nominal stresses develop (see stress distribution at the bottom of Figure 5). Furthermore, there is a positive effect of glassblasting on the fatigue and corrosion-fatigue, as documented by the less fluctuating crack path and the reduction of the roughness compared to the untreated SLM. 4. Conclusions The current investigation offers insights in a scientific area with limited contributions, comparing the functional properties (fatigue) with simultaneous corrosion of bulk wrought maraging steel C300 with SLM specimens of the same grade, surface-treated by glass-blasting",
            " Fatigue and corrosion-fatigue performance of all the examined specimens at various loads. Fatigue stress ratio R=0. Fatigue frequency: 40 Hz. A simple linear structural model was defined with a Young\u2019s modulus of 190 GPa and a Poisson ratio of 0.3. The example presented at the bottom of the figure, corresponds to a maximum loading of the C-ring at 700 N, which yields to a maximum von Mises stress of 875 MPa, developing at the outer face of the specimen. There is a highly stressed area along the specimen, which is likely to cause fracture, indicated as critical zone in Figure 5. The different surface-initiated fracture modes during pure fatigue and corrosion-fatigue of the specimens can be visualized from the selection of characteristic fractographs taken by stereo microscope (Leica MS5 equipped with Leica DFC490 digital camera) and presented in Figure 6. A clear outcome of this investigation is that the specimens tested in a corrosion environment are more susceptible to brittle failure, judging from the crack propagation shown in low magnification images (left column of micrographs. Multiple smaller and bigger cracks are present, and the crack path is more fluctuating than in the case of corrosion-free specimens. A further outcome yielding from the comparison of the wrought with SLM specimens is that the presence of high Fig. 5. The FEM model created to calculate the stress distribution within the C-ring. Example in the case of 700N. roughness at the SLM samples is the cause for the multiple crack initiation sites. Some of the crack initiation points are marked with red arrows. In extreme cases, the crack elevates at sites different than the ones where the maximum nominal stresses develop (see stress distribution at the bottom of Figure 5). Furthermore, there is a positive effect of glassblasting on the fatigue and corrosion-fatigue, as documented by the less fluctuating crack path and the reduction of the roughness compared to the untreated SLM. 4. Conclusions The current investigation offers insights in a scientific area with limited contributions, comparing the functional properties (fatigue) with simultaneous corrosion of bulk wrought maraging steel C300 with SLM specimens of the same grade, surface-treated by glass-blasting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002133_s11771-015-2967-y-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002133_s11771-015-2967-y-Figure1-1.png",
        "caption": "Fig. 1 Bottom-following schematic of underactuated UUV",
        "texts": [
            " The bottom-following control law is divided into pitch adjustment and surge velocity tracking on the dynamic level. The estimation of the parameter perturbation and environmental disturbance are not required. The problems regarding the pitch velocity persistent excitation (PE) have been resolved. Following standard practice, it is well known that the kinematic and dynamic equations can be developed using a global inertial coordinate frame {I} and a body- fixed coordinate frame {B}, as shown in Fig. 1. To analyze the motion of the underactuated UUV in the vertical plane, the following notations will be used in the sequel. The symbol [x, z]T denotes the coordinate for the origin Q of the body-fixed coordinate frame {B} in the inertial coordinate frame {I}. Let \u03b8B be the pitch angle, which parameterizes the rotation matrix from {B} to {I}. And then, the posture of the UUV is expressed as T[ , , ] .I Bx z p Let T t [ , ]u wv denote the velocity of Q in {I} expressed in {B}, where u and w are the surge (longitudinal) and heave (vertical) velocities, respectively",
            " To solve the problem of bottom-following, the following two control objectives must be achieved: 1) the distance between the origin Q of the {B} and the reference point P on the desired path should be reduced to zero; 2) the direction of the vehicle\u2019s total velocity vector vt is aligned with the tangent to the desired path at P. To achieve two control objectives, a Serret-Frenet frame {F} must be introduced at the reference point P, which moves along the desired path. The {F} plays the role of a \u201cvirtual target vehicle\u201d that should be followed by the \u201creal vehicle\u201d. Let T R R R[ , , ]Fx z p denote the generalized coordinates of the virtual vehicle\u2019s posture in the {I}. In Fig. 1, P is an arbitrary point on the desired path to be followed. The reference point P along the desired path is stated by the curvilinear abscissa s. According to the geometric relationship, the posture errors expressed in the {F} are described as ( ) ( ) (( ) ( ) )F F F I I I I IPQ PQ OQ OP       R R (4) where F IR denotes the rotation matrix from {I} to {F}. Let T e e e e( , , )x z p define the generalized coordinates of the posture errors in the {F}, and the following errors equations are re-described as e R( )( )F I F Ip  R p p (5) where \u03b8F is the pitch angle of the \u201cvirtual target vehicle\u201d, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002127_cjme.2015.0710.091-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002127_cjme.2015.0710.091-Figure1-1.png",
        "caption": "Fig. 1. Spatial four-bar linkage mechanism with double spherical pairs",
        "texts": [
            " [15], which indicates that for single-loop mechanisms the number of over-constraints is just that of the independent reciprocal screws. After recognizing over-constraints the mobility of the mechanism can be calculated by the unified-mobility formula[7\u20138] expressed as follows: ( )6 1 iM n g f = - - + +\u00e5 , (1) where M denotes the mobility of the mechanism; n the number of links including the frame; g the number of the kinematic pairs; fi the freedom of the ith kinematic pair; and \u03bc the total number of over-constraints of the mechanism. It is named \u201cunified-mobility formula\u201d. Fig. 1 shows a spatial four-bar linkage mechanism ABCDA with two spherical pairs[16]. For its mobility analysis, it has no doubt that it is necessary to estimate whether and how many over-constraints exist in the mechanism firstly. To express its screw system a coordinate system A-XYZ is established in Fig. 1, where Z-axis is along the direction of the revolute pair A, Y-axis along the link AB, and X-axis accordance with the right-hand rule. Considering a spherical pair has three twist screws, for the whole mechanism the twist system including eight screws can be written as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 3 4 1 5 5 2 6 6 3 7 7 8 8 8 8 8 8 0 0 1; 0 0 0 , 1 0 0; 0 0 , 0 1 0; 0 0 0 , 0 0 1; 0 0 , 1 0 0; 0 , 0 1 0; 0 , 0 0 1; 0 , ; , A B B B C C C D f d e f d f d e a b c d e f = = = = = = = = $ $ $ $ $ $ $ $ (2) where the subscript in the lower right corner of each screw denotes the corresponding kinematic pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure8-1.png",
        "caption": "Fig. 8. Adjusting theory of the backlash.",
        "texts": [
            " The essence of the backlashadjustable is based on the characteristics of the helicoid surface, which is that the rotation angle of the helical surface around its axis corresponds to the translational motion distance along its axial direction. Therefore, the displacement h b of IHB gear is translational along its axis direction, and the rotation angles of the two tooth surfaces can be expressed as follows: \u03c6L = h b cos \u03b1 tan \u03b2L / r b , \u03c6R = h b cos \u03b1 tan \u03b2R / r b (25) Where, \u03c6L and \u03c6R are the rotation angles of the left and right side tooth faces, respectively. Based on the above descriptions, the schematic diagram of this novel hourglass worm drive backlash adjustment is illustrated in Fig. 8 . The backlash of the hourglass worm drive refers to the gap between the non-working flanks when a pair of hourglass worm mesh. At the current position, the backlash of the hourglass worm drive on the reference circle of IHB gear is \u03b4b , as shown in Fig. 8 (a). After the IHB gear has moved the displacement h b along its axial direction, the gap between the non-working flanks is 0, this means that the hourglass worm drive has non-backlash, as shown in Fig. 8 (b). Point P l is the practical contact point between the left flank tooth surface of IHB gear and the OPE hourglass worm tooth surface. Point P r1 is the theoretical contact point on the tooth surface of the OPE hourglass worm. The theoretical contact point on the right flank tooth surface of the IHB gear is point P r2 . The distance between the point P r1 and the point P r2 on the reference circle of the IHB gear is \u03b4b . After the backlash has adjusted, Point P 1 \u2019 is the practical contact point between the left flank tooth surface of the IHB gear and the OPE worm tooth surface, and the practical contact point between the right flank tooth surface of IHB gear and the OPE worm tooth surface is point P r . Based on the geometric relationship shown in Fig. 8 , the adjusted backlash \u03b4b can be represented as follows: \u03b4b = r 2 ( \u03c6L + \u03c6R ) = r 2 ( h b cos \u03b1 tan \u03b2L / r b \u2212 h b cos \u03b1 tan \u03b2R / r b ) (26) = h b ( tan \u03b2L \u2212 tan \u03b2R ) Therefore, the axial position of the IHB gear can be adjusted to regulate backlash between the OPE hourglass worm and the IHB gear, and the requirements for the adjustable-backlash of the worm drive in the precision electromechanical systems are attained. The major design parameters of the new hourglass worm drive in each example are illustrated in Table 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.3-1.png",
        "caption": "Figure 10.3. Forces on a rigid crate in a moving elevator.",
        "texts": [
            "25) and (10.26) clearly show that our earlier use of Newton's laws for a particle, a center of mass object, in applications to bodies of finite size was correct and well-modeled; but for bodies there is more-the effects of external torques must be described. Similar principles for the external torque, impulsive torque, and moment of momentum of a body are presented later. The quantities used in the proof of the first equation in (10.18) are illustrated next. Example 10.1. A 400 lb crate shown in Fig. 10.3 is lifted in an elevator that weighs 2000 lb. The tension in the hoisting cable is 3000 lb. (i) What total force N acts on the bottom of the crate? (ii) Relate the various forces here to those identified in the construction of the mutual action principle. Ignore the mutual gravitational body force between ,q)\\ and ~2 , and assume that g = 32 ft/sec\" . 420 Chapter 10 Solution of (i). First consider the crate YB I alone; its free body diagram is shown in Fig . 10.3b. Thus , with the total external force F(YBI , t) = N +WI acting on YB I , (10",
            "31 b) that acts on the part YB I , while f2 = W2 + T is that part of the total force (10.31b) that acts on the part YB2\u2022 Hence, F(YB, r) = f l + f2 in (10.13) is equivalent to (10.3lb). We shall ignore the mutual body force between YB] and YB2\u2022 Then N = b'2 is the mutual contact force Dynamics of a Rigid Body 421 exerted on a'l l by a'l2; and in accordance with the law of mutual action, we wish to demonstrate that b21= -b12 = -N for the mutual contact force exerted on a'l2 by a'l ]. (The reader should now draw the free body diagrams suggested in Fig. 10.2. for the problem in Fig. 10.3a.) Therefore, with the aid of (10.15) and the foregoing identification of terms, the total force (l 0.14) on the free body a'l ], the crate alone, is (l0.31c) and on a'l2, the elevator alone, is F2 =W2+ T + b21 = - . (l0.31d) dt Adding (l0.31c) and (l0.31d) and noting (l0.31b), we reach A A d F 1+ F2 = F(a'l, t) + N + b21 = dt (PI + P2). (l0.31e) However, by (5.11), p(a'l, t) == pea'll U a'l2, t) = p(a'l] , t) + P(a'l2, t), and hence the far right-hand side of (l0.31e) is the total force F(a'l , t) on a'l "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002930_1.4043206-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002930_1.4043206-Figure2-1.png",
        "caption": "Fig. 2 Ease-off topography of a pinion tooth surface",
        "texts": [
            " The models required for the ease-off topology modification approach include the following: (i) Theoretical reference tooth surface models of the gear and the pinion to create reference tooth surface coordinates and formulate pinion theoretical reference tooth surfaces [2]. (ii) A fourth-order PTE model to calculate ease-off values of pinion tooth surfaces [24]. (iii) An ease-off tooth surface model to describe ease-off topography of pinion tooth surfaces. (iv) An error sensitivity analysis method to analyze the effects of misalignments on the moving velocity of a contact point. Ease-off topography is defined as a set of modifications, and it is represented as a grid of a tooth surface, as shown in Fig. 2. Modifications can be represented as normal deviations between the pinion ease-off topography and its theoretical reference tooth 093302-2 / Vol. 141, SEPTEMBER 2019 Transactions of the ASME Downloaded From: https://mechanicaldesign.asmedigitalcollection.asme.org on 05/29/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use surface. Theoretical reference tooth surfaces of the pinion and the gear are fully conjugated with each other, which can be calculated following Ref. [2]. The normal deviations can be calculated by the fourth-order PTE model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003329_j.mechmachtheory.2019.103753-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003329_j.mechmachtheory.2019.103753-Figure3-1.png",
        "caption": "Fig. 3. The schematic diagram of Bricard-like mechanism.",
        "texts": [
            " Suppose DAB = \u03b8 , AD = BC = l , AB = CD = l 1 , we can obtain the lengths of S 2 S \u2032 2 , S 2 S \u2032\u2032 2 , AS \u2032 2 , CS \u2032\u2032 2 and the angle of S \u2032 2 S 2 S \u2032\u2032 2 as follows ( Appendix A.1 ) S 2 S \u2032 2 = S 2 S \u2032\u2032 2 = ( l 2 \u2212 l 2 1 ) sin \u03b8 2(l cos \u03b8 \u2212 l 1 ) (1) \u2220 S \u2032 2 S 2 S \u2032\u2032 2 = arccos ( l 2 + l 2 1 ) cos \u03b8 \u2212 2 l l 1 ( l 2 + l 2 1 ) \u2212 2 l l 1 cos \u03b8 + \u03b8 (2) A S \u2032 2 = C S \u2032\u2032 2 = ( l 2 \u2212 l 2 1 ) cos \u03b8 2 l cos \u03b8 \u2212 2 l 1 (3) By connecting three anti-parallelogram units along their side links using three revolute joints, a new Bricard-like mech- anism is obtained, as shown in Fig. 3 . The mechanism consists of 12 links and 15 revolute joints. The axes of the revolute joints in the same anti-parallelogram unit are parallel to each other, and perpendicular to the axes of revolute joints lying on the side links. The lengths of A j D j and B j C j are denoted as l , and they are all equal, the lengths of A j B j and C j D j are denoted as l j , the angle between A j D j and A j B j of the j th anti-parallelogram unit are denoted as \u03b8Aj , where j = 1, 2, 3. Actually, the redundant revolute joints along axes of revolute joints S 1 , S 3 , and S 5 do not affect the movement and freedom of the mechanism, so the mechanism can be connected by more redundant revolute joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002724_j.ymssp.2015.04.033-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002724_j.ymssp.2015.04.033-Figure10-1.png",
        "caption": "Fig. 10. Formation of the EHL film (dark grey) for two axial positions of the outer ring (a and b).",
        "texts": [
            " As the axial stiffness increases at higher levels of the axial load, the response of the axial displacement deviates from a linear trend (Fig. 9b). During axial displacement of the outer ring w.r.t. the inner ring, the lubricant film thickness and surface area of each contact change. The electrical resistance responds to these variations. Also, introducing an axial load leads to the formation of a contact angle \u03b1. The contact angle varies sinusoidally when applying the dynamic excitation. The dark grey areas in Fig. 10 show the Please cite this article as: W. Jacobs, et al., The influence of external dynamic loads on the lifetime of rolling element bearings: Experimental analysis of the lubricant film and surface wear, Mech. Syst. Signal Process. (2015), http://dx.doi. org/10.1016/j.ymssp.2015.04.033i locations where the pressure builds up and the EHL film is formed for two positions of the outer ring. Due to the nonlinear motion of the rolling elements and the variation of the EHL film location, the response of the lubricant film is strongly nonlinear at high load levels (Fig",
            " A strong sine excitation (Fr, d\u00bc35 N and fe\u00bc320 Hz) is added in the radial direction. Fig. 12b, d and f summarises the results. When increasing the axial load, a stronger lubricant film forms and the response of the electrical resistance decreases. 3. The influence of the radial static load on the response of an axial excitation. The radial static load is varied from 0 to 1600 N. A strong sine excitation (Fa,d\u00bc35 N and fe\u00bcaxial rigid body mode) is added in the axial direction. Fig. 14a, c and e shows the results. Recalling Fig. 10, the contact angle \u03b1 follows the axial displacement. When increasing the radial static load, the variation of the contact angle reduces and the response of the lubricant film becomes more linear. The second and higher harmonics of the lubricant's response reduce. Also when increasing the radial static load, a stronger lubricant film forms. A consequential decrease of the lubricant's response is observed (Fig. 14e). 4. The influence of the axial static load on the response of an axial excitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002814_j.mechmachtheory.2019.03.022-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002814_j.mechmachtheory.2019.03.022-Figure4-1.png",
        "caption": "Fig. 4. Free body diagram of the nuts.",
        "texts": [
            " The latter are represented through a Coulomb-Stribeck-viscous model [66] which allows lubricant effects to be considered and the simulation results to be more realistic. In the present work, this was neglected since the goal is to investigate only the mechanism\u2019s performance, without hindrances of supporting elements or different mounting conditions. The considered system has two nuts which are preloaded inserting a thickness between them, as in [67] . The preload force acts to separate the nuts, as illustrated in Fig. 4 . The external force is shown applied on the nut\u2019s flange, but in the model it is considered equally distributed on both the nuts, basing on the assumption that all the spheres are equally loaded, without geometric errors and considering that the preload force is imposed as a constant force instead that as a spring, therefore it is not able to transmit the external force from one nut to the other. The matching forces between the spheres and the nut grooves are represented along the grooves: the total force F Z, j on each nut is derived from the projection and sum of all the contact forces from each sphere along the z axis. Since the analysed ball screw has a right-hand thread, to a positive rotation of the screw corresponds a backwards displacement of the nut assembly with regards to the z axis. Each nut dynamic equilibrium equation is: Z F Z, j \u2212 F f r, j + F ext 2 \u00b1 F pr \u2212 M n \u0308z j = 0 (4) As shown in Fig. 4 , the preload sign is positive on the first nut ( j = 1 ) and negative on the other one ( j = 2 ). F fr is the friction force applied on each nut and, as for the screw, it is composed by two parts: the friction given by the rolling/sliding spheres and the one due to the presence of linear guides, modelled by means of a Coulomb\u2013Stribeck\u2013viscous function as well. In the same way as for the screw, the latter has been disregarded in the present analysis to investigate only the ball screw itself. This means that idealized frictionless constraints have been adopted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001262_978-3-662-43645-5_11-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001262_978-3-662-43645-5_11-Figure4-1.png",
        "caption": "Fig. 4. Amplitude modulation. A crankshaft is used to convert the rotating movement of the motor (positioned outside of these image sections on the left) into an oscillating movement of the wing (lower right-hand corner of these image sections). The crankshaft leaves the housing containing the motor in a straight line. However, the distal part is tilted. The mechanical crosspoint can be shifted along the crankshaft as marked by the arrows using a servo motor. This enables the amplitude of the wing stroke to be modulated continuously (see animation for further details).",
        "texts": [
            " This crankshaft is used to convert the rotating movement actuated by the motor into an oscillating movement of the wing. The interesting aspect of the crankshaft is that the proximal part of the crankshaft leaves the housing containing the motor in a straight line. However, the distal part is tilted. Since the position of the mechanical crosspoint can be shifted along the crankshaft from a more distal to a more proximal position the offset of the crankshaft changes and by this the amplitude of the wing movement changes (See Fig. 4). The movement of the crosspoint is actuated by a servo motor. The resulting deflection varies between 80 and 130 . A second servo motor actively changes the twisting angle of the wing by up to 90 . Taken together, we can control the frequency of all four wings together, and the amplitude and twisting angle of each wing independently, resulting in 9 degrees of freedom. This way the direction of thrust and the intensity of thrust for all four wings can be adjusted individually, thereby enabling the remote-controlled dragonfly to move in almost any orientation in space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.5-1.png",
        "caption": "Fig. 15.5 Pinion with eight cylindric pins. Circles k1 and k2 of Fig. 15.4a",
        "texts": [
            " Hence two wheels having the diameter ratio 1 : 2 can be used for guiding the endpoints of a rod along two lines under an arbitrary angle \u03b1 (see Fig. 15.4b). If is again the rod length, the radius of the small wheel is /(2 sin\u03b1 ) . This follows from the theorem that in the small circle the central angle subtended by the chord equals 2\u03b1 . During two full revolutions of k2 the rod moves through all four quadrants of k1 . From an engineering point of view the generation of this motion by means of two toothed wheels is better than by sliding two points along straight guides. The simplest possible forms of toothed wheels are shown in Fig. 15.5 . On the small wheel cylinders of arbitrary diameter are fixed with their centers on the circumference of k2 . Every cylinder is moving in a slot cut into the big wheel. The cylinders and the slots are the flanks of the teeth. The minimum number of teeth is two. Pins, as the cylinders are called, are the historically oldest forms of teeth. See also Sec. 16.1.5 . 15.1 Instantaneous Center of Rotation. Centrodes 457 In what follows, the trajectory of an arbitrary point Q fixed in \u03a32 is investigated",
            " The latter one is the prolate epitrochoid e described by the functions without the terms with factor \u03c1 = 1/5 . Flank f2 is generating nine teeth which are meshing with the ten pins on wheel 1 . All pins are meshing simultaneously. At every contact point the contact normal is passing through the pitch point 16.1 Parallel Axes 543 P12 . The line of contact itself is not shown. It is not passing through P12 . This means that there is sliding at every contact point in every position of the wheels. End of example. In Fig. 15.5 the geometrically simplest case of internal pin gearing is illustrated. It is the case with the inner pitch circle being half the size of the outer and with pins located on the inner wheel. The cycloids traced by the centers of the pins are straight lines and so are the parallel curves, i.e., the tooth flanks on the outer wheel. It is easy to show that also in this case the line of contact is a limac\u0327on of Pascal. In well-lubricated gears (no friction force in the common tangent plane) the force transmitted by one tooth on the other has the direction of the contact normal (line BP12 in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001851_gt2016-56084-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001851_gt2016-56084-Figure1-1.png",
        "caption": "Figure 1. A blade with a penetrating cooling system [1].",
        "texts": [
            " A few new designs of HPT blades with penetrating and deflector type CS, as well as blade designed by TO, are considered for AM applications and are discussed in this paper. A blade with a so-called penetrating CS (PCS) has been designed in the CIAM department of gas turbines under the guidance of Kharkovsky S.V. [1]. This blade has a double-wall shape, where the interior wall is connected with an internal cooling passage. The air passes between the inner and external walls and cools the external ones. In addition, this blade has many film cooling holes. Figure 1 shows a solid model as well as a middle cross-section. This blade\u2019s higher cooling effectiveness is achieved because the exterior parts of the blade walls are thin compared to the interior ones, which have comparatively low temperatures but are subject to a greater part of the centrifugal forces. The originally designed blade (blade # I) and the blade (# II) with PCS are in the operation condition of non-stationary heating and centrifugal and gas loading. A comparative finite element numerical investigation of the thermal and strength states was carried out for both blades"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.21-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.21-1.png",
        "caption": "Fig. 17.21 Circle of singular foci",
        "texts": [
            " End of proof. The existence of six intersection points of a coupler curve and a circle can be expressed in the following alternative form. Given three circles a , b , c and a triangle (A,B,C), there exist six (not necessarily real) positions of the triangle in which A lies on a , B on b and C on c . This result is important for Sect. 17.10 on planar robots. The equation \u0394 = 0 can be written in the form( x\u2212 2 )2 + ( y \u2212 2 cot\u03b2 )2 = ( 2 sin\u03b2 )2 . (17.87) It is the equation of the circle shown in Fig. 17.21 . The circle passes through A0 and B0 . It has the central semi-angle \u03b2 and, hence, the peripheral angle \u03b2 . It was shown that \u03b2 is also the angle at C0 in the triangle (A0,B0,C0) of Fig. 17.15 . Therefore, also C0 is located on the circle. From this fact Roberts concluded Theorem 17.2 on the existence of three cognate four-bars generating one and the same coupler curve. The three centers A0 , B0 and C0 are referred to as singular foci, and the circle itself is called circle of singular foci. Since \u0394 equals zero on the circle, cos\u03b1 and sin\u03b1 are indeterminate if the coupler point is located on the circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002895_02670836.2019.1705560-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002895_02670836.2019.1705560-Figure3-1.png",
        "caption": "Figure 3. Schematic diagram of laser scanning mode: (a) checkerboard scanning; (b) uniform scanning.",
        "texts": [
            " The change of the process parameters has a great influence on the quality and properties of the selective laser melting sample, especially on the residual stress of the sample. Therefore, in this experiment, the laser scanning strategy, scanning speed, preheating temperature and so on can be used to change the process parameters of the selective laser melting forming sample. The setting of process parameters in this experiment as shown in Table 3. According to different process parameters, four samples are formed. The related process parameters are shown in Table 4, and the scanning strategy is shown in Figure 3. The measurement methods of residual stress can be divided into destructive and non-destructive methods. Destructive methods include drilling method, ring-core method, segmented strip method and so on [26\u201329]. This kind of method has perfect theory and high measurement precision. However, it will cause some damage to the workpiece. The non-destructive methods include neutron diffraction method, X-ray diffraction method [13,30,31]. In this experiment, after samples are formed, samples are separated from the substrate [32,33] and the residual stress of samples are measured by the TEC 4000X-ray diffraction system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.1-1.png",
        "caption": "Fig. 7.1 Example compliant mechanisms. (a) An artificial spinal disc. (b) A compliant centrifugal clutch. (c) A lamina emergent mechanism. (d) A compliant constant-force exercise machine",
        "texts": [
            "hapter 7 Compliant Mechanisms Larry L. Howell Compliant mechanisms1 gain their motion from the deflection of elastic members. Examples of compliant mechanisms are shown in Fig. 7.1. Because compliant mechanisms gain their motion from the constrained bending of flexible parts, they can achieve complex motion from simple topologies. Traditional mechanisms use rigid parts connected at articulating joints (such as hinges, axles, or bearings), which usually requires assembly of components and results in friction at the connecting surfaces [21, 31, 46]. Because traditional bearings are not practical in many situations (e.g. microelectro-mechanical systems) and lubrication can be problematic, friction and wear present major difficulties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000281_978-3-540-88464-4_2-Figure2.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000281_978-3-540-88464-4_2-Figure2.16-1.png",
        "caption": "Fig. 2.16. Coordination between ipsilateral legs in crayfish. a) rostrally directed influence prolongs swing movement, b) caudally directed influence shortens swing movement. The left part of each figure shows body and range of movement of two neighbouring legs (upward is anterior). The right part indicates the movement of the reference leg; posterior leg in (a), anterior leg in (b). The behaviour of the other leg is schematically shown by plotting several traces with different phase shifts. The wedges and arrows indicate the coordinating influences.",
        "texts": [
            " Three such rules have been describe for the crayfish, five similar, but different in detail, for the stick insect (see Fig. 2.2; [47]. For the cat, four mechanisms have been described [60]). Fig. 2.14 shows the effect of a brief interruption of stance movement of one leg in the crayfish. The leg resumes normal coordination by shortening or prolonging the swing movement and/or the stance movements of some of the neighbouring legs. To illustrate the evaluation procedure, two responses to disturbances of legs 3 and 4 are shown. The situations in which prolongation of a swing occurs are presented in Fig. 2.16 in a form similar to a phase-response curve. The sketches below the abscissa symbolize the rhythmic movement of the two legs in a normally coordinated walk (solid lines). The values on the abscissa are given as absolute values rather than as relative phase, which is usual in a phase-response curve. The ordinate does not show the absolute duration, but rather the difference relative to the swing duration of a normal step. Thus, the zero value corresponds to an unchanged swing. Leg Coordination in Crayfish: a Simple Case: How can a system be constructed to produce a stable spatiotemporal pattern and, at the same time, to tolerate disturbances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.10-1.png",
        "caption": "Figure 7.10. Schema for the torque about a line through the moment point O.",
        "texts": [
            "K determines the speed at B, and hence the horizontal component of the particle's velocity at C is given by i = VB = J2gR. o Exercise 7.8. What is the normal force exerted on m by the surface at B? 0 7.8.3. The Principle of Conservation of Moment of Momentum The moment of momentum principle (6.79) also has the form (7.66). Therefore, for a fixed direction e, d Mo . e = dt (ho . e), (7.70) where Mo . e, the component of Mo in the direction e, characterizes the turning effect of the force about a line L'through 0 having the direction e, as shown in Fig. 7.10. Thus, M o . e is the moment of the force about the axis e through O. Similarly, ho . e is the moment ofmomentum about the axis e through O. In these terms, the following conservation theorem is evident from (7.70). Momentum, Work, and Energy 251 The principle of conservation of moment of momentum: The moment of the force about an axis e througha fixed point 0 in an inertialframe <t> vanishes for all time when and only when the correspondingmoment ofmomentumabout that axis is constant: M o . e = 0 {:::::::} ho "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003718_s40430-021-02834-8-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003718_s40430-021-02834-8-Figure1-1.png",
        "caption": "Fig. 1 Joint clearance model with massless virtual link[24]",
        "texts": [
            " The rest of the study is organized as follows: Sect.\u00a01 presents kinematic and dynamic analysis of slidercrank mechanism with joint clearance; the joint clearance simulation method is presented in Sect.\u00a02; Sect.\u00a03 presents the definition of the optimization problem, and results and discussions are finally presented in Sect.\u00a04. To model the clearance, a massless virtual link with a length equal to the extent of clearance obtained from the journal and bearing radius was used. The model employed in this regard is shown in Fig.\u00a01. The link begins from the center of the base link pin and ends at the center of the socket connected to the next link. Clearance is the difference between the radius of the bearing and the journal, indicated by r as shown in Fig.\u00a01. Joint clearance can be simulated with one and two degree of freedom models. For each of these models, many studies have been done by researchers in planar mechanisms (often crank-slider and four-bar mechanisms), which are discussed in detail in the introduction. In this paper, the massless virtual link model or permanent contact between the bearing and the journal is selected to model joint clearance. However, the fact that the pin and bearing are separated at some Journal of the Brazilian Society of Mechanical Sciences and Engineering (2021) 43:185 1 3 185 Page 4 of 18 moments and they are in touch with each at other moments cannot be denied in this case. When constant contact between the journal and bearing at each joint is assumed, clearance can be modeled as a vector equivalent to a massless virtual link with a length equal to the length of joint clearance. In this case, analysis of a mechanism with joint clearance becomes analysis of a mechanism with ideal joints (without clearance) and more members. As Fig.\u00a01 shows, the amount of clearance is equal to the difference between the radius of the journal and the bearing. According to this assumption and also neglecting friction, the direction of the clearance vector is always in the direction of the common vertical of two surfaces at point of contact. In this model, each joint clearance adds an uncontrolled degree of freedom to the mechanism and the unknown variable is the angular vector of joint clearance. For example, if clearance in one joint is considered, then a four-bar mechanism with one degree of freedom will convert to a five-bar mechanism with two degrees of freedom, and this complicates kinematic and dynamic analysis of the mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003287_s00170-020-06104-0-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003287_s00170-020-06104-0-Figure8-1.png",
        "caption": "Fig. 8 The effect of the part thickness on the deformation of the thin-walled part with a 60-mm part length and a 20-mm part height: a X-direction displacement distribution, b \u0394Lmax",
        "texts": [
            " It can be seen that\u0394Lmax stabilizes about 100 \u03bcm after the part length exceeds 100 mm. The reason for this is attributed to the fact that the shrinkage of the part is approximately proportional to the part length in LPBF [10]. However, when further increasing the length, the contact area between the substrate and the part also increases with the part length, resulting in an increase of the constraint strength provided by the substrate. Therefore, the \u0394Lmax no longer increases and tends to be stable. Fig. 8a depicts the simulated X-direction displacement distribution with different part thicknesses when the part length and height are constant at 60 and 20 mm, respectively. It can be seen that the deformation level decreases with the part thickness. When the part thickness increases from 1 to 5 mm, the \u0394Lmax decreases from 151.4 to 81.4 \u03bcm.When the part thickness is small, the thermal accumulation effect between tracks is obvious due to short scanning track and low thermal conductivity of the material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001629_iet-epa.2016.0728-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001629_iet-epa.2016.0728-Figure1-1.png",
        "caption": "Fig. 1 Configuration of 12/8 DSEM",
        "texts": [
            " The remainder of this paper is organised as follows. Section 2 presents the configuration and operation principle of DSEM. In Section 3, several control strategies are presented and analysed. A novel control strategy is proposed, with its operation principle is described in detail. Besides, the new control strategy is compared with other control strategies. In Section 4, field-circuit cosimulation results and experimental results verify the theoretical analysis. At last, the concluding remarks are given in Section 5. Fig. 1 shows the configuration of a 12/8-pole DSEM with threephase armature windings. A1\u2013A4, B1\u2013B4, and C1\u2013C4 are four stator poles for phases A, B, and C, respectively. The armature windings are wound around every stator pole, with four groups connected in series. The field winding is constituted by four pairs of coils in series connection, which is wound around every three poles. Three groups of windings are in a star connection. The salient pole width in stators is half of its pole distance. So, the overlapped angle of salient poles is irrelevant to the rotor's position, just a fixed value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure9.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure9.5-1.png",
        "caption": "Figure 9.5. A homogeneous block !1B havinga drilled hole.",
        "texts": [
            " In consequence, we shall need to know how to transform the inertia tensor components for each of the separate parts, from a reference frame at a point P conveniently chosen for calculation of the components for a separate part, to another reference frame at another point Q appropriate for the tensor components for the composite body. Before we tackle this problem, however, let us consider two examples of homogeneous bodies that require only a single reference frame . The second example is noteworthy because it shows that neither symmetry nor material homogeneity of a body is necessary for the vanishing of products of inertia . Example9.3. A homogeneous rectangular parallelepiped of length e and square cross section of side h has a circular hole of radius R drilled lengthwise through its center, as shown in Fig. 9.5. Determine the moment of inertia tensor components of the drilled block referred to the center of mass body frame rp = {C;ik}. The Moment of Inertia Tensor 369 Solution, The center of mass of the homogeneous drilled block !?l3 = !?l3s \\ fl is at the center of the hole. Here !?l3s denotes the solid rectangular block and fl identifies a homogeneous circular cylinder of the same material which we imagine fills the hole. Thus, with respect to ip, (9.36) yields (9.37a) Recalling (9.26) for a homogeneous solid parallelepiped with w =hand (9.31) for a homogeneous solid cylinder of radius R, bearing in mind the arrangement of the coordinate axes in Fig. 9.5 and in Fig. 5.3, page 13, for the cylinder, we obtain from (9.37a), referred to the body frame cp = {C; it}, f7l) msh 2 , . ms 2 2 ' . ' .IcCJOJ) = -6-111+12(h +e )(122+133) [ meR 2 ,. me ( 2 e 2 ) ' . ,.]- -2-111 + 4 R +\"3 (122 + 133) , (9.37b) wherein the mass m s of the solid block and me of the cavity body are given by (9.37c) Hence, by (9.4) , the mass of the drilled block is m(!?l3) = m s - me = pe(h2 - 7TR2). (9.37d) Use of (9.37c) and (9.37d) in (9.37b) yields the moment of inertia tensor components for the homogeneous, drilled parallelepiped referred to the center of mass frame ip: 1 m("
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000377_s11740-007-0041-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000377_s11740-007-0041-9-Figure2-1.png",
        "caption": "Fig. 2 Principle of gear rolling according to the round rolling procedure",
        "texts": [
            " Klug (&) U. Hellfritzsch Fraunhofer Institut Werkzeugmaschinen und Umformtechnik, Reichenhainer Stra\u00dfe 88, 09126 Chemnitz, Germany e-mail: dirk.klug@iwu.fraunhofer.de R. Neugebauer e-mail: reimund.neugebauer@iwu.fraunhofer.de U. Hellfritzsch e-mail: udo.hellfritzsch@iwu.fraunhofer.de \u2022 Cross rolling with flat tools \u2022 Cross rolling with round tools \u2022 Cross rolling with tools with inside profiles. Among these cross rolling processes, the cross rolling of gear teeth profiles on the round rolling principle (Fig. 2) is a technology that is on track for the future because it can produce very high piece numbers in shortest periods of time with optimum material application (constant volume when rolling). However, applying this principle to produce gear teeth of high or even quality makes it necessary to replace the previous empirical process layout with a process layout that encompasses and applies the overall interactions of machines, tools and process. Selected research findings will be showcased below on this problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000471_la904117e-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000471_la904117e-Figure4-1.png",
        "caption": "Figure 4. Sketch of the profile, z= \u03b6(x), of an elastic surface layer subjected to unidirectional compression (along the x-axis) in a Langmuir trough. The barriers are located at x = (L/2; ex is the unit vector of the x-axis; a1 is the respective unit vector of the surface basis, which is tangential to the curved membrane.",
        "texts": [
            " 146 DOI: 10.1021/la904117e Langmuir 2010, 26(1), 143\u2013155 balance, eq 2.2, in the form:10,11 r\u03bc\u03c3 \u03bcR \u00fe 2kcb R\u03bcr\u03bcH \u00bc 0 \u00f02:11\u00de b\u03bc\u03bd\u03c3 \u03bd\u03bc -2kca \u03bc\u03bdr\u03bcr\u03bdH \u00bc \u00f0pII-pI\u00des \u00f02:12\u00de See eqs C.60 and C.62 in Appendix C. Equations 2.11 and 2.12 represent the basis of our subsequent analysis. 3. Unidirectional Compression of an Initially Flat Langmuir Layer 3.1. Equations for the Shape of theDeformedMembrane. Let us consider a unidirectional compression of the membrane along the x1 axis, which leads to membrane wrinkling (Figure 4). We assume that initially the membrane has been flat, of length L\u00fe\u0394L along the x1 axis, and has been located in the plane z=0. It is convenient to introduce the notations: x \u00bc x1, y \u00bc x2, z \u00bc \u03b6\u00f0x\u00de \u00f03:1\u00de where z = \u03b6(x) describes the shape of the deformed membrane (Figure 4). For the considered case of unidirectional compression, in Appendix D (Supporting Information), it is proven that with the help of the rheological constitutive relation, eq 2.7, we can bring eqs 2.11 and 2.12 in the form: dux dx \u00fe 1 2 d\u03b6 dx 2 - dux dx 2 \" # \u00bc \u03c3L - kc 2 \u00f02H\u00de2 a Em \u00f03:2\u00de \u00f02H\u00de\u03c3m - kc 2 \u00f02H\u00de3 - kc a1=2 d dx 1 a1=2 d\u00f02H\u00de dx \u00bc g\u0394F\u03b6 \u00f03:3\u00de where the mean curvature, H, and the metric coefficient, a, are given by the expressions: 2H \u00bc 1 a3=2 d2\u03b6 dx2 , a \u00bc 1\u00fe d\u03b6 dx 2 \u00f03:4\u00de \u03c3L \u03c3m -\u03c30, Em Ed \u00feEsh \u00f03:5\u00de Equation 3",
            "12, we have taken into account the effect of the hydrostatic pressure, namely, (pII- pI)s = g\u0394F\u03b6, where g is the acceleration due to gravity and \u0394F is the difference between the mass densities of the two adjacent fluid phases. Equations 3.2 and 3.3 represent a system of two ordinary differential equations for determining the functions \u03b6(x) and ux(x). We consider the deformations of an elastic Langmuir layer with edges fixed to the barriers in the Langmuir trough, which leads to the following two boundary conditions (Figure 4): \u03b6 L=2 \u00bc \u03b6 -L=2 \u00bc 0 \u00f03:6\u00de ux L=2 \u00bc -\u0394L=2, ux -L=2 \u00bc \u0394L=2 \u00f03:7\u00de where \u0394L is the decrease of the distance between the two barriers upon compression of the Langmuir layer. 3.2. Area of the DeformedMembrane. For simplicity, here we will assume that z = \u03b6(x) is a single-valued function; see Figure 4. Then, the area of the membrane, Sm, can be expressed in the form: Sm \u00bc Ly Z L=2 -L=2 a1=2 dx \u00f03:8\u00de where a is given by eq 3.4 and Ly is the length of the membrane along the y-axis. Let us define the dimensionless area parameter, \u03b8, as follows: \u03b8 \u00bc Sm -Sp Sin -Sp \u00f00 < \u03b8 < 1\u00de \u00f03:9\u00de As before, Sm is the area of the deformed membrane (Figure 4); Sp is the projection of Sm on the xy-plane; Sin is the area of the membrane in its initial flat state (before the compression). If the membrane shrinks upon compression remaining flat, then Sm = Sp and the area parameter is\u03b8=0.For 0< \u03b8<1, themembrane simultaneously shrinks and curves (i.e., acquires a nonplanar shape). In the limiting case of an incompressible membrane, we haveSm=Sin, and then eq 3.9 yields\u03b8=1; that is, themembrane bends like a sheet of paper, without any changes in its area. The membrane is not expected to expand upondecreasing the distance between the barriers in the Langmuir trough, so that the expected values of the area parameter are in the interval 0 e \u03b8 e 1",
            "10, we obtain \u03b8 \u00bc Sm -Sp Sp Sp Sin-Sp \u00bc Sm -Sp Sp L \u0394L \u00f03:11\u00de Combining eqs 3.8, 3.10, and 3.11, we derive \u03b8 \u0394L L \u00bc Sm -Sp Sp \u00bc 1 L Z L=2 -L=2 \u00f0a1=2 -1\u00de dx \u00f03:12\u00de Equation 3.12, along with the expression for a in eq 3.4, allows one to calculate the area parameter, \u03b8, for a given \u0394L/L and membrane shape z = \u03b6(x). 3.3. Energy of the Deformed Membrane. As already mentioned, we consider the compressed state of an elastic Langmuir layer (membrane), whose edges are fixed to the barriers of the Langmuir trough (Figure 4). The boundary conditions, eqs 3.6 DOI: 10.1021/la904117e 147Langmuir 2010, 26(1), 143\u2013155 and 3.7, are insufficient for determining a unique solution of the system of eqs 3.2 and 3.3. To determine the physical solution of the problem, we will use also the natural requirement that the shape of the membrane must correspond tominimal energy of the system. Our next goal is to derive the expression for calculating the energy. Let us consider the change in the energy of the system upon an out-of-plane deformation of the membrane, \u0394W Wm -Wp \u00f03:13\u00de whereWp andWm are the energies of the system, respectively, in the states with planar and deformed membrane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure15-1.png",
        "caption": "Fig. 15. Pressure distribution in the oil film for Dd = 0.6 swivel angle change.",
        "texts": [],
        "surrounding_texts": [
            "On the basis of the presented theoretical background a computer program has been developed. By using this program, the influence of machine settings for pinion finishing as are: the sliding base setting (c), basic radial (e), basic offset setting (g), basic tilt angle (b), basic swivel angle (d), machine root angle (c1), velocity ratio in the kinematic scheme of machine tool (ig) and basic cradle angle (w0) (Fig. 2), on maximum oil film pressure (pmax) and temperature (Tmax), EHD load carrying capacity (W), and on power losses in the oil film (fT) was investigated. In this paper, the term of \u2018\u2018EHD load carrying capacity\u201d is used for the load calculated by Eq. (17) for a prescribed value of the minimum oil film thickness. The investigation was carried out for the hypoid gear pair of the design data given in Table 1. The starting machine tool setting parameters for the generation of pinion tooth blanks are given in Table 2, and the lubricant characteristics and operating parameters in Table 3. The obtained results are presented in Figs. 3\u201318. Factors kpmax , kTmax , kW and kfT represent the ratios of the maximum oil pressure and temperature, EHD load carrying capacity, and power losses in the oil film, calculated for varied machine tool setting parameters, and the same EHD characteristics obtained for the basic set of machine tool settings for pinion teeth finishing, given in Table 2. The pressure and temperature distributions in the oil film for the basic set of machine tool setting parameters are shown in Figs. 3 and 4. The maximum temperatures across the oil film are plotted. As it was mentioned earlier, a modified hypoid gear pair with theoretical point contact is treated. The investigations have shown [45] that as the tooth surface modifications are relatively small and the conjugation of the mating surfaces is relatively good, thus the point contact under load spreads over a surface along the whole or part of the \u2018\u2018potential\u201d contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal. In Figs. 3 and 4, this line of minimal separations is plotted. It can be noted that the crest of the pressure surface corresponds to this line. The influence of sliding base setting (c) on EHD lubrication characteristics is shown in Fig. 5. Several observations can be made: a small change in sliding base setting causes sharp increase in the maximum oil pressure and a moderate improvement of the EHD load carrying capacity. The change of the friction factor is quite opposite than that of the EHD load carrying capacity: with an increase in W the friction factor is reduced, and vise versa. Finally, the change in sliding base setting appears to have very little influence on maximum oil temperature. From Fig. 6, it can be seen that a sliding base setting change of Dc = 0.125 mm causes an increase in maximum oil pressure of 21% and 7% in EHD load carrying capacity, and also a reduction in friction factor of 4%. The influence of basic radial setting (e) is similar to that for sliding base setting (Figs. 7\u20139), but there is a significant drop in maximum oil pressure and EHD load carrying capacity for negative values of De, followed by a significant increase in power losses. Therefore, such a change of basic radial setting worsens the conditions of EHD lubrication and it should be avoided. The basic offset setting (g) of the head-cutter has a significant influence on the EHD lubrication characteristics, by its decrease the EHD load carrying capacity can be considerably improved and the friction factor reduced (Figs. 10 and 11). The adjustment of the basic tilt angle (b) should be made very carefully: a small decrease in its value significantly improves the EHD load carrying capacity, but its bigger change sharply reduces W and increases the friction factor (Figs. 12 and 13). The effects of the change of basic swivel angle (d, Figs. 14 and 15) and of machine root angle (c1, Fig. 16) are very similar to that of basic tilt angle. The other two machine tool setting parameters, the velocity ratio in the kinematic scheme of machine tool (ig, Fig. 17) and the basic cradle angle (w0, Fig. 18) have an almost identical effect on EHD lubrication as the other machine tool setting parameters: a small change in their adjustment moderately improves the load carrying capacity and reduces the friction factor, but their bigger changes have a negative effect on EHD lubrication."
        ]
    },
    {
        "image_filename": "designv10_12_0002866_s11012-019-01053-9-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002866_s11012-019-01053-9-Figure3-1.png",
        "caption": "Fig. 3 Model of a cracked tooth",
        "texts": [
            " According to the Timoshenko beam theory [29] and the structure of the tooth model, it is noteworthy that the integral between 0 and xb can be regarded as mainly determined by the deflection of the gear body, and the integral between xb and xF can be regarded as mainly determined by the deflection of gear tooth. To add the effect of teeth contact, the results derived by Yang and Sun [30] was taken into consideration to calculate the Hertzian contact stiffness as follows: kh \u00bc pEL 4\u00f01 t2\u00de \u00f017\u00de where t represent the Poisson\u2019s ratio. 2.3 Mesh stiffness model of a cracked tooth Assuming that there is a straight line crack at the root of the pinion, the crack is determined by crack depth lc and inclination angle h see Fig. 3. It should be note a1 \u00bc h p 2N1 inva0 \u00fe tan arccos N1 cos a0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0N2 \u00fe 2\u00de2 \u00fe \u00f0N1 \u00fe N2\u00de2 2\u00f0N2 \u00fe 2\u00de\u00f0N1 \u00fe N2\u00de cos arccos N2 cos a0 N2\u00fe2 a0 r 2 664 3 775 \u00f09\u00de that, in previous studies [15\u201318, 22\u201328], they supposed the cracked tooth is still a cantilever beamwith a fixed boundary at the root of the tooth, and the deflection of the gear body does not affected by the crack",
            " As for the case without axial compressive stiffness, it seems that the axial compressive stiffness has the least impact on the total mesh stiffness. 3.2 Effect of crack length and inclination angle on mesh stiffness According to the proposed analytical models, the stiffness of the cracked tooth and the adjacent tooth with different crack lengths and inclination angles are able to be calculated, the effect of crack on the mesh stiffness can be investigated. By defining the distance from point B to point E (lBE) as the maximum crack length (see Fig. 3), the cases where the inclination angle h = 45 and crack length lc increases by 25% of the maximum crack length lBE from 0 to lBE are calculated. The mesh stiffness with different percentage of crack length is plotted in Fig. 10. It is observed that the stiffness decreases with propagation of the crack length for both the cracked tooth and the adjacent tooth. For the purpose of evaluation the impact of the crack inclination angle on mesh stiffness, the cases where crack length lc = 50%lBE, lc = 2 mm, and inclination angle h increasing by 15 from 30 to 75 are simulated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000414_tac.2007.902750-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000414_tac.2007.902750-Figure5-1.png",
        "caption": "Fig. 5.",
        "texts": [
            " Then there exists a point x1 2 2 such that the reachable set R(x1) 6= 2. Now, there must exist a point z 2 @(R(x1)), where @(R(x1)) is the boundary of R(x1). Finally, we prove the sufficiency of Theorem 2.1 by considering the following two cases, and either case will result in a contradiction. Case 1. det(f(x1); g(x1)) 6= 0. By the Jordan curve-like theorem and Lemma 4.1, the control curve 1 passing through z separates the plane into two disjoint components, which are also named Side-A and Side-B, respectively, as shown in Fig. 5. For any small neighborhood U(z) of z; 1 separates U(z) into two disjoint parts, and we call them Part-A and Part-B which are included in Side-A and Side-B, respectively. Therefore, U(z) is separated by 1 into three parts, Part-A, Part-B and the segment of 1 in U(z). By Lemma 4.3, it is easy to know that there must exist infinite many reachable points in Part-A or Part-B of any small neighborhood U(z) of z . Therefore, without loss of generality, we assume that there exist infinite many reachable points in R(x1) which lie in Part-A. Let a normal vector of 1 be ~g(x) = ( g2(x); g1(x)) T ; x 2 1. Then ~g(x) must point to one of the two side separated by 1. Without loss of generality, we suppose ~g(x) points to the Side-B as shown in Fig. 5. By the condition of Theorem 2.1, there exists a point y 2 1 such that g1(y)f2(y) g2(y)f1(y) > 0, then the vector field of (2) at y under any control u must point to the Side-B. We may suppose that there exists a small enough neighborhood U(y) of y such that g1(x)f2(x) g2(x)f1(x) > 0;8x 2 U(y), and the control curve in U(y) can be viewed as a series of parallel straight-lines. By our assumption above, there exists a point z1 2 R(x1)\\ Part-A such that the control curve 2 passing through z1 reaches U(y). Since z1 is in the Part-A, 2 Side-A as shown in Fig. 5. LetL be a straightline passing the point y and perpendicular to 1 in U(y) as shown in Fig. 5. By Lemma 4.2, there exist two controls u2(x) and u1(x) such that the positive semi-trajectory 2 and the negative semi-trajectory 1 with initial z1 and z reachL at z2 and z3, respectively, and z2 is located above z3 as shown in Fig. 5. By the methods of Lemma 4.3, we have z3 2 R(z2), therefore, z 2 R(x1) by Lemma 4.4. Hence, z is the inner point ofR(x1), which contradicts with our assumption. Therefore, R(x1) = 2. Case 2. det(f(x1); g(x1)) = 0. Let 3 denote the control curve of (2) passing through x1. By the condition of Theorem 2.1, there is a point x2 such that det(f(x2); g(x2)) 6= 0. By Lemma 4.2, there exists a control u1(x) such that the positive semitrajectory 1 with initial point x1 reach a point x3, i.e., x3 2 R(x1) and det(f(x3); g(x3)) 6= 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003106_aris50834.2020.9205794-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003106_aris50834.2020.9205794-Figure9-1.png",
        "caption": "Figure 9. Robot's Configuration.",
        "texts": [
            " However, all the current methods using conventional machine learning with stationary cameras suffer from some severe limitations, perceptual aliasing (e.g., different places/objects can appear identical), occlusion (e.g., place/object appearance changes between visits), seasonal / illumination changes, significant viewpoint changes, etc. This work [7] proposes a perception module using end-to-end deeplearning and visual SLAM (Simultaneous Localization and Mapping) for an effective and efficient object recognition and navigation using a differential-drive mobile robot as shown in Figure 9. The detection result is shown in Figure 10. This work proposes the use of ground mobile robots equipped with micro-spectrometers as shown in Figure 11 for remote chemical content detection [8]. The proposed navigation system is robust under various uncertain factors, and the robot can effectively and efficiently act in various environments. The micro-spectrometer identification system successfully classified various samples. The mobile robot is a two-wheel differential drive mechanism with 8 forward sonars"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001311_icuas.2013.6564711-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001311_icuas.2013.6564711-Figure1-1.png",
        "caption": "Fig. 1. arm 3D model and built prototype.",
        "texts": [
            " In order to fulfill these objectives, the strategy followed has considered the following steps: first, a realisation of this novel concept has been designed using COTS materials to produce a prototype quadrotor; second, a mathematical model has been developed of all the relevant actuation phenomena; third, based on this model a conventional control system has been designed to stabilise the vehicle; and finally the vehicle has been flight tested and some fault tolerance experiments have been carried out. In following sections, the design and prototyping of the quadrotor will be first presented. Then, an overview of the simulation model will be described. Next, the tests performed will be introduced after outlining the design of the control system. Finally, an analysis and discussion of the results are presented. A realisation of this novel arm concept is shown in Figure 1(a). Here we have used commercially available parts to minimise the number of custom manufactured parts. This design is based around the servoblock [13] part which serves as a frame to mount a standard size RC servo which allows it to move the whole arm around its axis. Another servo mounted in the arm is connected through a pushpull mechanism to the motor mount which swivels parallel to the servo lever. Thus, the propeller rotational axis can be freely configured with the two angles generated by the servomotors. These two angles/motions are named push-pull and servoblock. The vehicle prototype can be seen in Figure 1(b). The dimensions of the vehicle with a nominal three Kg weight is illustrated in the plans of Figure 2. The servomotors used at the servoblock and pushpull are the HS-7940TH by Hitec. The propellers are three bladed because of the even distribution of its mass and inertia, the model is the master airscrew 3 blade 12x6 in. The motors used are the brushless DC outrunners MK3638 by Mikrokopter. The ESC used were the Roxxy Bl Control 930-6 from Robbe. The vehicle had two batteries, one to power the servomotors, a LiPo 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003616_16878140211034431-Figure33-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003616_16878140211034431-Figure33-1.png",
        "caption": "Figure 33. Methods of metal powder embedding: powder mechanically inserted into the tool.93",
        "texts": [
            " While cold spraying,96 laser melting,97 thermal spraying,98 and other surface additive technologies only modify the surface of the substrate, defects such as poor bonding performance, pores, and cracks may exist. Metal powder assisted AM uses friction stir processing or friction surfacing in the subsequent process to make up for these defects.99,100 There are many ways to add metal powder in the additive process. Some scholars have changed the friction stirring tool to act as a carrier of metal powder. Figure 33 shows one typical powder embedding methods. The method of adding powder includes embedding to the substrate or the rod, cold spraying and hot spraying. The metal powder processing methods are friction stir processing and friction surfacing. Table 4 summarizes the parameters of metal powder, including the size of metal particles, layers, rotation speed, traverse speed, shape and size of stirring tool, and processing method. Powder size. The smaller the size of the metal powder, the easier to bond with the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002284_j.advengsoft.2018.05.005-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002284_j.advengsoft.2018.05.005-Figure1-1.png",
        "caption": "Fig. 1. Main components and the loads on the studied TRB when the external loads on it have standard values: (a) Values of gap \u03b4top and \u03b4bottom that are similar. (b) Contact stress distribution on the outer raceway when there is no roller takeoff. The external loads on the TRB have values that are correct: (c) Different values of gap \u03b4top and \u03b4bottom. (d) Outer raceway contact stress distribution when there is roller takeoff [1].",
        "texts": [
            " In order to achieve this, the proposed machine learning methods were applied to the dataset that was obtained from the FE model of the double-row TRB under several loads that define the operating conditions following the Design of Experiments (DoE). Then, several models were created and trained. Meanwhile, feature reduction and transformation, and tuning of parameters were carried out. Later, the models that were selected were tested to determine their degree of generalization on the basis of to several robustness criteria [13\u201315]. Fig. 1(a) shows how the combination of loads (P, Fa, Fr and T) are applied on each of the TRB parts. P loads are applied on the inner raceway, whereas Fa, Fr and T loads are applied on the outer raceway. The inner raceway has two equal parts, which are separated by \u03b4 to enable the TRB to be disassembled, as well as to be able to apply the P. It is understood that how the loads that affect the TRB are combined, the bearing may malfunction. For example, if the combined loads on the TRB are equal in value to what the manufacturer recommended, the \u03b4 on the top (\u03b4top) should be the same as that on the bottom (\u03b4bottom) (Fig. 1(a)). Also, the outer raceway's top and bottom zones have contact stresses with a value other than zero (Fig. 1(b)). In this situation, all rollers maintain mechanical contact with the inner and outer raceways at all times. Also, there will not be high values of contact stresses and the localized deformations (\u03b1). This will avoid the appearance of fatigue spalling and pitting. In contrast, if the values of the loads on the bearing were not correct (i.e., high values of Fr and T, highly combined with low values of P), the gap on the top (\u03b4top) and the bottom (\u03b4bottom) they would have been different. Consequently, there would be faulty operation of the TRB (Fig. 1(c)). Further, there a value of normal contact stresses of nearly zero for only a small area of the outer raceway's upper zone (Fig. 1(d)). In this situation, the contact stresses on the top zone of the outer raceway will be very high (even higher than 1000 MPa), whereas the outer raceway's bottom zone has a contact stress value of zero. This would lead to the appearance of pitting and fatigue spalling and, therefore, to a malfunction of the TRB. In order to quantify the take-off effect of the contact rollers with both raceways, the S ratios for each of the two columns of rollers of the TRB are defined by the below equation. =Contact Ratio S S S ( ) \u00b7100top bottom (1) where Stop is the top contact stress and Sbottom is the bottom contact stress obtained for each of the two columns of rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure8.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure8.4-1.png",
        "caption": "Fig. 8.4 Stand for measurement of the precession torque acting around axis oy",
        "texts": [
            " The results of the deactivation of the inertial forces present a new direction in the study of the physics for the complex action of inertial torques generated by the rotating objects [20]. The blocking of the gyroscope rotation around axis oy deactivates all inertial torques generated by the rotatingmass elements of the spinning rotor. However, this blocking does not lead to the deactivation of the precession torque of the change in the angular momentumacting around axisoy. The validation of the action of the precession torque and the measure of its value is conducted on the stand that represented in Fig. 8.4. The gyroscope stand additionally equipped with the angular rocker that transfers the action of the precession torque to the digital scale. The sketch of the stand is represented in Fig. 8.5. The bar of the gimbal is contacted with the angular rocker that presses the platform of the digital scale of Model TS-SF 400A with division one gr. The digital scale has demonstrated the value of the force generated by the precession torque. The practical result is compared with the theoretical value of the force of the precession torque computed for the horizontal location of the running gyroscope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001394_jab.29.3.279-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001394_jab.29.3.279-Figure2-1.png",
        "caption": "Figure 2 \u2014 Top view (left) and back view (right) at the moment of ball bat impact by a batter (middle). Impact Z deviation is the distance between the ball center (rImp) and the sweet spot of the bat (white circle; rSS) in the direction of bZ.",
        "texts": [
            " A recording of the calibration points with cameras 1 and 2 was conducted both before and after the batting tasks. To test the accuracy and reliability of this measurement method, one investigator digitized two reference markers on a swung bat for five frames on two separate occasions. The standard error between actual value (0.450 m) and calculated value (mean \u00b1 SD = 0.453 \u00b1 0.0004) was less than 2%. For the test-retest reliability of the distance, r was = 0.953. To clarify the spatial relationship between the bat\u2019s sweet spot and the ball at the point of impact, the \u201cimpact Z deviation\u201d is calculated (Figure 2). First, the bat vector is defined as lying on the long axis of the bat and as being oriented from the bat grip to the top. Then, the impact Z deviation can be computed as Impact Z deviation = bZ \u00b7 (rImp \u2013 rSS) (1) where bZ = unit vector that is perpendicular to the bat vector directed upward in the vertical plane, rImp = position of the ball center at impact, and rSS = position of the sweet spot at impact. The impact Z deviation provides a measure of hitting accuracy in the direction perpendicular to the bat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000963_robot.2010.5509785-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000963_robot.2010.5509785-Figure2-1.png",
        "caption": "Fig. 2. Models for ankle (a) and hip (b) strategies.",
        "texts": [
            " In these cases, a straightforward modification of the above equations can be done, as shown in [24] under the name \u201cselective Reaction Null Space.\u201d In our previous work [21], [25], we have introduced a way of implementing the ankle and hip strategies for generating response and balance recovery patterns with a small humanoid robot HOAP-2 [22], subjected to impacts on the back or on the chest while standing upright. The ankle and hip strategies are phenomena occuring in the sagittal plane. Therefore, simple planar models have been used to develop the response patterns for each of the strategies (see Fig. 2). The ankle strategy was modeled with the help of a simple inverted pendulum (Fig. 2 (a)). A virtual spring\u2013damper was attached to the ankle joint to ensure compliant response to the impact force. The initial response rate in that joint was calculated via impact force estimation from the built-in acceleration sensor. The hip strategy, on the other hand, was modeled with the help of a double\u2013inverted pendulum (Fig. 2 (b)). A virtual spring\u2013damper was attached to the hip joint, thus ensuring compliant response to the impact force with predominant motion in the hip. In addition, the CoM ground projection 2With static initial conditions. was kept constant by applying the RNS method. Thus, a small compensatory motion in the ankle joint was generated. In what follows, we will describe an extension of the method, such that the robot will be equipped with the ability to respond to a continuous external force, in addition to the impacts. In the absence of external forces, the equation of motion for the model shown in Fig. 2 (a) can be written as: (I + ml2g)\u03b8\u03081 \u2212 mgrx = \u03c41 \u2212 Ca\u03b8\u03071 \u2212 Ka\u03b81, (9) where m = m1 + m2 is the total mass, lg is the distance from the ankle to the CoM, rx = lg sin \u03b81 is the CoM ground projection, g is the gravity acceleration, I is the moment of inertia, and the other parameters are obvious from the model. Further on, denote by p the position of the ZMP. Then, the moment equilibrium on the foot can be expressed as: mg(p \u2212 rx) = mr\u0308xrz + mr\u0308z(p \u2212 rx), (10) where rz = lg cos \u03b81 is the vertical projection of the CoM",
            " Considering (7), we note first that, for the double invertedpendulum model under consideration, the coupling inertia Hfl \u2208 1\u00d72 and the joint coordinate vector contains the two joint angles (ankle and hip). Further on, integrate (7) to obtain the constant coupling momentum: Hfl\u03b8\u0307 = L. (12) Zero initial conditions are assumed: L = 0. Hence, we obtain the following set of reactionless joint velocities: {\u03b8\u0307RL} = {bn}, (13) where b is an arbitrary scalar and n \u2208 2 is in the kernel of Hfl. Referring to the model in Fig. 2 (b), we can write: n = [ \u2212m2lg2C12 (m1lg1 + m2l1)C1 + m2lg2C12 ] , (14) where C1 = cos \u03b81 and C12 = cos(\u03b81 +\u03b82). Then, from (13) and (14) we obtain the following relation: \u03b8\u03071 ref = \u2212m2lg2C12 (m1lg1 + m2l1)C1 + m2lg2C12 \u03b8\u03072 ref . (15) \u03b8\u03072 ref is the reference hip joint rate. It is calculated from the single inverted pendulum equation for the upper body link. Referring to (11), we can write: \u03b8\u03082 ref = 1 I2 + m2l2g2 ( m2g (p \u2212 rx) \u2212 Ch\u03b8\u03072 \u2212 Kh\u03b82 ) , (16) where I2 is the inertia moment of the upper body, and the rest of the parameters should be clear from Fig. 2. Consider the displacement of the CoM during the two strategies. As seen from Fig. 2 (a), during the ankle strategy, the CoM is displaced in a way that its ground projection rx remains within the base of support (BoS). On the other hand, during the hip strategy, the CoM is displaced only in the vertical direction, whereas its ground projection remains stationary (cf. Fig. 2 (b)). The aim of the transition between the ankle and the hip strategy is to ensure that, in addition to hip motion initialization, the CoM ground projection will also move back swiftly to the position of the erected posture, after reaching the BoS boundary during the ankle strategy. In order to ensure such movement of the CoM, we have to consider the CoM velocity: r\u0307 = Jc\u03b8\u0307, (17) where Jc \u2208 2\u00d72 denotes the CoM Jacobian matrix. This equation is projected onto the x axis: r\u0307x = Jcx\u03b8\u0307. (18) Note that matrix Jcx \u2208 1\u00d72 is related to the coupling inertia matrix: Jcx = 1 m Hfl"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure18.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure18.1-1.png",
        "caption": "Fig. 18.1 Spherical four-bar mechanism. General case (a) and planar case (b)",
        "texts": [
            "12b is a cluster of four congruent quadrilaterals Q1 , Q2 , Q3 , Q4 grouped around center 01 . In what follows, it is referred to as cluster 1 . When it is isolated from the surrounding quadrilaterals, it represents a spherical four-bar with constant angles \u03b11 , \u03b12 , \u03b13 , \u03b14 and with axes along unit vectors n1 , n2 , n3 , n4 pointing away from 01 . Notation: \u03b1i (i = 1, 2, 3, 4) is the internal angle of Qi at 01 . The variable angle of rotation of Qi relative to Qi\u22121 about ni is called \u03d5i (i = 1, 2, 3, 4 cyclic; \u03d5i = 0 in the planar position). This is the notation used in Fig. 18.1a . For a given angle \u03d51 the spherical four-bar can assume two positions. Two solutions \u03d54 as functions of \u03d51 are determined by Eqs.(18.2), 4.2 Illustrative Examples 155 (18.3). With cyclic permutations of indices the same equations relate other pairs of neighboring angles so that also \u03d52 and \u03d53 are determined as functions of \u03d51 . If (\u03d51 , \u03d52 , \u03d53 , \u03d54 ) is a solution then, because of the symmetry to the plane, also (\u2212\u03d51 , \u2212\u03d52 , \u2212\u03d53 , \u2212\u03d54 ) is a solution. In what follows, \u03d51 > 0 is assumed. The equations reveal the following facts",
            ") (1976) Autorenkollektiv: Getriebetechnik \u2013 Lehrbuch VEB, Berlin 43. Volmer J (ed.) (1979) Getriebetechnik-Koppelgetriebe. VEB, Berlin 44. Volmer J (ed.) (1992) Getriebetechnik-Grundlagen. Verl. Technik, Berlin 45. Watson G A (1980) Approximation theory and numerical methods. Wiley, New York 46. Wunderlich W (1970) Ebene Kinematik. BI-Verl. Mannheim Chapter 18 Spherical Four-Bar Mechanism From Sect. 5.4.1 it is known that the spherical four-bar mechanism or briefly spherical four-bar is a special mechanism RCCC . Figure 18.1a is a copy of Fig. 5.4 . The four-bar has four revolute joints the axes of which intersect in a single point 0 . The links are shown as arcs of great circles on the unit sphere about 0 . Constant parameters \u03b1i > 0 , joint variables \u03d5i and associated unit vectors ni and ai (i = 1, . . . , 4) were defined as follows. The unit vectors n1, . . . ,n4 along the joint axes are pointing away from 0 . The unit vector ai has the direction of ni \u00d7 ni+1 (here and in what follows, i = 1, . . . , 4 cyclic). The angle \u03b1i is the angle about ai from ni to ni+1 ",
            " Since the spherical four-bar is a special mechanism RCCC , it is governed by the same 639 J. Wittenburg, Kinematics, DOI 10.1007/978-3-662-48487-6_ 18 \u00a9 Springer-Verlag Berlin Heidelberg 2016 640 18 Spherical Four-Bar Mechanism equations relating joint variables \u03d51, . . . , \u03d54 and parameters \u03b11, . . . , \u03b14 . On the other hand, the spherical four-bar shares many characteristics with the planar four-bar. In the limit \u03b1i \u2192 0 (i = 1, 2, 3, 4) it is a planar four-bar in a plane tangent to the sphere (Fig. 18.1b). The transfer function relating the angles \u03d51 and \u03d54 is known from the analysis of the mechanism RCCC . It is copied from (5.43) and (5.44): A cos\u03d54 +B sin\u03d54 = R (18.1) with coefficients (abbreviations Ci = cos\u03b1i and Si = sin\u03b1i ) A = \u2212S3(S4C1 + C4S1 cos\u03d51) , B = S1S3 sin\u03d51 , R = C2 \u2212 C3(C4C1 \u2212 S4S1 cos\u03d51) . } (18.2) The equation has two solutions \u03d54 which are determined by their sines and cosines: cos\u03d54k = AR+ (\u22121)kB \u221a A2 +B2 \u2212R2 A2 +B2 , sin\u03d54k = BR\u2212 (\u22121)kA \u221a A2 +B2 \u2212R2 A2 +B2 \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (k = 1, 2) . (18.3) In the case \u03b1i 1 (i = 1, 2, 3, 4), when the spherical four-bar approximates a planar four-bar in a plane tangent to the sphere the coefficients A , B , R are represented by their second-order approximations A \u2248 \u2212\u03b13(\u03b11 cos\u03d51 + \u03b14) , B \u2248 \u03b11\u03b13 sin\u03d51 , R \u2248 \u03b11\u03b14 cos\u03d51 \u2212 1 2 (\u03b1 2 2 \u2212 \u03b12 1 \u2212 \u03b12 3 \u2212 \u03b12 4) . } (18.4) Compare this with the transfer function of the planar four-bar given in (17.10) and (17.11). In these equations the following changes of notation are necessary (see Fig. 18.1b). The input angle \u03d5 of the planar four-bar is identified with \u03d51 \u2212\u03c0 and the output angle \u03c8 with 2\u03c0\u2212\u03d54 . The link lengths r1 , a , r2 , of the planar four-bar are given the new names \u03b11 , \u03b12 , \u03b13 , \u03b14 , respectively. Following these changes (17.10) and (17.11) are identical with (18.1), (18.4). 18.2 Grashof Type Conditions 641 Grashof\u2019s conditions for the planar four-bar were deduced from Figs. 17.1a,b,c which show limit positions of the input link. These positions are characterized by collinearity of coupler and output link",
            " Equation (18.47) yields C7 = \u22121/3 . The coupler curve with these parameters is bicursal with two cusps in each branch. It is shown in Fig. 18.6 together with the curve \u03c4 in the same stereographic projection that was used in Fig. 18.5 . 656 18 Spherical Four-Bar Mechanism In Fig. 18.7 a spherical four-bar with coupler triangle and with coordinate systems x, y, z and x\u2217, y, z\u2217 is shown. The parameters \u03b11, . . . , \u03b17 , the variables \u03d51 , \u03d54 and the axial unit vectors n1 , n2 , n3 , n4 are those of Fig. 18.1a . The x, y, z-system with unit basis vectors ex , ey , ez is defined in the text preceding (18.25). The x\u2217, y, z\u2217-system is rotated against the x, y, zsystem through the angle \u03b14 about the y-axis. The transformation is\u23a1 \u23a3x y z \u23a4 \u23a6 = \u23a1 \u23a3 C4 0 S4 0 1 0 \u2212S4 0 C4 \u23a4 \u23a6 \u23a1 \u23a3x\u2217 y z\u2217 \u23a4 \u23a6 . (18.49) The coupler triangle is defined as usual by the parameters \u03b15 , \u03b16 , \u03b17 . In addition, angular parameters \u03b7 , \u03b6 of the coupler point C and the auxiliary angle \u03c7 are introduced. The parameters \u03b7 , \u03b6 are equivalent to the parameters of equal name in the coupler triangle of the planar four-bar in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.27-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.27-1.png",
        "caption": "Fig. 15.27 Wheel 1 inside wheel 0 . For the straight-line position shown the parameters are r0 = 5 , r1 = 2 , b = 1 . In the small figure wheel 0 is inside wheel 1",
        "texts": [
            " From this it follows that the two areas denoted A2 and A3 are identical and that, furthermore, A(0) = \u22122A1 = A(1) \u2212 \u03c0 2 . With the side length L of the triangle A(1) = L2 \u221a 3/4 and = L \u221a 3/4 . Hence the area of the oval is A1 = 1 32L 2(3\u03c0 \u2212 4 \u221a 3) . Trochoids are trajectories of points C fixed on a planetary wheel 1 which is rolling on a stationary sunwheel 0 . In Figs. 15.26 and 15.27 all possible arrangements of wheels are shown. In Fig. 15.26 the wheels are touching each 496 15 Plane Motion other from the outside, and in Fig. 15.27 one wheel is inside the other. The one inside may be either wheel 1 or wheel 0 (see the small figure). The point C fixed on wheel 1 is located at a radius which is either smaller than or equal to or larger than the radius of wheel 1 . Depending on the arrangement of the wheels and on the location of C on wheel 1 trochoids come in many different shapes. This makes them interesting for engineering applications. Mathematical investigations of trochoids started very early because of their role in the explanation of orbits of solar planets by cycles and epicycles (de la Hire [14], J"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.17-1.png",
        "caption": "Fig. 13.17 Point Q fixed at radius a on the rotating shaft 1 (rotation angle \u03d5 ) is projected parallel to the z1-axis into the point P(\u03d5) in the fixed x, y-plane. Another point P0(\u03d5) in the x, y-plane",
        "texts": [
            "42) Solving for sin\u03b21,2 results in the formulas sin\u03b21,2 = (h/r) tan\u03b1/2\u00b1 \u221a 1 + tan2 \u03b1/2\u2212 (h/r)2 1 + tan2 \u03b1/2 . (13.43) An animation of the motion is on display in Wikipedia Homokinetisches Gelenk. The tripod joint shown in Fig. 13.16 is another ball-in-track coupling. Its kinematics was investigated by Roethlisberger/Aldrich [16], Duditza [5], Duditza/Diaconescu [6], Durum [8], Orain [12, 13] and Akbil/Lee [1, 2]. In what follows, an elementary analysis is presented. Imagine that in the fixed cartesian x1, y1, z1-system of Fig. 13.17 the shaft labeled 1 is rotating about the z1-axis. The rotation angle is \u03d5 . A point Q fixed on the shaft at radius a is moving on a circle. In the position \u03d5 of the shaft Q has the coordinates x1(\u03d5) = a cos\u03d5 , y1(\u03d5) = a sin\u03d5 . The circle and this point Q(\u03d5) are 4 The dimensions chosen in the figure are unrealistic because they allow only small variations of the angle \u03b1 408 13 Shaft Couplings projected parallel to the z1-axis onto the x, y-plane of another fixed x, y, zsystem which is inclined against the x1, y1, z1-system by an angle \u03b1 about the x1-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003194_s40684-020-00203-9-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003194_s40684-020-00203-9-Figure3-1.png",
        "caption": "Fig. 3 Distortion measuring of specimens Fig. 4 Sheet thickness distribution from ATOS measurements (before deposition)",
        "texts": [
            " The preformed specimens are slightly bent, so they were previously measured with the 3D scanner. The bending occurs because of springback effects after the laser cutting of the flat pyramid walls. The given surface model of the sheet is referenced to a plane and the maximum distance of the surface of the sheet to the reference plane is the initial offset of distortion w0. After the LMD process the sheets are measured again to determine the caused distortion of the additive process due to the difference between these two displacements into z-direction w1. The measuring setup is shown in Fig.\u00a03 schematically. The maximum melt pool temperature was measured with the temperature measuring system \u201cE-MAqS\u201d by the Frauenhofer institute IWS Dresden. This system is directly integrated into the laser head and measures in\u00a0situ and coaxial along the powder nozzle so that the melt pool is recorded from the top. The field of view is about 2 \u00d7 2\u00a0mm2, the sampling rate is 100\u00a0Hz and the average temperature deviation was \u00b1 3\u00a0K. The data of the melt pool temperature is combined with the local and temporal laser position by the 1 3 software AMAnalyzer by DMG MORI"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001366_1.4745081-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001366_1.4745081-Figure3-1.png",
        "caption": "FIG. 3. Scheme of SLM (Fraunhofer ILT Refs. 13, 23, and 27).",
        "texts": [],
        "surrounding_texts": [
            "Both LAM processes LMD as well as SLM are welding processes with powder (or wire) additives, resulting in almost 100% dense parts. Hence, the often\u2014and wrongly\u2014used synonym \u201csintering\u201d in the case of SLM is misleading because SLM is not a diffusion controlled process in the solid state such as hot isostatic pressing or sintering itself. The mechanical properties of the parts built-up are comparable to those that are conventionally manufactured mechanically by subtractive methods. Depending on the thermal history of the part built-up due to the layer-by-layer thermal manufacturing process, achieving proper mechanical properties can also be reliant on the appropriate post weld heat treatment in order to (re-)adjust the microstructure.2\u20135 Selected characteristics of both processes are provided in Fig. 5. Both processes are rapid melt and (re-)solidification processes and the driving forces for the microstructure formation are the local cooling rates and temperature gradients at the liquid\u2013solid interface. Melting and (re-) solidification is ca. 100 times faster in terms of SLM compared to LMD, resulting in a finer microstructure. The main differences between LMD and SLM are as fol- lows (Fig. 5): \u2022 The part dimensions in terms of SLM are restricted due to the fact that the process is conducted in a processing cham- ber with a limited volume, e.g., 250 250 250 mm3. \u2022 The\u2014geometric\u2014part complexity in terms of SLM is almost unrestricted due to the powder bed based process. Internal hollow structures can be produced. \u2022 Due to the powder bed based principle of SLM, the part can only be built-up on a flat substrate or preform. The current main R&D foci in LMD as well as in SLM are process layout specific, material, monitoring, fundamental (light/matter interaction) and systems engineering areas\u2014 compare Fig. 6\u2014such as \u2022 Enlargement of the processible materials toward other metals [e.g., Al (Ref. 6) and Cu (Ref. 7) alloys] directionally solidified and single crystal nickel base alloys [e.g., CMSX-4 (Refs. 8 and 9)] intermetallics [e.g., TiAl (Refs. 10 and 11) and NiAl (Ref. 12)] polymers and biodegradable materials [e.g., PEEK, polylactide (Ref. 13), b-TCP (Ref. 14), calcium polyphosphate (Ref. 15)] metal matrix composites (MMCs) and ceramic metal composites CMCs [e.g., TiC/Ti (Ref. 16) and hard particles (Ref. 17)], and ceramics [e.g., Al2O3\u2013ZrO2 (Ref. 18)] \u2022 Increase in the deposition rate (Refs. 19 and 20) \u2022 Increase in the detail resolution by decrease of the achiev- able minimum structure size (Ref. 21) \u2022 Decrease in the distortion and the surface roughness (Refs. 22\u201326) \u2022 Process monitoring and control (Refs. 27 and 28) \u2022 New design methods including topography and topology optimization (Ref. 23). Although many aspects have been already addressed process specifically and the advantages of AM become obvious and visible, the number of industrial implementations is still limited and AM remains a niche application for the most markets. Industrial production requires manufacturing processes and machines/systems that are of certain \u2022 speed, \u2022 robustness, \u2022 reliability, \u2022 affordability, \u2022 traceability, and \u2022 reproducibility. The first industrial implementation for a (customized) large-scale production of dental implants, bridges, and crowns has been in the dental sector since 2002. The rate of This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 138.251.14.35 On: Sat, 20 Dec 2014 23:38:17 production, and subsequently the deposition rate, was not crucial due to the small size and individual manufacture of the parts. The improvement of SLM from a niche application in dental restoration and the improvement of LMD from a pure cladding process for wear and corrosion protection and for maintenance, repair, and overhaul (MRO) of high-value components toward industrial relevant AM processes for large-scale production, e.g., in the tool, die, mold making, turbo machinery, and automotive fields of application, necessitate consideration of the existing industrial environment consisting of entire process and supply chains and the resources, time, material, energy, and humans."
        ]
    },
    {
        "image_filename": "designv10_12_0002664_j.mechmachtheory.2019.103608-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002664_j.mechmachtheory.2019.103608-Figure2-1.png",
        "caption": "Fig. 2. Planar revolute joint.",
        "texts": [
            " However, that involved in the constraint conditions below actually are parameterized in Cartesian coordinate system. In essence, when the displacement is infinitely small, it is supposed that there is no distinction between these two parameterizations. Accordingly, the constraints in what follows are available for both parameterizing ways, and we no longer deliberately distinguish them. 2.1. Planar revolute joint The influence of clearance on the pose deviation is discussed at first. As shown in Fig. 2 , the presence of clearance makes the frame fixed on the journal have a free translation relative to that fixed on the bearing. Let x prc = (0, x, y ) T represent the relative pose error. In a homogenous form, g prc = exp ( X prc ) (8) where X prc = x \u2227 prc = [ 0 0 x 0 0 y 0 0 0 ] . (9) Here, the \u2227 operator is opposite to \u2228 and converts a column vector into a matrix-form Lie algebra. Because of the geometric restriction, the journal actually has to locate within the bearing. Mathematically, x 2 + y 2 \u2264 r 2 pr (10) where r pr is the clearance size and equals r b \u2212r j "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001610_s11071-017-3369-5-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001610_s11071-017-3369-5-Figure3-1.png",
        "caption": "Fig. 3 Interpretation of nonlinearities as input-dependent disturbance: a dead zone and b backlash",
        "texts": [
            " Assumption 1 The poles and zeros of the linear part of the system, (A, B, C), are on the open left half-plane. Assumption 2 The linear part of the system, (A, B, C), is controllable and observable. Assumption 3 The output of the nonlinearity is not measurable. That is, the coefficients br and bl in (2) and sr and sl in (3) are unknown. Assumption 3 is an obstacle to constructing an inverse of the dead zone or backlash. So, the method in [9] cannot be used to compensate for them. We decompose the input nonlinearity,\u03a8 (\u00b7), into two parts (Fig. 3): \u03a8 (u(t)) = u(t) + d(u(t)), (4) where u(t) is the linear part and d(u(t)) is the rest. For the dead zone, d(u(t)) = \u23a7\u23a8 \u23a9 \u2212br , u(t) > br , \u2212u(t), bl \u2264 u(t) \u2264 br , \u2212bl , u(t) < bl (5) and for the backlash, d(u(t))= \u23a7\u23a8 \u23a9 \u2212sr , u\u0307(t)>0 & \u03a8\u0307 (u(t))>0, \u2212sl , u\u0307(t)<0 & \u03a8\u0307 (u(t))<0, u(t_) \u2212 u(t), otherwise. (6) It is clear from Fig. 3 that d(u(t)) is bounded, and there exists a constant dM > 0 such that |d(u(t))| \u2264 dM , \u2200t > 0. (7) Substituting (4) into (1) enables us to write the system (1) as (Fig. 4){ x\u0307(t) = Ax(t) + B[u(t) + d(u(t))], y(t) = Cx(t) (8) and treat the nonlinear part, d(u(t)), as an inputdependent disturbance. In this way, we have transformed the problem of compensating for the nonlinearity of the system (1) into the problem of rejecting the disturbance, d(u(t)), in the system (8). This section explains how to use the EID approach to devise a mechanism that automatically estimates and compensates for the disturbance, d(u(t))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure2-1.png",
        "caption": "Fig. 2. General model of a conventional CDPR.",
        "texts": [
            " Section III introduces ACTRs with land-fixed winches and finds the limitations of UAVs in providing tension in their connected cables. Section IV finds the collision-free arrangement of the UAVs. Section V defines and formulates the performance index and provides an optimization approach to find it. Section VI presents a case study and simulation results. Finally, Section VII concludes this article. In this section, AW and SAW derivation in the conventional pointmass CDPRs is reviewed. Consider a generic point-mass CDPR, illustrated in Fig. 2, where n cables are kept under tension to hold a point-mass platform with mass mP in position p = [xyz]T . The unit-vector and tension-magnitude of cable i are denoted by ui and \u03c4i. The interval 0 \u2264 \u03c4imin \u2264 \u03c4i \u2264 \u03c4imax is considered as the allowable tension range, where\u03c4imin and \u03c4imax denote the minimum and maximum tensions of cable i. According to definitions of SW and SAW and the proposed approaches in [11] and [12], a point of a CDPR\u2019s footprint is in SW iff the SAW in such point contains the force-space origin, where SAW = AW \u2295 {JT \u03c4min} \u2295 {mpg}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.10-1.png",
        "caption": "Fig. 15.10 Rod AB moving tangentially to a unit circle. The endpoint A is moving along a diameter of the circle (a) or along a tangent to the circle (b). Fixed centrodes kf and moving centrodes km",
        "texts": [
            "22) follows directly from the first Eq.(15.19). If Q is located on km , the trajectory has a cusp on kf in the position when Q is the pole P . The condition for Q to be located on km is obtained from (15.17) by replacing (x , y , a , b) by (v , u , b , a) : u2 \u2212 b(v \u2212 b) = a \u221a u2 + (v \u2212 b)2 . Example 4 : Rod moving tangent to a circle and with one point along a straight line The rod AB in Figs. 15.10a,b is constrained to move tangentially to a unit circle and with its endpoint A along a straight line. In Fig. 15.10a this line is a diameter of the circle and in Fig. 15.10b it is a tangent to the circle. To be determined are in either case the equations of the fixed centrode kf in the x, y-system with origin 0 and of the moving centrode km in the \u03be, \u03b7-system with origin A . Solution: In both figures the instantaneous center P is the intersection of the normal to the circle at the point of contact and of the normal to the straight line at A . The coordinates x, y and \u03be, \u03b7 of P as functions of the angle \u03b1 are obtained from triangles. First, Fig. 15.10a is analyzed. The coordinates of P are x = 1 cos\u03b1 , y = x tan\u03b1 = sin\u03b1 cos2 \u03b1 , \u03be = tan\u03b1 , \u03b7 = y sin\u03b1 = tan2 \u03b1 . \u23ab\u23ac \u23ad (15.25) Elimination of \u03b1 yields for kf and km the equations kf : y2 = sin2 \u03b1 cos4 \u03b1 = 1 cos4 \u03b1 \u2212 1 cos2 \u03b1 = x2(x2 \u2212 1) , km : \u03b7 = \u03be2 . (15.26) In Fig. 15.10b P has the coordinates 464 15 Plane Motion x = 1 cos\u03b1 + tan\u03b1 = 1 + sin\u03b1 cos\u03b1 , y = x tan\u03b1 = sin\u03b1 1\u2212 sin\u03b1 , \u03be = (1 + y) cos\u03b1 = cos\u03b1 1\u2212 sin\u03b1 \u2261 x , \u03b7 = (1 + y) sin\u03b1 = sin\u03b1 1\u2212 sin\u03b1 \u2261 y . \u23ab\u23aa\u23ac \u23aa\u23ad (15.27) The first two equations yield x2 = (1 + sin\u03b1)/(1\u2212 sin\u03b1) = 1 + 2 sin\u03b1/(1\u2212 sin\u03b1) = 1+2y . Hence the centrodes are the congruent parabolas x2 = 2y+1 and \u03be2 = 2\u03b7 + 1 . These parabolas are shown in Fig. 15.10b . The foci are 0 and A , respectively, and the directrices are the line y = \u22121 and the line \u03b7 = \u22121 , respectively. Through a comparison of angles it is verified that (0,A,P) is an isosceles triangle. From this it follows that the parabolas are located symmetrically with respect to the altitude h of the triangle, and that this altitude is the common tangent at P . The motions shown in Figs. 15.10a and b can be interpreted in a different way as follows. The body-fixed line \u03b7 = \u22121 is moving through the fixed point 0 , and the body-fixed point A is moving along a fixed line y =const ( y = 0 in Fig. 15.10a and y = \u22121 in Fig. 15.10b ). With this interpretation both motions turn out to be special cases of Fig. 15.9. The notation is different, however. Figure 15.10a is the special case b = 0 , and Fig. 15.10b is the special case a = b = 1 . From (15.17) it was deduced that in the former case one of the centrodes is a parabola, and that in the latter case both centrodes are congruent parabolas. Example 5 : Centrodes of couplers in four-bar mechanisms The quadrilateral A0ABB0 shown in Fig. 15.11 is a foldable four-bar mecha- 15.1 Instantaneous Center of Rotation. Centrodes 465 nism in antiparallelogram configuration. The fixed link A0B0 and the coupler AB have equal length , and the crossed cranks A0A and B0B have equal length r > "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure24-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure24-1.png",
        "caption": "Fig. 24. Simulated temperature distributions on radial cross section of the motors made from different rotor core materials. (a) 2605SA1. (b) 10JNEX900.",
        "texts": [
            " To consider the temperature difference of the windings at different positions, precise three-dimensional model is built and the mesh of the model is presented in Fig. 23. To improve the cooling performance, the stator is encapsulated with highthermal conductivity epoxy resin. In the simulation models, the ambient and the inlet water temperatures are 300 K (26.85 ). The inlet water velocity is 1 m/s. The temperature distributions of the two motors at maximum speed and rated torque are compared in Fig. 24. Because the losses of copper windings close to the air gap are higher than those at the bottom of slots and the cooling condition at the bottom is better, the windings close to the air gap is much hotter than the bottom windings. The maximum temperatures of each component of the two motors are listed and compared in Table IV. It is found that the HM has lower temperature than the AM. IV. VERIFICATION BY TESTING OF A PROTOTYPE To verify the FEA and CFD analysis results, the tested results of a prototype made from 2605SA1 are compared with the simulated results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001414_56601-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001414_56601-Figure1-1.png",
        "caption": "Figure 1. Underwater vehicle with both inertial and body-fixed reference frames.",
        "texts": [
            " In this context, the ideal mathematical model would be composed of a system of ordinary differential equations, to represent rigid-body dynamics, and partial differential equations to represent fluid dynamics. In order to overcome the computational problem of solving a system with this degree of complexity, in the majority of publications [1, 3, 4, 7, 13\u201316, 23, 28] a lumped-parameters approach is employed to approximate the vehicle\u2019s dynamic behaviour. The equations of motion for underwater vehicles can be presented with respect to an inertial reference frame or with respect to a body-fixed reference frame, Fig. 1. On this basis, the equations of motion for underwater vehicles can be expressed, with respect to the body-fixed reference frame, in the following vectorial form: M\u03bd\u0307 + k(\u03bd)zdvh(\u03bd) + g(x) = \u03c4 (1) where \u03bd = [\u03c5x, \u03c5y, \u03c5z, \u03c9x, \u03c9y, \u03c9z] is the vector of linear and angular velocities in the body-fixed reference frame, x = [x, y, z, \u03b1, \u03b2, \u03b3] represents the position and orientation with respect to the inertial reference frame, M is the inertia matrix, which accounts not only for the rigid-body inertia but also for the so-called hydrodynamic added inertia, k(\u03bd) is the vector of generalized Coriolis and centrifugal forces, h(\u03bd) represents the hydrodynamic quadratic damping, g(x) is the vector of generalized restoring forces (gravity and buoyancy) and \u03c4 is the vector of control forces and moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000837_ac60316a055-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000837_ac60316a055-Figure1-1.png",
        "caption": "Figure 1. Enzyme determination set-up",
        "texts": [
            " Solutions of cyanide and thiosulfate were combined on the day of use, aliquots taken and diluted with buffer to keep pH and ionic strength constant. The latter solution as calculated is taken as the final substrate composition. Procedure for Rate Measurement. All measurements were carried out in a double walled thermostated cell with temperature control of 1 0 . 1 \"C. The cell was covered with insulating foam which served as a holder for the Orion 94-06A cyanide activity electrode and an Orion 90-01 sleeve type reference electrode together with a mercury thermometer as shown in Figure 1. Reaction solutions were stirred by means of a Corning L M - 2 vibratory stirrer. Potentials were monitored and automatically displayed on a Beckman model 1055 pH recorder. To measure rhodanese activity, 10 ml of the substrate solution is pipetted into the cell and allowed to equilibrate to the desired temperature, e.g., 35.0 \"C. Then 100 pl of the rhodanese enzyme preparation is rapidly delivered by means of an Eppendorf microliter pipet into the system at equilibrium. The cyanide consumed during the reaction is monitored by the electrodes and a plot of potential us",
            " The initial velocity increases with the temperature, but overall linearity of the reaction is maintained only at 25 \"C over the period of observation of 4 minutes. At 30, 35, and 40 \"C, the bending curves indicate that the amount of active enzyme available decreases continuously. At 43 \"C, the curve bends sharply after a short period indicating a rapid enzyme denaturation process. Measurement of Rhodanese Activity. To measure rhodanese activity, 100 pl of enzyme solution is rapidly delivered into 10 ml of substrate previously equilibrated at the desired temperature-e.g., 35.0 \"C in the cell shown in Figure 1. The electrodes used to monitor the reaction develop a potential proportional to the cyanide activity or concentration at constant pH and ionic strength. RT E = Eo - - In [CN-] nF (3) The Nernst slope has a theoretical value of 61 and an experimental value of 62 mV/decade at this temperature. Differentiating Equation 3 with time and rearranging in a manner we have previously described (151, we arrive at d[CN-1 dE dt dt - - - - X 0.372 (4) ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972 1369 Table 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003738_s41403-021-00228-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003738_s41403-021-00228-9-Figure2-1.png",
        "caption": "Fig. 2 Schematic of a LPBF b LDED",
        "texts": [
            " Laser additive manufacturing system primarily consists of three primary subsystems such as high power laser, material feeding and job/beam manipulator, as depicted in Fig.\u00a01. The most commonly used lasers in LAM are Nd:YAG, diode, fibre and CO2 lasers. Considering the higher absorptivity of laser energy by metals at a lower wavelength, Nd:YAG, diode and fibre lasers are more commonly used in the modern LAM systems (Paul et\u00a0al. 2013). LAM processes can be classified into powder bed fusion (LPBF) and directed energy deposition (LDED) based on material feeding (Jinoop et\u00a0al. 2019b). Figure\u00a02a, b presents the schematic of LPBF and LDED technology, respectively. In LPBF technology, a uniform layer of powder is spread over the substrate/ build plate through a powder-filled hopper and it is levelled with a wiper. The laser beam is scanned over the pre-placed powder bed for selectively melting and consolidation of the powder as per the 2D geometry of a layer (Sames et\u00a0al. 2016; Nayak et\u00a0al. 2020a). The layers are built one over the other to build a 3D component. Most commonly used powder particle size range for LPBF system is 15\u201345 microns, which allows the use of smaller layer thickness and helps in achieving the geometric accuracy of the fabricated components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.4-1.png",
        "caption": "Fig. 12.4 Angular velocity triangles",
        "texts": [
            "11) Gears not shown in the figure keep the angular velocity ratio \u03bc = \u03c92/\u03c91 constant. Without loss of generality, it is assumed that \u03bc > 0 . Subject of investigation is the velocity screw of body 2 relative to body 1 . Let this relative velocity screw be denoted \u03c9(n , a\u00d7 n+ pn) . It is the difference \u03c9(n , a\u00d7 n+ pn) = \u2212\u03c91(n1 , a1 \u00d7 n1) + \u03c92(n2 , a2 \u00d7 n2) . (12.12) This equation is a special case of (12.2). Equations (12.3) and (12.6) are replaced by the equations \u03c9 \u03c91 n = \u2212n1 + \u03bcn2 , (12.13) \u03c9 \u03c91 (ue3 \u00d7 n+ pn) = 2 e3 \u00d7 (n1 + \u03bcn2) , (12.14) and Fig. 12.2 is replaced by Fig. 12.4 . The direction of n relative to n1 and to n2 is described by the angles \u03b11 and \u03b12 , respectively. The ratio \u03c9/\u03c91 as well as these angles are functions of \u03bc . The cosine and sine laws yield the formulas 12.2 Relative Velocity Screw. Raccording Hyperboloids 363 \u03c9 \u03c91 = \u221a 1 + \u03bc2 \u2212 2\u03bc cos\u03b1 , (12.15) sin\u03b11 = \u03c91 \u03c9 \u03bc sin\u03b1 , cos\u03b11 = \u03c91 \u03c9 (\u03bc cos\u03b1\u2212 1) , sin\u03b12 = \u03c91 \u03c9 sin\u03b1 , cos\u03b12 = \u03c91 \u03c9 (\u03bc\u2212 cos\u03b1) . \u23ab\u23ac \u23ad (12.16) Equation (12.14) is dot- and cross-multiplied by n (the same operations were performed with (12",
            " The hyperboloid with the smaller gorge circle radius is in tangential contact either outside or inside the other hyperboloid. External contact requires that r1 > 0 as well as r2 > 0 . Under the initial assumption \u03bc > 0 these conditions are satisfied with | cos\u03b1| < \u03bc < 1 | cos\u03b1| . (12.22) In addition to tangential contact along the resultant screw axis the hyperboloids may have an intersection curve. An equation for this curve is determined in the x, y, z-system whose x-axis coincides with the common perpendicular e3 and whose z-axis coincides with the resultant screw axis. Figure 12.4 yields the transformation relationships (abbreviations ci = cos\u03b1i , si = sin\u03b1i (i = 1, 2) ) x1 = x+ r1 , x2 = x\u2212 r2 , yi = ciy \u2212 siz , zi = siy + ciz (i = 1, 2) . (12.23) With these expressions Eqs.(12.19) of the hyperboloids become x2b2 + y2(b2c2i \u2212 r2i s 2 i ) + z2(b2s2i \u2212 r2i c 2 i )\u2212 (\u22121)i 2xb2ri \u2212 2yzcisi(b 2 + r2i ) = 0 (12.24) (i = 1, 2) . The arguments leading to (12.21) showed that r2i = b2 tan2 \u03b1i (i = 1, 2). From (12.16) it follows that tan\u03b11/ tan\u03b12 < 0 if r1 and r2 are both positive and > 0 otherwise",
            " The spatial generalization of this method is explained in the next section. For simplifying the comparison of both methods the same notation for points, lines and angles is used. In Fig. 16.18 P10 and P20 are the endpoints of the common perpendicular of the axes of the raccording hyperboloids 1 and 2 . At P12 the axis of the relative velocity screw is shown normal to the plane of the drawing (unit vector n ). The axes of the hyperboloids (unit vectors n1 and n2 ) are tilted against n through the angles \u03b11 and \u03b12 , respectively, defined in Fig. 12.4 and in (12.16). The absolute values of the vectors r1 and r2 are the radii of the gorge circles of the hyperboloids. Let flank f1 on wheel 1 be some 16.2 Skew Axes 559 arbitrarily prescribed smooth surface subject only to the condition that the normal to f1 at B1 (arbitrary) intersects the hyperboloid 1 . Let N1 be this wheel-fixed point of intersection. In Fig. 16.18 f1 is shown when wheels 1 and 2 are in some arbitrarily chosen initial position. To each pair (point B1 , normal B1N1 ) a conjugate pair (point B2 , normal B2N2 ) of flank f2 in the initial position of f2 is constructed as follows",
            " Conjugate means that (B1 , B1N1 ) and (B2 , B2N2 ) are the points and normals which coincide in the course of meshing at a certain point B . This point B is determined by Theorem 16.3. In contrast to the planar case in Fig. 16.6, it cannot be constructed graphically. Analytically it is determined as follows. From (2.25) it is known that a line with Plu\u0308cker vectors (v1 , w1) belongs to a linear complex (a ; b) if a \u00b7w1 + b \u00b7 v1 = 0 . (16.85) The vectors are represented in the x, y, z-system shown in Fig. 12.4 which has the origin at P12 , the x-axis along r1 and the z-axis along the axis of the relative velocity screw. In this reference frame the vectors of the linear complex are a = n and b = pn (see the text following (2.29)). The displacement from B1 to B is a rotation through an unknown angle \u03d51 about n1 . Let z1(0) be the given position vector of B1 and z1(\u03d51) the position vector of B . With the rotation tensor R(n1, \u03d51) defined in (1.40) z1(\u03d51) = r1 + R(n1, \u03d51) \u00b7 (z1(0)\u2212 r1) . (16.86) Let v1(0) be the given unit vector along the normal B1N1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure16.15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure16.15-1.png",
        "caption": "Fig. 16.15 Involutes generated by all points B of line e are forming involute helicoids contacting along the line with common normal n .",
        "texts": [
            "67) The equation for \u03b1\u2032 results from the condition that the tooth thickness d(r\u20321) given by (16.60) equals the space width w(r\u20322) between neighboring teeth on wheel 2 and that the latter is given by (16.60) with the index 1 replaced by 2 . The pitch circles p1 , p2 and the base circles c1 , c2 (radii r01 , r02 ) shown in Fig. 16.10 and the string A1A2 wound around the base circles are the front views (cross sections) of pitch cylinders, of base cylinders c1 , c2 and of a belt wound around the base cylinders. Figure 16.15 is a perspective view. In the frame-fixed x, y, z-system the moving planar section E of the belt is defined by the pressure angle \u03b1 . The following statements repeat what has been said in the context of Fig. 16.10 . Seen from an observer fixed on c1 the trajectory of a belt-fixed point B is an involute in the plane z = const in which B is located and seen from an observer fixed on c2 the trajectory of B is another involute. At B the involutes are in tangential contact the 16.1 Parallel Axes 553 common tangent being normal to E . With points B located on a belt-fixed straight line parallel to the z-axis two conjugate involute tooth flanks of spur wheels with straight-line teeth are generated. In Fig. 16.15 the belt-fixed points B are located on a belt-fixed straight line e which is making an angle \u03b20 against lines parallel to the z-axis. The involutes are shown for only two points on this line. The conjugate tooth flanks formed by the manifold of involutes for all points of the line are surfaces h1 and h2 called involute helicoids. Both helicoids are instantaneously in tangential contact along the generating line e . The common tangent plane intersects E orthogonally. This means that a helicoid is a ruled surface of the special kind called torse (distribution parameter \u03b4 = 0 on every generator; see the end of Sec",
            "81) or, in terms of the parameters \u03c6 and \u03b1 = \u03c6+ \u03c8 instead of \u03c6 and \u03c8 , x(\u03c6, \u03b1) = r0(\u2212 sin\u03b1+ \u03c6 cos\u03b1) , y(\u03c6, \u03b1) = r0( cos\u03b1+ \u03c6 sin\u03b1) , z(\u03c6, \u03b1) = r0(\u03b1\u2212 \u03c6) cot\u03b20 . \u23ab\u23ac \u23ad (16.82) The line \u03c8 = const (arbitrary) is the involute rotated through \u03c8 in the plane z = r0\u03c8 cot\u03b20 . The line \u03c6 = const (arbitrary) is a helix on the cylinder of radius \u221a x2 + y2 = r0 \u221a 1 + \u03c62 . The line \u03c6 = 0 , in particular, is the base helix with coordinates x(\u03c8) = \u2212r0 sin\u03c8 , y(\u03c8) = r0 cos\u03c8 , z(\u03c8) = r0\u03c8 cot\u03b20 . Lines \u03b1 = const are straight lines because each of the three coordinates is a linear function of \u03c6 with constant coefficients. These lines are swept through by the line e of Fig. 16.15 . In Fig. 16.17 the involute helicoid is shown. Figure 15.39 explains why it consists of two surfaces emerging from the base helix on the base cylinder. On each surface lines \u03b1=const tangent to the base helix are shown. The surfaces extend to infinity. In the figure they are truncated by lines \u03c6=const. The unit vector n normal to the helicoid is n = \u2202\u03c1 \u2202\u03c6 \u00d7 \u2202\u03c1 \u2202\u03b1\u2223\u2223\u2223\u2223\u2202\u03c1\u2202\u03c6 \u00d7 \u2202\u03c1 \u2202\u03b1 \u2223\u2223\u2223\u2223 . (16.83) With (16.82) this formula yields the coordinates nx = cos\u03b1 cos\u03b20 , ny = sin\u03b1 cos\u03b20 , nz = sin\u03b20 . \u23ab\u23ac \u23ad (16",
            " With the pertinent solution \u03d51 the position vector z2(0) of B2 and the unit normal vector v2(0) at B2 are determined by subjecting z1(\u03d51) and v1(\u03d51) to the rotation \u03d52 = \u2212(n1/n2)\u03d51 about n2 . This is done by Eqs.(16.86) and (16.87) with indices changed accordingly. Let h1 and h2 be two involute helicoids on skew axes. Each helicoid hi (i = 1, 2) has its own base cylinder ci of radius r0i , its own base helix angle \u03b20i and its own angle \u03b1i which determines the radius ri = r0i/ cos\u03b1i of the pitch cylinder pi (see Fig. 16.15). The pitch cylinder is rolling on the pitch plane of the rack cutter used for producing the helicoid. Let h1 be the helicoid on gear 1 in Fig. 16.15. The axis of h2 intersects the x-axis orthogonally at a point x = d \u2265 r1 + r2 . The projected angle between the two axes is called \u03bb (rotation about the x-axis in the positive mathematical sense). Thus, the x-axis is the common perpendicular of the axes, and d is the minimal distance. The situation shown in Fig. 16.15 is the special case \u03b201 = \u03b202 = \u03b20 , \u03b11 = \u03b12 = \u03b1 , d = r1 + r2 , \u03bb = 0 . Following Giovannozzi [9, 10] and without reference to Theorem 16.3 it is shown that under certain conditions h1 and h2 are conjugate tooth flanks. In particular, it is shown that the distance d has no influence on any of the angular relationships which follow. The reason is that involute helicoids are torses. On every generator the tangent plane is the same for all points of this generator. Let P be a point of contact. For each of the two helicoids hi (i = 1, 2) the statements made in the context of Fig. 16.15 are valid, namely: The contact point P is located on a generator ei of hi in a plane Ei which is tangent to the base cylinder ci and defined by the angle \u03b1i . The generator ei is making the base helix angle \u03b20i with lines parallel to the axis of ci . The contact normal at P lies in E1 as well as in E2 and it is normal to e1 as well as to e2 . From the skewness of the axes it follows that h1 and h2 have single-point contact and that the frame-fixed line of intersection of E1 and 16.2 Skew Axes 561 E2 , referred to as g , is the common contact normal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.9-1.png",
        "caption": "Figure 7.9. Application of the principles of conservation of momentum and work-energy.",
        "texts": [
            "34) shows that the linear momentum is a constant vector when and only when the total f orce on the particle is zero. The same result follows from (7.69) for all directions e. The principle (7.69), valid for all time in the motion, differs from our earlier conservation rule (7.12) for a system of two particles whose momentum is constant only during the impulsive instant. An easy application of the rule (7.69) follows. Example 7.10. A particle of mass m is released from rest at A and slides down a smooth circular track of radius R shown in Fig. 7.9. At the lowest point B , the particle is projected horizontally and continues its motion until it strikes the ground at C. Determine the horizontal component of the particle's velocity at C . Solution. The free body diagram in Fig. 7.9 on the path from B to C shows that no horizontal forces act on the particle. Therefore, the linear momentum in Chapter 7 the fixed horizontal direction i is conserved: p . i = mx = y, a constant. Consequently, on the entire path BC, specifically at C, the horizontal component of the particle's velocity v . i = i is a constant whose value is determined by its speed at point B. This value may be found by application of the work-energy principle. The free body diagram of the particle on the circular path AB is shown in Fig. 7.9. The normal force N is workless on AB, while gravity does work 1I/g = mgR in reaching B. Hence, the total work done by the forces acting on m is 11/=mg R . The increase in the kinetic energy as the particle slides from rest at A to the end state at B is f::..K = 4mv~ . The work-energy principle 71' = f::..K determines the speed at B, and hence the horizontal component of the particle's velocity at C is given by i = VB = J2gR. o Exercise 7.8. What is the normal force exerted on m by the surface at B",
            " Clearly, since forces of constraint perpendicular to the path do no work in the motion, these normal forces contribute nothing to the energy of an otherwise conservative system of forces . Accordingly, the energy principle can provide no information about such forces of constraint. The forgoing conclu sions and remarks are illustrated in an example. Example 7.12. (i) Apply the principle of conservation of energy to find the velocity VB at which the particle in Example 7.10, page 249, is projected from point B shown in Fig. 7.9, and show that an arbitrary constant reference potential energy does not alter the conclusion. (ii) Derive from the energy equation the equivalent Newton-Euler scalar equation of motion for the mass on the circular path AB. Solution of (i), First, we need to confirm that the energy principle (7.73) may be applied. The forces that act on the mass m on the circular path AB are shown in Fig. 7.9. Since the weight W is a conservative force and the normal surface reaction force does no work on AB , the total energy is conserved. The point A is clearl y a convenient datum for zero gravitational potential energy. However, we recall that only differences in the potential energy are relevant. Moreover, an arbitrary reference potential energy Va does not alter the energy balance in (7.73), for the same constant potential energy will appear in both sides of the equation. To demonstrate this, let us choose an arbitrary value Va for the reference potential energy at A",
            "mR2\u00a22 and V = -mgR sin\u00a2, where we now fix Vo = 0 at A. Since E = 0 at A, (7.73) yields the energy equation on the path AB, ~mR2\u00a22 - mgR sine = O. Differentiation of (7.77c) with respect to the path variable \u00a2 (or with respect to t) yields the equivalent tangential component of the Newton-Euler equation of motion, namely, mR\u00a2 - W cos \u00a2 = O. (7.77d) Notice, in agreement with (7.76), that R\u00a2 = s is the tangential component of the acceleration, and W cos \u00a2 = F, is the conservative tangential component of the total force F = W +N acting on m in Fig. 7.9, whose workless normal component is Fn = N - W sin \u00a2 . 0 Let the reader consider the following example . Exercise 7.10. Apply the principle of conservation of energy to solve Example 7.7, page 238. Derive the equation for the maximum spring deflection resulting from the impact by a mass m falling through a height h shown in Fig. 7.7. 0 The centripetal acceleration of a particle in a moving frame tp = {O ; ek} gives rise to a central directed, apparent centrifugal force P(x, t)= -mw X (w X x). So, consider a radial motion with x = re, in tp and wet) = w(t)ez = cae"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001488_s00604-014-1444-x-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001488_s00604-014-1444-x-Figure2-1.png",
        "caption": "Fig. 2 Effect of electrode compositions on the amperometric responses in 0.1 mol L\u22121 phosphate buffer solution (pH =7.0) in the presence of 0.05 mmol L\u22121 H2O2",
        "texts": [
            "1 %, w/w) were coated onto the SPCNTE, and allowed to stay in air to dry. Then the disposable HRP/ BSA/SPCNTE was obtained. The resulted electrode was rinsed with double distilled water and stored in phosphate buffer solution with pH 7.0 at 4 \u00b0C when not in use. Optimization of the preparation of the disposable biosensor Since the different loading of CNTs and CA might affect the performance of the biosensor, the effect of the electrode compositions (CNTs/CA ratio) on response current were studied as shown in Fig. 2. When the ratio of CNTs/CA ratio was 1: 6, no current response to H2O2 could be observed. This may be due to the increased electrode resistance and mass transfer resistance. However, the current response gradually increased and reached a maximum with decreasing CA content for a CNTs/CA ratio of 1:0.6 (150 mg CNTs/90 mg CA). Further decreasing the amount of CA led to a decrease of the response, possibly because of fall off of CNTs from epoxy substrate. As a result of this experiment, the CNTs/CA ratio of 1:0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002076_j.triboint.2014.09.014-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002076_j.triboint.2014.09.014-Figure1-1.png",
        "caption": "Fig. 1. (a) Single-row deep groove ball bearing; (b) Shield plates were removed.",
        "texts": [
            " Sections 4 to 6 describe the results from analysis of the failed bearings using scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR), and optical profilometry. Section 7 examines the correlation between the parameters from the sensor signal analysis and the results of the failure analysis in order to determine the failure precursors. On the basis of the test data and analysis, the failure mechanisms are discussed in Section 8. This study investigated a single-row deep groove ball bearing (NSK Ltd., part number 693ZZ; See Fig. 1). The bearings were composed of balls, a cage, shields, and inner and outer races. The balls and inner and outer races were made of stainless steel (SUJ 2) whose chemical elements include carbon (0.95 1.10%), silicon (0.15 0.35%), manganese (o 0.5%), phosphorus (o 0.025%), sulfur (o 0.025%), chromium (1.3 1.6%), and molybdenum (o 0.08%). The cage was made of polyamide (90% by weight) and reinforced with glass fiber (10% by weight). Polyamide is composed of carbon, oxygen, and hydrogen, while glass fiber is composed of silicone, calcium, and oxygen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000221_s0006-3495(83)84406-3-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000221_s0006-3495(83)84406-3-Figure5-1.png",
        "caption": "FIGURE 5 Shown are three elementary coordinate transformations used to build up the finite transformation from central pair body coordinate to ith doublet. The solid horizontal arrows between similar views imply a transformation of coordinates. The dashed vertical arrows between different views denote merely a change in the observer's viewpoint to allow easy visualization of the following transformation.",
        "texts": [
            " To carry out this program, it is first necessary to find a transformation matrix, which we denote Ajo, from central pair body coordinates to ith outer doublet body coordinates. Once the vectors of interest (i.e., bending moment vectors) are expressed in the same coordinate system, conventional vectorial operations can be done component by component. Ajo(s), the transformation from central pair body coordinates to the ith outer doublet body coordinates at arc length s1(s) is simply the product of three elementary rotations, Aio = BCD. The first of these, ID, is a rotation about the central pair z axis by an amount 0, so that the new x' axis is along Li (Fig. 5): cos Oi sin 0, 0 D = -sinOi cos0i . O O 1 (18) HINES AND BLUM Three-dimensional Mechanics ofEukaryotic Flagella 71 The matrix B is the transformation for a rotation about z\" by an angle 4 and therefore has the same form as that of matrix D (see Eq. 18). Notice that because of matrix C, Ajo is a function of curvature. The bending moment of the axoneme as a whole can then be written as follows, axoneme \" io fbiAio)IK.Ebo (A-US (23) Next, we rotate about the x' axis by the amount required for the new z\" axis to be in the direction Ti"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.3-1.png",
        "caption": "Figure 7.3. A ballistic pendulum model.",
        "texts": [
            " If other impulsive forces act on either particle, however, (7.12) does not hold , rather, the impulse-momentum principle (7.7) must be applied separately to each particle, accounting for the total impulsive force that acts on each. Example 7.2. A ballistic pendulum is a device used to determine the muzzle speed of a gun . A bag of wet sand of mass M is suspended by a rope, and a bullet of mass m is fired into the sand with unknown muzzle speed f3. The pendulum then swings through a small angle eo from its vertical position of rest as shown in Fig. 7.3 . Replace the sack by its center of mass object, and find the muzzle speed of the gun . Solution. During the infinitesimally small time interval of impact of the bullet with the sack of sand, the only external forces that act on the pair are their weight Momentum, Work, and Energy 227 (7.13a) and the tension in the rope. These are finite external forces that contribute nothing to the instantaneous impulses and may be ignored. In fact, the resultant of the rope tension and the weight of the sand is zero during the impulsive instant",
            " The bag being at rest, the linear momentum of the pair just prior to the instant t* of impact is mf3i. Immediately afterward, when the bullet is lodged in the bag (captured by the center of mass object), which now has an instantaneous velocity Vo = voi, the linear momentum is (m + M)voi.Application of the momentum equation (7.12) yields mf3i = (m + M)voi , and hence m+M f3 = --Vo\u00b7 m However, Vo remains unknown . To find it, we consider a familiar problem. After the impulse, the bag swings as a simple pendulum of length I and small amplitude eo so that h \u00ab \u00a3. in Fig. 7.3.Therefore, the equation of motion for the bag carrying both the sand and the bullet is given by (6.67d), whose general solution for the initial conditions e(O) =aand \u00a3.0(0)= Vo is provided by (6.67e). Hence, with B = 0 and A = vol pt; the solution is e(t) = (vol p\u00a3.)sin pi, from which the amplitude of the swing is eo = vol pt: With (6.67c), this yields Vo = eoM. Finally, use of this relation in (7.13a) delivers the muzzle speed of the gun: m+M en f3 = --eov g\u00a3. .m (7.13b) Since M \u00bb m, the muzzle speed is closely estimated as f3 = (M1m )eoM",
            " On the other hand, if the value of 11/ depends on the path, and we want to determine the particle 's path, the work-energy rule might not be helpful. In other situations where the trajectory of the particle is known, or the force that acts on the particle does no work or is conservative so that its work is path independent, and especially when work is readily evaluated , the work-energy principle is most useful. The easy application of this rule is demonstrated in some examples that follow. Example 7.5. Recall the ballistic pendulum problem in Fig. 7.3, page 226. Find the muzzle speed of the gun when the total angular placement may not be small enough to admit the approximate solution (7.l3b) for which h \u00ab e. Momentum, Work, and Energy 237 Solution. The muzzle speed is still given by (7.13a), and vo, the initial speed of the pendulum system, is the unknown of interest. The other end state condition and the path of the center of mass of this one-degree of freedom system are known. These facts strongly suggest that the work-energy principle will be helpful in this case. The total force that acts on this system is its total weight and the tension of the rope. The line tension is always normal to the circular path on which the center of mass moves, so it does no work as the system swings to its maximum placement eo. The work done by the constant force of gravity is determined by (7.28). Accordingly, in Fig. 7.3, the vertical height h through which the weight (m + M)g is raised is h = eo - cos eo), and hence 11/= -em +M)geo - cos eo). Since the system is at rest at eo and has initial speed vo, the change in the kinetic energy is !::!.K = -!(m + M)V5 ' Thus, the work-energy principle (7.36) yields -!(m +M)V5 = -em +M)geo- cos eo) . This gives the unknown vo, and its use in (7.13a) provides the precise muzzle speed relation: m+M ,------ f3 = --y'2geo- cos eo). m When h /e= 0 - cos eo) is very small so that I - cos eo = ",
            " Apply the energy method to derive the equation for the frequency of small plane oscillation s of the rod described in Problem 10.12. 10.50. Apply the energy method to derive a formula for the period of the small amplitude oscillations of the plate described in Problem 10.13, expressed in terms independent of its mass. 10.51. Use the energy method to solve Problem 10.15 for the period of the small amplitude oscillation. 10.52. Solve Problem 10.18 by use of the energy principle. 10.53. The sandbag body of the ballistic pendulum described in Fig.7.3, page 226, is replaced with a solid block B of mass M and moment of inertia 10 about point O. The block is supported by a rigid rod of negligible mass, and the length from 0 to the center of mass C of B is e.A bullet of mass m is fired horizontally into the block in the direct ion of C, as shown previously, and the pendulum suffers a finite,maximum angular displacementeo' Find the muzzle speed of the bullet. 10.54. What is the small oscillat ion frequency of the mass m in Problem 6.57 when the mass M of the thin, rigid supporting rod, which has length e = a + b, is taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure6.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure6.10-1.png",
        "caption": "Fig. 6.10 Mechanism R1R2CR4P converting rotation into harmonic translation",
        "texts": [
            " The polyhedron has n = 14 faces (bodies) and m = 21 edges (revolute joints). With these numbers Gru\u0308bler\u2019s formula (4.1) yields the degree of freedom F = \u221227+d . Since F equals one, the system of altogether 5\u00d7 21 constraint equations has the defect d = 28 . See http://www.mathematik.com/Steffen/ for a display of the motion. 6.6 RRCRP Mechanism 233 A closed kinematic chain RRCRP has six joint variables. Hence it is rigid unless it is overconstrained. It will be seen that the special chain shown in Fig. 6.10 is overconstrained with degree of freedom one. The assembly position shown is characterized as follows. The axis of the revolute R4 is orthogonal to the x, y-plane of the frame-fixed x, y, z-system with origin 0 . The other four joint axes are in this plane (the prismatic joint P parallel to the revolute R1 at y = = const; the axes of the revolutes R1 and R2 and of the cylindrical joint C intersecting at 0 ; R1 and R2 under an angle \u03b1 = const and R2 and C orthogonally). After a rotation through \u03d51 (arbitrary) in R1 the unit vector n2 along the axis of R2 has the coordinates n2 = [cos\u03b1 \u2212 sin\u03b1 sin\u03d51 \u2212 sin\u03b1 cos\u03d51] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003912_8.942-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003912_8.942-Figure3-1.png",
        "caption": "FIG. 3.",
        "texts": [
            " Since such deflections should be very small in the usual fuselage, it may be assumed that no radial forces will be applied by the skin to the ring, or at least that such radial forces are negligible compared to the tangential forces. A couple or moment applied to the ring will then have skin reactions distributed uniformly around the circumference, as shown in Fig. 2. The intensity of F I G . 2. these skin reactions, per unit of length of circumfer ence, will then be dp = M0/2irR2 (1) A radial force will have skin reactions as shown in Fig. 3, assuming that the common theory of flexure is valid for this case. P is the radial force applied to the ring. F is the transverse force transmitted to right of ring {i.e., total shear). / is unit fiber stress in skin, at plane defined by angle <p. d and C2 are total compressive forces beyond plane defined by angle 0. SH is horizontal shear on two longitudinal radial planes through skin. 460 D ow nl oa de d by U N IV E R SI T Y O F C A L IF O R N IA - D A V IS o n Fe br ua ry 2 , 2 01 5 | h ttp :// ar c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000433_s0022112007005514-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000433_s0022112007005514-Figure5-1.png",
        "caption": "Figure 5. (a) Experimental set-up for droplet system with a steady pressure bias in the lower chamber and transient applied pressure pulse in the upper chamber. Images of the states when the system is bi-stable where (b) is before and (c) is after a positive pulse P (t) is applied.",
        "texts": [
            " For oscillations symmetric about \u0398 = 0 (branch 1 with \u03bb< 1 and the looping solutions), \u0398\u2212 = \u2212\u0398+ and expression (2.11) can be evaluated as the amplitude \u0398 \u2261 \u0398+ of the disturbance is increased. Figure 4(b) shows how the frequency changes with amplitude for sub-hemispherical droplets. For finite-amplitude oscillations, the restoring capillary force varies from soft to hard as \u03bb is increased from 0 to 1. The experimental set-up consists of a Teflon plate (1.82 mm thick) with a small circular hole (0.83 mm radius) bored through, as depicted in figure 5(a). A microsyringe is used to feed water to control the volume of the droplets. Pinned contact lines are maintained well as verified through image analysis. The plate separates two pressure-controlled chambers. Gravity is weak relative to surface tension (Bond number B \u2261 \u03c1gr2/\u03c3 \u223c 0.1) yet gravity has a non-negligible effect. It adds a hydrostatic head to the bottom droplet to make its mean pressure greater and along the length of both droplets it distorts the droplet shape from spherical. To counter the head, a pressure bias in the lower chamber is applied. Further details of the experimental set-up are given by Hirsa et al. (2005). We begin by fixing the total volume of the droplet then slightly adjusting the pressure bias to achieve an equilibrium state of zero volume difference. A microstepper motor is then used to apply a pressure pulse in one air chamber to perturb the droplet. The duration of the pressure pulse is less than 100 ms and only after this time has elapsed are the data analysed. Figure 5(b, c) shows images of the bistable droplet states at equilibrium. Depending on the amplitude of the pulse, four different dynamical behaviours are observed in experiments: (i) small vibrations about a static shape; (ii) bi-stable oscillations that toggle up, down and so forth n-times before coming to rest (up to n= 5); (iii) deformations that blow the liquid completely out of the tube and (iv) deformations where some liquid is left in the tube with the rest breaking off as a satellite droplet. A high-speed video camera is used to capture the droplet motions (Redlake MotionPro HS2-C-4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001196_j.triboint.2013.06.016-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001196_j.triboint.2013.06.016-Figure1-1.png",
        "caption": "Fig. 1. Schematic view of the rolling bearing assembly.",
        "texts": [
            " The elements identified were Zinc (Zn), Magnesium (Mg), Phosphorus (Ph), Calcium (Ca), Boron (B) and Sulphur (S). It is clear that the formulations are significantly different, both in terms of base oil and additive package. A complete characterization of physical properties of the lubricants was performed. A detailed description of the physical properties are presented in Appendix A and the results are presented in Table 1. The rolling bearing tests were performed on a modified Four-Ball machine, where the Four-Ball arrangement was replaced by a rolling bearing assembly, as shown in Fig. 1. This assembly was developed to test several rolling bearings andmeasure the friction torque as well as the operating temperature in several different points. A detailed presentation of this assembly can be found in [25]. The rolling bearing assembly is divided in two parts: the shaft adapter (6), directly connected to the machine shaft and supporting the bearing upper race (5); a lower race support (2) and the bearing lower race (3), both clamped to the bearing housing (1). In operation, the internal bearing torque (or friction torque) is transmitted to the torque cell (11) through the bearing housing (1). The friction torque was measured with a piezoelectric torque cell KISTLER9339 A, ensuring high-accuracy measurements even when the friction torque generated in the bearing was very small compared to the measurement range available. This assembly includes five thermocouples (I\u2013V), measuring temperatures at strategic locations (see Fig. 1) which are used to monitor the temperature inside the bearing assembly (IV), near to the rolling bearing and the lubricant (III) and to evaluate the heat evacuation from the bearing housing into the surrounding environment (I, II and V). The system is also monitored by two thermocouples to monitor the chamber and room temperatures. For the axial loads applied (700 and 7000 N) each contact element (roller) reach the conditions presented in Table 2. When assembled in the modified Four-Ball machine the rolling bearing assembly is submitted to a continuous air flow, forced by two 38 mm diameter fans running at 2000 rpm, cooling the chamber surrounding the bearing house"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001230_tmag.2011.2120599-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001230_tmag.2011.2120599-Figure3-1.png",
        "caption": "Fig. 3. Uneven magnetization patterns of (a) 1/4 model of 8P12S and (b) 1/3 model of 12P9S.",
        "texts": [
            " 2 shows the geometry of the teeth curvature. Table III shows the three models with their respective radii of 0018-9464/$26.00 \u00a9 2011 IEEE Since there are many different cases of uneven PM magnetization, a reasonable numerical model which represents all cases of uneven magnetization is required to generalize the effect of the interaction between a PM and teeth curvature. Akihiro et al. showed that the overall uneven magnetization pattern of a model can be presented by investigating one of the partial periodic models [5]. Fig. 3 shows the uneven magnetization patterns of a 1/4 partial model with 2P3S from the full model with 8P12S and a 1/3 partial model with 4P3S from the full model with 12P9S. Tables IV and V show the frequency components of cogging torque and their amplitudes due to the uneven magnetization patterns of 8P12S and 12P9S, respectively. The amplitudes of the frequency components are normalized to the amplitude of the least common multiple harmonic of the poles and slots in the ideally magnetized case. The data in the tables show that uneven magnetization of one pole generates all of the possible harmonic frequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000525_ichr.2010.5686851-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000525_ichr.2010.5686851-Figure4-1.png",
        "caption": "Fig. 4. Details of the foot.",
        "texts": [
            ", 6 are the actuated joint variables such that: \u03b4\u03b81 = \u03b4q1 \u2212 \u03b4qp1 , \u03b4\u03b82 = \u03b4q4 \u2212 \u03b4qp2 \u03b4\u03b83 = \u03b4\u03b11 , \u03b4\u03b86 = \u03b4\u03b12 \u03b4\u03b84 = \u03b4q5 \u2212 \u03b4q2 , \u03b4\u03b85 = \u03b4q5 \u2212 \u03b4q3 with: \u03b4\u03b11 = \u2212\u03b4q2 + \u03b4qg12 and \u03b4\u03b12 = \u2212\u03b4q3 + \u03b4qg22 (3) 1Notation T means transposition This formulation of the dynamic model is valid only if the stance foot does not take off and there is no sliding during the swing phase. The vertical component of the ground reaction force has to be positive and the ground reaction force must be inside the friction cone. The center of mass Gf of the foot is assumed located on the vertical axis, crossing the joint ankle (Fig.4). The ground reaction force can be calculated by applying the second Newton law at the center of mass of the biped: m\u03b3 = R1 +R2 +mG (4) Here m is the mass of the biped, \u03b3 = [x\u0308g, z\u0308g] T are the horizontal and vertical components of the acceleration for its center of mass in the world frame. ~R1 and ~R2 are the reaction forces on the feet. ~G = [0,\u2212g]T is the vector of the acceleration of the gravity. During the single support phase, reaction ~R2 of the ground on the swing leg tip is null. This equation allows directly getting the reaction force ~R1 of the ground during single support"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003071_s00707-020-02713-8-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003071_s00707-020-02713-8-Figure6-1.png",
        "caption": "Fig. 6 Geometrical models for square and hexagonal unit-cell (MD pattern). The actual unit-cell model using 3D continuum (left) and the simplified model using beam (right) elements",
        "texts": [
            " The unit-cells of the square pattern were subjected to uniaxial, biaxial, and bending tests, while the unit-cells with the hexagon pattern were subjected to uniaxial and bending tests. We also performed a bending test on kerf panels with square and hexagon kerf patterns in order to create a dome shape. The testing setup is shown in Fig. 5. The same device was used for testing with custom-built grips and push rod to deform the center of the panel. In order to analyze the deformations of the kerf unit-cells and panels, we consider representing the segments (prismatic bars) in the kerf systems with beam elements of a solid rectangular cross section, see the illustration in Fig. 6. The side length s is equal to 1 inch. The actual unit-cell model is generated using 3D continuum finite elements, while the simplified model is generated using beam finite elements. Each beam has a thickness of 0.125 in, which is the thickness of the MDF panel, and the width of the beam depends on the cut density and pattern of the kerf panel. The width of the beam is defined based on the number of cutline and the gap from laser cutting the specimen, which is around 0.025 in. Tables 1 and 2 present the cross-sectional dimensions of the beam for the square and hexagon patterns with different cut densities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003384_s12555-019-0904-9-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003384_s12555-019-0904-9-Figure5-1.png",
        "caption": "Fig. 5. The model of the PVP.",
        "texts": [
            " Thus, in the next subsection, we use the NA method to ensure that the SUL stops rotating when the FAL reaches to its target states. 3.3. Stable control for PVP In this subsection, we design a cycle controller to make the two links of PVP be stationary, and to ensure that the SUL reaches to a middle angle, while states of the FAL at the starting moment of each period are the same as that at the last moment. Meanwhile, the states of TAL are kept being zero during the whole control stage, which ensures that the system is always a PVP. Fig. 5 shows the model of PVP. Its dynamic model is expressed as M\u0303 (q\u0303) \u00a8\u0303q+ H\u0303 ( q\u0303, \u02d9\u0303q ) = \u03c4\u0303, (21) where M\u0303 (q\u0303) = [ M\u030311 M\u030312 M\u030321 M\u030322 ] , H\u0303 ( q\u0303, \u02d9\u0303q ) = [ H\u03031 ( q\u0303, \u02d9\u0303q ) H\u03032 ( q\u0303, \u02d9\u0303q ) ] , (22) q\u0303 = [q\u03031 q\u03032] T , \u02d9\u0303q = [ \u02d9\u0303q1 \u02d9\u0303q2 ]T , \u03c4\u0303 = [\u03c4\u03031 0]T , (23)  M\u030311 = b1 +b2 +2b3cosq\u03032, M\u030312 = M\u030321 = b2 +b3cosq\u03032, M\u030322 = b2, H\u03031 =\u2212b3 ( 2 \u02d9\u0303q1 \u02d9\u0303q2 + ( \u02d9\u0303q2 )2 ) sinq\u03032, H\u03032 = b3 ( \u02d9\u0303q1 )2sinq\u03032 (24)  b1 = m1Lc1 2 +(m2 +m3)L1 2 + J\u03031, b2 = (m2 +m3)(Lc2 +Lc3) 2 + J\u03032, b3 = (m2 +m3)L1 (Lc2 +Lc3) . (25) The underacutated constraint of (21) is M\u030321 \u00a8\u0303q1 + M\u030322 \u00a8\u0303q2 + H\u03032 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001482_s10846-013-9927-2-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001482_s10846-013-9927-2-Figure4-1.png",
        "caption": "Fig. 4 Navy procedure 1: forward facing landing",
        "texts": [
            " Two components of the wind vectors are considered: head wind \u2212\u2192 H is caused by the ship velocity\u2212\u2192 V and the other is the true wind \u2212\u2192 W over the sea environment. The relative wind is the sum of these two vectors and is calculated in Eq. 1. \u2212\u2192 H = \u2212\u2212\u2192 V \u2212\u2192 A = \u2212\u2192 H + \u2212\u2192 W (1) The crosswind component of the relative wind can be computed by Eq. 2: \u2212\u2192 A cross = A \u21c0 \u2217 sin(\u03d5) (2) where \u03d5 denotes the direction angle of the relative wind. The optimal landing procedure is determined from \u2212\u2192 A cross. If the crosswind is less than 5 m/s, the \u201cforward facing landing procedure\u201d is the optimal method for shipboard landing (Fig. 4). The sequence given below explains the forward facing procedure [11]. 1. The vehicle approaches the ship to a hover position alongside the ship. At this time, the helicopter is aligned with the longitudinal axis of the ship. 2. Next, the aircraft flies sideways to the hover position over the landing zone. 3. Finally, the vehicle decreases the altitude and then touches down on the landing zone. 4. If there is a possibility of a crash or a failure to touchdown, the vehicle immediately increases its altitude and moves sideways, to reinitiate the landing steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003753_j.jfca.2021.103983-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003753_j.jfca.2021.103983-Figure1-1.png",
        "caption": "Fig. 1. The scheme of online SPE coupled with heart-cutting 2DLC system.",
        "texts": [
            " After centrifuging at 104 rpm min\u2212 1 the liquid supernatant was collected and filtered by 0.2 \u03bcm nylon membrane. Y. Zhang et al. Journal of Food Composition and Analysis 101 (2021) 103983 The chromatographic system was assembled of Agilent 1260 Infinity II, which constructed with three pump modules (SPE pump, First Dimensional Separation (1D) pump and Second Dimensional Separation (2D) pump), two Two-Positions-Six Ports switching valves, one column compartment and two UV detectors to implement online SPE and heartcutting 2DLC (Fig. 1). The CDS software was Agilent OpenLab CDS2.4 version. Sample solution (100 \u03bcL) was loaded onto SPE column (PLRPS,4.6 \u00d7 12.5 mm,15\u2212 20 \u03bcm, Agilent technology) to enrich the target analytes by SPE pump. The effluent from SPE composed of high proportional organic phase was refocused onto 1D column (Poroshell 120 PFP, 4.6 \u00d7 100 mm, 4 \u03bcm, Agilent technology). Online dilution of 1D column with high proportional aqueous phase was delivered by 1D pump. Separation of vitamins A, vitamin E and purification of vitamin D were carried out on 1D column"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure4-1.png",
        "caption": "Fig. 4. Generating of OPE hourglass worm tooth surface.",
        "texts": [
            " In the fixed coordinate system \u03c3 m , the equation of right flank tooth surface r g R of the medium gear is expressed as follows: r g R (v , t) = [ x gR 1 y gR 1 z gR 1 ] = [ v \u2212 r g b + t sin \u03b2bR t cos \u03b2bR ] (4) Similarly, the equation of left flank tooth surface r g L can be expressed as follows: r g L (v , t) = [ x gL 1 y gL 1 z gL 1 ] = [ v r g b \u2212 t sin \u03b2bL \u2212 t cos \u03b2bL ] (5) Here, v and t represent the planar parameters of tooth surface g . The OPE worm tooth surface is considered to be a conjugate surface, which is generated by the medium gear tooth surface. The medium gear tooth surface g is the generating plane x a o a z a as shown in Fig. 4 . In order to simplify the calculation without losing the generality, assuming that the angular velocity of the OPE hourglass worm is \u03c9 1 = 1 rad/s, and then the angular velocity of the medium gear is \u03c9 2 = i 12 rad/s. The relative velocity vector v R 12 of the enveloping process of OPE hourglass worm can be determined and represented in the coordinate system \u03c3 a by the following equations: v R 12 ( \u03d5 1 ) = [ v xaR 1 v xaR 1 v xaR 1 ] = \u23a1 \u23a2 \u23a2 \u23a3 i 12 cos \u03d5 1 z gR 1 \u2212 y gR 1 ( x gR 1 \u2212 z gR 1 i 12 sin \u03d5 1 ) sin \u03b2R + i 12 cos \u03b2R ( y gR 1 sin \u03d5 1 \u2212 x gR 1 cos \u03d5 1 + a ) i 12 sin \u03b2R ( \u2212x gR 1 cos \u03d5 1 + y gR 1 sin \u03d5 1 + a ) \u2212 cos \u03b2R ( x gR 1 \u2212 z gR 1 i 12 sin \u03d5 1 ) \u23a4 \u23a5 \u23a5 \u23a6 T (6) Because the medium gear tooth surface g is an oblique plane, in coordinate system \u03c3 a , the unit normal vector of tooth surface g is represented by n R a = [ n R xa n R ya n R za ]T = [ 0 0 1 ] T (7) Based on the meshing theory of gearing [27] , the necessary and sufficient condition of existences for the OPE hourglass worm tooth surfaces generated by the medium gear tooth surface is expressed by meshing equation as follows: = v R 12 n R a = 0 (8) Substituting v R 12 and n R a into Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001469_tie.2013.2279382-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001469_tie.2013.2279382-Figure1-1.png",
        "caption": "Fig. 1 Prototype SFPM machine with all poles wound.",
        "texts": [
            " Thus, the influence of the primary and secondary saliencies of the prototype SFPM machine on the HF injection-based sensorless control performance can be fully investigated without the need of any information of parameter values for the first time. The effectiveness of the proposed experimental method and investigation will be proved by the several experiments on a dSPACE platform with a laboratory SFPM machine. In addition, the sensorless current and speed control based on HF pulsating voltage signal injection will be implemented to verify the conclusion of the saliency investigation. In the SFPM prototype machines as shown in Fig.1, the salient pole stator core includes \u201cU-shaped\u201d laminated iron segments which are allocated around magnetized PMs. The magnetization is kept in opposite polarity from one magnet to the following one. A stator pole, established by two iron legs from adjacent segments and a magnet, is wound by coils, which is a part of the stator winding. A prototype 12/10 stator/rotor pole SFPM prototype machine is shown in Fig. 2. The parameters of the prototype SFPM machine used in this work are summarized in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000259_robot.2008.4543696-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000259_robot.2008.4543696-Figure2-1.png",
        "caption": "Fig. 2. Control modeling",
        "texts": [
            " We decided to use human data for modeling our HR [13][9][7]. Unilateral contacts seen as Coulomb frictional contacts are ruled by a non linear model i.e.: | f t c| < \u00b5 f n c with f n c , f t c respectively the normal and tangent contact forces and \u00b5 , the dry-friction factor. As a linear formulation for our optimization problem is needed, we use a linearized Coulomb model. Like J.C. Trinkle et al. [20], contact cones are linearized into multifaceted friction cones in order to get linear constraints (Fig. 2(a)). The linearized contact force of the k-th contact (denoted f k c , 3 DoF) computed by our control law must lay inside the friction cone,that is: \u2200i \u2208 [1,ne], Ek ci f k c + dk ci \u2265 0 with ne, the number of edges, and Ek ci f k c +dk ci , distance between f k c and each i-th oriented facet. The grasp wrench (denoted Wg, 6 DoF) computed by our control law must not exceed a certain limit wrench, which we write: |Wg| \u2264 W max g . Geometrically, that means that Wg must lay inside a certain polytope of R6; if we restrain the wrench to its force or torque component only, it must lay inside a cube (Fig. 2(b)). Although the lower level of our controller is not a new contribution [6], a rough description is given hereunder. The goal of this module is to compute all the control torques which have to be applied to HR joints. To this end, as in [21] [1], the control problem is stated as a constrained optimization problem (Quadratic Programming : QP). All wrenches affecting the HR (control torque, contact and grasp wrenches) are taken into account, as well as joint acceleration. The solution of the dynamic QP problem induces a realizable set of desired forces acting on the HR"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003545_s40195-021-01214-4-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003545_s40195-021-01214-4-Figure2-1.png",
        "caption": "Fig. 2 a Schematic of the SEM chamber with high temperature in-situ tensile testing set-up; b view of the tensile stage with heating core",
        "texts": [
            " For metallographic study, the specimens were etched by the kroll\u2019s solution of 2\u00a0ml HF, 4\u00a0ml HNO3 and 94\u00a0ml of H2O [27]. The phase percentage was examined by X-ray diffraction (XRD) testing with region detector and radiation of CuK\u03b1. The macrostructure and microstructure were examined by an Olympus optical microscope (OM) and a scanning electron microscope (SEM), respectively. To study the real time deformation mechanism appropriate to the extracted specimens, in-situ tensile testing was executed by a multi-step gear-drive system installed in the S8000 SEM chamber shown in Fig.\u00a02a. The set-up is operated on the principle of bi-axial tension along the principal axis at a speed of 1\u00a0\u00b5m/s. The right and left clamps of the tensile testing stage were moved in the opposite directions controlled by the gear-drive system. 8-mm diameter heating core was used to heat the specimen by conduction process, shown in Fig.\u00a02b. To measure the test specimen temperature, a K-type thermocouple was contacted with the lower surface of the specimen within SEM observation space. The required temperature for the experiment was 500\u00a0\u00b0C, which was given to the specimen in step-by-step mode. Prior to tensile testing, the temperature of the specimen was kept at 500\u00a0\u00b0C for about 30\u00a0min to ensure the temperature uniformity in the testing zone. The specimen was stretched by applied tensile load at the speed of 1\u00a0\u00b5m/s. To observe the real time microstructural changes during deformation, the tensile loading was paused and the time interval for the images capturing was 4 frames/s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000733_0022-2569(71)90002-4-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000733_0022-2569(71)90002-4-Figure12-1.png",
        "caption": "Figure 12. Double-cam followers.",
        "texts": [
            " As ~ is of constant breadth, the yoke might be completed to form a square. The cam and the square then work like a pair of gears according to the law ~ = 3~/4. A commonly used cam mechanism has at the end of its follower a circular roller which is in steady contact with the rotating cam disk. The profile of the d i s k - not necessarily c o n v e x - i s a parallel curve ~ of the path c described by the roller cen te rA in the course of the relative motion EJE1. The constant distance between c and ~ is equal to the roller radius a (Fig. 12). From the geometric point of view the curve c (the \"pitch profile\") is more important than the working cam profile ~ itself. When c is given by means of its polar equation r = r(z), corresponding rotation angles ~, ~ of cam and follower are obtainable from the triangle O A P , for instance by double application of the cosine theorem: cos (~o + z) L2- -12- - r2(z ) LZ+12--r2(T) = 2/r(z) , cos qJ = 21L (5.1) 14 The constants L = P A and l = O P denote the length of the follower lever and the central distance of the pivot P, respectively. Formulae (5.1) determine the motion law t0(~) in parametr ic form by means of the auxiliary functions ~ (v) and t0(7). If the motion law tO(~) is prescribed, the pitch curve c can be obtained as follows: Starting with arbitrary pairs of corresponding values ~, tO we get from the triangle O A P (Fig. 12) the polar coordinates r, ~\" by r'-' = l \u00b0- + L\"- - 21L cos to, L . sin ( 7 + .~) = - sin ~. (5.2.) r mechanism with two rigidly connected oscillating roller To provide the return motion a second follower PA- may be added which is rigidly connected with the first follower P A and hence turning about the same pivot P. Its contact r o l l e r - w i t h the same radius a for s i m p l i c i t y - i s operated by a second cam disk, whose profile is the parallel curve in a distance a inside the path (_7 described by the roller cen te r ,~ during the relative motion Xz/Xt",
            " It is sufficient to know the pitch profiles c and 0, the working cam profiles being parallel curves of c and 0 offset by the distance a; c and ~ may be considered as ideal cam profiles for vanishing roller radius. If the first pitch profile c is given directly or determined by the motion law 0(.~), it is a mere routine task to derive the second pitch profile ~. We have only to consider the relative motion X2/X~ of the triangle A P , ~ : This motion is defined by the path c o f A and the circle path o of P (center O, radius l). Using a sheet of t ransparent paper (vellum) for the moving sys tem x_._,, the path (\" o f / f is quickly constructed. An axial symmet ry of 15 c, as assumed in Fig. 12, does not induce a symmetry of C'. Tangents of C are simply added by means of the instant center I which is the point of intersection of the normal of c in A with the line OP; the tangent ofC in,,~ then is perpendicular to I,'{. If the center of curvature A* of c belonging to A (and valid also for ? in C) is known, the center of curvature ,'t* of 6\" belonging to ,'t (and valid also for the corresponding point C of the cam profile) is to be found again by Bobillier's construction (Fig. 12). Devices for automatic grinding of the second cam profile have been indicated by Hagedorn [3]. The idea consists in fixing the system E., and replacing the second roller by a grindwheel which is steered by the first roller led along the first profile. A problem analogous to that which was treated in Section 3 concerns the question whether it is possible that the two cam disks operating a pair of rigidly connected oscillating followers as considered in Fig. 12, may coincide. The answer depends on the question whether there exist identical non-trivial pitch profiles c and C. For simplicity let us assume that the two follower levers PA and P,4 be of equal length L. To get a better insight into the transformation V: A ---* ,~ which maps c onto C, we may introduce the circular arc A,,t = v with center P and radius L as a material element into the system ~..,. This arc v envelopes a circle w in ~ with center O and radius L - - l. When the initial point A is led along the curve c and the arc v is sliding along the fixed circle w, the end-point,,{ will trace the curve e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001796_s12541-015-0346-0-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001796_s12541-015-0346-0-Figure1-1.png",
        "caption": "Fig. 1 TRB global coordinate system and loading",
        "texts": [
            " This model can be used also for run-out or vibration analysis of bearings by using the transfer function method,20-22 and the finite element method.23 This section describes a five-degree-of-freedom (5-DOF) dynamic model of a TRB with inner and outer races with out-of-roundness error. Details of the bearing model without error were described in a previous study by de Mul et al.17 This section focuses on the modification of the dynamic bearing model to include races with out-of-roundness error. A 5-DOF bearing model with an external load {F} = {Fx, Fy, Fz, My, Mz} T applied to the inner race is shown in Fig. 1. The associated displacement is given by {\u03b4} = {\u03b4x, \u03b4y, \u03b4z, \u03b3y, \u03b3z} T. Fig. 2(a) shows a cross section of the bearing at a particular roller. Because the inner race cross section and the roller are displaced from their original positions by {u\u03ba} = {u\u03be, u\u03b6, \u03b8}T and {v\u03ba} = {v\u03be, v\u03b6, \u03c8}T, respectively, contact forces between the roller and races are generated. Fig. 2(b) shows the free body diagram of a roller, where Qf, Fc, and Mg are the flange force, centrifugal force, and gyroscopic moment, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.48-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.48-1.png",
        "caption": "Fig. 2.48 Braking intervention to limit M-M differential slip [CZINCZEL 1995].",
        "texts": [
            " It is important to measure the yaw rate for calculating the wheels\u2019 actual values of angular velocity, because when cornering, if the tilting of the wheels is not monitored, the angular velocity (speed) sensors may report incorrect data that could lead to a change in traction by the actuator when it is already satisfactory. Overall, an ATC system relies on three different sorts of sensors: angular velocity (speed) sensors, steering angle sensors, and yaw rate sensors (see Figure 2.47). When used together, they are quite effective in delivering the information required by the controller for effective ATC. Figure 2.48 exemplifies the system dynamics of a M-M drive shaft, differential, and drive wheels on on/off road surfaces affording differing levels of traction with adhesion coefficients \u03bcH and \u03bcL (high wheel and low wheel) [CZINCZEL 1995]. 2.1 Introduction 191 The torque activating from the driveshaft is disseminated equally between the wheels. The low wheel acts in response to imperfect adhesion potential by spinning during concise wheel acceleration. The acceleration force transmitted because of the high wheel, then corresponds to the sum of the accelerative force at low wheel added to its inertia. When the low wheel attains its determined angular velocity, the accelerative force accessible at both wheels is restricted to the maximum at the low wheel. The simply means to intensify the acceleration force at the wheel is to prevent the low wheel from spinning. The first variety, action of the wheel brake, is shown in Figure 2.48. The action of braking force FB at low wheel prevents it from spinning. This creates the supplementary acceleration force FB * (the product of FB multiplied by the ratio of effective braking radius to wheel radius) accessible at high wheel. The second variety for maximum use of traction potential is characterised by the action of fix-ed, variable, or controlled M-M differential-slip limitation mechanisms. These give a fixed coupling to guarantee the same slippage rates at the drive wheels, by this means permitting them to multiply the maximum accelerative force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001547_iros.2013.6696825-Figure21-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001547_iros.2013.6696825-Figure21-1.png",
        "caption": "Figure 21. New head section.",
        "texts": [
            " Figure 19 shows an image of the head section climbing over a step that is between an elbow and a straight pipe. First, to climb over the step, the ABS part needs to proceed in the direction of travel, therefore the tip of the head section needs to be flexible. Figure 20 shows an image after the head section has climbed over the step. If the head section is flexible, the base of the head section buckles, therefore the head unit collides with the elbow. Thus, the base of the head section needs a pulling force that pulls it backward because the head unit needs to proceed in the direction of traveling. Figure 21 shows an image of the new head section we developed, and Table 3 shows the specifications. The new head section climbs over the step using the flexibility of a compression spring, and pulls itself backward by using the pulling force of the extension spring. We determined this length (140 mm) so that the head section can pass through a continuous elbow first as the robot passes through a continuous elbow. Figure 22 shows an image of the robot developed for continuous elbows and Table 4 shows the specifications of the unit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001732_c4sm00280f-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001732_c4sm00280f-Figure2-1.png",
        "caption": "Fig. 2 Triaxial Helmholtz coils. (a) Photograph of our experimental triaxial Helmholtz coil system. (b) Schematic illustrating one possible configuration for the relative orientations of the high-frequency (blue), low-frequency (yellow), and dc (red) coils.",
        "texts": [
            " Instead, this theory is based solely on details concerning the symmetries of the applied symmetry-breaking rational elds, and as such highlights the novelty of this phenomenon. Although this paper is largely theoretical in nature, select experimental results are presented to demonstrate the predictive capabilities of the 3994 | Soft Matter, 2014, 10, 3993\u20134002 theory. In fact, a detailed experimental study quantifying the torque densities produced by vortex uids comprising a variety of particle shapes is forthcoming. Our experimental system consists of a series resonant triaxial Helmholtz coil44 (Fig. 2) that produces uniform magnetic elds over the uid volume, which is typically about 10 mL. Field frequencies from 50\u20131000 Hz and eld strengths as high as 500 Oe can be produced, but typical rms eld strengths are 150 Oe for each component. A variety of particle geometries were used in these experiments. The spherical particles were 4\u20137 micron carbonyl iron, obtained from ISP technologies, Inc. The Ni nanorods were 500 nm in diameter and 5 microns in length and were synthesized for us by R. Bell, Penn"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002783_tie.2018.2889629-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002783_tie.2018.2889629-Figure4-1.png",
        "caption": "Fig. 4. Transmission test platforms. (a) Dynamic parameter monitoring platform. (b) Tested gears.",
        "texts": [
            " On the other aspect, it is hard to collect sufficient instances if the value of \u03b1 is too small. This is a trade-off between improving the accuracy and obtaining sufficient instances. In this case, we use a small \u03b1 with empirical value and repeatedly resample new instances with our generative model in Fig. 1. In this paper, the proposed generative model is applied to reliability classification of transmission gears. Existing data of gear parameters have been examined on test platforms in Qingshan industry. The test platform (illustrated as in Fig. 4 (a)) has 4 main components: power engine, bearing, transmission, and bus communication. Power engine provides energy, and bearing adjusts the speed. Tested gears in the transmission are shown in Fig. 4 (b). Gear parameters that have passed safety operation test of transmissions and gears are collected as real data in the experiments. The number of collected real data is 214. Gaussian kernel function is adopted in the generator to reduce computational complexity. The generative model is implemented on a single Nvidia TITAN Xp GPU. All simulations run on an Intel i7-6800K CPU. There are initial settings of model coefficients: \u03b711 and \u03b712 are initiated as 0.9; \u03b721 and \u03b722 are 0.9999; \u03b5 is set as 10\u22128; \u03b1 is 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001692_s1068366615020038-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001692_s1068366615020038-Figure4-1.png",
        "caption": "Fig. 4. Schematics with the mixed contact of bodies: (a) shaft with the trilobing; (b) shaft with the tetralobing.",
        "texts": [
            ",\u0394\u03b1 = \u00b0 \u00b0 2\u0394\u03b1 2n 1B > 2B n= 2n 2,n 2 2 2 1 1 ''1 * , k k m k km k k h k k L H t h H S L \u2212 \u03b1\u2212 \u03b1 \u03b1 \u23a1 \u23a4 \u2212\u23a2 \u23a5= \u2212 \u23a2 \u23a5\u03a3 \u23a2 \u23a5\u23a3 \u23a6 ( )2, ;h hS fp h= \u03b1 \u03b5 1 1'(1 ),h\u03a3 = \u2212 \u2212 2 2'(1 );h\u03a3 = \u2212 ( )0 1 ;km k k k h k kL B S m= \u03c4 \u2212 \u03a3v 1 1;h h\u03b5 = \u03a3 1 2 1' ,h h h= 2 1 2'h h h= ( ) ( ) 21 12 1 10 0 20 1 2 20 0 10 ' , mm mm B h B \u03c4 \u03c4 \u2212 \u03c4 = \u03c4 \u03c4 \u2212 \u03c4 ( ) ( ) 12 21 2 20 0 10 2 1 10 0 20 ' ; mm mm B h B \u03c4 \u03c4 \u2212 \u03c4 = \u03c4 \u03c4 \u2212 \u03c4 ( ) 2 0 2 0k kH \u03b1 = \u03c4 \u03b1 \u2212 \u03c4 ( ) 2 0 2 2 0,k kH n \u03b1 = \u03c4 \u03b1 \u2212 \u03c4 ( ) ( )0 2 2,fp\u03c4 \u03b1 = \u03b1 \u03b4 ( ) ( )0 2 2 2, , , ;n fp h\u03c4 \u03b1 = \u03b1 \u03b4 0, ,k k kB m \u03c4 Time of the interval of the interaction tribocon tact at angular displacement of the shaft is (2) where is the sliding friction path at the shaft revolution by 1\u00b0, is the sliding velocity, and are shaft revolutions per minute. The mixed contact of bodies with the roundness of the shaft profile (Fig. 2) has five phases of the contact interaction: three phases of the single area contact (I, III, V) and two phases of the double area contact (II, IV) (Fig. 3). The phases of the single and double area contacts are not interrelated. For the scheme with the trilobing of the shaft pin (Fig. 4a), there are seven phases of the contact (phases I, III, V, and VII of the single area contact and phases II, IV, and VI of the double area contact) and, for the scheme with the tetralobing of the shaft pin (Fig. 4b), there are nine phases of the contact (phases I, III, V, VII, and IX of the single area con tact and phases II, IV, VI, and VIII of the double area contact). Correspondingly, initial contact semiangles ( for the single area contact and for the double area contact) at wear are determined according to [8] using the following con dition of the equilibrium of forces acting on the shaft: (3) (4) where (5) where = \u03bb2 = are angles that determine the direction of forces and (6) (7) '' * t 2\u0394\u03b1 ' 2 2 2 '' ,* 6 Lt n \u0394\u03b1 = \u0394\u03b1 = v ' 22 360L R= \u03c0 2 2R= \u03c9v 2 2 30,n\u03c9 = \u03c0 2n 0 2( )\u03b4\u03b1 \u03b1 2( )\u03b3 \u03b1 ( ) 0 2 2( ( ), ( ))s h h\u03b4 \u03b4\u03b1 \u03b1 \u03b3 \u03b1 for the single area contact, 2 0 2 2 ( ) 4 sin 4 N R E \u03b4 \u03b4 \u03b4 \u03b1 \u03b1 = \u03c0 \u03b5 \u03b4 \u03b4 \u03b3 \u03bb = = \u03c0 \u03b5 for the symmetrical double area contact, 2 1 2 2 ( ) 4 sin 4 N N R E 1 2 2 cos ;N N N= = \u03bb ( ) \u03b4 \u03b4 \u03b3 \u03b1 \u2260 = \u03c0 \u03b5 for the asymmetrical double area contact, ( ) 2 2 1 2 24 sin 4 s N N R E 2 2 1 sin(90 ) , sin(180 2 ) N N \u03b1 \u00b0 + \u03bb \u2212 \u03b1 = \u00b0 \u2212 \u03bb N2\u03b12 \u2212 \u00b0 + \u03bb + \u03b1 \u00b0 \u2212 \u03bb 2sin( 90 ) , sin(180 2 ) N 1 2 (90 ),\u03bb = \u03b1 \u2212 \u2212 \u03bb \u2212 \u03bb \u2212 \u03bb1(2 ) 21 ,N \u03b1 22 ,N \u03b1 1 2 2 ;\u03bb + \u03bb = \u03bb ( ) ( )2 0 2 24 sin , 4 h h hN R E E \u03b4 \u03b4 \u03b4 \u03b1 \u03b1 = \u03c0 \u03b5 + \u03b5 ( ) ( ) ( )( ) 2 2 1 2 24 sin , 4 s h h hN N R E E \u03b4 \u03b4 \u03b4 \u03b3 \u03b1 = \u03c0 \u03b5 + \u03b5 166 JOURNAL OF FRICTION AND WEAR Vol",
            " 3); is the Young modulus, are the modulus of shear elastic ity and the Poisson\u2019s ratio, \u00d7 and Correspondingly, at the asymmetrical contact, At the symmetrical contact, 2 4 cos , 4 E e R\u03b4 \u03b1 = ,\u03b1 = \u03bb + \u03b1 ,\u03b8 = \u03bb + \u03b8 0 ,\u2264 \u03b1 \u2264 \u03b8 0 ,\u2264 \u03b8 \u2264 \u03b3 (1) (1) 1 2 ,\u03b3 \u2264 \u03b1 \u2264 \u03b3 ( ) ( )( )1 1(1) 1,2 0 00.5 ,\u03b4 \u03b4\u03b3 = \u03bb \u00b1 \u03b2 \u2212 \u03b1 ( ) ( )( )2 2(2) 1,2 0 00.5 \u03b4 \u03b4\u03b3 = \u2212\u03bb \u00b1 \u03b2 \u2212 \u03b1 ,\u03b4 \u03b4\u03b5 = \u03b5\u03a3 4 1 24 ,e E E Z= ( )2 1E G= + \u00b5 ,G \u00b5 ( ) ( )1 11 1Z = + \u03ba + \u03bc ( ) ( )2 2 2 11 1 ,E E+ + \u03ba + \u03bc 3 4 ;\u03ba = \u2212 \u03bc ( ) ( )1 2 1 1 2 21 . 2 2 D D\u03b4 \u03b4 \u03b4 \u03a3 = \u2212 \u03b1 \u2212 \u03b1 \u03b5 \u03b5 1 0 ,\u03b1 = \u00b0 20 360 .\u2264 \u03b1 \u2264 \u00b0 for the shaft with ovality (Fig. 2), for the shaft with trilobing (Fig. 4a), for the shaft with tetralobing (Fig. 4b). Out of roundness characteristics of profiles of the bushing and the shaft are as follows: and is a circular bushing and shaft with ovality (Fig. 2), and is a circular bushing and shaft with trilobing (Fig. 4a), and is a circular bushing, shaft with the tetralobing (Fig. 4b). The determination of angles and should be based on where is the interval number for the discretization of the shaft contour. Zones of the single and double area contacts are deter mined by angles which are found based on the con dition where At angles initial contact pressures are 1 0 ,\u03b1 = \u00b0 2 0 ,90 ,180 ,270 ,360\u03b1 = \u00b0 \u00b0 \u00b0 \u00b0 \u00b0 1 0 ,\u03b1 = \u00b0 2 0 ,60 ,120 ,180 ,...,360\u03b1 = \u00b0 \u00b0 \u00b0 \u00b0 \u00b0 1 0 ,\u03b1 = \u00b0 2 0 ,45 ,90 ,135 ,180 ,...,360\u03b1 = \u00b0 \u00b0 \u00b0 \u00b0 \u00b0 \u00b0 ( ) ( )1 2,D D\u03b1 \u03b1 1 1D = 2 21 3 cos 2D = \u2212 \u03b1 1 1D = 2 21 8cos 3D = \u2212 \u03b1 1 1D = 2 21 15cos 4D = \u2212 \u03b1 0 h\u03b4\u03b1 ( )s h\u03b4\u03b3 21 11 , j h h \u03b1 \u03b5 = \u2211\u2211 2360j = \u00b0 \u0394\u03b1 2*,\u03b1 ( )11 2\u03b4\u03a3 = \u2212 \u03b4 \u03b5 ( ) ( ) ( )1 1 2 2 22 0,D D\u03b1 \u2212 \u03b4 \u03b5 \u03b1 = 1 0 ,\u03b1 = \u00b0 20 360 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002127_cjme.2015.0710.091-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002127_cjme.2015.0710.091-Figure3-1.png",
        "caption": "Fig. 3. Couplings with double right angle slider",
        "texts": [
            " Since its rank is six and when adding the serial chain with these seven screws to the first loop, it is clearly impossible to bring into any over-constraint to the linkage, that means, 2 0 = The whole mechanism has thirteen links and fourteen pairs, and the total over-constraints are 1 2 1.  = + = (8) By mobility calculating, it could be concluded that ( ) ( )6 1 6 13 14 1 14 1 3.iM n g f = - - + + = - - + + =\u00e5 (9) The mobility of this mechanism is three. From this double-loop example it is found that there is neither any kinematic couple between the two loops nor any new over-constraint in the new loop. That is because only the rank of new screw system for these \u201cnew pairs\u201d of the new loop is up to six. Fig. 3(a) shows a mechanical coupler with double sliding rods which can transmit a motion between two shafts with a 90\u00b0 orthogonal angle[17]. Axis of disk A is input and that of B is output, both disks are connected with the frame by two R pairs. There are five links, two revolute pairs and four cylindrical pairs. The two cylindrical links connect with the driving and passive dicks in the mechanism. In the problem, there is a sub-mechanism, CDEF, and it brings real troublesome to find out its over-constraint because of the complicated structure. Firstly the submechanism CDEF is taken into consideration. (1) Estimate the over-constraint of sub-loop CDEFC As shown in Fig. 3(b), a coordinate system A-XYZ is set, in which X-axis and Y-axis are parallel to the two sides of the right-angle link, respectively, and the origin point A locates at the center of circle CF. The screw system can be obtained: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 3 3 2 1 5 5 2 1 7 7 2 1 0 0; 0 , 0 0 0; 1 0 0 , 0 1 0; 0 , 0 0 0; 0 1 0 , 0 1 0; 0 , 0 0 0; 0 1 0 , 1 0 0; 0 , 0 0 0; 1 0 0 , C C D D E E F F e f d f d f e f = = = = = = = = $ $ $ $ $ $ $ $ (10) which can be simplified as ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 3 3 2 1 7 7 1 0 0; 0 , 0 0 0; 1 0 0 , 0 1 0; 0 , 0 0 0; 0 1 0 , 1 0 0; 0 ",
            "=$ (12) LU Wenjuan, et al: Over-Constraints and a Unified Mobility Method for General Spatial Mechanisms Part 2: Application of the Principle \u00b74\u00b7 It is a constraint couple limiting a rotation about Z-axis. There is one over-constraint in the sub-mechanism, 1 1 = . Consequently, we have n=4, g=4 and 1 1 = in this sub-mechanism, and its mobility is ( ) ( )1 16 1 6 4 4 1 8 1 3.iM n g f = - - + + = - - + + =\u00e5 (13) From this analysis, taking CF as the frame, the output link ED has three degree of freedoms(DOFs), including two translations along X- and Y-axes, and a rotation around X-axis. (2) Estimate the over-constraint of the second closedloop The mechanical coupler, as shown in Fig. 3(a), will be obtained by adding two revolute pairs A and B in front and at back of the sub-mechanism, respectively. Meanwhile the second closed loop, Fig. 3(c), will be formed, and the new over-constraints will appear when reclosing the revolute pair B with the frame. Here it needs to check the relative motions between the two elements in closure to determine the over-constraints by using \u201cmethod to recognize over-constraints by analyzing relative movement\u201d. For the spatial mechanism the over-constraint must be analyzed from six aspects including three translations along and three rotations around X-, Y- and Z-axes, respectively. Each of which should be checked to determine which constraint is real and which one is virtual",
            " It is just the basic idea of the \u201cmethod of analyzing the relative movements between closed elements\u201d for determination of over-constraints. Connecting pair A of the sub-chain to the base, and link ED becomes the end-link of the open chain. Before further closing the revolute pair B, the end link ED of the open chain ACFED has four DOFs including two translations along X- and Y-axes, two rotations around X- and Y-axes, that is because pair A has been added and connected to the base and one more DOF is added to the sub-loop. The four screws for the four mobilities form a virtual-open chain waiting for reclosure, Fig. 3(c) Correspondingly, after closing the virtual chain to the base by using the revolute pair B, the virtual loop AMPQB is formed, as shown in Fig. 3(d), where three virtual pairs M, P, Q, denote the three screws for the three DOFs in Eq. (11). The reclosure pair B will bring into five constraints to the end link ED. To analyze how many and what kinds of constraints are there in closure, here a method named \u201cover-constraint determination tabulation method\u201d, Table 1, will be applied. Table 1 makes some comparisons on the relative movements and constraints before and after the closing, and determines the over-constraints. In analysis, if one certain DOF of the end-link of the open chain exists before closing, while it is restricted by the closure pair in closing, it means the closure pair brings a real constraint to the end link of the open chain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003544_j.jmapro.2021.02.002-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003544_j.jmapro.2021.02.002-Figure7-1.png",
        "caption": "Fig. 7. Failure modes of edge joints under tear loading.",
        "texts": [
            " It could be seen that the heat input increased with the duty ratio increasing. That caused the crack length increasing. When the continuous laser was used the crack length reached the peak value. So was the het input. However when the duty ratio was 25 % the joint formation was not good because of the low heat input. Therefore similar with the energy density the crack length could be decreased by controlling the duty ratio of the pulse laser. The photograph of the experiment setup for tearing test was shown in Fig. 7(a). Under tear loading there were two failure modes for the edge joints with cracks. One was the fracture along the fusion line. The fracture position was at the fusion line, shown in Fig. 7(b), Fig. 8(a) and (b). Another was the fracture along the original crack. The original crack grew under the tear loading to cause the final fracture, shown in Figs. 7 (c) and 8(c). The appearances of the fractures were observed under SEM. The fractures of the failed joints were shown in Fig. 9(a) and (b). There were some deep dimples observed both on the fractures of the two failure modes. That suggested that there was an obvious ductile characteristic for the edge joint under tear loading. The relationship between the tear loading and the original crack length was shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000742_j.aca.2009.11.052-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000742_j.aca.2009.11.052-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the micro-fluidic device: (a) monolith channel, 600 m wide, 50 m deep and 20 mm long; (b) electrochemical detection channel, 1.5 mm wide, 50 m deep and 20 mm long; (c) link channel, 100 m wide, 50 m deep and 5 mm",
        "texts": [
            " Milli-Q water 18 M cm) was used in the preparation of all aqueous solutions. .2. Micro-fluidic device fabrication, preparation of ilica-monoliths, enzyme immobilization and detection Glass micro-fluidic devices were fabricated in house using stanard photolithography technology followed by wet etching and hermal bonding [25]. The device used comprised of a channel in hich a monolith could be generated and a region where the elecrodes for the amperometric detector could be located. A schematic f the micro-fluidic device is shown in Fig. 1A. The dimensions of he channels were 600 m wide, 50 m deep and 20 mm long for he monolith channel and 1.5 mm wide, 50 m deep and 20 mm ong for electrochemical detection channel. The connecting chanel between the monolith and detector was 100 m wide, 50 m eep and 5 mm long. The preparation of silica-monoliths and the onolith functionalization with PEI polymer were carried out using imilar methods to those reported previously [38]. In a typical reparation, 18 l of TMOS and 69 l of MTMOS (at 1:4 molar ratio) ere added to dilute HCl solution (8 l of 1 mM HCl and 13",
            " The monolith was then kept in a fridge (4 \u25e6C) for 1 h followed by vacuum drying for 30 min to generate a monolith immobilized enzyme micro-reactor where enzymes were efficiently immobilized via electrostatic interaction between electronegative enzymes and electropositive PEI polymers [38\u201340]. The amperometric detector was constructed from a Pt disc-working electrode (0.5 mm diameter), a Pt wire counter electrode (1 mm diameter) and a Ag/AgCl (1 mm diameter) reference electrode which were placed into the holes in the detection channel (Fig. 1a) of the device and sealed by using epoxy resin. Before measurements were carried out, using a PalmSens Electrochemical Sensor (IVIUM Technologies, The Netherlands) at a fixed electrode potential (650 mV versus Ag/AgCl, room temperature), the micro-reactor was washed for 5 min with a working buffer solution (0.05 M pH 7 Tris\u2013HCl buffer containing 10 mM KCl) and the washings collected. 2.3. Enzyme activity assay and measurements of free and immobilized enzyme inhibition Enzyme activity was measured using the FIA system shown in Fig. 1B, which consisted of a syringe pump (PHD 2000, Harvard), a himica Acta 659 (2010) 9\u201314 11 m t o e s a w o w a a c H i s ( i t f m s a m r w I a 2 d t 2 r o t 3 3 d a i d o a i c i o a o a e i i c w A are based on evaluating the experimental data according to the Lineweaver\u2013Burk double reciprocal plot and/or the Dixon method [44]. For the Lineweaver\u2013Burk method the data obtained from the amperometric measurements were treated based on the electro- P. He et al. / Analytica C icro-injector with a sample loop of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001420_s11431-013-5433-9-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001420_s11431-013-5433-9-Figure9-1.png",
        "caption": "Figure 9 Three configurations of the PPR1R2-4R1P reconfigurable limb.",
        "texts": [],
        "surrounding_texts": [
            "Four planar five-bar metamorphic linkages and sixteen LFC chains are obtained in the previous sections. Reconfigurable limbs and parallel mechanisms are constructed in this section."
        ]
    },
    {
        "image_filename": "designv10_12_0000993_med.2012.6265864-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000993_med.2012.6265864-Figure2-1.png",
        "caption": "Fig. 2. UPAT\u2013TTR hardware setup",
        "texts": [
            " The principal concept behind the design of the UPAT Tri\u2013TiltRotor (UPAT\u2013 TTR) is the development of a UAV-experimental platform characterized by high quality equipment, robust assembly and a high-end interface allowing for seamless future system expansion capabilities (by incorporating advanced sensorial equipment). In this article, the issues and considerations towards the implementation of the aforementioned unmanned system are addressed. The article is structured as follows: In Section II the design of the UPAT\u2013TTR is presented. In Section III the system modeling process is presented. In Section IV experimental results of the system\u2019s attitude stabilization response are presented. The article is concluded in Section V. The complete setup of the UPAT\u2013TTR, depicted in Figure 2, consists of the hardware components as well as the software implementation. The main components of our UAV experimental platform are: a) the Actuators and their Control System, b) the Sensors and c) the Main Control Unit. The system is composed of 3 actuator types. The two main rotors are positioned on the wing axis and consist of two lowKV, high-power (max power of 800W each) DC brushless motors and two 3-bladed 13x8\u201d propellers. The tail rotor 978-1-4673-2531-8/12/$31.00 \u00a92012 IEEE 1579 consists of a Ducted Fan system, driven by a high-RPM, small-size brushless DC (BLDC) motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000412_156855309x420039-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000412_156855309x420039-Figure4-1.png",
        "caption": "Figure 4. Quartet 4 with a rollable body.",
        "texts": [
            " It consists of two bipedal passive dynamic walkers and is connected by what we call the body (Fig. 2). Each passive dynamic walker is developed to achieve stable passive dynamic walking and the length of the legs can be changed. Each foot has a spherical surface. K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 485 We adopted two types of bodies \u2014 a flat rigid body and a rollable body \u2014 and examined the change of locomotion based on the change of the body. Quartet 4 with a flat rigid body is shown in Fig. 3 and Quartet 4 with a rollable body is shown in Fig. 4. The parameters of the robot are given in Table 1. Quartet 4 has no actuators. Therefore, so as to not disturb the walking gait, a motion capture system was used to obtain walking data. In this research, four cameras recorded Quartet 4 walking as in Fig. 5 and tracked the markers. Having linked recorded tracking data to calibration data (Fig. 6), we could get three-dimensional 486 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 (3-D) coordinate walking data. This data analysis was processed on Move-Tr/32 (Fig. 7), which was developed by Library Inc. The flat rigid body (Fig. 3) and rollable body (Fig. 4) were used in these experiments. Front foot length was variable from 22 to 25 cm. Hind foot length was fixed to 23 cm. Slope angle was varied from 2.3\u25e6 to 4.5\u25e6. K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 487 488 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 Table 2 shows the results of the experiments. The vertical axis shows the front foot length (cm). The horizontal axis shows the slope angle (\u25e6). The letters in each grid represent the walking state: \u2018S\u2019 means Quartet 4 gradually stops walking, \u2018O\u2019 means pace gait, \u2018D\u2019 means the length of stride becomes longer to roll over, \u2018T\u2019 means trot gait, \u2018W\u2019 means walk and \u2018X\u2019 is roll over"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.2-1.png",
        "caption": "Figure 2.2. CAD model of a spatial 6-dof parallel mechanism with revolute actuators",
        "texts": [],
        "surrounding_texts": [
            "A spatial six-dof parallel mechanism with revolute actuators is illustrated in Figures 2.2 and 2.3. It consists of six identical legs connecting the base to the platform. Each of these legs consists of an actuated revolute joint attached to the base, a first moving link, a passive Hooke joint, a second moving link and a passive spherical joint attached to the platform. A parallel mechanism of this type was described in [2.14]. The coordinate frame of the base, designated as the O-xyz frame is fixed to the base with its Z-axis pointing vertically upward. Similarly, the moving coordinate frame O'-x'y'z' is attached to the platform. The Cartesian coordinates of the platform are given by the position of point O' with respect to the fixed frame, noted p = [x, y, z]T and the orientation of the platform (orientation of frame O'-x'y'z' with respect to the fixed frame), represented by matrix Q, which can be written as 333231 232221 131211 qqq qqq qqq Q (2.12) where the entries can be expressed as functions of Euler angles, quadratic invariants, linear invariants or any other representation. Finally, the coordinates of centre points Pi (Figure 2.3) of the S-joints relative to the moving coordinate frame of the platform are noted (ai, bi, ci) with i = 1, \u2026, 6. A reference frame noted Oi1-xi yi zi is attached to the first link of the ith leg. Point Oi1 is located at the centre of the first revolute joint. The coordinates of point Oi1 expressed in the base coordinate frame are (xio, yio, zio), where i = 1, \u2026, 6. Moreover, the unit vectors defined in the direction of axes xi, yi and zi are denoted xi1, yi1 and zi1, respectively. Vector zi1 is defined along the axis directed from point Oi1 toward point Oi2 while vector xi1 is defined along the direction of the first revolute joint axis. Finally, vector yi1 is defined as 6...,,1, 11 11 1 i ii ii i xz xzy (2.13) Also, points Cil and Ciu denote respectively the centre of mass of the lower and upper link of each leg. Let i be the joint variable associated with the first revolute joint of the ith leg and i be the angle between the positive direction of the x axis of the base coordinate frame and the coordinate axis xi1, where it is assumed that vector xi1 is contained in the xy plane of the fixed reference frame. One can write the rotation matrix giving the orientation of frame Oi1-xi yi zi with respect to the reference frame attached to the base as 6...,,1, cossin0 sincoscoscossin sinsincossincos i ii iiiii iiiii ilQ (2.14) Moreover, it is assumed that the centre of mass of the second link of the ith leg lies on line Oi2Pi. One can then write 6...,,1,1 iililioi lQrp (2.15) where pi1 and rio are respectively the position vectors of points Oi2 and Oi1 expressed in the base coordinate frame, while lil is the vector pointing from Oi1 to Oi2 and expressed in the local coordinate frame, and 6...,,1,0 0 ,, 1 1 1 1 i lz y x z y x il il i i i i io io io io lpr (2.16) where lil is the distance from Oi1 to Oi2. Equation (2.15) can be written in component form as 6...,,1,sinsin1 ilxx iiilioi (2.17) 6...,,1,sincos1 ilyy iiilioi (2.18) 6...,,1,cos1 ilzz iilioi (2.19) Then, one can compute the position vector of the centre of mass of the second link of the ith leg from the position vectors of points Oi2 and Pi as 6...,,1,1 i l l ii iu ic iiu pppr (2.20) where riu is the position vector of the centre of mass of the upper link of the ith leg and where liu and lic are respectively the distance from Oi2 to Pi and from Oi2 to Ciu. Moreover, position vector pi can be expressed as a function of the position and orientation of the platform, i.e. 6...,,1, iii pQpp (2.21) where 6...,,1,, i c b a z y x i i i ipp (2.22) The global centre of mass of the mechanism, noted r can then be written as 6 1i iuiuililpp mmmM rrrr (2.23) where M is the total mass of all moving links of the mechanism, mp, miu and mil are respectively the masses of the platform, the upper link and lower link of the ith leg, and 6 1i iuilp mmmM (2.24) while rp and ril are respectively the position vectors of the centre of mass of the platform of the mechanism and of the centre of mass of the lower link of the ith leg, namely pp Qcpr (2.25) 6...,,1, iililioil cQrr (2.26) where cp and cil are the position vectors of the centre of mass of the platform and of the lower links expressed in the local reference frame, and whose components are given as 6...,,1,, i x y x z y x ic ic ic il p p p p cc (2.27) Substituting Equations (2.20), (2.25) and (2.26) into Equation (2.23), one then obtains z y x r r r Mr (2.28) where 6 1 6 cossinsinsin i iiiiiix DDr xoDqDqDqDxD 13161215111413 6 1 6 sincoscoscos i iiiiiiy DDr yoDqDqDqDyD 23162215211413 zo i iiiiz DqDqDqDzDDDr 33163215311413 6 1 6 sincos where Dxo, Dyo and Dzo are constant coefficients, and where 6...,,1, iml l l zmD iuic iu il icili 6...,,1,6 iymD icili 6 1 13 1 i iu ic iup l l mmD 6 1 14 1 i iu ic iiupp l l amxmD 6 1 15 1 i iu ic iiupp l l bmymD 6 1 16 1 i iu ic iiupp l l cmzmD In the above expressions for rx, ry and rz, if the coefficients of the joint and Cartesian variables vanish, then the global centre of mass of the mechanism will be fixed for any configuration of the mechanism. Hence, one obtains sufficient conditions for static balancing as follows .16...,,1,0 iDi (2.29) An example of balanced mechanism is represented schematically in Figure 2.4."
        ]
    },
    {
        "image_filename": "designv10_12_0001128_9781118562857.ch1-Figure1.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001128_9781118562857.ch1-Figure1.1-1.png",
        "caption": "Figure 1.1. General scheme of LRM",
        "texts": [
            " The model obtained thus is sliced into thin layers along the vertical axis. The thin layers are converted into corresponding numerical controlled (NC) code and are sent to a LRM station in a suitable format (e.g. G&M code). A LRM station employs a laser beam as a heat source to melt a thin layer onto the surface of the substrate/deposited material and fed material to deposit a new layer as per the shape and dimensions defined in NC code. A number of such layers deposited one over another result in 3D components directly from the solid model. Figure 1.1 presents the general scheme of the LRM technique. LRM eliminates many manufacturing steps such as materials-machine planning, man-machine interaction, intermittent quality checks, assembly and related human errors, etc. Therefore, LRM offers many advantages over conventional subtractive techniques, such as reduced production time, better process control and the capability to form functionally graded parts. It is also an attractive candidate for refurbishing applications because of the low heat input, limited dilution with minimal distortion and capability of adding finer near-net shaped features to the components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002100_s026357471400071x-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002100_s026357471400071x-Figure1-1.png",
        "caption": "Fig. 1. Forward kinematics of an n-DOF serial robot.",
        "texts": [
            " Therefore, the explicit error models suitable for position measurement are eventually derived while taking the tool frame as reference frame and then their applicable conditions are given in this paper, which would be very beneficial to kinematic parameter identification and further to kinematic calibration of serial robot. 2. Error Model 2.1. Kinematic model In calibrating an n-DOF serial robot modeled by POE formula, only the base frame {S} and the tool frame {H} need to be allocated as shown in Fig. 1. The base frame {S} is attached to any position of the robot which remains relatively stationary to link 0. Similarly, the tool frame {H} is attached to the end-effector of the robot. gSH(0) represents the initial transformation from {H} to {S} when the robot is in its reference configuration with all joint variables being zero. Each joint is also associated with one joint twist and the ith joint twist is denoted as \u03be\u0302 i \u03be\u0302 i = [ \u03c9\u0302i vi 0 0 ] , http://journals.cambridge.org Downloaded: 06 Apr 2014 IP address: 68"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000717_s12541-010-0076-2-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000717_s12541-010-0076-2-Figure6-1.png",
        "caption": "Fig. 6 CBN wheel for machining the rotors",
        "texts": [
            " Meanwhile, the radii of the arc interpolations should be calculated to check whether they are greater than the maximal radius of the interpolation of machine controller. Lines, instead of arcs, should be used in NC code generation directly if the radii are greater than the maximal radius. The selected CBN materials were electroplated on the wheel base body after the base body was completed. The base body of the CBN wheel and the CBN wheel for machining the rotors of the twin-screw kneader are shown in Figure 6. In order to evaluate the machining error, the influences of tooth profile errors affected by mounting angle error and mounting distance error as well as the wear of CBN wheel are analyzed as followings. The tooth profile error of in rotor surface increased with the increasing of mounting angle error .\u2206\u03a3 However, for the male rotor mentioned above, the tooth profile errors of the rotor first decreased then increased from bottom to top of screw groove when given same mounting distance error u A\u2206 (see Figure 7(b))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003450_j.matchar.2020.110616-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003450_j.matchar.2020.110616-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of WAAM fabrication of alloy specimens.",
        "texts": [
            " In the WAAM system, a tungsten inert gas torch was used, which was installed on a three-axis computer numerical control machine. The entire deposition process and subsequent cooling step were carried out in an Ar atmosphere with a purity of 99.99% to prevent the oxidation of the deposited material. Hot-rolled Ti-6Al-4 V plates with dimensions of 150mm\u00d7150mm\u00d75mm were used as the substrates for deposition. The deposited thin specimens were 70mm in length, 50mm in width, and 9mm in thickness, as schematically illustrated in Fig. 1. The deposition strategy is single-pass at each layer, and the deposition path is also shown in Fig. 1. For comparative analysis, a thin specimen of the Ti-6Al-4 V alloy with the same dimensions was also deposited via WAAM under the same conditions. The \u03b2-transus temperature of the as-fabricated Ti-6Al4 V and Ti-6Al-4 V-0.1B alloys was determined to be 965 \u00b1 5 \u00b0C by the metallographic method. The deposition parameters of both alloys were similar and listed in Table 1. Each deposit was created by moving the welding torch in a linear direction and feeding wire into the molten pool, which solidified to make a layer",
            " A subsequent layer was then deposited over the first by increasing the height of the torch; however, between layers the direction of torch travel was reversed so that the component was constructed in a zig\u2013zag fashion. To control the microstructure and relieve the thermal stress, annealing treatments were performed at a \u03b2-field temperature of 1000 \u00b0C for a soaking time of 1 h using a box furnace; and then the specimens were allowed to cool within the furnace. To ensure the uniform microstructures, all the specimens were cut at the center section of the WAAM built specimens, as shown in the Fig. 1(b). The microstructures of the specimens were characterized by optical microscopy (OM) and scanning electron microscopy (SEM) system equipped with an electron backscatter diffraction (EBSD) system attachment (JEOL-7100 SEM system with a TSL-EDAX probe). The system was operated at 20 kV, and the step sizes were 0.8 \u03bcm (magnification: 100\u2013200\u00d7) and 0.08 \u03bcm (magnification: 2000\u00d7). The Confidence Index of all EBSD data were greater than 0.6. The software TSLOIM was used to process the EBSD data. The Confidence Index of all EBSD data in this manuscript were greater than 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000444_s12206-008-0110-9-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000444_s12206-008-0110-9-Figure13-1.png",
        "caption": "Fig. 13. 3-D modeling for FEA; (a) Full model, (b) 1/2 model, (3) 1/4 model.",
        "texts": [
            " 12 where acoustic resonance is observed near 650Hz. In many cases, noise independent of the motor RPM can be regarded as structural resonance. However, for the test motor, acoustic resonance seems to be more dominant than structural resonance. To confirm the existence of acoustic resonance near 650Hz, acoustic mode analysis is performed with commercial FEM software Sysnoise to consider complexity of the motor internal geometry.[14,15] The internal airspace of the motor is modeled by using 39,288 elements and 29,088 nodes as shown Fig. 13. For better recognition of geometry, 1/2 and 1/4 symmetry models are additionally shown and the analysis results are listed in Table 2; the first acoustic resonance occurs at 658.4Hz, confirming that the motor noise near 650Hz originates from the acoustic resonance. The first acoustic mode shape is shown in Table 2. Analysis results of acoustic resonant frequency. Acoustic mode 1 2 3 4 5 Resonant frequency [Hz] 658.4 1243.3 1243.3 2033.9 2033.9 Fig. 14. 1st acoustic mode shape; (a) Iso. view, (b) Top view, (c) Front view"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002100_s026357471400071x-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002100_s026357471400071x-Figure7-1.png",
        "caption": "Fig. 7. The digitalized stereotactic apparatus.",
        "texts": [
            " (12) is faster than that of the identification algorithm using Eq. (8) but slower than that of ref. [8]. However, when the base frame is chosen as reference frame, the identification algorithm based on position measurement is divergent. 4.2. Experiment 4.2.1. Experiment setup. The experimental system for the kinematic calibration consists of the digitalized stereotactic apparatus and the INFINITE 2.0 portable CMMs with ScanWorks laser scanner (with an accuracy of 0.04 mm), shown in Fig. 6. It can be seen from Fig. 7, the digitalized stereotactic apparatus is in its reference configuration and kinematic parameters are given in Table V. 4.2.2. Experiment procedure and result. The three scanning planes, which are relatively stationary to link 5, are used to create the measurement coordinate frame {M}, as shown in Fig. 8. To establish the tool frame {H}, the origin of {M} should be translated to the probe so that the origin of {M} coincides with the centroid of the probe. Suppose the base frame {S} coincides with the tool frame {H} when the P O E -based calibration for serialrobotusing position m easurem ents 11 http://journals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000280_s0076-6879(76)44043-0-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000280_s0076-6879(76)44043-0-Figure9-1.png",
        "caption": "FIG. 9. This diagram shows the pad inside the cell holder and the relationship of the pad to the incident beam.",
        "texts": [
            " Black binders were placed on both sides of the two entrance and exist slits so that smaller slits, about two-thirds the length of the pad used, would restrict the radiation that entered and left the cell cavity. The cell was constructed of a cylindrical aluminum rod with a slot, approximately twice the length of the pad, located toward the end of the rod. The depth of the slot was such that the pad, with its contents, received the full beam of incident radiation. The cell was painted a dull black to avoid scattered light. A drawing of the cell and cell holder is depicted in Fig. 8. A drawing of the pad inside the cell holder and its relationship with the incident beam is given in Fig. 9. G. (]. Guilbault and A. Vaughan, Anal. Chim. Acta 55, 107 (1971). 624 APPLICATION OF IMMOBILIZED ENZYMES [41] The concentration of substrate participating in an enzyme reaction can be calculated in one of two general ways. The first method measures, by chemical, physical, or enzymic analysis, either the total change that occurs in the end product or the unreacted starting material. In this method, large amounts of enzyme and small amounts of substrate are used to ensure a complete reaction. In the second method, which is a kineti~ method, the initial rate of reaction is measured, in one of many conventional ways, by following the production of product or the disappearance of the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001996_s10035-018-0848-4-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001996_s10035-018-0848-4-Figure6-1.png",
        "caption": "Fig. 6 Method of calculation of virtual AOR showing a side view of conical pilewith vertical zoneswhere reddotsmark the exterior particles for that slice and the best fit line, b plan view of conical pile with radial slices, and c partitioning of the pile in the calculation (color figure online)",
        "texts": [
            " The collection dish sizewas varied (1mm, 2mm, and 5 mm diameters), as was the number of particles. The 1 mm diameter dish started with 7000 particles in the noncontacting cloud, while 30,000 and 189,000 were used in the 2 mm and 5 mm diameter dishes, respectively. Multiple clouds were generated and settled in order to fill the 5 mm diameter dish. The AORs for the DEM simulations were calculated through a post-processing step in which the particle locations and radii were exported and partitioned as shown in Fig. 6, where z was the vertical coordinate. Each partition corresponded to a range of z-coordinates (i.e., vertical zones) which were also partitioned radially into slices. The exterior particle (i.e., farthest radially from the center shown in red) in each partition was identified and a linear function (as shown in Fig. 6a) was fit through the particle location values for each radial slice. The angle between each of the fit lines and the horizontal plane was then calculated and then the AORs for all of the slices were averaged to obtain the AOR for the conical pile. This numerical process was adopted because the DEMdata for the pile of powderwasnot precisely conical and the fewer number of particles than in the experiment meant that the surface was rougher (see Fig. 4). In this way, the sim- ulated pile images could be more precisely fit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.81-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.81-1.png",
        "caption": "Fig. 2.81 Torque-distributing ratio between front and rear axles of a three-mode M-M DBW 4WD propulsion mechatronic control system [SZ 1986].",
        "texts": [
            "4 M-M Transmission Arrangement Requirements 237 The M-M DBW 4WD propulsion mechatronic control system brings peace of mind under difficult circumstances, and may automatically default to \u2018AUTO\u2019 mode once the velocity builds up and the problem recedes. The three-mode M-M DBW 4WD propulsion mechatronic control system offers instant and increased security when starting on snow or ice, when driving on side slopes, or under a whole range of what would normally be difficult circumstances, such as encountered on icy roads or maybe on outings to ski slopes or rural areas. In three-mode M-M 4WS DBW propulsion mechatronic control systems, there are not many torque-distributing ratios of propulsive torque from single to two axes, as shown in Figure 2.81 [SZ. 1986]. The three-mode M-M 4WS DBW propulsion mechatronic control system described above is integrated into the electronic stability program (ESP), which isoptional on ECE, and ICE, as shown in Figure 2.82 [NISSAN 2002B]. Automotive Mechatronics 238 Offering more than conventional ESP systems, a recent version uses sensors and other detectors to control a variety of situations both on and off roads. The yaw rate sensor, the G-sensor, anti-lock braking system (ABS) sensor three-mode 4WD controller and throttle control are all mechatronic and communicate with each other to detect a potential loss of traction or grip on any given wheel and then react accordingly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure3-1.png",
        "caption": "Fig. 3. Dimensions and picture of the toroidal core for electromagnetic properties measurement.",
        "texts": [
            " has a lower Vickers hardness. The cutting of 10JNEX900 is easier. Considering massive production and degradation problem, 10JNEX900 may be a better candidate. To assess the feasibility of using 10JNEX900 and to find out the problems 2605SA1 facing with in the proposed IPM rotor structure, the properties of the two materials are tested and compared. Toroidal cores are used in the test and the dimensions of the cores are based on the standard IEC-60404-6. The dimensions and a picture of the sample core are presented in Fig. 3. The structure of the measurement system is shown in Fig. 4. The toroidal core is wound with two sets of windings. The primary winding is excited with ac current i1 fed by a linear power amplifier. Sinusoidal voltage u2 in the secondary winding will be induced by regulating the primary voltage u1. The regulating variable of the primary voltage u1 is obtained by comparing the secondary voltage u2 with a sinusoidal reference. Due to flux leakage, the core magnetization and resistance loss, the primary current i1 and voltage u1 may not be sinusoidal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.11-1.png",
        "caption": "Figure 8.11. Motion of a chain on a smooth plane curve.",
        "texts": [
            " + vi;2g. Finally, use of (8.98b) leads to [ ( m )2] ( m )2 v 2 h- f. 1- 0 + 0 --.Q. - mo+m I mo +m I 2g' for the greatest height attained by mo, for VI =I 0, i.e. Vo > .j2gf.; otherwise, h= L Let us consider the motion of a simple \"deformable\" body, a perfectly flexible and inextensible uniform chain, modeled as a contiguous system of particles. The chain has length 21 and mass p per unit length , and slides under gravity along a smooth, plane curved track ti' in the vertical plane, as shown in Fig. 8.11. The energy principle is applied to find the speed of the chain along the track . Then its motion along a cycloid is described . Let s denote the arc length coordinate along (jf of the midpoint A of the chain from the origin O. Since ti' is smooth, only the gravitational force does work on the chain . The potential energy of the element of mass dm = pdo at the position y(a ) in Fig. 8.11 is dV = gy(a)dm = pgy(a)da, wherein a is the variable arc 338 Chapter 8 (8.99a) length parameter along the chain from O. Thus, the total potential energy of the contiguous system of chain elements is r +\u00a3 Yes) = pg }s- t y(a)da. The chain is inextensible, so all particle s move with the same speed s along fl; hence, the total kinetic energy of the chain is With (8.99a) and (8.99b), the energy principle (8.86) gives [ s+t p\u00a3S2 + pg y(a )da = E. s-t (8.99b) (8.99c) (8.9ge) The constant E is determined from the assigned initial speed and position of A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001364_j.electacta.2012.11.030-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001364_j.electacta.2012.11.030-Figure1-1.png",
        "caption": "Fig. 1. Photograph of the unit used to prepare the CNT-Web electrodes using alumina substrates (left) and a schematic describing the process of modifying the GC electrode w ort (e C layers e",
        "texts": [
            " Analysis by TGA, EDX, and TEM of the CNT forest hows very low amorphous carbon content and no trace of the iron atalyst (data not shown). a Acta 101 (2013) 209\u2013 215 A prototype CNT web electrode (Figs. 1 and 2) was constructed using drawn CNT webs laid down onto alumina strips (33.8 mm \u00d7 10.0 mm \u00d7 0.635 mm) or glass slips (8.5 mm \u00d7 26 mm \u00d7 0.16 mm) and solvent densified/bound to the surface with acetone to enable good adhesion with the support. Sets of six matched samples were prepared simultaneously using the winding device shown in Fig. 1 with the amount of CNT being controlled by the width of the web, the degree of insulation, and the number of turns applied. Typically, about 8.0 mm wide and 30 turns are used. In order to modify GC electrodes (3.0 mm diameter) (CH Instruments, Austin, TX, USA) with the prepared CNT webs, after placement of 30 CNT web layers on a glass slip or alumina plate, they were removed from the support after densification and immediately placed on the GC surface. A few drops of acetone were added for further densification",
            " Cleaning and regeneration of the electrode surface from any dsorbed pesticide were performed by incubating the electrode or 3 min in ACN followed by washing thoroughly with double disilled water. A clean DPV baseline was ensured before each new ncubation experiment with MP. . Results and discussion CNT-Webs have high degree of flexibility that enables the design f electrodes with different geometries, such as planar, yarn, ring, nd ribbon [16]. The simplest configuration of these is the planar or isc electrode which is shown in Fig. 2. This configuration is suitble for the mass production of electrodes using the system shown n Fig. 1 and will be used throughout this study. This is followed y peeling the CNT webs off the substrate, placing them on the C electrode surface, and securing and insulating with parafilm. o maintain better compactness between the CNT web layers and o have good adhesion to the GC electrode surface, the CNT web ayers were densified by using a few drops of a volatile organic solent such as acetone. Upon densification, the thickness of the CNT eb layers decreased to one-third of the original thickness as was eported earlier [15]. The amount of CNT can be controlled by the umber of CNT-Web layers determined by the number of winding evice turns (Fig. 1) or by the electrode electroactive surface area ontrolled by the insulation process afterwards. It is apparent from .g. alumina plates) is used and a winding device is used to continuously draw the is removed, (d) the CNT-Web is peeled off the support, and (e) placed on the GC Figs. 1 and 2 that CNT webs maintain a high degree of alignment with occasional cross CNT fibers in between. CNTs shown in the SEM image of Fig. 2b are grouped together in the form of larger bundles and each single CNT within the webs is made of an average of seven inner walls (multiwall); about 450 m long and around 10 nm in diameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003733_j.mechmachtheory.2021.104320-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003733_j.mechmachtheory.2021.104320-Figure14-1.png",
        "caption": "Fig. 14. Free body diagrams of the driven and driving bodies of a gear.",
        "texts": [
            " M i 2 (\u03be , i ) M 2 = F i N s,h \u00b7 r b2 floor ( \u03b5 ) \u2211 i = \u2212floor ( \u03b5 ) ( F i N s,h \u00b7 r b2 ) \u21d4 M i 2 (\u03be , i ) = M 2 \u00b7 F i N s,h floor ( \u03b5 ) \u2211 i = \u2212floor ( \u03b5 ) F i N s,h (41) The load supported by all the meshing teeth pairs in action must balance the driven torque, Eq. (42) . F N s,h = M 2 r b2 = floor ( \u03b5 ) \u2211 i = \u2212floor ( \u03b5 ) F i N s,h (42) Combining Eqs. (39) , (41) and (42) the fraction of the torque that is supported by each teeth pair can be calculated according to Eq. (43) . M i 2 (\u03be , i ) = M 2 \u00b7 kl i s,h Kl u s,h \u00b7 T l s,h (43) Fig. 13 is the free body diagram of a gear considering just a single meshing teeth pair. In order to understand the effect of the friction forces the driving and driven bodies must be separated. Fig. 14 a is the free body diagram of the driven body. From this diagram a load balance equation of the driven body can be established, Eq. (44) . M i 2 + F i a \u00b7 T 2 L i \u2212 F i N s \u00b7 r b2 = 0 (44) In Fig. 14 a, the friction force F i a is represented as if the meshing process was between A and C, see Fig. 13 . At the moment that the contact line passes through C, the friction force F i a reverses and remains like that between C and E. In order to account for the reversal of the friction force at the pitch line, CC\u2019, the switching function S i f (\u03be , i ) was introduced, Eq. (45) , see Fig. 15 . In S i f (\u03be , i ) , \u03bb is the normalised distance AC ( Figs. 5 and 13 ), as defined by Eq. (46) . S i f (\u03be , i ) = 1 \u2212 2 \u00b7 H ( \u03be \u2212 \u03bb \u2212 i ) (45) \u03bb = AC p bt (46) Assuming a constant average friction coefficient and a Coulomb friction model, where the friction coefficient is defined as the ratio between the friction and normal forces, the friction force F i a (\u03be , i ) accounting for the reversal of direction at CC\u2019 is written according to Eq. (47) . F i a (\u03be , i ) = F i N s \u00b7 \u03bc \u00b7 S i f (47) Taking Eq. (47) and substituting in Eq. (44) , the normal force, F i N s (\u03be , i ) , is obtained, Eq. (48) . F i N s (\u03be , i ) = M i 2 r b2 \u2212 \u03bc \u00b7 S i f \u00b7 T 2 L i (48) Consider Fig. 14 b, the free body diagram of the driving body. Since the friction, F i a (\u03be , i ) , and normal, F i N s (\u03be , i ) , forces result from the separation of the driving and driven bodies, Eqs. (47) and (48) can be substituted in the torque balance equation of the driving body, Eq. (49) . In Eq. (49) , rb 1 is the base radius of the driven body, r b1 = O 1 T 1 , see Fig. 13 . Simplifying, the driving torque considering friction forces is obtained, Eq. (50) . M i 1 + F i a \u00b7 T 1 L i \u2212 F i N s \u00b7 r b1 = 0 (49) M i 1 (\u03be , i ) = M i 2 \u00b7 r b1 \u2212 \u03bc \u00b7 S i f \u00b7 T 1 L i r b2 \u2212 \u03bc \u00b7 S i f \u00b7 T 2 L i (50) If the torque at the driven body is imposed, a common situation, the total torque at the driving body is the theoretical frictionless driving torque plus a friction term, T i V ZP s (\u03be , i ) , Eq",
            " F i N A,E (\u03be , i ) = F P i A,E \u00b7 F i N h cos \u03b2b (60) Considering a Coulomb friction model and assuming a constant average friction coefficient, the resulting friction forces F i a A,B (\u03be , i ) that act over L \u03b3 L\u2019 and L L \u03b3 are defined according to Eqs. (61) and (62) , respectively. F i a A (\u03be , i ) = F P i A \u00b7 F i N h cos \u03b2b \u00b7 \u03bc (61) F i a E (\u03be , i ) = \u2212F P i E \u00b7 F i N h cos \u03b2b \u00b7 \u03bc (62) Plugging Eqs. (61) and (62) in Eq. (59) and solving to find F i N h (\u03be , i ) yields Eq. (63) . F i N h (\u03be , i ) = M i 2 r b2 + \u03bc cos \u03b2b \u00b7 ( F P i E \u00b7 T 2 L E i \u2212 F P i A \u00b7 T 2 L A i ) (63) Eq. (64) is the torque balance of the driving body around its centre, O 1 , see Fig. 14 b. M i 1 + F i a A \u00b7 T 1 L A i + F i a E \u00b7 T 1 L E i \u2212 F i N h \u00b7 r b1 = 0 (64) Considering that F i N h (\u03be , i ) and F i a A,E (\u03be , i ) must be the same for the driving and driven bodies, substituting Eqs. (61) \u2013(63) in Eq. (64) yields the driving torque considering friction, M i 1 (\u03be , i ) , Eq. (65) . M i 1 (\u03be , i ) = M i 2 \u00b7 r b1 + \u03bc cos \u03b2b \u00b7 ( F P i E \u00b7 T 1 L E i \u2212 F P i A \u00b7 T 1 L A i ) r b2 + \u03bc cos \u03b2b \u00b7 ( F P i E \u00b7 T 2 L E i \u2212 F P i A \u00b7 T 2 L A i ) (65) From the imposed torque assumption at the driven body, the torque at the driving body can be specified as the sum of a theoretical frictionless torque and a friction torque, Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.129-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.129-1.png",
        "caption": "Fig. 2.129 6 \u00d7 6.6 or 8 \u00d7 8.8 or especially 4 \u00d7 4.4 HEVs [FIJALKOWSKI 1999].",
        "texts": [
            " The number of wheels activated (driven) will depend on the tractive effort needed and may be selected by the AI ECI or by the driver through a push bottom. A smooth transition to a coasting mode can be reached by moving the reference control signals into zero or near-zero accelerator-pedal position. Series HE transmission arrangements for the HE DBW 8WD propulsion mechatronic control system, for example, include an integrated M-E/E-M generator/motor not only driven through the ECE or ICE but also cranked, respectively, six or eight SM&GWs with the in-wheel-hub motors/generators and the CH-E/ E-CH storage battery. Automotive Mechatronics 328 Figure 2.129 shows an overall view of the 6 \u00d7 6.6 or 8 \u00d7 8.8 or especially 4 \u00d7 4.4 HEVs [FIJALKOWSKI 1999]. Tractive effort is created by the function of six or eight wheels with in-wheel-hub E-M motors. These motors take advantage of IPM technology that presents a high torque and a most advantageous dynamic capacity that is indispensable for challenging traction applications. In-wheel-hub E-M motors are collected into an integrated in-wheel drive that consists of the motor, final-drive mechanism, and service/parking brake modules for enhanced maintenance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure16-1.png",
        "caption": "Fig. 16 a The initial Kresling tube. The bottommost and topmost nodes are constrained with the Z-displacement 0 and \u2013 3H, respectively. b The bottommost layer of the tube. H = R = 0.05",
        "texts": [
            " This is also reflected by the magnitudes of the curvature in Fig. 15b, d. The animation videos for Miura-ori in the two different views are given in Online Resources 11 and 12 whilst those for the derived kirigami are given in Online Resources 13 and 14. 5.6 Kresling tube under compression The Kresling pattern is a well-known origami pattern for deployable cylindrical tubes (Kresling 2008; Guest and Pellegrino 1994). The tube considered here consists of three layers along Z-axis and each layer is made up of 16 identical triangular facets as shown in Fig. 16a. There is no quadrilateral facet. The initial configuration is folded. It is specified by the height of the layer H = 0.05 and the radius of circumscribed circle R = H, see Fig. 16b. The Z-displacement W of the bottommost nodes A1 to A8 at Z = 0 are set to zero. To avoid rigid bodymovements, U at A3 and A7 are set to zero whilst V at A1 is set to zero. The topmost nodes at Z = 3H are prescribed with W = - 3H for compressing the tube. Figure 17a\u2013c plot the vertical reaction force, energies and maximum principle stress against the normalized vertical displacement of the topmost nodes, respectively. Since this problem converges very rapidly, the initial and maximum time increments are respectively set to be 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure6.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure6.1-1.png",
        "caption": "Fig. 6.1 Overhead view of a typical swing of a baseball bat showing the position of the bat every 0.04 s, starting 0.19 s into the swing. The knob end of the bat rotates at relatively low speed in an approximately semi-circular path, while the tip of the bat rotates at higher speed along a path that spirals outward",
        "texts": [
            " Does the batter push or pull on the handle or does one hand push while the other hand pulls? The answer here is also surprising. If you watch a batter in action, and if the batter is swinging as fast as he or she can, then you will see that the batter is leaning backward and pulling the handle toward his or her body as hard as possible, with both hands. That is, the force on the handle is almost at right angles to the direction of motion of the handle. The nature of bat swinging is illustrated in Fig. 6.1. The positions of the bat here were measured by filming a batter using a video camera mounted about 10 ft above his head. A batter usually starts off the swing with the bat near or above one shoulder 88 6 Swinging a Bat Fig. 6.2 Speed of the knob and the tip of the bat for the swing shown in Fig. 6.1. Just before impact with the ball, the knob end slows down (and so do the batter\u2019s arms) as the barrel end speeds up 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 V ( m /s ) Time (s) Tip speed Knob speed Bat mass = 871gm and then swings it around through 180\u0131 or more so that it impacts at right angles with the incoming path of the ball. In Fig. 6.1, the bat started off at almost zero speed. After 4/10 of a second, the tip was traveling at 26 m s 1 D 58 mph, as shown in Fig. 6.2. Not a particularly fast swing, but one that is relatively common in the game of baseball or softball. Despite the fact that it is easy to swing a bat like this, it is not easy to explain what the batter needs to do to achieve this result. There is probably not a batter alive who could explain what he does when he swings a bat, at least in terms of the forces on the bat",
            " There is a simple explanation for this effect. The object of the exercise is not to swing the arms as fast as possible but to swing the bat or the club as fast as possible. That is best done by first accelerating the arms and then by transferring the energy in the arms to the bat or club. The action is the same as that of a double pendulum, as described in the previous chapter. To transfer energy from the arms to the bat, the arms must slow down so that the bat can reach maximum speed [2]. We will analyze the swing in Fig. 6.1 in some detail in this chapter, not because it was a particularly good swing but rather to highlight some of the physics issues. One issue is that the swing took 0.4 s. The last 180\u0131 of the swing took only 0.15 s. Some batters complete the last 180\u0131 of the swing in only 0.10 s. There is, therefore, an issue as to when the swing actually starts. In Fig. 6.1, we started counting when the bat was as far back as it went and when the bat then started to rotate forward. There was some movement of the bat even before this time. Whenever film of a baseball game is taken showing both the pitcher and the batter in view at the same time, the film shows clearly that the batter starts his first move 6.3 Effect of a Force Acting on an Object 89 before the pitcher releases the ball. As the pitcher raises his front foot, the batter crouches down slightly by bending at the knees, like a tiger getting ready to pounce",
            " By the time the batter plants his front foot on the ground, the ball is already half way to its destination and the batter has commenced his final rapid swing. The ball takes only 0.4\u20130.5 s to arrive in the hitting zone after the pitcher releases the ball. The batter is in motion the whole time, sizing up the situation and getting ready to slog the ball. When he is finally ready, he swings the bat with an acceleration that is 40 times greater than that of a Ferrari at a Grand Prix. A Ferrari can accelerate to 60 mph in 4 s. A batter can accelerate a bat to 60 mph in 0.1 s. The batter in Fig. 6.1 was filmed in the laboratory for convenience and didn\u2019t actually strike a ball. That might have influenced his swing technique and timing to a small extent, but it didn\u2019t alter the physics of what did happen. In fact, the swing was almost a carbon copy of the one analyzed in considerable detail by Adair in his book [3]. The question we now ask is, what does a batter actually do when he swings a bat? A batter grabs hold of the bat handle with both hands. What force does he apply to the handle with each hand, and in what direction do those forces act",
            "70 m) from the knob end of the handle, while the CM is about 23 in (0.58 m) from the knob. The CM is slightly closer to the center of the circular path and therefore travels at a slightly lower speed than the impact point. For example, if m D 1 kg, v D 25 m s 1 and R D 0:65 m then F D 625=0:65 D 962 N. This is quite a large force, equal to the weight of a 98 kg (216 lb) mass. Even though the bat mass is only 1 kg, the force needed to swing it around in a circle at 25 m s 1 is 98 times larger than its weight. 6.6 Close Inspection of the Swing in Fig. 6.1 93 A bat is not normally swung at constant speed in a circular path since it accelerates along the way. That means there needs to be a force acting at right angles to the bat, in a direction along the path, so the CM can accelerate along that path. Suppose the bat CM accelerates from rest to a maximum speed of 56 mph (25 m s 1) in 0.15 s. The average acceleration is then 25=0:15 D167 m s 2 and the average force on the bat acting along the circular path is F D ma D 1 167 D 167 N (38 lb). It seems that all the batter needs to do is to push the bat sideways with a force of about 38 lb and to pull it toward his chest with a force that increases with time up to about 200 lb",
            " The force acting along the path acts to increase the speed of the bat CM, and the force perpendicular to the path causes the bat to follow a curved path rather than a straight line path. The two forces are shown in Fig. 6.7. Both of the force components were calculated from changes in position of the bat CM, but the forces are actually applied at the handle end of the bat. An alternative plot is shown in Fig. 6.8 where we show the total force, F , acting at the handle end, and the angle, , 6.6 Close Inspection of the Swing in Fig. 6.1 95 96 6 Swinging a Bat Fig. 6.7 The force components M dV=dt and MV2=R acting on the bat \u221250 0 50 100 150 200 250 300 350 0 0.1 0.2 0.3 0.4 0.5 F or ce c om po ne nt s (N ) Time (s) MV2 R M dV dt between the line of action of F and the long axis of the bat. At the start of the swing, D 90\u0131, meaning that the batter exerts a force at right angles to the handle. As the bat swings around, drops to zero and remains close to zero from t D 0:2 to t D 0:3 s. During this time, the batter pulls in a direction that is essentially along the handle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003036_j.eml.2020.100731-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003036_j.eml.2020.100731-Figure5-1.png",
        "caption": "Fig. 5. (a) Illustration of the preset point, and comparison between numerical prediction and experimental validation. (b) Time consumption for reaching the first peak with respect to reactant amount and gas volume fraction. (c) Comparisons between different soft actuation methods.",
        "texts": [
            " The desirable controllability requires the soft membrane to be able to accurately reach a predefined location with high efficiency. The minimum distance ratios between the maximum displacements obtained in the numerical and experimental results and the predefined points (i.e., P1, P2 and P3) are defined as\u23a7\u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23a9 \u03bb Exp P1 = PExp 1 P1 OP1 \u03bbSimu P1 = PS\u0131mu 1 P1 OP1 , (13) where PExp 1 P1 and PS\u0131mu 1 P1 represent the minimum distances between the simulation and experimental results and P1, respectively, and OP1 is the goal height of predefined P1. Fig. 5(a) presents the comparison of the maximum displacement hmax between the empirical formula prediction and experiments, and all the minimum distance ratios are below 5%.Fig. 5(b) shows the time consumptions for reaching the first peak with respect to different premixed ratios and reactant amounts. It can be seen that the driving process is longer when the gas volume fraction is high, and the reactant amount is low. The time consumption interval is 2.2 \u223c 3 ms, which demonstrates the extremely rapid driving property of the TDM. Fig. 5(c) compares the soft actuation methods between the combustion, Shape Memory Alloy (SMA), dielectric elastomers (DE), ionic polymer metal composite (IPMC) and responsive gels. According to the existing studies in the literature, the TDM provides a satisfactory actuation performance in generating high movement speed. Taking the advantages of the extreme reaction-soft material interaction, the TDM provides a suitable selection to solve instantaneous rapid starting problems. The drawback of the TDM in the literature, however, is the relatively lower control accuracy due to the over-transient driving time [7,10\u201313,30\u201336]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure24-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure24-1.png",
        "caption": "Fig. 24. Stress results of dangerous points.",
        "texts": [
            " The corresponding fatigue life is estimated by Eq. (16), as shown in Table 7. The experimental fatigue life of this steel wheel on the fatigue test machine is 1.79 million revolutions and the cracking position is consistent with the simulation results, as shown in Fig. 22. The model of wheel 2 is 14 5 J with four bolt holes, and the stress distributions of wheel 2 is shown in Fig. 23 under the load applied at 0-deg, in which the dangerous area locates at the connecting position between the bolt hole and the strengthening rib, as shown in Fig. 24. One typical point in this position (Point C) is also selected to calculate the operating stress. A comparison of the operating stress before and after superposing the residual stress in one cycle is shown in Fig. 25, and the corresponding fatigue life of the wheel is estimated and shown in Table 8. The experimental fatigue life of this steel wheel on the fatigue test machine is 550,401 revolutions and the cracking position is also consistent with the simulation results, as shown in Fig. 26. The fatigue lives of wheels 1 and 2 predicted in simulation without considering the residual stress are much less than the experimental fatigue lives of two wheels respectively, meanwhile the deviations between predicted and tested fatigue life of two wheels are more than 90%"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.115-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.115-1.png",
        "caption": "Fig. 2.115 Layout of the dynamic-absorbing steered, motorised and/or generatorised wheel [Bridgestone Corporation; BRIDGESTONE 2003]",
        "texts": [
            " Their own vibrations absorb that from the on/off road and wheel-tyres, which permits for enhanced traction and a more-comfortable ride than is practicable with other systems or with other modes of AE or HE DBW AWD propulsion. In dynamic-absorbing SM&GWs (Fig. 2.114), dynamic shock absorbers suspend the shaftless in-wheel-hub E-M/M-E motors/generators to insulate them from the unsprung mass [BRIDGESTONE 2003]. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 301 The in-wheel-hub E-M motor\u2019s vibration, as well as the vibration from the on/off road and wheel-tyres damp each other, which enhances a road-handling performance. The flexible coupling (Fig. 2.115) consists of four cross guides that transfer smoothly the drive power from each in-wheel-hub E-M/M-E motor/generator to its wheel. The cross guides balance the continuous, satisfactory shifting in the rotational positioning of the in-wheel-hub E-M/M-E motor/generator and wheel. Analytical comparisons of the performance of a conventional AEV or HEV with a single E-M/M-E motor/generator, an AEV or HEV equipped with conventional SM&GWs with in-wheel-hub motors and an AEV or HEV equipped with dynamic-absorbing SM&GWs emphasise differentials in road-handling performance (contact force fluctuation) and necessary quality (vertical acceleration frequency) on a rough on/off road surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002140_s1758825116500149-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002140_s1758825116500149-Figure14-1.png",
        "caption": "Fig. 14. Schematic of multiple inclusions embedded within a half-space.",
        "texts": [
            " The maximum von Mises stress \u03c3v = 0.52p0 is observed at the depth of hv = 0.5a0 on the plane y = 0 for the compliant coating and \u03c3v = 0.70p0 at hv = 1.0a0 for the stiff coating. 3.4. Heterogeneous half-space containing multiple inclusions under rough contact A sinusoidal contact surface of the half-space beneath which multiple inclusions are distributed is concerned. The inclusions have the same length lx = ly = lz = 0.5a0. The other dimensions are set to be hi = 0.25a0, d1 = 0.5a0 and d2 = 0.5a0 (Fig. 14), and the lubricant flows at the speed ue = 100m/s. The sinusoidal wavy surface 1650014-13 In t. J. A pp l. M ec ha ni cs 2 01 6. 08 . D ow nl oa de d fr om w w w .w or ld sc ie nt if ic .c om by U N IV E R SI T Y O F Q U E E N SL A N D o n 04 /2 6/ 16 . F or p er so na l u se o nl y. 2nd Reading March 28, 2016 15:54 WSPC-255-IJAM S1758-8251 1650014 K. Zhou & Q. Dong (a) 0.5 1.5 2.0 -2.0 -1.5 -1.0 -0.5 0.0 1.0 1.5 2.0 0.5 1.0 0.5 1.5 2.0 -2.0 -1.5 -1.0 -0.5 0.0 1.0 1.5 2.0 0.5 1.0 y = 0 plane 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure4.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure4.5-1.png",
        "caption": "Fig. 4.5 Closed chain with planar four-bars 1 , 2 , 3 , 4 connecting bodies 1 , 2 , 3 , 4",
        "texts": [
            " In the present case, P13 is, indeed, located on the line P16P36 . However, this is true only in the instantaneous position of the mechanism. Hence the conclusion: In the position shown the mechanism in Fig. 4.4a has the degree of freedom F = 1 . Neighboring positions cannot be assumed. In statics the system is called an infinitesimally mobile or shaky truss. Gru\u0308bler\u2019s formula and the formula used for checking statical determinacy of trusses are directly related. 144 4 Degree of Freedom of a Mechanism The planar system shown in Fig. 4.5 can be interpreted in different ways. For one thing, it is a multiloop system with m = 12 bodies (the shaded bodies plus eight rods) and with n = 16 revolute joints each joint having the individual degree of freedom f = 1 . With these numbers Gru\u0308bler\u2019s Eq.(4.2) yields the total degree of freedom F = d+1 . In a much simpler interpretation each pair of rods interconnecting two shaded bodies constitutes a joint with the individual degree of freedom f = 1 . In this interpretation the system consists of bodies 1 , 2 , 3 , 4 and of joints 1 , 2 , 3 , 4 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003285_17452759.2020.1823093-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003285_17452759.2020.1823093-Figure5-1.png",
        "caption": "Figure 5. (a) Four surface roughness measuring spots; (b) a photo shows sample profile scanning using a 3D scanner; (c) a photo shows surface roughness measurement using a confocal laser scanning microscopy (CLSM); (d) a 3D reconstruction model generated by the 3D scanner and three cross-sections of it; (e) the measuring principle of circularity and cylindricity.",
        "texts": [
            " A series of reduced laser linear energy densities as shown in Equation. (2) is used to fabricate the downskin part. E = pt dp (2) where E is the linear energy density; p is the laser power; t is the exposure time; dp is the point distance. Detailed process parameters used in improving the channel quality are listed in Table 5. 2.4 Profile and surface roughness measurements The profile of each fluid channel sample was measured using an optical 3D scanner (OKIO-3M, Shining 3D Ltd, China) as shown in Figure 5(b). The 3D scanner has a measuring accuracy of 0.005 mm and a scanning distance of 0.04 mm. The optical 3D scanner is used in the work, which is not only efficient in measuring a large number of sample profiles but also low cost compared to a commonly used industrial CT scanner. Point clouds are created by scanning and then the 3D model is reconstructed as shown in Figure 5(d,e) shows the basic principle of circularity and cylindricity, which is automatically conducted by a commercial software Geomagic Control X installed in the 3D scanner. The circularity was measured on the three cross-sections (1, 2, and 4 mm from the sample end face) as indicated in Figure 5(d). The cylindricity was measured through the entire profile of the fluid channel sample. The hydraulic diameter Dh, which is commonly used to evaluate the flow capacity of non-circular channels, was calculated based on Equation. (3) using profile data. Dh = 4A P (3) where A is the cross-sectional area, P is the wetted perimeter of the cross-section. The surface roughness measurements were performed using a confocal laser scanning microscopy (VK150, Keyence, Japan) on four spots of each sample: top, bottom, left, and right, which are shown in Figure 5 (a,c). Each measurement was performed by scanning a 1 mm \u00d7 1.39 mm area. Such measurement was repeated three times on each spot of the sample along the axial direction. Sa, a 3D surface roughness parameter represents areal arithmetical mean height, was calculated while the S filter was set to 5 \u03bcm and the L filter was set to 2 mm. It is noted that Sa is the extension of Ra (arithmetical mean height of a line, 2D) to a 3D surface according to ISO 25178. The friction loss of the SLM fabricated fluid channels was measured using a customised test rig as shown in Figure 6(a,b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.104-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.104-1.png",
        "caption": "Fig. 2.104 Principle layout of the steered, motorised, and/or pumped wheel [Valentin Technologies Inc. (USA)]",
        "texts": [
            " An AWD function, with or without locked M-M differentials, can be selected through the driver. The E-TMC ECU or CPC selects these modes automatically if wheels are spinning during acceleration or are locked during braking. Start and Acceleration The driver turns the key to activate the E-TMC ECU or CPC. The latter senses the position of the accelerator foot pedal and opens the fluidic valve at the FES (A-F accumulator) and provides the wheel-hub F-M motors with pressurized fluid. The swash-plate at the steered, motorised and/or pumped wheels (SM&PW), as shown in Figure 2.104, may be adjusted from zero to a large angle to produce sufficient torque to accelerate the HFV [VALENTIN TECHNOLOGIES INC., USA]. An increased fluidic pressure at the accelerator foot pedal creates a greater swash-plate angle and a faster acceleration. For low and medium values of acceleration, only one in-wheel-hub F-M motor may be activated. At high values of acceleration or traction forces, two or more motors may drive the HFV. The E-TMC ECU or CPC may correct the steering to compensate for off-centre thrust of the wheels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure4-1.png",
        "caption": "Fig. 4. The tooth profile with k1 = 0.2.",
        "texts": [],
        "surrounding_texts": [
            "Based on the analysis above, a design for an example gear drive with a variation of the parabolic parameters is taken to illustrate the proposedmethod and study the impact. The example drive has a modulus ofm = 2 mm, a transmission ratio of i = 1.2, an addendum coefficient of ha\u204e = 1, a bottom clearance of C\u204e = 0.25, and a tooth number of Z1 = 15. According to Eqs. (52) and (54), the range of the parameters k1 and k2 without undercutting and interference was calculated to be 0.2 \u2264 k1 b 0.457 and 0.2 \u2264 k2 b 0.448 respectively. 4.1. The impact of parameter k1 on the shape of the tooth profiles In order to study the influence of parameter k1 on the shape of the tooth profiles designed by the proposed method, k1 is so chosen that it varies from 0.2 to 0.4 with an increment of 0.1, while k2 is equal to 0.2. The tooth filet is an arc, whose radius is 0.38 \u2217 m, connecting the tooth profile and the root circle of a gear. The tooth profiles of the driving gear and the driven gear are established in Figs. 4, 5 and 6 corresponding to k1 = 0.2, 0.3, and 0.4, respectively. For the reason of comparison, three sets of the tooth profiles of the driving gear with different parameters of k1 and k2 are drawn in Fig. 7, while another three sets of the tooth profiles of the driven gear are shown in Fig. 8. According to the results, the following conclusions can be made: (i) The parameter k1 changes the shape of the part of the addendum of the tooth profile for the driving gear, without changing the shape of the part of the dedendum. On the contrary, as for the tooth profile of the driven gear, the parameter k1 is only relevant to the shape of the part of the dedendum. (ii) In the part of the addendum, the tooth thickness of the driving gear increases with the growth of the parameter k1, but in the part of the dedendum for the driven gear, the tooth thickness shows the opposite trend. 4.2. Impact of parameter k2 on the shape of the tooth profiles In this subsection, the effects of the parameter k2 on the shape of the tooth profile are studied. The parameter k1 is chosen as 0.2, and the parameter k2 is so chosen that it varies from 0.2 to 0.4 with an increment of 0.1, while the other parameters keep the same as example 1. The tooth profiles of the driving gear and the driven gear are shown in Figs. 4, 9 and 10 corresponding to k2 = 0.2, 0.3, 0.4, respectively. Three sets of the tooth profiles of the driving gear and driven gear with different parameters of k2 are drawn in Figs. 11 and 12, respectively. From above discussion, the following conclusions to the specified gears can be drawn: (i) In the part of the addendum of the tooth profile for the driving gear and in the part of the dedendum of the tooth profile for the driven gear, the tooth thickness will not change with the changes of the parameter k2. (ii) The tooth thickness of the part of the addendum of the tooth profile for the driven gear increases with the growth of the parameter k2, while the tooth thickness of the part of the dedendum of the tooth profile for the driving gear decreases with the growth of the parameter k2. (iii) The minimum teeth number of the proposed gear without undercutting is affected by k1 and k2, for example, according to Eq. (54), when k2 is equal to 0.2, the minimum teeth number of the driving gear is 2, which is much less than that of the involute gear."
        ]
    },
    {
        "image_filename": "designv10_12_0002160_icra.2016.7487629-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002160_icra.2016.7487629-Figure4-1.png",
        "caption": "Figure 4. The TriCal\u2019s measuring device and its calibrator.",
        "texts": [
            " These indicators are fixed, orthonormal to each other to a custom co- nical fixture (Fig. 3). A Mitutoyo U-WAVE-T wireless transmitter, attached on the back of each indicator, sends collected data to a Mitutoyo U-WAVE-R receiver, which is connected to a PC via a USB cable. On the TriCal\u2019s conical fixture, three 0.5-inch precision balls are temporarily attached to the magnetic nests, for the purpose of zeroing the device. These balls are called kinematic coupling spheres, and they are used to constrain the three dial indicators on the center sphere of the calibrator, as shown in Fig. 4. This process will be discussed further in Section IV. 2) The calibrator The calibrator, as shown in Fig. 4, consists of a starshaped bracket that holds three vee-grooves, a magnetic nest and a 0.5-inch precision ball (center sphere). It is used to set the device\u2019s TCP at the same position w.r.t. the conical fixture. On the calibrator itself, the center sphere can be replaced with a standard spherically mounted retroreflector (SMR), to gather measurements with a laser tracker for validation. The calibrator\u2019s purpose is to accurately constrain the three digimatic indicators on the center sphere. Once the calibrator has been coupled with the measuring device, each indicator is manually set at zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003640_j.mechmachtheory.2021.104532-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003640_j.mechmachtheory.2021.104532-Figure1-1.png",
        "caption": "Fig. 1. Virtual prototype and schematic diagram of the 3-DOF spindle head.",
        "texts": [
            " In Section 4, a two-step calibration methodology is proposed on the basis of a hierarchical identification strategy. A set of calibration experiment is carried out to verify the effectiveness of the proposed calibration methodology in Section 5. Finally, some conclusions are drawn. S. Jiang et al. Mechanism and Machine Theory 167 (2022) 104532 In this section, a newly proposed 3-DOF spindle head is taken as an example to demonstrate the error modeling process. The virtual prototype and schematic diagram of the spindle head are shown in Fig. 1. As can be seen from Fig. 1, the topological architecture behind the 3-DOF spindle head is a RAPM of 2UPR&2RPS. Herein, \u0300 U\u2019, \u0300 R\u2019, `S\u2019 and \u0300 P\u2019 represent universal joint, revolute joint, spherical joint and actuated prismatic joint, respectively. It consists of a fixed base, a moving platform, two identical UPR limbs and two identical RPS limbs. To be specific, limb 1 and limb 3 are two symmetrically distributed UPR limbs; limb 2 and limb 4 are two symmetrically distributed RPS limbs. Each limb is connected to the fixed base and moving platform at point Ai and Bi, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure3-1.png",
        "caption": "Fig. 3. Procedure formalizing relation between fundamental components of polynomial expression and deviation of tooth surface form.",
        "texts": [
            "06mmfocusing the position of tooth contact pattern of the slew bevel gears of the gear member with large pitch circle diameter of more than 1000 mm. Therefore, the formalization of the deviations is simplified and the third order functions are utilized for convenience. We define (X, Y) whose X and Y are toward the directions of the tooth profile and tooth trace, respectively, and form the following polynomial expression: \u03b4 \u00bc \u03b411 \u00fe \u03b412 \u00fe \u03b421 \u00fe \u03b422 \u00fe \u03b431 \u00fe \u03b432 \u00fe \u03b441 \u00f08\u00de where \u03b411, \u03b412, \u03b421, \u03b422, \u03b431, \u03b432, and \u03b441 are defined as follows: Fig. 3 shows the procedure formalizing the relation between the fundamental components of polynomial expression and the deviation of tooth surface form. First, the tooth trace deviation \u03b411 and tooth profile deviation \u03b412 are expressed as the following first order equations of X and Y using fundamental components a11 and a12, respectively [see Fig. 3(a)]: \u03b411 \u00bc a11X a11 \u00bc \u03b411 0:5H \u03b412 \u00bc a12Y a12 \u00bc \u03b412 0:5T \u00f09\u00de where H and \u03a4 are defined as the ranges of the evaluation of the tooth surface in X and Y directions, respectively. Next, the tooth trace deviation \u03b421 and tooth profile deviation \u03b422 are expressed as the following second order equations of both X and Y using fundamental components a21 and a22, respectively [see Fig. 3(b)]: \u03b421 \u00bc a21X 2 a21 \u00bc \u03b421 0:5H\u00f0 \u00de2 \u00bc 4\u03b421 H2 \u03b422 \u00bc a21Y 2 a22 \u00bc \u03b422 0:5T\u00f0 \u00de2 \u00bc 4\u03b422 T2 \u00f010\u00de where \u03b4 can be calculated in consideration of only (a) and (b) in Fig. 3 by the following equation: \u03b4 \u00bc \u03b411 \u00fe \u03b412 \u00fe \u03b421 \u00fe \u03b422 \u00bc a11X \u00fe a12Y \u00fe a21X 2 \u00fe a22Y 2 : \u00f011\u00de The deviations may occur in the directions of the bias-in and bias-out according to \u03b4 in Eq. (11). Therefore, the deviations \u03b431 and \u03b432 in the directions of the bias-in and bias-out are expressed as the following second order equations of both X and Y using fundamental components a31 and a32, respectively [see Fig. 3(c)]: \u03be1 \u00bc tan\u22121 T H L0 \u00bc H cos\u03be1 \u03b431 \u00bc a31 X cos\u03be1\u2212Y sin\u03be1\u00f0 \u00de2 a31 \u00bc \u03b431 0:5L0\u00f0 \u00de2 \u00bc 4\u03b431 L20 \u03b432 \u00bc a32 X cos\u03be1 \u00fe Y sin\u03be1\u00f0 \u00de2 a32 \u00bc \u03b432 0:5L0\u00f0 \u00de2 \u00bc 4\u03b431 L20 : \u00f012\u00de Finally, the tooth trace deviation \u03b441 is expressed as the following third order equations of X and Y using fundamental components b1, b2, and b3, respectively [see Fig. 3(d)]: \u03b441 \u00bc b3X 3 \u00fe b2 X 2 \u00fe b1X \u00f013\u00de where b1, b2, and b3 are determined from the following conditions: \u03b4 is equal to zero when X=\u22120.5H and X=0.5H. Moreover, \u03b4 is equal to \u03b441 when X= 0.25H. The deviation \u03b4 is calculated in consideration of Eq. (12) by the following equation: \u03b4 \u00bc A1X \u00fe A2Y \u00fe A3X 2 \u00fe A4Y 2 \u00fe A5XY \u00fe A6X 3 \u00f014\u00de where A1 \u00bc a11 \u00fe b1 A2 \u00bc a12 A3 \u00bc a31 \u00fe a32\u00f0 \u00de cos2\u03be1 \u00fe a21 \u00fe b2 A4 \u00bc a31 \u00fe a32\u00f0 \u00de sin2\u03be1 \u00fe a22 A5 \u00bc 2 a32\u2212a31\u00f0 \u00de cos\u03be1 sin\u03be1 A6 \u00bc b3: \u00f015\u00de Reflecting the polynomial expression \u03b4 to the theoretical tooth surface, the position vector is represented by xa \u00bc x\u00fe \u03b4 n \u00f016\u00de where xa represents the theoretical tooth surface in consideration of the tooth surface formdeviations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure9.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure9.3-1.png",
        "caption": "Figure 9.3. A homogeneous semicircular ring of variable cross section having an xy-plane of symmetry.",
        "texts": [
            " Thus, these products of inertia vanish upon integration with respect to the 362 Chapter 9 (9.23) y variable. To see this, consider 112 in (9.15). With dm = pdxdzdy == dudy, we have ! [j ! (X' Z) ] (x ,Z) - I (x ,Z) Therefore, referred to coordinate planes that include a body plane of symmetry, at least two of the products of inertia for a homogeneous body will vanish. We shall return to this important property momentarily in some general remarks on axisymmetric bodies . Example 9.2. What are the matrix and tensor forms of I Q for the homogeneous body in Fig. 9.3 referred to the body frame rp = {Q; id? Solution. Since the xy-plane is a body plane of symmetry for this homogeneous body, by (9.15),113 = 123 = 0 in tp, Therefore, referred to the body frame rp in Fig. 9.3, we have the component matrix o ] , h3 (9.24) Now, consider a body having two orthogonal planes of symmetry. The line formed by the intersection of two orthogonal planes of symmetry of a body is called an axis ofsymmetry, and a body having an axis of symmetry is called axisymmetric. The plane geometrical figure formed by a cut through the body normal to an axis of symmetry is called a cross section. The cross section describes both the exterior and interior axisymmetric shapes of the body. Any line in the cross section through the axis of symmetry intersects the body at boundary points equidistant from the axis, and hence the point on the axis of symmetry in the cross ",
            "37b) wherein the mass m s of the solid block and me of the cavity body are given by (9.37c) Hence, by (9.4) , the mass of the drilled block is m(!?l3) = m s - me = pe(h2 - 7TR2). (9.37d) Use of (9.37c) and (9.37d) in (9.37b) yields the moment of inertia tensor components for the homogeneous, drilled parallelepiped referred to the center of mass frame ip: 1 m(!?l3)e2 122 = 133 = - III + (9.37e) 2 12 D 370 Chapter 9 Example 9.4. The complex structured body g(J = g(J1 U g(J2 in Fig. 9.6 consists of a semicircular ring g(J1 of variable cross section, shown in Fig. 9.3, and a right conical shell g(J2. The bodies are made of different homogeneou s materials welded together along their common circular boundary in the xy-plane. Find the matrix of the moment of inertia tensor for the composite body g(J referred to ({J = (Q;id\u00b7 Solution. Let IQ(g(3I) and IQ(g(32) denote the moment of inertia tensors for g(3 l and g(32 referred to the same body frame ({J = {Q; ik } in Fig. 9.6. For the composite body g(3 = g(3 l U g(32, (9.35) yields I Q(g(3) = IQ(g(3I) + IQ(g(32)' The matrix of IQreferred to ({J = {Q ;id has the form (9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003293_s40430-020-02645-3-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003293_s40430-020-02645-3-Figure1-1.png",
        "caption": "Fig. 1 Phase plane of the state variables",
        "texts": [
            " The experimental and numerical results have been used to evaluate the effectiveness of the controllers and discussed at the end. A controlled nonlinear dynamic system is described by the following state space form: (1)x\u0307 = f (x) + [B] u where x, f(x), [B], u represent states, nonlinear terms, control matrix and control inputs. The aim of the controller is to control the variable x under the system uncertainties and hold the system on a sliding surface S. In order to obtain a stable solution of the system, it must stay on this surface as shown in Fig.\u00a01. The surface is described as: The sliding surface equation for a control system can be selected as follows: \u0394x is the difference between the reference value and the system response which results in error vector e. [G] is the matrix which represents the sliding surface slopes. This equation can be rearranged as follows: or For stability, the following Lyapunov function candidate has to be positive definite and its derivative has to be negative semi-definite: (2)S = {x \u2212 \u2236 \u2212 (x, t) = 0} (3) = [G] \u0394x = [G](xref \u2212 x) = [G]e (4) = [G] x r \u23df \u23df (t) \u2212[G]x (5) = (t) \u2212 [G]x (6)\ud835\udf08 ( \ud835\udf0e ) = \ud835\udf0eT\ud835\udf0e 2 > 0 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:561 1 3 561 Page 4 of 13 If the limit condition is applied: Since \u03c3 cannot be zero, than d\u03c3/dt = 0, From Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure9.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure9.11-1.png",
        "caption": "Figure 9.11. Application of the method of Lagrange multipliers to the design analysis of a bell crank mechanism .",
        "texts": [
            " The method may be extended to q < P constraints by introduction of q undetermined Lagrange multipliers Ar \u2022 In this case, we introduce the auxiliary function G(u) == D(u) - 2::;=1 ArFr(u), in which the q constraints to be satisfied at the stationary points are Fr(u) = O. Then the necessary conditions for an extremum of D(u) = 0 subject to these constraints are given by aG(u)/au = aD(u)/au - 2::;=1 ArClFr(u)/Clu = O. By setting ClG(u)/ClAr = -Fr(u) = 0, we may recover the q constraint equations. An application of Lagrange's method to a mechanical control problem whose solution is easily visualized follows . Example 9.8. A bell crank mechanism having a telescopic control ann 0 P is shown in Fig. 9.11. The control pin P is constrained to move in a straight slot defined by the equation y = 1 - x . To design the crank, the designer must know the shortest distance d from the origin to the line of motion of P, an easy geometry The Moment of Inertia Tensor 381 problem. Find by geometry and then by the method of Lagrange multipliers the point on this line which is closest to the origin, and thus determine d. Solution. The geometrical solution is evident in Fig. 9.11. The shortest line oA is the perpendicular bisector of the hypotenuse of the isosceles right triangle whose length is J'i. Hence, d = J'i/2 is the shortest distance from 0 to the line of motion of P, the nearest point to 0 being the midpoint A at x = ~(i + j). Now let us see how the method of Lagrange multipliers is used to find the place x = ~i + I]j on the line y = 1 - x which is nearest the origin in Fig. 9.11. The problem is to minimize the function d(P) = (x\u00b7 X)I/2, or more conveniently, the related squared distance function subject to the constraint relation F(x) = ~ + I] - I = 0, (9.59a) (9.59b) specifying that the point (~, 1]) is constrained to the line y +x = 1. Notice that neither of(x)/o~ nor of(x) /ol] vanishes, as required below (9.56). Now use (9.59a) and (9.59b) to form the auxiliary function G(x) =D(x) - AF(x) = ~2 + r? - A(~ + I] - I), (9.59c) in accordance with (9.55). Then, by (9.57), the extremal points are determined by oG(x) -- =2~-A=0, o~ oG(x) -- = 21] - A = o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001469_tie.2013.2279382-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001469_tie.2013.2279382-Figure2-1.png",
        "caption": "Fig. 2 12/10 stator/rotor pole prototype SFPM machine.",
        "texts": [
            " In addition, the sensorless current and speed control based on HF pulsating voltage signal injection will be implemented to verify the conclusion of the saliency investigation. In the SFPM prototype machines as shown in Fig.1, the salient pole stator core includes \u201cU-shaped\u201d laminated iron segments which are allocated around magnetized PMs. The magnetization is kept in opposite polarity from one magnet to the following one. A stator pole, established by two iron legs from adjacent segments and a magnet, is wound by coils, which is a part of the stator winding. A prototype 12/10 stator/rotor pole SFPM prototype machine is shown in Fig. 2. The parameters of the prototype SFPM machine used in this work are summarized in Table I., where the inductances are measured under no-load condition. The parameter optimization and electromagnetic performance of the three-phase SFPM machine has been well analyzed since it has several advantages for its performance that can be summarized as following five points [24]: 1. Non-overlapping windings for better efficiency; 2. Flux focusing for high torque density; 3. The torque capability is similar to the fractional-slot SFPM machines; 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001128_9781118562857.ch1-Figure1.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001128_9781118562857.ch1-Figure1.4-1.png",
        "caption": "Figure 1.4. Schematic arrangement of (a) a pneumatic screw type and (b) a vibration assisted gravity powder feeder",
        "texts": [
            " Moreover, laser energy utilization is also greater in dynamic powder blowing, as the laser beam passes through the powder cloud to the substrate/previously deposited layer, resulting in the preheating of powder particles by multiple reflections. Various powder feeders are used for this application. They are based on the following working principles: a) a pneumatic screw type powder feeder; b) a vibration assisted gravity powder feeder; c) a volumetric controlled powder feeder. A pneumatic screw type powder feeder is one of oldest methods. The powder is fed by a rotating screw mounted at the bottom of the hopper, as shown in Figure 1.4a. The controlled amount of the powder is fed into a pneumatic line and transported to the powder nozzle with an inert gas like Argon (Ar), Helium (He), etc. The rotational speed and dimensions of the screw control the powder feed rate [LI 85]. Frequent choking and the need for cleaning are the problems observed in this feeder. In a vibration assisted gravity powder feeder, a combination of pneumatic and vibration forces are used to feed the powder into a pneumatic line [PAU 97]. The powder is taken in a hopper and some vibrating device, such as a rotating wheel or standard ultrasonic vibrator, is fitted at the bottom of the hopper. The powder flows freely through an orifice. The dimensions of the orifice are controlled to regulate the powder flow rate. The vibrating device generates the vibration and maintains the free flow of powder under gravity into the pneumatic line. Thus, the powder is delivered to the substrate with the help of an inert gas, as shown in Figure 1.4b. This approach has limitations in regulating the powder flow rate in finer steps and it is widely used for applications involving a constant powder flow rate. In a volumetric controlled powder feeder, the powder is filled in the hopper and it falls on the annular slot of rotating disc. The hopper and the chamber enclosing the rotating disc are pressurized equally. The rotating disc carries the powder to an exit with a descending pressure gradient. This pressure gradient sucks the powder particles into a pneumatic line and the powder is delivered to the desired point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003050_j.jmatprotec.2020.116745-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003050_j.jmatprotec.2020.116745-Figure2-1.png",
        "caption": "Fig. 2. (a) diagrammatic sketch of the tubular cored wire, (b) the cross-sectional metallographic image of the wire, (c) the processed image of the wire cross-section for measuring the area of the sheath (As) and powder (Ap), (d) measurements of the wire linear mass (e) measurements of the area of the sheath and powder.",
        "texts": [
            " (1995), B and Si elements are shown to shield the liquid metal from oxidation. The initial volume fraction of the ceramic particles filled inside the wire is regarded as the maximum particle content in the coatings. To get the initial volume fraction, the wire linear mass and the area occupied by powders and sheath on the wire cross-section were measured. Five sections about 100mm in length were cut from the wire and numbered consecutively from No.1 to No.5. The weight of each section was measured three times and the measurements were presented in Fig. 2(d). The average wire linear mass lm was about 0.018 g/mm. The regions includ ing the sheath and the internal area filled with powder were manually selected and marked with recognizable colors in the image processing software, as shown in Fig. 2(c). The total pixels in the different selected areas were counted and converted into an area in square millimeter using the pixel-length ratio. Each of the sections was measured three times and the results were shown in Fig. 2(e). The average area of the sheath and the powder on the wire cross-section was 1.071mm2 and 0.833mm2 respectively. The particle volume fraction fP is a function of wire linear mass lm (0.018 gmm\u22121), density of the tungsten carbides \u03c1 (16.67 g cm-3), weight factor of the powder fm (45 %), the sheath area As (1.071mm2). Taking the variables into Eq. (1), the volume fraction of particles in the wire was calculated to be about 30 %. = \u00d7 \u00d7 + \u00d7 \u00d7f f l f l A \u03c1 100%m m m m s P (1) The arrangements of laser deposition with wire feeding was illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000377_s11740-007-0041-9-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000377_s11740-007-0041-9-Figure3-1.png",
        "caption": "Fig. 3 Tools and workpiece in the process area",
        "texts": [
            " 2) is a technology that is on track for the future because it can produce very high piece numbers in shortest periods of time with optimum material application (constant volume when rolling). However, applying this principle to produce gear teeth of high or even quality makes it necessary to replace the previous empirical process layout with a process layout that encompasses and applies the overall interactions of machines, tools and process. Selected research findings will be showcased below on this problem. With cross rolling on the round rolling principle (Fig. 3), the rolling blank that is symmetric to rotation is chucked between the tips in the axial direction (tightener). Two round tools shape the gear teeth in the blank with the same direction of rotation and at a constant speed. The tool teeth penetrate into the workpiece by reducing the axle clearance of the round tools in the radial direction. The chucking equipment for the workpiece has to be mobile in the feed direction to guarantee centering during the deformation processes. The mathematical design of the rolling tools has to be adjusted with the constantly changing kinematic involute gearing conditions with the tool teeth penetrating into the rolling part [3, 4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.5-1.png",
        "caption": "Fig. 14.5 Triangle in its original position (A1,A2,A3) and following a translatory displacement t , a rotation about P and reflection in the line g",
        "texts": [
            " This shows that there are displacements preserving the sense and others reversing the sense. We begin by defining three elementary displacements called translation, rotation and reflection. During a translation, abbreviated T , every point experiences the same translatory displacement t . A rotation, abbreviated C , is carried out about a fixed point called pole P through an angle \u03d5 (positive 416 14 Displacements in a Plane counterclockwise). A reflection in a line g , abbreviated S , produces a mirror image the line g being the mirror. The triangle (A1,A2,A3) in Fig. 14.5 is used for demonstrating a translatory displacement t , rotation about a pole P and reflection in a line g . Translation and rotation are both sense-preserving displacements. From Sect. 1.16 it is known that reflection is a sense-reversing displacement. The three elementary displacements are formulated analytically as follows. The reference plane \u03a30 is interpreted as complex plane. Let z be the complex number representing an arbitrary point of \u03a3 prior to the displacement, and let z\u2032 be the complex number representing the same point in its position after the displacement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.23-1.png",
        "caption": "Figure 5.23. Free body diagram of a particle P and principal interacting bodies-the Earth, the Moon, and the Sun.",
        "texts": [
            "23, acted upon by the particle P, the moon M, and the sun S. The equation of motion for the center of mass of the Earth is thus given by (5.86) (5.87) in which gs , gM, and gp are the respective gravitational field strengths at C due to the principal surrounding bodies S, M, and P; and FE is the resultant of all other forces that may act on E, including other weak gravitational force s and the contact force exerted by the Earth's atmosphere, for example. This estimates ac in (5.85) . Now consider the free body diagram of the object P in Fig. 5.23. The total force acting on P is F = m(g \\ +g2+g3)+ F0 ' where g\" g2, g3 are the field strengths at P due to the bodies S, M , and E , respectively, F 0 is the total of all other forces acting on P and mEgp = -mg3 is the mutual gravitational force between E and P. Use of these relations and (5.86) in (5.85) yields the equation of motion (5.81) for the object P in the Earth frame cp: maip = F0 +mg3 (I + :E) +m (g\\ - gs) +m (g2 - gM) m --FE-m (0 x (0 x r)+20 x vip) ' mE In view of the great distances separating the principal bodies, some further approximations are introduced to simplify (5.87) . For the motion of P on or near the Earth's surface, we have [r] = rs in Fig. 5.23. Hence, the other distances shown there may be approximated by r\\ = rs and rz = ru so that gl = gs and The Foundation Principles of Classical Mechanics 73 g2 = gM, very nearly. Clearly, the ratio mimE is infinitesimal, hence negligible compared with unity, and even though IFE I may be large, we may assume that m IFEI [mE \u00ab IFa I. Use of these further approximations in (5.87) yields the final reduced form of Newton's equation ofmotion for a particle in the noninertial Earth frame : (5.88) where mg3 is the gravitational force on P due to the Earth, Fa is the total of all contact and nongravitational body forces that act on P, and the other terms are inertial forces due to the Earth's rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure11.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure11.6-1.png",
        "caption": "Fig. 11.6 Method used to measure the performance of baseball and softball bats",
        "texts": [
            " the impact distance d , for L D 33 in., I6 D 9; 000 oz in.2 bats, assuming that e D 0:50 at the impact point. For any given bat, the sweet spot is located at only one point along the barrel, but it could be anywhere in the region from about d D 5 in. to about d D 8 in. depending on the design of the bat. If the sweet spot is located at d D 7 in. for example, and if e D 0:50 at the sweet spot, then e will actually be less than 0.50 at points either side of the sweet spot (as shown in Project 9 and in Fig. 11.6). Figure 11.5 does not represent the variation of batted ball speed with d for a given bat. Rather, it represents the variation of batted ball speed with d for a range of different bats, all having the same swing weight, when the sweet spot happens to be located at the distance d plotted in the graph and when e D 0:5 at the sweet spot. The question of interest is where the sweet spot would be best located, given that it is the point where the COR is a maximum. Figure 11.5 shows that if the ball is incident at 50 mph, then the batted ball speed will be maximized if the sweet spot is located as close to the tip of the barrel as possible",
            " The advantages are that the method is simpler (since there is no need for additional apparatus to swing the bat), safer (since the ball rebound speed off a stationary bat is a lot smaller than that off a swung bat) and more accurate. The same method is used to test softball bats, although the incident ball speed is reduced to 110 mph since the relative speed of the bat and the ball is generally lower in softball. In both cases, the bat is supported 11.7 ASA and NCAA Performance Tests 197 horizontally and allowed to swing freely about an axis in the handle 6 in. from the knob, as shown in Fig. 11.6. The incident and rebound speeds of the ball are measured using laser beams. The rotational speed, !, of the bat after the collision can also be measured to obtain additional information, such as a direct measurement of the COR or an indirect measurement of the bounce factor in cases where the ball rebound speed is too low for the ball to pass back through the laser beams. In practice, it is easier to measure the speed of the ball in the laboratory tests than it is to measure the speed of the bat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.112-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.112-1.png",
        "caption": "Fig. 2.112 Principle layout of a high-density mechanical energy-storing TDUF \u2013 Left image; layout of an M-M transmission arrangements for E-M DBW 2WD propulsion \u2013 Right image [FIJALKOWSKI AND KROSNICKI 1995B, FIJALKOWSKI 2000D; CHAN AND CHAU 2001 \u2013 Left image, DRIESEN 2006 \u2013 Right image].",
        "texts": [],
        "surrounding_texts": [
            "To increase the total efficiency of an E-M transmission arrangements for a DBW 2WD and/or 4WD propulsion mechatronic control system, the application specific integrated matrixer (ASIM) macroelectronic converter-based commutators (ASIM macrocommutators) and application specific integrated circuit (ASIC) artificial intelligence (AI) neuro-fuzzy (NF) micro-electronic computerbased controllers (ASIC AI NF microcontrollers) include the optimum control that is considered to be the variable factors of the mechanical energy-storing highvelocity motorised and/or generatorised flywheels (M&GF) with the twin-disc flywheel\u2019s E-M/M-E motors/generators, respectively; chemical energy-storing CH-E/E-CH storage battery; and steered, motorised and/or generatorised wheels (SM&GW) with the in-wheel-hub E-M/M-E motors/generators, respectively. The DBW 2WD and/or 4WD propulsion mechatronic control system for an environmentally friendly BEV may be designed so that brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator reluctance and/or magneto- Automotive Mechatronics 292 electrically-excited in-wheel-hub motors/generators may be installed on the inner side of each SM&GWs. The structure features are Reduction in mass of the BEV and higher mechanical energy efficiency of the novel axleless E-M transmission arrangement achieved by eliminating the MT or SAT or FAT or CVT, M-M differentials, propeller shafts, driveshafts, and other driving gears that are required for moving conventional automotive vehicles; Effective use of space for in-wheel-hub motors/generators; Achievement of an ideal E-M DBW 2WD and/or DBW 4WD propulsion performance, for instance, controlling the two or four SM&GWs independently. For contemporary environmentally friendly BEVs, a single in-wheel-hub E-M/ M-E motor/generator may be capable of motoring a maximum output power of 25 - 50 kW and a maximum torque of 425 kNm. The maximum value of theangular velocity at the top-gearless vehicle velocity of 180 km/h may be 26 rev/s. In Figure 2.111 a BEV that is called a \u2018Poly-Car\u2019 is shown. The powertrain consists of four SM&GWs with brushless AC-AC, AC-DC-AC, or DC-AC/ AC-DC macrocommutator reluctance and/or magnetoelectrically excited inwheel- hub motors/generators [FIJALKOWSKI 2000D]. The latter, as well as its armatures, IPM exciters, and ASIM macrocommutators, and the charge AC-DC rectifier form compact units. The AC-AC, AC-DC-AC, or DC-AC/AC-DC macrocommutators\u2019 mechatronic controls also allow for electrical energy recovery in braking, cornering, and during downhill coasting. The CH-E/E-CH storage battery is protected by a staggered deep-draw protective scheme that prolongs its life. A charger is carried onboard, making it possible to charge the storage battery (SB) on any fused outlet. A BEV is not suitable, however, for very long distances, because, the reach of the vehicle is too short and the eight-hour recharging period is too long. The full-time E-M DBW 2WD and/or 4WD propulsion mechatronic control system offers two main advantages: 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 293 Increased traction obtainable from the four SM&GWs that is especially useful on soft or slippery ground; If the two front SM&GWs run into a ditch, they tend to be forced downwards, except when the AE DBW 2WD propelled HEV is driven in reverse, in which case, the disadvantage of the lower traction of AE DBW 2WD-propelled HEV remains. In a full-time E-M DBW 4WD-propelled HEV starting, with the single SM&GW, efficiency in a part-load operation may be increased if low torques are not equally distributed onto each SM&GW. It may be better to start with single SM&GW first and to increase its torque to the rated value before the next may start. This mode of starting may be repeated for all SM&GWs. Of course, the yaw stability of the BEV has to be guaranteed. Thus, synchronous and/or differential modes of operation of the two SM&GWs of a single FWD or RWD are to be preferred. Then, the torque and/or angular velocity controls of the AE DBW 4WD propulsion mechatronic control system\u2019s SM&GWs represent a compromise between high part-load efficiency and driving stability. Automotive scientists and engineers have taken the next step forward a PolyCar\u2019 BEV high-performance DBW 4WD in-wheel-hub E-M motor test automotive vehicle. After removing the ECE or ICE, fuel tank, M-M transmission, M-M differential, drive shaft, and other DBW 4WD propulsion components from a production vehicle, newly developed outer-rotor in-wheel-hub E-M motors were installed on all four SM&GWs. Fitted under the floor between the front and rear SM&GWs in the place vacated by the conventional DBW 4WD propulsion components, a CH-E/E-CH storage battery may power the in-wheel-hub E-M motors. The in-wheel-hub E-M motor may deliver a maximum the output value of 25 \u2013 50 kW and its unique attribute is its outer-rotor structure. In the conventional type of in-wheel-hub E-M motor, as used in the past, the rotor turns inside the stator. The outer-rotor in-wheel-hub E-M/M-E motor/generator, however, uses a hollow doughnut structure that sites the rotor outside the stator. The major benefits of this arrangement are as follows: The arrangement creates increased power output and easier torque and creates useless the speed reducer, which decreases energy losses and suppresses the augmentation of unsprung mass. Removal of the speed reducer makes the in-wheel-hub E-M motor easier to install into the wheel housing. The doughnut structure creates space in the centre of the in-wheel-hub E-M motor for the brake assembly and other components. The outer-rotor structure also permits the in-wheel-hub E-M motor to be installed on the front SM&GWs, something not practicable until now due to the presence of SBW AWS conversion components. Automotive Mechatronics 294 From the viewpoint of DBW 4WD propulsion and 4WB BBW dispulsion components, AEVs and HEVs have evident advantages over conventional ECEor ICE-powered automotive vehicles. These advantages may be as follows: Torque generation of an in-wheel-hub E-M motor is very fast and precise for both accelerating and decelerating. This should be an advantage. Anti-lock braking system (ABS) and traction control system (TCS) should be integrated into \u2018full TCS\u2019 since an in-wheel-hub motor can both accelerate or decelerate the SM&GW. Its performance should be prepared in advance if the driver can fully use the fast torque response of the in-wheel-hub E-M motor [FIJALKOWSKI AND KROSNICKI 1990, FIJALKOWSKI 1990, HORI ET AL. 1998]. An in-wheel-hub motor can be attached to each SM&GW. With miniature E-M motors like in-wheel-hub E-M motors [FIJALKOWSKI AND KROSNICKI 1990, FIJALKOWSKI 1990, JOHNSTON 2000], even the generation of anti-directional torque is feasible on left and right SM&GWs. In automotive engineering, such an approach is known as direct yawmoment control (DYC) [SHIBATA ET AL. 1992, MOTOYAMA ET AL. 1992]. Distributed in-wheel-hub E-M motors may enhance its performance. An in-wheel-hub E-M motor\u2019s torque is easily comprehensible. Some uncertainty exists in driving or braking torque generated by an in-wheelhub E-M motor, relative to that of ECE, ICE, or F-M brake. Therefore, an unsophisticated \u2018driving force observer\u2019 may carry out a real-time observation of driving/braking force between the wheel tyre and on/off road surface [SAKAI ET AL. 2000]. This second advantage may add a great deal for some applications similar to the estimation of on/off road circumstances. Optimistically, these represent the novel approach for vehicle motion control. High-Density Inertial Mechanical Energy-Storing High-Angular-Velocity TwinDisc Ultra-Flywheel with In-Flywheel E-M/M-E Motor/ Generator - An auxiliary inertial mechanical energy store (IMES), i.e., the secondary-energy-source, high-density mechanical energy-storing high-angular-velocity twin-disc ultra-flywheel (TDUF) with a brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator twin composite-disc flywheel motor/generator, i.e., IMES with an integrated electrical machine that can operate as an in-flywheel M-E generator (discharging the IMES) or as an in-flywheel E-M motor (charging IMES) as required. The TGUF, shown in Figures 2.111 and 2.112 exploits the unusual magnetic repulsion in superconductors: non-superconducting elements are then dispersed in superconducting material, to \u2018pin\u2019 the magnetic fluxes of the levitation magnet and suspension magnet, respectively [FIJALKOWSKI AND KROSNICKI 1995B, FIJALKOWSKI 1998, 1999A, 2000D]. This means that magnet disc shaped rotors can be levitated above and suspended under the superconductor disc-shaped stator, and so, because there may be a slice of air between the two, the magnet disc 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 295 shaped rotors can rotate freely in the opposite senses (arrows) of rotation\u2019s direction. These properties could make it possible to construct high-density mechanical energy-storing super-high-angular-velocity TDUFs with near-frictionless magnetic bearings. The prototype may consist of two disc-shaped rotors, made of Sm-FE-Ti-B, Sm-Fe-Mo, or Nd-Fe-B magnet rings embedded in aluminium that may float 10 mm above and under a stationary superconducting disc-shaped stator. The latter may contain plenty of yttrium-based bulk superconductors, cooled by liquid nitrogen. Both discs may be about 30 cm in diameter. On a large scale, such a high-density mechanical energy-storing super-highangular-velocity TDUF of 26.18 rad/s (250,000 rpm) can help the topmost compact AE BEV prime mover, and CH-E/E-CH storage battery balance their power requirements. The TDUF could store kinetic mechanical energy during periods of the BEV\u2019s low velocity cruising and regenerative normal coasting (low mechanical energy usage) and regenerative normal braking and/or cornering during the pivot skid steering and then generate electrical energy to meet the peak power demands Automotive Mechatronics 296 during periods of rapid-acceleration starting, hill climbing, as well as highvelocity travelling and cruising. Steered, Motorized and/or Generatorised Wheels (SM&GW) - In-wheel-hub E-M/M-E motors/generators applied to planetary-geared and/or planetary-gearless mechatronically-controlled SM&GWs there may be low-angular-velocity (low frequency), brushless DC-AC/AC-DC macrocommutator IPM magnetoelectrically-excited in-wheel-hub motors/generators. The rotating housing may be made in the form of wheel hubs, designed to fit standard rim sizes. The mechatronically-controlled in-wheel-hub E-M/M-E motor/generator APVT may allow complete freedom in the design of smart AEVs. The in-wheel-hub E-M/M-E motor/generator may require minimum space and may be installed directly into the rim of the SM&GW because of its compact design. The result may be substantially increased ground clearance and the space between the direct-driven SM&GWs may be used to locate implements, for example. Figure 2.113 shows the principle layouts of the planetary-gearless SM&GWs with brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator reluctance and magneto-electrically excited [unwound mild-soft-iron (MSI) outer rotor and wound and IPM inner stator] in-wheel-hub motors/generators. The wheel-hub is designed so as to realise high stiffness with fewer materials by using \u2018modal (resonance frequency) analysis\u2019 and, together with the use of specially sealed, double row angular contact ball bearings, lubricated-for-life, and having pre-adjusted internal clearance, an excellent torque/mass ratio [Nm/kg] is realised, which is no comparison with the other in-wheel-hub motors/generators, and even with the conventional brushed DC-AC/AC-DC mechanocommutator in- 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 297 wheel-hub motors/generators, it is still better [FIJALKOWSKI 1990, 1985A, 1997C, FIJALKOWSKI AND KROSNICKI 1994]. The planetary-gearless mechatronically-controlled SM&GW with a brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator reluctance and/or magnetoelectrically-excited in-wheel-hub motor/generator may completely eliminate backlashes or hysteresis that are inevitable. The SM&GW hub may be designed using finite-element modal analysis methods and double-row angular contact ball bearings can be used to support the outer rotor, resulting in high radial stiffness and slim construction. The high torque and light mass previously mentioned result in a lower torque/mass ratio [Nm/kg] being obtained. The novel \u2018single-shaft\u2019 DBW 2WD and/or 4WD propulsion mechatronic control systems are also expected to be smaller in size, lighter in mass, more energy efficient, less expensive, durable and reliable, as well as being better suited to high-volume manufacture than any other well-known mechatronic control systems under development today. Thus, the wheel that is steered, motorised and/or generatorised is fitted with an in-wheel-hub motor/generator. [FIJALKOWSKI 1990, 1997C, FIJALKOWSKI AND KROSNICKI 1994]. As a result of the solid-state high-power ASIM AC-AC, AC-DC-AC or DCAC/AC-DC macrocommutator design principle [FIJALKOWSKI 1997], the following features can be obtained: Full torque for AEV or HEV starting is directly exerted on the wheel without loss of efficiency caused by intermediate mechanical reduction gearing \u2013 planetary gearless; Low in-wheel-hub motor armature current while the AEV or HEV accelerates; Gradual torque application to eliminate mechanical shock; Superior smoothness in torque and/or angular velocity control through outstanding by high torque at low angular velocity performance; Superior AE and/or HE DBW 2WD and/or 4WD propulsion mechatronic control \u2013 in-wheel-hub E-M motor rotor angular velocity can be controlled within \u00b1 \u03c0/30 rad/s over the full 0 \u2013 160 km/h velocity range; Superior propulsive efficiency \u2013 efficiency can be up to 86% at full load; Very smooth rotation, even under slow angular velocity from very low to the maximum velocity values; Constant torque throughout the full rotation \u2013 flat torque/angular velocity characteristics make for high controllability; Regenerative braking and/or cornering \u2013 the in-wheel-hub E-M motors can also act as in-wheel-hub generators, the with electrical load being applied to provide braking and/or cornering during the pivot skid steering; Built-on parking and emergency brake; Reversible; Free-wheeling; Extremely low noise; In-wheel-hub mounting for simple alignment; Minimum space requirement; Automotive Mechatronics 298 Lighter mass \u2013 there are no conventional toothed gearboxes and planetary reduction gearing, long propeller shafts or drive shafts, M-M differentials, or axles \u2013 complete freedom in the design of smart AEVs or HEVs; High torque/mass ratio; Low maintenance \u2013 clean and free from maintenance by its nature; Competitive price with high performance; Emergency power plant \u2013 the M&GF\u2019s M-E generator output can be used to provide of 50 or 500 Hz as well as 60 or 400 Hz power supply. Many other planetary-gearless SM&GWs with AC-AC or AC-DC-AC or DC-AC/ AC-DC macrocommutator reluctance and/or IPM magnetoelectrically-excited inwheel-hub motors/generators have been conceived. Whether or not all of these magneto-mechano-dynamical (MMD) electrical machines qualify as E-M/M-E motors/generators tends to be a controversial question. Whatever their form is, the common operational mode is that a discrete quantum of angular rotation occurs in response to a pulse. For continual rotation to take place, a properly coded pulse train must be applied so that there is a sequential \u2018stepping\u2019 motion of the outer rotor. In essence, the pulse coding is such that a rotating magnetic field is produced. One of the salient features of these MMD electrical machines is the ability to repeat positional data. No feedback loop is required for such a performance. The principal layout of a particularly interesting planetary-gearless SM&GW with a MMD electric machine of this kind, is the one with the AC-AC or AC-DCAC or DC-AC/AC-DC macrocommutator reluctance and IPM magneto-electrically excited (unwound MSI outer rotor as well as wound and IPM inner stator) inwheel-hub motor/generator shown in Figure 2.111(b). It is evident that there are no windings on the MSI outer rotor, no slip rings, and no mechano-commutator with sliding-copper segments and carbon brushes. The nature of the inner-stator polyphase (three- or five-phase) winding is also not evident. If the inner stator is a six-pole, three-phase structure with a large number of \u2018teeth\u2019, then the outer rotor is also toothed and magnetised so that the south pole occupies one-half of the peripheries while the north pole occupies the other half. Although the inner stator has only six poles and the outer rotor has only three poles, the presence of \u2018teeth\u2019 on both members affords a large number of opportunities for the positional \u2018lock-up\u2019 of the outer rotor. Poles N1, S4, N7 and S10 form the first phase; poles N2, S5, N8 and S11 form the second phase; poles N3, S6, N9 and S12 form the third phase. The in-wheel-hub motor/generator with different pole numbers on the unwound MSI outer rotor, as well as the wound and IPM inner stator, can provide traction if the stator polyphase winding phase-coils are sequentially energised. Here the unwound MSI outer rotor is made to \u2018chase\u2019 sequentially switched wound and IPM inner-stator poles. As soon as magnetic alignment occurs, the attracting pole is de-energised. A variation of this basic scheme employs Hall-effect elements to directly sense the position of either the outer rotor itself or a suitably magnetized disc on the shaft. The in-wheel-hub motor/generator adopts the \u2018IPM bias\u2019 method, the IPM made of SM-Fe-Ti-B, Sm-Fe-Mo or Nd-Fe-B rare-earth metal alloy, is located at the centre of the inner-stator core. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 299 Both the IPM and the polyphase armature winding phase coils on the inner stator create the magnetic field and the output torque is proportional to the square of the sum of both magnetic fields. Thus, the torque is proportional to the square of the sum of the magnetic flux of the IPM inductor and the inner-stator\u2019s poly-phase armature winding. Significantly, the in-wheel-hub motor/generator is designed both as reluctance and as an IPM magnetoelectrically excited in-wheel motor/generator. Moreover, it is described as an IPM inductor (unwound MSI outer rotor as well as wound and IPM inner stator) in-wheel-hub E-M/M-E motor/generator. The finite-element method may be used to optimise the shape of the outer rotor and inner stator \u2018teeth\u2019, for optimum magnetic flux distribution \u2013 to minimise cogging at the maximum value of torque. The outer rotor design also helps to minimise torque. Torque ripple is a result of saturation of the magnetic circuits. In in-wheel-hub E-M motors/generators, balanced three-phase sine wave excitation is used, resulting in a torque ripple as low as 5% without any ripple compensation. This ripple occurs at the maximum output value of torque; in the range where the torque/current characteristic is linear, the observed ripple is no greater than 2%. A high-angular-velocity sample and hold circuit used to monitor in-wheel-hub E-M motor current and constant-current feedback may be used to minimise the fall in in-wheel motor torque with angular velocity. The result is an in-wheel-hub motor that is capable of fast acceleration and deceleration, as well as stable operation at high values of angular velocity. The planetary-gearless SM&GW uses a variable reluctance stepping in-wheelhub E-M/M-E motor/generator with IPM inductor, operated as an AC-AC or ACDC-AC or DC-AC/AC-DC macrocommutator reluctance and IPM magnetoelectrically excited in-wheel-hub motor/generator. The magnetic circuit elements are composed of high-energy-product rare-earth SmFeTiB, SmFeMo or NdFeB magnets for in-wheel E-M motor high efficiency. Torque/angular-velocity characteristic of the DC-AC/AC-DC macrocommutator reluctance and IPM magnetoelectrically excited in-wheel-hub motor is very flat. It means fast acceleration, even at high velocity ranges and good controllability. Thus, an in-wheel-hub E-M motor makes it possible to adjust the propulsion torque and braking force independently at each wheel without the necessity for any M-M transmission, drive shaft, or other complicated mechanical components. Experience in tropical climate zones has underlined the fact that AEV and HEVs using SM&GWs with in-wheel-hub E-M motors necessitate the capability to operate at high ambient temperatures. Test reports claim that measuring vehicle frame temperatures of over 70\u00b0C have been measured. Such conditions may easily cause in-wheel-hub E-M motors to fail. Thin-air gaps in-wheel-hub E-M motors, in which the iron core is eliminated and the windings (coils) are wound onto an aluminium structure, conducting heat directly to the mounting, have proved capable of reliable operation despite high temperatures. Automotive Mechatronics 300 Dynamic-Absorbing Steered, Motorised and/or Generatorised Wheels (SM&GW) - A dynamic-absorbing in-wheel-hub E-M motor DBW AWD propulsion mechatronic control system uses the in-wheel-hub motors to absorb vibration, which enhances handling, safety, and comfort in AEVs and HEVs. These dynamicabsorbing SM&GWs overcome disadvantages existing in-wheel-hub E-M motor DBW AWD propulsion mechatronic control systems that have down-graded the applicability of those systems. Installing E-M/M-E motors/generators inside the wheel-hubs helps to control each wheel independently which provides for first-rate road-handling performance. It also eliminates the necessity for the M-M differential and driveshaft (or chains and sprockets) and therefore allows greater freedom in designing automotive vehicles. Designers may provide more space to the driver and passengers without increasing the overall mass and size of the vehicle. An intractable disadvantage of in-wheel-hub motors/ generators has been the mass that they add to each wheel. That influences comfort and road-holding performance unfavourably, and it has restricted the applicability of in-wheel-hub E-M/M-E motors/generators in AEVs and HEVs. New technology overcomes this disadvantage by using in-wheel-hub E-M/M-E motors/generators to absorb vibration. The in-wheel-hub motors/generators themselves operate as vibration shock absorbers (dampers). Their own vibrations absorb that from the on/off road and wheel-tyres, which permits for enhanced traction and a more-comfortable ride than is practicable with other systems or with other modes of AE or HE DBW AWD propulsion. In dynamic-absorbing SM&GWs (Fig. 2.114), dynamic shock absorbers suspend the shaftless in-wheel-hub E-M/M-E motors/generators to insulate them from the unsprung mass [BRIDGESTONE 2003]. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 301 The in-wheel-hub E-M motor\u2019s vibration, as well as the vibration from the on/off road and wheel-tyres damp each other, which enhances a road-handling performance. The flexible coupling (Fig. 2.115) consists of four cross guides that transfer smoothly the drive power from each in-wheel-hub E-M/M-E motor/generator to its wheel. The cross guides balance the continuous, satisfactory shifting in the rotational positioning of the in-wheel-hub E-M/M-E motor/generator and wheel. Analytical comparisons of the performance of a conventional AEV or HEV with a single E-M/M-E motor/generator, an AEV or HEV equipped with conventional SM&GWs with in-wheel-hub motors and an AEV or HEV equipped with dynamic-absorbing SM&GWs emphasise differentials in road-handling performance (contact force fluctuation) and necessary quality (vertical acceleration frequency) on a rough on/off road surface. The dynamic-absorbing in-wheel-hub motor DBW AWD propulsion mechatronic control system results in enhanced road-holding performance and a more comfortable ride than is practicable with conventional systems. It also offers advantages over conventional, single E-M motor AEVs and HEVs in safety and comfort [BRIDGESTONE 2003]. Electro-Mechanical (E-M) Differentials \u2013 While the basic principles of the E-M transmission arrangements for a E-M DBW 2WD and/or 4WD propulsion mechatronic control system remain the same for virtually all categories of AEVs, the actual arrangements vary \u2013 for instance, some may have DBW 2WD propulsion, that is either front-wheel drive (FWD) or rear-wheel drive (RWD), and others DBW 4WD propulsion. Another requirement stems from the fact that, when the AEV is cornering, the outer SM&GWs must roll faster than the inner ones that will be traversing circles of smaller radii, yet their mean value of wheel angular velocity, and mean value of vehicle velocity, may be required to remain constant. Automotive Mechatronics 302 So far as effectiveness of traction is concerned, FWD is better than RWD, especially on difficult terrain including ice or snow. This is partly because the mass of the CH-E/E-CH storage battery on the front SM&GWs enables them to grip the road surface better. This also applies to rear CH-E/E-CH storage battery RWD AEVs. Principally, however, the advantage is gained by virtue of the fact that the propulsive force, i.e., tractive effort is always delivered along the line in which the front SM&GWs are steered. Another factor is that front SM&GWs tend to climb out of holes or ruts, whereas rear SM&GWs tend to thrust the front undriven wheels deeper down and, in any case, not necessarily in the sense (arrow) of direction in which they are being steered. The application for full-time DBW 4WD propelled AEVs may grow rapidly over the next few years. This is due to increasing demand for AEVs with higher performances and power. It is well known that the distribution of gross tractive effort (thrust) and slip between the front and rear SM&GWs of DBW 4WD and/or 4WS SBW AEVs has considerable effect on the efficiency of operation. The function of a series electrical connection is to transfer the electrical energy from the EES to both the front and/or rear SM&GWs. The centre-wheel-drive (CWD) E-M differential, in the series electrical connection, is also necessary to distribute the drive equally between the front and/or rear SM&GWs, and to allow for the fact that when the AEV is driven in a circle, the mean values of the wheel angular velocity of the front SM&GWs are different from those of the rear SM&GWs and therefore the values of the wheel angular velocity of the two FWD and RWD units must differ too. Other factors include different degrees of wear and, perhaps, different values of the wheel-tyre pressure. Thus, a CWD E-M differential improves steering response and traction performance by controlling the angular-speed difference between the FWD and RWD units. Provision is usually made for locking this differential out of operation to improve the performance and reliability of traction when the AEV is driven over slippery ground. For AEVs intended mainly for operation on soft ground, the CWD E-M differential may be omitted from the drive E-M powertrain line, but some means of disengaging DBW 4WD propulsion, leaving only a single pair of SM&GWs to do the driving, is generally provided for use if the AEV is required to operate on metalled roads. As it is well known from the principle of Ackermann\u2019s SBW 2WS conversion, the front SM&GWs always tend to roll further than the fixed-geometry rear SM&GWs, because their radius of turn is always larger, a parallel electrical connection (cabling) can be interposed between the EES as well as FWD and RWD units and the CWD E-M differential may be omitted from the E-M powertrain line drive (see Fig. 2.116). In practise, this usually takes the form of two separate FWD and RWD units, single on each front and rear SM&GWs on which there are rotary controls that can be locked by the driver, but the driver has to stop and alight to do so. As soon as the driver again drives the AEV on firm ground, however, the driver must remember to unlock the FWD and RWD units. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 303 Should the rear SM&GWs lose traction, on the other hand, and therefore tend to rotate further than the front ones, the drive may be automatically transferred to the front SM&GWs, even if they are in the freewheeling mode. A conventional M-M DBW 4WD automotive vehicle has numerous disadvantages in comparison to a 2WD version: its fuel consumption is poorer, it is heavier, due to the presence of the drive shaft and other components, and it also requires a floor tunnel for the drive shaft to pass through. Accordingly, it may be decided to use E-M DBW 4WD to optimise (minimise) these disadvantages and to ensure adequate performance in actual driving, for instance, as the AEV shown in Figure 2.117 [MITSUBISHI 2005]. Also, the reduction of fuel consumption in DBW 4WD may be minimised by using DBW 4WD propulsion only when necessary and by recuperating braking and/or cornering mechanical energy using both the FWD and RWD. Automotive Mechatronics 304 CH-E/E-CH Storage Batteries - A CH-E/E-CH storage battery consists of two or more cells that may be linked in series (to provide multiples of cell voltage) and/or in parallel (to provide more capacity [Ah] from the resulting voltage). In Figure 2.118, the Ragonne plot (log-log plot) of different CH-E/E-CH devices is presented [DLA 2008]. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 305 An overview of the properties of the different CH-E/E-CH storage batteries is presented in Table 2.3. The values in the table are typical ones and can vary with different manufacturers. For example, a lithium-polymer (LiPo) storage battery with a \u20186s2p\u2019 configuration has two parallel sets of six cells in series. It weighs 1.117 kg, and provides a capacity of 7.40 Ah. Since a LiPo cell has a nominal voltage of 3.7 VDC that of this battery is 22.2 VDC. Nickel-metal hydride (NiMH) and nickel-cadmium (NiCd) cells have a nominal voltage of 1.2 VDC, thus requiring three in series to give the voltage of one Li-Po cell. Most CH-E/E-CH storage batteries used in advanced applications employ secondary (rechargeable) cells, although primary (disposable) cells offer some performance advantage. Automotive Mechatronics 306 For instance, the AEV may achieve 60 -- 90 min rides with rechargeable CH-E/E-CH storage batteries, but 80 -- 100 min with single-use units. An endurance of three hours is reported with a rechargeable battery, but four hours with a disposable unit. Extreme endurance basically depends on employing two or more storage batteries in parallel, and cells of high specific energy. Endurance may be traded against payload. Specific energy has recently increased dramatically, from 60 Wh/kg of the NiCd storage battery to 80 Wh/kg for NiMH, 160 Wh/kg for Li-Ion and 200 Wh/kg for today\u2019s Li-Polymer storage batteries. The major emphasis for AEV applications has been on reducing CH-E/E-CH storage battery mass, thus making possible increases in payload and/or endurance. However, today\u2019s storage batteries are still not completely user-friendly. Early NiCd storage batteries had to be fully discharged before recharging, otherwise they would not take a full charge. The NiMH storage batteries that followed may cause corrosion and may explode if abused. Likewise, LiIon storage batteries may be dangerous if mistreated. The nominal voltage for a LiIon cell is 3.6 VDC, and, like the LiPolymer cell, it may be seriously damaged by discharging below 2.8 VDC. If the cathode should reach 100oC it may emit pure oxygen, producing a high risk of fire. The LiPolymer storage battery first appeared in the mid-1990s. The anode is carbon in which lithium ions are dissolved, while the cathode is lithium cobalt oxide or lithium manganese oxide. The electrolyte is a polymer film in which lithium is dissolved. The electrodes and electrolyte form three sheets that are laminated together, thus avoiding the need for a metal casing. The LiPolymer cell may be extremely thin and is normally manufactured as a long sheet, which is rolled or folded, then sealed in a soft plastic cover. If wired in parallel, these cells must be \u2018balanced\u2019 to ensure uniform voltages so that none will drop below 2.8 VDC. The solid polymer electrolyte of a LiPolymer is not flammable; hence such batteries are somewhat less hazardous than their LiIon forbears. However, they need to be \u2018broken in\u2019 with a series of short discharges, and they also need careful charging. If more than 4.235 VDC is applied, they may explode and catch fire, and the flames cannot be extinguished with water. Shorting the CH-E/E-CH storage battery may also cause an explosion. Overdischarging LiPolymer storage batteries, which would render them useless, is avoided by using a low-voltage cut-off (LVC) that prevents it falling below 3.0 VDC. The next stage of development is represented by solid-state lithium storage batteries, giving 300 -- 400 Wh/kg. In late 2008, the author rode his Melex golf cart with a rechargeable lithiumsulphur (LiS) storage battery using cells rated at 350 Wh/kg. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 307 Whereas, in earlier rides, using LiPolymer cells, the Melex had an endurance of 70 min, the innovative cells lasting more than two hours. When used in conjunction with solar arrays, it is anticipated that in time LiS storage batteries may sustain such AEV for the night time part of multi-day missions. Despite these advances, it is noteworthy that the specific energy of gasoline (20 kWh/kg) is around 50 times that of the supreme CH-E/E-CH storage battery foreseen in the near-term."
        ]
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.16-1.png",
        "caption": "Fig. 2.16 Accelerator pedal module [MCKAY ET AL. 2000].",
        "texts": [
            " Appliance requirements are absolutely fulfilled both in terms of control performance and controller cost. For instance, one of the well-known TVC systems [MCKAY ET AL., 2000] uses a minimum of two accelerator-pedal sensor potentiometers and two throttle sensor potentiometers (see Fig. 2.15). Additional voltage references, sensor grounds, or a third accelerator pedal sensor are available to increase the overall accelerator pedal position sensing reliability depending upon the customer requirements (see Fig. 2.16). 2.1 Introduction 165 Electrically isolated voltage references and grounds may be used so that a single-point electrical short/open condition does not invalidate all pedal/throttle position sensors. The sensor-output characteristics are diversified to improve the detectability of common mode failures using correlation rationality diagnostics (see Figs 2.17 and 2.18). The TVC system also uses redundant brake switches that are logically opposed, one normally open and one normally closed. As with the throttle and pedal sensors, brake switch redundancy and diversity facilitates reliable braking signals and rationality diagnostics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002965_j.ijheatmasstransfer.2019.118464-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002965_j.ijheatmasstransfer.2019.118464-Figure1-1.png",
        "caption": "Fig. 1. Scheme of powder-based LMD process.",
        "texts": [
            " Unlike the level set methods, which use a flow-based evolution equation for the formation of the molten bath surface, a method is applied here that explicitly takes into account the capillary forces given as the product of the surface tension with the mean curvature. For the calculation of the geometry of the molten bath surface, a mathematically equivalent functional is used instead of the Young-Laplace, which calculates the surface energy. After each time step, a local minimum is calculated, allowing each node of the melt pool surface to move freely in the normal direction. The present work will explain and present the physical model and its numerical implementation and show first results. In the powder-based LMD process (see. Fig. 1), a focused laser beam is used to generate a melt onto the substrate. Powder particles are injected into the melt through a powder nozzle and lead to an increase in melt volume. A welding bead is generated by the movement of the laser beam. A layer is built up by overlap machining and a volume by several layers. The powder particles attenuate the incident laser beam and only the transmitted portion into the process zone is available for direct heating of the substrate. By selecting the relative position of the substrate surface to the laser beam focus, the power density distribution in the process zone can be varied according to the beam caustics and thus influence the melt pool width and process temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000475_j.optlaseng.2010.06.010-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000475_j.optlaseng.2010.06.010-Figure1-1.png",
        "caption": "Fig. 1. Geometric and mesh of the model. (a) Entire model and (b) the melting zone enlarged drawing to show the detail of mesh division.",
        "texts": [
            " During LSM, an additional volumetric strain is induced by microstructure evolution during solid-state phase transformation along with thermal strain. With microstructure change, transformation induced plasticity is also generated. Therefore, the total strain rate can be written as the individual components as _e \u00bc _ee \u00fe _ep \u00fe _eth \u00fe _eph \u00f010\u00de where _ee, _ep, _eth and _eph are elastic strain, plastic strain, thermal strain and phase transformation strain, respectively. Commercial finite element analysis software was used to establish a mathematical model for calculating temperature fields of roller steel by multi-track LSM, as shown in Fig. 1. Determination of optimal time stepping and mesh were essential for solution of these nonlinear and coupled governing equations. An FE mesh, which was refined in the melted zone and adjacent area (Fig. 1), was created using eight-node hexahedral elements. Because of large temperature gradients and phase transformations, those regions were critical for solution accuracy and convergence. The laser beam as an external thermal current on the surface must be considered to simulate LSM process. Its continuous scanning was described as a moving heat source with Gaussianlike distribution [21] and handled as a volumetric heat source, which was determined by the beam penetration depth. The volumetric heat source term, q(x,y,z), can be expressed as q\u00f0x,y,z\u00de \u00bc 2P pr2 f 0 d rf rf 0 2 exp 2\u00f0x2\u00fey2\u00de r2 f \" # u\u00f0z\u00de \u00f011\u00de where P is the laser power, d is the beam penetration depth, and rf and rf0 are the beam\u2019s focal radius at the surface and depth, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001293_0954406214543490-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001293_0954406214543490-Figure4-1.png",
        "caption": "Figure 4. (a) Transverse cross section of the sun\u2013planet mesh with misalignment error and (b) zoom plot of (a).",
        "texts": [
            " For the point E on the line OG in Figure 2, with z coordinate z0, the x and y coordinate values are x0 \u00bc z0 tan y0 \u00bc z0 tan = cos \u00f01\u00de at UNIV CALIFORNIA SAN DIEGO on February 16, 2016pic.sagepub.comDownloaded from Perfect pinion-sun mesh when there is no misalignment error is shown in Figure 3(a). Each contact line in the base plane is discretized into several potential contact points. As the carrier is titling, all planets are assumed to incline in the same degree regardless of the effect of the bearing clearance as shown in Figure 3(b). For individual mesh point, arbitrary crosssection I perpendicular to the rotational axis is selected as shown in Figure 4. In Figure 4, Opn is the center of the circle of the perfect planet and G is the center of the circle of the planet section after the carrier is titled. The whole section I of the nth planet all move along the vector OpnG. It can be observed that the original in meshing state will shift to a new condition. It should be further analyzed whether the new state is just in mesh, in separation, or in penetration. Due to the translation of planet, the new LOA is generated. The profile of the planet intersects with the new LOA at Q and the profile of the sun intersects with the new LOA at R",
            " as, ar sun\u2013planet and ring\u2013planet pressure angle aks , a k r kth section of sun\u2013planet and ring\u2013 planet pressure angle C, Cb viscous mesh and bearing damping matrix esp, erp initial separation between sun\u2013planet and ring\u2013planet along the LOA esnk initial separation of the kth section between nth planet\u2013sun Fsnk mesh force of kth section between the nth planet\u2013sun mesh Fm excitation caused by the misalignment error hsnk tooth contact coefficient Is mass moment of inertia for the sun K, Kb mesh stiffness matrix and the bearing supporting stiffness Kb, Ks, Ka, Kf, Kh Ke ksx, ksy ending stiffness, shearing stiffness, axial stiffness, additional stiffness caused by fillet-foundation, Hertzian contact stiffness total mesh stiffness of spurs gear bearing stiffness in horizontal and vertical direction ksnk mesh stiffness of kth section of nth pinion-sun M mass matrix ms mass of the sun Rbp, Rbs base radius of the planet, the sun Rc distance between the planet center and sun center T external excitation wk, wk0 the elastic deformation for the point k and k0 on the gear surfaces xc, xr, xs, xpn horizontal displacements of the ring, sun, carrier, and planet xG deviation of the planet due to carrier misalignment error in horizontal direction yc, yr, ypn, ys, vertical displacements of the ring, sun, carrier and planet yG deviation of the planet due to carrier misalignment error in vertical direction b angle shown in Figure 4 sn rigid body displacement of nth planet\u2013 sun along LOA \"k initial separation between the potential contact points k and k0 , 0 angle shown in Figure 4 misalignment error on plane XOZ misalignment error on plane YOZ c, r, s, pn rotational displacements of the ring, sun, carrier, and nth planet at UNIV CALIFORNIA SAN DIEGO on February 16, 2016pic.sagepub.comDownloaded from"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.5-1.png",
        "caption": "Fig. 9.5 Bevel gear pair (a) and angular velocity diagram (b)",
        "texts": [
            "71) Three bodies i , j and k (arbitrary, different) with a common fixed point have relative to each other angular velocities \u03c9ij , \u03c9jk and \u03c9ki . Repeated application of (9.8) yields the equation \u03c9ij + \u03c9jk + \u03c9ki = 0 (i, j, k arbitrary) . (9.72) This shows that the instantaneous axes of rotation are coplanar and that the angular velocities form a closed planar triangle. Because of (9.71) this equation can also be written in the form \u03c9ij + \u03c9jk = \u03c9ik (i, j, k arbitrary) . (9.73) The equation is illustrated by the bevel gear pair shown in Fig. 9.5a . Two bevel wheels 1 and 2 are mounted in the frame 0 . Their angular velocities \u03c910 and \u03c920 relative to the frame have the directions of the axes. The relative angular velocity \u03c921 has the direction of the common generator of the two pitch cones. These pitch cones represent the fixed and the moving cone of the motion of one wheel relative to the other. Thus, the directions of the three angular velocities are prescribed by the design. If one of the angular velocities is prescribed, the other two are determined by (9.72). The equation requires that the vector triangle in Fig. 9.5b be closed. The geometrical construction just demonstrated for two wheels is applicable to arbitrarily complicated bevel gear trains with degrees of freedom F \u2265 1 . All wheel axes as well as all generators of all pitch cones are passing through a common point. Every wheel axis and every generator common to the cones of two wheels determines the direction of a relative angular velocity. 9.7 The Ancient Chinese Southpointing Chariot 307 This fact in combination with (9.71), (9.72) or (9.73) determines all angular velocities if F angular velocities are arbitrarily prescribed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.59-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.59-1.png",
        "caption": "Fig. 2.59 Automotive vehicle states associated with the single-track half-vehicle (bicycle) physical model [LYNCH 2000].",
        "texts": [
            " For ride analysis, it is normally indispensable to consider the wheels as discrete lumped masses. In that instance, the lumped mass symbolising the body is the \u2018sprung mass\u2019, and the road wheels are symbolised as \u2018unsprung masses\u2019. B.T. Fijalkowski, Automotive Mechatronics: Operational and Practical Issues, Intelligent Systems, Control and Automation: Science and Engineering 47, DOI 10.1007/978-94-007-0409-1_17, \u00a9 Springer Science+Business Media B.V. 2011 210 For single mass depiction, the vehicle is considered as a mass focused at its centre of gravity as shown in Figure 2.59 [LYNCH 2000]. The point mass at the centre of gravity, with relevant rotational moments of inertia, is dynamically comparable to the automotive vehicle itself for all motions in which it is sensible to presume the vehicle to be of rigid body. The relationship of the automotive vehicle\u2019s fixed coordinate system to the earthfixed co-ordinate system is recognised by Euler angles. These are created by a series of three angular rotations. Beginning at the earth fixed system, the axis system is first rotated in yaw\u03c8 (around the z axis), then in pitch\u03b8 (around the y axis), and then in roll\u03c6 (around the x axis) to line up with the vehicle\u2019s fixed coordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002848_s12555-019-0023-7-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002848_s12555-019-0023-7-Figure4-1.png",
        "caption": "Fig. 4. An infinitesmal mooring line segment.",
        "texts": [
            " [31\u201333] show that, when the chain angle is between 30\u25e6-60\u25e6 and the mooring lines are symmetrically distributed, the DPM platform can compensate the environmental disturbance from any direction with less positional deviation. Three components mooring line is selected as shown in Fig. 3. Each mooring line is divided into three sections. s1 and s3 segments are anchor chain, s2 segment is steel cable. For convenience, the tension force on mooring lines is obtained by piecewise extrapolation proposed in the following. The force analysis for an infinitesmal segment on the mooring line is shown in Fig. 4. F and D are the unit current force in tangential and normal directions, respectively. w is the mooring line\u2019s weight per unit length in the water. \u03b8 is the angle between T and the horizontal direction; ds is the unit length. \u03b5 is the elongation of the unit length. According to the force analysis of the unit mooring line on the tangential and normal directions, we can obtain the following equations: (T +dT )cosd\u03b8 +F (1+ \u03b5)ds = T +wdssin\u03b8 , (9) (T +dT )sind\u03b8 = wdscos\u03b8 +D(1+ \u03b5)ds. (10) In general, the magnitude of sea current force is far smaller than the weight of mooring line, so the effect of current on the mooring system can be ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002865_j.ymssp.2019.106335-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002865_j.ymssp.2019.106335-Figure1-1.png",
        "caption": "Fig. 1. The overall mechanical structure of the soft robot.",
        "texts": [
            " However, these variable stiffness systems either increase the complexity and weight of the soft robot or have long activation timescales that are not ideal for practical environments. Furthermore, these works primarily focus exclusively on robot stiffness control without simultaneously considering position control. Relative to electric, hydraulic, and pneumatic actuators, shape-memory alloy (SMA) actuators have a high power-toweight ratio, low driving voltages, low cost, and silent operation, making them suitable for a wide variety of applications [5,6]. In this paper, we use the same prototype of soft robot as in our previous research [7]. As shown in Fig. 1, three types of SMA wires, termed SMA-1, SMA-2 and SMA-3, are embedded in a soft robot. SMA-1 is used as the bone structure to support the soft robot. To actuate the soft robot, one SMA-2 fiber is used for large contractions because of its low strain; it is placed into the soft robot in a U shape to double its driving capacity. The stiffness of the soft robot is changed when the four SMA-3 wires are heated; these wires have a memorized straight-line shape that does not change in length when heated from the martensite phase to the austenite phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001345_j.electacta.2013.10.039-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001345_j.electacta.2013.10.039-Figure1-1.png",
        "caption": "Fig. 1. (A) Diagram of the experimental setup employed for DBD plasma treatment. (B) The process for activation of MWCNTs in helium plasma and functionalization of",
        "texts": [
            " In order to remove most of the defects and functional roups formed on the surface of the nanotubes during its syntheis processes, the temperature of pristine samples was raised to 000 \u25e6C at a ramp rate of 5 \u25e6C min\u22121 in helium. The resulting samles are denoted as annealed MWCNTs. All other chemicals from ommercial sources were of analytical grade and used as received, ithout further purification. All aqueous solutions were prepared n double distilled water. .2. Apparatus and measurements .2.1. Plasma treatment Amine functionalization of MWCNTs was carried out using a BD plasma system. Fig. 1 represents the diagram of the plasma ystem and the process for amine functionalization. As shown, BD plasma reactor consists of a function generator (Pintek FG-32, aiwan) connected to a high voltage amplifier (TREK 10/40A, USA). 20 MHz oscilloscope (Hameg, Germany) was used along with a igh impedance and high voltage probe for monitoring the genrated current and phase shift. Two mass flow controllers (MFCs, nit UFC-7300, USA) were used for adjusting the flow of helium nd ammonia gas to the plasma reactor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.30-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.30-1.png",
        "caption": "Fig. 15.30 First and second generation of the trochoid of Fig. 15.27. Parameters r0 = 5 , r1 = 2 , b = 1 (first generation) and r\u22170 = \u22125/2 , r\u22171 = \u22123/2 , b\u2217 = \u22123 (second generation)",
        "texts": [
            " The dashed lines parallel to the lines P20P12 and P12C form the parallelogram with the corner P\u2217 12 opposite P12 . The point P\u2217 12 is the center of wheel 1\u2217 . The pole P\u2217 10 is determined by the fact that it is on the line P\u2217 12P20 as well as on the normal P10C to the tangent of the trochoid. The poles P20 , P \u2217 10 and P\u2217 12 determine the positions of the wheels 0\u2217 and 1\u2217 . The parallelogram is seen to accomplish the interchange of angles as is prescribed by the last two Eqs.(15.123). In the case of opposite signs of \u03d52 and \u03d51 (Fig. 15.30), interchanging the angles has the effect that the cranks of the two generating mechanisms must be rotated in opposite directions in order to trace the trochoid in the same sense. The two generating mechanisms have some properties in common. By other properties they can be distinguished. First, a distinguishing property. If P20 is outside the circle of wheel 1 in one generation, P20 is inside the circle of wheel 1 in the other generation (see Figs. 15.29 and 15.30). By convention, the generation with P20 outside the circle of wheel 1 is called first generation. Next, a property common to both generating mechanisms. Wheel 0 is 500 15 Plane Motion touched by wheel 1 either in both mechanisms from the outside (Fig. 15.29) or in both mechanisms from the inside (Fig. 15.30). Trochoids generated by mechanisms of the former type are called epitrochoids, and trochoids generated by mechanisms of the latter type are called hypotrochoids. Epitrochoids and hypotrochoids alike are divided into three families: 1. Trochoids have double points if in the first generation the generating point C is outside the circle of wheel 1 , i.e., if |b/r1| > 1 . Such trochoids are called curtate trochoids (Fig. 15.26 and the limac\u0327on of Pascal in Fig. 15.8a ). 2. Trochoids have cusps on the circumference of wheel 1 if the generating point C is located on the circumference of wheel 1 (in both generations; |b/r1| = 1 )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003749_s00170-021-07105-3-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003749_s00170-021-07105-3-Figure5-1.png",
        "caption": "Fig. 5 a CT-scanned cylinder after reconstruction, b transverse cross section, and c modification of the transfer function to remove the powder particles and observe the single tracks",
        "texts": [
            " The temperature-dependent IN625 material properties used in the simulation are shown in Fig. 4. Besides, other properties are listed in Table 4. The laser source is modeled as a Gaussian heat source, and complex physics such as laser multiple reflections, material evaporation, and recoil pressure are included in the model to accurately predict the laser melting and keyhole formation. The CT scanned cylinder samples are analyzed to obtain the pore number and pore volume formed inside the single tracks. Figure 5 a shows the 3D image of a typical cylinder sample obtained after the CT image reconstruction. The grayscale image is based on the density of the sample. The light gray region is the solid In625, dark gray contained inside the cylinder is the In625 powder, and the black region represents the void. A transverse section of the sample is shown in Fig. 5b. Three tracks are identified based on the surface profile, and one of the tracks shows the formation of the pore inside the track. Besides, the density-based transfer function is modified to remove the powder material inside, and the 3D clipping is performed to observe the single track formed over the base, as shown in Fig. 5c. This feature enables the comparison of the surface morphologies formed with different laser parameters. Figure 6 presents the micro-CT image of the keyhole pores formed with 0.98 J/mm LED along the scan direction. The higher LED resulted in deep penetration melting. Hence, the pores are formed deep inside the track. However, the depth of the single track is not known from micro-CT, although the formation of the pore is apparent. Figure 6 also shows the 3D-rendered pores, which show that the pores formed are mostly spherical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure2.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure2.3-1.png",
        "caption": "Fig. 2.3 The stiffness of a cylinder, a ball or a length of wood is defined by stiffness k D F=x. A graph of F vs. x is usually not a straight line. If the line curves upwards, then the stiffness, F=x, increases as x increases",
        "texts": [
            " Whenever we use the word stiffness in this book it will be clear from the context whether we are referring to bending or compression, but the reader should remain alert to the fact that bending and compression are two different, but related things. If you bend a long wood or metal rod or bar, one side lengthens or stretches and the opposite side shortens or compresses. Consequently, a material that is easy to stretch or compress will also be easy to bend. 32 2 Bats and Balls A bat can bend in different ways. For example, if you were to place each end of a bat on a brick and stand on the bat in the middle, then the bat would bend in the middle, as shown in Fig. 2.3. If you put the barrel in a vice and tighten the vice, the bat would bend out of shape and squash across its diameter. In either of these circumstances, a stiff bat or ball will not bend or squash as much as a flexible bat or ball. A bat is not necessarily stiff along its whole length. In fact, the handle end is always more flexible than the barrel end since the handle is thinner. Stiffness depends on several factors. One is the nature of the material. For example, rubber is a very flexible material, wood is stiffer, and steel is stiffer than wood"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000687_s12206-009-1153-2-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000687_s12206-009-1153-2-Figure7-1.png",
        "caption": "Fig. 7. Stacked motor configuration.",
        "texts": [
            " It can operate from the lowest applied voltage of around 500V. However, to obtain practical force, it requires higher voltage than 1kV. With such a high voltage of over 1kV, electric discharge may occur in the atmospheric air, which disturbs the electrostatic field inside the motor and causes improper motor behavior. To prevent such discharge, a dielectric liquid like Fluorinert is used for insulation. The force output capability can be easily increased by stacking many pairs of slider and stator films as shown in Fig. 7. With the same applied voltage, thrust force is proportional to overlapping electrode area between slider electrodes and stator ones, which can be increased by stacking many pairs of films. Motor housings are typically made of plastic to avoid the risk of electric leakage. Some examples of such are shown in Fig. 8. 50-layer stacked films are contained in a plastic package as shown in Fig. 8(a). Fig. 8(b) is a plastic film package, which has flexibility. In some prototypes, metal housings were utilized to enhance overall stiffness for precise positioning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002454_control.2016.7737529-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002454_control.2016.7737529-Figure2-1.png",
        "caption": "Fig. 2. Schematic model of a quadrotor",
        "texts": [
            " It is derived using Euler-Langrange formalism and follows the development in Sharifi et al. [12] with the following assumptions: \u2022 the structure is rigid and symmetric, \u2022 the propellers are rigid, \u2022 the rotor thrust and the drag are proportional to the square of the speed of the rotor, \u2022 the rotor axes are parallel and lie in the z direction, \u2022 ground effect is neglected, \u2022 the inertia matrix is diagonal, \u2022 the wind forces are not included, \u2022 and the motor dynamics are ignored. The axes system and forces are shown in Figure 2. The center of gravity is assumed to be at the origin of the body axis reference frame. The orientation of the quadrotor is given by (\u03c6, \u03b8, \u03c8) measured with respect to the Earth coordinate frame E. The rotational and vertical accelerations are given by \u03c6\u0308 = \u03b8\u0307\u03c8\u0307 ( Iy \u2212 Iz Ix ) \u2212 J Ix \u03b8\u0307\u03c9 + lU1 Ix (1) \u03b8\u0308 = \u03c6\u0307\u03c8\u0307 ( Iz \u2212 Ix Iy ) + J Iy \u03c6\u0307\u03c9 + lU2 Iy (2) \u03c8\u0308 = \u03c6\u0307\u03b8\u0307 ( Ix \u2212 Iy Iz ) + U3 Iz (3) Z\u0308 = \u2212g + cos\u03c6 cos \u03b8 1 m U4 (4) where g is gravitational field constant, l is the arm length, m is the mass, Ix, Iy , Iz are the moments of inertia about their respective axes, J is the rotor inertia, and \u03c9 = \u03c94 +\u03c93\u2212\u03c92\u2212 \u03c91 where \u03c9i, i = 1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.1-1.png",
        "caption": "Fig. 12.1 Velocity screws with skew axes. Unit vectors ni and pitches pi (i = 1, 2). Parameters \u03b1 , and reference basis e1,2,3",
        "texts": [
            " Sabrea Pereira M F O, Ambro\u0301sio J A C (eds.) (1989) Computer-aided analysis of rigid and flexible mechanical systems. Kluwer, Dordrecht 2. Wittenburg J (1977) Dynamics of systems of rigid bodies. Teubner Stuttgart 3. Wittenburg J (1989) Topological description of articulated systems. In [1]:159\u2013196 4. Wittenburg J (2007) Dynamics of multibody systems. Springer, Berlin Heidelberg New York Chapter 12 Screw Systems In this chapter the investigation of velocity screws is resumed. Definitions see in Sect. 9.3 . The system shown in Fig. 12.1 has two helical joints with skew axes and with pitches p1 and p2 . The terminal body 2 has relative to frame 0 the degree of freedom two. The length of the common perpendicular of the joint axes is , and the projected angle is \u03b1 . Unit vectors n1 and n2 having the directions of the axes are attached to the midpoint 0 of the common perpendicular. This point 0 is the origin of a frame-fixed basis e . The basis vector e1 is directed along the bisector of the angle \u03b1 between n1 and n2 , and e3 is directed along the common perpendicular",
            "10) These equations are identical with Eqs.(3.158) and (3.159) governing the resultant of two infinitesimal screw displacements. Compare also Fig. 12.2 with Fig. 3.15 and Eqs.(12.7) and (3.156). The formal identity is explained by the equation d(\u03d5 + \u03b5s) = (\u03c9 + \u03b5v) dt . A change of variables led to Eqs.(3.160) \u2013 (3.171) which show that the resultant screw axis is generator of a cylindroid (Fig. 3.16). The same equations and the same figure are valid for the resultant velocity screw. Let P be an arbitrary point fixed on body 2 of Fig. 12.1 . In the case \u03c92 = 0 , P has a velocity v1 proportional to \u03c91 , and in the case \u03c91 = 0 , P has a velocity v2 proportional to \u03c92 . Superposition determines the velocity v = v1+v2 . If the point P is chosen at random, v1 and v2 are not collinear. Together they determine a certain plane. The direction of v in this plane depends on the ratio \u03c91/\u03c92 . The question arises: Are there body-fixed points such that v1 and v2 are collinear so that the direction of v is independent of \u03c91/\u03c92 ? The answer is as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.20-1.png",
        "caption": "Figure 6.20. Model of a damped spring-mass system.",
        "texts": [
            " On the other hand, magnification of induced motions is essential in the design of seismographs and certain flight instruments. The analysis of the kinds of problems described above generally is quite complex, especially when vibrational effects are nonlinear; however, a great variety of problems that involve damping and induced motions can be adequately modeled by a simplified damped spring-mass system that consists of a load of mass m, a linear spring of constant stiffness k, and a linear viscous damper or dashpot . A typical model of a damped spring-mass system is shown in Fig. 6.20. A dashpot consi sts of a piston that moves within a cylinder containing a fluid, usually oil. When the piston is moved by the load , it exerts a viscous retarding force on the load. For simplicity, we model this viscous force by Stokes's law (6.29) and 152 Chapter 6 write FD = - di, in which c is a constant damping coefficient. The spring force is a restoring force given by Fs = -kxi, where x(t) denotes the displacement of the load from the natural state of the system . The other applied forces in Fig. 6.20 include a disturbing force F*(t) = F*(t)i, attributed to certain environmental effects of the sort mentioned above.The free body diagram in Fig. 6.20a shows that the weight W is balanced by the normal reaction force N of the smooth surface , and hence the motion x(t) is determined by the differential equation mx +d +kx = F*(t). (6.82) If the disturbing force F*(t) = Fois constant, the motion is called afree vibration; otherwise, it is called aforced vibration .When c is zero or may be considered negligible, the motion is said to be undamped.The undamped, free vibrational motion is just the simple harmonic motion (6.65a) studied earlier. We next consider the problem of damped, free vibrations of the load. 6.11.1. The Equation of Motion for Damped, Free Vibrations In a free vibration, the only effect of a constant disturbing force F* = Fo, such as gravity, is to shift the origin to the new position z == x - XE , where XE = Fo / k is the unique time independent, relative equilibrium solution of (6.82). Therefore, by this simple transformation, all damped, free vibrations of the system in Fig. 6.20 are characterized by the differential equationfor the damped,free vibrational motion of the load m about its relative equilibrium position: wherein the coefficients are constants defined by (6.83) c 2v== -, m (6.84) Dynamics of a Particle 153 in which p is the circular frequency of the familiar undamped spring-mass system . The coefficient v is named the damping exponent.The damping coefficient has the physicaldimensions[c] = [FV- 1] = [MT-1],andhence[v] = [p] = [T-1] .The dimensionless ratio v c ~ = p= Zmp' is known as the viscous damping ratio",
            " Let z(r) = u(t)eh (l) and find h(t) and r2(t) in order that (6.83) may be transformed to an equation of the form (6.86b) for the function u(t). The solution u(t) will now depend on the nature of the function ret); so, in general, u(t) need not be a periodic function . 0 6.12. Steady, Forced Vibrations with and without Damping The oscillatory motion of a mechanical system subjected to a time varying external disturbing force is called aforced vibration. In this section, we investigate the forced vibration of the system in Fig. 6.20 due to a steady, sinusoidally varying disturbing force F*(t) = Fosin Qt . (6.87) The constant Fo is the force amplitude and the constant circular frequency Q is called the forcing or driving frequency. The motion of a load induced by a time varying driving force of the kind (6.87) is known as a steady, forced vibration; otherwise, the response is called unsteady or transient. In general, a vibratory motion consists of identifiable steady and transient parts . The transient part of the motion eventually dies out, and the subsequent remaining part of the motion is called the steady-state vibration",
            " When this is done for aI , the dotted curve in Fig. 6.23 is transformed into its mirror reflection shown as the solid right-hand curve above it. Interpretation of the general physical relevance of the magnification factor (6.94a) in its relation to the response graph shown in Fig. 6.24 is a bit different. In accordance with (6.92b), for a small operating frequency the magnification factor Dynamics of a Particle 165 ao ~ I, as shown in Fig. 6.24. This means that the steady-state motion of the mass shown in Fig. 6.20 has an amplitude equal to the static displacement of the spring due to a force Fo.The motion is in phase with the driving force, so the mass moves in the direction of this force. As ~ -+ I at resonance, the amplitude grows indefinitely great, as described earlier. Beyond resonance ~ > I; so, the steady-state motion in (6.92a) is out of phase with the driving force, and hence the mass in Fig. 6.20 moves in a direction opposite to the disturbing force .Under a high frequency driving force for which ~ -+ 00 in Fig. 6.24, the steady-state amplitude response ao(~) -+ 0, and hence the steady-state amplitude in (6.92b) approaches zero . Therefore, the high frequency vibration of the supporting structure has virtually no effect on the motion of the system, and the mass in Fig. 6.20 remains essentially stationary. Of course, some sort of damping or friction is always present in real mechanical systems . Damping effects in the forced vibration of a load are studied next. 6.12.2. Steady-State Vibrational Response of a Damped System When damping is present , the free vibrational part of the motion , the first term in (6.90c) called the transient state, eventually dies out, and the vibrational motion thus converges toward a harmonic motion having the same frequency as the disturbing force, the steady-state heartbeat of the system. In consequence, only the steady-state part of the motion (6.90c) of a damped system need be considered. Let Xa denote the steady-state solution. Then by (6.90c) Xa = H sin(fU - A), (6.95a) (6.95b) where H is defined in (6.90d) and, from (6.90a) , the initial phase A is given by C2 2~l;tan A = -- = --. C, I - ~2 Clearly, for ~ = I , A = 90\u00b0 at resonance; and in this case, when Qt = If / 2, F* = Fo in (6.87) and Xa = 0 in (6.95a). Hence, at resonance, the vibrating body in Fig. 6.20 is moving through its mid position in its steady-state motion at the same instant when the driving force is at its greatest value. Notice that the response amplitude H in (6.90d) does not depend on any initial data. Thus, regardless of how the system may be set into motion initially, after a time, it settles down to the steady-state motion (6.95a) whose amplitude (6.90d) and phase (6.95b) depend upon the damping and frequency ratios. The amplitude factor defined by I H a= =J(l - ~2)2 + (2~n2 x, (6",
            " 168 6.12.3. Force Transmissibility in a Damped System Chapter 6 The vibrating load in its steady-state obviously transmits force to the supporting structure of the system. Therefore, it is important to have a measure of the intensity of this force . In this section, a certain transmissibility factor is introduced, and effects due to variat ion in the damping and in the operating frequency are discussed. In the steady-state motion (6.95a), the spring and damping forces for the mechanical system in Fig. 6.20 are given by Fs = kx; = kH sin(Qt - A), FD = cXa = cQH cos(Qt - A), (6.96a) whose amplitudes are Fs = kH and FD = cHQ.Each force in (6.96a) contributes to the total force transmitted to the support: Fs + FD = FT sin(Qt - A+ 1{;) where tan 1{; == cQ/ k and the maximum impressed force , denoted by FT, is defined by (6.96b) Then the ratio of the total impressed force to the maximum value of the disturbing force Fo = kK, defines the transmission ratio TR, also known as the transmission factor or the transmissibility",
            " A heavy bead of mass m slides freely in a smooth circular tube of radius a in the vertical plane . The tube spins with constant angular speed about the vertical axis, as shown. Problem 6.66. 218 Chapter 6 (a) Derive the equation of motion two ways: (i) by use of the moment of momentum principle and (ii) by application of the Newton-Euler law. (b) Examine the infinitesimal stability of all relative equilibrium positions of the bead. 6.67. Experiment shows that the undamped, forced horizontal motion of the system shown in Fig. 6.20, page 152, has a steady-state amplitude HI when the driving frequency is n1\u2022 When the machine is speeded up to double the driving frequency, the amplitude is reduced to 20% of its previous value. What is the resonant frequency of the system? Was the test data obtained above or below the resonant frequency? 6.68. The supporting hinge H of a simple pendulum of mass m and length e is attached to a horizontal slider that has a constant acceleration a. The pendulum is released from rest in a horizontal position relative to the slider, as shown in the figure",
            "3ge) , (11.39j) is an equation that determines R(t). In particular, for \u00a2 =w, a constant, (l1.39j) gives R = 2mawO cos e,which is the same nonconservative, rheonomic constraint force obtained in (11.39g) . The original Lagrange method eliminates the need to determine the inconsequential working rheonomic constraint force, which may be found by other methods, if needed. D Exercise 11.7. Apply Lagrange's equations (11.38) to derive the equation of motion for the forced vibration of the system shown in Fig. 6.20, page 152, for a linear viscous damper and a linear elastic spring. D 11.9. Lagrange's Equations for a System of Particles Lagrange's equations for a single particle are equivalent to the Newton-Euler equations of motion ; they contain no new principles. Unlike the Newton-Euler approach, however, the Lagrangian method never involves workless forces ofholonomic constraint, the sometimes laborious calculation of accelerations is avoided, and for conservative systems the equations of motion are readily derived from a single scalar Lagrangian function "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002051_tmag.2015.2436913-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002051_tmag.2015.2436913-Figure6-1.png",
        "caption": "Fig. 6. Coil systems composing the MNS [9].",
        "texts": [
            " The NdFeB cylindrical magnet with a magnetization of 955 kA/m has a 5 mm length and 5 mm diameter, and the magnet is magnetized along the diametric direction. The spiral microrobot performs drilling and navigating motions by the application of a magnetic field generated from MNS. MNS consists of coil systems, a power supply, biplane cameras, a joystick controller, and monitors, as shown in Fig. 5 [8], [9]. The coil system is composed of an MC, HC, a gradient saddle coil (GSC), and two uniform saddle coils [USC(y) and USC(z)], as shown in Fig. 6. The motion of the spiral microrobot is controlled by the magnetic field in the working space inside of the coil system. The magnetic gradient is generated by MC and GSC, and the rotating uniform magnetic field is generated by HC, USC(y), and USC(z). The major specifications of the MNS are shown in Table I. Table II shows the maximum voltage, current, magnetic flux density, and gradient in the developed MNS. The spiral microrobot can perform linear propulsive motions through a magnetic gradient that is generated from MC and GSC of the MNS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001654_s00170-017-1048-9-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001654_s00170-017-1048-9-Figure13-1.png",
        "caption": "Fig. 13 Interaction of feed rate and finishing allowance on average roughness (a, b) and mean roughness depth (c, d) using ANN and Poisson statistical analyse",
        "texts": [
            " In this study, we used a Spinner U620 CNC machine centre with high rigidity and bearing system, so axial force leads to buckling effect and because of the reaction force from the bearing system the values of cutting forces and roughness increase. Figure 12a\u2013d shows approximately 33 and 20% increase in surface roughness for Ra and Rz respectively when increasing the scallop height [26, 39]. Figures 3 and 5d, e show that the finishing allowance has the lowest impact on the value of surface roughness compared to other parameters that were used in this study. Figure 13 shows that increasing finishing allowance leads to generation of rougher surfaces while our previous research showed that increasing finishing allowance leads to 8\u201330% reduction in the value of cutting forces. This occurrence is associated with the alternation on the place of the cutting edge. According to Figs. 7b\u2013d and 10a\u2013d, the location of the cutting edge is moved from point 1 toward point 2 due to an increase in the value of finishing allowance. To that end, the lag angle decreases and based on Eqs",
            " Kte \u00bc \u2212 FxeSef \u00fe FyeTef Sef 2 \u00fe Tef 2 ; Ktc \u00bc 4 FxcPef \u00fe FycQef Pef 2 \u00feQef 2 \u00f018\u00de Kre \u00bc KteSef \u00fe Fxe Tef ; Krc \u00bc KtcPef\u22124Fxc Qef \u00f019\u00de Kae \u00bc \u2212 2\u03c0 DcN Fze \u03b8ex\u2212\u03b8st ; Kac \u00bc Fzc Tef \u00f020\u00de where F\u0305xc and F\u0305xe are the average cutting and edge forces, and \u03b8st and \u03b8ex are the start and exit angles of the cut. On the other hand, an increase in th radial depth of cut leads to generation of a larger surface crest height according to Eq. 21. This tends to increase the value of the surface roughness for both average roughness and mean roughness depth [54]. h\u2248 D2 c 8R0 ; h \u00bc R\u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4R2 0\u2212D 2 c q 2 \u00f021\u00de Figure 13a\u2013d shows that increasing the value of surface roughness can be associated with the stronger effect of the explained phenomenon versus reduction in cutting forces. The slope of the contour colors is small and shows the variations in finishing allowance which has a small effect on increasing the surface roughness [55]. Figure 14 illustrates that by increasing heat treatment temperature, both surface roughness parameters decreased, which is related to change in the microstructure, strain, stress and hardness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001264_we.1530-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001264_we.1530-Figure2-1.png",
        "caption": "Figure 2. Four-contact-point slewing bearings in WTGs.1",
        "texts": [
            " On the other hand, mechanical adjustment of the rotor blade pitch angle is used to modify the aerodynamic angle of attack, thus allowing a sensitive and stable control of aerodynamic power capture and rotor speed. In this case, the blade is also turned by a bearing, located at the blade root, i.e. in the rotor hub (blade pitch control).1,2 These bearings are illustrated in Figure 1. Although small turning speed and range are required in both cases, it must be ensured that the bearings\u2019 friction moment remains as small as possible, in order to avoid unnecessarily large pitching or yawing forces; for this reason, ball bearings are generally used. Figure 2 shows angular four-contact-point bearings for yaw and pitch control. These bearings (yaw and blade bearings) are subjected to high static loads; moreover, continuous deformation of the bearing support is unavoidable.1 Figure 3 shows the topology of this type of bearing, together with the usual load system acting on it: axial and radial forces, as well as a tilting moment; in the most unfavourable load case, the radial force is perpendicular to the tilting moment. Bearings of WTGs must withstand both static (extreme) and fatigue loads; static loads can easily be estimated at early stages of the design process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002962_rpj-03-2019-0067-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002962_rpj-03-2019-0067-Figure5-1.png",
        "caption": "Figure 5 The meshed model of the single-layer six-pass component",
        "texts": [
            " Then the thermal boundary condition considers the convection and Influence of interlayer dwell time Rong Li and Jun Xiong Rapid Prototyping Journal Volume 25 \u00b7 Number 8 \u00b7 2019 \u00b7 1433\u20131441 radiation heat loss, the effects of which are assumed as (Abid and Siddique, 2005): a \u00bc \u00ab ems bol\u00f0T4 Tamb 4\u00de \u00f0T Tamb\u00de 1acon (4) where a, acon, \u00ab em, sbol are the combined heat transfer coefficient, convection coefficient, emissivity and Stefan\u2013 Boltzmann constant, respectively, T is the temperature variable andTamb is the ambient temperature. Figure 5 shows the meshed model of the single-layer six-pass component used to confirm residual stress distributions in deposition layers as discussed in the experimental section. The model consists of 30,108 elements and 34,580 nodes in total. Six passes are deposited in the clockwise direction from the inside to the outside. 4. Results and discussion 4.1Model verification The accuracy of the finite element model must be checked before analyzing its calculated results, such as the temperature gradient, thermal stress and residual stress"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001296_tie.2014.2314053-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001296_tie.2014.2314053-Figure4-1.png",
        "caption": "Fig. 4. Cross section of the proposed induction motor.",
        "texts": [
            " The circuit and FEM simulator employed in this paper are Portunus and EasiMotor, respectively. The simulation model of a squirrel-cage induction motor is carried out with a strong coupling scheme in which the circuit and FE equations are solved simultaneously to validate the proposed coupling method. The electric machine employed in the system is a three-phase 36-stator-slot 33-rotor-slot Y-connected induction motor, whose main parameters are given in Table I. The cross section of the machine is shown in Fig. 4. The power supply is a sinusoidal voltage with 220 V rms and 50 Hz. The rating power of the proposed machine is 110 W at the speed of 958 r/min. In this example, the start-up process of the machine is comprehensively investigated by the strong coupling simulation and the proposed coupling method. The reference speed in the system is set as 1000 r/min with no-load condition, while the initial rotor state of the machine is standstill. The bar current response of the proposed machine during the start-up process from the strong coupling and the proposed coupling simulations are estimated and compared in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure12-1.png",
        "caption": "Figure 12. Temperature map distribution for a piston with two insert voids.",
        "texts": [
            " Internal Void above the Pin Bore As a first approximation to the analysis of a piston with an insert of a lattice structure it has been considered the too aggressive assumption of introducing two voids on the studied region has been studied. Under that assumption piston weight was reduced 12% For these studies the same two cases as explained before have been analyzed. In order to perform a conjugated heat transfer analysis of revised piston design, the same heat transfer coefficients in the previous section has been used. Using those boundary conditions, the temperature map presented on Figure 12 has been obtained and later used for piston finite element stress analysis. External temperature (top). Internal temperature (bottom). Equivalent von-Misses stress has been analyzed in detail at the same three numbered piston regions that were presented before. As it is observed from Table 7 and Figure 13, assuming two voids inserted on piston model have little effect on the crown peak stress or fatigue safety factor. However they have been detrimental at the undercrown and pin bore. Including a cooling effect from the oil gallery is unlikely to improve this, as this would only increase the fatigue life adjacent to the crown and ring grooves"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002003_tfuzz.2018.2883369-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002003_tfuzz.2018.2883369-Figure5-1.png",
        "caption": "Fig. 5. A two DOF helicopter (CE150). .",
        "texts": [
            " Design parameters are set to: The initial conditions are fixed as: . The additive disturbances are taken as square signals with an amplitude of and a frequency of 1/ . Simulation results of this example are displayed in Fig.4. Despite the presence of disturbances and uncertainties, it is clear from this figure, that this MIMO system successfully follows the desired trajectories. The corresponding control signals are admissible and bounded. Example 3: Consider a 2 DOF helicopter (CE150), as shown in Fig.5, [29,30]: with , , , and where and This helicopter model can be rewritten in the following form: with 1063-6706 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. and . The desired trajectories are taken as and . For our proposed controller (19), two fuzzy systems, namely and , have been constructed, where and . One defines for each input variable, as in [28], three membership functions (one triangular and two trapezoidal) being uniformly distributed on the following selected intervals: [-2,2] for ; [-2,2] for and [-10,10] for "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.26-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.26-1.png",
        "caption": "Fig. 17.26 Cognate four-bars generating a symmetrical coupler curve",
        "texts": [
            "101) Each equation expresses the cosine law for one of the triangles of Fig. 17.13 . The elimination of sin\u03b1 is possible without imposing the constraint equation cos2 \u03b1 + sin2 \u03b1 = 1 . Simple linear combination of the equations results in (17.100). Only those real solutions of this equation are admissible solutions for which Eqs.(17.101) yield | sin\u03b1| \u2264 1 . Symmetrical coupler curves of a different nature are generated if the fourbar and the coupler triangle satisfy the symmetry conditions r1 = r2 = r and b1 = b2 = b , respectively. Fig. 17.26 shows the system in its symmetrical trapezoidal position. The coupler curve of point C is symmetrical with respect to the midnormal of the base A0B0 . The figure shows also one of the cognate four-bars which, according to the Roberts-Tschebychev theorem, generate the same coupler curve. The third four-bar is the reflection of the second in the midnormal of the base A0B0 . The parameters of the second four-bar are denoted r\u20321 , a \u2032 , r\u20322 , b \u2032 1 , b \u2032 2 . They satisfy the condition r\u20322 = b\u20322 = a\u2032 ",
            " From the identity \u03b16 = \u03b17 = \u03c0/2 it follows that also the length \u03b12 of the coupler equals \u03c0/2 . Thus, the coupler triangle is isosceles with two right angles. The case \u03b11 = \u03b15 = \u03b17 = \u03c0/2 differs from the case \u03b13 = \u03b16 = \u03b17 = \u03c0/2 only in that input link and output link change their roles. From the planar four-bar it is known that coupler curves are symmetrical with respect to the midnormal of the base if the four-bar and the coupler triangle satisfy the symmetry conditions r1 = r2 and b1 = b2 , respectively (see Fig. 17.26). The equivalent statement for the spherical four-bar is the following. If the four-bar and the coupler triangle satisfy the symmetry conditions \u03b13 = \u03b11 and \u03b16 = \u03b15 , respectively, the coupler curve is symmetrical with respect to the plane spanned by the y-axis and the bisector of the angle \u03b14 . With C3 = C1 , S3 = S1 , C6 = C5 , S6 = S5 Eq.(18.26) takes, after simple re-arrangements of terms, the form 2[C2 1 \u2212 C2 5z 2p2 \u2212 C1C5(z + p)(1\u2212 zp)] + (C2 5 \u2212 C2 1 )(z 2 + p2) \u2212 2[C2 1 + C2 5zp\u2212 C1C5(z + p)][S4S7y + C7(C4 \u2212 zp)] = S2 5 [S4C7y \u2212 S7(C4 \u2212 zp)]2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001519_s11249-013-0122-1-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001519_s11249-013-0122-1-Figure1-1.png",
        "caption": "Fig. 1 Tribogyr specimen (left) and contact geometry with the a and j angles (right) (Color figure online)",
        "texts": [
            " It was designed to fulfil the requirements for studying the flange roller-end lubricated contacts in rolling bearings under controlled operating conditions in terms of kinematics, contact geometry, normal load, lubricant temperature at the inlet, etc. For more details concerning the Tribogyr test-rig capacity, the interested reader is referred to [1]. The contact implies a disc made of steel or glass and a spherical-end specimen made of steel of radius of curvature R2 = 80 mm. The material properties of steel and glass are reported in Table 1. 2.1 Kinematics The lower assembly supporting the spherical-end specimen may be tilted (i.e. inclined) according to two different directions (see Fig. 1): \u2013 a rotation of angle k along the x! axis within a range of [-10 , ?10 ], \u2013 and a rotation of angle j within a range of [-3 , ?3 ] along the yk ! axis, the later being obtained after the rotation of the y! axis of the k value. The test-rig design allows the centre of rotation for imposing k and j to be located at the contact centre. Once these angles are set to the desired values, the upper assembly (i.e. the disc) may be translated along the y! direction to adjust the disc track radius (RD) value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000799_j.automatica.2011.05.016-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000799_j.automatica.2011.05.016-Figure1-1.png",
        "caption": "Fig. 1. Determination of periodic and decaying oscillations.",
        "texts": [
            " Example. Analysis of the system with the linear plant Wl(s) = 1/(s2 + s + 1) and the twisting controller with c1 = 50, c2 = 5 shows the convergence time of T \u2217 \u2248 4.85 that is close to the theoretical convergence time. Now we consider the frequency-domain interpretation of the problem of the existence of periodic motions, of asymptotic and finite-time convergence. Periodic motions can exist in the system if the Nyquist plot of the plant W (j\u03c9) intersects the negative reciprocal of the DF \u2212N\u22121(a) (Fig. 1). In Fig. 1, two Nyquist plots corresponding to the second-W1(j\u03c9) and third-orderW2(j\u03c9) plants and two negative reciprocal DFs corresponding to the relay control \u2212N\u22121 1 (a) and to the twisting algorithm \u2212N\u22121 2 (a) are depicted. The intersection of W2(j\u03c9) with either of the DFs provides a periodic solution of finite frequency and amplitude. Plot W1(j\u03c9) has no points of intersection with either \u2212N\u22121 1 (a) or \u2212N\u22121 2 (a) except the origin. However, the character of the process in the system is different depending on whether the control is an ideal relay (plot \u2212N\u22121 1 (a)) or the SOSM control (plot \u2212N\u22121 2 (a))",
            " In the second case, a periodic motion cannot occur at any frequency (including \u2126 = \u221e). There is a condition that we shall term as the phase deficit. Quantitatively, let us refer to the phase deficit as to the minimum phase value that needs to be added (with the negative sign) to the phase characteristic of the plant to make the phase balance condition hold at some frequency (including the case of \u2126 = \u221e). Note we do not consider now the case of possibly non-monotone frequency characteristics. The phase deficit is depicted in Fig. 1 as \u03d5d. Therefore, \u03d5l(\u2126) \u2212 \u03d5d + argN(a) = \u2212\u03c0 , assuming that \u03d5d \u2265 0 and argN(a) \u2265 0 for SOSM. Now consider controllers which include a nonlinearity with infinite slope in zero. For this type of nonlinearity, the DF N(a) \u2192 \u221e if a \u2192 0 and, therefore, \u2212N\u22121(a) \u2192 0 if a \u2192 0. Assuming that \u2212N\u22121(a) is a straight line in the complex plane (other types of \u2212N\u22121(a) will be considered below) we formulate the following theorem. Theorem 2. For the second-order plant given by (1) and the controller having the describing function N(a) that satisfies the condition: ImN(a)/ReN(a) = const"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000007_978-1-4613-2811-7_7-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000007_978-1-4613-2811-7_7-Figure7-1.png",
        "caption": "Figure 7. Roughing cuts in -Z Setup of MBB test piece.",
        "texts": [],
        "surrounding_texts": [
            "adding pointers so that future analysis will be based on up-to-date details of the workpiece. Derivation of Setups-The method adopted here works from a list of setups to be tried. Initially thls list contains all six of the setups assumed possible. These are with the 1001 axis aligned to the positive or negative X, Y, or Z axes of the PADL-I system. Each setup on the list is examined to find the volume of material which can be removed. This is done by analysing the smallest tool pos sible passing along each face in each cel\\. Each tao I is selected from a tool file which holds available tool diameters and their maximum cutting length. Once all the setups have been considered, the one in which the most stock can be machined away becomes the confirmed setup and is removed from the list. The cell representation is then updated to reflect the removal of material during the setup. This is repeated until all the stock material has been removed or no more setups remain on the list. This is shown in Figure 5. References pp. 153-154 Derivation of Roughing Cuts-A simple strategy consisting of a number of parallel paths running along the length or width of the workpiece has been im plemented. The user must choose to which axis the paths are to be parallel. He must also specify a single tool size since the algorithm has not been imple mented for multiple tools. Only those cells accessible by the tool are selected and as the cutter paths within a cell are derived they are concatenated to any previous path if no colli sion is detected. If a collision is detected, then paths are generated to lift the tool to a safe plane above the workpiece, to rapidly traverse to the next position directly above where material removal may continue, and then lower the tool into the workpiece. If a cell is marked as having had all material removed in a previous setup, the feed rate is changed to rapid within that cell (see Figures 6 and 7). Derivation of Finishing Cuts-The spatially ordered cells are scanned until a face is found that requires machining, then the continuation of the face in the neighbouring cell is found, in the direction that would cause climb milling.* The next linked face or boundary is found, and so on, until either the starting point is revisited or the workpiece boundary is encountered. At this stage, gen eration of the finishing path may proceed in the opposite direction, causing con ventional milling. All faces are flagged once they have been machined, to prevent repeated machining later (see Figure 8)."
        ]
    },
    {
        "image_filename": "designv10_12_0001144_20110828-6-it-1002.03266-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001144_20110828-6-it-1002.03266-Figure5-1.png",
        "caption": "Fig. 5. Schematic of sOAT equipped VTOL aerial vehicle.",
        "texts": [
            " Therefore, the fans tilting for full and proper pitch control of the UAV will be in an oblique direction. Hence the name of this control method in either of its two executions is single-axis or dual-axis OAT. Single-Axis Oblique Active Tilting (sOAT): In the simplest method, called single-axis OAT or sOAT, the fans or propellers tilt about a fixed and oblique horizontal axis, and the corresponding tilt path lies along a vertical plane oriented at a fixed angle \u03b1 from the longitudinal direction Fig. 5. The tilt angle \u03b2 is measured along the tilt-path plane, and is zero when the propeller spin axis is vertical. sOAT provides full, helicopter-like pitch control of the vehicle. Moreover, it also improves stability and control in yaw and roll either by reducing their high degree of coupling intuitively associated with dual-fan rotorcrafts or by taking advantage of that coupling. This distinct superiority, together with its simplicity, makes sOAT an exceptional choice of control method for small UAVs",
            " In this section, the translational and the rotational dynamic equations of the tilt-rotor aerial vehicle are presented. In this modeling, a general form of this vehicle is considered with dOAT ability, in which each of its ducts can have different lateral and longitudinal angles and different propeller speeds that have not been considered in previous works, see Kendoul et al. (2006) and Gress (2007). The equations of motion for a rigid body subject to body force Ftot \u2208 R3 and torque \u03c4 \u2208 R3 applied at the center of mass are given by Newton-Euler equations with respect to the body coordinate frame (B) (see Fig. 5) and can be written as { mv\u0307B + \u03c9 \u00d7mvB = Ftot I\u03c9\u0307 + \u03c9 \u00d7 I\u03c9 = \u03c4 where vB \u2208 R3 is the body velocity vector, \u03c9 \u2208 R3 is the body angular velocity vector, m \u2208 R specifies the mass, and I \u2208 R3 is an inertia matrix. In this subsection the Cartesian equations of motion for the VTOLs vehicle having lateral and longitudinal tiltrotors are defined. Aerodynamic forces and moments are derived using a combination of momentum and blade element theory Leishman (2006). The VTOL has two motors with propellers. The direction of the thrust can be redirected by tilting the propellers laterally and longitudinally"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003277_tmag.2020.3020589-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003277_tmag.2020.3020589-Figure1-1.png",
        "caption": "Fig. 1. (a) Dual-rotors and segmented-stator AFPMM. (b) Segmented-stator module structure.",
        "texts": [
            " Index Terms\u2014 Axial flux permanent magnet motor (AFPMM), equivalent model, Halbach, motor optimization. I. INTRODUCTION THE axial flux permanent magnet motor (AFPMM) has high efficiency, compact structure, and high-torque density [1], [2], so it has received more and more attention in the field of electric vehicles and propulsion motors [3], [4]. With the development of the stator materials such as soft magnetic composite (SMC) materials [5], [6], the topology of AFPMMs with dual-rotor and segmented-stator has emerged in recent years, as shown in Fig. 1(a). The dual rotors are located on both sides of the motor and the segmented-stator modules are located in the middle of the motor. In each stator module, a coil is wound around a stator core, as shown in Fig. 1(b). The stator core is made of SMC materials, which not only reduces the manufacturing difficulty but also improves the performance of the motor [7]. The AFPMM of this structure has no stator yoke, which reduces the weight of the stator core and avoids iron loss in the stator yoke [8]. In addition, this article also uses permanent magnets (PMs) of the Halbach array in the rotor to further improve the air gap flux density distribution [9], [10]. In the optimization program of the AFPMMs, it is crucial to quickly and accurately calculate the motor performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure10.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure10.2-1.png",
        "caption": "Fig. 10.2 A ball impacting on a stationary bat, at distance b from the bat CM, will cause the bat to rotate. The speed and acceleration of the impact point is greater than that for an impact at the CM, so the effective mass at the impact point is less than the mass of the whole bat",
        "texts": [
            " (g) Light Balls Suppose that the ball mass is reduced to such an extent that m=M is almost zero. Suppose also that e D 1 so that the ball bounces as fast as possible. Then q D 1 10.4 Effective Mass of a Bat 163 and the batted ball speed in the previous example increases to 70 2 C 80 1 D 220 mph. That is why baseballs and softballs are relatively heavy and why the COR is relatively low. We mentioned earlier that only part of the total mass of a bat was involved in a collision with the ball. To find an appropriate value for the \u201ceffective\u201d mass of the bat, consider the situation shown in Fig. 10.2. A ball of mass m collides with a bat at a distance b from the bat center of mass (CM). Let the mass of the whole bat be M and suppose that the bat is initially at rest and freely supported. That is, no-one is holding onto the handle, although the bat could be suspended using a long length of string. In that case, the ball will bounce off the bat and the bat will be set in motion. The bat CM recoils at speed VCM and the impact point on the bat recoils at speed V . Because the bat rotates when it is struck by the ball, V will be greater than VCM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002879_tie.2019.2952801-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002879_tie.2019.2952801-Figure9-1.png",
        "caption": "Fig. 9. Field distributions of conventional and H2, H5, H10 current profiles under the rated condition. (Irms=4A, rotor position is 90 elec. deg.). (a) Conventional. (b) H2. (c) H5. (d) H10.",
        "texts": [
            " However, from H2 onwards, the average torque is not increasing but decreasing with the highest harmonic order. The output torque of H5~H10 is even smaller than the conventional one. This can be explained by the saturation effect on the inductance distributions. As can be seen in Fig. 7, the peak value of the proposed current profiles is increasing with the highest harmonic order and significantly larger than the conventional square waveform, which will lead to severe saturation in cores and eventually reduce the magnitude of the 1st inductance component L1. For validation, Fig. 9 compares the field distributions of SRM cores when the conventional, H2, H5 and H10 current profiles are applied. The rotor position is selected as 90 elec. deg., where all the currents reach their peak values. It can be clearly observed that the larger the highest harmonic number is, the more saturation the stator teeth and yoke have. By using the frozen permeability method [27], the inductance under the nonlinear condition is calculated, as shown in Fig. 10. Due to the saturation effect, the inductance distributions are distorted, which eventually leads to a significant drop in the 1st inductance component"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002664_j.mechmachtheory.2019.103608-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002664_j.mechmachtheory.2019.103608-Figure11-1.png",
        "caption": "Fig. 11. Planar five-bar mechanism.",
        "texts": [
            " Numerical cases In this section, we provide four cases to verify the proposed method. The first one is used to demonstrate the correctness and efficiency of the closed-form error propagation formulas on independent and non-independent motion groups. Then, the following three cases separately cover three different parallel manipulators to reveal the generality of the proposed method. All numerical cases were run in Matlab 2016a on a PC with 3.30 GHz CPU and 4G RAM. Case 1. A planar five-bar mechanism As shown in Fig. 11 , the simplest parallel mechanism\u2014a planar five-bar mechanism was chosen as a numerical example to verify the error propagation formulas. The driving actuators are mounted on joints A and B that are connected to the base. First of all, two reference frames, o b - x b y b and o p - x p y p , are created. To be specific, o b - x b y b is the global frame fixed on the base while o p - x p y p is the mobile one attached on the end of link 4 with x axis along it. The length of each link is set to 0.05 m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003210_tie.2020.2988219-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003210_tie.2020.2988219-Figure4-1.png",
        "caption": "Fig. 4. Communication and information flow diagram of our quadrotor.",
        "texts": [
            "Drone quadcopter, the system also suffers from uncertain dynamic models in addition to the presence of other uncertainties, such as cross-coupling among loops (e.g. lateral and longitudinal loops with respect to the vertical loop). FIS\u2019s capability to deal with uncertainties simplifies the tuning process of complex control systems with multiple parameters as well as improve the system robustness. Hence combining the advantages of both worlds will provide a reasonably good solution for challenging applications, thanks to its high accuracy in trajectory tracking performance for aerial robots. For our experiments, we employ an AR.Drone quadcopter as in Fig. 4. The aircraft is a low-cost platform that is readily available to be used worldwide. The system has a foam hull which protects the blades and makes it easier to do experiments. However, it is very susceptible to wind gusts and has sensors of low quality only. Most researches on aerial robotics still focus on the use of traditional mathematical-based approaches (e.g. Adaptive Feed-forward Cancellation (AFC) [24] and Lyapunov designs [25]). To date, SNI autopilot systems have not been thoroughly investigated in the literature",
            " The real-time flight data, including the position, the velocity, the acceleration, the Euler angles, and the angular rates, are then directly analyzed and stored using the Vicon Motion Tracker (VMT) software. We use the AR. Drone autonomy package available for the Robot Operating System (ROS) to control the AR. Drone quadcopter. The package enables the drone to be controlled using the pitch rate, the roll rate, the yaw rate and the thrust commands from the Ground Station (GS) which communicates to the drone over a WiFi channel at the frequency of 200 Hz (see Fig. 4). To validate the feasibility and to perform the stability analysis of the proposed control strategy, we first derived the transfer functions of the vertical, the horizontal and the yaw loops using collected flight test data. To do so, PID controllers were applied with properly tuned values to stabilize the inner loop speed control loops. During flight tests, to capture the overall dynamic behavior of the drone, a sinusoidal wave, in which the frequency varies from 0 Hz to 20 Hz and the maximum amplitude is at 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000448_j.jsv.2008.09.050-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000448_j.jsv.2008.09.050-Figure8-1.png",
        "caption": "Fig. 8. A schematic of the simple model for the equation of motion of an eccentric gear pair.",
        "texts": [
            " (20) As linear tangential velocity is equal to the angular velocity multiplied by the distance to the centre of rotation, v \u00bc r_y we may obtain _u1 \u00bc _y1reff1 cos\u00f0p\u00fe z1 g\u00fe x\u00de, (21) _u2 \u00bc _y2reff2 cos\u00f0p\u00fe z2 g\u00fe x\u00de, (22) where u1 is the motion of the driving gear along the line of action and u2 is the motion of the driven gear along the line of action. By substituting in the simplified variables derived previously, Eqs. (21) and (22) can be ARTICLE IN PRESS J.R. Ottewill et al. / Journal of Sound and Vibration 321 (2009) 913\u2013935 923 simplified to become _u1 \u00bc _y1rb 1\u00fe E1 R cos\u00f0y1\u00de , (23) _u2 \u00bc _y2rb 1 E2 R cos\u00f0y2\u00de . (24) Fig. 8 shows a schematic of a driven gear. u1 is the linear displacement of the drive gear along the line of action and is a function of the displacement input to the drive shaft and the distance from the gear centre to the pitch point (see Eq. (23)). b is the size of the half backlash and k is a lumped stiffness. u2 is the linear displacement of the driven gear along the line of action and is a function of the angular position of the driven gear and the distance from the gear centre to the pitch point (see Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002847_s00170-019-04096-0-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002847_s00170-019-04096-0-Figure11-1.png",
        "caption": "Fig. 11 Arrangement of test specimens on the base plate in SLM experiment. a Schematic drawings, and b the actual specimens obtained",
        "texts": [
            " The SLM experiment was used to make the workpieces of the same size and geometry used in simulation, and it was based on a selective laser melting system (model SLM 280) from SLM Solutions. The machine has a build envelope of 280 \u00d7 280 \u00d7 365 mm, and is equipped with a 400-W fiber laser system. In addition, to mimic the simulation conditions, no support structure was used and the workpieces were directly used with the baseplate. In the end, the test workpieces in the size of\u04245 \u00d7 2 mm were obtained in the same batch, based on the schematic arrangement in Fig. 11a. The workpieces attached to the baseplate are shown in Fig. 11b. The measuring positions are labeled as \u201c1\u201d in the samples. Note that residual stress computation in simulation does not involve the removal of parts from the base plate, in that doing so could lead to significant amount of stress relief in the parts. This practice was carefully followed in the experiment to ensure the results on residual stress are comparable. Therefore, after the SLM process, the samples were kept on the base plate without any wire EDM sectioning or post treatment. The residual stress measurement was directly carried out on the samples attached to the base plate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002415_access.2016.2569537-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002415_access.2016.2569537-Figure5-1.png",
        "caption": "FIGURE 5. Configuration of shaft model for 2,200 TEU container.",
        "texts": [
            " ILLUSTRATION OF SHAFT ALIGNMENT PROBLEM This section illustrates the use of the IHTGA to solve shaft alignment problems in 2200 TEU container series vessels, which are real-world practical design cases in the CSBC (http://www.csbcnet.com.tw/csbc/EN/index.asp). The problem was considered in Hno. \u00d762 (delivered at Keelung shipyard, Taiwan in 2001) and Hno. \u00d796 (to be delivered at Kaohsiung shipyard, Taiwan at the end of 2003). Although Hnos. \u00d762 and \u00d796 had different designers, shaft alignment is performed by the classical local search methods with some trial-and-error procedures in both vessels. Figure 5 shows the layouts of their shaft systems. The shaft alignment problem is to optimize the vertical offsets of bearings to minimize normal stresses and shear forces on the shaft under normal conditions and under the constraints of cold and hot conditions. The system is considered a static system because the maximum rotary speed of the shaft is quite low (approximately 91 rpm). Figure 6 shows that the design variables considered in this system are the intermediate shaft bearing vertical offset (X1 and X2) and the main engine bearing vertical offset (X3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001230_tmag.2011.2120599-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001230_tmag.2011.2120599-Figure2-1.png",
        "caption": "Fig. 2. Geometry of teeth.",
        "texts": [
            "2120599 This research developed finite element models of two BLDC motors of computer hard disk drives, one with eight poles and twelve slots (8P12S) and another with twelve poles and nine slots (12P9S). Table II shows the specifications of these motors. The developed finite element models have 9,948 and 10,098 triangular elements with three nodes, and the cogging torque is calculated at every degree for 360 degrees by using the Maxwell stress tensor. In this research, teeth are modeled by gradually reducing the radius of curvature of the teeth and using the smaller radius of tooth curvature, , instead of the outer radius of a stator, R. Fig. 2 shows the geometry of the teeth curvature. Table III shows the three models with their respective radii of 0018-9464/$26.00 \u00a9 2011 IEEE Since there are many different cases of uneven PM magnetization, a reasonable numerical model which represents all cases of uneven magnetization is required to generalize the effect of the interaction between a PM and teeth curvature. Akihiro et al. showed that the overall uneven magnetization pattern of a model can be presented by investigating one of the partial periodic models [5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002281_0278364918765620-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002281_0278364918765620-Figure4-1.png",
        "caption": "Fig. 4. 3D SEA walker.",
        "texts": [
            " Phase durations are defined implicitly by characteristic state- and control-dependent switching events. Furthermore, we explicitly allow for discontinuities in the state functions to model the impact of foot touchdown. \u2022 Third, a twice continuously differentiable objective function. As stated, in the context of inverse optimal control, we formulate the objective as a linear combination of different criteria. Note that the criteria themselves can be highly nonlinear. We consider the three-dimensional dynamic template model (3D SEA walker, Figure 4), which we first introduced in Clever and Mombaur (2014), and slightly tailor it to the arising needs. It consists of an upper body (torso) and two legs, which are attached to the center of mass of the torso. Both legs have a compliant knee, modeled by a damped SEA, and a point foot with appropriate mass. Denoting the absolute positions of the center of mass of the torso and the feet by qM :=   xM yM zM   , qm1 :=   xm1 ym1 zm1   , qm2 :=   xm2 ym2 zm2   and defining the torso mass M , the foot masses m1 and m2, the leg length of the ith leg li, and the inertia tensor of the torso 2, the dynamics of the motion are defined by M q\u0308M = F1 l1 ( qM \u2212 qm1) + F2 l2 ( qM \u2212 qm2) \u2212Mg (8) m1q\u0308m1 = RHSm1, m2q\u0308m2 = RHSm2 (9) 2\u03b1\u0308 = u\u03c41 + u\u03c42 (10) We set \u03b1 := ( \u03b1x \u03b1y ) , u\u03c41 := ( ux1 uy1 ) , u\u03c42 := ( ux2 uy2 ) , g :=   0 0 g   with gravitational acceleration g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003249_s00170-020-05509-1-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003249_s00170-020-05509-1-Figure2-1.png",
        "caption": "Fig. 2 Schematic illustration of the wear test",
        "texts": [
            " The microstructure was studied using a scanning electron microscope Zeiss EVO MA 15 equipped with two different detectors: a backscattering electron detector to determine the phase composition and a secondary electron detector to analyze the surface microrelief. In addition, to assess the coating composition, an energy-dispersive X-ray spectrometer Oxford Instruments XMax 80 mm2 was used. The microhardness was measured using a microhardness tester Wilson Hardness Group Tukon1102 by Vickers tester at a load of 300 g. Wear behavior of the composites that was evaluated using a testing is carried out by loading a sample pin against abrasive-coated paper supported on a solid backing (Fig. 2). The use of a spiral track on the abrasive paper achieves a steady process of wear by ensuring abrasion against fresh particles. The samples were created in the shape of a cylinder with a length of 10 mm and a diameter of 2 mm. Working surface\u2019s size is 2 \u00d7 2 mm, and its roughness before the test should not be higher than Ra = 2,5. The tests were carried out under applied loads of 10 N, rotated at 60 rpm, and 60-min application time in air. The weight loss of the specimens during the test was measured with an accuracy of \u00b10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003776_j.rcim.2021.102193-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003776_j.rcim.2021.102193-Figure5-1.png",
        "caption": "Fig. 5. Illustration of the constructed spline of the remaining linear segment for (a) position path and (b) orientation path.",
        "texts": [
            " [23], by converting the remaining linear segments to the cubic B-splines, the whole tool orientation path and tool position path are guaranteed to be C1 continuous. In this paper, to achieve jerk continuity, the whole path is constructed to be C3 continuous by converting the remaining linear segments to the specially constructed quintic B-splines. Besides, to improve the performance of the angular kinematics on the remaining linear segments during the parameter synchronization, the transition lengths of the inserted splines are adapted, which will be discussed in this section. Without loss of generality, two adjacent corner segments as shown in Fig. 5 are adopted to illustrate the synchronization process. In Fig. 5(a), Pi(u), Pi+1(u) are the inserted position splines for the corner i and i+1 using the method in Section 2.2, and Pli(u) is the constructed B-spline for the remaining linear segment which is expressed as Pli(u) = \u22117 i=0 N\u0303i,5(u)Vi 0 \u2264 u \u2264 1 (14) where Vi is the control point of the constructed linear B-spline, N\u0303i,5(u) is spline basis function defined with the knot vector [0,0,0,0,0,0,0.5,0.5,1,1,1,1,1,1]. This choice of the knot vector ensures the constructed B-spline passing through the first and the last control points",
            " Then, the transition length for the inserted position spline at the i-th corner should satisfy lpe,i \u2264 min {\u2016 pipi+1 \u2016 9 , \u2016 pi+1pi+2 \u2016 9 } (19) Combining Eqs. (7) and (19), the transition length of the inserted position spline that satisfies the constraint for position smoothing error and the C3 continuity condition is finally expressed as lpe,i = min { \u2016 pipi+1\u2016 9 , \u2016 pi+1pi+2\u2016 9 , 4\u03b5\u2217p 3cos(\u03b2i/2) } (20) For the orientation path, the above procedure can be directly applied to make the composed orientation path to be C3 continuous. As shown in Fig. 5(b), the orientation linear spline Oli(u) of the remaining linear segment is constructed as J. Peng et al. Robotics and Computer-Integrated Manufacturing 72 (2021) 102193 Oli(u) = \u22117 i=0 N\u0303i,5(u)Hi 0 \u2264 u \u2264 1 (21) where Hi is the control point and the spline basis function N\u0303i,5(u) is the same as that of the constructed position spline. The control points H0,\u2026, H7 are arranged on the remaining linear segment in the same manner as those for the position path. Denote \u2016 H0H1\u2016= lloa, \u2016 H6H7\u2016= llob. Referring to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002392_0954406215616835-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002392_0954406215616835-Figure9-1.png",
        "caption": "Figure 9. Real tooth contact analysis model.",
        "texts": [
            " xg \u00bc xg0 cos \u2019g yp0 sin\u2019g yg \u00bc xg0 sin \u2019g \u00fe yg0 cos \u2019g zg \u00bc zg0 8>< >: \u00f017\u00de nxg \u00bc nxg0 cos \u2019g nyg0 sin \u2019g nyg \u00bc nxg0 sin \u2019g \u00fe nyg0 cos \u2019g nzg \u00bc nzg0 8>< >: \u00f018\u00de xp \u00bc xp0 cos \u2019p yp0 sin \u2019p yp \u00bc xp0 sin\u2019p \u00fe yp0 cos \u2019p zp \u00bc zp0 8>< >: \u00f019\u00de nxp \u00bc nxp0 cos \u2019p nyp0 sin \u2019p nyp \u00bc nxp0 sin \u2019p \u00fe nyp0 cos \u2019p nzp \u00bc nzp0 8>< >: \u00f020\u00de at UNIV OF VIRGINIA on June 5, 2016pic.sagepub.comDownloaded from P \u00bc P nzp G \u00bc G nzg E \u00bc E nyg \u00bc nzg xg nxg zg 8>>>< >>>: : \u00f021\u00de Tooth contact analysis for real tooth surface Real tooth contact models The method for real tooth contact analysis is shown in Figure 9. The calculation is performed according to the following procedure. Assume that the real tooth surface of the pinion is coated with a layer of coating. The coating surface and the real tooth surface of the gear contact at point D, as shown in Figure 9(a); then, the point D0 is the contact point of point D on real tooth surface of pinion, when the pinion is turned to obtain a certain amount of relative phase angle. In this case, interference of the tooth surfaces occurs for the driving and driven gears. The interference area is AB, as shown in Figure 9(b). na, nb and nd are normal vectors of point A, B and D. Additionally, if there is waviness on the tooth surface, in some cases, the contact line is divided into several portions instead of one contact line. In this case, those partial interference areas caused by the contact of a pair of teeth at a certain instant can be obtained as following. Assume that the minimum value of composite error on one of contact lines is min epg \u2018, j\u00f0 \u00de; and the minimum value of composite error on those instantaneous contact lines is emin",
            " Numerical analysis for real tooth contact To calculate the interference area AB on real tooth surfaces by numerical analysis, it is necessary to calculate the depth in the direction of pinion rotate at the minimum composite error point\u2019s location. eDe\u00f00\u00de \u00bc RDe\u00f00\u00de yg\u00f00\u00de nxg\u00f00\u00de \u00fe xg\u00f00\u00de nyg\u00f00\u00de \u00f022\u00de where xg(0), yg(0) are coordinates of the minimum composite error point in the X and Y directions of the gear, respectively. nxg(0) and nyg(0) are normal vectors of the minimum composite error point in the X and Y directions of the gear, respectively. RDe(0) is the depth of coating, RDe(0)\u00bcDe, as shown in Figure 9(b). The endpoints of interference segment on each contact line can be calculated by equations (23) and (24). The endpoint near the root epg\u00f0\u2018, j \u00f0n\u00de\u00de emin5eDe\u00f0n\u00de epg\u00f0\u2018, j \u00f0n\u00de \u00fe 1\u00de emin 5 eDe\u00f0n\u00de : \u00f023\u00de at UNIV OF VIRGINIA on June 5, 2016pic.sagepub.comDownloaded from The endpoint near the tip epg\u00f0\u2018, j \u00f0n\u00de 1\u00de emin 5 eDe\u00f0n\u00de epg\u00f0\u2018, j \u00f0n\u00de\u00de emin5eDe\u00f0n\u00de \u00f024\u00de where \u2018 is the number of teeth which contact simultaneously. eDe(n) is the maximum interference depth on this contact line. As shown in Figure 11, two interference areas on this contact line is from j1(n) to j3(n) and from j4(n) to j2(n)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001235_tro.2012.2228132-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001235_tro.2012.2228132-Figure5-1.png",
        "caption": "Fig. 5. Sequence of rotations that satisfies the constraint: vT 1 Cu1 = w1 . Let e3 = u1 , e2 = u 1 \u00d7v1",
        "texts": [
            " The constraint is satisfied for arbitrary rotations around the other two axes u1 and v1 . Instead of using rotations around perpendicular axes, in this case, we parameterize the rotation matrix as a product of three consecutive rotations around axes spanning 3-DOF: C = C(v1 , \u03b1)C(e2 , \u03b2)C(u1 , \u03b3) (77) where e2 := u1 \u00d7v1 \u2016u1 \u00d7v1 \u2016 if v1 is not parallel to u1 ; otherwise, e2 is any unit vector perpendicular to u1 . Substituting (77) into (75), we have vT 1 C(e2 , \u03b2)u1 \u2212 w1 = 0. (78) From the geometry6 of Fig. 5, we can find two particular solutions for the rotational angle \u03b2: \u03b2 = \u03b21 \u2212 \u03b22 = arccos(uT 1 v1) \u2212 arccos(w1), or (79) \u03b2 = \u03b21 + \u03b22 = arccos(uT 1 v1) + arccos(w1). (80) However, later on we will prove that choosing any one of the two solutions leads to exactly the same set of eight solutions for the relative rotation matrix. For now, we select the first solution for \u03b2 and continue solving for the other two rotation angles. Next, we will find the rotation angles \u03b1 and \u03b3 from \u2211 vT 2 C(v1 , \u03b1)C(e2 , \u03b2)C(u1 , \u03b3)u2 = w2 (81) \u2211 vT 3 C(v1 , \u03b1)C(e2 , \u03b2)C(u1 , \u03b3)u3 = w3 ",
            " Back-substituting each of the eight solutions for s\u03b1 into (87), we get one solution for c\u03b1, because (87) is linear in c\u03b1 after replacing all even order terms of c\u03b12k by (1 \u2212 s\u03b12)k and c\u03b13 by (1 \u2212 s\u03b12)c\u03b1. Finally, each pair of solutions for c\u03b1 and s\u03b1 corresponds to one solution for c\u03b3 and s\u03b3 using (86). We now prove that the two particular solutions of \u03b2 lead to the same set of eight solutions for the rotation matrix. Let the two particular rotation matrices be C1 = C(e2 , \u03b21 \u2212 \u03b22) and C2 = C(e2 , \u03b21 + \u03b22). From the geometry of Fig. 5, we have C1u1 = C(v1 , 180\u25e6)C2u1 (89) \u21d2 CT 1 C(v1 , 180\u25e6)C2u1 = u1 . (90) Therefore CT 1 C(v1 , 180\u25e6)C2 = C(u1 , \u03b8) (91) where \u03b8, as shown in Appendix A, equals 180\u25e6, i.e., C2 = C(v1 ,\u2212180\u25e6)C1C(u1 , 180\u25e6). (92) Given eight solutions for the rotational matrix C corresponding to the particular solution C1 : C1,i = C(v1 , \u03b1i)C1C(u1 , \u03b3i), i = 1 . . . 8 (93) and another eight solutions corresponding to the particular solution C2 : C2,j = C(v1 , \u03b1j )C2C(u1 , \u03b3j ), j = 1 . . . 8 (94) we assume that at least one of the C2,j s is different from all the C1,is, i",
            " In particular, we will seek to determine the sequence of locations, where the robots should move to so as to collect the most informative measurements, and, thus, achieve the desired level of accuracy in minimum time. SUPPLEMENTAL DERIVATIONS FOR SYSTEMS 8\u201310 In what follows, we show that in equation (91), C(u1 , \u03b8) = C(u1 , 180\u25e6). Using the Rodrigues formula for C(v1 , 180\u25e6), we have C(u1 , \u03b8) = CT 1 C(v1 , 180\u25e6)C2 = C(e2 , \u03b21 \u2212 \u03b22)T (\u2212I + 2v1vT 1 )C(e2 , \u03b21 + \u03b22). Substituting v1 = C(e2 , \u03b21)u1 (see Fig. 5) into the aforementioned equation, we have C(u1 , \u03b8) = \u2212C(e2 , 2\u03b22) + 2C(e2 , \u03b22)u1uT 1 C(e2 , \u03b22) = C(e2 , \u03b22)(\u2212I + 2u1uT 1 )C(e2 , \u03b22) = C(e2 , \u03b22)C(u1 , 180\u25e6)C(e2 , \u03b22) = C(e2 , \u03b22)C(u1 , 180\u25e6)C(e2 , \u03b22)C(u1 ,\u2212180\u25e6) \u00b7 C(u1 , 180\u25e6) (113) = C(e2 , \u03b22)C(C(u1 , 180\u25e6)e2 , \u03b22)C(u1 , 180\u25e6) = C(e2 , \u03b22)C(\u2212e2 , \u03b22)C(u1 , 180\u25e6) = C(u1 , 180\u25e6) (114) where, from (113) to (114), we have used the relation C(u1 , 180\u25e6)C(e2 , \u03b22)C(u1 ,\u2212180\u25e6)=C(C(u1 , 180\u25e6)e2 , \u03b22). Hence, \u03b8=180\u25e6. SUMMARY OF THE 14 SYSTEMS A summary of the problem formulation and solutions are listed in Table III"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000144_ip-b.1987.0046-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000144_ip-b.1987.0046-Figure10-1.png",
        "caption": "Fig. 10 Approximate equivalent circuit and its application a Circuit b Phasor diagram",
        "texts": [
            " This was obtained using a fluxmeter and two of the stator bars as a single-turn search coil. In addition this test revealed that the effective peak flux density provided by the magnet system was 0.4 T which is very close to the design value of 0.39 T indicated by Section 3.2. The circuit of Fig. 9 gives a good representation of the behaviour of the unit but it is advantageous to consider a simplified version in which the transformer magnetising impedance and the motor iron loss are ignored. The simplified circuit and its use is indicated in Fig. 10. Fig. 10b shows the phasor relationship of the three voltages in the (i) heat sink (vii) case (ii) connection area (viii) transformer secondary bar (iii) end ring (ix) case connector (iv) transformer secondary bar (x) motor connection joint (v) primary winding (xi) motor (vi) toroidal core IEE PROCEEDINGS, Vol. 134, Pt. B, No. 6, NOVEMBER 1987 293 circuit of Fig. 10a when divided by the circuit impedance Z. This diagram is appropriate for permanent magnet machines in which \u00a3 is a constant and V may be varied. The voltage E is used as a reference and a circle diameter OM = E/X described as shown so that the phasor E/Z = OS lies at some point on the circle determined by the ratio X/R. The current phasor / = ON, for a given generated mechanical power, must lie on some line such as AB which is parallel to the horizontal axis because the resolved component of / onto the vertical axis (i.e. in the direction of \u2014 E) is proportional to the generated power. The phasor triangle is completed by V/Z which cuts the circle of diameter OM at some point R say. It may be shown by geometry that the direction of V is along OR so that the input power factor angle is Z_NOR. When point N lies on this circle, the input power factor is unity. The design point on Fig. 10b is the point P which has an input current 1.29 A and a torque angle 9 = 60\u00b0. The operating region in Fig. 10b is confined by heating to within a circle of radius 1.29 A passing through P. The boundary PQ coincides with the core flux density being at the maximum permitted value Bs = 0.6 T and is obtained from eqn. 1 with Bb = 0.6 T and RJR0, H/Ro and B set at their design values. As it is known that \\i0JAX oc / , and that Bb = 0.6 T when / , = 1.29 A and 0 = 60\u00b0, an equation relating 77 and 6, when Bb = Bs, can be deduced directly from eqn. 1. Operating points to the left of PQ correspond with the core flux density exceeding Bs. Fig. 10b indicates the locus of / (AB) for 11 W gross output. This gives a useful output of 10 W, because running-light tests on the unit have indicated an internal windage and friction loss of 1 W at 150000 rev/min. A scale of supply voltage is shown on AB. This scale is deduced from the expression (SN/OS x E) as the point N moves along AB. In fact, operation at constant supply voltage implies operation on a circle centred on S. Thus for example with a supply voltage of 7 v, the removal of 10 W load would imply the onset of some saturation",
            " The unit was loaded using a 5 mm diameter brake pulley having a calibrated windage load of 0.7 W at 150000 rev/ min. As with previous high-speed load tests, a nitrogencooled floss-silk braking cord was found to be the most satisfactory method of applying load. The supply voltage was varied over as wide a range as possible and the brake loaded until 9.3 W was being dissipated on the pulley. It was found to be impossible to reduce the supply voltage in these tests below approximately 6 V as might be thought possible by the steady-state diagram of Fig. 10b. This was the result of the onset of dynamic instability with lower values of V/E. A consideration of this problem is presented in Reference 6. Fig. 11 shows the results of these load tests together with corresponding data calculated from the equivalent \u2014\u2022\u2014 input power, W \u2014 # \u2014 efficiency, x 10 \u2014A\u2014 input current, x l O \" 1 A \u2014O\u2014 power factor, x 10 \u2014(-\u2014 case temperature rise on 50% duty cycle, x 10\u00b0C calculated from circuit of Fig. 9 circuit of Fig. 9. In general, when it is considered that the internal windage and friction is not accounted for in the equivalent circuit, agreement is very good"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.7-1.png",
        "caption": "Fig. 12.7 Robot arm with frame 0 , revolute joint 1 , prismatic joint 2 , helical joint 3",
        "texts": [
            "46) where and \u03b1 (both positive or zero or negative) are the length of the common perpendicular and the projected angle between the screw axes. Equations (12.40) and (9.37) defined the dual screws: F+ \u03b5M = F (1 + \u03b5p1)n\u03021 , \u03c9 + \u03b5v = \u03c9(1 + \u03b5p2)n\u03022 , n\u0302i = ni + \u03b5ai \u00d7 ni (12.47) (i = 1, 2) . The scalar product of the dual unit screws is (1+\u03b5p1)(1+\u03b5p2)n\u03021\u00b7n\u03022 = n1\u00b7n2+\u03b5[(a1\u2212a2)\u00b7n1\u00d7n2+(p1+p2)n1\u00b7n2] . (12.48) The reciprocity condition (12.44) is satisfied if the dual part of the scalar product is zero. Example: The robot arm shown in Fig. 12.7 is mounted on a stationary frame 0 . Bodies 0, 1, 2 and 3 are interconnected by a revolute joint 1 , a prismatic joint 2 and a helical joint 3 with given pitch p3 . The joint axes are defined by their unit vectors n1 , n2 , n3 . Joint variables are rotation angles \u03d51 , \u03d53 in joints 1 and 3 , respectively, and translatory displacements s2 and s3 = p3\u03d53 in joints 2 and 3 , respectively. Each of these variables describes the position of the outer body relative to the inner body, and in each joint the positive direction is the direction of the axial unit vector",
            " Body 3 is subject to a force F applied at P and to a torque MP about P . Determine the column matrix [M1 F2 M3] T of axial joint torques and forces to be produced by motors in the joints such that the robot is in equilibrium. Formulate the conditions M1 = 0 , F2 = 0 and M3 = 0 . Solution to Problem 1 : The principle of superposition yields for \u03c93 and vP the expressions \u03c93 = \u03d5\u03071n1+\u03d5\u03073n3 , vP = \u03d5\u03071a1\u00d7n1+s\u03072n2+\u03d5\u03073a3\u00d7n3+p3\u03d5\u03073n3 (12.49) with vectors a1 and a3 pointing from P to arbitrary points of the joint axes 1 and 3 , respectively (see Fig. 12.7). The matrix form of the equations is [ \u03c93 vP ] = [ n1 0 n3 a1 \u00d7 n1 n2 a3 \u00d7 n3 + p3n3 ]\u23a1\u23a3 \u03d5\u03071 s\u03072 \u03d5\u03073 \u23a4 \u23a6 . (12.50) The left-hand side is the velocity screw of body 3 . The right-hand side represents the sum of the velocity screws of the three joints. Column j of the 12.5 Virtual Power of a Force Screw. Reciprocal Screws 371 coefficient matrix (j = 1, 2, 3) is the unit screw of joint j (see (9.33) and (9.34)). Solution to Problem 2 : Equilibrium requires that under virtual velocities the virtual power \u03b4P of all forces and torques acting on the system equals zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003755_wemdcd51469.2021.9425634-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003755_wemdcd51469.2021.9425634-Figure1-1.png",
        "caption": "Fig. 1: IPM and HEPM motor configurations",
        "texts": [
            " INTRODUCTION The continuous effort of the Automotive Companies is to increase the electric motor performance: the maximum power and the maximum torque [1], [6]. This is carried out paying particular attention to optimize the machine geometry, considering both electromagnetic and mechanical performance and thermal capability [4]. This paper deals with the comparison among three configurations of Hybrid Excitation Permanent Magnet (HEPM) motors compared to an Interior Permanent Magnet (IPM) motor, whose geometries are shown in Fig. 1. As described in [3] the hybrid excitation synchronous machines combine a field due to a rotor winding with that of permanent magnets (PMs). Using two excitation field sources the goal is to combine advantages of both PM excited machines and wound field synchronous machines. Rotor field excitation is used to control the excitation flux in the air gap, to improve both overload and flux weakening (FW) capability [5], [8]. The model is sufficiently accurate for a prediction of the motor performance in different working conditions and suitable for the motor design",
            " The magnetic thickness tm and the PM height hm are slightly changed in each configurations. Each analysis focuses on the performance from the rated speed nb (3000 rpm) up to 5 \u00d7 nb (15000 rpm). In this operating range, average torque, losses and efficiency are evaluated for HEPM motors and compared to a IPM Vshape motor with the same geometry. The comparison aims to evaluate which configuration among the three analysed which exhibits higher capability in FW operations, lower losses and lower amount of PM and Copper material. Fig 1 shows the configurations of the HEPM motor under comparison. The acronyms adopted refers to as: P refers to a \u201dparallel\u201d configuration, where the fluxs due to the rotor excitation and the PM follow different paths; RC means \u201dRotor Coils\u201d and it is followed by the corresponding number of excitation coils wound in the rotor. HEPM motor is obtained from an PM motor where two coils replace two PMs. The first configuration is labelled PRC2, and it is shown in Fig 1b, while IPM is shown in Fig 1a. Rotor data are reported in TABLE II. The substitution reduces the apparent inductance Ld, decreasing the saliency ratio \u03be = Lq Ld , since iron path is added to the d-axis. This reduction increases the stator linkage fluxes developed by the excitation rotor currents but decreases the reluctance torque component performed by the machine. However this machine exhibits interesting capability at high speeds. The use of a double arrowhead in the figure means that the flux due to the excitation coils is used both to increase the PM flux and to reduce the PM flux",
            " Restrictions apply. At the beginning of FW operations, the IPM motor efficiency results slightly higher, because there are no joule rotor losses, as illustrated in Fig 7. However, a higher efficiency is observed at higher speeds because the output power of HEPM motor is much higher than that of the IPM motor. Summing up all these aspects the HEPM motor could be a valid alternative to IPM motor, guaranteeing good performance in a wide speed range with a lower overall losses percentage. This motor is shown in Fig.1c and data motor are summarizes in TABLE III. It is different from the previous one since all PMs are supported by the flux of the excitation coils. This machine is referred to as PRC-8 (Eight Parallel Rotor Coil) HEPM motor. Again, the flux of the excitation coils flows through different paths with respect to the flux due to the PMs, that is, on the lateral edges of the PMs. This motor is analysed according to two different excitation modes: TABLE III: PRC-8 rotor geometry PRC-8 PM thickness tm 10 mm PRC-8 PM width hm 20 mm Slot excitation area Sslot,exc 125 mm2 Rotor current density Jexc 10 Amm\u22122 \u2022 The winding excitation is used only to reduce the flux due to the PMs. The motor is drawn on the right part of Fig 1, highlighting the single arrow of the direction of the flux due to the excitation coils. It will be referred to as PRC-8(\u21d3). In this case, the excitation current is higher so that the rotor slots need a higher cross-section area. \u2022 As in the previous HEPM machine, the flux due to the excitation coils is used both to increase the PM flux and to reduce the PM flux. A double arrowhead is used in the central part of Fig 1, and this mode will be referred to as PRC-8(\u21d1\u21d3) The motors analysed have the same geometry reported in TABLE III, but the control of the excitation winding is different. The range of operating speed is kept constant for both the machines. Both the configurations are compared in term of rated torque at rated speed, power and efficiency, as done for the previous configuration. The excitation rotor winding in the PRC-8(\u21d3) HEPM motor analysed is used only to reduce the PM flux in Fig.8aso that it is zero up to 4000 rpm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003365_tmrb.2020.2988462-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003365_tmrb.2020.2988462-Figure1-1.png",
        "caption": "Fig. 1. (A) Schematic drawing showing manipulation coil array and highlighted manipulation area. (B) Schematic of purse string suture pattern. (C) Schematic drawing showing ligation of tubular intestine tissue. (D) Schematic drawing showing tissue penetration.",
        "texts": [
            " achieved penetration through sheep brain by hammering a millibot into the soft brain tissue using an onboard spring and a magnetic ball placed inside a hollow cavity in the robot body [33]. However, the penetration of other types of tissues by magnetically actuated needles is still unsolved. In this paper we demonstrate a system capable of performing the aforementioned tasks in vitro using ex vivo tissues and a sharpened NdFeB suture needle guided by magnetic fields, as conceptually illustrated in Fig. 1. In our MagnetoSuture system magnetic fields and gradients are supplied by an electromagnet array which is controlled using a hand-held remote controller. The contributions of this paper include demonstration of the ability to tetherlessly recreate a purse string suture pattern (Fig. 1B), ligation of an excised segment of rat intestine (Fig. 1C), and penetration of rat intestine via magnetic pulling only (Fig. 1D). To the best of our knowledge, this work presents the first demonstration of tissue penetration using a customized suture needle and thread guided using only magnetic gradient pulling. We also demonstrate the formation of a complex, medically relevant suture pattern performed tetherlessly using a suture needle with thread. Additional contributions include characterization of the force needed to penetrate rat intestine, pig intestine, and synthetic tissue using our custom magnetic needle and a comparison of our custom NdFeB needle with a clinical suture needle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure1-1.png",
        "caption": "Fig. 1. Applied coordinate systems of meshing spur gears.",
        "texts": [
            " In Section 5, the contact and the bending stresses of the gear drive designed are analyzed and compared with the involute gear drive. Finally, a conclusive summary of this study is given in Section 6. 2. Geometrical modeling of tooth profiles based on the line of action First of all, it is necessary to set up appropriate coordination systems and clarify the terminologies used in this paper before discussion of the tooth profiles. Three coordinate systems \u03a31 (O1, x1, y1), \u03a32 (O2, x2, y2) and \u03a30 (O0, x0, y0) are designated as illustrated in Fig. 1. Coordinate system \u03a30 is a fixed coordinate system whose origin O0 coincides with the pitch point P, while coordinate systems \u03a31 and \u03a32 are moving coordinate systems rigidly connected to the center of the driving gear and the driven gear, respectively. The line of action passes through the centrode point O0. To begin the design process, the following basic parametersmust be set: (1) the tooth number of driving gear z1 and of driven gear z2; and (2) the modulem, which describes the tooth size, defined as two times the pitch radius divided by the number of teeth. The gear ratio i describes the speed ratio between the input and output gears. For gears with a constant speed ratio, it can be defined as the ratio of the number of teeth of the input gear to that of the output gear. The equation can be expressed as where i \u00bc z2 z1 \u00bc \u03c61 \u03c62 \u00f01\u00de \u03c61 and \u03c62 represent the rotation angle of the driving gear and the driven gear, respectively, as shown in Fig. 1. where The center distance a is the distance between the center of pitch circle of the driving gear and that of the driven gear. It can be defined as a \u00bc r1 \u00fe r2 \u00bc m z1 \u00fe z2\u00f0 \u00de 2 \u00f02\u00de r1 and r2 denote the radii of the pitch circle of the driving gear and of the driven gear respectively. 2.1. Equation of the tooth profile of the driving gear As mentioned previously, a gear drive transmits a rotating movement through a pair of contacting profiles from one gear to another. The theory of gearing, developed based on differential geometry and the theory of envelopes, presents the existence and conditions of such profiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000041_s0022-0728(81)80191-x-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000041_s0022-0728(81)80191-x-Figure7-1.png",
        "caption": "Fig. 7. Voltammograms of LiTCNQ- in the absence (1) and in the presence (2) of glucose oxidase. Glassy carbon electrode, potential scanning rate 100 mV/min, arrows indicate the scanning direction. Concentrations of LiTCNQ-, glucose oxidase and glucose are 0.4 raM, 61 nM and 3 mM respectively, incubation time with enzyme 30 min, 0.1 M Li-phosphate buffer, pH 7.0, 25\u00b0C. Electrode potential v s . AglAgC1 in saturated LiC1.",
        "texts": [
            " TABLE I Electrochemical parameters of mediators and oxidation constants of reduced glucose oxidase at 25\u00b0C (potential vs. AglAgC1) 2.303RT Electron Vl/2 1 - - 0/1 k o x X 1 0 --4 acceptor (mV) (1 -- a I )n~t\" M-l c-1 (mV) TCNQ 199 -+ 2 63.5 -+ 3 0.93 300 -+ 8 TCNQ- --2 -+ 3 65.9 -+ 2 0.90 6.6 -+ 0.2 NMp+a --114-+2 30 -+1 1.0 9 +0.5 NMA + -- -- -- < 10-4 a At 30\u00b0C [12,13]. Oxidat ion- -reduc t ion o f L i T C N Q - on glassy carbon electrode LiTCNQ- exhibits two pronounced waves of oxidat ion--reduct ion in a Liphosphate buffer (Fig. 7). Linearization of vol tammogram data in the polarization equation coordinates, 2 .303RT [i~ -- I~ U = U , n + ( l _ a l ) n s r l o g [ : ~ ) (1) (where / i is the current plateau, I the current at the applied potential U, U1/2 the half-wave potential , al the coefficient of electron transfer and n the number of electrons), indicates that each wave corresponds to a one-electron transfer (Table 1). In the cathodic region TCNQ- is reduced to TCNQ 2-, whereas in the anodic region it is oxidized to the TCNQ deposited on the electrode. The reduct ion of deposited TCNQ determines the appearance of peaks during the cathodic scanning of the potential (Fig. 7). Oxidat ion o f FADH2 in the active center o f glucose oxidase by TCNQ or T C N Q - In the presence of glucose and enzyme the LiTCNQ- solution is discolored and the wave of TCNQ- reduct ion disappears (Fig. 7). The cyclic voltammogram of LiTCNQ- is shifted towards the anodic current region. It follows from this, that in the presence of glucose oxidase and substrate TCNQ- is reduced to TCNQ 2-. The dependence of the initial rate of TCNQ- reduct ion on its concentrat ion exhibits a plateau. The data linearize in the Linuiver--Berk coordinates, that is, consistent with the action scheme of glucose oxidase [9]: kl k 2 Enzox + S ~ EnzoxS -~ EnZ~ed + P1 (2) k - 1 where Enzox and EnZ~ed are the oxidized and reduced glucose oxidase respectively, EnzoxS the enzyme substrate complex and S is glucose"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003572_10775463211013245-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003572_10775463211013245-Figure2-1.png",
        "caption": "Figure 2. Dynamic model of the gear pair; (a) rigid\u2013flexible gear pair and (b) rigid gear pair.",
        "texts": [
            " The vibration of the hub can be reduced significantly because of the elastic deformation. Metal rubber is a porous material built from metallic wire meshing, which not only has the inherent properties of metals but also has the elasticity like rubber. The metal rubber plays an important role in reducing the rigid impact on the teeth so that the smooth meshing process of the gear can be ensured. Simplified models of the rigid\u2013flexible gear pair and the rigid gear pair are established. The quasi-static models are presented in Figure 2(a) and (b). As shown in Figure 2(a), the ring gear and the hub are connected by the metal rubber. kMR and cMR are, respectively, the stiffness and damping of the metal rubber. The dynamic meshing transmission error of the gear pair is the relative displacement on the meshing line, which can be expressed as Y \u00bc y1 y2 \u00fe \u03b81rbp \u00fe \u03b82rbg e\u00f0t\u00de (1) where y1 and y2 are the vibration displacement of the driving gear and driven gear, respectively; \u03b81 and \u03b82 are the angular vibration displacement of the driving gear and driven gear (or ring gear of the driven gear), respectively; rbp and rbg are, respectively, the radius of the basic circle of the driving gear and driven gear; and e(t) is the static transmission error"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001713_j.procir.2014.03.034-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001713_j.procir.2014.03.034-Figure7-1.png",
        "caption": "Fig. 7: Special gear forms machined with gearMILL software",
        "texts": [
            " Additionally, these forms will continue to evolve and there will be many more forms designed in future. Multi-tasking machines are very flexible. If a parametric model or a CAD model can be defined for the form, the form can be machined using these machines. While it cannot be said with certainty, but Multi-tasking machines offer the best possibility for a customer to be able to make not only today\u2019s gear forms but also the ones that will be designed in the future. As an example, the gears shown in the Fig. 7 are special forms of gears that are equivalent to herringbone gears. These gears offer significantly better capability to absorb shock and offer excellent application for locomotives. The adaptability of these gears can increase (in turn increasing the overall efficiency of transportation) if they can be manufactured efficiently. Multi-tasking machines will reduce one of the hurdles in doing that. If the customer/ designer can define the forms mathematically and has a solid model, these forms can be efficiently manufactured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001909_c7sm01828b-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001909_c7sm01828b-Figure1-1.png",
        "caption": "Fig. 1 (a) Schematic diagrams of the protocol followed to fabricate samples, with (b) corresponding photographs of each step of the experimental process. Samples were fabricated by first, (1) clamping the foundation layer (elastic disk) between two acrylic plates, (2) pressurizing the system to pre-stretch the disk and achieve a nearly hemispherical shape, (3) pouring a liquid polymer onto the foundation layer, which then (4) polymerizes into a thin shell coating. After depressurizing the system, (5) buckling modes are observed on the surface of the bilayer. The scale bar represents 2 cm.",
        "texts": [
            " We observe the process by which these ridges form and quantify parameters such as their width, height, and characteristic speed of propagation. Our analysis suggests that the propagation speed of ridges depends on both the film strain and the stiffness ratio between the film and the foundation. Interestingly, throughout the ridge formation process, their aspect ratio remains constant. Moreover, the propagation of these ridges bears analogies with hierarchical fracture of thin-film coatings. In Fig. 1a, we present a schematic diagram of the experimental protocol followed to create our samples. Photographs of the corresponding experiments are provided in Fig. 1b. First, a thick elastomeric disk is fabricated to be subsequently used as the substrate of the bilayer system. This disk is hydraulically inflated from its initially flat configuration to a nearly hemispherical shape, thereby setting a prescribed pre-stretch.8 A second liquid elastomeric polymer is then poured onto the now bulged substrate, which, upon curing, results in a thin shell that is bound to the bulged pre-stretched substrate.34,35 The system is then slowly deflated and, as the pre-stretch is released, the film buckles to accommodate the excess in surface area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001787_j.proeng.2015.12.511-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001787_j.proeng.2015.12.511-Figure4-1.png",
        "caption": "Fig. 4. Large-sized spiral bevel gear",
        "texts": [
            "0 in this case, different roughing, semi-finishing and finishing milling paths were programmed with the final goal of finding the optimal cutting strategy. Apart from using standard tools, with a greater number of suppliers and consequently a better price, a new technology will be evaluated, the air turbine. The air turbine, due to his constant high speed and torque, will allow to evaluate different finishing tools to obtain a greater tooth surface accuracy. 2. Methodology and experimental procedure The case of study is a large-sized spiral bevel gear (Fig. 4), one of the more complex gear typologies. F1550 was used in test. In Table 1 the design parameters of the large-sized spiral bevel gear are shown. The spiral bevel machining has taken place in two different machines. The first was machined on a universal 5- axis milling machine (Ibarmia ZV25/U600). The second one was machined on a multi-tasking machine (Ibarmia ZVH38/L1600 Multiprocess). On the 5-axis milling machine a special self-centering precision clamping system was a b used, making it particularly suitable for working on 5-axis machining centres"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001692_s1068366615020038-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001692_s1068366615020038-Figure3-1.png",
        "caption": "Fig. 3. Phases of the combined contact of bodies with the ovality.",
        "texts": [
            ",\u0394\u03b1 = \u00b0 \u00b0 2\u0394\u03b1 2n 1B > 2B n= 2n 2,n 2 2 2 1 1 ''1 * , k k m k km k k h k k L H t h H S L \u2212 \u03b1\u2212 \u03b1 \u03b1 \u23a1 \u23a4 \u2212\u23a2 \u23a5= \u2212 \u23a2 \u23a5\u03a3 \u23a2 \u23a5\u23a3 \u23a6 ( )2, ;h hS fp h= \u03b1 \u03b5 1 1'(1 ),h\u03a3 = \u2212 \u2212 2 2'(1 );h\u03a3 = \u2212 ( )0 1 ;km k k k h k kL B S m= \u03c4 \u2212 \u03a3v 1 1;h h\u03b5 = \u03a3 1 2 1' ,h h h= 2 1 2'h h h= ( ) ( ) 21 12 1 10 0 20 1 2 20 0 10 ' , mm mm B h B \u03c4 \u03c4 \u2212 \u03c4 = \u03c4 \u03c4 \u2212 \u03c4 ( ) ( ) 12 21 2 20 0 10 2 1 10 0 20 ' ; mm mm B h B \u03c4 \u03c4 \u2212 \u03c4 = \u03c4 \u03c4 \u2212 \u03c4 ( ) 2 0 2 0k kH \u03b1 = \u03c4 \u03b1 \u2212 \u03c4 ( ) 2 0 2 2 0,k kH n \u03b1 = \u03c4 \u03b1 \u2212 \u03c4 ( ) ( )0 2 2,fp\u03c4 \u03b1 = \u03b1 \u03b4 ( ) ( )0 2 2 2, , , ;n fp h\u03c4 \u03b1 = \u03b1 \u03b4 0, ,k k kB m \u03c4 Time of the interval of the interaction tribocon tact at angular displacement of the shaft is (2) where is the sliding friction path at the shaft revolution by 1\u00b0, is the sliding velocity, and are shaft revolutions per minute. The mixed contact of bodies with the roundness of the shaft profile (Fig. 2) has five phases of the contact interaction: three phases of the single area contact (I, III, V) and two phases of the double area contact (II, IV) (Fig. 3). The phases of the single and double area contacts are not interrelated. For the scheme with the trilobing of the shaft pin (Fig. 4a), there are seven phases of the contact (phases I, III, V, and VII of the single area contact and phases II, IV, and VI of the double area contact) and, for the scheme with the tetralobing of the shaft pin (Fig. 4b), there are nine phases of the contact (phases I, III, V, VII, and IX of the single area con tact and phases II, IV, VI, and VIII of the double area contact)",
            " Correspondingly, initial contact semiangles ( for the single area contact and for the double area contact) at wear are determined according to [8] using the following con dition of the equilibrium of forces acting on the shaft: (3) (4) where (5) where = \u03bb2 = are angles that determine the direction of forces and (6) (7) '' * t 2\u0394\u03b1 ' 2 2 2 '' ,* 6 Lt n \u0394\u03b1 = \u0394\u03b1 = v ' 22 360L R= \u03c0 2 2R= \u03c9v 2 2 30,n\u03c9 = \u03c0 2n 0 2( )\u03b4\u03b1 \u03b1 2( )\u03b3 \u03b1 ( ) 0 2 2( ( ), ( ))s h h\u03b4 \u03b4\u03b1 \u03b1 \u03b3 \u03b1 for the single area contact, 2 0 2 2 ( ) 4 sin 4 N R E \u03b4 \u03b4 \u03b4 \u03b1 \u03b1 = \u03c0 \u03b5 \u03b4 \u03b4 \u03b3 \u03bb = = \u03c0 \u03b5 for the symmetrical double area contact, 2 1 2 2 ( ) 4 sin 4 N N R E 1 2 2 cos ;N N N= = \u03bb ( ) \u03b4 \u03b4 \u03b3 \u03b1 \u2260 = \u03c0 \u03b5 for the asymmetrical double area contact, ( ) 2 2 1 2 24 sin 4 s N N R E 2 2 1 sin(90 ) , sin(180 2 ) N N \u03b1 \u00b0 + \u03bb \u2212 \u03b1 = \u00b0 \u2212 \u03bb N2\u03b12 \u2212 \u00b0 + \u03bb + \u03b1 \u00b0 \u2212 \u03bb 2sin( 90 ) , sin(180 2 ) N 1 2 (90 ),\u03bb = \u03b1 \u2212 \u2212 \u03bb \u2212 \u03bb \u2212 \u03bb1(2 ) 21 ,N \u03b1 22 ,N \u03b1 1 2 2 ;\u03bb + \u03bb = \u03bb ( ) ( )2 0 2 24 sin , 4 h h hN R E E \u03b4 \u03b4 \u03b4 \u03b1 \u03b1 = \u03c0 \u03b5 + \u03b5 ( ) ( ) ( )( ) 2 2 1 2 24 sin , 4 s h h hN N R E E \u03b4 \u03b4 \u03b4 \u03b3 \u03b1 = \u03c0 \u03b5 + \u03b5 166 JOURNAL OF FRICTION AND WEAR Vol. 36 No. 2 2015 CHERNETS where (Fig. 3); is the Young modulus, are the modulus of shear elastic ity and the Poisson\u2019s ratio, \u00d7 and Correspondingly, at the asymmetrical contact, At the symmetrical contact, 2 4 cos , 4 E e R\u03b4 \u03b1 = ,\u03b1 = \u03bb + \u03b1 ,\u03b8 = \u03bb + \u03b8 0 ,\u2264 \u03b1 \u2264 \u03b8 0 ,\u2264 \u03b8 \u2264 \u03b3 (1) (1) 1 2 ,\u03b3 \u2264 \u03b1 \u2264 \u03b3 ( ) ( )( )1 1(1) 1,2 0 00.5 ,\u03b4 \u03b4\u03b3 = \u03bb \u00b1 \u03b2 \u2212 \u03b1 ( ) ( )( )2 2(2) 1,2 0 00.5 \u03b4 \u03b4\u03b3 = \u2212\u03bb \u00b1 \u03b2 \u2212 \u03b1 ,\u03b4 \u03b4\u03b5 = \u03b5\u03a3 4 1 24 ,e E E Z= ( )2 1E G= + \u00b5 ,G \u00b5 ( ) ( )1 11 1Z = + \u03ba + \u03bc ( ) ( )2 2 2 11 1 ,E E+ + \u03ba + \u03bc 3 4 ;\u03ba = \u2212 \u03bc ( ) ( )1 2 1 1 2 21 . 2 2 D D\u03b4 \u03b4 \u03b4 \u03a3 = \u2212 \u03b1 \u2212 \u03b1 \u03b5 \u03b5 1 0 ,\u03b1 = \u00b0 20 360 ",
            ",360\u03b1 = \u00b0 \u00b0 \u00b0 \u00b0 \u00b0 \u00b0 ( ) ( )1 2,D D\u03b1 \u03b1 1 1D = 2 21 3 cos 2D = \u2212 \u03b1 1 1D = 2 21 8cos 3D = \u2212 \u03b1 1 1D = 2 21 15cos 4D = \u2212 \u03b1 0 h\u03b4\u03b1 ( )s h\u03b4\u03b3 21 11 , j h h \u03b1 \u03b5 = \u2211\u2211 2360j = \u00b0 \u0394\u03b1 2*,\u03b1 ( )11 2\u03b4\u03a3 = \u2212 \u03b4 \u03b5 ( ) ( ) ( )1 1 2 2 22 0,D D\u03b1 \u2212 \u03b4 \u03b5 \u03b1 = 1 0 ,\u03b1 = \u00b0 20 360 .\u2264 \u03b1 \u2264 \u00b0 2*,\u03b1 min 20.6 .p N R= JOURNAL OF FRICTION AND WEAR Vol. 36 No. 2 2015 PREDICTION OF THE LIFE OF A SLIDING BEARING 167 The maximum contact pressures subject to wear at the jth every interval in the first shaft revolution are determined as follows: (8) where, for the scheme represented in Fig. 3, F I, III, V are phases of the single area contact and F II, IV are phases of the double area contact. The initial pres sures and their changes due to wear are determined for the jth every inter val as follows: (a) for the single area contact, (9) (b) for the double area contact: (10) where Eh = and For subsequent shaft revolutions n2, the maximum contact pressures are determined as follows: (11) The linear wear of the shaft and bushing after shaft rev olutions is determined as follows: (a) in the single area contact, \u23affor the bushing, is the shaft with the ovality, is the shaft with the trilobing, is the shaft with the tetralobing; ( ) ( ) ( ) 2 2 2 2 2 1 1 , , , , , F j j p h p p h \u2212 \u03b1 \u03b4 = \u03b1 \u2212 \u0394\u03b1 \u03b4 + \u03b1 \u2212 \u0394\u03b1\u2211\u2211 ( )2 2,p \u03b1 \u2212 \u0394\u03b1 \u03b4 ( )2 2, jp h\u03b1 \u2212 \u0394\u03b1 ( ) ( ) ( ) ( ) 0 2 2 2 0 2 2 2 , tan , 2 ', tan ; 2 h j h h p E p h E \u03b4 \u03b4 \u03b4 \u03b4 \u03b1 \u03b1 \u03b1 \u2212 \u0394\u03b1 \u03b4 \u2248 \u03b5 \u03b1 \u03b1 \u03b1 \u2212 \u0394\u03b1 = \u03b5 ( ) ( ) ( ) ( ) tan 2 2 2 ( ) 2 2 2 , tan , 2 ', ; 2 s h j h h p E p h E \u03b4 \u03b4 \u03b4 \u03b3 \u03b1 \u03b1 \u2212 \u0394\u03b1 \u03b4 \u2248 \u03b5 \u03b3 \u03b1 \u03b1 \u2212 \u0394\u03b1 = \u03b5 ( )2 0 2 4 2cos , 4 h hE e R\u03b4\u03b1 \u03b1 = ( )\u03b4\u03b3 \u03b1 ( ) 2 2 4 2cos , 4 s he R 21 1' "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003321_j.matpr.2020.11.415-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003321_j.matpr.2020.11.415-Figure5-1.png",
        "caption": "Fig. 5. Shear stress for ASTM-A226 carbon steel spring.",
        "texts": [
            " Total deformation for AST torsional \u00bc 16FsR pd3 \u00f06\u00de directshearstress \u00bc 4Fs pd2 \u00f07\u00de max \u00bc tortional \u00fe directshearstress \u00f08\u00de There are various types of solutions available in software but for the analysis of coil spring\u2019s deformation and stresses, ANSYS software was used for Finite Element Analysis (FEA). For the simplified results, few assumptions were taken. The assumptions were that damping effect was considered zero, complete load was exerted on spring and design was considered under worst conditions. Fig. 4 shows the results of total deformation for ASTM-A226 carbon steel spring by finite element analysis. While Fig. 5 refers to the outcome of Shear stress for ASTM-A226 carbon steel spring. Also, Table 2 refers to the ANSYS outcome of deformation and shear stress of different materials. Whereas, Table 3 demonstrates the analytical results of deformation and shear stress of different materials. Fig. 6 shows the comparison of ANSYS and analytical results of shear stress induced in different materials of spring. Whereas Fig. 7 refers to the comparison of ANSYS and analytical results of deformation in different materials of spring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001700_icra.2015.7140053-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001700_icra.2015.7140053-Figure1-1.png",
        "caption": "Fig. 1. The CTS variables defined for two subsystems in a humanoid: upper-body and lower-body subsystems [1].",
        "texts": [
            ". INTRODUCTION Modeling and control of humanoid robots are quite challenging because of their large number of degrees-offreedom (DoF) and the task and environment constraints imposed on their movements. Thus, it is advantageous to view a humanoid robot in terms of two subsystems [1] \u2013 a manipulation subsystem (i.e., the upper-body subsystem) and a locomotion subsystem (i.e., the lower-body subsystem) as illustrated in Fig. 1. In this paper, we focus on the manipulation subsystem of humanoid robots and present a general framework by extending the Cooperative-TaskSpace representation [2]\u2013[5] to model various kinematic coordinations and constraints in performing human bimanual tasks by humanoid robots. There are two main efforts for describing cooperative manipulation for two-arm robotic systems [6], [7]. The Cooperative-Task Space (CTS) representation has been used to model one type of coordination present in manipulating a common rigid load by two-arm systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001670_access.2017.2783319-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001670_access.2017.2783319-Figure1-1.png",
        "caption": "FIGURE 1. Earth-fixed frame and body-fixed frame.",
        "texts": [
            " CONTROL PROBLEM FORMULATION In this paper, \u03bamin(\u00b7) denotes the minimum eigenvalue of a matrix, \u2016\u00b7\u2016 denotes the standard Euclidean norm and \u2016\u00b7\u2016F denotes the Frobenius norm of a vector or matrix. A. MATHEMATICAL MODEL We consider the three degrees of freedom kinematics and dynamics equations with respect to the surface vessel: \u03b7\u0307 = R(\u03c8)\u03c5 M \u03c5\u0307 + C(\u03c5)\u03c5 + D(\u03c5)\u03c5 = \u03c4 + \u03c9 (1) where \u03b7 = [x, y, \u03c8]T denotes the positions (x, y) and yaw angle \u03c8 of the vessel expressed in the earth-fixed reference frame XEYEZE , while \u03c5 = [u, v, r]T represents the vector of the surge, sway, and yaw velocities in the body-fixed reference frame XBYBZB, as shown in Fig. 1. R(\u03c8) is a transformation matrix from XBYBZB to XEYEZE , its form is (note that RT (\u03c8) = R\u22121(\u03c8)): R(\u03c8) = cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1  (2) 2426 VOLUME 6, 2018 M \u2208 <3\u00d73 is the inertia matrix defining the mass moment of the system inertia. C(\u03c5) \u2208 <3\u00d73 denotes the Corioliscentripetal matrix and D(\u03c5) \u2208 <3\u00d73 represents the damping matrix. \u03c4 \u2208 <3 and \u03c9 \u2208 <3 denote the generalized control forces and external disturbances in the body-fixed reference frame, respectively. More details are provided in [34]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001237_iros.2011.6095061-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001237_iros.2011.6095061-Figure2-1.png",
        "caption": "Fig. 2. Coupled oscillator model",
        "texts": [
            " The suggested method was tested on the open humanoid platform DARwIn-OP as in Fig. 1. A. Coupled Oscillator Model The proposed coupled oscillator model is composed of two kinds of oscillator groups. Two movement oscillator groups represent the each foot trajectory, and the balance oscillator group manages the fixed Center Of Mass (COM) trajectory. All oscillator groups have six sub oscillators taking charge of R 978-1-61284-456-5/11/$26.00 \u00a92011 IEEE 3207 each axis, and there are 18 oscillators in Cartesian coordinate system as shown in Fig. 2. The total foot trajectory of a humanoid can be expressed by the superposition of the movement oscillator and balance oscillator as in (1). Whereas the balance oscillator activates in the entire walking period , the movement oscillator is restrained during Double Support Phase (DSP). We define the oscillator parameters, amplitude , angular velocity , phase shift , offset , and DSP ratio . From the definition above, we can express the balance oscillator as in (2) and the movement oscillator as in (3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001517_j.crme.2013.06.001-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001517_j.crme.2013.06.001-Figure3-1.png",
        "caption": "Fig. 3. Post-bifurcation patterns obtained with the envelope model and a full shell model. Colour available online.",
        "texts": [
            " Along the short sides, a uniform tensile stress is applied in the axial direction and the displacements in the X-direction are locked. Full nonlinear analyses of this problem have been done, first by a Q8 discretisation of the new model \u2013 Eqs. (17)\u2013(19) \u2013, second by a Q8 discretisation of the nonlinear pure membrane model \u2013 Eqs. (17) and (21) \u2013, last by quadratic shell elements S825 of the Abaqus code that will be considered as the reference. The nonlinear problems associated with the first two models have been solved by the Asymptotic Numerical Method [25]. In Fig. 3, one sees that the post-bifurcation patterns obtained by the new reduced model \u2013 Eqs. (17)\u2013(19) \u2013 are quite similar to those provided by the full shell model. This establishes the relevance of this new reduced model to represent the wrinkling modes in a case with a nonuniform pre-buckling stress field. In Fig. 4, we have plotted the maximal deflection as a function of the applied tensile load for these three models. One sees that the new reduced model \u2013 Eqs. (17)\u2013(19) \u2013 gives about the same bifurcation point as the reference model as well as the post-bifurcation response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003754_tim.2021.3078523-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003754_tim.2021.3078523-Figure1-1.png",
        "caption": "Fig. 1 The geometric model of the MCDHM",
        "texts": [
            " {lc} at the end-effector to the calibration board frame {cb} during the ith measurement; 1 lc lc i i+ T represents the HTM of the hand-eye camera frame {lc} from the i-th measurement to the (i+1)-th measurement; 1 mk mk i i+ T represents the HTM of the reference marker frame {mk} from the i-th measurement to the (i+1)-th measurement; b eh\u03c6 represent the Z-Y-X Euler attitude angle of b ehR ;   T 1 2= , , n \u0398 represents the joint angle of the MCDHM; represents the L2-norm of a vector or a matrix; || \u2022 ||F stands for the Frobenius norm of a matrix; | \u2022 | denotes the determinant of a matrix. I. INTRODUCTION OMPARIED with traditional industrial manipulators, multilink cable-driven hyper-redundant manipulators(MCDHMs) have higher flexibility and reliability [1]-[3], especially in obstacle avoidance [4][5], narrow space crossing [6][7], and fault-tolerant control [8]. Recently, a segmented linkage MCDHM was developed to obtain good performance with fewer actuators, based on hybrid active/passive driving concept [9], shown as Fig. 1. However, the modeling and control accuracy become lower, since there exist multiple couplings between the active cables, passive cables, joints, and the end-effector. In fact, in many occasions, MCDHMs needs to be visually guided [10][11]. At this time, the hand-eye calibration and kinematic parameter calibration of the MCDHM need to be considered. The calibration accuracy is the key to the success of the operation task. A. Related Work With regard to the classic hand-eye calibration problem of AX=XB [12][13], the kernel of the classic method [14][15], which was first proposed by Shiu and Ahmed [16], Tsai and Lenz [17], Park and Martin [18], Horaud and Dornaika [19], and quaternion-based one from Chou and Kamel [20]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure6.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure6.10-1.png",
        "caption": "Fig. 6.10 The total force acting on a bat can be regarded as the sum of four different components",
        "texts": [
            " The force of gravity also acts on the bat but it is much smaller than the force exerted by the batter. To understand how the batter influences the motion of the bat, it is useful to divide the total force acting on the bat handle into four separate components. A similar situation would arise if four people were lifting a heavy load. Each person would exert a separate force, but there is only one total force on the load, which is the sum of the four separate forces. Similarly, when swinging a bat there is only one total force on the bat, arising from four separate components, as shown in Fig. 6.10. The four components are: (a) A \u201cpush\u201d force Fa exerted by the batter at right angles to the bat, (b) A \u201cpush\u201d force Fb exerted by the batter at right angles to his foream, (c) A \u201cpull\u201d force Fc exerted by the batter in a direction along the bat, and (d) A \u201cpull\u201d force Fd exerted by the batter along his forearm. A batter usually uses both arms but it is simpler to imagine that the combined effect of both arms is equivalent to that of a single forearm. The formula for each force component is relatively simple, but it helps to consider that the motion of the bat consists of two parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001278_j.engfailanal.2013.02.030-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001278_j.engfailanal.2013.02.030-Figure2-1.png",
        "caption": "Fig. 2. 1/8th FEM-model of roller\u2013raceway contact (a), FEM-mesh (b).",
        "texts": [
            " This is due to the calculation costs because of the large number of rolling elements and contacts (two contacts for each element). In computational procedure used in this research, special built-in connectors (Fig. 3b) are used as a part of the FEM software Abaqus [16]. These connectors are defined as non-linear elastic connectors in compression with no stiffness in tension. The exact non-linear d\u2013Q behaviour in compression was determined in a separate 3D FEM-analysis of the contact between the roller and the raceway (Fig. 2). In these analyses 1/8th symmetry models of different roller types and sizes (for details see Section 2.2) were pressed against the raceway, while the actual elastic material properties were considered. As a result, relations between contact deflection d and resulting contact forces Q are determined. Actual d\u2013Q dependence for different roller types with nominal diameter D = 25 mm are shown in Fig. 3a. As a reference, the d\u2013Q behaviour for line contact according to [17] is depicted. The cylindrical roller has the highest contact stiffness, while the ZB and logarithmic rollers have virtually the same displacement\u2013contact force characteristics",
            " As the overturning moment MT is considered as the predominant external load, the radial row is not considered in this model. The second part of the presented model focuses on the numerical analysis of a contact problem between the roller and the raceway. Here, the contact force distribution in the bearing, of which calculation is described in the previous section, serves as an input for determination of stress field in the contact area between rollers and raceway. The numerical analysis is performed using a 1/8th 3D FEM-model as shown in Fig. 2. For meshing of both, the roller and the raceway, 8-node linear brick elements (C3D8) with full integration are used. The mesh is structured with a higher density at the position of the contact (Fig. 2b) and the contact behaviour is defined as a \u2018\u2018hard-contact\u2019\u2019 without friction, as described in [16]. At the contacts position finer local mesh is utilized. A higher mesh density is also present at the end of the rollers where edge contact stress concentrations are expected. The optimal mesh size for these model sizes was determined by a convergence analysis. As mentioned in the introduction, three different roller types were analysed in this study: Cylindrical roller \u2013 roller without profile correction (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.19-1.png",
        "caption": "Figure 6.19. Motion of a pendulum having a moving support.",
        "texts": [
            "e. when and only when the velocity of o is parallel to the velocity of the particle P ; otherwise, 0 must be a fixed point. 150 Chapter6 In general, then, the modified principle (6.80) must be used when 0 is a moving reference point. An application of this rule follows . Example 6.14. A pendulum bob B attached to a rigid rod of negligible mass and length \u00a3 is suspended from a smooth movable support at 0 that oscillates about the natural undeformed state of the spring so that x(t) = Xo sin Qt in Fig. 6.19. Apply equation (6.80) to derive the equation of motion for the bob. Solution. The forces that act on the pendulum bob B are shown in the free body diagram in Fig. 6.19. Notice that the tension T in the rod at B is directed through the moving point O. Moreover, the spring force and normal reaction force of the smooth supporting surface also are directed through 0; but these forces do not act on B, so they hold no direct importance in its equation of motion. Consequently, the moment about the point 0 of the forces that act on B at XB = fer in the cylindrical system shown in Fig. 6.19 is given by M o = XB X W = -\u00a3W sinek. (6.81a) (6.81b) The absolute velocity of B is determined by VB = Vo+W X XB , in which ca = \u00a2k and Vo = xi = xoQ cos Qti = voi. Thus, VB = voi + \u00a3\u00a2e</>, with Vo = xoQ cos Qt . With the linear momentum p = mVB and use of (6.81b) , we find Vo x p = voi x m\u00a3\u00a2e</> = mvo\u00a2\u00a3sin\u00a2k. (6.81c) The moment of momentum about 0 is given by ho = XB X P = m\u00a3(vo cos \u00a2 + \u00a3\u00a2 )k, and its time rate of change is lio = m\u00a3(ao cos \u00a2 - vo\u00a2 sin \u00a2 + \u00a3\u00a2)k, (6.81d) Dynamics of a Particle 151 in which ao = Vo = -xoQ2 sin Qt",
            " Suppose, however, that the initial data may be chosen so that xo = 0 and Vo = H Q for a fixed forcing frequency . Then A = B =0 and the motion (6.92a) reduces to the steady-state, periodic motion x(t) = H sin Qt. The effects of damping and the critical case when ~ = I will be discussed momentarily. First, we consider an example that illustrates the application of these results to a mechanical system. Example 6.15. The equation for the undamped, forced vibration of the pendulum device described in Fig. 6.19, page 150, is given in (6.8Ie). Solve this equation for the case when both the motion of the hinge support and the angular motion of the pendulum are small. Assume that the pendulum is released from rest at a small angle \u00a2o. Solution. The differential equation (6.8Ie) describes a complicated nonlinear, undamped, forced vibrational motion of the pendulum. To simplify matters, we consider the case when the angular placement is sufficiently small that terms greater than first order in \u00a2 may be ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003384_s12555-019-0904-9-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003384_s12555-019-0904-9-Figure1-1.png",
        "caption": "Fig. 1. Planar APA System.",
        "texts": [
            " According to the target value of end-point and the angle constraint of PVA, we calculate the two links\u2019 target angles of PVA using PSO algorithm [20]. Then, the controllers are designed to make the TAL reach to its target states and to keep the FAL at its target states. Meanwhile, the SUL is adjusted to its target states based on the angle constraint. Thus, the end-point of the planar APA system can reach to the target position. At last, one simulation example is taken to verify our presented strategy. 2. THE MODEL The model of the planar APA system is shown in Fig. 1, where } represents the active joints and\u00a9 represents the passive joint. The parameters of the ith (i = 1,2,3) link are: qi is the angle, mi is the mass, Li is the length, Lci is the distance from its joint to its center of mass, Ji is the moment of inertia, and \u03c4i is the torque of the ith joint, (x,y) is the end-point coordinate. The dynamic equations of the system is M(q)q\u0308+H(q, q\u0307) = \u03c4, (1) where q = [q1 q2 q3] T , q\u0307 = [q\u03071 q\u03072 q\u03073] T , and q\u0308 = [q\u03081 q\u03082 q\u03083] T are the vector of angle, angular velocity and angular acceleration, respectively; \u03c4 = [\u03c41 0 \u03c43] T is the input torque vector; M(q)\u2208R3\u00d73 is the inertia matrix with the characteristic of the symmetric positive definite, and H(q, q\u0307) \u2208 R3\u00d71 contains the Coriolis and centrifugal forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000188_s00170-008-1785-x-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000188_s00170-008-1785-x-Figure1-1.png",
        "caption": "Fig. 1 Schematic illustration of DLF",
        "texts": [
            " Accordingly, firstly, we will address the features of DLF temperature field modelling, facing difficulties and propose corresponding solving measures, and then we will discuss heat transfer theories and equations related to the modelling. Finally, we will describe a laser-repairing case study, which has been solved by the commercial finite element software ABAQUS according to our strategy, and estimate the influence of non-linear thermal properties in pure nickel on the temperature distribution in the model. The DLF process can be described by the following steps, illuminated by Fig. 1: From the first layer, high-energy laser melts powder and shallow layer of substrate, via the forced convection and diffusion of fluid, forming the instantaneous liquid temperature field and, at the same time, the heat conduction begins to happen in the substrate with the laser continuously moving to new positions, the former melted pool instantly consolidates and also begins to conduct heat as the substrate. The same process is durative with the laser moving along the preset path, then except the conduct heat and convection phenomenon, the building part also produces heat exchange with the surrounding gas and disperses some heat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.130-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.130-1.png",
        "caption": "Fig. 2.130 AHED 8 \u00d7 8.4 Phantom HEV view revealing power and propulsion modules [TRZASKA 2002].",
        "texts": [
            " At low values of vehicle velocity, the tri-mode HE SBW 6WS or 8WS conversion mechatronic control system may arrange differential wheel velocity between the wheels to induce skid steering to enhance the indispensable steering angle. This feature may give the 6 \u00d7 6.6 or 8 \u00d7 8.8 HEV innovative mobility capability in familiar areas such as conurbation environments. In this position, swept volume necessary for steering is minimised and wheel pairs are sustained to accept the advantage of track overlays to the wheels in operational circumstances where supplementary flotation and traction are indispensable. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 329 Figure 2.130 shows a computer-aided-design (CAD) integration physical model of the advanced hybrid electric wheel drive (AHED) 8 \u00d7 8.4 Phantom HEV indicating the power and propulsion modules [TRZASKA 2002]. Modular in-wheel drives with E-M/M-E motors/generators provided by the Magnet Motor are installed in each wheel hub. In-wheel-hub motors/generators are rated at 110 kW each. Figure 2.131 shows the mechatronic architecture of the HE DBW 8WD propulsion mechatronic control system and energy-and-information network (E&IN) for a AHED 8 \u00d7 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003050_j.jmatprotec.2020.116745-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003050_j.jmatprotec.2020.116745-Figure9-1.png",
        "caption": "Fig. 9. (a) schematic of relative position between wire and laser beam (P=1400W, vs = 1mm/s, vf = 2mm/s, \u2212d/2 < w < 0) when the wire tip is placed at the leading region of the molten pool, (b) schematic of wire spreading transfer, cross-section (c) and clad appearance (d) of the single track.",
        "texts": [
            " Due to the fact that the particles could hardly transfer to the molten pool when the droplet stuck to the wire tip, almost no retained particles were found in the coating. After the discussion above, the occurrence of the wire droplet transfer was depended on the distance between the wire tip and the laser irradiated region. When the wire was aligned with the rear zoon of the molten pool, it melted before reaching the molten pool, which could result in the formation of droplet rather than a consistent track as illustrated by the schematic configuration shown in Fig. 7. As shown in Fig. 9(a), when the wire tip was positioned to the leading region of the molten pool(-d/2<w<0), the wire spreading transfer mode (Fig. 9(b)) was obtained under the No.2 parameters in Table 2. At initial stage of laser deposition with a low wire feed speed (2mm/s), the laser energy was almost absorbed by the substrate then a molten pool (Fig. 10(a)) was produced. As the wire approached the to the molten pool, it melted by the heat radiation from the molten pool and its interaction with the laser beam. With continued wire feeding, a liquid bridge (Fig. 10(c)) was formed when the melted wire interacted with the molten pool. The liquid bridge was enlarged (Fig",
            " 10(d)) by surface tension and in this way the melted wire was transferred to the molten pool thus increasing the volume of the pool. Due to lack of additive material at a low wire feeding speed, the liquid bridge was broken (see Fig. 10(e)) and the liquid metal flowed backwards (see Fig. 10(f)) in the molten pool. Similarly, as shown in Fig. 10(g) to (i), the wire was melted continuously which appeared like the liquid metal was spreading on the substrate. The coating showed a continuous appearance (Fig. 9(d)) in this wire liquid spreading transfer mode. Because most laser energy was absorbed by the workpiece, as shown in Fig. 9(c), the coating had a larger dilution ratio of 39 % and a low retained particle content (8.6 %). Only a few particles were found in the coating which might be caused by the spattering during the transfer process through liquid bridge and the extensive dissolution of the particles under laser irradiation. Additionally, when the high the laser power was employed, the less viscous the melt pool solution would be and a rigorous liquid convection was produced in the molten pool. The ceramic particles experienced heavily heat damage under the laser irradiation as the particles entered into the molten pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001521_j.automatica.2013.11.017-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001521_j.automatica.2013.11.017-Figure2-1.png",
        "caption": "Fig. 2. Tait\u2013Bryan angles are \u03c61, \u03c62, \u03c63 where \u03c6i is counterclockwise head rotation, with respect to Axis i.",
        "texts": [
            " We assume that the third axis rotates with respect to the first two axes by angles \u03c61 and \u03c62 respectively. Finally, we assume that the head rotates anticlockwise by an angle \u03c63 with respect to the nested third (roll) axis. A specific rotation in SO(3) can be parameterized by the three angles \u03c61, \u03c62 and \u03c63, and these are called the Tait\u2013Bryan angles. Donders\u2019 surface is implemented as a constraint on the three angles, to be described later in this paper. The yaw, pitch and roll are respectively the axes 1, 2 and 3 in Fig. 2. This figure also shows the picture of a generalized gimbal, establishing the connection. We present the study of head movement using two control strategies, potential and optimal control. The potential control strategy assumes that the muscles actuating the head movement are guided by an \u2018artificial\u2019 potential function, the minimum of which is adjusted by the final orientation of the specific head movement maneuver. Likewise, the optimal control strategy assumes that the three generalized torques on the model of the head are chosen to minimize a suitably defined quadratic cost function",
            " (2007), between S3 and SO(3) given by rot : S3 \u2192 SO(3). (3) The image of the composite map \u2018\u2018rot \u25e6 \u03c1(\u03b8, \u03c6, \u03b1)\u2019\u2019 is a rotation matrix which rotates a vector in R3 around the axis (cos \u03b8 cos\u03b1, sin \u03b8 cos\u03b1, sin\u03b1)T (4) by a counterclockwise angle \u03c6. Note that when \u03b1 = 0, the axis (4) lies in a plane called Listing\u2019s plane. It follows that \u03b1 is the angle between the axis of rotation and Listing\u2019s plane and \u03b8 is the angle between the projection of the axis of rotation on Listing\u2019s plane and the positive x-axis (Axis 2 in Fig. 2). Remark. The alpha parameters are not subsequently used in this paper except in describing the coordinate map \u03c1. Going back to the Fick strategy for head movements, we can represent the horizontal rotation about the fixed vertical axis, by the quaternion \u03c11 = \u03c1 \u03c0 2 , \u03c61, 0  . We can also represent the vertical rotation about the nested horizontal axis, by the quaternion \u03c12 = \u03c1 (0, \u03c62, \u03c61) . The resultant quaternion \u03c1fick is obtained as a quaternion product (see Altmann, 2005) \u03c1fick = \u03c12 \u2217 \u2217\u03c11 given by \u03c1fick(\u03c61, \u03c62) =  cos \u03c61 2 cos \u03c62 2 , cos \u03c61 2 sin \u03c62 2 , sin \u03c61 2 cos \u03c62 2 , \u2212 sin \u03c61 2 sin \u03c62 2  "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002568_j.ymssp.2018.05.036-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002568_j.ymssp.2018.05.036-Figure6-1.png",
        "caption": "Fig. 6. Amplitu",
        "texts": [
            " The beforedamage complex harmonic amplitude can be expressed as ab \u00bc rbeihb : \u00f028\u00de The complex harmonic contribution arising from damage can be expressed as aD \u00bc AeihD \u00f029\u00de and the after-damage complex amplitude as aa \u00bc raeiha \u00f030a\u00de \u00bc rbeihb \u00fe AeihD \u00f030b\u00de because, for each harmonic n, the damage contribution is superimposed on the before-damage contribution. The ratio of after-damage to before-damage complex amplitude, for any harmonic, is by incorporating Eq. (30b), aa ab \u00bc ra rb ei\u00f0ha hb\u00de \u00f031a\u00de \u00bc raeiha rbeihb \u00f031b\u00de \u00bc rbeihb \u00fe AeihD rbeihb \u00f031c\u00de \u00bc 1\u00fe A rb ei\u00f0hD hb\u00de \u00f031d\u00de which is illustrated in Fig. 6. (Actually, Fig. 6 is the complex plane, rotated 90 degrees then viewed from the backside of the paper. Eq. (31a) describes the amplitude ra=rb shown in Fig. 6, and Eq. (31d) describes its two components). It is important to recognize that the phase hD of the damage contribution in Eqs. (29) and (30) can take on any value 0 6 hD < 2p. Hence, damage contributions to non-negligible tooth-meshing, low-order rotational, and sideband harmonics can be manifested in real-amplitude reductions as well as real-amplitude increases in these harmonics, as is readily seen from Fig. 6. From Fig. 6, the trigonometric \u2018\u2018law of cosines\u201d yields the (squared) fractional amplitude change as Rotational-harmonic complex amplitude components of before-damage contribution, b, damage contribution, D, and after-damage contribution, a. des denoted by r and phases by h. See Eqs. (28)\u2013(31). A rb 2 \u00bc 1\u00fe ra rb 2 2 ra rb cos\u00f0ha hb\u00de \u00f032\u00de which is a function of real amplitude ratios and the difference in phase angles measured in radians. In particular, Eq. (32) shows that a significant fractional amplitude change A=rb can take place with no change in real amplitudes, i.e., \u00f0ra=rb\u00de \u00bc 1: Moreover, Fig. 6 shows that phase differences jhD hbj > \u00f0p=2\u00de arising from damage contributions, Eq. (29), yield reductions in the real after-damage amplitudes ra relative to the before-damage amplitudes rb. The fractional amplitude change is given by the square root of Eq. (32). For high-quality undamaged gears, the transmission-error frequency-domain spans centered between adjacent toothmeshing harmonics normally exhibit only exceedingly weak contributions arising from gear manufacturing errors. Fractional increases in rotational-harmonic amplitudes caused by damage, Eq",
            "21) pQt\u00f0n=N\u00deD0=D \u00bc p=2 \u00f0A:22\u00de or Qt D0 D n N \u00bc 0:5: \u00f0A:23\u00de Each of the solutions, Eqs. (A.11), (A.19), and (A.23) has the same form, but with modestly differing numerical values on the right hand sides. In each case, smaller fractional damage spans D0=D yield proportionally larger rotational harmonic locations n=N of maximum transmission error generation. A.1. Independent verification of above solutions A simple verification of the solutions for \u2018 \u00bc 1;2; and 3, Eqs. (A.11), (A.19), and (A.23), is obtained as follows. The independent variable (abscissa coordinate) in Fig. 6(a) of [25] for \u2018 \u00bc 1, and Fig. 3(a) and (b) herein, for \u2018 \u00bc 2 and 3, respectively, is Qt\u00f0n=N\u00deD0=D. The above solutions, Eqs. (A.11), (A.19), and (A.23), for \u2018 \u00bc 1;2; and 3, respectively, in each case, is in the region of these three figures where they are very nearly linear. Placing a straight line tangent to this linear region on each of these figures yields abscissa values of these straight line intersections for \u2018 \u00bc 1;2; and 3 of \u00f0Qt n N D0=D\u00de0 \u00bc 1:68;1:32, and 1.0 respectively. For each of these three figures, denote the ordinate intersection of this straight-line tangent approximation by y0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003616_16878140211034431-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003616_16878140211034431-Figure19-1.png",
        "caption": "Figure 19. New type of friction surfacing: (a) cross section schematic of the beginning of the AFS-D process where the tool plunges into a substrate while spinning at a predetermined rotational speed, (b) the tool is then raised to the layer height during which time an actuator drives a solid, or powder, feedstock through the tool as the tool traverses across the substrate, producing a layer, (c) at the completion of a layer, the spindle raises to the next layer height and repeats the process to build consecutive layers, (d) photograph of the actual AFS-D process applied to AA6061, and (e) image of the teardrop featured tool.69",
        "texts": [
            "64 Through the lateral movement of the consumable, a continuous additive material is left on the substrate. Repeating the processing on the first layer of additive samples, the height of the additive material increases.65 Friction surfacing AM has been used as an industrial forming technology.66 Its application fields include surface processing,67 aircraft manufacturing,68 manufacturing metal composites,64 and so on. In recent years of research, a more novel form of friction surfacing has appeared. As shown in Figure 19, Phillips et al.69 used a special stirring tool for friction surfacing. A square through hole was machined in the middle of the mixing tool to feed the material. There are four tear-like bulges around the bottom of the square hole. Perry et al.70 also conducted a similar study, with two small spherical protrusions at the bottom of the square hole. With the stirring effect of the protrusions, a non-planar interface was created, and the effective combination of the deposition material and the substrate was observed on the non-planar interface, as illustrated in Figure 20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure5.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure5.1-1.png",
        "caption": "Fig. 5.1 Cross-sectional view of a brushed separately excited and permanent magnet DC machine [4]",
        "texts": [
            "27 Dynamic model of two-mass drive train . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Fig. 4.28 Scope signals from two-mass drive train model . . . . . . . . . . . . . . . . . . . 123 Fig. 4.29 Simulation of speed control example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 List of Figures xxvii Fig. 4.30 Simulation results for speed and reference torque versus time without and with anti-windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Fig. 5.1 Cross-sectional view of a brushed separately excited and permanent magnet DC machine [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Fig. 5.2 Vector diagram for brushed DC machine with constant armature current ia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Fig. 5.3 Cross-sectional view of a brushed separately excited DC machine with compensation windings (left) and interpoles (right) 131 Fig. 5.4 Vector diagram for brushed DC machine with current commutation in the neutral zone",
            "1007/978-3-030-48977-9_5 127 128 5 Modeling and Control of DC Machines To give a brief review of DC machine concepts, the cross-sectional views as well as the symbolic and generic models are presented together with the relevant equations. A more extensive examination can be found in [3]. A comprehensive treatment of basic machine concepts for the uninitiated reader is given, for example, in [1] and [2]. Cross-sectional views of two typical one pole pair brushed DC machine examples, namely the separately excited DC machine and the permanent magnet DC machine, are given in Fig. 5.1. Common to both machines is the armature, which is the rotational component of the motor that is linked to the brush/commutator assembly which ensures that the current distribution in said armature is stationary with respect to the \u03b1\u03b2 coordinate system that in turn is tied to the stator of the machine. The magnetic excitation for both types is noticeable different: the separately excited machine carries a field winding, which implies that the excitation air-gap flux \u03c6f that is aligned with the \u03b1 axis can be altered using the field current if",
            " The effects of this angular displacement of the resultant armature flux due to armature reaction are twofold, namely: \u2022 The neutral zone is no longer aligned with the \u03b2 axis of the machine and therefore current commutation takes place outside the neutral zone. This can result in severe arcing across the commutator segments due to the so-called under 130 5 Modeling and Control of DC Machines commutation. This refers to the current not being fully reversed after the armature passing through the brush assembly. The resultant current discontinuity will lead to voltage spikes that cause arcing under the brushes [1]. \u2022 For machines with poles, the pole regions located in the second and fourth quadrant of the separately excited motor shown in Fig. 5.1 are exposed to a higher flux density, which causes saturation and may cause local higher induced voltages in the conductors that traverse these regions. This in turn can cause arcing across the affected commutator segments. Due to the effects described above, the effect of armature reaction should be reduced. This can be achieved in three ways, namely: \u2022 By shifting the commutator/brush assembly such that it is aligned with the neutral zone. This approach is used in Fig. 5.4a, which is why the current vector ia is not aligned with the \u03b2 axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002664_j.mechmachtheory.2019.103608-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002664_j.mechmachtheory.2019.103608-Figure13-1.png",
        "caption": "Fig. 13. Planar 3- R PR parallel manipulator.",
        "texts": [
            " Meanwhile, we should see the disagreement is overall staying at a low level, even for large errors. Considering errors in practical engineering are small, it can be supposed that the closed-form approximations of covariance propagation definitely satisfy the requirement. In addition, it is worth mentioning that the time consumed by the proposed method is 0.160 s while that of the BFEM is 3.820 s. In fact, the time cost of the BFEM will be more expensive as the sampling amount increases. Case 2. Planar 3- R PR parallel manipulator Fig. 13 gives the schematic diagram of the planar 3- R PR manipulator, which is designed as follows: \u2013 The rotational actuator is mounted on the first revolute joint; \u2013 Triangles P 01 P 02 P 03 and P 1 P 2 P 3 are equilateral; \u2013 The radius of the base is 0.4 m and that of the mobile platform 0.1 m; The error ellipsoid is shown in Fig. 14 . Based on the theory in Section 5 , the maximum angular error is \u00b10.0011 rad and the maximum translational errors along x b and y b axes are \u00b10.1588 mm and \u00b10.2528 mm, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000988_j.msea.2012.05.083-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000988_j.msea.2012.05.083-Figure1-1.png",
        "caption": "Fig. 1. Material deposition and specimen extraction schematic.",
        "texts": [
            " The increase in beta transus temperature as a result of the luminum addition provides high temperature phase stability due o the much slower coarsening kinetics provided by the hcp alpha hase. Ti\u20136Al\u20134V is a standard \u2013 alloy in which both aluminum nd vanadium are used for solid solution strengthening. Electron beam deposited Ti\u20138Al\u20131Er and Ti\u20136Al\u20134V materils were supplied for this study by Lockheed-Martin. Cylindrical eposits were made using a Sciaky electron beam additive manuacturing system from which test specimens were extracted along he build direction, parallel to the z-axis (Fig. 1). The original eposits were approximately 150 mm in diameter with a wall hickness of 25 mm and a finished height of 200 mm. Each layer was reated using an outward spiral pattern such that eight full revoluions around the z-axis were completed with each concentric spiral verlapping the previous by approximately 33%. Upon completion f each layer, the z-axis was incremented up 1 mm and indexed ack to the starting position. This process was repeated until 200 ayers were deposited for a total build height of 200 mm. From hese deposits, cylindrical test blanks with a diameter of 16 mm nd length of 160 mm were extracted with the text axis parallel to he z orientation in the deposit (see Fig. 1). The Ti\u20138Al\u20131Er blanks were annealed at 700 \u25e6C for 2 h to provide stress relief and aid in secondary precipitation of Er2O3 dispersoids, then subsequently air cooled. The Ti\u20136Al\u20134V blanks were given a heat treatment similar to a anneal, specifically 1010 \u25e6C ( phase field) for 35 min, air cooled to room temperature, then 730 \u25e6C for 2 h and then air cooled. The bars were machined into cylindrical dogbone test specimens with threaded ends and 6.3 mm diameter test sections. A columnar grain structure with the long axis of the grains parallel to the z-axis build direction is often observed in electron deposited parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure1.25-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure1.25-1.png",
        "caption": "Fig. 1.25 Applications of in-vehicle energy and information network (E&IN) [SONG 2005].",
        "texts": [
            "4 Harnessing Energy and Information Networks 51 Automotive E&IN solutions must satisfy a number of requirements [YAZAKI 2006]: Reliability \u2013 the network must be able to perform error-free under adverse conditions for the life of the vehicle; Flexibility -- content variation across models and compatibility with aftermarket devices requires network scalability and upgradeability; EMC -- unwanted electromagnetic fields may disrupt the network and nearby devices; Connector optimisation -- number of connectors, connector size and functional integration are critical variables in network design; Cost -- performance and other benefits must be carefully balanced against cost and competitive impact; Fault tolerance -- susceptibility to faults and the necessity for system redundancy are major issues; Modularity -- standardised modules mean shorter design cycles and lower costs. In-vehicle E&INs may be differentiated by data-handling speed. This, in turn, governs the types of devices served and data-communication protocols applied. In general, as network data speed rises, technical sophistication and costs increase accordingly (see Fig. 1.25) [KIRMANN 2005; SONG 2005; YAZAKI 2006]. Automotive Mechatronics 52 This is one reason why devices with relatively modest data needs are often networked separately, as is shown in Figure 1.25 [SONG 2005]. Class A networks, for example, include devices that operate through simple on/off control of power loads. These copper-based networks generally run at speeds below 10 kb/s and include devices such as seat controls, power mirrors and trunk releases. Class A data protocols include a local interconnect network (LIN) and time triggered protocol/class-A (TTP/A). Class B networks are designed to allow sharing of basic information between various vehicle devices, thereby eliminating redundant sensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001240_1.5062261-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001240_1.5062261-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the main elements of a laser deposition set-up.",
        "texts": [
            " The model can be used in applications such as lateral or thin wall cladding. Additionally, the model is not excessively demanding in terms of computing resources, thus it is well suited to produce tracks of reasonable lengths that can be compared against experimental samples. Although there are some variations in the setting-up of a nozzle for a deposition equipment, this work is based on the use of a coaxial nozzle, as it is the most widely used configuration. A typical coaxial deposition equipment has the elements shown in Fig. 1. The powder is supplied by a disk powder feeder at a constant rate using argon gas as the conveying media. The powder flow is then shaped through the nozzle to produce a converging annular stream of powder particles which are focused towards the substrate. A high-energy laser beam is fired on the substrate to create a melt pool. As powder particles arrive at the pool, they are melted and incorporated. The substrate moves relative to the deposition head and a solidified track is formed behind the laser beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002953_c9sm00488b-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002953_c9sm00488b-Figure9-1.png",
        "caption": "Fig. 9 Schematic representation of mapping the dynamics of two active Janus particles with parameters (be,ba;w,d\u0302) for particle \u2018\u2018A\u2019\u2019, and (be 0,ba 0; w, d\u0302) for particle \u2018\u2018B\u2019\u2019. The specific choice {be 0 = ba, ba 0 = be} ensures that the linear and angular velocities of the two particles are proportional with a positive proportionality factor (see the main text).",
        "texts": [
            " Consequently, the density field in excess over its bulk value changes as n0\u00f0r; y; w0; d\u0302 0 ;Qe\u00de n1 \u00bc 1 w 1\u00fe w n\u00f0r; y; w; d\u0302;Qe\u00de n1 ; (35) i.e., the excess number density field n nN for a particle with the parameters (w, d\u0302, Qe), is \u2013 up to the prefactor (1 w)/(1 + w) \u2013 equivalent to that for a particle with the parameters ( w, d\u0302, Qe). (We note that, by construction, the transformation keeps the parameter Qe unchanged.) Thus, an enhanced/depressed number density for the unprimed particle is mapped onto a depression/ enhancement, respectively, for the primed particle. As shown schematically in Fig. 9, these two configurations correspond to interchanging \u2018a\u2019 - \u2018e\u2019 and \u2018e\u2019 - \u2018a\u2019 (i.e., flipping red 2 blue) in the left panel (particle \u2018\u2018A\u2019\u2019) such as to obtain the right panel (particle \u2018\u2018B\u2019\u2019). Now we turn to the hydrodynamic flow and to the velocity of the particle. We consider the primed particle with dimensional mobility parameters be 0 and ba 0. From the definition of the phoretic slip (eqn (5) and (35)) one obtains (see also Fig. 9) vs 0 \u00f0be 0 ; ba 0 ; w0; d\u0302 0 \u00de: \u00bc b0\u00f0n\u0302\u00dersn 0\u00f0r \u00bc a; y; w0; d\u0302 0 \u00de \u00bc rsn 0\u00f0r \u00bc a; y; w0; d\u0302 0 \u00de be 0 ; d\u0302 0 r\u03024 w0 ba 0 ; d\u0302 0 r\u0302o w0 8< : \u00bc 1 w 1\u00fe w rsn\u00f0r \u00bc a; y; w; d\u0302\u00de ba 0 ; d\u0302 r\u03024 w be 0 ; d\u0302 r\u0302o w 8< : : (36) By choosing be 0 = ba and ba 0 = be, one thus arrives at vs 0 \u00f0be 0 \u00bc ba; ba 0 \u00bc be; w0; d\u0302 0 \u00de \u00bc 1 w 1\u00fe w rsn\u00f0r \u00bc a; y; w; d\u0302\u00de be; d\u0302 r\u03024 w ba; d\u0302 r\u0302o w 8< : \u00bc 1 w 1\u00fe w vs\u00f0be; ba; w; d\u0302\u00de: (37) (The identification of the slip velocity in the second equality follows, e.g., by comparison with the second equality in eqn (36) with all the primes dropped"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003287_s00170-020-06104-0-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003287_s00170-020-06104-0-Figure7-1.png",
        "caption": "Fig. 7 The effect of the part length on the deformation of the thin-walled part with a 20-mm part height and a 5-mm part thickness: a X-direction displacement distribution, b \u0394Lmax",
        "texts": [
            " 6b, the \u0394Lmax increases from 34.8 to 147.4 \u03bcm as the part height increases from 10 to 50 mm. Then, the \u0394Lmax stabilizes about 150 \u03bcm after the height exceeds 50 mm. This is because the constraint strength provided by the substrate decreases with an increase of the deposition height, leading to an increase of the material contraction at the middle of the part. However, the \u0394Lmax no longer increases when the height exceeds 50 mm due to the stabilized post-heating effect and residual stress distribution. Fig. 7a depicts the simulated X-direction displacement distribution with different part lengths when the part thickness and height are constant at 5 and 20 mm, respectively. It can be found that the deformation distributions of the parts are similar, but the deformation level increases with the part length. As shown in Fig. 7b, with the part length increasing from 10 to 180 mm, the\u0394Lmax increases from 17.6 to 100.4 \u03bcm. It can be seen that\u0394Lmax stabilizes about 100 \u03bcm after the part length exceeds 100 mm. The reason for this is attributed to the fact that the shrinkage of the part is approximately proportional to the part length in LPBF [10]. However, when further increasing the length, the contact area between the substrate and the part also increases with the part length, resulting in an increase of the constraint strength provided by the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.40-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.40-1.png",
        "caption": "Fig. 15.40 Dwell mechanism",
        "texts": [
            " Another special case is h = \u2212r0 ( P is at the center 0 of the circle in the position \u03c6 = 0 ). In this case, the equations are \u03c1 = r0\u03c6 and \u03d5 = \u03c6 \u2212 \u03c0/2 . These are the equations of Archimedes\u2019 spiral. The coordinate x is zero if \u03c6 satisfies the equation \u03c6 = [(r0+h)/r0] tan\u03c6 . This equation has the solution \u03c6 = 0 and one more solution if h < 0 . These 15.5 Trochoids 509 curves have a double point on the axis of symmetry. They are curtate, and those with h > 0 (without double point) are prolate. In the mechanism shown in Fig. 15.40 the crank 2 causes the planetary wheel 1 (radius r ) to roll inside the sunwheel 0 (radius R ). In the position \u03d5 = 0 point A lies on the x-axis at xA = R \u2212 2r . Rod 3 (length ) connects A to the slider 4 . The figure shows the case R/r = 3 . In what follows, the general case R/r = n (n \u2265 3 ; integer) is investigated. In the interval \u2212\u03d50 \u2264 \u03d5 \u2264 +\u03d50 with \u03d50 = \u03c0/n the hypocycloid traced by A is a rather good approximation of a circular arc. For this reason it is possible to render the ratio \u03be(\u03bb, \u03d5) = xB(\u03bb, \u03d5)/r in the interval \u2212\u03d50 \u2264 \u03d5 \u2264 +\u03d50 approximately constant provided the ratio \u03bb = /r is chosen appropriately",
            " An appropriate value \u03bb1 is obtained if is the radius of curvature of the hypocycloid at the point \u03d5 = 0 . Another appropriate value \u03bb2 is obtained from the condition \u03be(\u03bb2, 0) = \u03be(\u03bb2, \u03d50) . To be determined are \u03bb1 and \u03bb2 as functions of n . The optimal value \u03bb0 is obtained from the condition that the difference between the absolute maximum and the absolute minimum of the function \u03be(\u03bb, \u03d5) in the interval \u2212\u03d50 \u2264 \u03d5 \u2264 +\u03d50 is minimal. This is Tshebychev\u2019s criterion of optimality. Determine \u03bb0 and the minimal difference in the cases n = 3 and n = 4 . Solution: Figure 15.40 shows the poles P10 , P20 and P12 . With these poles (15.6) yields the angular velocity ratio \u03c910/\u03c920 = \u2212(n \u2212 1) . This is Eq.(15.120). This ratio yields for the angle of rotation \u03b1 of wheel 1 rel- 510 15 Plane Motion ative to the x, y-system the expression \u03b1 = (n \u2212 1)\u03d5 (positive clockwise; see the figure). This determines the coordinates of A and B : xA = r[(n\u2212 1) cos\u03d5\u2212 cos(n\u2212 1)\u03d5] , yA = r[(n\u2212 1) sin\u03d5 + sin(n\u2212 1)\u03d5] , } (15.138) \u03be(\u03bb, \u03d5) = xB r = 1 r ( xA + \u221a 2 \u2212 y2A ) = (n\u2212 1) cos\u03d5\u2212 cos(n\u2212 1)\u03d5 + \u221a \u03bb2 \u2212 [(n\u2212 1) sin\u03d5+ sin(n\u2212 1)\u03d5]2 ",
            "146) becomes sin\u03d5 ( cos2 \u03d5\u22121 2 )[\u221a \u03bb2 \u2212 16 sin2 \u03d5 ( cos2 \u03d5+ 1 2 )2 \u22124 cos\u03d5 ( cos2 \u03d5+ 1 2 )] = 0 . (15.158) It has the roots \u03d51 = 0 , \u03d52 = \u03d50 = 45\u25e6 and cos[\u03d53(\u03bb)] = 1 2 \u221a \u03bb\u2212 2 . The associated stationary values are \u03bes1(\u03bb) = 2 + \u03bb , \u03bes2(\u03bb) = 2 \u221a 2 + \u221a \u03bb2 \u2212 8 , \u03bes3(\u03bb) = 4 \u221a \u03bb\u2212 2 . (15.159) As in the case n = 3 , the optimal ratio \u03bb0 is identical with \u03bb2 . The smallest difference between the maximum and the minimum of \u03be(\u03bb, \u03d5) is \u03bes2(\u03bb0)\u2212 \u03bes3(\u03bb0) \u2248 0.040 . What follows next, is valid again for the general case with n \u2265 3 (integer). The pole P10 in Fig. 15.40 lies on the line AB if the points A , B and P10 satisfy the condition (xB\u2212xA)(y10\u2212yA)+yA(x10\u2212xA) = 0 . The coordinates in this equation are x10 = nr cos\u03d5 , y10 = nr sin\u03d5 and xA, yA , xB = r\u03be from (15.138) and (15.139). Substitution of these expressions yields, surprisingly, Eq.(15.146) again. This identity has to be interpreted as follows. At \u03d5 = 0 and also at \u03d5 = \u03d50 P10 lies on the line AB independent of the value of \u03bb . In the interval \u2212\u03d50 \u2264 \u03d5 \u2264 +\u03d50 P10 lies on the line AB independent of \u03d5 if \u03bb has the optimal value \u03bb0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.14-1.png",
        "caption": "Fig. 15.14 Planetary gear (a) , velocity diagram (b) and angular velocity diagram (c)",
        "texts": [
            " Examples: The center P20 is the intersection of the lines P62P60 = EP60 and P10P21 = AB . The center P30 is the intersection of the lines E\u2032P70 and AB\u2032 . The center P23 is the intersection of the lines P20P30 and P21P31 = BB\u2032 . Example 8 : Kutzbach\u2019s angular velocity diagram for spur gears In spur gears all bodies move in one common plane. All axes of gear wheels and also all pitch points are instantaneous centers of rotation. Since the distances of these points are constant, also all angular velocity ratios are constant. The planetary gear shown in Fig. 15.14a is used as illustrative example for explaining Kutzbach\u2019s general-purpose method for determining angular velocities [22]. The gear consists of the stationary frame 0 , the pinion cage 1 and gear wheels 2 , 3 and 4 . The degree of freedom is one. A single, arbitrary angular velocity is prescribed, for example, \u03c910 (pinion cage 1 relative to the frame). To be determined are all angular velocities \u03c9ij (i, j = 0, . . . , 4 ; i = j ). Solution: The instantaneous centers P30 , P32 and P24 in Fig. 15.14a are pitch points, and the centers P31 , P21 , P10 and P40 are located on wheel axes. From these centers lines parallel to the axes are drawn thus creating the r, v-velocity diagram in Fig. 15.14b . This velocity diagram consists of straight lines i = 0, . . . , 4 . Definition: The line i is the graph of the function vi(r) . This function determines the velocity (relative to body 0 ) of the point fixed on body i at the radius r from the center line. The line 0 for the frame and the line v1(r) = \u03c910r for the pinion cage 1 are given by the problem statement. These lines are drawn first (with arbitrary scale). Wheel 3 has at the radius of P30 the same velocity body 0 has, and at the radius of P31 the same velocity body 1 has. Through these two points the line 3 470 15 Plane Motion is determined. Subsequently, the lines 2 and 4 are determined in the same way. The diagram in Fig. 15.14c is the angular velocity diagram. It is constructed by drawing, from a point on the center line, lines parallel to all lines in the velocity diagram. These lines have the equations vi(r) = \u03c9i0r . The function values at an arbitrarily chosen radius r = r0 are \u03c9i0r0 . Thus, these values together with the scale chosen for the prescribed angular velocity \u03c910 determine the directions and magnitudes of all other angular velocities \u03c9i0 (i = 1 . . . , 4). With these velocities also all relative angular velocities \u03c9ij = \u03c9i0 \u2212 \u03c9j0 (i, j = 1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003293_s40430-020-02645-3-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003293_s40430-020-02645-3-Figure4-1.png",
        "caption": "Fig. 4 Robot model",
        "texts": [
            " Two motors were used at the rear of the line following robot to take corrective action based on the error signal. Therefore, pulse width modulated (PWM) signals were provided to control the motors and the right or left wheel was span to move the robot forward or to change the direction of the robot. Power input was made with 11.1\u00a0V 2100 mAh lipo battery. DC to DC step down converter was used to adjust the voltage (Fig.\u00a03). On the other hand, before starting experiment, the mathematical model is derived and simulated on computer using the model in Fig.\u00a04. The mathematical model of the line following robot is shown in equations below, and the experimental line following robot was run afterwards. The parameters used in simulation, the list of electronic components Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:561 1 3 561 Page 6 of 13 and Arduino connection pins are given in the \u201cAppendices A1 and A2\u201d. Iz is the total inertia, \u03b1 is the angle between vertical global y axis and the direction of robot displacement p, whereas mt is the total mass of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002147_lra.2016.2528293-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002147_lra.2016.2528293-Figure1-1.png",
        "caption": "Fig. 1. unicycle model of a beveled-tip needle.",
        "texts": [
            " Section II presents a review of the unicycle model and introduces the controller structure. In section III the stability of the system and convergence of the error is discussed and the parameter constraints are derived. In section IV the proposed method is experimentally validated and the results are presented. Section V gives a comparison of the proposed method and other methods in the literature. The kinematics of a bevel tip needle inserted into soft tissue can be expressed using the kinematics of a unicycle moving on a circular path in plane [17] as shown in Fig. 1 : z\u0307 = v cos \u03b8 (1) y\u0307 = v sin \u03b8 (2) \u03b8\u0307 = kv (3) Here \u02d9(.) denotes the time derivative and z and y represent the position of the needle tip in the (y\u2212 z) plane (the insertion direction is z and the orthogonal direction is y, respectively). \u03b8 \u2208 [\u2212\u03c0/2, \u03c0/2] gives the needle tip angle found as the anglebetween the z-axis of the moving frame {B} attached to the needle tip and the z-axis of the fixed frame {A}. v is the constant insertion velocity and k denotes the needle path curvature. For a planar motion, k can be written as \u00b1k0 with k0 > 0 where \u00b1 determines the orientation of the bevel tip, which specifies the concavity of the needle path curve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.4-1.png",
        "caption": "Figure 2.4. Complete balancing using counterweights",
        "texts": [
            ",,1,6 iymD icili 6 1 13 1 i iu ic iup l l mmD 6 1 14 1 i iu ic iiupp l l amxmD 6 1 15 1 i iu ic iiupp l l bmymD 6 1 16 1 i iu ic iiupp l l cmzmD In the above expressions for rx, ry and rz, if the coefficients of the joint and Cartesian variables vanish, then the global centre of mass of the mechanism will be fixed for any configuration of the mechanism. Hence, one obtains sufficient conditions for static balancing as follows .16...,,1,0 iDi (2.29) An example of balanced mechanism is represented schematically in Figure 2.4. As discussed above, gravity compensation can be obtained without necessarily imposing force balancing by using elastic components to store potential energy. To this end, Equation (2.7) can be used. As an example, the gravity compensation of a 6-dof parallel mechanism is now presented. In this architecture, each of the legs is mounted on a passive revolute joint having a vertical axis of rotation, as shown in Figure 2.5. The leg itself is a planar mechanism with a parallelogram ABCD, a distal link CPi and a spherical joint at point Pi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.10-1.png",
        "caption": "Figure 5.10. Gravitational field strength g(X) due to the mass point mo.",
        "texts": [
            " The Gravitational Field of a Particle A gravitational field fl is said to exist in all of space due to the mass m; whenever a force of attraction is felt by another \"test\" particle placed anywhere in fl. Hence , m; is named the origin , or source, of the gravitational field. The attractive force due to m.; per unit mass of the test particle , is called the strength of the field fl. Let g(X) denote the field strength at X. Then, in accordance with (5.46), Gm; g(X) = --e, r2 (5.47) where e is the unit vector directed from the source m; to the field point X whose distance from m; is r, as shown in Fig. 5.10. Since g is the gravitational force that a particle of unit mass will experience when placed at X in \u00a7, the gravitational force F( P;X) exerted on a particle P of mass m at X is given by F(P ;X) =m(P)g(X). (5.48) The Foundation Principles of Classical Mechanics 35 Alternatively, with (5.47), F(P ;X) = -Gmome/r 2, which is the same as (5.46) . Observe again that the gravitational force is independent of the reference frame that may be used to identify the place X. 5.6.2. The Gravitational Field of a System of Particles The law of gravitation (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002160_icra.2016.7487629-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002160_icra.2016.7487629-Figure3-1.png",
        "caption": "Figure 3. Components of the TriCal\u2019s measuring device.",
        "texts": [
            " The main purpose of TriCal is to accurately position the device\u2019s TCP at the center of a sphere. 1) The measuring device The TriCal\u2019s measuring device is mounted on the robot via a tool changer. The mass of the TriCal\u2019s measuring device is 1.7 kg (including all parts attached to the robot flange) with a position of center of gravity that meets ABB\u2019s load specifications. The TriCal includes three Mitutoyo ID-C112XB indicators, which each have a resolution of 0.001 mm. These indicators are fixed, orthonormal to each other to a custom co- nical fixture (Fig. 3). A Mitutoyo U-WAVE-T wireless transmitter, attached on the back of each indicator, sends collected data to a Mitutoyo U-WAVE-R receiver, which is connected to a PC via a USB cable. On the TriCal\u2019s conical fixture, three 0.5-inch precision balls are temporarily attached to the magnetic nests, for the purpose of zeroing the device. These balls are called kinematic coupling spheres, and they are used to constrain the three dial indicators on the center sphere of the calibrator, as shown in Fig. 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003012_rpj-03-2019-0090-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003012_rpj-03-2019-0090-Figure12-1.png",
        "caption": "Figure 12 A 3D scanned die (12a) and its octree (12 b)",
        "texts": [
            " For example, an octree of depth 11[14] takes around a minute to compute[15] if the analyzed mesh has less than 200,000 triangles. The 3D scan process returns a very dense mesh, with millions of facets. Thus, a trade-off between resolution and computational load needs to be achieved. For these reasons, timings and effort can vary significantly from case to case. For example, the computation of the octree of a 3D scan with 867,911 facets requires 51 s resulting in 8 million leaves. The result of this test is visible in Figure 12. When both octrees (representing nominal and damaged geometry) are available, DUOADD can proceed by computing the Boolean difference. That process lasts a few seconds only, as only recursive iteration over the two tree structures is needed. Starting from the two octree roots, one has to check where the corresponding nodes are either both inside or both outside, while nodes that do not satisfy the comparison will be marked as \u201cdifference\u201d in the resulting octree. Listing (1) proposes a possible implementation of the algorithm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000741_s11668-010-9395-y-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000741_s11668-010-9395-y-Figure2-1.png",
        "caption": "Fig. 2 Effect of initial crack orientation on predicted crack propagation path",
        "texts": [
            "fr crack growth and gear life predictions have been investigated [8, 9]. In addition, gear crack trajectory predictions have been addressed in a few studies [10\u201313]. The phenomenon of gear tooth crack propagation has, amply, been the center of interest for much research concerning the mechanical and dynamic behaviors of gears. Some analytic and experimental studies have determined the direction of the gear tooth crack propagation. Lewicki et al. [14, 15] studied, numerically (Fig. 1) and experimentally (Fig. 2), how to validate predicted results by considering the gear body rim thickness and gear speed effects on the crack propagation angle when the crack occurs in a gear tooth foot. This study used the Finite Element computer programs FRANC (Fracture Analysis Code) to determine stress distributions and mode I crack propagation. The program predicts the direction in which a crack will grow, whether through the gear tooth or through the rim. Linear elastic fracture analysis was used to analyze gear tooth bending fatigue in standard and thin-rim gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003329_j.mechmachtheory.2019.103753-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003329_j.mechmachtheory.2019.103753-Figure7-1.png",
        "caption": "Fig. 7. The geometric diagram of Bricard-like mechanism.",
        "texts": [
            " The axes of revolute joints S 1 , S 3 , and S 5 of this Bricard-like mechanism are either intersecting or parallel during the movement, and the axes of revolute joints S 2 , S 4 , and S 6 of this Bricard-like mechanism are also either intersecting or parallel during the movement. Obvious, the six axes can be divided into four cases, however, this mechanism does not exist when the axes S 1 //S 3 //S 5 and S 2 //S 4 //S 6 . Only the following three cases are available. Case 1: when the axes of revolute joints S 2 , S 4 , and S 6 intersect at one point and the axes of revolute joints S 1 , S 3 , and S 5 also intersect at one point. As shown in Fig. 7 , point S is the intersection point of lines AD and CB, and the points E, F, and S are on the same straight line. Suppose the lengths of the links and the angles of BAD, BCD, FAD, FED, FCB, and FEB are as follows: AD = BC = EF = l, AB = DC = l 1 , AF = DE = l 2 , CF = BE = l 3 (13) \u2220 BAD = \u2220 BCD = \u03b8A 1 , \u2220 FAD = \u2220 FED = \u03b8A 2 , \u2220 FCB = \u2220 FEB = \u03b8A 3 (14) Let the dihedral angles of the faces ADBC and ADFE be \u03b2 . A coordinate system is established, o ( x, y, z ) is set to the point A, the x -axis is set along the axis of revolute joint S , the y -axis is set along the line that is perpendicular to the x -axis 3 and in the plane ABCD, and the z -axis can be obtained according to the right-hand rule as shown in Fig. 7 . Therefore, the coordinates of points E and F can be obtained E = ( (l \u2212 l 2 cos \u03b8A 2 )( l 2 \u2212 l 2 2 ) ( l 2 + l 2 2 ) \u2212 2 l l 2 cos \u03b8A 2 , l 2 (l 2 2 \u2212 l 2 ) sin \u03b8A 2 ( l 2 + l 2 2 ) \u2212 2 l l 2 cos \u03b8A 2 cos \u03b2, l 2 (l 2 2 \u2212 l 2 ) sin \u03b8A 2 ( l 2 + l 2 2 ) \u2212 2 l l 2 cos \u03b8A 2 sin \u03b2 ) (15) F = ( l 2 cos \u03b8A 2 , l 2 sin \u03b8A 2 cos \u03b2, l 2 sin \u03b8A 2 sin \u03b2) (16) Moreover, the coordinates of S can be calculated as S = ( l 2 \u2212 l 2 1 2 l \u2212 2 l 1 cos \u03b8A 1 , 0 , 0 ) (17) According to the coordinates of points E, F and S, which are on a same straight line, we can obtain the equation of \u03b8A 2 with respect to \u03b8A 1 as follows: cos \u03b8A 2 = l ( \u2212l 2 1 + l 2 2 ) + l 1 ( l 2 \u2212 l 2 2 ) cos \u03b8A 1 ( l 2 \u2212 l 2 1 ) l 2 (18) Similarly, the relationship between \u03b8A 1 and \u03b8A 3 can be obtained as follows: cos \u03b8A 3 = l ( \u2212l 2 1 + l 2 3 ) + l 1 ( l 2 \u2212 l 2 3 ) cos \u03b8A 1 ( l 2 \u2212 l 2 1 ) l 3 (19) Substituting Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003702_j.euromechsol.2021.104229-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003702_j.euromechsol.2021.104229-Figure1-1.png",
        "caption": "Fig. 1. Schematics of the spur gear transmission system with idler.",
        "texts": [
            " In section 4, one of the unstable periodic orbits embedded in the chaotic attractors is found by an efficient algorithm. In section 5 based on SMC and ASMC, the control solution for eliminating the chaotic vibration problem is presented and numerical simulations are used to illustrate the effectiveness of the control method. Finally, a brief conclusion is drawn in section 6. In this section, a dynamic model of spur gear transmission system with idler is established and the equations of motion are extracted. Fig. 1 presents the schematics of the system under investigation, which consists of three gears forming two gear meshes. For simplicity, only the torsional motion of the gears is considered and the centers of three gears are aligned. In this model, meshing gears are represented by their base circles with radius ra, rb and rc. The variables \u03b8a, \u03b8band \u03b8crepresent angles of each gear, and \u03c9a, \u03c9band \u03c9crepresent angular velocities. External excitations are represented by Ta and Tc. The interaction between gear and idler (gear (a) and gear (b)) and the interaction between idler and pinion (gear (b) and gear (c)) are modeled by two spring damper sets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000963_robot.2010.5509785-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000963_robot.2010.5509785-Figure3-1.png",
        "caption": "Fig. 3. Transition between ankle and hip strategies.",
        "texts": [],
        "surrounding_texts": [
            "Consider the displacement of the CoM during the two strategies. As seen from Fig. 2 (a), during the ankle strategy, the CoM is displaced in a way that its ground projection rx remains within the base of support (BoS). On the other hand, during the hip strategy, the CoM is displaced only in the vertical direction, whereas its ground projection remains stationary (cf. Fig. 2 (b)). The aim of the transition between the ankle and the hip strategy is to ensure that, in addition to hip motion initialization, the CoM ground projection will also move back swiftly to the position of the erected posture, after reaching the BoS boundary during the ankle strategy. In order to ensure such movement of the CoM, we have to consider the CoM velocity: r\u0307 = Jc\u03b8\u0307, (17) where Jc \u2208 2\u00d72 denotes the CoM Jacobian matrix. This equation is projected onto the x axis: r\u0307x = Jcx\u03b8\u0307. (18) Note that matrix Jcx \u2208 1\u00d72 is related to the coupling inertia matrix: Jcx = 1 m Hfl. (19) From the model, it is straightforward to obtain: Jcx = [ rz kmlg2C12 ] , (20) where km = m2/m. Hence, the solution to (18) can be written as: \u03b8\u0307 = J# cxr\u0307x + bn. (21) Henceforth, we will use the pseudoinverse as a generalized inverse."
        ]
    },
    {
        "image_filename": "designv10_12_0002603_j.ifacol.2018.11.560-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002603_j.ifacol.2018.11.560-Figure1-1.png",
        "caption": "Fig. 1. The hexarotor and the reference frames.",
        "texts": [
            " Part III analyses the controllability of the hexarotor in case of actuators failures and ends with a controllability table. Part IV is dedicated to develop the proposed system recovery algorithm. Real outdoor experimental validation of the results are shown in V, and finally part VI is reserved for conclusion and perspectives. 2. HEXAROTOR DYNAMICS AND CONTROL STRATEGY The hexarotor is an under-actuated system with six-degrees of freedom and only four inputs. It consists of six motors on which propellers are fixed. They are attached at the ends of arms under a symmetric body frame as shown in Fig. 1. Its dynamic model is similar to the quadrotor UAV model as follows: \ud835\udc65\ud835\udc65 = \ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc5c\ud835\udc60\ud835\udc60\ud835\udf11\ud835\udf11\ud835\udc60\ud835\udc60\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b\ud835\udf03\ud835\udf03\ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc5c\ud835\udc60\ud835\udc60\u0471 + \ud835\udc60\ud835\udc60\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b\ud835\udf11\ud835\udf11\ud835\udc60\ud835\udc60\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b\u0471 \u2217 \ud835\udc62\ud835\udc62\ud835\udc53\ud835\udc53 \ud835\udc5a\ud835\udc5a \ud835\udc66\ud835\udc66 = \ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc5c\ud835\udc60\ud835\udc60\ud835\udf11\ud835\udf11\ud835\udc60\ud835\udc60\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b\ud835\udf03\ud835\udf03\ud835\udc60\ud835\udc60\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b\u0471 \u2212 \ud835\udc60\ud835\udc60\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b\ud835\udf11\ud835\udf11\ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc5c\ud835\udc60\ud835\udc60\u0471 \u2217 \ud835\udc62\ud835\udc62\ud835\udc53\ud835\udc53 \ud835\udc5a\ud835\udc5a \ud835\udc67\ud835\udc67 = \ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc5c\ud835\udc60\ud835\udc60\ud835\udf11\ud835\udf11\ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc5c\ud835\udc60\ud835\udc60\ud835\udf03\ud835\udf03 \u2217 \ud835\udc62\ud835\udc62\ud835\udc53\ud835\udc53 \ud835\udc5a\ud835\udc5a \u2212 \ud835\udc54\ud835\udc54 \ud835\udc5d\ud835\udc5d = (\ud835\udc3c\ud835\udc3c\ud835\udc66\ud835\udc66\ud835\udc66\ud835\udc66\u2212\ud835\udc3c\ud835\udc3c\ud835\udc67\ud835\udc67\ud835\udc67\ud835\udc67) \ud835\udc3c\ud835\udc3c\ud835\udc65\ud835\udc65\ud835\udc65\ud835\udc65 \ud835\udc5e\ud835\udc5e\ud835\udc5f\ud835\udc5f \u2212 \ud835\udc3d\ud835\udc3d\ud835\udc5f\ud835\udc5f \ud835\udc3c\ud835\udc3c\ud835\udc65\ud835\udc65\ud835\udc65\ud835\udc65 \ud835\udc5e\ud835\udc5e\ud835\udefa\ud835\udefa + \ud835\udf0f\ud835\udf0f\ud835\udf11\ud835\udf11 \ud835\udc3c\ud835\udc3c\ud835\udc65\ud835\udc65\ud835\udc65\ud835\udc65 \ud835\udc5e\ud835\udc5e = (\ud835\udc3c\ud835\udc3c\ud835\udc67\ud835\udc67\ud835\udc67\ud835\udc67\u2212\ud835\udc3c\ud835\udc3c\ud835\udc65\ud835\udc65\ud835\udc65\ud835\udc65) \ud835\udc3c\ud835\udc3c\ud835\udc65\ud835\udc65\ud835\udc65\ud835\udc65 \ud835\udc5d\ud835\udc5d\ud835\udc5f\ud835\udc5f + \ud835\udc3d\ud835\udc3d\ud835\udc5f\ud835\udc5f \ud835\udc3c\ud835\udc3c\ud835\udc66\ud835\udc66\ud835\udc66\ud835\udc66 \ud835\udc5d\ud835\udc5d\ud835\udefa\ud835\udefa + \ud835\udf0f\ud835\udf0f\ud835\udf03\ud835\udf03 \ud835\udc3c\ud835\udc3c\ud835\udc66\ud835\udc66\ud835\udc66\ud835\udc66 \ud835\udc5f\ud835\udc5f = (\ud835\udc3c\ud835\udc3c\ud835\udc65\ud835\udc65\ud835\udc65\ud835\udc65\u2212\ud835\udc3c\ud835\udc3c\ud835\udc66\ud835\udc66\ud835\udc66\ud835\udc66) \ud835\udc3c\ud835\udc3c\ud835\udc67\ud835\udc67\ud835\udc67\ud835\udc67 \ud835\udc5d\ud835\udc5d\ud835\udc5e\ud835\udc5e + \ud835\udf0f\ud835\udf0f\u0471 \ud835\udc3c\ud835\udc3c\ud835\udc67\ud835\udc67\ud835\udc67\ud835\udc67 (1) x, y and z are defined as the coordinates of the UAV\u2019s center of gravity in the fixed earth frame, and \u03c6, \u03b8 and \u03c8 are the Euler angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003190_j.ijheatmasstransfer.2020.119536-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003190_j.ijheatmasstransfer.2020.119536-Figure2-1.png",
        "caption": "Fig. 2. Geometry and domain composition of the numerical model.",
        "texts": [
            " In the record of the high-temperature distribuion, the emissivity of metal materials significantly affects the meaurement accuracy. Therefore, for emissivity calibration, the meaurements obtained by the infrared thermal imaging camera are ompared with the measurements detected by thermocouples. The missivity is set to 0.6 based on the comparisons and empirical alue provided in Flir user\u2019s guide. . Numerical model .1. Physical model A numerical model coupled with electromagnetic and temperture fields is developed with COMSOL Multiphysics. Fig. 2 shows he geometry and calculation domains of the numerical model. The umerical model is composed of five calculating domains, namely, ir, induction coil, metal wire, deposited layer, and substrate. The ir domain is further divided into five subdomains (i.e., Air 1 \u2013Air 5 ) nd is supposed to be an auxiliary approach to realize relative moion between the substrate and metal wire. As shown in Fig. 2 , the metal wire is included in the numerical odel, unlike in previous numerical studies on laser and arc depoition with wires. Nie et al. [21] investigated the temperature varition during laser wire additive manufacturing, and the metal wire m p a t c f m 1 w m t t m a d r 3 d w s r m b n i was excluded in the numerical model. Bai et al. [22] simulated the temperature distribution during wire arc additive manufacturing on the basis of a numerical model and also ignored the metal wire. An approach that ignores the metal wire in the numerical model is suitable for laser and arc deposition methods",
            " Given the consistency between the numerical model and experimental condition, the metal wire is included in the present numerical model. Hascoet et al. [16] simulated the heat transfer in the deposition process with high frequency induction heat, and the metal transfer behavior was simplified as the temperature movement from the metal wire tip to the deposited layer. For calculation simplification, the metal transfer behavior in our numerical simulation is also simplified by the temperature movement. The metal wire in this study is in contact with the deposited layer, as shown in Fig. 2 . The total size of the numerical model is 65 \u00d7 mm 30 \u00d7 mm 20 \u00d7 mm , and the specific dimensions of the domains in this l odel are listed in Table 2 . The cross-section dimensions of the de- osited layer are set according to the experimental samples. A tringle mesh is utilized to discretize the numerical model, and the otal number of mesh elements is 1.5 \u00d7 10 5 . In consideration of alculation efficiency and accuracy, the meshing size varies in diferent domains. As shown in Fig. 3 , domain Air 3 -Air 5 are coarsely eshed, while domain Air 1 is meshed with a small element size of mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000228_0378-3804(82)90017-1-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000228_0378-3804(82)90017-1-Figure1-1.png",
        "caption": "Fig. 1. Dimensions of (a) workpiece, (b) workpiece grooving, and (c) anvil grooving.",
        "texts": [],
        "surrounding_texts": [
            "From a practical point of view, predictions of upsetting pressures and determination of f low stress are of greatest importance."
        ]
    },
    {
        "image_filename": "designv10_12_0000421_cec.2007.4424647-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000421_cec.2007.4424647-Figure8-1.png",
        "caption": "Fig. 8. Degrees of freedom for the organism when working in different configurations. (a) 1 DOF when robots are assembled by using only the back connector; (b) 3 DOF when using one rotational connector; (c) 5 DOF when using two rotational connectors.",
        "texts": [
            " 7(c), or they create only some autonomous parts of the organism. When robots are docked, they start electrical and logical processes of integration in the organism. After that organism starts its own locomotion (e.g. stands up) and starts its own \u2019life\u2019 as an organism, see Fig. 7(d). 2007 IEEE Congress on Evolutionary Computation (CEC 2007) 1487 2. Individual and collective degrees of freedom. We are interested whether the chosen individual degrees of freedom (DOF) allow enough collective DOF for the organism. In Fig. 8 we demonstrate a few configurations of the organism and appeared DOF. Generally, we can say that each connection to the rotational connector increase DOF by one. Using different rotational connectors, the organism can obtain different vertical, horizontal and rotational DOF. Combining several DOF, the organism can demonstrate different locomotion principles, as shown in Fig. 9: - Wheeled Motion. The most simple locomotion principle is using its own wheels, as shown in Fig. 7(a),(b). In this stage robots are alone (robot swarm scenario) or have small two-, three robots conciliations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001851_gt2016-56084-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001851_gt2016-56084-Figure7-1.png",
        "caption": "Figure 7. A blade with a transverse CS (# IV.1).",
        "texts": [
            " The thickness of the walls in the area of the trailing edge, as well as gap between them, is 0.35 mm. 3 Copyright \u00a9 2016 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/89507/ on 04/07/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Inspection by 3D tomography and 3D laser scanning was performed in order to check the quality of the blade # IV produced by SLM (particularly the interior parts). Figure 9 shows the tomographic images of some blade sections shown in Figure 7. Results show good geometrical correlation between the CAD-model and the blade produced by SLM (checking was performed by overlapping the scanned data on the CAD-model and by verifying the numerical deviations). However, there were few internal waste support structures (shown as S in Fig.9). To avoid such structures interior CS was slightly modified and maximum unsupported overhang angle was decreased [12]. Afterwards, the blade was redesigned in order to increase cooling effectiveness (Fig. 14)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001772_1.4027166-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001772_1.4027166-Figure1-1.png",
        "caption": "Fig. 1 Surface parameters of the standard rack cutter",
        "texts": [
            " To obtain the anti-twist helical gear tooth flank with longitudinal crowning, this study proposes a nonlinear function of additional rotation angle for the helical gear in its hobbing process. Two numeral examples are presented to illustrate and verify the merits of the proposed gear hobbing method in longitudinal tooth crowning of helical gears with the anti-twist gear tooth flank. The profile of the generating surface of the hob is the same as that of the standard helical gear. Assume that the helical gear is generated by a standard rack cutter, a schematic standard rack cutter is shown in Fig. 1, while the generation mechanism of standard involute helical gear is shown in Fig. 2, where the coordinate 1Corresponding author. Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 8, 2013; final manuscript received February 27, 2014; published online April 17, 2014. Assoc. Editor: Zhang-Hua Fong. Journal of Mechanical Design JUNE 2014, Vol. 136 / 061007-1Copyright VC 2014 by ASME Downloaded From: http://mechanicaldesign",
            " The generated gear rotates an angle w1 about the z4-axis, while the rack cutter translates a distance ro1w1 without rotation. Accordingly, the position vector and unit normal vector of the rack cutter\u2019s right-hand side profile can be expressed in coordinate system S7\u00f0x7; y7; z7\u00de as follows: r7 \u00bc \u00bdx7; y7; z7; 1 T \u00bc \u00bdu1 cos aon; u1 sin aon; v1; 1 T (1) and n7 \u00bc \u00bdnx7; ny7; nz7 T \u00bc \u00bdsin aon; cos aon; 0 T (2) where u1 and v1 are the surface parameters, and aon is the pressure angle of the standard rack cutter, as shown in Fig. 1. According to Fig. 2, by applying the homogenous coordinate transformation matrix equation, the locus and unit normal vectors of rack cutter surface represented in coordinate system S3\u00f0x3; y3; z3\u00de are attained by r3 \u00bcM37 r7 \u00bc cos w1 cos bo1 sin w1 sin bo1 sin w1 ro1\u00f0cos w1 \u00fe w1 sin w1\u00de sin w1 cos bo1 cos w1 sin bo1 cos w1 ro1\u00f0sin w1 \u00fe w1 cos w1\u00de 0 sin bo1 cos bo1 0 0 0 0 1 2 6666664 3 7777775 r7 (3) 061007-2 / Vol. 136, JUNE 2014 Transactions of the ASME Downloaded From: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.36-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.36-1.png",
        "caption": "Fig. 15.36 Generation of a two-cusped epicycloid by means of reflected light",
        "texts": [
            " The reason is that acceleration as well as curvature depend on first- and second-order derivatives of position vectors only, whereas the difference between curve and circle of curvature depends on higher-order derivatives. Thus, a0 is the acceleration produced by the rolling motion of the circle of curvature of k2 on the circle of curvature of k1 . This acceleration is taken from (15.127) in the chapter on cycloids. For the present purpose the notation has to be changed as follows. The radius r0 must be replaced by 1 , r1 by 2 and the angular velocity \u03d5\u03071 by \u03d5\u0307 . The 486 15 Plane Motion sign conventions remain unchanged. The positive real axis of Fig. 15.36 has the direction of en . With this change of notation 1 2 \u2212 1 1 = \u03d5\u03072 a0 = 1 y2 . (15.89) Comparison with (15.73) and (15.74) shows that the relationship between Mp 1 and Mp 2 is the same as the relationship between associated points M and Q on the line en . Equation (15.75) establishes between 1 , 2 and the radii R , r of any pair of associated points M and Q the relationship( 1 r \u2212 1 R ) sin\u03b1 = 1 2 \u2212 1 1 . (15.90) When 1 and 2 are known, this equation determines the center of curvature M for every point Q in the entire plane",
            "131) Comparison with (15.130) shows that this is the rotation angle of a wheel with radius 2r1 instead of r1 rolling on the same sunwheel 0 . In the figure this wheel is shown in the position \u03b1 as dashed line. The tangent t is a diameter fixed on this wheel. These results are summarized in 15.5 Trochoids 505 Theorem 15.8. A cycloid generated as point trajectory in a system r0, r1 is enveloped by a diameter fixed on the planetary wheel in the system r0, 2r1 Consider the special case r0 = \u22122r1 shown in Fig. 15.36. The circle of vertices has the radius R = 2|r0| . The epicycloid has two cusps. From Fig. 15.35 the general formula \u03b2 = (P10P \u2217 12C)= 1 2\u03c0\u2212 1 2 (\u03d51\u2212\u03d52) is known. In the special case under consideration, this becomes \u03b2 = 1 2\u03c0\u2212\u03d52 . In Fig. 15.36 it is seen that \u03b2 is also the angle between the line P20P \u2217 12 and the perpendicular s to the line P20C0 . A light beam having the direction of s is reflected on the circle of vertices in the direction of the tangent to the cycloid. This explains a phenomenon which can be observed in a cup of coffee in early-morning sunshine. Parallel sun rays are reflected on the inner wall of the cup (circle of vertices of radius R ). The reflected rays envelope an epicycloid with two cusps on the circle of radius R/2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001817_physreve.91.012403-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001817_physreve.91.012403-Figure1-1.png",
        "caption": "FIG. 1. (Color online) (a) Cylindrical core-shell model. The surface pattern is characterized by two mode numbers mcrit and ncrit, and the circumferential and axial wavelengths are given by 1 = 2\u03c0R/mcrit and 2 = 2\u03c0/ncrit, respectively. (b) Schematic of the volumetric tissue growth configurations.",
        "texts": [
            " The geometric and material conditions are discussed for the occurrence of square and hexagonal patterns observed in experiments. The transition between different patterns is also revealed from the viewpoint of energy. Finally, the main conclusions derived from this study are summarized in Sec. VII. 1539-3755/2015/91(1)/012403(8) 012403-1 \u00a92015 American Physical Society To analyze the buckling and postbuckling behavior of a soft core-shell cylinder, a 3D model is established within the framework of finite elasticity as shown in Fig. 1. Refer to the cylindrical coordinate system X = (R, ,Z) for the initial undeformed configuration and x = (r,\u03b8,z) for the current configuration. Assume that only the shell grows, but the conclusions can be extended to more general cases where both the shell and the core grow. Due to the constraint effect of the soft core, the growth of the shell will lead to residual stresses in the composite system. The volumetric growth model originally established for biological tissues [28,29] is invoked to describe this mechanism",
            " The stresses in the core (0 R A) are \u03c3 c rr = \u03bccg 2 3c\u03b1 \u22122 \u2212 pc, \u03c3 c \u03b8\u03b8 = \u03bcc\u03b1 2 \u2212 pc, (13) \u03c3 c zz = \u03bccg \u22122 3c \u2212 pc, where pc = pin + C4, pin = Jc\u03bcc 2 [ \u2212 C1 g2 1cr 2 + 2 ln(r) g2 1c \u2212 ln(r2 \u2212 C1) g2 2c ] , (14) C4 = ( \u03bccg 2 3c\u03b1 \u22122 \u2212 pin \u2212 \u03c3 s rr )\u2223\u2223 R=A . In this section, we use the incremental deformation theory [12,29] to analyze the wrinkling behavior of the core-shell soft tissue. With growth and deformation, the incremental form of a line element dx in the current configuration is (dx)\u2217 = F\u0307 \u00b7 dX, where dX represents the line element in the initial configuration. With respect to the current configuration, we can write (dx)\u2217 = F\u0307 \u00b7 dx, where F\u0307 = F\u0307 \u00b7 F and F\u0307 = \u2202 x\u0307/\u2202x [30] as shown in Fig. 1(b). Assuming that the growth is not influenced by the stresses or strains in the system, we have the incremental forms F\u0307 = A\u0307 \u00b7 G and A\u0307 = F\u0307 \u00b7 A. Introduce an incremental displacement field, x\u0307 = u(r,\u03b8,z)er + v(r,\u03b8,z)e\u03b8 + w(r,\u03b8,z)ez, (15) where the functions u, v, and w are incremental displacements; er , e\u03b8 , and ez are the unit base vectors in the radial, circumferential, and axial directions, respectively. The corresponding increment of the geometric deformation tensor F\u0307 is written as F\u0307 = \u23a1 \u23a2\u23a3 u,r u,\u03b8\u2212v r u,z v,r v,\u03b8+u r v,z w,r w,\u03b8 r w,z \u23a4 \u23a5\u23a6 , (16) where the comma denotes the partial differentiation",
            " (23) In the considered volumetric growth problem, the cylindrical surface may wrinkle both in the circumferential and in the axial directions. In this case, we assume the incremental displacement field x\u0307 and the incremental hydrostatic pressure p\u0307 in the following form: u(r,\u03b8,z) = U (r) cos(m\u03b8 ) cos(nz), v(r,\u03b8,z) = V (r) sin(m\u03b8 ) cos(nz), (24) w(r,\u03b8,z) = W (r) cos(m\u03b8 ) sin(nz), p\u0307(r,\u03b8,z) = P (r) cos(m\u03b8 ) cos(nz), where m and n are the wave numbers characterizing the wrinkling modes in the circumferential and axial directions, respectively (Fig. 1). When n = 0, the wrinkling pattern degenerates to that in Cao et al. [21]. In the case of m = 0, Eq. (24) represents the axial buckling mode explored by Vandiver and Goriely [22]. 012403-3 Substituting the incremental displacement mode (24) into Eqs. (17) and (21) gives g2 3r [ (g1rp \u2032 + 2g2g3\u03bc)\u03b12U \u2032 \u2212 g1r\u03b1 2P \u2032 + g1g 2 3\u03bc(rU \u2032\u2032 \u2212 U \u2032) ] + g1g 2 3p\u03b12(mrV \u2032 + nr2W \u2032 + r2U \u2032\u2032 + rU \u2032 \u2212 mV ) \u2212 2g1g 2 3\u03bcm\u03b14V \u2212 g1\u03b1 2 [ \u03bcg2 3(m2 + 1)\u03b12 + \u03bcn2r2 + g2 3p ] U = 0, (25) g1g 4 3\u03bcr(V \u2032 \u2212 rV \u2032\u2032) + g1g 2 3\u03bcm2\u03b14V + g1g 2 3mr\u03b12(p\u2032U \u2212 P ) + 2g1g 2 3\u03bcm\u03b14U + g1g 2 3r\u03b1 2p\u2032V + g1g 2 3\u03bc\u03b14V + g1\u03bcn2r2\u03b12V \u2212 2g2g 3 3\u03bcr\u03b12V \u2032+g1g 2 3mp\u03b12(mV + nrW + rU \u2032 + U ) = 0, (26) g1g 4 3\u03bcr(W \u2032 \u2212 rW \u2032\u2032) + g1g 2 3\u03bcm2\u03b14W + g1g 2 3nr2\u03b12p\u2032U \u2212 g1g 2 3nr2\u03b12P + g1\u03bcn2r2\u03b12W \u2212 2g2g 3 3\u03bcr\u03b12W \u2032 + g1g 2 3nrp\u03b12(mV + nrW + rU \u2032 + U ) = 0, (27) U + rU \u2032 + mV + nrW = 0, (28) where a prime denotes the differentiation with respect to r "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.11-1.png",
        "caption": "Fig. 13.11 Clemens coupling with three identical parallel chains RSR",
        "texts": [
            "4 Homokinetic Shaft Couplings 403 In the shaft couplings described in the previous section permanent symmetry of a five-d.o.f. chain with respect to plane \u03a3 is achieved by a central spherical joint S closing the chain. The same constraints that are exerted by the spherical joint S can be exerted by placing two additional five-d.o.f. chains parallel to the first one. For reasons of dynamic balancing and of simplicity of design three identical chains are placed at intervals of 120\u25e6. The so-called Clemens coupling shown schematically in Fig. 13.11 is derived from Fig. 4.11. The serial chain R1S2R2 of this coupling is placed three times in parallel. On each shaft the three revolute axes fixed on the shaft are placed 120\u25e6 apart. The three spherical joints are permanently in the bisecting plane \u03a3 . The shafts 1 and 2 in Fig. 13.12 are connected to the sides of the rigid isosceles triangle (01,C,02) of base length 2 and apex angle 2\u03b2 by two pairs of revolutes R1 , R2 and R3 , R4 . At 01 the axis of R1 intersects both shaft 1 and R2 orthogonally, and at 02 the axis of R4 intersects both shaft 2 and R3 orthogonally"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003342_1.g004710-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003342_1.g004710-Figure1-1.png",
        "caption": "Fig. 1 Quadrotor reference frames:I is the inertial frame,B is the body frame, andU is the wind frame. The flow probe is situated at pointP, and u1 is aligned with the horizontal component of the wind V\u221e.",
        "texts": [
            " MomentMthrust is due to propeller thrusts andMaero is the aerodynamic moment due to interaction between the rotors D ow nl oa de d by U N IV E R SI T Y O F C A M B R ID G E o n Fe br ua ry 6 , 2 02 0 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .G 00 47 10 and the wind. (The hat map \u2227 denotes the skew-symmetric matrix representation of the cross product, such that for any vectorsx andy in R3, x\u0302y x \u00d7 y. Thevee operator \u2228 extracts the corresponding vector in R3 from a skew-symmetric matrix.) The quadrotor vehicle is modeled as two perpendicular uniform beams of length l attached at their centers to create four arms, with one rotor located at the end of each arm, as in Fig. 1. Rotors are located at position db3 above each arm, where d \u226a l\u22152. The moment of inertia is J diagfmll2\u221512 2mml2; mll2 \u221512 2mml2; mll2\u22156 4mml2g. Rotors are assumed to spin about the b3 axis, with rotation directions shown in Fig. 1. This choice of rotor directions results in zero net torque in the b3 direction under nominal conditions with each rotor operating at the same speed and no outside aerodynamic forces. We position the multihole probe P above the quadrotor\u2019s center of massO 0 to reduce the effect of the vehicle drag and propeller inflow on the probe, and so we must account for the quadrotor\u2019s rotation when determining the wind velocity at O 0. The vector measured by the flow probe is Vprobe, the inertial wind velocity in body-frame components is V\u221e, the quadrotor translational velocity in body components is V, the location of the probe relative to the center of mass is Xprobe, and the contribution of the quadrotor rotational velocity is \u03a9\u0302Xprobe. The value measured by the probe is Vprobe V\u221e \u2212 V \u2212 \u03a9\u0302Xprobe (2) Let \u0394V\u221e V\u221e \u2212 V Vprobe \u03a9\u0302Xprobe denote the velocity of wind at the center of mass of the quadrotor. Define thewind reference frame U \u225c O 0; u1; u2; u3 , shown in Fig. 1, such that u1 describes the direction of the wind in the plane of the hub and u3 b3. Note that Eq. (2) assumes that the probe measures all three vector components of the wind in the body frame; in the experimental testbed, we measure only the b1 and b2 components. The position and attitude control architecture is shown in Fig. 2, with separate inner- and outer-loop controllers that are detailed below. A. Inner-Loop Attitude Control The feedback control design is based on the geometric controller developedbyLee et al",
            " (4), the attitude error dynamics become [35] _eR 1 2 trfRTRdgI \u2212 RTRd e\u03a9; _e\u03a9 \u2212kReR \u2212 k\u03a9e\u03a9 (17) which are exponentially stable according to Proposition 1 in [22]. Considering the inherent limitations of the motors and propellers, the thrust of each propeller is saturated above by some maximum thrust Tmax and below by zero, that is, 0 \u2264 Tj \u2264 Tmax; j 1; : : : ; 4. The following lemma is modified from [35] to reflect the \u201cX\u201d quadrotor configuration used in the experiment, with the forward direction along the b1 axis pointing between two rotors as in Fig. 1, rather than the \u201c \u201d configuration, with the forward direction b1 axis pointing toward one of the rotors. Lemma 1 [35]: Let T 0 min Tmax \u2212 T0; T0 > 0. We have Tj \u2264 Tmax, for all j 1; : : : ; 4, provided that j\u03bd1j j\u03bd2j j\u03bd3j \u2264 4T 0 (18) Proof (this proof is shown for T1, but may be adapted for the other propellers): From Eq. (18) we have \u22124T 0 \u2264 \u2212\u03bd1 \u03bd2 \u03bd3 \u2264 4T 0 (19) which implies \u2212T0 \u2264 1 4 \u2212\u03bd1 \u03bd2 \u03bd3 \u2264 Tmax \u2212 T0 (20) Rearranging Eq. (20) yields 0 \u2264 T0 1 4 \u2212\u03bd1 \u03bd2 \u03bd3 \u2264 Tmax (21) and substituting terms from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003759_09544062211016889-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003759_09544062211016889-Figure7-1.png",
        "caption": "Figure 7. Determination of the force Qj in the output mechanism.",
        "texts": [
            " The determined backlash Dj, shown in Figures 3 to 6 is the backlash resulting from the manufacturing of elements with deviations and the assembly of a trans- mission. During transmission operation, the backlash distribution on individual pins changes. In the work- ing gear, MK torque is generated on each of the planet wheels. It is assumed that an MK torque of an equal value acts on each planet wheel. This moment is bal- anced by the forces Qj occurring in the contact of the bushings with the holes of the planet wheel and which act on the rolling radii hj, as shown in Figure 7. It is assumed that after loading the mechanism with the moment MK, displacements dj occur at the places of force Qj, which result from the rotation of the planet wheel (considered as a rigid disc) by an angle Du with regards to the point O2, due to the deflection of the pins with the bushings and the defor- mations of the bushing in contact with the holes of the planet wheel (Figure 7). Then, the increase in dis- tance between the hole center of the Okj planet wheel and the hole center of the Otj bushing is:21 De \u00bc Otj 0Okj OtjOkj \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e\u00fe Rwk Du sinukj 2 \u00fe Rwk Du cosukj 2q e (11) The ingredient Rwk Du cosukj 2 assumes a small value, and can therefore be omitted, so: De \u00bc Rwk Du sinukj \u00bc hj Du (12) Each force occurring in the output mechanism Qj is a linear displacement function dj and is proportional to the force Qmax, which can be written as follows: Qj \u00bc Qmax hj hmax \u00bc Qmax dj dmax (13) where: hj \u2013 rolling radius; hmax \u2013 max",
            " On the other hand, negative values of backlash Djw also prove that in those places the force Qj is greater than zero and its value results from the value of displacement dj. In turn, for consecutive pins the backlash Djw is greater than zero. In view of this, there was no contact with the holes of the planet wheel, i.e. the backlash Dj (Figure 6) was not reduced to zero as a result of the deflection of the pins fj and the deformation of the bushing ddj. The moment MK is balanced by a flat system of forces Qj acting on hj rays (Figure 7): MK \u00bc X Qj hj \u00bc Qmax X dj Dj\u00f0 \u00de hj dmax (20) After transforming the expression (20), we get: Qmax \u00bc MK dmaxX dj Dj\u00f0 \u00de hj (21) Substituting the expression (21) to the expression (13) and after transformations one obtains: Qj \u00bc MK dj DjX dj Dj\u00f0 \u00de hj (22) In the case when dj Dj< 0, it is assumed that the bushing does not come into contact with the hole of the planet wheel in a given pair, i.e. Qj\u00bc 0 [N]. Based on expressions (22), (13), (14), (16) and (17) diagrams of the distribution of forces Qj in the output mechanism were built, which is shown in Figure 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure2.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure2.3-1.png",
        "caption": "FIGURE 2.3. Stresses in the plane perpendicular to r and z direction.",
        "texts": [
            " The following sections provide a succinct review of essential topics needed for the establishment of the governing elasto-dynamic equations. 2.1 State of Stresses at a Point A three dimensional state of stress in an infinitesimal cylindrical element is shown in the following three figures. Figure 2.1 depicts such an element with direct stresses, dimensions, and directions of the cylindrical coordinate. Figure 2.2 represents the direct and shear stresses in the radial and transverse directions (r and \u03b8), and the variation of direct and shear stresses in these two directions. Figure 2.3 shows direct and shear stresses associated with the planes perpendicular to the r and z directions, as well as their variations along these directions. In the above graphical representations the changes in direct and shear stresses are given by considering the first order infinitesimal term used in Taylor series approximation. The series approximation has been truncated after the second term. Further terms within the series representation contain terms of an infinitesimal length squared. Assuming that the second 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure3.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure3.1-1.png",
        "caption": "Fig. 3.1 Schematic of the spinning disc",
        "texts": [
            " The known publications contain the mathematical models for motions of the spinning disc that do not coincide practice [4\u201310]. Analysis of motions of the spinning thin disc demonstrates the centre mass and mass element of the rotating disc, whose locations and actions are different, generate several inertial forces. The analysis of the action of the inertial torques generated by the rotating masses is considered on the example of the thin spinning disc. The action of centrifugal forces on a disc rotating around axis oz with an angular velocity of \u03c9 in a counterclockwise direction is considered in Fig. 3.1. The disc\u2019s mass elements m are disposed on the circle of radius (2/3)R and rotate around axis oz with a constant tangential velocity. \u00a9 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 R. Usubamatov, Theory of Gyroscopic Effects for Rotating Objects, https://doi.org/10.1007/978-981-15-6475-8_3 33 The direction of the vector of tangential velocity changes continuously, i.e. the mass elements move with acceleration. The rotation of mass elements with acceleration generates the plane of centrifugal forces, which disposes of perpendicular to the axis of the spinning disc [6\u20139]",
            "12 \u00d7 3000\u00d72\u03c0 60 \u00d7 0.05\u00d72\u03c0 60 = 0.025469 Nm where all parameters are as specified above. A.2 Inertial Forces Acting on a Spinning Circular Cone A.2.1 Centrifugal Forces Acting on a Spinning Cone The inertial forces acting on of the spinning cone are generated by its centre mass and mass elements that distributed on the line forming the cone. In uniform circular motions, the rotation of mass elements generates the centrifugal forces, which act strictly perpendicular to the axis oz of the spinning cone (Fig. 3.1, Chap. 3). The action of an external torque on the spinning cone inclines the plane of the rotating centrifugal forces that resist the action of the external torque. The circular cone\u2019s mass elements m are located on the cone whose arbitrary radius is r and the length b, creating their rotating cone around axes oz. The analytical approach for the modelling of the action of the centrifugal forces generated by themass elements of the spinning cone is the same as represented for the spinning disc in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure9-1.png",
        "caption": "Fig. 9. Kinematic scheme of the HALF* parallel manipulator with prismatic actuators.",
        "texts": [
            " On the other hand, to decrease the operational failure, the demand on the parallelism of the C axes in the first and second legs should be very high. As mentioned in the last section, the kinematics of the new manipulators proposed in this paper will be simpler than that of the old manipulators introduced in ref. [13]. As an example, we here investigate the inverse kinematic problem of the HALF* parallel manipulator with prismatic actuators shown in Fig. 2(a). The kinematical scheme of the manipulator is shown in Fig. 9. Vertices of the mobile platform are denoted as platform joints Pi (i = 1, 2, 3); and central points of the three revolute joints attached to the sliders are denoted as Bi (i = 1, 2, 3). A fixed global reference frame O \u2212 xyz is located at the center point of the line segment ab with the z-axis normal to the plane abc and the y-axis directed along ab. Another reference frame, called the moving frame (O \u2032 \u2212 x \u2032y \u2032z\u2032), is located at the center of the side P1P2. The z\u2032-axis is perpendicular to the moving platform and the y \u2032-axis is directed along P1P2",
            " The kinematic problem of the manipulator can be solved by writing |bi pi | = BiPi. (3) Then, there are (R \u2212 r + y)2 + (z1 \u2212 z)2 = R2 2 (4) (R \u2212 r \u2212 y)2 + (z2 \u2212 z)2 = R2 2 (5) (z3 \u2212 z \u2212 L1 sin \u03c6)2 + (L3 \u2212 L1 cos \u03c6)2 = L2 2 (6) For a given pose (y, z, \u03c6), the inputs yi (i = 1, 2, 3) can be obtained as z1 = \u00b1 \u221a R2 2 \u2212 (R \u2212 r + y)2 + z (7) z2 = \u00b1 \u221a R2 2 \u2212 (R \u2212 r \u2212 y)2 + z (8) z3 = \u00b1 \u221a L2 2 \u2212 (L3 \u2212 L1 cos \u03c6)2 + z + L1 sin \u03c6 (9) Therefore, there are eight inverse kinematic solutions for the manipulator. The configuration shown in Fig. 9 corresponds to the solution when the \u201c\u00b1\u201d signs in Eqs. (7)\u2013(9) are all \u201c+\u201d. Observing the kinematic equations of the HALF and HALF* parallel manipulators, one may see that the kinematics of the HALF* manipulator is relatively simpler. Equations (4), (5), and (6) can be differentiated with respect to time to obtain the velocity equations, which can be written as \u03c1\u0307 = J p\u0307 (10) where p\u0307 is the vector of output velocities defined as p\u0307 = ( y\u0307 z\u0307 \u03c6\u0307 )T, \u03c1\u0307 is the vector of input velocities defined as \u03c1\u0307 = ( z\u03071 z\u03072 z\u03073 )T , and J is the Jacobian matrix of the manipulator that can be written as J = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 r \u2212 R \u2212 y z1 \u2212 z 1 0 r \u2212 R + y z2 \u2212 z 1 0 0 1 (z3 \u2212 z) L1 cos \u03c6 \u2212 L1L3 sin \u03c6 z3 \u2212 z \u2212 L1 sin \u03c6 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (11) For the configuration shown in Fig. 9, letting the \u201c\u00b1\u201d signs in Eqs. (7)\u2013(9) be \u201c+\u201d, the Jacobian matrix should be J = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 r \u2212 R \u2212 y\u221a R2 2 \u2212 (R \u2212 r + y)2 1 0 r \u2212 R + y\u221a R2 2 \u2212 (R \u2212 r \u2212 y)2 1 0 0 1 [ \u221a L2 2 \u2212 (L3 \u2212 L1 cos \u03c6)2 + L1 sin \u03c6] L1 cos \u03c6 \u2212 L1L3 sin \u03c6 \u221a L2 2 \u2212 (L3 \u2212 L1 cos \u03c6)2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (12) As most kinematic designs of parallel manipulators are based on the workspace and indices defined with respect to the Jacobian matrix, the information in the matrix is very important. From Eq. (12), we may see that there is no z parameter in the matrix, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002671_b978-0-12-814245-5.00029-3-Figure29.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002671_b978-0-12-814245-5.00029-3-Figure29.3-1.png",
        "caption": "FIGURE 29.3 Mechanisms for constructing steerable arthroscopic tools: (A) SMA-based [10]; (B) hinged-joint-based [11]; (C) lobed-feature-based [12]; (D) notched-tube-based [13]; (E) tube-and-slider-based [14]; and (F) spine-and-hinge-based [15] SMA, Shape-memory alloy.",
        "texts": [
            " In some operations in arthroscopy, the tools are used to exert some forces on the hard/ soft tissues inside the knee. In these applications, a good force transmission ability is necessary. This is, however, very challenging when the tools are made steerable. A compromising design should be taken for these situations where both the force transmission ability and the steerability are desired. To address these challenges, researchers have proposed different mechanisms. Some of the mechanisms that have been proposed for the steerable robotic arthroscopic tools are depicted in Fig. 29.3. Traditional serial-link robots have three structural components: links, joints, and motors. Links are the main body of a robot and are connected by joints; joints are actuatable mechanisms that can move the links they connect; motors are actuators that drive the motion of the joints. Steerable tools for arthroscopy usually do not have the same structures, but we can map their components to those of the serial-link robots by mimicking their functions. In this way, the mechanical structures of the prototypes shown in Fig. 29.3 can be summarized in Table 29.1. The characterization of the prototypes shown in Fig. 29.3 is also summarized in Table 29.1. As discussed previously, size, dexterity, and force transmission ability are three important factors for steerable arthroscopic tools. In Table 29.1, these factors are embodied by the diameter of the tool, the number of DoFs, and the applied force, respectively. Generally, most of the prototypes can be made as small as less than 6 mm in diameter. The prototype in Ref. [10] was slightly larger than the others, with a diameter of 8 mm. However, according to the authors, it could be reduced to 4 mm, which is rational considering the simplicity of the design",
            " 496 Handbook of Robotic and Image-Guided Surgery In terms of the dexterity, most designs chose to endow the device with only one bending DoF. Since the device is handheld, it naturally has four additional DoFs (three rotations and one translation) empowered by the motion of the hand. In consideration of this, one DoF at the tip is sufficient for some operations inside the joint. The prototype in Ref. [15] added another bending DoF to the proximal part of the tool and a pivoting DoF to the distal tip. The additional TABLE 29.1 Mechanical structure and characterization of the prototypes shown in Fig. 29.3. Fig. 29.3 Mechanical structure Characterization Links Joints Motors Diameter (mm) DoF Applied force A [10] Plastic disks Special arrangement of SMA wires SMA wires 8 1 1 N B [11] Disks and spines Hinges Cables 4.2 1 At least 1 N C [12] Disks and spines Lobed features Tendons 4.2 1 At least 3 N D [13] Two nested tubes Asymmetric notches on the tubes Cables 5.99 1 At least 1 N E [14] A distal link and two proximal tubes A hinge composed by two sliders Rotation of outer tube 5 1 Axial 100 N Lateral 20 N F [15] Disks and a central spine Space between disks and deformation of spine Cables 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure8-1.png",
        "caption": "Fig. 8. The surface responses of sensitivity change in X direction: (a) The influe",
        "texts": [
            " The addition of the bearing branches will reduce the sensitivity of the force sensing mechanism, and the structural parameters of the measuring branches will also have a certain impact on the sensitivity of the force sensing mechanism. In this paper, the configuration size of the force sensing mechanism is optimized with the sensitivity as the optimization objective to determine the final prototype size. Through the force loading of the mechanism in the X direction, the relationship between the configuration parameters and the equivalent index of the force sensitivity is shown in Fig. 8. From the figure, the smaller a, d, rs, b, the bigger h, D, the greater the sensitivity in X direction. In this paper, the six directional sensitivities of the six-component force sensing mechanism are optimized, and the final dimensional parameters are obtained based on the optimization results of each direction. Here, the Fx direction is taken as an example. Finally, the basic structure parameters of the force sensing mechanism are shown in Table 2. The material of the force sensing mechanism is titanium alloy (Ti6Al4V)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002948_s12206-019-0501-0-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002948_s12206-019-0501-0-Figure1-1.png",
        "caption": "Fig. 1. The schematic diagram of deep groove ball bearing.",
        "texts": [
            "1 Dynamic model of deep groove ball bearing In order to establish the kinematic equations, following hypotheses are made: (1) \u201cRigid ring hypothesis\u201d is adopted, namely, only the local elastic contact deformation between balls and raceways is considered, and the elastic-plastic deformation of the whole bearing rings is ignored. (2) The balls are in pure rolling on the bearing raceways. For deep groove ball bearing, the orbital angular velocity of steel balls is i c i i e D D D w w= \u00d7 + (1) where \u03c9i is the angular velocity of inner ring, Di and De are the groove bottom diameters of inner raceway and outer raceway, respectively. Without loss of generality, it is assumed that the outer ring of the bearing is rigid and fixed. As shown in Fig. 1, due to the radial force Fr, the center of inner ring has the displacements in both x and y directions. At any instant t, the displacement of inner race groove bottom at the azimuth angle \u03c6j can be written as cos sinj j jd x yj j= + (2) where \u03c6j is the azimuth angle of jth ball. Assuming that the bearing has a total of Z balls, \u03c6j can be written as ( )2 1 / .j cj Z tj p w= - + \u00d7 (3) Assume that the radial clearance of the bearing is u; then the elastic deformation between the jth ball and raceways at the azimuth angle \u03c6j is "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure2.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure2.1-1.png",
        "caption": "Fig. 2.1 Normal vector m of a plane. (a) The plane is not passing through the origin: |m| = 1/d ; (b) The plane is passing through the origin: |m| arbitrary",
        "texts": [
            " Wohlhart K (1992) Decomposition of a finite rotation into three consecutive rotations about given axes. 6th IFToMM Conf., Liberec:325\u2013332 Chapter 2 Line Geometry Line geometry was invented by Plu\u0308cker. The basic idea is to consider as elements of three-dimensional space not points with point coordinates, but lines with line coordinates. A line is understood to be a straight line. In the present chapter some basic elements of line geometry are introduced. Literature: Plu\u0308cker [5, 6], Sauer [9], Sturm [11], Kruppa [3], Timerding [12], Zindler [13], Hoschek [1], Salmon [7], Salmon/Fiedler [8]. Figure 2.1a shows a plane in a cartesian basis with origin 0 . The plane does not pass through 0 . Let P0 be the foot of the perpendicular from 0 onto the plane, and let, furthermore, d > 0 be the length of this perpendicular. The normal vector m of the plane is defined to be the vector having the absolute value |m| = 1/d and the direction from P0 to 0 . The position vector of P0 is \u2212m/m2 . The vector r of an arbitrary point located in the plane satisfies the equation m \u00b7 r = \u22121 . (2.1) From the coordinate form mxx+myy+mzz = \u22121 it is seen that the points of intersection of the plane with the coordinate axes have the coordinates x = \u22121/mx , y = \u22121/my and z = \u22121/mz , respectively. If the plane passes through 0 (Fig. 2.1b), Eq.(2.1) is replaced by m \u00b7 r = 0 , (2.2) where m is a vector normal to the plane with arbitrary absolute value |m| = 0 and with arbitrary sense of direction. 63 J. Wittenburg, Kinematics, DOI 10.1007/978-3-662-48487-6_2 \u00a9 Springer-Verlag Berlin Heidelberg 2016 64 2 Line Geometry Figure 2.2 shows a line in a cartesian basis with origin 0 . The line is uniquely determined by two points P and P\u2032 with position vectors r and r\u2032, respectively. The line is also uniquely determined by the vectors v = r\u2032 \u2212 r , w = r\u00d7 v = r\u00d7 r\u2032 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001208_j.cnsns.2011.03.043-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001208_j.cnsns.2011.03.043-Figure1-1.png",
        "caption": "Fig. 1. A two-degree of freedom polar robot manipulator.",
        "texts": [
            " In the absence of friction or other disturbances, the dynamic of an n-link rigid robotic manipulator system can be described by the following second order nonlinear vector differential equation: M\u00f0q\u00de\u20acq\u00fe C\u00f0q; _q\u00de _q\u00fe G\u00f0q\u00de \u00bc s \u00f01\u00de where q; _q; \u20acq 2 Rn, q is n-vector joint variable and s is n-vector of generalized forces. M(q) 2 Rn n is a symmetric and positive definite inertia matrix, C\u00f0q; _q\u00de _q is coriolis/centripetal vector, and G(q) is the gravity vector. In general, a robot manipulator always presents uncertainties such as frictions and disturbances. The controller has a duty to overcome these problems [5]. As shown in Fig. 1 a two-degree of freedom polar robot manipulator has one rotational and sliding joint in the (x,y) plane. Neglecting the gravity force and normalizing the mass and length of the arm, a mathematical model of two-degree of freedom polar robot can be expressed as follows _x1 \u00bc x2 _x2 \u00bc \u00bdlx1\u00feM\u00f0x1\u00fea\u00de x2 4\u00feu1\u00fed1 \u00f0l\u00feM\u00de _x3 \u00bc x4 _x4 \u00bc 2\u00bdM\u00f0x1\u00fea\u00de\u00felx1 x2x4\u00feu2\u00fed2 J1\u00feJ2\u00felx2 1\u00feM\u00f0x1\u00fea\u00de2 \u00f02\u00de where X = [x1x2x3x4] is the state vector, where x1 is the position of the center arm, x2 is center arm speed, x3 is angular position of the arm, x4 is angular velocity of the arm, l is the mass of motional link, M is the payload, J1 and J2 are moments of inertia of the motional link with respect to the vertical axis through c and o, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.8-1.png",
        "caption": "Figure 2.8 Ultrasonic additive manufacturing (UAM) process: (A) ultrasonic welding of aluminum and titanium tape; (B) periodic machining operations. Courtesy: Adam Hehr & Mark Norfolk, Fabrisonic LLC.",
        "texts": [
            " However, the limitations include: \u2022 Parts have residual stress and often need stress relieving; \u2022 Residual stress can cause distortion; \u2022 Repair of damaged parts is difficult; \u2022 Metal addition on existing parts is difficult and limited; \u2022 Multiple materials on single build is very difficult and not available commercially. An ultrasonic additive manufacturing (UAM) process has been applied to process components containing copper, titanium and aluminum. The UAM process involves building up solid metal objects through ultrasonic welding of a succession of metal tapes into a three-dimensional shape, with periodic machining operations to create the detailed features of the resultant object. Fig. 2.8A shows a rolling ultrasonic welding system, consisting of an ultrasonic transducer, a booster, a (welding) horn, and a \u201cdummy\u201d booster. The vibrations of the transducer are transmitted, through the booster section, to the disk-shaped welding horn, which in turn creates an ultrasonic solid-state weld between the thin metal tape and base plate. The continuous rolling of the horn over the plate welds the entire tape to the plate. This is the essential building block of UAM. It is 23Additive manufacturing technology to be noted that the \u201chorn\u201d shown in Fig. 2.8B is a single, solid piece of metal that must be acoustically designed, so that it resonates at the ultrasonic frequency of the system (typically at 20 kHz). Through welding a succession of tapes, first side-by-side to create a layer, and then one on top of the other (but staggered in the manner of bricks in a wall so that seams do not overlap), a 3D component is fabricated. During the build, periodic machining operations add features to the part, for example the slot in Fig. 2.8B, remove excess tape material, and true up the top surface for the next stage of welds. Thus in this case, the so-called \u201cadditive manufacturing\u201d involves both additive and subtractive steps in arriving at a final part shape. The advantages include: \u2022 Offers free form fabrication; \u2022 Multiple materials possible in different layers; \u2022 Material capability. Examples: aluminum, titanium. However, the limitations include: \u2022 Limited overhang capability; \u2022 Limited material capability; \u2022 Typically, materials with lower melting point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001358_s11634-014-0168-4-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001358_s11634-014-0168-4-Figure4-1.png",
        "caption": "Fig. 4 Structural diagram of the two-stage planetary gearbox: LS1 and LS2 are low-sensitivity sensors, HS1 and HS2 are high-sensitivity sensors",
        "texts": [
            "1 Planetary gearbox test rig and experiments We designed a planetary gearbox test rig shown in Fig. 3 to perform fault experiments. The test rig aims to investigate advanced methods of fault diagnosis for planetary gearboxes. The test rig has a 15 kW drive motor, a one-stage bevel gearbox, a twostage planetary gearbox, two speed-up gearboxes, a 30 kW load motor, a control system, and a lubrication system. Table 3 provides details on the numbers of gear teeth and transmission ratios of each gear stage. The focus of the experiments is on the two-stage planetary gearbox that is shown in Fig. 4. Four vibration sensors, including two identical low-sensitivity sensors (LS1 and The number of planet gears is indicated in parentheses BI bevel input gear, BO bevel output gear, S sun gear, P planet gear, R ring gear, LI large gear on input shaft, SI small gear on input shaft, LO large gear on output shaft, SO small gear on output shaft LS2) and two identical high-sensitivity sensors (HS1 and HS2), are installed on the housing of the two-stage planetary gearbox. LS1 and HS1 are located on the first-stage of the planetary gearbox, and LS2 and HS2 are on the second-stage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000848_1.48175-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000848_1.48175-Figure10-1.png",
        "caption": "Fig. 10 A 3-D view of an intersection at 0 of the estimated Cm due to a change in the center-of-gravity position for a fully partitioned flight envelope, a single partition flight envelope, and the true change of theCm coefficient caused by this shift.",
        "texts": [
            " 8, which shows that when a new part of the flight envelope is visited after the failure, first the filtered residuals increase, after which they converge back to zero when the estimates for the active partitions are updated. The estimated incremental model parameters during the simulation are shown in Fig. 9a. The failure is detected very rapidly, as shown in Fig. 9b, and several of the active partitions are reset almost immediately. When a different part of the flight envelope is visited during the maneuvering, the partitions that become active and have not been updated yet are also reset. To show that the update is only local, Fig. 10 shows the estimated Cm at the end of the simulation compared with a cross section of the interpolated lookup table value CZ ; ; e at 0, which is a main contributor to the effect of the center-of-gravity shift. The figure clearly shows that the identifier only estimated in the part of the envelopewhere the aircraft has flown and that the estimation is accurate. The proposed control design with a single partition, i.e., one local model, for the whole flight envelope has been simulated. The tracking performance of the controller is of the same level as the partitioned controller, as shown in Fig. 11; the scheme has less capability, however, to store its estimated data for different parts of the flight envelope. Although the single incremental model control design is capable of accurately approximating the incremental dynamics over a limited portion of the flight envelope, it will never yield a globally valid approximation using the same model structure as for each of partitions of the fully partitioned flight envelope. This limitation is illustrated in Fig. 10, in which the single partition controller achieves a good approximation of Cm for a small portion of the complete envelope: it fits a tangent plane to the true function. The fully partitioned envelope only approximates accurately in the visited part of the flight envelope, and its estimate in the unvisited 0 10 20 30 40 50 60 \u22121 0 1 x 10 \u22129 \u03b5 V t,\u03b5 \u03b1,\u03b5 \u03b2 0 10 20 30 40 50 60 0 5 10 x 10 \u22124 t [sec] \u03b5 p s, \u03b5 q s,\u03b5 r s Fig. 8 Filtered residuals for the adaptive controller for a sudden center-of-gravity shift after 6 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002069_1.4030242-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002069_1.4030242-Figure1-1.png",
        "caption": "Fig. 1 Meshed spur gear model along with the boundary conditions: (a) point A, (b) point B, (c) point C, (d) point D, and (e) point E",
        "texts": [
            " These contact stress values were further used to develop the friction factor for different coefficients of friction and for different helical gear pairs. (2) The inner hub of the gear was constrained in axial, radial, and tangential directions. (3) The left and right boundaries of the gear were constrained in radial direction. (4) The inner hub of the pinion was constrained in axial and tangential directions. (5) The left and right boundaries of the pinion were constrained in radial direction. The sample of meshed model of a spur gear at different contact positions along with the above boundary conditions are shown in Fig. 1. Validation of the FE Model. The FE calculation of the contact stress is done on the meshed model of the gear pairs. The von Mises equivalent stress distribution sample for the torque of 302 Nm is shown in Fig. 2. The theoretical results obtained from Eq. (2) along the path of contact were used for the validation of FE model. The calculation of values corresponding to every point along the contact line will be tedious and time consuming. Hence, the characteristic contact points were selected and their corresponding values were plotted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure5-1.png",
        "caption": "Fig. 5. The 4-4/4-4 type ring structure sensor with isometric legs.",
        "texts": [
            " The 8/4-4 type ring structure possesses inner circle used for bearing load and outer circle used for fixation. Moreover, if we set Rs = Rw = R and \u03b32 = \u03b22 in Eq. (12), the 8/4-4 type ring structure will be obtained in the basis of the 4/8/4 type platform structure. The 4-4/4-4 type ring structure sensor with isometric legs [25] is proposed according to the 8/4-4 type ring structure redundant parallel six-axis force sensor with isometric legs which is shown in Fig. 4. The drawing of the 4-4/4-4 type ring structure sensor with isometric legs is shown in Fig. 5. The difference between this structure and the 8/4-4 type ring structure is that the inner spherical joints are divided into two sets which are placed on the upper and lower circles of the inner cylindrical surface, respectively. The configuration is determined by the following parameters: R, r,H, \u03b11,\u03b12, \u03b21 and \u03b22 which have the same meanings as those in Fig. 4. For the 4-4/4-4 type ring structure sensor, the force Jacobian matrix Eq. (3) can be got: GIV \u00bc A1\u2212B1 A1\u2212B1j j A2\u2212B2 A2\u2212B2j j A3\u2212B3 A3\u2212B3j j \u2026 A8\u2212B8 A8\u2212B8j j B1 A1 A1\u2212B1j j B2 A2 A2\u2212B2j j B3 A3 A3\u2212B3j j \u2026 B8 A8 A8\u2212B8j j 2 664 3 775 \u00f017\u00de where Ai\u2212Bi \u00bc r cos \u03b1i\u2212R cos \u03b2i r sin \u03b1i\u2212R sin \u03b2i 2H\u00bd T i \u00bc 1;2;3;4\u00f0 \u00de; A j\u2212B j \u00bc r cos \u03b1 j\u2212R cos \u03b2 j r sin \u03b1 j\u2212R sin \u03b2 j \u22122H T j \u00bc 5;6;7;8\u00f0 \u00de; Ai\u2212Bij j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00fe r2\u22122Rr cos \u03b1i\u2212\u03b2i\u00f0 \u00de \u00fe 4H2 q i \u00bc 1;2;3;4\u00f0 \u00de; A j\u2212B j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00fe r2\u22122Rr cos \u03b1 j\u2212\u03b2 j \u00fe 4H2 r j \u00bc 5;6;7;8\u00f0 \u00de; Bi Ai \u00bc rH sin \u03b1i \u2212rH cos\u03b1i Rr sin \u03b1i\u2212\u03b2i\u00f0 \u00de\u00bd T i \u00bc 1;2;3;4\u00f0 \u00de; B j A j \u00bc \u2212rH sin \u03b1 j rH cos\u03b1 j Rr sin \u03b1 j\u2212\u03b2 j h iT j \u00bc 5;6;7;8\u00f0 \u00de; \u03b1 \u00bc \u03b11 \u03b12 \u03b13 \u03b14 \u03b15 \u03b16 \u03b17 \u03b18\u00bd \u00bc \u03b11 \u03b11 \u00fe \u03c0 2 \u03b11 \u00fe \u03c0 \u03b11 \u00fe 3\u03c0 2 \u03b12 \u03b12 \u00fe \u03c0 2 \u03b12 \u00fe \u03c0 \u03b12 \u00fe 3\u03c0 2 and \u03b2 \u00bc \u03b21 \u03b22 \u03b23 \u03b24 \u03b25 \u03b26 \u03b27 \u03b28\u00bd \u00bc \u03b21 \u03b21 \u00fe \u03c0 2 \u03b21 \u00fe \u03c0 \u03b21 \u00fe 3\u03c0 2 \u03b22 \u03b22 \u00fe \u03c0 2 \u03b22 \u00fe \u03c0 \u03b22 \u00fe 3\u03c0 2 : The lengths of two sets of the limbs are shown in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.1-1.png",
        "caption": "Figure 6.1. Motion in an accelerating reference frame.",
        "texts": [
            " The example demonstrates the importance of our distinguishing the inertial reference frame in applications of the Newton-Euler law.The second exercise illustrates an application in which the acceleration of one body is known, and a Coulomb condition for relative sliding of another contacting body is to be determined. The results will be used in the third example to illustrate 98 Chapter 6 the converse problem in which the forces are known and information about the motion is to be obtained . The form of the law in (6.2) is evident in the applications. Example 6.1. A rocket propelled test vehicle V in Fig. 6.1 is used to study man's ability to function at high rates of acceleration and deceleration. * (a) Suppose the vehicle is accelerating at 5g along a straight track in the inertial frame <I> = {F; Id . What force does the operator need to apply to a 2 lb control device D to impart to its center of mass a relative acceleration aDV = 16i+ 80j It/sec? in the vehicle frame IfJ = {V; id? (b) Compare the result with the force required to perform the same task when the vehicle has a uniform motion in <1> "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000204_tasc.2008.921967-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000204_tasc.2008.921967-Figure3-1.png",
        "caption": "Fig. 3. Magnetic field generated by a bulk superconducting magnet.",
        "texts": [
            " The , and are the speeds of the particle and the fluid, respectively. The is the viscosity of the fluid, the particle diameter, strength of the magnetic field. As the difference between and is the force to the particle, the equation of motion of the particle was solved with time evolution. The viscosity of water were assumed to be . In the calculation up to 0.5 T the intensity of magnetization was proportional to magnetic field (the volume magnetic susceptibility was 8000), and then came to be constant as saturated magnetization (0.6 T). Fig. 3 shows the contour line of the magnetic field generated by the bulk superconducting magnet. A disk shaped balk superconductor of which dimension was 40 mm in diameter and 15 mm in thickness was used in the calculation assuming the critical current density as A/m . The magnetic flux density at the surface of the magnet was 4.5 T. The critical current density was set to reproduce the measured magnetic flux density. The particle trajectories of the ferromagnetic particles in water were calculated in the magnetic filed generated by the bulk superconducting magnet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002939_j.jfranklin.2019.03.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002939_j.jfranklin.2019.03.003-Figure1-1.png",
        "caption": "Fig. 1. Coaxial octorotor configuration.",
        "texts": [
            " Finite time convergence and stability analysis of the complete system is provided in Section 4 . Numerical simulation results and discussions are presented in Section 5 . Finally some concluding remarks are given in Section 6. 2. Mathematical modeling The coaxial octorotor UAV is a complex nonlinear underactuated system with six DOF (three DOF translational and three DOF rotational) output motions. The octorotor comprised of four pairs of coaxial rotors attached at the ends of a cross frame structure in inverted configuration, as shown in Fig. 1 . The rotor speed is defined as \u03c9 i and thrust of each rotor in the direction of the rotor axis is defined as T i where i = 1 , 2, . . . , 8 . Each rotor in the coaxial pair rotates in the opposite direction. Also, the adjacent rotors rotate in opposite direction. Therefore rotors 1, 4, 5, 8 rotate in clockwise direction and rotors 2, 3, 6, 7 rotate in counter clockwise direction. The thrust and torque generated by the rotors causes the octorotor to attain desired attitude and perform pitch, roll, and yaw motions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.1-1.png",
        "caption": "Fig. 2.1 Basic mechanical layout of the front ICEs driving the rear wheels [Triumph \u2013Dolomite; DUFFY 2008].",
        "texts": [],
        "surrounding_texts": [
            "As a generalisation, the rear ECE or ICE layout, that is, rear-wheel-drive (RWD) tends to make an automotive vehicle light and inexpensive but unstable in side winds, whereas the front-wheel-drive (FWD) arrangement gives more inherent stability, but transmitting mechanical energy to steered and driving wheels adds mass and cost. All kinds of DBW AWD propulsion mechatronic control systems have been use on automotive vehicles, including thermo-mechanical (TH-M) steam engines, as well as fluido-mechanical (F-M), that is hydro-mechanical (H-M) or pneumo-mechanical (P-M) or electro-mechanical (E-M) motors. These latter run from ECE- or ICE-driven mechano-fluidical (M-F) pumps, mechanopneumatical (M-P) compressors, or mechano-electrical generators or even chemo-electrical/electro-chemical (CH-E/E-CH) storage batteries or fuel cells (FC), respectively. 2.1 Introduction 151 Due to many factors such as cost to buy and to run, ease of driving, reliability, quick availability, quietness, freedom from smell, and good power-to-mass ratio, the four-stroke petrol ICE has come to dominate the scene. It is an ICE that has a wide but not unlimited crankshaft angular-velocity range, having a minimum as well as a maximum useful rotational velocity that results in it needing some sort of gradually-engaged M-M clutch to be able to start an automotive vehicle from rest, and change \u2013 velocity gearing to suit various values of the vehicle velocity and gradients while running. Like so many technologies nowadays, DBW AWD propulsion mechatronic control systems are primarily a response to tightening emission standards. As with fuel injection and integrated engine management controllers (EMC), these systems improve ECE or ICE energy efficiency while cutting exhaust emissions. They do this by replacing clunky and inaccurate M-M, F-M or P-M systems with highly advanced and precise electronic sensors. Currently, DBW AWD propulsion applications are being used to replace the throttle-cable system on newly developed vehicles. These systems work by replacing conventional throttle valve control (TVC) systems. Instead of relying on a mechanical cable that winds from the back of the accelerator pedal, through the automotive vehicle firewall, and onto the throttle body, a DBW AWD propulsion mechatronic control system consists of a sophisticated pedal-position sensor (PPS) that closely tracks the position of the accelerator pedal and sends this information to the EMC. This is superior to a cableoperated throttle system for the following reasons: By eliminating the M-M elements and transmitting an automotive vehicle\u2019s throttle position mechatronically, DBW AWD propulsion greatly reduces the number of moving parts in the throttle system; this means greater accuracy, reduced mass, and, theoretically, no service requirements (like oiling and adjusting the throttle cable). Automotive Mechatronics 152 The greater accuracy not only improves the driving experience (increased responsiveness and consistent pedal feel regardless of outside temperature or pedal position), but it allows the throttle position to be tied closely into EMC information like fuel pressure, engine temperature, and exhaust gas recirculation (EGR); this means improved fuel economy and power delivery as well as lower exhaust emissions. With the pedal inputs reduced to a series of electronic signals, it becomes a simple matter to integrate a vehicle\u2019s throttle with non-engine specific items like ABS, gear selection and traction control; this increases the effectiveness of these systems while further reducing the amount of moving parts, service requirements, and vehicle mass. But what may occur if the \u2018wire\u2019 in the DBW AWD propulsion mechatronic control system, breaks? In other words, what if a mechatronic malfunction disrupts the flow of information between the TPSs and the EMC? It could give a whole new meaning to the term \u2018sticking throttle\u2019, couldn\u2019t it? The reality is that, just like fuel injection and an anti-lock braking system (ABS), a DBW AWD propulsion mechatronic control system is only as good as its programmers and manufacturers. While the first generation of fuel-injected ICEs had its share of technical gremlins, the fuel system of the average 2005 model is far more accurate, and dependable, than any carburettor-equipped vehicle from 25 years ago. Because DBW technology was first used on civil and military aircraft over 20 years ago (except it was termed fly-by-wire (FBW) back then), consumers can be assured that its reliability under less-than-ideal circumstances has been tested. It is now used on everything from industrial equipment (like heavy-duty machines) to cutting-edge ground-assault vehicles (like the future Grizzly tank). Speaking of aircraft (air-plane), many of modern jets use FBW technology for turning and braking, in addition to throttle mechatronic control. Could the same thing sooner or later be subjected to automotive vehicles? Could an unsophisticated joystick in the future substitute a vehicle\u2019s steering hand wheel, accelerator pedal, and brake pedal? That would be like suggesting that sooner or later vehicles may be able to drive themselves without any driver input [BRAUER 2004]. To achieve an overall improvement in vehicle safety, a fully-controlled powertrain is necessary. For instance, the technical objective of a powertrain equipped with intelligent technologies (PEIT) project [PEIT 2004] might be thus to build up an integrated self-stabilising powertrain that provides an interface to add all accident prevention and driver assistance functions of the vehicle. The powertrain interface may make it possible to integrate DBW AWD propulsion, BBW AWB dispulsion, ABW AWA suspension, and SBW AWS conversion mechatronic control systems and fail operative energy management into the RBW or XBW integrated unibody or chassis motion mechatronic control system, for example as shown in Figure 2.4 [PEIT 2004] 2.1 Introduction 153 To connect the functionalities and their mechatronically controlled devices, a failure tolerant system architecture is developed with two or even three central electronic control units (ECU) derived from the avionics industry co-ordinating the powertrain functions. Thus, only a single input, the motion vector providing the information of vector length and vector angle for acceleration/deceleration and yaw angle, respectively, vehicle body sideslip angle, may be necessary to control the whole motion task. The integrated engine-transmission management control (E-TMC) system is responsible for the coordination of safety and redundancy functionality. This key technology function may serve as a new standard in the automotive industry to coordinate a powertrain\u2019s automotive mechatronics. DBW AWD propulsion mechatronic control systems could eventually use joystick-like mechatronic controls that would eradicate the necessity for a steering wheel as well as accelerator and brake pedals, freeing up room in the interior for other potential innovative advancements. Besides, DBW AWD propulsion mechatronic control systems allow faster, more accurate interfacing with vehicle stability control (VSC) systems, as well as \u2018smart\u2019 ACC and ATC, and they also leave room for future active safety measures like collision-avoidance systems and park-assist gadgets. DBW AWD propulsion mechatronic control systems allow a level of integration not possible with M-M systems. For instance, a vehicle\u2019s airbag system could take into account the throttle position at the time of impact (or release the throttle on impact), an automatic suspension system could stiffen in response to a punch of the gas, or the steering system could take the throttle position into account when deciding how much boost to give [HALVORSON, 2004]. Automotive Mechatronics 154 There are many advantages in replacing a vehicle\u2019s M-M, F-M and/or P-M hyposystems with mechatronic ones (for example, sidebar, \u2018DBW AWD\u2019, and so on). Mechatronic control systems are inherently more reliable, more efficient, add less mass to an automotive vehicle, and can offer more functionality than M-M systems can. Lighter mass and more efficiency equate to better fuel economy -- an average of 5% improvement over traditional systems, a factor on everyone\u2019s mind in recent times of skyrocketing fuel prices. However, the mechanical-to-electrical shift is hampered by several factors, including the inertia of the automotive industry and a vehicle\u2019s available power source [LIPMAN 2004]. In not-too-distant automotive vehicles, in place of the steering hand wheel (HW) and floor acceleration and brake pedals mechatronic control systems may be used. The accelerator, gear shifting, and clutch actuator, as well as brakes and steering may be mechatronically controlled by DBW AWD technology. DBW AWD propulsion mechatronic control systems may be mechatronically controlled by the proof-of-concept driver interface shown in Figure 1.5 [SAE INTERNATIONAL, 2004; CITRO\u00cbN 2005]. Gearshift and clutch operation are so closely coupled that the systems may be considered together. The gearbox for the automotive vehicle may be based on an existing production unit employing a conventional H-pattern manual shift configuration. However, to accomplish the second-third and fourth-fifth movements of the selector mechanism inside the gearbox, more precise linear and rotational movements may be required. Up and down shifts are handled via the \u2018+\u2019 and \u2018-\u2018 buttons on the right-side side of the driver interface, with neutral being a logical \u20180\u2019. 2.1 Introduction 155 Reverse is selected via a dedicated button and is protected from inappropriate application by algorithms in the actuator control unit. Both clutch and gearshift-actuating units may be on a conventional 14 VDC or future 42 VDC energy-and-information network (E&IN). For the BBW AWB dispulsion mechatronic control systems, compact E-M actuating units may be coupled with brake calliper and braking design. At its current, interim stage of development, the braking system is said to rival conventional F-M arrangements in performance. Significant progress has been made in mass and size reductions during development, with the complete mechatronic brake calliper assembly now being a compact unit with a mass comparable to that of the conventional F-M design it replaces. Control of the braking mechatronic control system is duplicated on both the left and right driver interface yokes and is enabled by squeezing the handgrips. The M-M design incorporates a progressive resistance and a small, discernible free-play at the beginning of the movement to provide the driver with a tactile indication when the brakes begin to operate. The system controls each brake as an individual subsystem under an umbrella control for the complete vehicle braking system. The driver interface\u2019s left and right steering control yokes are linked mechanically and have a full movement of just 20 deg. Movement of the vehicle\u2019s front wheels is aided by full logic mechatronic control, with feedback to the driver being provided by a high-torque motor. driver \u2018feel\u2019 is programmable, as is the relationship between yoke and front-wheel movement. A next-generation steering actuator fits easily into the front subframe assembly of the future production automotive vehicle. The vehicle of the future gives the impression of being just similar to this: it has no ECE or ICE, no steering column, and no brake pedal. It needs no petrol (gasoline), emits no pollution (only a little water vapour) and hitherto handles similarly to a high-performance vehicle. It might seem not unlike an ecologist\u2019s imagination, in place of an ICE, for example, the vehicle of the future may be energised by fuel cells (FC) similar to those used in the orbiting space station [HM-MILTON, 2002]. Electrical energy is generated by an electro-chemical (E-CH) reaction of hydrogen and oxygen that submits only thermal energy (heat) and water (H2O) as its side-effect. No smelly exhaust, no smog, no greenhouse gases. Misplaced too are the cables and mechanical links that have held together automotive vehicles since the beginning of the automobile age a century ago. As a substitute, the steering and braking are fully mechatronically controlled; using techniques originated in FBW aircraft cockpits. Instead of a steering column there is a miniature colour screen and two handgrips, as shown in Figure 2.6 [THIESEN 2003, SCHMIDT 2004]. Automotive Mechatronics 156 To accelerate, drivers twist the grips. To have an effect on the brakes, drivers squeeze them. To turn left or right, drivers reposition the grips up or down. In place of a rear-view mirror, there is a video camera that visualises an image of the road travelled, along with such driving data as vehicle velocity and hydrogen-fuel levels. For the reason that the automotive vehicle is properly programmable, drivers can adjust their performance preferences. (Brakes ought to be soft or hard? ECE or ICE sporty or fuel saving?) Eradicating all the mechanical controls frees up the space where an ECE or ICE would normally dwell; for example, in the automotive vehicle of the future, drivers can watch straight through the front of the vehicle. Without a steering column, vehicle designers can locate the mechatronic controls anywhere in the vehicle for maximum comfort and safety, even in the backseat. The core of the vehicle of the future, however, is an aluminium, skateboardlike chassis that runs the length of the automotive vehicle. Incorporated within it are the FCs, an electro-mechanical (E-M) motor, tanks of compressed hydrogen and all the mechatronics. Since the fibreglass body is principally a shell, different models can be exchanged similar to cell-phone covers. Consequently drivers could in theory drive a sports car on the weekends and alter it into a minivan to take the children to school. For one thing, the roadside infrastructure that fuels and services nowadays \u2018gas guzzlers\u2019 would have to be modified to distribute hydrogen and reprogram out-of-order mechatronic control systems. However, if the effect may be a fleet of safe, fuel-efficient, non-polluting vehicles that downgraded or eradicated the world\u2019s dependence on fossil fuel, it would be worth the effort. 2.1 Introduction 157 Automotive engineers and scientists seek future enhancements to the automotive vehicles of the future to principally approach from systems engineering efficiencies prior to breakthroughs in specific components. For example, separated wheel E-M motors are likely may be made possible by fully integrating the brake, suspension, and wheel into an optimised corner module. Although part of the concept platform was unveiled some time ago, such technology is not on the driveable automotive vehicle of the future that features a central electrical system to power the wheels. But the automotive vehicle manufacturers maintain their goal remains to put an in-wheel-hub E-M motor at each wheel -- if it can find a way to fit them into the skateboard-chassis along with the FC system, drivetrain, storage tanks, and various mechatronics. Some vehicle manufacturers are working on a solid-state system that uses sodium alienate hydride material to store hydrogen. The system can store a relatively large amount of hydrogen but it currently takes too long to infuse the hydride and release the hydrogen. Another challenge is reducing the amount of expensive precious metals from the FC stack and costly carbon fibre in the fuel tank. It is estimated that three-quarters of the cost of the tank may be attributed to the carbon fibre shell [AUTOTECH 2003]. All of the emerging automotive vehicle\u2019s working parts may reside in a skateboard-chassis of less than a foot thick. The chassis may contain, for example, the FC, hydrogen tanks and E-M motors to drive the front and rear wheels. What appears to be a kind of video game to a conventional driver is actually a unique innovation based on a revolutionary concept known as \u2018DBW AWD\u2019. This new system not only offers improved safety, comfort, and ergonomics, but also provides extra advantages in terms of vehicle design and production. It\u2019s all made possible by a mechatronic control system that replaces the mechanical and fluidical connections linking the steering wheel and pedals with the steering, drive, and brakes. Designed so that it can only be moved to the left or right, a unique sidestick (see Fig. 2.7) enables drivers to steer with high precision. Automotive Mechatronics 158 At the same time, an integrated E-M motor gives them a more realistic feeling of steering resistance. A two-dimensional force-measuring sensor that reacts to forward or backward hand pressure, registers commands to accelerate or brake. The DBW AWD propulsion mechatronic control system takes over control of the ECE or ICE plus the braking and steering functions. In this manner, it can control the automotive vehicle as the driver would wish, even in a situation where the driver might not be able to react in time. Today, there are in normal driving operations \u2018DBW AWD\u2019 automotive vehicles of the future without steering hand wheels, acceleration or brake pedals that are steered only by sidesticks, as shown in Figure 2.8. Appearances can be deceiving: The easy-to-use sidestick is based on a complex mechatronic system with redundant safeguards. A DBW AWD propulsion mechatronic control system consists of sensors and control elements connected by a redundant data bus (black). The driving dynamics controller plays an important role here, actively taking over when the driver loses control of the vehicle. All mechatronic components have a backup system to ensure maximum safety. To achieve this ambitious objective, automotive scientists and engineers disconnected the fluidical and mechanical connections and replaced them with E-M servomotors and electronic switching elements. Both types of mechatronic components are controlled by a fault-tolerant microcomputer system. The latter receives its data not only from the driver, who issues commands to the system, but also from sensors that continually monitor the vehicle\u2019s status. \u2018DBW AWD\u2019 automotive vehicles of the future may offer numerous benefits: Their safety systems react automatically to potentially dangerous driving situations within fractions of a second; The push of a button on a sidestick (side-mounted joystick) may be sufficient to make parking and other difficult manoeuvres child\u2019s play; The advanced concept may also enable designers to completely revamp automobile interiors. 2.1 Introduction 159 High values of the vehicle velocity, tight curves, and wet cobblestones -- even experienced race car drivers would struggle with the steering under such conditions. As far as automotive scientists and engineers are concerned, two fingers are sufficient to control the vehicle; the driver is driving with a hand-sized sidestick, or side-mounted joystick. The driver\u2019s left elbow may be supported against the centrifugal force by the arm console in the door and the right elbow may rest on the centre console. The driver literally has a handle on the automotive vehicle. The most important driving operations -- accelerating, braking, steering, signalling, and honking the horn -- are integrated, for instance, in two sidesticks in the vehicle\u2019s armrests, as shown in Figure 2.9. [DaimlerChrysler]. Much like a modern jet fighter, the automotive vehicle can be accelerated by lightly pushing forward the compact joysticks that are linked electronically. Automotive Mechatronics 160 Once the vehicle is on its way, the integrated ACC automatically maintains vehicle velocity. When the driver wants to brake, he or she simply pulls back the side-stick (see Fig. 2.10). by lightly pushing forward the compact joysticks that are linked electronically [DaimlerChrysler]. A significant safety feature of DBW AWD is that, unlike the electronic stability program (ESP) currently in use, it can be extended to act on the steering as well as on the brakes (see Fig. 2.11), even sceptical drivers end up delighted by the system. While the sidestick is held comfortably in the hand that sets the course, the wheels dance over wet, slippery cobblestones, controlled by microcomputers that automatically compensate for every bump with a corrective steering adjustment. 2.1 Introduction 161 [DaimlerChrysler]. A test procedure in which strong winds are directed at the side of a vehicle also demonstrates the effectiveness of the stabilising algorithms. When the wind corridor is reached, a conventional vehicle immediately swerves off course and the driver must steer accordingly to counteract its effect. With DBW AWD, drivers hardly notice the wind at all. This is because the sensors immediately register the deviation it causes, while the computer already \u2018knows\u2019 the direction that the driver wants to take due to the position of the sidestick. As a result, the wheels are automatically turned in the right direction to offset the effect of the side wind. With the stabilising algorithm of DBW AWD, however, sensors, computers, and actuators react so quickly that the vehicle neither skids nor swerves out of the lane. Instead, it maintains the desired course. Passive Safety - Integrating driving functions into a sidestick offers additional passive safety benefits, too. It is well known that, if there is no steering column, then there is also no danger of the chest injuries often caused in an accident and if the driver\u2019s foot can no longer get caught in one of the pedals during a collision, then the number of foot injuries may also be reduced. Braking Speed - But the sidestick concept\u2019s ace in the hole is braking speed. In order to brake, drivers of conventional vehicles require an average of 0.2 s to move their feet from the acceleration to the brake pedal. At a speed of circa 50 km/h (30 mph), this translates into an additional braking distance of roughly 2.9 m (9.5 feet). The quicker reaction time of the sidestick system could therefore prevent many collisions [DAIMLERCHRYSLER 1998-2004]. Automotive Mechatronics 162 Automatic Vehicle Velocity Adjustion - DBW AWD -- whether by means of sidestick or mechatronic steering wheel -- also offers a general advantage. Because there is no longer a direct mechanical or fluidic (hydraulic) connection between the driver and the wheel, the steering ratio can be automatically adjusted to the vehicle\u2019s velocity."
        ]
    },
    {
        "image_filename": "designv10_12_0002261_s12555-016-0545-1-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002261_s12555-016-0545-1-Figure2-1.png",
        "caption": "Fig. 2. The setup of the vertical GRF measurement.",
        "texts": [
            "03% full scale and repeatability of 0.02% full scale. The hip and knee joints have the same configuration. The smart shoe which is equipped with the pressure sensors is installed at the exoskeleton foot to measure the vertical GRF. The following section presents the method for calculating the vertical GRF with the smart shoe. 2.2. Measurement of vertical GRF with the insole pressure sensors A smart shoe with the insole pressure sensors measures the vertical GRF during over-ground walking. As shown in Fig. 2(a), the smart shoe consists of air bladders with winding silicon tubes and air pressure sensor. When the foot contacts the ground and presses on the air bladder, it deforms and the pressure change is measured by the air pressure with the repeatability of 0.1% full scale. The four units of the air bladder are attached to the insole at the toe, medial, lateral, and heel part, as shown in Fig. 2(b). To calculate the vertical GRF from the measured pressure, the linearity test was performed. Fig. 3(a) represents the experimental setup. A universal testing machine (Testone Inc., T101; load range: 0-250 kgf, resolution: 0.01% full scale) was utilized to apply variable loads (compression force) to each air bladder unit. The loads were applied over several steps in 50 N increments to the maximum measurable range of each air bladder unit (toe: 1000 N, heel: 900 N, medial: 450 N, lateral: 450 N)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003807_j.wear.2021.204043-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003807_j.wear.2021.204043-Figure2-1.png",
        "caption": "Fig. 2. Sampling position of surface and section in the gears after tests.",
        "texts": [
            " Element C Si Mn Cr Ni Cu P S Fe Weight % 0.45\u20130.5 0.17\u20130.37 0.5\u20130.8 \u22640.25 \u22640.25 \u22640.25 \u22640.035 \u22640.035 Balance S. Zhang et al. Wear 484-485 (2021) 204043 of the test gears are listed in Table 3. The tooth profiles of pinion and wheel were measured by using CMM (Wenzel-Xorbit87, accuracy: (3+L/300) \u03bcm in axial and (3.8+L/300) \u03bcm in space) before and after the test to achieve the wear depth. Wear depth is defined as the change of tooth profile at the corresponding radius of the gears in this study (along the circumferential direction). Fig. 2 shows the sampling position of gear surface after tests. Three teeth were taken from each gear and each tooth was separated by about 120\u25e6. The surface damage was characterized using scanning electron microscope (FEI Inspect F50, America). As described in section 2, seven pairs of gears were monitored during the experiment. Fig. 3 shows the wear depth measurement results of three randomly selected pinions and three randomly selected wheels. It was found that each pair of pinion and wheel had very similar wear patterns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001224_icra.2011.5980498-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001224_icra.2011.5980498-Figure11-1.png",
        "caption": "Fig. 11. Definition of the moving coordinate system.",
        "texts": [
            " ( )error t\u03b8 is the attitude angle error that is calculated as follows: { } { } ( ) ( ) (0) sin ( ) (0) cos ( ) ( ) sin ( ) cos error roll roll pitch pitch error roll pitch t t t t t t \u03b8 \u03b8 \u03b8 \u03d5 \u03b8 \u03b8 \u03d5 \u03b8 \u03b8 \u03d5 \u03b8 \u03d5 = \u2212 \u22c5 + \u2212 \u22c5 = \u22c5 + \u22c5 (2) where ( )roll t\u03b8 and ( )pitch t\u03b8 are attitude angles about the roll and pitch axes respectively, which are acquired from the attitude sensor mounted on the robot\u2019s trunk. \u03d5 is the angle between the X axis of the robot\u2019s moving coordinate system and the axis connecting the CoP of each foot as shown in Fig. 11. \u03d5 is calculated as follows: 2 2 1cos , sin , 1 1 Lcop Rcop Lcop Rcop a Y Ya X Xa a \u03d5 \u03d5 \u2212 = = = \u2212+ + (3) where ( ) ( ), ,,Rcop Rcop Lcop LcopX Y X Y are the reference CoP positions of each foot in the moving coordinate system. The robot\u2019s attitude is stabilized by the above-mentioned control. But there is a singularity when a point contact of heel is in alignment with a line contact of toe. Before and after the y axis of the moving coordinate system coincides with the axis connecting the CoP of each foot (where \u03d5 is 90 degrees), the modification direction of the standing on the tiptoe according to the attitude error is inverted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001958_tmag.2018.2841874-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001958_tmag.2018.2841874-Figure13-1.png",
        "caption": "Fig. 13. ISG prototype. (a) Rotor. (b) Stator with DTP-FL winding. (c) Prototype.",
        "texts": [
            "8% when winding layout adopts TP-DL and three segments per pole in axial direction. This is due to relatively small winding MMF harmonic magnitude for TP-DL winding layout. V. ISG EXPERIMENT PLATFORM Wang et al. [6] did a lot of work for a radial flux ISG under starter and generator mode. We take a 3.7-kW single-stator single-rotor axial flux ISG prototype as the study subject in this paper, which includes rotor with radial segmented PM, stator with DTP-FL winding and secondary winding as shown in Fig. 13. An ISG adopts 12-slots/10-poles combination. Eddy current losses in PMs cause the temperature rise of PMs. Therefore, we can gather their temperature by infrared thermometer. Stator winding temperature is collected by PT100 thermal resistance, and displayed by paperless recorder. No-load and load test platform for axial flux ISG with DTP-FL and secondary windings are established in Fig. 14(a) and (b), respectively. The surface temperature distribution of ISG under 100- resistance load is given by thermal infrared imager as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002203_j.cirpj.2016.11.002-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002203_j.cirpj.2016.11.002-Figure2-1.png",
        "caption": "Fig. 2. Fly cutting analogy test \u2013 kinematics and arrangement.",
        "texts": [
            " Meeting the state of the art, tools made of powder metallurgical high speed steel (PM-HSS) with an Al-Cr-based wear resistance coating were used. of the tool profile on the wear behaviour in gear hobbing. CIRP doi.org/10.1016/j.cirpj.2016.11.002 B. Karpuschewski et al. / CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx\u2013xxx2 The workpieces were made of AISI 5115 (16MnCr5). To save time and material, the well-established fly cutting analogy test was utilized for the examination [6]. The general functional principle of the test is illustrated in Fig. 2. A single tooth, which was parted from a real hob by Wire-EDM, is being moved tangentially at multiple axial positions to simulate all generating positions and enveloping cuts. That way the fly cutting tooth is able to reproduce the process load of a real shifted hob and corresponding wear phenomena. The general frame of the cutting tests performed is summarized in Table 1. To examine two different levels of load, the cutting tests were performed at Hoffmeister chip thicknesses [2] of hcu,max,1 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002618_b978-0-12-814062-8.00015-7-Figure13.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002618_b978-0-12-814062-8.00015-7-Figure13.3-1.png",
        "caption": "Figure 13.3 Geometry of tension-compression rotating fatigue (R521) sample.",
        "texts": [
            " The \u201cPerformance\u201d samples then went through an annealing treatment at 800 C for 2 hours. After stress-relieve heat treatment, \u201cIntermediate\u201d samples were Hot Isostatic Pressed (HIPed) at 850 C under 150 MPa Argon gas pressure for 4 hours. A tension-compression rotating fatigue test with a stress ratio R521 was carried out on a GUNT WP140s tester. Machined samples (Ra ,1 \u03bcm) and net-shaped sample (Ra .7 \u03bcm depending on SLM processing parameter) after SLM and postSLM treatments were adopted for the fatigue test (Fig. 13.3). Fatigue strength was determined at the run-out 107 cycles. The Ra values were measured from surfaces with various inclination angle \u03b8 are plotted in Fig. 13.4. Based on the staircase effect, the theoretical Ra values can be calculated, assuming the step edge of each layer is rectilinear (Eq. 13.1). According to this simplified prediction, the roughness of an inclined surface increases with layer thickness and cosine of inclination angle \u03b8. \u201cSpeed\u201d samples were fabricated with a layer thickness (100 \u03bcm) that is two times the layer thickness for \u201cPerformance\u201d and \u201cIntermediate\u201d samples (50 \u03bcm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.12-1.png",
        "caption": "Figure 6.12. Plotsof the hyperbolicfunctions sinhz and coshz.",
        "texts": [
            " The identity (6.63) shows that, unlike their trigonometric cousins, cosh z > sinh z for all values of z. This means that their graphs never intersect; the graph of cosh z lies always above the graph of sinh z. Moreover, (6.56) and (6.62) show that sinh z vanishes at z = 0 where its slope, cosh z, has value 1. Since d2(sinh z)/dz2 = 0, the graph of sinh z has an inflection at z = O. Equation (6.56) shows that sinh( - z) = - sinh z is an odd function of z. The graph of sinh z thus has the form shown in Fig. 6.12. The graph of cosh z, also shown there, has a minimum at z = 0 where its value is I, and, by (6.56), cosh( - z) = cosh z shows that cosh z is an even function of z. Clearly, as z grows indefinitely large, (6.56) indicates that both functions grow indefinitely, as shown in Fig. 6.12. It can be proved from statics that the graph of the hyperbolic cosine function , also called the catenary, is the shape assumed by a uniform, heavy cord supported at its ends and hanging under its own weight, an easy experiment for the reader. 132 Chapter 6 6.7. The Simple Harmonic Oscillator The differential equations (6.48) and (6.54) occur in a wide variety of dynamical problems, the simplest kind being those for which h(t) = O. These equations reduce in this case to the respective homogeneous equations (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.21-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.21-1.png",
        "caption": "Figure 5.21. Model of a torpedo exploder mechanism.",
        "texts": [
            " In an oblique, glancing impact, the frictional effect was less severe and the torpedoe s often exploded on impact. So, nearly 2 years after the start of the war, between July and September 1943, as a fortuitou s consequence of Daspit' s failed attack on the Tonan Maru , the torpedo exploder mechani sm problem was finally identified and solved.f The problem of U.S. Navy torpedo failures was finally explained by elementary princip les of mechanics involving Coulomb friction. To explore this, consider the simple model of the exploder mechani sm shown in Fig. 5.21. The free body diagram of the firing pin modeled as a block of weight W = mg is shown in Fig. 5.2I a. The actual direction of g may vary from that chosen in the example. The trigger spring driving force from its precompressed state is a known function FAy ) of the firing pin displacement y; N denotes the normal (impulsive reaction) force exerted by the guide rods, and Cd is the dynamic friction force. So, the total force on the block in its sliding motion is F = F, + N +W +Cd = - Ni + (FAy ) - W - /d )j, in which f d = vN and W = mg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002149_physreve.90.012704-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002149_physreve.90.012704-Figure1-1.png",
        "caption": "FIG. 1. (a) Schematic of an individual moving cilium attached to a cell surface. (b) A collective wave pattern of ciliary beating, whose envelope (solid) oscillates about a neutral surface (dashed) tangential to the cell surface substrate. The coordinates (x,y), used in Appendix A, are also indicated.",
        "texts": [
            " All these studies ultimately trace back to Lighthill\u2019s inaugural exploration [27] of how swimming in a Newtonian fluid is induced by asymptotically small squirming shape deformations of a sphere, which has been dubbed the \u201cLighthill *ishimoto@kurims.kyoto-u.ac.jp \u2020gaffney@maths.ox.ac.uk squirmer.\u201d Blake [28,29] corrected the results of Lighthill [27] and used these to explore the swimming dynamics of the ciliates, a phylum of unicells that drive motility via a coordinated collective beating of a dense sheet of short cellular appendages on the cell surface. These appendages are known as cilia and are schematically illustrated in Fig. 1. Note that each individual cilium has a cyclic beating [Fig. 1(a)], which contains two phases: the effective stroke, with the cilium extended from the cell surface, which generates a larger propulsion force; and the recovery stroke, with the cilium traveling near the surface, inducing a smaller force in the opposite direction. In turn, this induces a net propulsion for the cell. In addition, the collective wave of ciliary beating illustrated in Fig. 1(b) is referred to as the metachronal wave [26,30], and for planar beating, it exists in two main forms: symplectic and antiplectic. This classification depends on the phase between the ciliary beating and the wave progression: symplecticity requires that the direction of the cilium\u2019s effective stroke and metachronal wave propagation are in the same direction, whereas they are in opposite directions for antiplectic metachronism [31]. In particular, the squirmer model of Lighthill and Blake [27\u201329] treats this time-dependent envelope of the ciliary wave as the effective cell surface, allowing an envelope modeling representation of the cell as a shape deforming swimmer with small-amplitude deformations, upon noting that the cilium length is much smaller than the cell size",
            " Subsequently, the accuracy of small-amplitude theory is examined as the deformation amplitude is increased, together with an exploration of novel behaviors with extensive squirmer deformations. II. MODELS AND METHODS A. The axisymmetric spherical squirmer For brevity, we only consider axisymmetric deformations and we nondimensionalize so that the sphere radius, the viscosity, and the period of the deformation envelope wave are all unity. Hence, below, the temporal frequency of the deformation wave is given by \u03c9 = 2\u03c0 . Following [7,28], we consider the deformation of the reference sphere, i.e., the neutral surface depicted in Fig. 1(b), which is parametrized by the spherical polar radius r = 1 and polar angle \u03b8 \u2208 [0,\u03c0 ]. During the surface deformation, (r,\u03b8 ) is mapped to (R, ), given by R = 1 + \u03b5 \u221e\u2211 n=1 \u03b1n(t)Pn(cos \u03b8 ), (1) = \u03b8 + \u03b5 \u221e\u2211 n=1 \u03b2n(t)Vn(cos \u03b8 ). (2) Here, the Pn(x) are Legendre functions, and thus orthogonal, while the Vn(x) are the associated Legendre functions, Vn(x) = 2 \u221a 1 \u2212 x2 n(n + 1) d dx Pn(x), (3) and hence also orthogonal. Throughout, we assume volume conservation for the swimmer and thus the series in (1) has no \u03b10 term",
            " Formulation The governing equations are those of Stokes, \u2207p = \u03bc u, \u2207 \u00b7 u = 0, (A1) coupled with the force-free condition for a swimmer. Zerovelocity boundary conditions are imposed asymptotically far from the squirming sheet, with the standard no-slip conditions on the squirming surface. The latter is denoted (X,Y ), which is defined by X(x,t) = x + \u03b5 \u221e\u2211 n=1 (an sin n(kx + \u03c9t) \u2212 bn cos n(kx + \u03c9t)), (A2) Y (x,t) = Y0 + \u03b5 \u221e\u2211 n=1 (cn sin n(kx + \u03c9t) \u2212 dn cos n(kx +\u03c9t)), (A3) where Y0 is a constant (which may be set to 0 without loss of generality) and the coordinates (x,y) are indicated in Fig. 1(b). X = X \u2212 x and Y = Y \u2212 Y0 represent the deformation of the surface. At leading order in \u03b5, the velocity of the neutral surface is parallel to the surface and given by (31) in Ref. [29], U = 1 2 \u03b52\u03c9k \u221e\u2211 n=1 n2 [ c2 n + d2 n \u2212 a2 n \u2212 b2 n + 2(andn \u2212 cnbn) ] . (A4) To consider the energy consumption of the swimmer, we define the power output per unit area on the fluid due to the surface deformation as P = \u222b S n \u00b7 \u03c3 \u00b7 u dS. The lowest order expression of the energy consumption is also obtained by [29] P = \u03b52\u03c92\u03bck \u221e\u2211 n=1 n3 ( a2 n + b2 n + c2 n + d2 n ) ",
            " (A10) Without loss of generality, we can set bn = 0, and we have the velocity, U = \u2213 1\u221a 2 W n\u03bc\u03c9 , (A11) which yields the optimal stroke for n = 1 with a1 = (\u22121 \u00b1\u221a 2)d1 with the optimal velocity, U = \u2213(1/ \u221a 2)(W/\u03bc\u03c9). Clearly, both the symplectic stroke [an = (\u22121 + \u221a 2)dn] and the antiplectic stroke [an = (\u22121 \u2212 \u221a 2)dn] maximize the absolute velocity in this case, and both optimal strokes require Lagrangian surface points (or cilia tips) to have ellipsoidal trajectories with the oscillation in the x and y direction possessing a phase difference of \u00b1\u03c0/2, as illustrated in Fig. 1(a). This degeneracy between the two metachronies originates from the simple relation in the change of variables ( X, Y ) \u2192 ( Y , X). This reflects a translational symmetry of the underlying geometry and corresponds to the change of variables, an \u2194 cn, dn \u2194 bn, which does not change the leading term of the absolute value of the translational velocity or the power consumption. Thus, geometric symmetry induces a degeneracy in the waveforms that generate maximal speeds at fixed power consumptions. Of course these results are restricted to a two-dimensional stroke: three-dimensional strokes are also observed and discussed in [30,51,53]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.16-1.png",
        "caption": "Fig. 13.16 Tripod joint. Balls sliding on the rays of the star-shaped tripod 2 are guided in tracks fixed on shaft 1",
        "texts": [
            " The position of C in the tracks is described by the angle \u03b2 = (001C) . It is a function \u03d5 . The extremal values \u03b21 and \u03b22 are obtained from the condition that the x, y-coordinates of C satisfy the equation x = y tan\u03b1/2 . This is the set of equations h\u2212 r cos\u03b21,2 = \u00b1r sin\u03b21,2 tan \u03b1 2 . (13.42) Solving for sin\u03b21,2 results in the formulas sin\u03b21,2 = (h/r) tan\u03b1/2\u00b1 \u221a 1 + tan2 \u03b1/2\u2212 (h/r)2 1 + tan2 \u03b1/2 . (13.43) An animation of the motion is on display in Wikipedia Homokinetisches Gelenk. The tripod joint shown in Fig. 13.16 is another ball-in-track coupling. Its kinematics was investigated by Roethlisberger/Aldrich [16], Duditza [5], Duditza/Diaconescu [6], Durum [8], Orain [12, 13] and Akbil/Lee [1, 2]. In what follows, an elementary analysis is presented. Imagine that in the fixed cartesian x1, y1, z1-system of Fig. 13.17 the shaft labeled 1 is rotating about the z1-axis. The rotation angle is \u03d5 . A point Q fixed on the shaft at radius a is moving on a circle. In the position \u03d5 of the shaft Q has the coordinates x1(\u03d5) = a cos\u03d5 , y1(\u03d5) = a sin\u03d5 ",
            " The projections of these points are three points Pi(\u03d5) (i = 1, 2, 3) on the ellipse. For each one of these points (13.48) yields the same point P0(\u03d5) since 3 \u00b7 120\u25e6 = 2\u03c0 . From this it follows that the rays P0(\u03d5)Pi(\u03d5) (i = 1, 2, 3) emanating from P0(\u03d5) form a rigid 120\u25e6-star with the center at P0 . This star is rotating with angular velocity \u03d5\u0307 while its center P0 is moving on the circle of radius with angular velocity 3\u03d5\u0307 . The lines Qi(\u03d5)Pi(\u03d5) (i = 1, 2, 3) are parallel to the axis of shaft 1 and fixed on shaft 1 . In the tripod joint shown in Fig. 13.16 the star, the three lines Qi(\u03d5)Pi(\u03d5) (i = 1, 2, 3) and the permanent intersection of each ray with the associated line at Pi are materially realized. Each ray is guide for a ball which is free to move along the ray. The associated line fixed on shaft 1 is the axis of a cylinder in which the ball is also free to move. Orthogonal to the star and through its center P0 a shaft 2 is rigidly attached to the star. The star and this shaft together constitute the tripod giving the joint its name. The tripod has the same angular velocity \u03d5\u0307 shaft 1 has independent of the direction of shaft 2 relative to shaft 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000918_j.fss.2011.06.001-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000918_j.fss.2011.06.001-Figure14-1.png",
        "caption": "Fig. 14. Two-link planar manipulator.",
        "texts": [
            " 5 and 10 show the tracking trajectories of the second output y2 and the reference output ym2. Also, the control inputs u1 and u2 are shown in Figs. 6, 7, 11, and 12. Figs. 8 and 13 show that the comparison of the estimated states and the simulated states. The simulation results in this case demonstrate that the trajectories of the actual outputs y1 and y2 also follow the reference signals ym1 and ym2, respectively, very well. Example 2. Consider a general robot system with n inputs and n outputs shown in Fig. 14. The dynamic equations are given as (32) H(q)q\u0308 + C(q, q\u0307)q\u0307 + g(q) = u + ud (32) with H(q) = [ (m1 + m2)l2 1 + m2l2 2 + 2m2l1l2 cos q2 m2l2 2 + m2l1l2 cos q2 m2l2 2 + m2l1l2 cos q2 m2l2 2 ] C(q, q\u0307) = [ \u2212m2l1l2q\u03072 sin q2 \u2212m2l1l2(q\u03071 + q\u03072) sin q2 m2l1l2q\u03071 sin q2 0 ] and g(q) = [ (m1 + m2)l1ge cos q1 + m2l2ge cos(q1 + q2) m2l2ge cos(q1 + q2) ] where q = [q1 q2]T \u2208 2 is the output vector of generalized coordinates, H(q) \u2208 2\u00d72 is the inertia matrix, C(q, q\u0307)q\u0307 \u2208 2 is the vector of centripetal and Coriolis torques, g(q) \u2208 2 is the vector of gravitational torques, u = [u1, u2]T \u2208 2 is the input vector of applied joint torques, and ud \u2208 2 is the vector of additive bounded disturbances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002252_s12289-017-1391-2-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002252_s12289-017-1391-2-Figure2-1.png",
        "caption": "Fig. 2 Schematic of the SLM numerical model",
        "texts": [
            " The effects of laser power and scanning speed on the configurations of the melt pool were analyzed. Moreover, a corresponding experiment was also conducted to validate the simulation results. Figure 1 schematically depicts the SLM process. After irradiation by high-power laser, the metal powder reaches the melting point and begins to change from a solid to liquid, which represents the so-called melt pool. The melt then cools by the ambient temperature as the laser beam moves away. Finally, the solidified melt is formed on the metal plate. As shown in Fig. 2, the domain of simulationmodel was 2mm * 0.216 mm * 0.125 mm, while the thickness of the substrate was 70um. There was no gap between the substrate and the powder bed, which indicates heat conduction is a dominant heat transfer mode. The space between the top boundary and the power bed was used to facilitate heat convection and free surface calculations. The Gaussian laser heat source is irradiated at the top surface of the powder bed. The laser energy in the simulation can be determined by laser power, spot size and scanning speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002558_j.addma.2018.05.022-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002558_j.addma.2018.05.022-Figure1-1.png",
        "caption": "Fig. 1. (a) Concept of in-situ welding during EBM process. Top view of (b) layer n/layer n+2 and (c) layer n+1. The arrows on the plate A and plate B indicate the scanning lines.",
        "texts": [
            " The present study tried to utilize the layer-by-layer fusion manner of EBM process to weld two parts at each sliced layer during EBM process. The lower layer thickness for the EBM process (ranged from 25 to 90 \u03bcm [6]) was expected to minimize the heat affect zone as compared to the conventional welding process. Moreover, the preheating manner (\u223c730 \u00b0C for Ti-6Al-4V) of the EBM process was also expected to further remove the microstructural difference between the welded zone, heat affect zone and base materials. As illustrated in Fig. 1, two threedimensional files, named plate A and plate B, were \u201cwelded\u201d together with an overlap zone. During the preparation of the EBM process, plate A and plate B were selected as two different print jobs, although both of them used the same process parameters. Thereafter, the Arcam EBM system would recognize them as two separate print jobs. During each printing layer, the plate A was printed firstly, and subsequently, the plate B (Fig. 1a) was printed. This process was repeated until the final object was completed. During the EBM process, the bidirectional scanning was changed with a 90\u00b0 rotation at each layer (Fig. 1b and c). In this case, the plate A and plate B were \u201cwelded\u201d for every single layer. Finally, a fully fused part with a combination of plate A and plate B was obtained by the EBM process. By applying the above concept, a Ti-6Al-4V plate with a dimension of 100\u00d7200mm and a build height of 4mm (Fig. 2a) by welding two 100\u00d7100\u00d74mm plates was successfully fabricated. The two plates were indicated by different colors. In the conventional EBM process, the fabrication of 100\u00d7200mm plate required a 200mm scan length, which caused lack of fusion defects [22,23]. In the current approach, the 200mm scan length was intentionally divided into two 100mm scan lengths (Fig. 1). The pre-alloyed Ti-6Al-4V powder with a particle size ranging from 45 to 105 \u03bcm [24], received from Arcam AB, was used in an Arcam A2X EBM system. To verify our concept, only the default EBM process parameters were applied. The detailed description of the standard preparation of EBM system and default process parameters can be found in our previous reports [3,12]. In this study, an in-situ welding zone of 0.5mm in width (Fig. 2a) was set to evaluate the possible (i) generation of defects, (ii) microstructural morphology changes and (iii) related variations in mechanical properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.55-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.55-1.png",
        "caption": "Fig. 3.55 Comparison between fluido-mechanical brake (FMB) and electro-mechanical brake (EMB) [MESSIER-BUGATTI 2005].",
        "texts": [
            " When the driver steps on the brake foot pedal, a computer sends information to a control box, which converts the electrical signals into an electrical command: the E-M actuators on the brake disc, ring or drum, replacing the fluidic pistons, press the discs against each other as in a conventional F-M BBW AWB conversion mechatronic control system. An \u2018EMB\u2019 automotive vehicle simply means one that uses electricity to replace all other forms of onboard energy, especially fluidical. This offers a host of advantages in terms of size, mass, reliability, safety (by eliminating the risk of oily-fluid or air leaks and associated fire hazards), and operating/ maintenance costs (Fig. 3.55). EMB technology enhances the efficiency of braking in general and of each individual brake, through faster response, simpler installation and easier diagnostics and maintenance. E-M friction disc, ring and drum brake mechatronic control technologies are gradually being developed and applied in stability control systems (SCS) systems and BBW AWB dispulsion mechatronic control systems based on the ABSs, and scientists and engineers have been working to develop an E-M friction disc, ring and drum brake mechatronic control system in terms of future BBW AWB dispulsion, to the practical application phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.32-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.32-1.png",
        "caption": "Fig. 17.32 Graph of the function \u03b2 = f(\u03b1) for /h = 0.5 (curve k ) and approximation by a Jeantaud mechanism with nonoptimal parameters ( , \u03b3)",
        "texts": [
            "31 the axes are shown in a vertical projection during a left turn. With an ideal steering mechanism the turning angles \u03b1 and \u03b2 are coordinated such that the two front axes and the rear axis of the car have, independent of the radius R of the curve, a common intersection point. The lengths and h are constant parameters. From triangles the equations are obtained: h = (R\u2212 /2) tan\u03b1 , h = (R+ /2) tan\u03b2 . Elimination of the variable R results in cot\u03b2 \u2212 cot\u03b1 = h . (17.132) This equation defines the function \u03b2(\u03b1) . It is an odd function. The curve denoted k in Fig. 17.32 is the graph of this function for the specific parameter value /h = 0.5 in the interval of interest up to the maximum steering angles (\u03b1max, \u03b2max) . If, for example, \u03b1max = 40\u25e6 , (17.132) yields \u03b2max \u2248 30.6\u25e6 . Jeantaud invented the steering mechanism shown in Fig. 17.33 . It is a symmetrical four-bar approximating (17.132). The input link and the output link of equal length r are rotating about A0 and B0 , respectively. They are rigidly connected with the front axes. The figure shows the mechanism in the symmetrical trapezoidal position (front axes not turned) and in a Fig",
            "135) After applying the addition theorem for the cosine function this takes the form A cos\u03b2\u2217 +B sin\u03b2\u2217 = C , (17.136) A = cos \u03b3 \u2212 cos(2\u03b3 \u2212 \u03b1) , C = 2 cos \u03b3 \u2212 cos 2\u03b3 \u2212 cos(\u03b3 \u2212 \u03b1) , B = \u2212 sin \u03b3 + sin(2\u03b3 \u2212 \u03b1) . } (17.137) The equation has two solutions \u03b2\u2217 . Their sines are sin\u03b2\u2217 = BC \u00b1A \u221a A2 +B2 \u2212 C2 A2 +B2 . (17.138) The pertinent solution is the one which has the same sign that \u03b1 has. This solution defines a two-parametric manifold of functions \u03b2\u2217(\u03b1, , \u03b3) with parameters and \u03b3 . Every parameter combination ( , \u03b3) determines a curve \u03b2\u2217(\u03b1) in the diagram of Fig. 17.32 . It is reasonable to require that the curve passes through the point \u03b1 = \u03b1max , \u03b2\u2217 = \u03b2max . This means that (17.135) is satisfied with \u03b1 = \u03b1max and \u03b2\u2217 = \u03b2max . This equation determines for every value of \u03b3 the associated value of . Thus, a one-parametric manifold of curves with parameter \u03b3 is left. In Fig. 17.32 a single nonoptimal curve is shown. The optimal value of \u03b3 is determined from the criterion that the maximum of the deviation |\u03b2\u2217(\u03b1)\u2212 \u03b2(\u03b1)| in the interval 0 \u2264 \u03b1 \u2264 \u03b1max be minimal. It turns out that this criterion yields two solutions \u03b31 > 0 and \u03b32 < 0 . Example: With /h = 0.5 , \u03b1max = 40\u25e6 and \u03b2max \u2248 30.6\u25e6 the solutions are \u03b31 \u2248 67\u25e6 , 1 \u2248 0.25 and \u03b32 \u2248 \u2212121\u25e6 , 2 \u2248 0.25 . The fourbar with \u03b32 is located in front of the front axis. The four-bar with \u03b31 is the one shown in Fig. 17.33 . It is located behind the front axis (Brossard [4])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002764_2971763.2971778-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002764_2971763.2971778-Figure1-1.png",
        "caption": "Figure 1. Example racket (without rubbers) showing the sensor placement. Sensor A was mounted on the left side at the outer edge, sensor B on the front side an sensor C at the same height on the right side. One conditioning circuit with its components is shown on the left side. The actual piezo-electric sensor is on the bottom side of the board, to have direct contact to the wood.",
        "texts": [
            " In [5], a twodimensional laser array was built-up as a light barrier array to detect ball contacts. The impact positions were detected if a ball interrupts the specific transmitter-receiver combination. Most of above mentioned approaches are not applicable to a real table tennis racket, since they are based on either video analysis, are too big and too heavy or affect the play characteristics of the racket. Therefore, our purpose was to develop a ball impact localization system which consists of a minimum number of sensors (as shown in Figure 1) and a small and simple data conditioning circuit, which can finally be unobtrusively integrated into the wooden racket core. This system should comply with the international table tennis regulations, which imply, that the racket (without the rubbers) must consist of 85% wood [21]. In case of a ball impact on the racket, the impact force generates vibrations which propagate with sound velocity in all directions over the blade first through the elastic rubber layers and then through the different wooden veneers",
            " This was the reason why we built-up a time difference distribution model per racket and rubber type, which was finally used to derive the initial ball impact position. We used three PKGS00LDP1R [13] shock and acceleration sensors from Murata as piezo-electric measurement devices. With dimensions of 6.4 mm x 2.8 mm x 1.2 mm, these sensors are small enough to be fully integrated into the wooden blade in the future. As the sensors possess only one sensing axis, all sensors were positioned perpendicular to the racket blade in the direction of the expected incoming transverse wave. Figure 1 shows the sensor placement. Every sensor including its conditioning circuit (overall size 12 mm x 5 mm, total weight < 1 % of racket weight) was mounted on the outer edge of the wooden racket core. If seen from top, sensor A was mounted on the left side, sensor B on the opposite of the handle and sensor C on the right side at the same height as sensor A. All sensors were glued onto the wooden core using curing adhesives to ensure proper vibration conduction. Thin connection cables were led from every sensor on the outer edge to the racket handle for further signal processing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.83-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.83-1.png",
        "caption": "Fig. 2.83 Principle layout of the flat skateboard-chassis concept [Scientific American, Inc.; General Motors; BURNS ET AL. 2002].",
        "texts": [
            " Recognising this design opportunity, some vehicle manufacturers came up with a concept that will be introduced in the early 2020s. The flat chassis concept and the automotive vehicle prototype may be created, literally, from the wheels up. The foundation for both is a thin, skateboard-chassis containing the FC, traction E-M motor(s), hydrogen storage tanks, mechatronic controls and heat exchangers, as well as throttling, braking, and steering mechatronic control systems. There are no ECE or ICE, transmission, drivetrain, axles, or mechanical linkages, as shown in Figure 2.83 [BURNS ET AL. 2002]. 2.4 M-M Transmission Arrangement Requirements 239 In a fully developed automotive vehicle, HE DBW AWD propulsion technology would require only one simple electrical connection and a set of mechanical links to unite chassis and body. The body could plug into the chassis much like a laptop connects to a docking station. Automotive Mechatronics 240 The single-electrical-port concept creates a quick and easy way to link all the body mechatronic control systems \u2013 controls, power and heating \u2013 to the skateboard"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002804_j.triboint.2019.03.065-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002804_j.triboint.2019.03.065-Figure3-1.png",
        "caption": "Fig. 3. Schematic representation of the experimental set-up employed to measure friction. The rheometer exerts a torque (T ) and a normal force (F ) to the ball. To maintain a commanded sliding speed, the rheometer applies the necessary torque to the ball. The normal load is fixed constant during the experiment in order to keep the ball and three plates in contact. The normal load",
        "texts": [
            " Rheological tests were performed by applying a shear torque which logarithmically increased from 10\u22124\u2013102mN\u00b7m. Tribological tests were carried out under pure sliding conditions in a ball-on-threeplates geometry with polydimethyl siloxane PDMS-PDMS tribopairs (Young modulus of 1.84MPa and Poisson ratio of approximately 0.5) [38,43]. PDMS tribopairs were prepared in situ using conventional techniques from a two-component silicone elastomer kit (SylgardTM 184, Dow Corning). A schematic representation of the experimental setup is shown in Fig. 3. The ball radius was =R 6.35mm and the plates were parallelepipeds with dimensions 3mm \u00d7 6mm \u00d7 16mm. The tribological experiments consisted of two intervals. In the first interval, the normal force was adjusted to 1 N. In the second interval, the ball was rotated and the rotational speed was logarithmically increased from 0.1 to 2000 rpm still at a normal force of 1 N. The friction coefficient was monitored during the second interval. Both rheological and tribological tests were carried out at 25 \u00b0C on fresh new samples in order to avoid water evaporation and undesirable changes in the particle volume fractions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.8-1.png",
        "caption": "Figure 6.8. Motion of a particle under a drag force FD .",
        "texts": [
            " Stokes's Law of Resistance The simplest model used to study the nature of phenomena arising from drag effects of air and water on an object moving at low speeds is described by Stokes 's law: The drag force FD on a particle is oppositely directed and proportional to its velocity v: FD = - cv. (6.29) The constant c > 0 is called the drag or damping coefficient. This model is applied later to investigate the motion of a projectile and of a particle falling with air resistance. First, however, we form ulate the problem for a more general model for which the drag force is an unspecified function of the speed. 6.5.2. Formulation of the Resistance Problem Figure 6.8 shows a particle P moving in the vertical plane of frame cp = (0 ; ik } , under a total force F(P, t ) = W + FD con sisting of its weight W = mg 120 Chapter 6 and the drag force FD == -R(v)t , where R(v) is an unspecified, positive-valued function of the particle speed v. The equation of motion, by (6.1), is mg - R(v )t = ma(P , t ). (6.30) Two cases are considered-rectilinear motion and plane motion. 6.5.2.1. Rectilinear Motion with Resistance Let us consider a vertical rectilinear motion in the direction of g = gt in Fig. 6.8a. Then with a(P , t ) = il t, (6.30) becomes . R(v ) v = g - - == F(v). (6 .31) m Integration of (6.31) yields the travel time as a function of the particle velocity in the resisting medium, t = ! ~~) + co, (6.32) where Co is a constant. Theoretically, this equation will yield v(t) = ds / d t which may be solved to find the distance s(t) traveled in time t. Alternatively, using iI = udufds in (6.31), we find the distance traveled as a function of the speed, s = ! ;::) + Cl, (6.33) in which Cl is another constant of integration",
            " First, recall the power series 122 expansion of e' about z = 0: Chapter 6 Z2 Z3 eZ = I + z+ - + - + .... (6.34d) 2! 3! Then use of (6.34d) in (6.34b) and (6.34c) yields, to the first order in v, an approximate solution for the case of small air resis tance: vet) = gt (I - ~t) , When v --+ 0, we again recover absent. 6.5.2.2. PlaneMotion with Resistance g 2 ( V )set) = \"it I - 3t . (6.24) for which air (6.34e) resistance is o Now, let us consider the plane motion of a particle in frame cp = {o; i, j}, as shown in Fig. 6.8. With t = v] \u00bb = i/vi + y/vj and g = - gj in (6.30), the component equation (6.2) yields .. R(v) .x = ---x , mv .. R(v) . y = -g - -y. mv (6.35) These equations are difficult to handle in this general form. For resistance governed by Stokes's law (6.29), however, the ratio R(v)/m v = clm is constant; and (6.35) simplifies to x = - vi , y = - g - vy with c v = - . m (6.36) Example 6.12. Projectile motion with air resistance. A projectile S of mass m is fired from a gun with muzzle speed Vo at an angle fJ with the horizonta l plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000144_ip-b.1987.0046-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000144_ip-b.1987.0046-Figure2-1.png",
        "caption": "Fig. 2 Motor design and constructional details",
        "texts": [
            " The handpiece consists of three sections, the first of which is the synchronous motor head occupying only 12% of the total volume. This motor is fed from three single-phase transformers which are housed in the second section. The third section is a heat sink which is arranged to be in good thermal contact with both the outer case and the transformer secondary windings. The heat sink houses the connections to the primary windings of the transformers. The motor section is illustrated in more detail in Fig. 2. A high-speed bearing system supports a simple 2-pole rotor and axial preload is maintained on these races by a thrust nut and spring washer. The larger bearing at the loading end has an internal diameter approximately equal to the motor airgap diameter and the pilot bearing at the rear of the rotor is made as small as possible. The rotor shaft and magnet casing are machined as a single component out of nonmagnetic stainless steel. Such an arrangement gives considerable mechanical strength and permits the standard friction-grip tool chuck, which accepts the driven tools, to be inserted alongside the rotor magnet",
            " The tolerance of the synchronous type motor to low slot numbers then led to a choice of three stator slots, each trapezoidal slot to carry one bar of a 3-bar, 3-phase system as indicated in Figs, la and 2. A particular design feature of the rotor, indicated by the very small diameter, was the decision to form the rotor magnet as a simple undrilled cylindrical slug. This slug is diametrically magnetised and bonded inside the hollow nonmagnetic stainless steel shaft. The detailed rotor construction is indicated in Fig. 2 where it will be apparent that a high-coercivity magnetic material is necessary to drive the working flux through the magnet casing. Samarium-cobalt was found to be a suitable material for the rotor magnet in this situation. The chosen rotor construction requires that the loading-end bearing must have an inside diameter which exceeds the diameter of the magnet slug by a sufficient amount so that adequate thickness for the bearing seating is available. An additional constraint here is that of providing the housing diameter for the standard friction-grip tool chuck",
            " A required output of 10 W at 150 000 rev/min would then leave the order of 2 g cm of torque to account for windage, friction and stray loads. In Fig. 5b the values of Wt/R0 are obtained from eqn. 9 and the values of t/R0 from eqn. 11. The design value of B/Bs is indicated by the lines D in Figs. 5a and b. In the absence of detailed knowledge of the bore and slot flux distributions at the design stage it was decided to set the lamination parameters at their values corresponding to when k = 1. The resulting lamination is shown to scale in Fig. 2. Subsequent numerical investigation of the flux distribution for this lamination in fact indicated k = 2.55 so that the parameters H/Ro and WJR0 differ slightly from their ideal values. It will be seen in Fig. 2 that the stator stack is extended 1 mm beyond each end of the magnetic slug. This is done to prevent stray flux from the highcoercivity magnet cutting stationary conducting circuits and generating rotor drag torques. The optimum slot design for the motor as deduced in the previous section has a cross-sectional area close to 20 mm2. The design value of slot current density then sets the rated transformer secondary current at 80 A (RMS). The rated secondary voltage of the transformer is of course frequency dependent but the most onerous duty for the transformer is motor synchronisation at a supply frequency of between 10 and 20 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.52-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.52-1.png",
        "caption": "Fig. 2.52 Basic mechanical layout of the classical integrated M-M powertrain that includes the ECE or ICE, M-M clutch, M-M transmission, universal-joints (UJ), M-M propeller shaft (drive-shaft), M-M differential and rear wheels [HOWSTUFFWORKS.COM 2001].",
        "texts": [
            " Customer requirements regarding vehicle performance are becoming increasingly demanding and complex. Legal regulations concern environmental aspects, but the expectations of the customer are strongly characterised by the desire for individuality, quality of mobility, and practicality [SCHOEGGL ET AL. 2001]. In order to meet customer demands, an approach involving the classical integrated M-M powertrain may be suggested where the aim might be to gain advantages by treating the M-M powertrain as a whole. Figure 2.52 shows the parts of the M-M powertrain: ECE or ICE, M-M clutch, M-M transmission, universal-joints (UJ), M-M propeller shaft (driveshaft), M-M differential and rear wheels. 2.1 Introduction 201 At present there is a general consensus that an M-M powertrain is an M-M driveline with an ECE or ICE. Integrated powertrain control (IPC), deals with all elements of a vehicle\u2019s M-M powertrain as parts in an integrated system, thus being the opposite of treating each part as an individual component. Problems that occur in modern vehicles involving the M-M powertrain are phenomena referred to as shunt and shuffle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001806_tasc.2016.2524026-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001806_tasc.2016.2524026-Figure4-1.png",
        "caption": "Fig. 4. The principle of generating the suspension force in 12/14-pole BFSPM motor.",
        "texts": [
            " The principle of generating the suspension force in 12/10- pole BFSPM motor is illustrated in Fig. 3. It can be seen that the flux density direction excited only by x-axis suspension winding current are identical with that of PMs in air gap 1 and opposite in air gap 2. Hence, the flux density is increased in air gap 1 and decreased in air gap 2. Then, the radial suspension force Fx is generated toward the positive direction in the x-axis. Similarly, the suspension force generated principle of the 12/14 pole BFSPM motor is shown in Fig. 4. In this section, the electromagnetic performances of the two BFSPM motors are calculated and compared using 2-D FEA, including the magnetic saturation, torque, suspension force, coupling and loss. Fig. 5 compares the flux density waveforms of the two motors in the air gaps with and without feeding 10 A suspending current. It can be seen that the maximum air gap density of the 12/10-pole and 12/14-pole BFSPM motors can reach 1.5 T and 2.3 T, respectively. At the same time, the flux density of 12/10-pole motor increases significantly while the flux density of 12/14-pole motor in the x positive directionis almost the same with 10 A suspension excitation currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000205_978-1-4615-9882-4_40-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000205_978-1-4615-9882-4_40-Figure8-1.png",
        "caption": "Figure 8 Producted leftway walking pattern",
        "texts": [],
        "surrounding_texts": [
            "Six types of preset walking patterns, forward, backward, rightway, leftway walking, CCW and CW turning, were designed according to the control laws aided by a simulation program named Walk Master having two-dimensional graphic output function. Forward walking, leftway walking and CW turning produced with Walk Master are shown in Figures 7 - 9. As a result of walking experiments with these patterns, smooth and stable quasi-dynamic forward walking is achieved, and stable static walkings are realized in other types of walking. Based on the experimental results, the response of machine model in forward walking is shown in Figure 10 by using graphical output function of Walk Master, and the trajectory in change over phase is shown in Figure 11. The walking time in each walking is shown in Table 1."
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.5-1.png",
        "caption": "Figure 5.5. A homogeneous, thin rigid rod under a uniformly distributed load.",
        "texts": [
            "29), each of these systems may be reduced to a single force The Foundation Principles of Classical Mechanics 19 acting at its center of force. Clearly, for a system of discrete forces, the procedure is similar. CSee Problem 5.35.) For further discussion on the reduction of force systems for the general case see the referenced texts on statics. Example 5.3. A homogeneous, thin rigid rod of length .e is supported at one end by a smooth hinge at Qand is subjected to a load of magnitude y per unit length distributed uniforml y over the region [a, .e ] shown in Fig. 5.5. (i) Find the force system with respect to Q that is equipollent to the distributed load. (ii) Determ ine the moment of the distributed load about the center of mass of the rod at C. Solution of (i), The total force FA = P equipollent to the distributed load FB = FdCge) for which dFdCP ) = y dx j is given by C5.28). Thus, P = ifydxj = yc.e - a)j . C5.30a) The total moment of the distribution about the hinge point Q is given by C5.22) in which xQCP) = x i+yj; M~ Cge) = i fxi x ydxj = r C.e2 - a2 )k",
            " Here we see that for the system A only the component Xi of xQthat is perpendicul ar to P contributes to the torque about Q. Thus, with C5.30b), C5 .29) yields x= !C.e + a); that is, with respect to Q, the center of force x'Q for P is at xQ= !C.e +a)i = [a + !C.e - a)] i. C5.30c) The line of action of P is traced by xQ= xQ+ yj for all values of y. Equation C5.30c) shows that the center of force for the uniforml y distributed load is at the geometrical center of the loaded portion of the rod in Fig. 5.5. The force system 20 ChapterS (5.30d) consisting of the single force P acting at the center of force x'Q in (5.30c) is equipollent to the assigned uniformly distributed force system; it consists of the same total force (5.30a) and produces the same total moment about Q in (5.30b). Solution of (ii), The moment of the same distribution about point C may be found from the transformation rule (5.25). In accordance with (5.26), consider the load P placed at the center of mass of the homogeneous rod at x'Q ((J)3) = "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure7-1.png",
        "caption": "Fig. 7. HANA* parallel manipulators: (a) with inclined angle \u03b1 and (b) with horizontal actuators.",
        "texts": [
            " However, there is a remarkable difference between these two manipulators in terms of the rotational DOF. The rotational DOF of HANA* is implemented with the combination of Legs 1 and 2 with the PRC chain. This situation is same to the HANA* with revolute actuators shown in Fig. 6(b). In the HALF*, the rotational DOF is reached by actuating only one leg, i.e. Leg 3. Similarly, the actuating direction of all sliders in the HANA* parallel manipulator with prismatic actuators may be inclined at an \u03b1 angle with respect to the vertical line as shown in Fig. 7(a). Figure 7(b) illustrates a typical example when the actuating direction is horizontal. They have the same mobility as that of the manipulator shown in Fig. 6. It is not difficult to find out that, compared with the HANA manipulators, the HANA* parallel manipulators introduced here also have the advantages in kinematics, architecture, manufacturing, energy cost, accuracy, and assembling for the similar reasons described in Section 2.1. Since there is no planar parallelogram in each manipulator of the new family, every leg can be designed as a telescopic link"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.13-1.png",
        "caption": "Fig. 14.13 Relationships between circle points, reflection point Q\u2032 and center Q0",
        "texts": [
            " From this it follows that both points are located on the circle. End of proof. Consequently, the three reflections of the circumcircle in the sides of the triangle (dashed lines) intersect at S . Next, relationships are formulated between the center Q0 , the reflection point Q\u2032 , the circle points Q1 , Q2 , Q3 and the poles. The point Q0 is the intersection point of the midperpendiculars of the triangle (Q1,Q2,Q3), and every midperpendicular passes through one pole. The midperpendiculars are shown in Fig. 14.13 . As an example, consider the perpendicular bisector passing through P12 . At P12 the angles satisfy the equation (P31P12P23) = \u03d512/2 as well as the equation (Q1P12Q0) = 1 2 (Q1P12Q2) = \u03d512/2 . Since the angles (Q1P12P31) and (P31P12Q \u2032) are equal, they are also equal to the angle (Q0P12P23) . In Fig. 14.13 these angles are denoted \u03b212 . By the same arguments angles \u03b223 and \u03b213 appear twice each at the other poles of the pole triangle. As is shown in the figure each angle is measured from two sides of the triangle with opposite signs. Through these relationships the point Q\u2032 is determined if Q0 is given and vice versa. If Q0 (if Q\u2032 ) is not located in a pole, Q\u2032 (or Q0) is uniquely determined. The circle points Q1 , Q2 , Q3 are obtained by reflecting Q\u2032 in the sides of the pole triangle. Obviously, the following statement is true: The center Q0 and the reflection 428 14 Displacements in a Plane point Q\u2032 can be interchanged",
            " Special case (a): Q0 coincides with a pole, for example with P12: In this case, Q\u2032=Q3 is an undetermined point on the line P23P31 ; Q1 lies on the dotted line P31P 1 23 , and Q2 lies on the line P23P 2 31 . Special case (b): Q\u2032 coincides with a pole, for example with P12: In this case, Q1=Q2=Q\u2032=P12 ; Q3 =P3 12 ; Q0 is an undetermined point on the line P23P31 . Infinitely Distant Center Point With a center point Q0 at infinity the circle points Q1 , Q2 , Q3 are on a straight line. Its location is explained by Fig. 14.14 . Let Q0 be prescribed as intersection of two arbitrarily directed parallel lines passing through P12 and P23 , respectively. In this case, the angles \u03b212 and \u03b223 explained in Fig. 14.13 are identical: \u03b212 = \u03b223 = \u03b2 . This has the consequence that Q\u2032 lies on the circumcircle of the pole triangle (equal angles \u03b2 subtended by the chord P31Q \u2032 ) . Since Q1 , Q2 , Q3 are the reflections of Q\u2032 in the sides of the triangle, each point lies on the reflection of the circumcircle in one side of the triangle. Since these reflected circles are concurrent in S , the line Q1Q2Q3 passes through S . 14.4 Relationships Between Three Positions 429 Infinitely Distant Circle Points The interchangeability of center point Q0 and reflection point Q\u2032 has the consequence: If Q0 is an arbitrarily prescribed point on the circumcircle of the pole triangle, the corresponding reflection point Q\u2032 and the corresponding circle points Q1 , Q2 , Q3 are at infinity",
            " Proposition: The direction toward the circle point Qi (i = 1, 2, 3) is normal to the line Q0S i . The proof is given for the case i = 3 : The lines leading from P23 toward Q\u2032 and Q3 , respectively, must be symmetric with respect to the line P23P31 . This is, indeed, the case since not only the two angles \u03b2 are equal, but also the two angles denoted \u03b1 are equal. The reason is that \u03b3 = 90\u25e6 \u2212 \u03b1 is the angle subtended by the chord S3P23 . End of proof. Sense of Triangle of Circle Points In Fig. 14.16 the pole triangle of Fig. 14.13 is shown again. Its sides 1 , 2 and 3 define the sense of the pole triangle. In the figure the sense is clockwise. In what follows, the side i of the pole triangle continued to infinity in both directions is referred to as line i (i = 1, 2, 3). The lines 1 , 2 and 3 divide the infinite plane into seven domains (the lines themselves do not belong to any of these domains). If the center point Q0 is inside the pole triangle, also Q\u2032 is inside, and the triangle of circle points Q1, Q2, Q3 has the same sense the pole triangle has",
            "47) It is quadratic-involutoric. Further applications of normal coordinates to the study of positions of a plane are found in Blaschke [3] p.165 . In what follows, analytical relationships are developed between the circle points Q1 , Q2 , Q3 and the center point Q0 . In an arbitrary cartesian coordinate system fixed in \u03a30 the coordinates of a point are interpreted as real part and as imaginary part of a complex number. This number is given the name of the point itself. Examples are the numbers Q1 and P12 in Fig. 14.13 . In this figure, the example i = 1 , j = 2 illustrates the fact that for arbitrary combinations of indices i and j = i the difference Q0\u2212Pij is rotated against the difference Qi\u2212Pij through the angle \u03d5ij/2 . This means that the numbers ei\u03d5ij/2(Qi \u2212 Pij) and (Q0 \u2212 Pij) have equal directions (i, j = 1, 2, 3 ; i = j ). According to (14.6) this is expressed in the form Im [( cos \u03d5ij 2 +i sin \u03d5ij 2 ) (Qi\u2212Pij)(Q\u03040\u2212 P\u0304ij) ] = 0 (i, j = 1, 2, 3 ; i = j ) . (14.48) Let the coordinates of the points be denoted as follows: Qi = \u03bei+i \u03b7i , Q0 = x+i y , Pij = uij+i vij (i, j = 1, 2, 3 ; i = j ) ",
            " The other two circle points are then found as is shown in Fig. 14.11 by 17.14 Four-Bars Producing Prescribed Positions of the CouplerPlane.BurmesterTheory 629 630 17 Planar Four-Bar Mechanism reflections in the sides of the pole triangle. The center point Q0 is the center of the circumcircle of the triangle (Q1,Q2,Q3). Instead of a single circle point the center point Q0 can be chosen arbitrarily. The associated circle points Q1 , Q2 , Q3 are determined either geometrically by the pole triangle (Fig. 14.13) or analytically from (14.50). Following Fig. 14.13 special cases (a) and (b) were explained when a pole is chosen either as center point or as circle point. Figure 14.14 explains how to determine solutions with a center point Q0 at infinity and with circle points Q1, Q2, Q3 along a straight line. The straight line is passing through the orthocenter S of the pole triangle. If the line is prescribed, the circle points are determined, and if a single circle point is prescribed, the line and the other two circle points are determined. Figure 14.15 explains how to determine solutions with circle points lying at infinity",
            " The problem of determining circle points associated with a chosen center point or of determining the center point associated with a chosen circle point is reduced to the previously solved problem with three prescribed positions since a solution satisfying four prescribed positions 1 , 2 , 3 , 4 satisfies any three positions, for example, positions 1 , 2 , 3 and positions 1 , 2 , 4 . Hence circle points associated with a chosen center point Q0 are determined either geometrically from pole triangles (Fig. 14.13) or analytically from Eqs.(14.50) which are now valid for the larger set of indices i, j = 1, 2, 3, 4 ( i = j ). Special case: As center point Q0 a pole is chosen, for example, Q0=P12 . From the text following Fig. 14.13 (special case (a)) it is known that in the pole triangle associated with positions 1 , 2 , 3 Q3 is an undetermined point on the line P23P31 . For the same reason, Q3 is an undetermined point on the line P34P41 in the pole triangle associated with positions 1 , 3 , 4 . Hence Q3 is the point of intersection of these two lines. There is only a single solution with a center point Q0 at infinity and with circle points Q1, Q2, Q3, Q4 along a straight line. The center point Q0 is the infinitely distant point on the asymptote of the pole curve",
            " As in the case of three positions, the directions Q0Qi (i = 1, 2, 3, 4) toward the infinitely distant circle points are determined from pole triangles (Fig. 14.15). A center point Q0 on p close to U is associated with a very long crank with very distant circle points. Circle point curves: The geometric locus of the circle point Qi is called circle point curve ki ( i = 1, 2, 3, 4 ). If a single circle point curve, say k1 , is known, the other three curves are obtained by rotating k1 about poles. From Fig. 14.13 and Eq.(14.50) it is known that Q1 and Q0 switch roles if 17.14 Four-Bars Producing Prescribed Positions of the CouplerPlane.BurmesterTheory 631 632 17 Planar Four-Bar Mechanism the angles \u03d512 and \u03d513 are replaced by \u2212\u03d512 and \u2212\u03d513 , respectively. This means that the pole P23 is replaced by its reflection P1 23 in the side P12P 31 of the pole triangle (see Fig. 14.12). With other indices the same is true for the other two pole triangles (P12,P24,P41) and (P13,P34,P41) associated with Q1 . In these triangles P24 and P34 are replaced by the reflected poles P1 24 and P1 34 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure12-1.png",
        "caption": "Fig. 12. Boundary conditions for finite element analysis.",
        "texts": [
            " 9 (a), (d) and (e), as the medium gear basic circle radius increases, it can be discovered that the contact points move along the axial direction of the IHB gear tooth surface, the contact areas on the left and right tooth surface are moved toward the middle plane and decreased, the distribution of contact points is more concentrated, and the contact ellipse area is bigger. According to the above-derived tooth surface equations, the precise three-dimensional models of the novel hourglass worm drive are established and shown in Fig. 10 . And the finite element model is shown in Fig. 11 , there are 18,230 elements with 23,157 nodes in the finite element model. Compared with the gears and bevel gears, the finite element analysis boundary conditions of the hourglass worm gear drive require special considerations, and it is set as shown in Fig. 12 . It is assumed that the IHB gear is at rest relative to the fully constrained at the rigid surface I. The OPE hourglass worm has only one degree of freedom as rotational motion of its axis z 2 , while other degrees of freedom are constrained. Therefore, the OPE hourglass worm is cylindrical supported through the rigid surface II. A torque M 2 is applied to the rigid surface II on each example while the IHB gear is at stationary state. After the finite element model is solved, the contact state on the tooth surface of the IHB gear of each example is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000700_s11044-009-9145-7-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000700_s11044-009-9145-7-Figure1-1.png",
        "caption": "Fig. 1 A 2(SP + SPR + SPU) manipulator and its composite platform",
        "texts": [
            " This manipulator has some merits: (1) The coupled structure constraints can be transformed into the decoupled structure constraints by the SP constrained active leg, so that the redundant self-motion can be removed effectively; (2) A workspace and flexibility are clearly enlarged; (3) A spherical joint has a simpler structure and a larger capability of load-bearing than a universal joint, when a motor shaft is installed across the joint, so that more valid extension of SP leg can be obtained. Therefore, this manipulator has some potential applications for the robot arm, leg, and twist, the serial\u2013parallel machine tools, the sensors, the surgical manipulators, the tunnel borers, the barbette of warships, the satellite surveillance platform, and so on. A 2(SP + SPR + SPU) serial\u2013parallel manipulator includes an asymmetrical lower SP + SPR + SPU parallel manipulator (lower manipulator) and an asymmetrical upper SP + SPR + SPU parallel manipulator (upper manipulator), see Fig.1. The lower manipulator and the upper manipulator are connected serially, so that the workspace and the flexibility are clearly enlarged. The lower manipulator includes a middle moving platform m, a fixed base B , one SP (spherical joint-active prismatic joint) active leg r1 with linear actuator, one SPR (spherical joint-active prismatic joint-revolute joint) active leg r2 with linear actuator, and one SPU (spherical joint-active prismatic joint-universal joint) constrained active leg r3 with linear actuator",
            " Let A1 be a general forward acceleration of m1 at o1 in {B}; a1 and \u03b51 be a linear and an angular acceleration of m1 at o1 in {B}, respectively. They can be expressed as follows: o1 = \u23a1 \u23a3 Xo1 Yo1 Zo1 \u23a4 \u23a6 , V 1 = [ v1 \u03c91 ] , v1 = \u23a1 \u23a3 vx1 vy1 vz1 \u23a4 \u23a6 , \u03c91 = \u23a1 \u23a3 \u03c9x1 \u03c9y1 \u03c9z1 \u23a4 \u23a6 , (22) A1 = [ a1 \u03b51 ] , a1 = \u23a1 \u23a3 ax1 ay1 az1 \u23a4 \u23a6 , \u03b51 = \u23a1 \u23a3 \u03b5x1 \u03b5y1 \u03b5z1 \u23a4 \u23a6 . A composite rotational matrix B c R from {c} to {B} can be derived as follows [1]: B c R = B mRm c R = B c R\u22121 = B c RT = \u23a1 \u23a3 c\u03b2 s\u03b2s\u03bb s\u03b2c\u03bb 0 c\u03bb \u2212s\u03bb \u2212s\u03b2 c\u03b2s\u03bb c\u03b2c\u03bb \u23a4 \u23a6 \u23a1 \u23a3 c\u03b8 \u2212s\u03b8 0 s\u03b8 c\u03b8 0 0 0 1 \u23a4 \u23a6 (23) where \u03b8 is an angle between x and xc (see Fig. 1(b)). o1,v1,\u03c91,a1 and \u03b51 can be derived from (15)\u2013(21) as follows [1, 2]: o1 = o + B c Rco1, v1 = v + B c Rcv1 + S(\u03c9)B c Rco1 = v \u2212 S ( B c Rco1 ) \u03c9 + B c Rcv1, (24) a1 = a \u2212 S ( B c Rco1 ) \u03b5 + B c Rca1 + 2S(\u03c9)B c Rcv1 + S(\u03c9)S(\u03c9)B c Rco1, \u03c91 = \u03c9 + B c Rc\u03c91, \u03b51 = \u03b5 + B c Rc\u03b51 + S(\u03c9)B c Rc\u03c91. A general forward velocity V 1 of o1 in {B} is derived from (20), (21) and (24) as follows: V 1 = JvV + JR cV 1 = JvJ\u22121vr + JR ( J\u22121 1 ) vr1, (25) Jv = [ E3\u00d73 \u2212S(B c Rco1) 03\u00d73 E3\u00d73 ] 6\u00d76 , JR = [ B c R 03\u00d73 03\u00d73 B c R ] 6\u00d76 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001547_iros.2013.6696825-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001547_iros.2013.6696825-Figure19-1.png",
        "caption": "Figure 19. Head section climbing over a step.",
        "texts": [
            "1 mm/s, respectively, which means the aluminum-sheet-coated robot passes through the elbow 1.7 times faster than the uncoated robot. Thus, we confirmed that the aluminum-sheet-coated robot can pass through an elbow smoothly. Thus, the proposed approach leads to reduced friction and steps of the robot, and is thus effective in enabling the robot to smoothly pass through an elbow. In this section we explain the requirement for the head section to guide the robot when the robot is passing through an elbow. Figure 19 shows an image of the head section climbing over a step that is between an elbow and a straight pipe. First, to climb over the step, the ABS part needs to proceed in the direction of travel, therefore the tip of the head section needs to be flexible. Figure 20 shows an image after the head section has climbed over the step. If the head section is flexible, the base of the head section buckles, therefore the head unit collides with the elbow. Thus, the base of the head section needs a pulling force that pulls it backward because the head unit needs to proceed in the direction of traveling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.6-1.png",
        "caption": "Fig. 12.6 Force screw (F,M) = F (n1,a1 \u00d7 n1 + p1n1) and velocity screw (\u03c9,v) = \u03c9(n2,a2 \u00d7 n2 + p2n2)",
        "texts": [
            " This force screw has either the general form (F,M) = F (n1,a1\u00d7 n1 + p1n1) or the special form M(0,n1) when only a free couple is acting. Imagine, furthermore, that the instantaneous state of motion of the body is given by its velocity screw. This screw has either the general form (\u03c9,v) = 12.5 Virtual Power of a Force Screw. Reciprocal Screws 369 \u03c9(n2, a2 \u00d7 n2 + p2n2) or the special form v(0,n2) in the case of pure translation. Virtual changes of the velocity screw are expressed in the form \u03b4\u03c9(n2,a2 \u00d7 n2 + p2n2) in the general case and in the form \u03b4v(0,n2) in the special case. In Fig. 12.6 the general case is shown with unit vectors n1 and n2 along the screw axes and with vectors a1 and a2 pointing from an arbitrary point 0 to points on the screw axes. For convenience, the points at the feet of the common perpendicular are chosen since the second Plu\u0308cker vectors a1 \u00d7 n1 and a2 \u00d7 n2 are independent of which points are chosen. The virtual power \u03b4P of the force screw calculated for the virtual change of the velocity screw is \u03b4P = F \u00b7 \u03b4v +M \u00b7 \u03b4\u03c9 . (12.41) For screws of the general form \u03b4P = \u03b4\u03c9F [ n1 \u00b7 (a2 \u00d7 n2 + p2n2) + n2 \u00b7 (a1 \u00d7 n1 + p1n1) ] (12",
            " Equilibrium requires that the virtual power is zero. If exactly one of the screws is special, this is the orthogonality condition n1 \u00b7n2 = 0 . In the general case, the condition is (a1 \u2212 a2) \u00b7 n1 \u00d7 n2 + (p1 + p2)n1 \u00b7 n2 = 0 (12.44) and in terms of the Plu\u0308cker vectors ni and wi = ai \u00d7 ni (i = 1, 2) of the screw axes n1 \u00b7w2 + n2 \u00b7w1 + (p1 + p2)n1 \u00b7 n2 = 0 . (12.45) The equations are symmetric with respect to the indices 1 and 2 . Two screws satisfying the condition are called reciprocal screws. From Fig. 12.6 it is seen 370 12 Screw Systems that the scalar form is (p1 + p2) cos\u03b1\u2212 sin\u03b1 = 0 , (12.46) where and \u03b1 (both positive or zero or negative) are the length of the common perpendicular and the projected angle between the screw axes. Equations (12.40) and (9.37) defined the dual screws: F+ \u03b5M = F (1 + \u03b5p1)n\u03021 , \u03c9 + \u03b5v = \u03c9(1 + \u03b5p2)n\u03022 , n\u0302i = ni + \u03b5ai \u00d7 ni (12.47) (i = 1, 2) . The scalar product of the dual unit screws is (1+\u03b5p1)(1+\u03b5p2)n\u03021\u00b7n\u03022 = n1\u00b7n2+\u03b5[(a1\u2212a2)\u00b7n1\u00d7n2+(p1+p2)n1\u00b7n2] . (12.48) The reciprocity condition (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003778_j.mechmachtheory.2021.104407-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003778_j.mechmachtheory.2021.104407-Figure9-1.png",
        "caption": "Fig. 9. The distribution of the friction coefficient and contact pressure on the contact surface.",
        "texts": [
            " (31) : E loss = Ne \u2211 i =1 4 \u2211 j=1 E loss , ij = Ne \u2211 i =1 4 \u2211 j=1 \u222b \u222b \u03bcs, ij ( \u02c6 \u03b4, l ) N ij ( \u02c6 \u03b4 )\u2202s ij \u2202 \u0302 \u03b4 d \u0302 \u03b4dl , (31) where the equivalent contact load N i j ( \u0302 \u03b4) in response to various roller-raceway contact states can be calculated from Eq. (22) , and \u03bcs,i j and s i j respectively represent the friction coefficient and sliding distance, which are analyzed in the subsequent section. To calculate the sliding friction between the roller and block interface, the distributions of the Hertzian contact pressure and friction coefficient on the contact surface are analyzed, as shown in Fig. 9 . Under non-uniform load distribution conditions, the maximum Hertzian pressure at an arbitrary section along the axial direction of the roller contact is adequately defined by the following equation [28] : P H i j ( l ) = \u221a d N i j \u00b7 E \u03c0d \u00b7 dl . (32) By substituting Eq. (17) into Eq. (32) , the maximum Hertzian pressure at an arbitrary section can be rewritten as P H i j ( l ) = \u221a KE \u03b4i j ( l ) 1 . 078 \u03c0d . (33) To induce a suitably explicit coefficient for the case of roller-raceway contact, the friction coefficient of the sliding contact due to the asperities and shear film can be obtained by the equation proposed by Tallian [29], which can be expressed as \u03bcs,i j = \u03bca exp ( \u2212 \u03bb2 2 ) \u221a 2 [ 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.17-1.png",
        "caption": "Fig. 15.17 Center of acceleration G at the intersection of the Bresse circles (solid lines). Inflection circle (dashed line) and center of acceleration G\u2217 of the inverse motion",
        "texts": [
            "6) a and v are collinear if the imaginary part of av is zero, and they are mutually orthogonal if the 474 15 Plane Motion real part is zero. With (15.41) av = \u03d5\u0307{\u03d5\u0308(x2 + y2) + a0x+ i [\u03d5\u03072(x2 + y2)\u2212 a0y]} . (15.42) Both conditions result in the equation of a circle. The first circle is called inflection circle (geometric locus of all instantaneous inflection points). Both circles are also referred to as Bresse circles [6]. Their equations are inflection circle: \u03d5\u03072(x2 + y2)\u2212 a0y = 0 , (15.43) second Bresse circle: \u03d5\u0308 (x2 + y2) + a0x = 0 . (15.44) In Fig. 15.17 both circles are drawn in solid lines. With the coordinate y2 = a0 \u03d5\u03072 (15.45) of the point denoted P2 the inflection circle has the equation x2 + y2 \u2212 y2y = 0 . (15.46) From the figure it is seen that at points of inflection tangents to trajectories are passing through P2 . At the origin P and at the center of acceleration G both circles intersect orthogonally. The coordinates of G are xG = \u2212y2 \u03d5\u0308/\u03d5\u03072 1 + (\u03d5\u0308/\u03d5\u03072)2 , yG = y2 1 1 + (\u03d5\u0308/\u03d5\u03072)2 . (15.47) 15.2 Velocity and Acceleration in Complex Formulation 475 The line passing through P2 and G passes also through the second point of intersection of the second Bresse circle with the x -axis",
            "44) yields for the Bresse circles of the inverse motion the equations 476 15 Plane Motion inflection circle: \u03d5\u03072(x2 + y2) + a0y = 0 , (15.51) second Bresse circle: \u03d5\u0308 (x2 + y2) + a0x = 0 . (15.52) Thus, the second Bresse circles of motion and inverse motion are identical, whereas the inflection circle of the inverse motion is the reflection of the inflection circle of the motion in the tangent to the centrodes. Also the center of acceleration G\u2217 is the reflection of the center of acceleration G . In Fig. 15.17 all centers and circles are shown. As before, an arbitrary continuous motion of a plane \u03a32 relative to a reference plane \u03a31 is considered. In the present section curvatures of trajectories of points of \u03a32 are investigated. Curvature is a differential-geometric property which is determined by the shape of the trajectory independent of the motion generating the trajectory. For this reason, the complex representation known from (15.30) is used with \u03d5 as independent variable: r(\u03d5) = rA(\u03d5) + ei\u03d5 ( = const) ",
            "57) also for rPn+1 and taking the difference results in the equation in(rPn+1 \u2212 rPn ) = r(n) + i r(n+1) (n = 1, 2, . . .) (15.60) and with the first Eq.(15.58) r (n) P1 = in(rPn+1 \u2212 rPn ) (n = 1, 2, . . .) . (15.61) The relationship dr/dt = \u03d5\u0307 dr/d\u03d5 shows that P1 is identical with the instantaneous center of velocity. In the special case of motion with \u03d5\u0307 = const, dnr/dtn = \u03d5\u0307n r(n) and, in particular, d2r/dt2 = \u03d5\u03072 r\u2032\u2032 . From this it follows that in the special case \u03d5\u0307 = const, P2 is identical with the instantaneous center of acceleration G . Already in Fig. 15.17 this point was denoted P2 . In the x, y-system of this figure the normal poles are, in the instantaneous position shown, rP1 = 0 , rP2 = i y2 , rPn = xn + i yn (n > 2) . (15.62) The coordinates y2 , xn and yn (n > 2) are determined by the motion of plane \u03a32 . Example: In Figs. 15.26 and 15.27 the rolling motion of a planetary wheel 1 on or inside a fixed sun wheel 0 is shown. The planetary wheel is the moving plane \u03a32 , and the sun wheel is plane \u03a31 . The point denoted P10 is the normal pole P1 ",
            " This shows that the normal poles are located on the normal to the centrodes, and that their distances from the center of the planetary wheel form a geometric series. The elliptic trammel in Fig. 15.4 is the planetary gear with \u03bb = \u22121 . In this special case, the normal poles coalesce alternatingly with P1 and with the center of the planetary wheel. End of example. Let P\u2217 n be the n th-order normal pole of the inverse motion (motion of \u03a31 relative to \u03a32 ). From Sect. 15.1 it is known that P\u2217 1 =P1 . Furthermore, from Fig. 15.17 it is known that P\u2217 2 and P2 are located symmetrically to P1 on the normal to the centrode. With (15.53) P\u2217 n (n \u2265 1 arbitrary) is expressed in terms of P1, . . . ,Pn as follows. In the inverse motion r is constant while rA(\u03d5) and (\u03d5) are variable. The derivatives of order n = 0 to n = 3 yield the equations n = 0 : r = rA + ei\u03d5 , n = 1 : 0 = r\u2032A + i ei\u03d5 + \u2032ei\u03d5 = r\u2032A + i (r \u2212 rA) + \u2032ei\u03d5 , n = 2 : 0 = r\u2032\u2032A \u2212 i r\u2032A + i \u2032ei\u03d5 + \u2032\u2032ei\u03d5 = r\u2032\u2032A \u2212 2i r\u2032A + (r \u2212 rA) + \u2032\u2032ei\u03d5 , n = 3 : 0 = r\u2032\u2032\u2032A \u2212 2i r\u2032\u2032A \u2212 r\u2032A + i \u2032\u2032ei\u03d5 + \u2032\u2032\u2032ei\u03d5 = r\u2032\u2032\u2032A \u2212 3i r\u2032\u2032A \u2212 3r\u2032A \u2212 i (r \u2212 rA) + \u2032\u2032\u2032ei\u03d5 ",
            " The result for n = 3 states that the two pairs of poles P1 , P2 and P\u2217 3 , P3 are the 15.3 Curvature of Plane Trajectories 479 parallel sides of a trapezoid and that the ratio of the lengths of these sides is 1 : 3 . From the sequence of Eqs.(15.67) continued for n > 3 the following explicit expression for rP\u2217 n is deduced: rP\u2217 n = n\u2211 k=1 ( n k ) (\u22121)k\u22121rPk . (15.68) The proof by induction is left to the reader. In this section the curvature of trajectories is investigated. An important role is played by the inflection circle shown in Fig. 15.18. As is known from Fig. 15.17 the circle is determined by the normal poles P1 and P2 . It is the geometric locus of all points of \u03a32 the trajectories of which have, instantaneously, an inflection point and a tangent passing through the normal pole P2 which has the coordinate (see (15.45)) y2 = a0/\u03d5\u0307 2 , a0 being the acceleration of the point of \u03a32 coinciding with P1 . For simplifying the figure the case y2 < 0 is illustrated.The tangent to the inflection circle in P1 is also the tangent to the centrodes which are in rolling contact at P1 ",
            " This yields for 1 the first equation below. Equation (15.89) then determines 2 : 1 = y22 y2 \u2212 y3 , 2 = y22 2y2 \u2212 y3 . (15.96) In Sect. 14.1.1 the curvature \u03ba of a curve and vertices of a curve were defined. The vertex condition d\u03ba/d\u03d5 = 0 is Eq.(14.22): 2r\u2032r\u2032(r\u2032r\u2032\u2032\u2032 \u2212 r\u2032r\u2032\u2032\u2032)\u2212 3(r\u2032r\u2032\u2032 \u2212 r\u2032r\u2032\u2032)(r\u2032r\u2032\u2032 + r\u2032r\u2032\u2032) = 0 . (15.97) This equation determines all points r of a moving plane \u03a32 which are momentarily at a vertex of their respective trajectories. Let x and y be the coordinates of r in the x, y-system of Fig. 15.17: r = x+i y . For the derivatives r\u2032 , r \u2032\u2032 and r\u2032\u2032\u2032 Eqs.(15.59) are used: r(n) = in(r \u2212 rPn ) (n = 1, 2, 3) . For rPn (n = 1, 2, 3) Eqs.(15.62) are substituted. This results in the expressions r\u2032 = i (x+i y) , r\u2032\u2032 = \u2212x\u2212i (y\u2212y2) , r\u2032\u2032\u2032 = y\u2212y3\u2212i (x\u2212x3) (15.98) and 488 15 Plane Motion r\u2032r\u2032 = x2 + y2 , r\u2032r\u2032\u2032 = y2x+ i (x2 + y2 \u2212 y2y) , r\u2032r\u2032\u2032\u2032 = \u2212(x2 + y2) + x3x+ y3y + i (y3x\u2212 x3y) . } (15.99) With these expressions (15.97) takes the form [(3y2 \u2212 y3)x+ x3y](x 2 + y2)\u2212 3y22xy = 0 (15.100) or (\u03bbx+ \u03bcy)(x2 + y2)\u2212 xy = 0 (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.19-1.png",
        "caption": "Fig. 17.19 Constant parameters \u03b7 , \u03b6 , b1 , b2 , \u03b2 and variable coordinates x, y of the coupler point C",
        "texts": [
            " The links A0A1B1 with B1 guided along f1 constitute a slidercrank mechanism, and the links A0A2B2 with B2 guided along f2 constitute another slider-crank mechanism. With both mechanisms the coupler-fixed point C traces one and the same coupler curve. Thus, the existence of two cognate slider-crank mechanisms is proved. The figure explains how to construct one from the other. 594 17 Planar Four-Bar Mechanism For the graphical display of coupler curves a parameter representation of the curve is required which determines, in the x, y -system of Fig. 17.19 , the coordinates x and y of the coupler point C as functions of the input angle \u03d5 . Constant parameters in these functions are , r1 , r2 , a and the coordinates \u03b7 and \u03b6 of C in the coupler plane. Using the inclination angle 17.8 Coupler Curves 595 \u03c7 of the coupler as auxiliary variable the coordinates of C are x = r1 cos\u03d5+ \u03b7 cos\u03c7\u2212 \u03b6 sin\u03c7 , y = r1 sin\u03d5+ \u03b7 sin\u03c7+ \u03b6 cos\u03c7 . (17.74) This is the desired parameter representation of the coupler curve. For cos\u03c7 and sin\u03c7 the expressions from (17.23) are substituted: cos\u03c7k = A\u0304C\u0304 \u2212 (\u22121)kB\u0304 \u221a A\u03042 + B\u03042 \u2212 C\u03042 A\u03042 + B\u03042 , sin\u03c7k = B\u0304C\u0304 + (\u22121)kA\u0304 \u221a A\u03042 + B\u03042 \u2212 C\u03042 A\u03042 + B\u03042 , \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (k = 1, 2) , (17",
            " This has the consequence that coupler curves of such four-bars are bicursal (two closed branches). The transition from unicursal to bicursal coupler curves occurs in foldable four-bars. In this case, the two closed branches of a bicursal curve create a singular point. The three coupler curves in Fig. 17.20 demonstrate the transition from unicursal to bicursal curves. Except for r1 the sets of parameters ( , r1 , r2 , a , \u03b7 , \u03b6) are the same for all three curves. The circle is explained following Eq.(17.87). Figure 17.19 is considered again. This time, the location of the coupler point C in the coupler plane is specified not by the parameters a , \u03b7 , \u03b6 , but by the parameters b1 , b2 , \u03b2 . The transformation equations between these two sets of parameters are b1 = \u221a \u03b72 + \u03b62 , b2 = \u221a (a\u2212 \u03b7)2 + \u03b62 , cos\u03b2 = b21 + b22 \u2212 a2 2b1b2 , a = \u221a b21 + b22 \u2212 2b1b2 cos\u03b2 , \u03b7 = b1(b1 \u2212 b2 cos\u03b2) a , \u03b6 = b1b2 sin\u03b2 a . \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (17.77) 596 17 Planar Four-Bar Mechanism For making statements about properties of coupler curves the parameters b1 , b2 , \u03b2 are more suitable",
            " In the case b1 = 0 (in the case b2 = 0 ), coupler curves are circles or arcs of circles with radius r1 about A0 (with radius r2 about B0 ). Coupler curves are confined to the area bounded by the concentric circles about A0 with radii |r1 \u2212 b1| and r1 + b1 and by the concentric circles about B0 with radii |r2 \u2212 b2| and r2 + b2 . In the case b1 , b2 , a , r1 , r2 , coupler curves are approximately circles or arcs of circles. The goal of the following analysis is an implicit equation of the coupler curve in the form f(x, y, , r1, r2, b1, b2, \u03b2) = 0 . In developing this equation the auxiliary variables \u03b1 and d shown in Fig. 17.19 are used temporarily. From the figure it is seen that x = r1 cos\u03d5+ b1 sin\u03b1 . (17.78) The cosine law applied to the triangles (A,D,A0 ) and (A,D,C) yields two expressions for d2 . The identity of these expressions is the equation r21 + x2 \u2212 2xr1 cos\u03d5 = b21 + y2 \u2212 2b1y cos\u03b1 . (17.79) For r1 cos\u03d5 the expression from (17.78) is substituted. This results in the following equation which is linear with respect to both sin\u03b1 and cos\u03b1 : 2b1(x sin\u03b1+ y cos\u03b1) = x2 + y2 + b21 \u2212 r21 . (17.80) The same equations are formulated for the triangles (B,D,C) and (B,D,B0 )",
            " For this it is necessary that sin\u03b2 = 0 . This means that the generating coupler point C lies on the coupler line AB (not necessarily between the points A and B ). The coupler curve in Fig. 17.2 is an example. According to the Roberts-Tschebychev theorem every such coupler curve is generated by two more four-bars. Also in these four-bars the coupler point lies on the coupler line. In Eq.(17.84) for symmetrical coupler curves with sin\u03b2 = 0 the parameters are b1 = \u03b7 and b2 = \u03b7\u2212a where \u03b7 is the parameter used in Fig. 17.19 . Of particular interest are intersection points of the coupler curve with the axis of symmetry. With y = 0 the following equation is obtained for these points which is of third order in x and in \u03b7 : 604 17 Planar Four-Bar Mechanism (\u03b7 \u2212 a)(x\u2212 )(x2 + \u03b72 \u2212 r21)\u2212 \u03b7x[(x\u2212 )2 + (\u03b7 \u2212 a)2 \u2212 r22] = 0 . (17.100) For given parameters the equation has either one or three real roots x . For this reason one does not expect coupler curves which do not intersect the x -axis. Such coupler curves do exist, however",
            "106) The position d = \u2212 r is always possible, the position d = + r only if the four-bar is a crank-rocker. It is left to the reader to show that the positions d = \u2212 r and d = + r of a crank-rocker yield identical values of y if the parameters satisfy the condition r2+ 2 cot2 \u03b2 = 4a2 cos2 \u03b2 . In this case, 606 17 Planar Four-Bar Mechanism the coupler curve has a quadruple point on the circle of singular foci. In Fig. 17.28 these conditions are satisfied. The slider-crank mechanism shown in Fig. 17.29a is derived from the four-bar in Fig. 17.19 by moving the point B0 in y-direction to \u2212\u221e . This has the effect that the endpoint B of the coupler of length a is guided along the straight line y = h = const. In the inverted slider-crank mechanism of Fig. 17.29b the coupler of length a has become the fixed link, while the fixed link with the parameter h has become the moving coupler. The parameter h can be positive or zero or negative. Arbitrarily, it is considered as positive in both figures. In both figures the crank angle \u03d5 is the input variable, and the inclination angle \u03c7 of the coupler and the position s of the slider are output variables",
            " Inverted Slider-Crank 607 (r cos\u03d5\u2212 a) cos\u03c7+ r sin\u03d5 sin\u03c7 = \u2212h , s = r sin\u03d5 cos\u03c7\u2212 (r cos\u03d5\u2212 a) sin\u03c7 . } (17.109) The first equation has two solutions cos\u03c71,2 and sin\u03c71,2 . The associated solutions s1,2 are obtained from the second equation. In both figures the equivalent to Grashof\u2019s Theorem 17.1 is Theorem 17.3. The link with the shorter of the two lengths a and r is fully rotating relative to all other links if h2 \u2264 (a\u2212 r)2 . (17.110) Coupler curves: In both figures the coupler-fixed point C is specified by constant parameters b1 , b2 and \u03b2 . In Fig. 17.29a the notation is the same as in Fig. 17.19, whereas in Fig. 17.29b b2 and \u03b2 are defined differently. Implicit equations for coupler curves in the form f(x, y, r, b1, b2, \u03b2) = 0 are obtained from two linear equations for the sine and cosine of the auxiliary variable angle \u03b1 . For both figures (17.78) and (17.79) are valid. Hence also the resulting Eq.(17.80) is valid: 2b1(x sin\u03b1+ y cos\u03b1) = x2 + y2 + b21 \u2212 r2 . (17.111) In Fig. 17.29a the second linear equation for cos\u03b1 and sin\u03b1 is y = h+ b2 cos(\u03b2 \u2212 \u03b1) . (17.112) In Fig. 17.29b the coordinates of point E satisfy the three equations xE = x\u2212 b2 sin(\u03b1\u2212 \u03b2) , yE = y \u2212 b2 cos(\u03b1\u2212 \u03b2) , xE = a\u2212 yE cot(\u03b1\u2212 \u03b2) ",
            " Each diagram is a compilation of four-bars (not only crank-rockers) and of coupler curves having the same singular foci and the same double points on the circle of singular foci (17.87). In what follows, some mathematical problems and methods of solution are discussed which are encountered in the generation of coupler curves with prescribed properties. The parameter representation of the coupler curve in the form of Eqs.(17.74) \u2013 (17.76) contains the six constant parameters , r1 , r2 , a , \u03b7 , \u03b6 and as seventh parameter the variable \u03d5 . These equations describe the coupler curve in the special x, y -system of Fig. 17.19 . Three additional constant parameters determine the location of this x, y -system in an x\u2032, y\u2032 -reference system. In a typical problem statement it is required that a coupler curve passes through prescribed points in the x\u2032, y\u2032 -system. Also the order in which these points are passed is prescribed. Let m be the number of prescribed points. The 2m prescribed coordinates result in 2m conditional equations. These equations contain 9 +m free parameters, namely, the nine constant parameters listed above and for every prescribed point the associated crank angle",
            " Every point C fixed on the coupler of a moving spherical four-bar traces a coupler curve which is located on a sphere. Without loss of generality the point C is chosen on the unit sphere. Together with the endpoints A and B of the coupler the point C creates a coupler-fixed spherical triangle (A,B,C). In Fig. 18.3 arcs of great circles are schematically represented by straight lines. As parameters of the coupler triangle the angles \u03b15 , \u03b16 and \u03b17 are chosen. They are equivalent to the parameters b1 , b2 and \u03b2 of the coupler triangle of the planar four-bar in Fig. 17.19. As coordinates of the coupler point C its geographical longitude u and its geographical latitude v are used (A0 and B0 lie in the equatorial plane; u = 0 at A0). The meridian passing through C defines the point D on the equator. 644 18 Spherical Four-Bar Mechanism To be determined is an implicit equation of the coupler curve in the form f(u, v, \u03b11, \u03b13, \u03b14, \u03b15, \u03b16, \u03b17) = 0 . The following derivation is due to Dobrovolski [1]. It is analogous to the development for the planar four-bar (see Fig. 17.19 and Eqs.(17.78) \u2013 (17.84)). Temporarily, the auxiliary variables \u03b1 , \u03b5 and \u03b4 are used. Spherical cosine and sine laws applied to the triangle (A,D,C) and the spherical cosine law applied to the triangle (A,D,A0) yield the equations cos\u03b1 = cos \u03b4 \u2212 C5 cos v S5 sin v , cos \u03b5 = S5 sin\u03b1 sin \u03b4 , cos \u03b5 = C1 \u2212 cos \u03b4 cosu sin \u03b4 sinu . (18.14) From the identity of the last two expressions it follows that cos \u03b4 = C1 \u2212 S5 sin\u03b1 sinu cosu . (18.15) Substitution of this expression into the first Eq.(18.14) results in the following equation which is linear with respect to both sin\u03b1 and cos\u03b1 : S5(sinu sin\u03b1+ cosu sin v cos\u03b1) = C1 \u2212 C5 cosu cos v ",
            " The x, y, z-system with unit basis vectors ex , ey , ez is defined in the text preceding (18.25). The x\u2217, y, z\u2217-system is rotated against the x, y, zsystem through the angle \u03b14 about the y-axis. The transformation is\u23a1 \u23a3x y z \u23a4 \u23a6 = \u23a1 \u23a3 C4 0 S4 0 1 0 \u2212S4 0 C4 \u23a4 \u23a6 \u23a1 \u23a3x\u2217 y z\u2217 \u23a4 \u23a6 . (18.49) The coupler triangle is defined as usual by the parameters \u03b15 , \u03b16 , \u03b17 . In addition, angular parameters \u03b7 , \u03b6 of the coupler point C and the auxiliary angle \u03c7 are introduced. The parameters \u03b7 , \u03b6 are equivalent to the parameters of equal name in the coupler triangle of the planar four-bar in Fig. 17.19. Cosine and sine laws establish the equations C2 = C5C6 + S5S6C7 , C5 = cos \u03b7 cos \u03b6 , C6 = cos(\u03b12 \u2212 \u03b7) cos \u03b6 , sin \u03b6 = S5 sin\u03c7 , cos\u03c7 = C6 \u2212 C5C2 S5S2 . \u23ab\u23ac \u23ad (18.50) The goal of the following analysis is to express the coordinates x, y, z of the coupler point C as functions of the single variable \u03d51 . Such parameter equations are the basis of graphical displays of coupler curves. Together with the x, y, z-coordinates the geographical coordinates u , v determined by (18.25) and the stereographic coordinates \u03be , \u03b7 determined by (18"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003183_j.jmatprotec.2020.116649-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003183_j.jmatprotec.2020.116649-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the deposition deviation phenomenon during omni-directional GTAW-based AM.",
        "texts": [
            " The results shown that the optimized wire feed geometry parameters and arc length control system can effectively guarantee the stability of the omni-directional GTAW-based AM process. What\u2019s more, This method also shown excellent stability in complex deposition paths, as investigated by our previous research (Wang et al., 2019a). However, these methods mentioned above do not take into account the accuracy of the deposition process. Omni-directional GTAW-based AM experiments shown a deposition deviation phenomenon when side feeding, as show in Fig. 1. Deposition deviation exists when the molten wire is not evenly distributed in the weld pool before solidification. Although this uneven filling does not affect the continuation of the deposition process, it will result in a stable weld bead dimensional deviation. This problem is not easy to be detected because the welding torch always moves along the established path and the deposition process is stable. Geng et al., 2017 studied the effect of wire feed behaviour on the deposition accuracy at the arc striking position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003174_s11012-019-01115-y-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003174_s11012-019-01115-y-Figure1-1.png",
        "caption": "Fig. 1 Healthy external gear tooth when the tooth number is less than 41: a approach process and b recess process",
        "texts": [
            " When the tooth number is greater than 41, the root circle is bigger than the base circle and the tooth profile is composed of the involute curves only which begin with the root circle and end up with the addendum circle. Both types of gears are widely used in modern industry and will be discussed respectively. When the tooth number is less than 41, the gear tooth profile consists of two kinds of curves: involute curves which go straight to the base circle (curves M0I and N 0J) and transition curves which start from the base circle and end up with the root circle, as shown in Fig. 1. Transition curves are not involute curves and usually are replaced by the straight linesMM0 andNN 0. During gear meshing, the contact process of the gear tooth has two phases: approach process and recess process [30]. The direction of sliding friction force f in these two phases is opposite and is always perpendicular to that of the normal contacting forceF. According to the Coulomb friction law, the friction force f is the product of friction coefficient l and the normal contacting force F: f \u00bc lF \u00f01\u00de There are various kinds of the sliding friction coefficient formulations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure5.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure5.6-1.png",
        "caption": "FIGURE 5.6. Longitudinal Mode and the First Three Thickness Modes, n = 0.",
        "texts": [],
        "surrounding_texts": [
            "Axially symmetric vibration occurs only in breathing mode with radial displacement (Markus 1988). Longitudinal modes occur with axial displacement, and torsional modes with transverse displacement around the circumference of the cross section. Figures 5.4 through 5.6 depict the three axisymmetric modes associated with the corresponding first three thickness modes of vibrations."
        ]
    },
    {
        "image_filename": "designv10_12_0001668_s40194-017-0533-y-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001668_s40194-017-0533-y-Figure5-1.png",
        "caption": "Fig. 5 Coil geometry without (a) and with (b) magnetic shield",
        "texts": [
            " At the end of the first step of the simulation\u2019s calculation\u2014 frequency analysis\u2014the current density is obtained. This gives knowledge which surfaces\u2014of the wire and substrate\u2014are the most affected by the magnetic field, which allows for an optimisation of the coil\u2019s geometry to have a better distribution of the magnetic field and therefore, of the current density. The results here are shown with a coil geometry that is optimised for a coil with a circular section, and which can be fabricated for experimental validation (Fig. 5a). The focus is on the current density J (A/m2) because of the link between the temperature field w (W/m3), in the substrate or/and in the layer, as Joule\u2019s law demonstrated [16]: w \u00bc \u03c1J 2 \u00f01\u00de with \u03c1 the electrical resistivity of the material (\u03a9.m). The temperature field is highly dependent on the density of current. As a consequence, the higher temperature field will be located where the current density is at its maximum. The coil geometry impacts the density of current but it is not the only parameter to take into account\u2014in the magnetic field",
            " The augmentation of these losses reduces exponentially the current density in the part and by implication, the maximal temperature reachable: T \u00bc T0e\u2212\u03b2:z \u00f02\u00de with T0 the maximal temperature for a coil distance with the substrate and z close to 0 mm. By definition, the magnetic field is all around the coil\u2019s open loop. There is also a magnetic loss in regions further away from the wire and the substrate. To minimise this loss and to have as a consequence, a better efficiency, a magnetic shield is added on the coil geometry (Fig. 5b). The thermal evolution increases by 50% when a magnetic shield is added (Fig. 8).With this system, it becomes possible tomove the coil slightly away from the substrate or/and to increase the speed of the deposition, for a given power. In conclusion, the increase of the magnetic heating in the part is directly coupled to the current density. At a fixed inductive power, the increase of coil inductor distance leads to a considerable reduction in the density of currents within the part. Thereby, to increase the heating, there are at least three possibilities: reducing the coil inductor distance with the part, adding a magnetic shield to the coil without changing the coil distance, or a coupling of these two solutions: reducing the distance and adding a magnetic field to the coil"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000587_3.7491-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000587_3.7491-Figure3-1.png",
        "caption": "Fig. 3 Normal and frictionai loads between ballast surface and cavity wall.",
        "texts": [
            " The equations of motion for the body are, in terms of nonrolling axes [ Angular velocities are related to Euler angle derivatives by ' Combination of these equations yields, for small 6, (la) (Ib) (Ic) Relative Orientation of Ballast and Projectile Figure 2 shows a cutaway view of the projectile and ballast with a form of mechanical coupling that can be closely approximated analytically. A ring of evenly spaced radial pins is positioned about the equator of the ballast, and these pins engage a series of longitudinal slots in the wall of the cavity within the projectile. Pin length is sufficient that pins cannot disengage from the slots. Slot width is sufficient that the ballast can assume a cocked position in the cavity without the pins binding in the slots* Figure 3a presents the view in the -z' direction of the ballast within the cavity. The ballast is assumed tilted, contacting the cavity wall at two points defined by f. This is taken to be the stable position for the ballast; a general analysis of ballast motion is not required here as a quasisteady solution D ow nl oa de d by U N IV E R SI T Y O F C A L IF O R N IA - D A V IS o n Ja nu ar y 29 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .7 49 1 JANUARY 1 978 PROJECTILE INSTABILITY PRODUCED BY INTERNAL FRICTION Fig",
            " The clearance A/* and the angle f completely define the orientation of the ballast axes with respect to the projectile axes. To transform the former into the latter, one must perform the following rotations: about x' (2a) These angles are illustrated in Fig. 4 for a large angle 0. Equations (2a-2c) are valid only for 6 small and A/V/-40, conditions which will be satisfied in applications discussed later. Transformation of torque components between the projectile and ballast axes is specified by (3) \"TV,.\" Ny. N,*. = \"\u2022 1 -A0 Ae \" A<\u00a3 7 -A0 -Ae A0 7 r^'i Ny, TV,, PROJECTILE ID) Figure 3b illustrates the forces, normal and frictionai, applied to the cavity wall by the ballast at the two points of contact. The ballast is driven by the mechanical coupling at the same rotational speed as the projectile. Since the cavity has a larger radius than the ballast, there must be a difference in peripheral velocity of the two bodies at the points of contact. As a result, the friction forces Fare directed so as to slow the rotation of the projectile. While it tends to slow the projectile, cavity wall friction acts to accelerate the ballast",
            " For clarity, slot width is exaggerated and only four slots are shown. can be shown that, for finite tilt angle Ar//, pin/slot clearance is minimum at positions which lie \u00b145 deg away from the direction of tilt defined by f. These points of minimum clearance are shown in Fig. 5. Under the action of the wall friction then, the ballast will rotate sufficiently to allow the necessary reactions to be provided by two diametrically opposed slots at 45 deg to the tilt direction. For the direction of rotation assumed in Fig. 3, the ballast tends to be accelerated counterclockwise (CCW) by the wall friction. Hence the reaction torque on the ballast must be clockwise (CW), and the pair of slot surfaces 1 and 2 in Fig. 5 will provide the reactions. The forces applied by the pins to surfaces 1 and 2 will be equal in magnitude but opposite in sense. Because there is relative motion between each pin and the surface it contacts, each force will have longitudinal and radial components, R{ and Rr, in addition to the circumferential component "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.46-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.46-1.png",
        "caption": "Fig. 15.46 Curves, points and domains of Figs. 15.44 and 15.45 for \u03b1 = 40\u25e6",
        "texts": [
            "170) reads (1 + y0)u 4 + 2x0u 3 \u2212 6u2 + 2x0u+ (1\u2212 y0) = 0 . This is the case \u03b1 < \u03c0/2 . Both domains \u03931 and \u03935 cover the entire sector between g1 and g2 . The curves E1(b) and E5(b) have the same equations as before. Phase 3 of the motion is restricted to the interval \u03c0/2\u2212\u03b1 \u2264 \u03d5 \u2264 \u03c0/2 . In this interval all previous results remain valid, i.e., Eqs.(15.161) \u2013 (15.163) for the curves E3(b) , Eq.(15.165) for K and Eq.(15.167) for the curved section of G35 . In the center \u03d5 = (\u03c0 \u2212 \u03b1)/2 of the interval all curves intersect the symmetry axis g . Figure 15.46 shows for \u03b1 = 40\u25e6 the curve K , the curved section of G35 and curves E3(b) for several values b \u2265 0 . At the final angle \u03d5 = \u03c0/2 the curve K and all curves E3(b) terminate on the line y = 1 . In particular, E3(0) terminates at the point Q0 with the coordinate x = cot\u03b1 , and K terminates at the point Q3 with the coordinate x = 2 cot\u03b1 . The curved section of G35 starts at the point S\u2217 (see Fig. 15.45 and (15.168)), and it terminates with \u03d5 = \u03c0/2 at the intersection of g2 and E3(0) . Reflection of G35 on g produces G31 ",
            "172) On E2(b) this equation as well as its partial derivative with respect to \u03d5 is satisfied: x cos(\u03d5+ \u03b1) + y sin(\u03d5+ \u03b1)\u2212 sin(2\u03d5+ \u03b1) + b cos(2\u03d5+ \u03b1) sin\u03b1 = 0 . (15.173) The solutions of these two equations for x and y are parameter equations of E2(b) : 15.6 Rectangle Moving Between two Lines and a Point 523 x(\u03d5, b) = sin\u03d5+ b cos\u03d5+ (cos\u03d5\u2212 b sin\u03d5) sin(\u03d5+ \u03b1) cos(\u03d5+ \u03b1) sin\u03b1 , y(\u03d5, b) = (cos\u03d5\u2212 b sin\u03d5) sin2(\u03d5+ \u03b1) sin\u03b1 \u23ab\u23aa\u23ac \u23aa\u23ad (\u03d50 \u2264 \u03d5 \u2264 \u03c0/2\u2212\u03b1) . (15.174) Figure 15.48 shows for \u03b1 = 40\u25e6 curves E2(b) for several values b \u2265 0 . At the end of the interval, i.e., for \u03d5 = \u03c0/2\u2212\u03b1 , all curves terminate on the normal to g1 through the point Q0 known from Fig. 15.46 . The interval starts with \u03d5 = \u03d50 given by (15.171). All curves E2(b) with b \u2265 cot\u03b1 start on the line y = sin\u03b1 . In particular, E2(b = cot\u03b1) starts at the point R0 with the coordinate x = (1 + 1/ sin2 \u03b1) cos\u03b1 . The curve E2(b) with b \u2264 cot\u03b1 (arbitrary) starts at the point with the coordinates x(b) = \u221a 1 + b2 cot\u03b1+ b\u221a 1 + b2 , y(b) = 1\u221a 1 + b2 (0 \u2264 b \u2264 cot\u03b1) . (15.175) These coordinates are obtained from (15.174) by substituting for sin\u03d5 and cos\u03d5 the expressions sin\u03d50 and cos\u03d50 , respectively, of (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001311_icuas.2013.6564711-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001311_icuas.2013.6564711-Figure3-1.png",
        "caption": "Fig. 3. Spinning body and arm numbering illustration.",
        "texts": [
            " One is the development of the rigid body relations of the tilting propeller that describe the torque as a function of the vehicle motion and the tilting motions. Another is the characterisation of the propellers in terms of thrust and torque coefficients. Finally, the individual actuators that create the tilting motion, servomotors, and the motors that vary the propeller\u2019s angular speed are dynamically characterised. The gyroscopic effects are modelled as the reactions generated by individual rotors spinning due to the vehicle motion and tilt motion of the actuators. In other words, it is assumed that each of the rotorpropeller assembly, shown in figure 3(a), act as a flywheel that, when tilted, creates the gyroscopic reaction torques. The relations between the motion of the jth rotor and the moments applied onto it expressed on the reference frame i are given by the Euler equation: iMj = iIj i\u03b1j + i\u03c9j \u00d7 iIj i\u03c9j (1) where iMj is the moment in the centre of gravity of the rotor in the jth arm in reference frame i (refer to Figure 3(b)), iIj is the inertia tensor about the CG in the reference frame i, i\u03c9j is the total angular velocity of the body j and i\u03b1j is the total angular acceleration of the body j in the reference frame i ,i.e. i\u03b1j = d dt i\u03c9j . As can be inferred from Figure 3(b) the vehicle presents symmetry both around the x-z plane and the y-z plane. Hence, the development of the equations is the same for all four arms if the reference frame is adequately transformed. For this reason, here only the equations with respect to arm 3 will be developed and then, the equations regarding the remaining arms can be obtained by an appropriate frame change. arm 3 will be referred to, herein, as Standard arm or arm 3 indifferently. With the nomenclature stablished in Figure 4 the angular velocity of the of rotor in arm 3, expressed in terms of reference attached to the motor stator (frame 3), will be given by: 3\u03c9 = 3i1p+3 j1q +3 k1r\ufe38 \ufe37\ufe37 \ufe38 Vehicle Motion + 3j1\u03b7\u0307\ufe38\ufe37\ufe37\ufe38 servoblock + 3i2\u03b3\u0307\ufe38\ufe37\ufe37\ufe38 push pull + 3k3\u2126\ufe38\ufe37\ufe37\ufe38 Motor (2) where the vectors iij ijj ikj represent the unit vectors of reference frame j expressed in terms of the reference frame i, see Figure 4 where the reference frames are detailed. The angular acceleration is the derivative of the angular velocity, hence 3\u03b1 = d3\u03c9/dt. The inertia tensor of the rotor, Figure 3(a), is symmetric because of the use of 3-blade propellers. The reference frame 3 is coincident with the principal inertia axes of the rotor, and so the inertia tensor is constant around those axes and it is given by: 3I =  Ixx 0 0 0 Iyy 0 0 0 Izz  (3) Thus, the moments can be calculated with the Euler equation around the reference frame 3: 3M = 3I3\u03b1+ 3\u03c9 \u00d7 3I3\u03c9 (4) Introducing and simplifying all the expressions above, the moments that the spinning body applies onto the airframe in the reference frame of the vehicle, 1MGyro, are obtained as: 1MGyro = R3to1(\u22123M) =  1MGyroX 1MGyroY 1MGyroZ  (5) where,1MGyroX , 1MGyroY and 1MGyroZ are the scalar moments in each axis which are specified on the appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000756_425501-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000756_425501-Figure1-1.png",
        "caption": "Figure 1. (a) Schematic diagram showing the SWNT chemiresistor structure. The black line indicates the carbon nanotubes. (b) Optical image of the interdigitated electrodes on the top of Si/SiO2 wafer. (c) AFM image of the SWNT network between interdigitated electrodes.",
        "texts": [
            " The DMMP was desorbed from the SWNT surface by N2 blowing together with illumination with a lamp (the wavelength was 710 nm and the power was 200 W). The sensor response was evaluated by the resistance change at a sampling voltage of 1 V. To measure the I \u2013V curves for each concentration of DMMP, the sensor device was exposed to the DMMM for 2 min. Before the next measurement of the I \u2013V curve, the resistance of the sensor was returned to its initial value by N2 blowing together with mild illumination with a lamp. Figure 1 panels (a) and panels (b) show the schematic and optical image of the SWNT chemiresistor structure, respectively. In this chemiresistive sensor, the SWNTs were used as conducting channels in the interdigitated electrodes. This electrode had a total area of 0.7 mm \u00d7 0.85 mm and line width of 10 \u03bcm. The random network of semiconducting SWNTs was formed between these interdigitated electrodes, as shown in the AFM image (figure 1(c)). The functionalization of the SWNT sensors was performed by dropping one drop of TFQ acetone solution onto the sensors and then vaporization of acetone at room temperature. The AFM image shows that many TFQ particles are absorbed on the SWNTs and the average height of the SWNTs increases from 4.5 to 14 nm after functionalization (figure S2, supporting information available at stacks.iop.org/Nano/22/425501/mmedia). A conductance between two electrodes was measured to investigate the sensory response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000085_j.cma.2005.05.055-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000085_j.cma.2005.05.055-Figure5-1.png",
        "caption": "Fig. 5. Deformed configurations and measurement of the elastic deformation.",
        "texts": [
            " The following is the description of the required steps: (i) The machine-tool settings applied for generation are known ahead, and then the pinion and gear tooth surfaces (including the fillet) may be determined analytically. (ii) Related angular positions \u00f0/\u00f0i\u00de1 ;/ \u00f0i\u00de 2 \u00de \u00f0i \u00bc 1; . . . ;N f\u00de are determined by (a) applying of TCA for Nf configurations (Nf = 8\u201316), and (b) observing the relation /\u00f0N f \u00de 1 /\u00f01\u00de1 \u00bc 2p N 1 . \u00f05\u00de (iii) A preprocessor is applied for generation of Nf models with the conditions: (a) the pinion is fully constrained to position /\u00f0i\u00de1 , and (b) the gear has a rigid surface that can rotate about the gear\u2019s axis (Fig. 5). Prescribed torque is applied to this surface. (iv) Finite element analysis is performed. The displacements of all nodes of the finite element model are obtained. (v) The nodal displacements of gear rigid surface provide the rotation angle of the gear D/\u00f0i\u00de2;e due to the applied torque. (vi) The total function of transmission errors for a loaded gear drive D/2;t\u00f0/ \u00f0i\u00de 1 \u00de is obtained considering: (i) the error D/2\u00f0/ \u00f0i\u00de 1 \u00de caused due to the mismatched of generating surfaces, and (ii) the elastic approach D/\u00f0i\u00de2;e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000423_tmag.2009.2012540-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000423_tmag.2009.2012540-Figure3-1.png",
        "caption": "Fig. 3. The complete model of the turbo-generator end part.",
        "texts": [
            " By applying 3-D FEM using the program Comsol Multiphysics 3.4, it is possible to represent an accurate 3-D geometry with its real complexity and to find more exact solution of the electromagnetic field even in the vicinity of the end core region. An application example is given, referring to a 200 MW turbine generator. The 3-D geometry of the machine is presented in Fig. 2 showing the stator and the rotor core with the rotor end windings. The complete model of the machine end zone is shown in Fig. 3. Because of the whole model complexity and especially the too large number of elements in the whole domain, in Fig. 4 is presented the stator core mesh only. There are described the number and the kinds of the elements for the stator core discretization. The technical characteristics of the investigated object are presented by its specification in Table I. The force densities are calculated using Maxwell stress tensor. The force distribution is determined outside the stator and the rotor cores. This study shows that as the temperature and the temperature gradient fields [8] the force density distribution closely depends on the working mode of the machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure16.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure16.5-1.png",
        "caption": "Fig. 16.5 If a ball is incident with topspin and bounces with topspin then a point at the bottom of the ball has a lower horizontal speed than the middle of the ball. The ratio ex D s2=s1 is called the tangential coefficient of restitution",
        "texts": [
            " Anything that can be done to make a ball bounce faster or spin faster is at the heart of modern sports technology and the hype that surrounds it. This is especially true in golf and tennis, although similar claims are often made in relation to aluminum bats. The only way to counter the hype is to take careful measurements of ball speed and spin to determine whether there is any substance to the manufacturer\u2019s claims. Some progress has been made in this direction but a lot more still needs to be done. Suppose that a ball is incident obliquely on a horizontal surface, at speed v1, and bounces at speed v2, as shown in Fig. 16.5. The horizontal components of the ball speed before and after the bounce are vx1 and vx2, respectively. The latter speeds refer to the speed of the ball center of mass (CM). Suppose also that the ball is incident with topspin and bounces with topspin, as shown in Fig. 16.3, with angular speeds !1 and !2, respectively. A point at the bottom of the ball will have a lower horizontal speed than the CM since the bottom of the ball is rotating backward. The horizontal speeds at the bottom of the ball are s1 D vx1 R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.132-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.132-1.png",
        "caption": "Fig. 2.132 Brushless DC-AC/AC-DC macrocommutator squirrel-cage-rotor hyposynchronous flywheel motor/generator including two M-M clutches [VW-Bosch\u2013LUK; STIFFER AND WALKER 1991].",
        "texts": [
            "8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 331 The supplementary electrical machinery is completed with little loss of comfort or luggage space of the vehicle. Embedded in place of the conventional ICE\u2019s flywheel is a compact DC-AC macrocommutator hyposynchronous squirrel-cage-rotor flywheel E-M motor. On the side to the ICE, as well as on the side to the MT or SAT or CVT, mechatronically activated M-M clutches are installed. The E-TMC system operates as stop-start (SS) clutches. Figure 2.132 shows the drive E-M motor and Figure 2.133 illustrates the operating rule arrangement. Only if the M-M clutch to the ICE is not turned on, the HEV is driven electrically, and during regenerative braking, electrical energy is being supplied to the CH-E/E-CH storage battery. If an ICE is propelling the vehicle, the M-M clutch on the ICE side is turned on; the squirrel-cage rotor of the DC-AC macrocommutator asynchronous squirrel-cage-rotor flywheel motor may then function as a flywheel. Besides, this electric drive unit acts as a starter E-M motor and as an onboard M-E generator [SEIFFERT AND WALZER 1991]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001186_1.3529411-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001186_1.3529411-Figure5-1.png",
        "caption": "FIG. 5. Schematic illustrating the deformation of the computational domain with the mean imposed shear flow, after Rogallo Ref. 57 .",
        "texts": [
            " This high dimensionality renders numerical solutions very expensive, and for this reason we developed a parallel scalable code, which was used in all the simulations. Typical grids of 1283 points in space and 162 points for the orientation angles were used, corresponding to a total of more than half a billion grid points. In order to use periodic boundary conditions for the solution of the flow equations, we employ Rogallo\u2019s method, in which the computational grid deforms to follow the mean imposed flow,57,58 see Fig. 5. This method shares similarities with the classic Lees\u2013Edwards boundary conditions59 commonly used in particle simulations. Specifically, if x, y, and z denote spatial coordinates in a fixed reference frame, we define a new set of coordinates x , y , and z in the deforming frame by This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.33.120.209 On: Sun, 04 Jan 2015 02:45:00 x = x \u2212 Syt, y = y, z = z "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002724_j.ymssp.2015.04.033-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002724_j.ymssp.2015.04.033-Figure3-1.png",
        "caption": "Fig. 3. Actuators (a) and their corresponding force vectors (b) of the test rig. The static force is provided by air springs in the radial (Fr,s) and axial (Fa,s) direction of the test bearing. The dynamic force is provided by an electrodynamic shaker in the radial (Fr,d) and axial (Fa,d) direction.",
        "texts": [
            " After inserting this auxiliary shaft into the main shaft of the spindle, the locknut is tightened forming a stiff connection between both shafts. Also, using an intermediate adaptor sleeve in between the bearing and the housing, different bearings can be fitted in the housing. The modular mounting system is shown in Fig. 2. The test rig allows applying an independently controlled load in the radial and axial direction. Furthermore, the load has a static and dynamic component in both directions. In this way, it is possible to simulate different real-life conditions, where e.g. gear meshing forces are acting on the bearing. Fig. 3 gives an overview of the actuator configuration. The static load is generated by four air springs, transferring their force to the bearing housing. Two air springs control the axial force (Fa,s) and two air springs control the radial force (Fr,s). The air springs apply a static force up to 10 kN in each direction. The dynamic load is directly introduced on the bearing housing using two electrodynamic shakers. One shaker provides the axial force (Fa,d) and one shaker provides the radial force (Fr,d)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure5-1.png",
        "caption": "Fig. 5. Required tooth contact pattern.",
        "texts": [
            " The tooth contact patterns and transmission errors with the tooth surface form deviations are analyzed using xa, that is, the numerical coordinates obtained using xa are considered as nominal data of the existing gear member. The position vector of i-th point of the theoretical tooth surface is expressed as xa(i). The real tooth surfaces of the existing gear member to be usedwere measured using a CMM as shown in Fig. 4 and the deviations between the real and theoretical tooth surface forms were formalized. Table 1 shows the dimensions of the skew bevel gears. The pitch circle diameter of the gear member is 1702.13 mm and it is very large. Fig. 5 shows the required tooth contact pattern. The position of the tooth contact pattern is somewhat near the toe side and the length is about 50% of the tooth width. Five points in the direction of the tooth profile and nine points in the direction of the tooth trace for the gridwere used. The amounts of tooth profile modification and crowning are \u0394c = 0.05 mm and \u0394s = 0.05 mm. Fig. 6 shows the formalized results based on the measured coordinates. Fig. 6(a) shows themeasured results using a CMMwithout formalization of the deviations \u03b4 between the real and theoretical tooth surface forms",
            "1mm in the toe side and of\u22120.3mm in the heel side were given. Fig. 9 shows the analyzed results of tooth contact pattern and transmission errorswhen taking into account the tooth surface form deviations in the samemanner as Fig. 8. The tooth contact pattern deviates slightly from the center on the tooth surface of both drive and coast sides, respectively. However, these contact patterns seem to be acceptable in practical use because the required tooth contact pattern is satisfied comparing with that of Fig. 5. Moreover, the transmission errors become large on the coast side. These transmission errors also seem to be acceptable in practical use. Therefore, the coordinates of the tooth surface of the pinion member are defined as nominal data and the pinion member is remanufactured based on these results. The pinion member was remanufactured using a 5-axis CNC machining center (DMGMoriseki Co., Ltd. DMU210P) based on the nominal data as mentioned in Section 4.2. In this case, the reference and hole surfaces in addition to the tooth surfaces can be machined, and tool approach is provided from optimal direction using multi-axis control since the structure of the 2-axis of the inclination and rotation in addition to translational 3-axis are added"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003357_0954406220911966-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003357_0954406220911966-Figure1-1.png",
        "caption": "Figure 1. Schematic of the integrated mechanical drive-train system in a large modern direct-drive wind turbine, and a 3D view of the main shaft which is supported by a DTRB in the front and a CRB in the rear of the shaft.2",
        "texts": [
            " Fatigue life, double row tapered roller bearing, offshore wind turbine, clearance, angular misalignment, oscillating load, rotating speed Date received: 9 December 2019; accepted: 17 February 2020 Wind energy industry has been growing rapidly due to the cost-effective and environmentally friendly nature of wind energy among various energy resources.1 In a large modern floating direct-drive wind turbine, a double-row tapered roller bearing (DTRB) and a cylindrical roller bearing (CRB) are commonly equipped in the front and rear of the main shaft as shown in Figure 1.2 These bearings provide the support for the whole weight of the rotor assembly including the generator, main shaft, nacelle, and blades. Hence, theses supporting bearings are one of the key components and their fatigue failure is a critical issue dominating the operation of wind turbines.3 It is noted that the failure rate of the main front DTRB is commonly higher than that of the rear CRB, because the front DTRB needs to support major radial and thrust loads.4 Therefore, the prediction of the fatigue failure of the front DTRB of wind turbines is of particular practical importance to ensure a safe operation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002661_s10010-019-00354-5-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002661_s10010-019-00354-5-Figure1-1.png",
        "caption": "Fig. 1 Gear operation test rig",
        "texts": [
            " Finally, the effectiveness of the proposed system is evaluated, and the crack or non-crack situation of the POM gear during working time is detected. In this section, the endurance experiment of plastic gears is described. Firstly, an automatic data acquisition system, which can measure the meshing vibration of plastic gears and capture images of gear tooth by a highspeed camera, is expressed. Then, an image data generation method is explained. In the method, the collected vibration signal is visualised as grayscale images for training input. The power-absorption-type gear operating test rig is shown in Fig. 1. In this figure, \u2460 is the driving motor and \u2465 is another motor to absorb the power of the driving motor. \u2461 is the driving gear called \u201csteel master gear\u201d, and \u2462 is the plastic test gear. Also, a torque meter \u2464 and an accelerometer \u2463 are installed for condition monitoring. Until now, there are no studies on which working condition is reasonable for plastic POM gear in endurance test. In this study, we attempt an unchanged testing condition with 7Nm of torque and 1000rpm of rotational speed, in which a test POM gear can work approximately 5h in an endurance test"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000846_0954405411407997-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000846_0954405411407997-Figure9-1.png",
        "caption": "Fig. 9 A fabricated universal joint: (a) 3D model of joint; (b) Tilted display; (c) fabricated joint; (d) joint cut from substrate",
        "texts": [
            " The process parameters were laser power 150 W, track spacing 0.12 mm, powder thickness 0.035 mm, and scanning speed 600 mm/s. All joints were produced without requiring assembly. A revolute joint was fabricated, shown in Fig. 8. The ring hole was designed to the drum shape; the clearance at both ends of the ring was 0.5 mm, and that at the peak was 0.2 mm. The vertical display was preferred, since the horizontal display led to too many overhangs. Figure 8(c) shows that the actual fabricated rings can rotate freely. In Fig. 9 the 3D model together with the build position and direction of a universal joint are shown. The joint consists of two yokes and a connecting cross hub. The hub was designed to the drum shape. The clearance at the peak was 0.2 mm and that at both ends was 0.4 mm. The assembly angle was adjusted to reduce overhang surface. Some supports were still needed within the clearances at this configuration, and were removed when the fabrication was done. The actual clearances, especially the clearance at the peak, are a little larger than the designed value, because the surfaces were damaged by violent Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure5.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure5.1-1.png",
        "caption": "Fig. 5.1 Bodies i\u22121 , i and i+1 with joint axes. Dual unit line vectors, body parameters and joint variables",
        "texts": [
            " This is the subject of the following Sect. 5.1 . Section 5.2 is devoted to coordinate transformations of relevant vectors. In Sect. 5.3 on closure conditions basic equations are formulated for the kinematics analysis. The application of these equations to the mechanisms of Table 5.1 is demonstrated in Sect. 5.4 . A single-loop mechanism with n bodies has n joints (4 \u2264 n \u2264 7). Bodies as well as joints are labeled from 1 to n in such a way that the joint axes i and i+ 1 are located on body i (i = 1, . . . , n cyclic). Figure 5.1 shows the bodies i\u2212 1 , i and i+ 1 together with their joint axes. The most general case is assumed that the two joint axes of each body are skew. Then the two joint axes of each body i have a common normal which is fixed on the respective body i . The joint axis i is, in turn, the common normal of the thus defined common normals on bodies i\u22121 and i . On the joint axis i the dual unit line vector n\u0302i is defined, and on the common normal of the joint axes i and i + 1 , i.e., also fixed on body i , the dual unit line vector a\u0302i is defined (i = 1, . . . , n). The unit line vector n\u0302i+1 is produced from n\u0302i by a screw displacement with a\u0302i being the screw axis. As shown in Fig. 5.1 the rotation angle about the screw axis is called \u03b1i and the translation along the screw axis is called i . These two constants (positive or negative) are the only kinematical parameters of body i . Together they define the constant dual screw angle \u03b1\u0302i = \u03b1i + \u03b5 i . (5.2) In the same way the unit line vector a\u0302i is produced from a\u0302i\u22121 by a screw displacement with the screw axis n\u0302i and with a dual screw angle \u03d5\u0302i = \u03d5i + \u03b5hi . (5.3) Figure 5.1 shows also \u03d5i and hi . In a cylindrical joint \u03d5i and hi are joint variables. In a revolute joint hi is a constant parameter and only \u03d5i is variable. In a prismatic joint \u03d5i is a constant parameter and hi is variable. The constant hi in a revolute joint is referred to as offset. The 4n quantities \u03b1i , i , \u03d5i , hi (i = 1, . . . , n) are the so-called Denavit-Hartenberg parameters of the mechanism (see Denavit/Hartenberg [3]). Seven among them are variables, and 4n \u2212 7 are constant system parameters",
            " In Fig. 5.4 a spherical four-bar is shown as quadrilateral A0ABB0 the links 1 , 2 , 3 , 4 of which are arcs of great circles on the unit sphere about the intersection point 0 of the joint axes. The unit vectors n1, . . . ,n4 along the axes are pointing away from 0 . The unit vector ai normal to both ni and ni+1 has the direction of ni \u00d7 ni+1 (here and in what follows, i = 1, . . . , 4 cyclic). The angle \u03b1i is the angle about ai from ni to ni+1 , and \u03d5i is the angle about ni from ai\u22121 to ai (see Fig. 5.1). The angle \u03b1i equals the arc of link i on the unit sphere. Link i is said to have the length \u03b1i . At this 180 5 Spatial Simple Closed Chains point the kinematics analysis is stopped. It is resumed in Chap. 18. Final remark: The expressions in (5.42) \u2013 (5.46) are moderately complicated. For mechanisms with up to twenty-one instead of nine constant parameters much more complicated expressions are generated. In every case the generation requires only two operations. One is copying terms from Table 5",
            " Another family of overconstrained mechanisms identified by Bricard [10] is referred to as plane-symmetric because of the pairwise symmetry of joint axes with respect to a plane \u03a3 . In Fig. 6.5 the spatial polygon of vectors hini and iai (i = 1, . . . , 6) is shown schematically. The symmetry requires the opposite joint axes 1 and 4 to lie in \u03a3 and to have zero offset: h1 = h4 = 0 . It is left to the reader to verify that the remaining Denavit-Hartenberg parameters satisfy the conditions (for definitions see Fig. 5.1) 6 = 1 , h6 = h2 , 5 = 2 , h5 = h3 , 4 = 3 , } (6.59) \u03b16 = \u03c0 \u2212 \u03b11 , \u03d56 \u2261 \u2212\u03d52 , \u03b15 = \u2212\u03b12 , \u03d55 \u2261 \u2212\u03d53 , \u03b14 = \u03c0 \u2212 \u03b13 . } (6.60) Dissection of joints 1 and 4 produces two symmetrical twin halves of the system. Consider the twin half consisting of bodies 1 , 2 and 3 and imagine body 2 to be fixed. Let body 1 be rotated relative to body 2 through an arbitrary fixed angle \u03d52 so that joint axis 1 assumes a certain position. Likewise, let body 3 be rotated relative to body 2 through the angle \u03d53 (variable) so that joint axis 4 generates an hyperboloid of revolution (in the case \u03b13 = 0 a cylinder of radius 3 and in the case \u03b13 = \u03c0/2 a plane every point of which outside a circle of radius 3 is located on two generators associated with different angles \u03d53 )",
            " Example: The mechanism with lengths ( 1, 2, 3, 4, 5, 6) = (16, 3, 9, 17, 5, 8) has the eight planar positions shown in Figs. 6.7a-h . In Fig. 6.7d all six rods are collinear, and the intersection points of both triples of joint axes are at infinity. End of example. The figures reveal the existence of two different types of trihedral mechanisms. In Figs. 6.7a-d the number of differences of lengths in the triangle is odd, and in Figs. 6.7e-h the number of sums of lengths is odd. According to the rules in Fig. 5.1 the following quantities are defined: \u2013 unit vectors n1 , . . . , n6 along the joint axes (sense of direction arbitrary) \u2013 vectors iai = \u2212\u2212\u2192 PiPi+1 (i = 1, . . . , 6) \u2013 constant angles \u03b1i and joint variables \u03d5i (i = 1, . . . , 6) . The angles \u03b11 , . . . , \u03b16 are either +\u03c0/2 or \u2212\u03c0/2 . Simple inspection reveals that, no matter how n1 , . . . , n6 are directed, the number of positive angles \u03b1i = +\u03c0/2 is even in Figs. 6.7a-d and odd in Figs. 6.7e-h . Wohlhart [33] who presented the first complete kinematics analysis speaks of a type 2 mechanism in the former case and of a type 1 mechanism in the latter",
            " Lines q1 = const (arbitrary) and q2 = const (arbitrary) on the surface are either circles or straight lines depending on whether the other variable not held constant is an angle in a revolute joint or a straight-line displacement in a prismatic joint. Each of the chains RR , RP , PR and PP has its own characteristic surface. The purpose of this section is to analyze, for each type of chain separately, the dependency of the surface upon the constant parameters of the chain. Parameters and variables are the Denavit-Hartenberg parameters explained in Sect. 5.1 (see Fig. 5.1). Unambiguous definitions require a chain of mutually orthogonal lines along joint axes and lines perpendicular to joint axes. For body 1 the situation is the same as for body i in Fig. 5.1 . Unit vectors along the joint axes are called n1 and n2 , and the unit vector along the common perpendicular is called a1 . Bodies 0 and 2 do not have a second joint axis. As lines perpendicular to the existing joint axes the axis e02 fixed on body 0 and the perpendicular from Q onto joint axis 2 are chosen. Let a2 be the unit vector pointing from the foot of this perpendicular toward Q . The lines thus specified define the Denavit-Hartenberg parameters \u03d51 , h1 , \u03b11 , 1 , \u03d52 , h2 and 2 of the chain. If joint i (i = 1 or i = 2) is a revolute joint, \u03d5i is variable and hi is constant. If joint i is a prismatic joint, \u03d5i is constant and hi is variable. The position vector x of Q is x = h1n1 + 1a1 + h2n2 + 2a2 . (7.1) The coordinates of n1 , a1 , n2 and a2 in basis e0 are taken from Table 5.2 by setting k = 0 . The abbreviations in the table are C1 = cos\u03b11 , S1 = sin\u03b11 and ck = cos\u03d5k , sk = sin\u03d5k (k = 1, 2) . By definition (see Fig. 5.1 and Eqs.(5.6), (5.7)), basis e0 is located not in joint 1 but in a joint 0 connecting body 0 to a preceding body \u22121 . In order to adapt to the present situation the angle \u03b10 between joint axes 0 and 1 must, formally, be defined as zero. This means that S0 = 0 and C0 = 1 . With these definitions Table 5.2 yields the coordinate equations 7.1 Work Space of Points of the Terminal Body 259\u23a1 \u23a3x1 x2 x3 \u23a4 \u23a6 = h1 \u23a1 \u23a3 1 0 0 \u23a4 \u23a6+ 1 \u23a1 \u23a30 c1 s1 \u23a4 \u23a6+ h2 \u23a1 \u23a3C1 S1s1 \u2212S1c1 \u23a4 \u23a6+ 2 \u23a1 \u23a3 s2S1 c2c1 \u2212 s2s1C1 c2s1 + s2C1c1 \u23a4 \u23a6 = \u23a1 \u23a3h1 + h2C1 + 2S1s2 ( 1 + 2c2)c1 \u2212 ( 2C1s2 \u2212 h2S1)s1 ( 1 + 2c2)s1 + ( 2C1s2 \u2212 h2S1)c1 \u23a4 \u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure3-1.png",
        "caption": "Fig. 3. (a) General model of an ACTR with land-fixed winches. (b) Free-body diagram (FBD) of robot\u2019s moving platform.",
        "texts": [
            " 3) Considering multiple/infinite collision-free arrangement of the UAVs, how we can find an optimal arrangement that provides the maximum size for SW? It is shown in this section that, differently from the presented approach in [14], the tension interval of UAV-connected cables cannot be established by relying on cables\u2019 characteristics only. Accordingly, after presenting the layout of a generic ACTRs with land-fixed winches, tension interval of the UAV-connected cables is derived as follows. Fig. 3(a) illustrates a generic ACTR with land-fixed winches, where m UAVs and n land-fixed winches are connected via cables to a point-mass platform with mass mP. In the illustrated robot, land-fixed winches are able to provide different lengths for their connected cables, where the UAVs are connected to short constant-length cables. Denoting the platform\u2019s position in XY Z frame by p and the fixed connection points of a land-fixed winch by ai, the vector of cable i is li = p\u2212 ai, where the length and unit vector of such cable are obtained as li = \u2016li\u2016 and ui = li/li",
            " In order to simplify such effects, the effects of cable sagging on deformation of the cable profile are assumed to be negligible and the cable is approximated by a straight line, as illustrated in Fig. 4(a)\u2013(c). Accordingly, the tension along the connecting line between any winch and the platform is \u03c4i and the weight of cable is considered as an evenly distributed force \u03b7ig along the cable length, where two concentric vertical force with magnitudes 1 2 \u03b7igli are applied on the cable\u2019s end points to satisfy the static equilibrium conditions. Accordingly, the free-body diagram (FBD) of the platform is considered as illustrated in Fig. 3(b), where in addition to \u03c4is and the platform\u2019s weight, the weight effect of winch-connected cables 1 2 \u2211n i=1 \u03b7ilig is also applied on it. Even though the tension intervals of the bottom cables, denoted by [\u03c4min, \u03c4max], can be established based on their mass and allowable tensions, the tension interval of UAV-connected cables [\u03c4\u2032min, \u03c4 \u2032 max] is a nonlinear function of their angles and also their connected UAVs\u2019 orientation. In order to find such function, UAV i is considered in an arbitrary position of the 3-D space as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure11-1.png",
        "caption": "Fig. 11. Finite element model.",
        "texts": [
            " 9 (a), (d) and (e), as the medium gear basic circle radius increases, it can be discovered that the contact points move along the axial direction of the IHB gear tooth surface, the contact areas on the left and right tooth surface are moved toward the middle plane and decreased, the distribution of contact points is more concentrated, and the contact ellipse area is bigger. According to the above-derived tooth surface equations, the precise three-dimensional models of the novel hourglass worm drive are established and shown in Fig. 10 . And the finite element model is shown in Fig. 11 , there are 18,230 elements with 23,157 nodes in the finite element model. Compared with the gears and bevel gears, the finite element analysis boundary conditions of the hourglass worm gear drive require special considerations, and it is set as shown in Fig. 12 . It is assumed that the IHB gear is at rest relative to the fully constrained at the rigid surface I. The OPE hourglass worm has only one degree of freedom as rotational motion of its axis z 2 , while other degrees of freedom are constrained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003339_tnsre.2020.2970207-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003339_tnsre.2020.2970207-Figure6-1.png",
        "caption": "FIGURE 6. Photo of the sensor with further plan.",
        "texts": [
            " The photo-transistors are placed directly in contact with the skin and their flat surfaces would not cause any discomfort to the wrist. The photo-transistors have nearly the same spectral responsivity at wavelength of 630nm and 880nm, which would have the same the sensitivity for better accuracy. The black cover wrist band attaches the structure to the wrist tightly to make it wearable, stable and comfortable, and also to reduce noise effect. 1564 VOLUME 2, 2014 The implemented sensor after many testing experiments is shown in Fig. 5, and the sensor with further plan is shown in Fig. 6. At the moment, the wireless data transmission module has not been implemented yet. VI. SIGNAL PROCESSING MODULE The Fig. 7 shows the diagram of the signal processing module consisting of pass filters and amplifiers, providing signal processing of wave filtering and amplifying. The received signal reflected from blood contains AC signal and DC signal, which are separated by the pass filters and then amplified respectively. The DC Component is filtered by low pass filter (LPF). Circuit Diagram of low pass filter is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure4.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure4.10-1.png",
        "caption": "Fig. 4.10 Second mobile configuration (a) and rigid configuration (b)",
        "texts": [
            " The mechanism can be assembled in two configurations. The change from one configuration to the other is achieved by opening and re-closing a single joint in such a way that body-fixed vectors along the opened joint axis have equal directions after if they have equal directions before. In Fig. 4.8 the first configuration is shown for the variable \u03d51 = 0 with \u03d52 = . . . = \u03d55 = 0 . In the second configuration \u03d51 = 0 is associated with \u03d53 = \u2212\u03c0/2 , \u03d54 = 0 , \u03d52 = \u03d55 = \u03d56 = \u03c0/2 . This configuration is shown in Fig. 4.10a . It is possible to open and to re-close a single joint in such a way that the said body-fixed vectors along the joint axis reverse their relative orientation. However, this re-closing is possible in a single position only in which the system is then rigid. This position is shown in Fig. 4.10b . Angular velocities: From (4.32) and (4.38) it follows that \u03d5\u03074 = \u2212\u03d5\u03071 , \u03d5\u03075 = \u03d5\u03072 , \u03d5\u03076 = \u2212\u03d5\u03073 and \u03d5\u03073k = \u03d5\u03072j (k, j = 1, 2 ; k = j ) . Therefore, it suffices to express \u03d5\u03072 in terms of \u03d5\u03071 and \u03d51 . Implicit differentiation of (4.35) in combination with (4.37) yields \u03d5\u03072k = \u03d5\u03071 s1s2k \u2212 c1 c1c2k \u2212 s2k = \u2212\u03d5\u03071 (\u22121)k c1(2\u2212 s1) + s1 \u221a 1 + 2s1(1\u2212 s1) (1 + c21) \u221a 1 + 2s1(1\u2212 s1) (k = 1, 2) . (4.39) 4.2 Illustrative Examples 153 The mechanism is a very special case of a nine-parametric family of linesymmetric Bricard mechanisms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002786_s12206-018-1216-3-Figure17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002786_s12206-018-1216-3-Figure17-1.png",
        "caption": "Fig. 17. Diagnosis results of the synthetic signal: (a) E-kurtgram; (b) ES of the signal corresponding to node (3, 6) in (a).",
        "texts": [
            " As seen, the REFF fe can be identified, but is very weak compared with the IRFF fi and the noise frequency. That is to say, the REFF fe is usually ignored. The compound fault synthetic signal is processed by WPTSK method. Fig. 16(a) displays that the node (4, 8) has the maximum kurtosis value. Fig. 16(b) presents the ES of the frequency band signal corresponding to node (4, 8). As seen, the INFF fi are identified productively whereas the REFF fe cannot be extracted. The compound fault synthetic signal is processed by EKurtogram method. Fig. 17(a) displays that the node (3, 6) has the maximum kurtosis value. Fig. 17(b) illustrates the ES of the frequency band signal corresponding to node (3, 6). As seen, the INFF fi and its doubling frequency 2fi are identified productively whereas the REFF fe cannot be extracted. The compound fault synthetic signal is processed by TEERgram method. Fig. 18(a) displays that the node (4, 9) has the maximum kurtosis value. Fig. 18(b) illustrates the envelope spectrum of the frequency band signal correspond- ing to node (4, 9). As seen, the INFF fi is identified productively whereas the REFF fe cannot be extracted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.11-1.png",
        "caption": "Fig. 7.11 A schematic of a thermomechanical in-plane microactuor (TIM) that uses compliant expansion legs to amplify the motion caused by thermal expansion",
        "texts": [
            " Acceleration causes a displacement of the inertial mass connected to the compliant suspension, and the capacitance change between the comb fingers is detected. Thermal Actuators A change in temperature causes an object to undergo a change in length, where the change is proportional to the material coefficient of thermal expansion [22]. This length change is usually too small to be useful in most actuation purposes. Therefore, compliant mechanisms can be used to amplify the displacement of thermal actuators. Figure 7.11 illustrates an example of using compliant mechanisms to amplify thermal expansion in microactuators. Figure 7.12 shows a scanning electron micrograph of a Thermomechanical In-plane Microactuator (TIM) illustrated in Fig. 7.11. It consists of thin legs connecting both sides of a center shuttle. The leg ends not connected to the shuttle are anchored to bond pads on the substrate and are fabricated at a slight angle to bias motion in the desired direction. As voltage is applied across the bond pads, electric current flows through the thin legs. The legs have a small cross sectional area and thus have a high electrical resistance, which causes the legs to heat up as the current passes through them. The shuttle moves forward to accommodate the resulting thermal expansion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000632_s10846-010-9445-4-Figure27-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000632_s10846-010-9445-4-Figure27-1.png",
        "caption": "Fig. 27 During flight test",
        "texts": [
            " The autopilot tries to correct the heading to reach the desired waypoint. The autopilot is also able to correct small roll and pitch angles during steady movement. The only part of the control that has not been tested is the speed control. It was decided that because there is a big difference between air resistance and road friction, it will be futile to adjust the throttle control during the ground test. The control has been adjusted according to the data gathered on the first flights and the experience of the pilot. Figure 27 shows the ARF UAV during the test in the field. At this point, four waypoints have been chosen but they can be changed during the course of the flight. Figure 28 shows the initial waypoints. There have been several attempts to test the autopilot in the last weeks of November and the beginning of December, but due to weather conditions flights have been cancelled. In this paper a hybrid fuzzy logic and adaptive control paradigm for UAVs is presented. During the final stages of the control algorithm, random wind gust of up to 15 miles per hour were added to the simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000085_j.cma.2005.05.055-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000085_j.cma.2005.05.055-Figure14-1.png",
        "caption": "Fig. 14. Formation of bearing contact of Example 4 at points 1, 2, and 3 of function of transmission errors of Fig. 13(b).",
        "texts": [
            " 13(a) shows the function of transmission errors D/2(/1) for an unloaded misaligned gear drive with error Dc = 3 0. The shape of function D/2(/1) confirms that the tooth surfaces of the pinion and gear are not conjugated, and edge contact exists. Fig. 13(b) shows the function of transmission errors D/2,t(/1) for a loaded gear drive, by application of a torque of 250 N m. The influence of load on transmission errors is favorable, since the magnitude of function of transmission errors is reduced. However, it cannot compensate the defects of non-conjugation (see Figs. 14 and 15). The drawings of Fig. 14 confirm existence of edge contact. Fig. 15 shows that the stresses are much higher in comparison with the design based on double-crowning or even profile crowning (see Examples 3 and 2). The output data of numerical Examples 2 and 3 (represented in Section 5) provide the information about the function of transmission errors of loaded gear drives, formation of bearing contact, and the stress analysis. The purpose of this section is to complement Examples 2 and 3 with comparison of the noise of the considered gear drives"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.18-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.18-1.png",
        "caption": "Figure 5.18. The contact forces exerted by the body !?i'I1on the body ga2 . and the free body diagram of !?i'I2.",
        "texts": [
            " To hurdle this obstacle, we adopt the advance strategy that the normal and tangential distributions of the contact force , whatever the actual area of contact may be, are equipollent to a resultant normal force N and a resultant frictional force f that acts to oppose the relative motion of two contacting separate bodie s YB I and YB2\u2022Thus , if ry(q) and r(q) denote the normal and tangential force distributions per unit area a of the apparent contact area A, then N = fA ry(q)da , f = fA r(q)da ; and the resultant contact force R = fA ,(q)da exerted by .93\\ on YB2 is R=N+f. (5.69) j See the classical treatise by Bowden and Tabor. Contemporary molecular theories of friction and modern surface measurement techniques are discussed in the referenced article by Krim. The Foundation Principles of Classical Mechanics 53 Thus, instead of having to deal with the unknown surface load distribution s, we may work with their result ants in (5.69). The resultant contact forces exerted by a body gJ ] on another body gJ2 are shown in Fig. 5.18a. Other contact and body forces may act on gJ2, but these are not shown here. Of course, the contact forces exerted by gJ2 on gJ ] are opposite to those exerted by gJ , on gJ2. 5.11.2. Governing Principles of Sliding Friction Perfectly smooth, frictionless surfaces do not exist. Nonetheless, sometime s the surface asperity is so fine that the surface feels perfectly smooth to our sensation of touch . Therefore, in situations where frictional effects may be considered negligible or unimportant, we may sometimes consider an ideal model of smooth contacting surfaces that offer no sliding resistance whatever, a model that brings to mind the seemingly effortless, graceful motion of a skater on virtually frictionless ice",
            " Further, when a layer of fluid, such as air or water, separates two surfaces, there is a resisting force exerted by the fluid which is called drag or viscous fri ction . Both rolling and viscous friction are determined by laws that are entirely different from Coulomb 's rules of sliding friction . The effects of viscous friction are discussed in Chapter 6. The interested reader may consult the sources cited at the end of this chapter for details on these additional matters . We now turn to some examples. 5.11.3. Equilibrium of a Block on an Inclined Plane Let us consider the familiar, elementary problem of equilibrium of a rigid block a'32 shown in Fig. 5.18a at rest on an inclined plane a'3\\ . Our focus is on the general procedure for setting up and solving this problem . In addition, some elementary results of static friction are also reviewed . First, choose a'32 as a free body (the system to be investigated). Now identify all of the contact and body forces that act on .9c32 alone .We may ignore the contact 56 Chapter 5 force of the surrounding air. (Why?) Then the only body that touches \u00a3I32 is the body \u00a3I3 I , so the total contact force acting on \u00a3I32 consists of the equipollent normal force N and frictional force f due to \u00a3I31, or the equivalent reaction force R",
            " All of the forces that act on \u00a3I32 , whether it be in equilibrium or in motion in an assigned inertial frame are shown in the free body diagram in Fig. 5.l8b. The direction of these forces must be consistent with the physical situation. In particular, f must act to retard the potential motion of \u00a3I32, N must support \u00a3I32, and W must be directed toward the center of the Earth. The vector g denote s in the figure the direction of the gravitational attraction of the Earth. Any inertial frame may be introduced to formulate the problem, but one choice may be mathematically more convenient than another. The inertial frame cp = {F ; ik } shown in Fig. 5.18b is a good choice because the forces are most easily related to it. The free body diagram shows that the total force acting on the block \u00a3I32 is F(\u00a3I32, t) =W + f + N. Next, express these forces in terms of their components in tp: W=W(sinO'i-cosO'j) , f=-ji, N=Nj. (5.74a) (5.74b) Here W = mg, j , and N denote the magnitudes of these forces. This completes the primary phase in the problem formulation. Since the block is in equilibrium in cp, in accordance with (5.45) , the total force (5.74a) and the total moment about a point fixed in cp of the forces in (5",
            " It cannot be too strongly emphasized that the free body formulation for the total force is the same for both a statics and a dynamics problem; and it is important that the student become thoroughly familiar with this method. The analysis of the block's motion follows . We now encounter our first application of dynamics in the analysis of the sliding motion of a block down an inclined plane. Let us continue from where we left off above and suppose that the plane's angle of inclination exceeds the critical angle of friction . Then the block slides down the plane without tumbling provided that ac < a < a, holds . The free body diagram for @ 2 is shown in Fig. 5.18b; it is the same as before. Consequently, the free body formulation for the dynamics problem is the same as that for the statics problem and leads again to (5.74a); but this time the block has a translational motion down the plane, and the appropriate dynamical equations of motion must be decided . Since the body @ 2 is rigid and does not tumble, its motion is determined by the Newton-Euler equation (5.43) for its center of mass: (5.75a) The next step is the formulation of the appropriate kinematics",
            " (i) Prove that MQ = 0 about a fixed point Q at the initial position of the center of mass of the crate, and thus solve for the location of N. (ii) Repeat the analysis for the torque Mo = fio about a fixed point 0 in the contact plane at the initial position. (iii) Prove that the total torque Me about the moving center of mass must vanish and thus locate the action line of N. (c) What is the critical angle 8e for impending tip expressed in terms of assigned quantitie s only? 5.29. The wedge body g(JI in Fig 5.18a, page 53, is accelerated at a constant rate a toward the right. The block g(Jz maintains contact with the plane throughout the motion. The gravitational force acts downward in the figure. Show that g(Jz will slide down the inclined surface if a > g tan(a - l/f), where tan a = J1 is the coeffic ient of static friction for the two surfaces and l/f < a . The Foundation Principles of Classical Mechanics Smooth Ring Problem 5.30. L v=1/3 93 5.30. The figure shows a block 8 1 of weight WI attached by an inextensible cable to a block 8z of weight Wz "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000357_00124278-200705000-00043-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000357_00124278-200705000-00043-Figure3-1.png",
        "caption": "FIGURE 3. Schematic model of the system used to determine swim force.",
        "texts": [
            " The dynamometer was connected by steel thread to a nylon belt attached to the swimmer\u2019s waist. Strain gauge deflection from swimmer effort was amplified by portable extensometer (SODMEX ME-01D; Sa\u0303o Paulo, Brazil). The signals were captured by computer interface and stored in a data acquisition program at 400 Hz. After reading and converting the data to units of force (N) with LabVIEW (6.1; National Instruments, Austin, TX) and MATLAB (5.3; MathWorks, Natick, MA) software, SF was determined through straight line calibration (with reference weights of 2 kg and 10 kg) (Figure 3). In this test, swimmers performed a standard 400-m, moderate intensity crawl warm-up, 5 strokes of restrained swimming, and concluded with a 200-m low intensity swim. After 15 minutes\u2019 rest, they performed a 30- second maximal effort front crawl. Blood samples (25 L) were collected with a calibrated capillary tube from ear lobes 1, 3, and 5 minutes after swimming; these samples were then transferred to 1.5-mL Eppendorf tubes containing 50 L 1% NaF. Homogenate (25 L) then was injected into a YSI model 1500 Sport Lactate Analyzer (Yellow Springs, OH) to determine maximal lactate concentration",
            " Our study involved an experimental training cycle submitting swimmers to intense effort without promoting damage in competition performances, because the swimmers were specifically submitted to taper for our investigation. We determined mean force during 30 seconds of effort in an attempt to simulate the Wingate test in swimming, where mean force value was assumed to be swimmer anaerobic condition. This strongly correlated with 200-m maximal performance in both pre- and posttaper (Table 3). The reliability of SF and Pmax measures were accomplished by ICC (2,1) showing ranges of 0.88\u20130.99, which indicate excellent reliability obtained for pre- and posttaper tests. However, as we can see from Figure 3, performance improvement did not occur at the same level as mean force. Trappe et al. (21) have attributed the high inconsistency between swim power gain (17%) and performance improvement (4%) in swimmers after 21 days of taper to other performance factors such as swim mechanics, body hair shaving, and psychological condition. Our study was able to isolate 2 of those effects: the psychological, because the tests did not include a real competition situation; and body hair, because our athletes were shaved throughout the experimental taper period"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002832_j.msea.2019.138057-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002832_j.msea.2019.138057-Figure3-1.png",
        "caption": "Fig. 3. The in-situ HEXRD tensile test set up.",
        "texts": [
            " Tensile samples were prepared for further examinations, primarily the in-situ high energy X-ray diffraction tensile test. 10 samples were prepared from the location and geometry as shown in Fig. 2a and Fig. 2b respectively. The samples labeled as B1\u2013B3 were samples cut out from the bottom of the wall close to the base plate. The samples T1-T3 were samples cut from the top of the wall, and L1-L2 and R1-R2 were the samples from the left and right side of the wall, respectively. The in-situ HEXRD tensile tests were performed at beamline 11-ID-C at the Advanced Photon Source (APS). Fig. 3 is a schematic illustration of the in-situ synchrotron-based HEXRD tensile test setup at beam line 11-ID-C of APS. The synchrotron beam energy and wavelength (l) were 106.42 keV and 0.01165 nm, respectively. Sub-sized dog-bone shaped sheet samples, with ~1.5 mm thickness, were used. During a test, a monochromatic synchrotron X-ray beam impinged the center of the sample gauge section. The incident beam was nearly square, (500mm by 500mm) and diffracted as it penetrated through the crystal aggregates of the entire thickness according to Bragg's law: =d \u03b8 \u03bb2 sinhkl hkl where hkl denote the Miller indices of the lattice planes, and dhkl and \u03b8hkl are the spacing and diffraction angle for the (hkl) planes, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure7.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure7.2-1.png",
        "caption": "Fig. 7.2 Torques acting on a spinning top",
        "texts": [
            " The spiral motion of the top is being considered in terms of machine dynamics. The acting forces on the top are its weight, frictional force of the leg\u2019s tip at the point of contact the leg with the horizontal surface and the system of inertial forces mentioned above. The analysis of top motions is conducted using the example of a top that is tilted and spinning in a counterclockwise direction. The motion of the top spinning in a counterclockwise direction is considered around the point of support O that demonstrated in Fig. 7.2. If the axis of a top is adjusted on the angle \u03b3 to \u00a9 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 R. Usubamatov, Theory of Gyroscopic Effects for Rotating Objects, https://doi.org/10.1007/978-981-15-6475-8_7 133 the horizontal and released, then, under the action of the weight of the top, frictional force and inertial torques, the top\u2019s axis will begin to presses at about the vertical and horizontal. The frictional force acting on the tip of the leg starts to move the top around its gravity centre, and the top\u2019s axis describes a conical surface",
            " The equation of motion is formulated by the action of several forces and torques on the top that is as follows: the external torque generated by action of the weight of an inclined top; the torque generated by the centrifugal force of the rotating top\u2019s centre mass around axis oy; the external torque generated by the frictional force acting on the top\u2019s leg and around its axis. Other acting inertial torques are generated by the rotating masses mentioned above and represented in several publications (Table 3.1, Chap. 3). All forces and torques acting on the top are demonstrated in Fig. 7.2. The parameters defined above allow for the formulation of a mathematical model for a top\u2019s motion around axes ox and oy in Euler\u2019s form. The torques acting on the top are similar to the torques acting on the gyroscope suspended from a flexible cord (Chap. 5). Both models consider the motion of the spinning disc with one side support. As such, the mathematical model for a top\u2019s motion is represented by the following system of equations: Jx d\u03c9x dt = T + Tct.my \u2212 Tctx \u2212 Tcrx \u2212 Tamy\u03b7 (7.1) Jy d\u03c9y dt = (Tinx + Tamx \u2212 Tcry) cos \u03b3 + T f (7",
            " The mathematical model for the top motions considers the action of the frictional torque, centrifugal forces of the top centre mass, inertial forces generated by themass elements of the disc and weight of the top. The rotation of the top is accepted in the counterclockwise direction around axes oy and ox, respectively. At this condition, the actions of the gyroscope external and internal torques and motions are demonstrated 136 7 Mathematical Models for the Top Motions and Gyroscope Nutation inFig. 7.2. The actionof the frictional torqueTf turns the top around axisoy and added to the action of the precession torques (Tp.x = T in.x + T am.x) generated by the top\u2019s weight. The value of the precession torque T am.y acting around axis ox also decreases due to the interrelated the actions of the inertial and frictional torques around axes. This action is expressed by the coefficient \u03b7 of the change in the precession torque T am.y that is presented by the following equation: \u03b7 = Tp.x cos \u03b3 + T f cos \u03b3 Tp",
            " 138 7 Mathematical Models for the Top Motions and Gyroscope Nutation Equation (7.8) is transcendental. The conditions of self-stabilization and turn down of the running top are defined by graphical solutions of multiparametric Eq. (7.8). The example considers the motion of a disc-type top whose technical data are represented in Table 7.1. The centre mass of the top is located on the plane of the thin disc. The spinning top initially possesses an inclined axle and rotating around a vertical axis (Fig. 7.2). Substituting initial data into Eq. (7.7) and transformation brings the following equation: Parameter Data Angular velocity, \u03c9 1000 rpm Radius of the disc, R 0.025 m Length of the leg, l 0.02 m Angle of tilt, \u03b3 75.0o Mass, M 0.02 kg Coefficient of friction, f 0.1 Mass moment of inertia, kgm2 Around axis oz, J = MR2/2 0.625 \u00d7 10\u22125 Around axes ox and oy of the centre mass, J = MR2/4 0.3125 \u00d7 10\u22125 Around axes ox and oy, Jx = Jy = MR2/4 + Ml2 1.1125 \u00d7 10\u22125 7.1 The Top Motions 139 The denominator on the left side of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure4.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure4.6-1.png",
        "caption": "Fig. 4.6 Spatial closed chain with six bodies and six revolute joints",
        "texts": [
            " Each of the former four sets has to be combined with each of the latter four sets. Thus, altogether sixteen combinations have to be investigated. For each combination Eqs. (4.8) are formulated. For at least one combination the degree of freedom is either F = 1 or F = 2 . It is F = 1 if for every \u03d51 (in a certain interval) unique real solutions \u03d52 , \u03d53 exist. It is F = 2 if both constraint equations are identical. A combination has the degree of freedom F = 0 if real solutions \u03d52 , \u03d53 do not exist for any angle \u03d51 . The mechanism shown in Fig. 4.6 is a spatial closed chain with six bodies (fixed body 0 and bodies 1, . . . , 5 ) and with six revolute joints 1, . . . , 6 . The two joint axes of each body are mutually orthogonal and nonintersecting. Bodies 0 , 2 and 4 are identical and bodies 1 , 3 and 5 are identical. Furthermore, body 1 is a mirror image of body 0 . In the position shown the bodies are inscribed in a cube with all joint axes and all common perpendiculars of adjacent joint axes aligned along edges of the cube. In this cube configuration the joint axes 1 , 3 , 5 form a trihedral intersecting at a single point, and the axes 2 , 4 , 6 form another trihedral",
            " According to Gru\u0308bler\u2019s formula there are altogether 30 constraints in the altogether six joints. It is not necessary to analyze this system of constraints. The kinematics analysis is much simpler if the joint between bodies 0 and 5 is cut. This results in a serial open chain with five joints. For this chain Gru\u0308bler\u2019s formula (4.3) yields the degree of freedom F = 5 . Reconstitution of the cut joint introduces five constraints. These are the constraints which have to be analyzed. This is done as follows. On each body i (i = 0, . . . , 5) a body-fixed basis ei is defined. In Fig. 4.6 only basis e0 is shown. In the cube configuration of this figure all body-fixed bases are aligned parallel. The locations of the origins are without interest. Three of the five constraint equations express the fact that, independent of rotation angles in the joints, the chain of vectors leading from the point P on body 0 along body edges to the coincident point P on body 5 is closed. This is the vector equation \u2212e02 \u2212 e13 + e21 + e32 + e43 \u2212 e51 = 0 . (4.11) Two more constraint equations express the fact that the vectors e51 and e52 are both orthogonal to e03 : e51 \u00b7 e03 = 0 , e52 \u00b7 e03 = 0 ",
            " Because of the equal character of all bodies and of all joints and because of the definitions of joint angles this equation holds true if the indices are increased by 1 and by 2 . This yields the other two constraint equations \u03d54 = \u03d52 and \u03d55 = \u03d53 . End of remark. The relationship (4.22) is illustrated in the diagram of Fig. 4.7 . Because of the conditions | sin\u03d51,2| \u2264 1 the angles are restricted to the intervals \u2212210\u25e6 \u2264 \u03d51 \u2264 +30\u25e6 and \u221230\u25e6 \u2264 \u03d52 \u2264 +210\u25e6 . Motion in these intervals is possible without collision of neighboring bodies if the angle \u03b3 shown in Fig. 4.6 is \u03b3 \u2264 30\u25e6 . The mechanism can undergo a continuous twisting motion similar to an elastic ribbon. Differentiation of (4.22) with respect to time yields the relationship between angular velocities: \u03d5\u03072 = \u03d5\u03071 cos\u03d51 (1\u2212 sin\u03d51)2 cos\u03d52 = \u03d5\u03071 cos\u03d51 (1\u2212 sin\u03d51) \u221a 1\u2212 2 sin\u03d51 . (4.24) Differentiating one more time produces for the angular acceleration the expression 4.2 Illustrative Examples 149 \u03d5\u03082 = \u03d5\u03081 cos\u03d51 (1\u2212 sin\u03d51) \u221a 1\u2212 2 sin\u03d51 + \u03d5\u03072 1 2\u2212 2 sin\u03d51 \u2212 sin2 \u03d51 (1\u2212 sin\u03d51)(1\u2212 2 sin\u03d51)3/2 . (4.25) The mechanism is highly special",
            "66) whence it follows that tan \u03d51 2 = 1\u2212 c1 s1 = S3(c2s3 + C2s2c3) + C3S2s2 C1S3(s2s3 \u2212 C2c2c3) + S2(S1S3c3 \u2212 C1C3c2)\u2212 S1C2C3 . (6.67) An equation for tan\u03d54/2 is obtained in the same way by expressing the product n3 \u00b7n1 in the two forms nk \u00b7nk\u22122 = nk \u00b7nk+4 with k = 3 . In view of the symmetry of Fig. 6.5 the equation is directly obtained by interchanging in (6.67) \u03b11 with \u03b13 and \u03d52 with \u03d53 : tan \u03d54 2 = S1(c3s2 + C2s3c2) + C1S2s3 C3S1(s2s3 \u2212 C2c2c3) + S2(S1S3c2 \u2212 C1C3c3)\u2212 S3C2C1 . (6.68) Example: The triple plane-symmetric mechanism shown in Fig. 4.6 is characterized by the parameters 1 = 2 = 3 = 1 , h2 = h3 = 0 and \u03b11 = \u03b12 = \u03b13 = \u03c0/2 . This is the special case with a single solution (\u03d51 , \u03d53) for a given angle \u03d52 . Equations (6.64) and (6.67) are c2 + c2c3 + c3 = 0 , tan \u03d51 2 = c2s3 c3 . (6.69) With c2 from the first equation the second becomes tan\u03d51/2 = \u2212s3/(1+c3) or \u03d51 = \u2212\u03d53 . Except for slightly different definitions of angles, the same results were obtained in (4.20) and (4.22). End of example. This mechanism was developed by Bricard [10] in search for a system having the property that in every position the six axes are lines of a special linear complex",
            " The construction of the system requires the specification of twelve parameters, namely, three coordinates for each of the points A and B and two direction cosines for each line of trihedral A . Six out of these twelve parameters determine the dimensions of the system and the remaining six its position in space. Of interest are only the first six parameters. Their number exceeds the number of independent lengths by one. The single free parameter constitutes the single degree of freedom. End of proof. Since in every position of the mechanism the six joint axes intersect the line AB , they are lines of the special linear complex with the axis AB . In Fig. 4.6 the special mechanism is shown in which the six lengths 1 , . . . , 6 are identical. 6.4 Kinematical Chains with Six Revolute Joints 225 A trihedral Bricard mechanism can assume so-called planar positions, i.e., positions in which the polygon of points P1, . . . ,P6 is planar. In these positions three joint axes are normal to the plane. They intersect at infinity. The other three joint axes are lying in the plane. They either intersect at a single point or are parallel. The two rods coupled by any of these three joints are collinear",
            " For every value of \u03d51 there exist four (not necessarily real) sets of solutions (\u03c3\u03d52i , \u03d53i , \u03c3\u03d54i , \u03d55i , \u03c3\u03d56i) (i = 1, 2 ; \u03c3 = \u00b11 ). Equations (6.77) and (6.83) fail in planar positions characterized by either s1 = s3 = s5 = 0 or by s2 = s4 = s6 = 0 . In these cases, the joint angles are determined from triangles (see Fig. 6.7). Example: For the lengths ( 1, 2, 3, 4, 5, 6) = (16, 3, 9, 17, 5, 8) and for \u03d51 = 80\u25e6 a type 1 mechanism has the solutions (\u03d52 , \u03d53 , \u03d54 , \u03d55 , \u03d56) \u2248 (\u03c336.8\u25e6, 142.9\u25e6, \u03c348.4\u25e6, 127.9\u25e6, \u03c327.3\u25e6) and (\u03c392.8\u25e6, 67.8\u25e6, \u03c398.3\u25e6, 83.7\u25e6, \u03c3111.5\u25e6) (\u03c3 = \u00b11 ). End of example. Example: The trihedral mechanism in Fig. 4.6 is a type 1 mechanism with identical lengths i \u2261 1 (i = 1, . . . , 6). It has four planar positions. Equations (6.80) reduce to 1. (c3 + 1)s1 \u2212 (c1 + 1)s3 = 0 , 2. (c4 + 1)s2 \u2212 (c2 + 1)s4 = 0 , 3. (c5 + 1)s3 \u2212 (c3 + 1)s5 = 0 , 4. (c6 + 1)s4 \u2212 (c4 + 1)s6 = 0 , 5. (c1 + 1)s5 \u2212 (c5 + 1)s1 = 0 , 6. (c2 + 1)s6 \u2212 (c6 + 1)s2 = 0 . \u23ab\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ad (6.84) For a given angle \u03d51 these equations and (6.77) have a single solution only, namely, \u03d53 = \u03d55 = \u03d51 , \u03d54 = \u03d56 = \u03d52 and c1 + c1c2 + c2 = 0 . Except for slightly different definitions of angles, the same results were obtained in (4",
            "38) can be solved explicitly for the constraint forces and constraint torques. Premultiplication by T yields X = T (m r\u0308\u2212 F) , Y = T (J \u00b7 \u03c9\u0307 \u2212M\u2217 \u2212C\u00d7X) . (19.40) The expression for X is substituted into the equation for Y . The numerical evaluation of these equations is done in parallel with the numerical integration of the equations of motion. From Chap. 4 it is known that the joint variables of a closed kinematical chain are subject to kinematical constraints. As illustrative example the trihedral Bricard mechanism shown in Fig. 4.6 is used. It is a simple closed chain with six joints. For the kinematics analysis see Eqs.(4.12) \u2013 (4.25). The analysis started with the removal of joint 6 thus creating a serial chain with five 1 In graph theory the matrices T and S are referred to as path matrix and incidence matrix, respectively. The matrix C represents a weighted incidence matrix. Whereas the path matrix is defined for tree-structured systems only, the definition of incidence matrix can be generalized to include multiloop systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.8-1.png",
        "caption": "Fig. 9.8 Angular velocity diagram of the bevel differential",
        "texts": [
            " This maneuver causes angular velocities \u03c921 > 0 and \u03c931 > 0 in the directions shown in the figure. The points fixed on wheels 2 and 3 which are in contact with the ground have, in negative z-direction, the velocities v2 = \u03c910(R \u2212 /2)\u2212\u03c921r and v3 = \u03c910(R+ /2)\u2212\u03c931r , respectively. The rolling conditions require that v2 = v3 = 0 . The difference of these two equations is \u03c931 \u2212 \u03c921 = r \u03c910 . (9.75) The given angular velocity ratio i yields \u03c961 = i\u03c921 , \u03c971 = \u2212i\u03c931 (> 0 in positive y-direction) . (9.76) In Fig. 9.8 the angular velocity diagram of the bevel differential composed of the members 6 , 7 , 8 and 9 is shown. The directions of all angular velocities except \u03c918 are prescribed by the design as shown. The magnitudes of \u03c961 and \u03c971 are chosen arbitrarily. They determine \u03c967 = \u03c961 \u2212 \u03c971 . First, \u03c986 is determined from the vector equation \u03c967 + \u03c978 + \u03c986 = 0 . Next, \u03c918 is determined by the vector equation \u03c961+\u03c918+\u03c986 = 0 . Finally, \u03c991 and \u03c989 are determined from the vector equation \u03c991 + \u03c918 + \u03c989 = 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001012_j.ijfatigue.2012.09.002-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001012_j.ijfatigue.2012.09.002-Figure6-1.png",
        "caption": "Fig. 6. (a) Transformation from (n01; n 0 2) to (x0 , y0) for boundary stress computation and (b) subdivision of a triangular boundary element for interior stress computation.",
        "texts": [
            " For any boundary or interior point, its stress state is determined by the displacement and traction distributions along the entire boundary as [28] rij\u00f0P\u00de \u00bc Z CF Ekij\u00f0P;Q\u00detk\u00f0Q\u00dedC Z CF\u00feCI Hkij\u00f0P;Q\u00deuk\u00f0Q\u00dedC \u00f016a\u00de where k = x, y, z and the third order kernel functions read [28] Ekij \u00bc 1 8p\u00f01 t\u00ded2 \u00f01 2t\u00de djk @d @i \u00fe dik @d @j dij @d @k \u00fe 3 @d @i @d @j @d @k \u00f016b\u00de Hkij \u00bc G 4p\u00f01 t\u00ded3 ni 3t @d @j @d @k \u00fe \u00f01 2t\u00dedjk \u00fe G 4p\u00f01 t\u00ded3 nj 3t @d @i @d @k \u00fe \u00f01 2t\u00dedik \u00fe G 4p\u00f01 t\u00ded3 nk 3\u00f01 2t\u00de @d @i @d @j \u00f01 4t\u00dedij \u00fe 3G 4p\u00f01 t\u00ded3 @d @n \u00f01 2t\u00dedij @d @k \u00fe t djk @d @i \u00fe dik @d @j 5 @d @i @d @j @d @k \u00f016c\u00de These kernel functions are on the order of 1/d2 and 1/d3, and hence, become singular when P and Q coincide. To circumvent such singularities, the stress components for the boundary points are computed using the strains and tractions according to the Hooke\u2019s law [28] in a local orthogonal coordinate system (x0, y0, z0) as shown in Fig. 6a. Here, the z0 axis points out of the surface. The area coordinate system (n1, n2) is related to (x0, y0) through n1 \u00bc 1 AC x0 y0 tan h ; n2 \u00bc y0 BC sin h \u00f017a;b\u00de Denoting the direction cosines of x0, y0 and z0 in the global (x, y, z) system as (ax, ay, az), (bx, by, bz) and (cx, cy, cz), respectively, and interpolating the displacements within an element using the linear shape function as ui \u00bc u\u2018i N\u2018, the displacements in the local (x0, y0, z0) system are found as ux0 \u00bc ai\u00f0u\u2018i N\u2018\u00de and uy0 \u00bc bi\u00f0u\u2018i N\u2018\u00de",
            " Similar to the treatment for Uij and Tij, the transformation of Fig. 4 is first applied to introduce the Jacobian of the order of O(d), weakening the kernel singularity of Ekij and Hkij from O(1/ d2) and O(1/d3) to O(1/d) and O(1/d2), respectively. Noticing the gradients of 1/d and 1/d2 increase sharply as d ? 0, a progressive subdivision method is developed here to sub-mesh the element in an efficient manner. This method introduces the transformation Jacobian that goes to zero at a faster pace than d does when Q approaches P. As illustrated in Fig. 6b, the size of the sub-elements along the local g1 direction (column), denoted as Lc m (m is the sub-element index in the g1 direction and 1 6m 6 j) is progressively reduced when approaching the load point P. In the local g2 direction (row), however, a uniform sub-element size of Lr is used since the singular behavior does not vary in this direction. The subdivision procedure can be summarized in the following three steps. (i) Determine the size for the column of sub-elements that is farthest away from P in the g1 direction, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000489_la1017505-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000489_la1017505-Figure1-1.png",
        "caption": "Figure 1. Aschematic illustrationof the procedure for the fabrication of 2D Si-EPAs by using PS EHAs as etching masks.",
        "texts": [
            " At least five measurements were averaged for all of the data reported here. Angle-resolved reflection spectroscopywasmeasuredwith aMaya 2000PROoptics spectrofluorometer, RSS-VA variable angle reflection sampling system, and a model DT 1000 CE remote UV/vis light source (Ocean Optics). The chemical compositions were determined by X-ray photoelectron spectroscopy (XPS, Thermo ESCALAB 250). 3. Results and Discussion 3.1. Formationof2DSiliconEllipticalPillarArrays. 3.1.1. Fabrication of 2DElliptical Hemisphere ArraysMask.Figure 1 outlines the procedure for the fabrication of 2D Si-EPAs. First, EHAs are fabricated through a micromolding method using stretched PDMS nanowell arrays as mold (Figure 2a). As shown in the SEM image, the EHA is composed of elliptical hemispheres molded from the stretched PDMS nanowell mold, and the aspect ratio of the EHAs is about 2.87, which is determined by the force used to stretch the PDMS mold.34 Moreover, the AFM image of the EHAs (Figure 2b) also shows that the average height of the hemisphere mask is about 369 ( 7 nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.14-1.png",
        "caption": "Fig. 7.14 Deflected positions of the baseline configuration",
        "texts": [
            " 6, doi:10.1115/1.4006543, 2012. Used with kind permission \u00a9 ASME. configuration is composed of two attachment posts, two flexures, and a central connecting beam. The two flexures and the central connecting beam form a C-shape. The bilateral components are positioned on either side of the two vertebral bodies to which they are attached. Optional inserts adjust the force-deflection response of the flexures to meet the target spinal kinetic response deemed appropriate for the individual patient. Figure 7.14 shows the baseline configuration deflected in the two modes of loading for which it was designed. The optional contact-aided insert design is configured as two parts which connect together and attach to the central connecting beams of the baseline device. The elliptical contact surfaces of the inserts are designed such that as the flexures of the baseline configuration deflect during spinal motion, they come into contact with the surfaces, altering the force deflection relationship in a controlled and specific manner, as shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003778_j.mechmachtheory.2021.104407-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003778_j.mechmachtheory.2021.104407-Figure7-1.png",
        "caption": "Fig. 7. Half of the slice model of the RLMG block.",
        "texts": [
            " Therefore, to obtain an accurate stiffness model, the relationship between the block displacement { q } while considering the block flexibility and the magnitude of the equivalent contact load N ij must be investigated. In this study, the rail deformation is neglected because the rail is fixed on the working platform by bolts with sufficient rigidity. To improve the calculation efficiency, the block is divided into many slices with length t w (the distance between the axial centers of two adjacent rollers), and only half of the block is analyzed due to its symmetric structure, as shown in Fig. 7 . The relationship between the block displacement { q } and the magnitude of the equivalent contact load N ij can be obtained via iterative calculation, which can yield the accurate deformation of the block under a complicated loading state. The calculation method is described as follows. Step 1: Input the 3D model into ANSYS software and mesh it with a hexahedron element (solid185) and 2D element (shell181) after setting the element edge length as shown in Fig. 7 . Then, extract and read the element and node information via the APDL and MATLAB programs, which is then used to assemble the stiffness matrix [ K ]. Step 2: Calculate the equivalent contact load of all rollers N ij using Eq. (22) under a certain external load { P } . Then, according to the displacement-based finite element method [24] , the displacement can be obtained through load-displacement relationship [ K ] { q } = { P } , (27) where [ K] is the stiffness matrix of the element assemblage, { q } is the displacement vector of each node on the block, and { P } represents the external load vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003287_s00170-020-06104-0-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003287_s00170-020-06104-0-Figure4-1.png",
        "caption": "Fig. 4 The deformation distribution when the part dimensions are 60 \u00d7 5 \u00d7 20 mm3: a X-direction displacement, b Y-direction displacement, c Z-direction displacement, and d X-direction deformation along the deposition direction",
        "texts": [
            " The lengths of all as-built thin-walled parts at different deposition heights were measured by a digital micrometer and took the average of five measurements. The sensitivity of the digital micrometer is 5 \u03bcm, which provides a high measurement accuracy [31]. The measurement position is shown in Fig. 3. For the 20 mm height part, the measurements were carried out every 5 mm from the bottom of the part. For the other height parts, the measurements were carried out every 10 mm from the bottom of the part. Fig. 4 depicts the simulated displacement distribution of the thin-walled part with dimensions of 60 \u00d7 5 \u00d7 60 mmwhen the part is cooled down to room temperature. The dotted line frame refers to the design profile of the thin-walled part, and the scale factor is 50 for expressing the part displacement distribution clearly. It can be seen that the part displacement distribution in three directions is significantly different. In regard to the displacement along the X direction, as shown in Fig. 4a, the thinwalled part has a large inward contraction at the middle of the part while a small inward contraction at the bottom and top of the part. Furthermore, it can be carefully found that the part contraction at the bottom is less than that at the top of the part. The displacement along the X direction at the bottom of the part is less than 15 \u03bcm. The length at the bottom of the part is therefore close to the design dimension. Similar results are also reported by Xie et al. [34]. As shown in Fig. 4b, the part displacement along the Y direction is very small (\u221210 to 10 \u03bcm) due to the small size (i.e., 5 mm). Fig. 4c depicts the part displacement along the Z direction, and it can be seen that the top surface of the part is concave. An upward displacement (+Z) occurs at the side center edges while a downward displacement (\u2212Z) occurs at the bottom, middle, and top center of the part. This is because a high tensile stress along the Z direction occurs at the side center edges while a high compressive stress along the Z direction occurs at the bottom and middle of the part [35]. However, the displacement at the top of the part is small, indicating that the height of the part is close to the design dimension. Based on the above analysis, the deformation along the X direction dominates for the thin-walled parts. To quantitatively describe the deformation level along the X direction, two specific values are defined as \u0394L \u00bc L0\u2212L \u00f07\u00de \u0394Lmax \u00bc max \u0394Lf g \u00f08\u00de where L is the length of the part at any height, L0 is the length at the bottom of the as-built part,\u0394L is the X-direction deformation, and \u0394Lmax is the maximum X-direction deformation. The specific meaning of these symbols can be seen in Fig. 4a and d. As shown in Fig. 4d,\u0394L increases first and then decreases with deposition height. The\u0394Lmax is found near the middle of the part with a value of 142.8 \u03bcm and is about 0.24% of the original design length. To reveal the variation of the X-direction deformation, a thinwalled part deformation mechanism (TPDM) is built in the present paper, as shown in Fig. 5. When the laser heats the first layer, as shown in Fig. 5a, the laser scanning length is equal to the design length of the part. When the laser heating is finished, the part shrinks due to the decrease in temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.67-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.67-1.png",
        "caption": "Fig. 3.67 Cross-section of the EBRAKE\u00ae EMB (a) and its high temperature test (b) [HARTMANN ET AL. 2004].",
        "texts": [],
        "surrounding_texts": [
            "So what is the future of the BBW AWB dispulsion mechatronic control system? Some vehicle manufacturers and other OEM supplyr companies have all developed next-generation BBW AWB dispulsion mechatronic control systems for potential use on future automotive vehicles. Innovative BBW AWB dispulsion mechatronic control systems that have been developed to date, essentially fall into one of two categories: electro-fluido-mechanical brake (EFMB) or electro-pneumo-mechanical brake (EPMB) and electro-mechanical brake (EMB). BBW AWB dispulsion mechatronic control systems still use conventional fluido-mechanical brake (FMB) or pneumo-mechanical brake (PMB) callipers at each wheel, but a microcomputer-controlled high-pressure E-M-F pump or E-M-P compressor and E-M actuator solenoids apply pressure. These kinds of BBW AWB dispulsion mechatronic control systems use inputs from a brake pedal position sensor (that works much like a throttle position sensor), wheel angular velocity (speed) sensors, a steering angle sensor, yaw rate, and lateral acceleration sensors to determine the optimum amount of brake oily-fluid or air (gas) pressure to apply at each wheel. With EMB BBW AWB dispulsion mechatronic control systems, there is no fluidics (hydraulics and/or pneumatics) whatsoever. Braking force is generated at each wheel by a fully electronic EMB calliper. Inside is a small, but powerful E-M motor that pushes the pads against the rotor. Many of these systems work best with higher voltages (such as 42 VDC) which means EMB BBW AWB dispulsion mechatronic control systems may probably remain on the shelf until automotive vehicle manufacturers decide whether or not to change to 42 VDC. The benefits of EMB BBW AWB dispulsion mechatronic control systems are essentially the same as EFMB and EPMB BBW AWB dispulsion mechatronic control systems, plus elimination of brake fluid or air, hoses and lines, the need for a high-pressure M-F pump or M-P compressor and accumulator, and provide improved braking safety by keeping three brakes operational should one calliper fail. Being able to precisely control the amount of braking force at each wheel electronically also means a BBW AWB dispulsion mechatronic control system may shift more braking effort to the rear brakes during normal braking. This, in turn, may reduce front pad wear while reducing the forward mass shift and nose drive that normally occurs when the brakes are applied. A trend that may impact BBW AWB dispulsion mechatronic control systems is the automotive industry\u2019s desire to reduce vehicle wiring through the use of multiplexing techniques. As increasing numbers of vehicles are fitted with anti-lock, this trend is expected to result in an increased number of anti B.T. Fijalkowski, Automotive Mechatronics: Operational and Practical Issues, Intelligent Systems, Control and Automation: Science and Engineering 47, DOI 10.1007/978-94-007-0409-1_35, \u00a9 Springer Science+Business Media B.V. 2011 542 -lock BBW AWB dispulsion mechatronic control systems communicating with other structural and functional systems through a multiplex link. In addition to the wheel angular velocity/vehicle velocity information (data) available from the anti-lock BBW AWB dispulsion mechatronic control system, the anti-lock ECU could benefit from this technology by being able to receive engine, transmission, steering angle, and other structural and functional subsystems information. Another trend in advanced mechatronically-controlled BBW AWB dispulsion mechatronic control systems is vehicle dynamics control during nonbraking manoeuvres as well as during braking. This is accomplished through use of the traction control actuators normally integrated in anti-lock fluidic or pneumatic modulators, the addition of sensors to more accurately determine the dynamic state of the automotive vehicle, and communication links with the DBW four-wheel-driven (4WD) propulsion mechatronic control system, the ABW four-wheel-absorbed (4WA) suspension mechatronic control system and, the SBW four-wheel-steered (4WS) diversion mechatronic control system ECUs. Vehicle dynamic control holds the promise of safer vehicle operation through improved handling stability in all manoeuvres. The automotive 4WB BBW dispulsion mechatronic control systems engineering community is also investigating the addition of laser radar to individual vehicles. This addition could lead to semi- or fully-automatic braking in emergency situations as the 4WB BBW dispulsion mechatronic control system anticipates the potential problem and aids the driver in safely applying the vehicle brakes in time to avoid a collision, This concept also lends itself to automatic braking in non-emergency situations to maintain safe distances between vehicles at high values of the vehicle velocity. Continuing interest in AEVs and HEVs and the need for regenerative braking in these automotive vehicles may significantly impact on future BBW AWB dispulsion mechatronic control systems. It is expected that the regenerative braking function will not be sufficient to provide adequate braking deceleration under all conditions and to provide drivers with the comfort and safety obtainable from conventional friction brake dispulsion mechatronic control systems augmented by anti-lock BBW AWB dispulsion mechatronic control systems. It is expected that a more sophisticated ECU may be used in conjunction with AEVs and HEVs to afford optimum power regeneration without sacrificing braking stopping distance, vehicle handling stability, or steerability. These trends point to the continued use of friction brake dispulsion mechatronic control systems through the next century and significant expansion of the role of automotive mechatronics in these structural and functional systems. BBW AWB vehicles are to become a fundamental part of the automotive industry within the next decade. The state-of-the-art technology replaces F-M (H-M and/or P-M) components with E-M ones. There are three types of BBW AWB dispulsion mechatronic control systems. 3.10 Future Automotive BBW AWB Dispulsion Systems 543 These are EFMB, EPMB and EMB. An EFMB system contains an F (H) or P back-up for the brake system, and in the case of an electrical failure, this F-M (H-M and/or P-M) system takes over and allows the driver to have some limited control of the braking system. EMB has no F-M (H-M and/or P-M) backup system, and is totally realised by electrical and E-M components. Automotive vehicle manufacturers are planning to use EFMB or EPMB as a bridge to EMB that may become an automotive industry standard. As EMB has no F-M (H-M and/or P-M) backup components, safety and fault tolerance is of the utmost importance in an EMB system. BBW AWB dispulsion is implemented through the application of sensors, E-M actuators, microcontrollers, wires, and communication networks. To power this, a 42 VDC CH-E/E-CH storage battery may be introduced as standard, either stand-alone or in parallel with the existing (12 VDC) CH-E /E-CH storage battery. When the brake is pressed, an electronic signal may be passed from the sensor to the electrical network. Microcontrollers may process this signal and send information out to the E-M actuators, causing the callipers to apply a brake force. The communication system can process and send signals from the pedal to the brakes in 100 ms, twice as quick as the FMB system, where the calliper may apply a force of a maximum value of 3 Mg, i.e. 30 kN. The application of brake-by-wire requires a real-time distributed system that is safety critical in nature and fault tolerant. In order to apply the fault tolerant nature required, the network\u2019s communication is handled by time-triggered architecture (TTA). The three major time triggered-architectures are TTP/C, for instance FlexRay\u2122 (developed by BMW and DaimlerChrysler), and TT-CAN. There are many important issues raised with this technology. BBW AWB reduces the risk of physical components injuring the passengers in an accident but problems raises of what happens when the electronic system fails. Although the chance of this is small, black boxes are to be introduced into vehicles, and legislation is set to change. Manufacturing plants and assembly lines may also have to change their business focus, shifting from fluidical as well as mechanical components to mechatronic ones. Most vehicle manufacturers believe, however, that the benefits of BBW AWB dispulsion far outweigh any initial hurdles, and that BBW AWB technology is the way of the future. Automotive vehicles have already been constructed with BBW AWB dispulsion, and the first commercially available mass-produced unit was released in 2002. With BBW AWB dispulsion, the vehicle may adapt to situations and determine the optimum force to apply to each different wheel, regardless of user input, to reduce the risk of injury in dangerous situations. The BBW AWB dispulsion mechatronic control system has ABS and TCS fully integrated into it, and performs these functions more efficiently and effectively. By fully integrating BBW AWB dispulsion with SBW AWS conversion and DBW AWD propulsion (where the steering and drive mechanics are Automotive Mechatronics 544 replaced respectively), it is possible to produce safer, more efficient vehicles that can find the optimum way to react to a situation if drivers are putting themselves at risk. It is also possible that, in the near future, a fully integrated by-wire automotive vehicle may obey velocity (speed) signs and eventually drive itself. Many in the automotive industry see the EMB BBW AWB dispulsion mechatronic system as the ultimate solution. It is said to offer a range of consumer, industrial, and environmental benefits such as elimination of brake fluid or air, increased fuel economy through automotive vehicle mass reduction, quieter braking, reduced maintenance costs, and the ability to tailor brake response to driver preferences. EBRAKE\u00ae [US PATENT 6,318,513; GERMAN PATENT 19819564] \u2013 an innovative \u2018BBW AWB\u2019 technology, was developed at the German Aerospace Centre, DLR e.V. This technology is based on an electrically powered and mechatronically controlled friction disc brake with high self-reinforcement capability. Whenever automotive scientists and engineers deploy existing forces, normally the unsophisticated concept is the most convincing. By intelligently controlling a brake wedge, the kinetic mechanical energy (momentum) of an automotive vehicle is transformed into braking power. As it can be seen from a physical model of the electrically powered and mechatronically controlled friction disc brake with high self-reinforcement capability, shown in Figure 3.65, the brake lining is equipped with a wedge on its backside which rests on an abutment, for example, a bolt [HARTMANN ET AL. 2002]. The E-M actuator presses the brake lining in between the abutment and the brake disc with the E-M motor force Fm. The braking force Fb resulting from the contact between the brake disc and the brake lining acts in the same direction as the E-M motor force that results in the anticipated self-reinforcement. 3.10 Future Automotive BBW AWB Dispulsion Systems 545 From the force balance \u03bc \u03bc\u03b1 \u2212= tan bm FF (3.31) may be derived. For the characteristic brake factor C* then applies: \u03bc\u03b1 \u03bc \u2212 == tan 2* m b F FC , (3.32) where Fm : E-M motor force; Fn : normal force; Faux : auxiliary force; Fb : braking force; Fb,ma : maximum braking force (nominal value); R : reaction force; \u03b1 : wedge angle; \u03bc : friction; c : calliper stiffness; x : wedge position/deflection. From this equation (3.32), it can be seen that for low coefficients of friction, C* is positive, so a steady pushing force is necessary to uphold the braking force. When the coefficient of friction is greater than the tangent of the wedge angle, then a steady pulling force is necessitated from the E-M actuator to stop the wedge being pulled further in. For optimum performance, it is best to operate around the point at which the characteristic brake factor is infinite, since this minimises the necessary control forces. From a control standpoint, this may be thought of as a point of neutral stability, since any small perturbation in the wedge position may result in it remaining in another position (and generating the corresponding braking moment). When the coefficient of friction rises, the wedge position becomes unstable and requires to be controlled to stop the wheel jamming. In Figure 3.66 a structural and functional block diagram of the mechatronic control system for an electrically powered and mechatronically controlled friction disc brake with high self-reinforcement capability is shown [HARTMANN ET AL. 2002]. Automotive Mechatronics 546 The essential problem with this simple but very efficient method of braking was to find a technique to prevent the jamming of the brake or, better said, to \u2018control\u2019 this jamming satisfactorily. The German Aerospace Centre, DLR e.V. was successful in solving this problem. A special mechatronic control technology developed under Matlab/Simulink and DSPACE stops the wedge from getting stuck. Despite the fact that the principle of a controlled wedge brake is relatively simple, the mechanical implementation is critical to its realisation. Key factors that need to be taken into account are Removal of free-play within the drivetrain, regardless of component wear; Minimisation of friction in the sense of the wedge travel direction; Action in both senses of direction. 3.10 Future Automotive BBW AWB Dispulsion Systems 547 The prototype EMB is best explicated by means of a cross section through the EMB that is presented in Figure 3.65 (a). The design is based around a modular concept suitable for laboratory testing, rather than being optimised for minimum size and mass, and uses off-theshelf industrial components wherever achievable. The EMB is driven by two rotary brushless DC-AC mechanocommutator brake-force-actuator motors [DLR ROBO DRIVE] mounted at either end of the assembly. Commutation and current control are realised using conventional E-M motor drives with an incremental encoder on each E-M motor shaft. For controlled braking, a moment sensor provides the feedback to the moment controller. On the other hand, the encoder may be used to provide E-M motor position control. E-M motor rotation is transformed to axial motion by means of roller-screws which are mounted within the rotors on pre-loaded angular thrust ball bearings. The roller-screws drive the so-termed brake heart, which contains the wedge mechanism. Within this component, forces are only transmitted by compression between neighbouring surfaces. This allows the E-M motors to either work together or to preload the system and so remove free-play [ESTOP GMBH]. Backlash is inevitable, both as an effect of construction tolerances and because of wear, predominantly in the bearing surface that allows the wedge to slide outwards from the E-M motor axis. If they are working together, then one roller-screw pulls the wedge in the appropriate sense of direction while the other one pushes against the first roller-screw. This reduces the E-M motor loads when the coefficient of friction is not near the optimum value. For a preload to be introduced, both roller-screws pull against their respective sides of the wedge. The wedge is actually composed of two ground \u2018W\u2019 surfaces. The inner one relative to the E-M motors is static, while the outer one moves both axially and in translation. This construction spreads the loads and may generate self-reinforcement in both directions of travel. Between these surfaces, there is a series of rollers which minimise the sliding friction from the high calliper forces. The outer part of the wedge, to which the brake pad is attached, is held against the static one by a preloaded spring. It is axially actuated by means of a bearing surface that allows it to move laterally away from the E-M motor centreline. The automotive industry is expected to move to the first stage of the adoption of BBW AWB dispulsion around 2010 through the introduction of electrically actuated rear brakes and then followed by full DBW AWB dispulsion around 2020. EFMB or EPMB is a BBW AWB dispulsion mechatronic control system that eliminates the physical connection between the brake pedal and brake fluidics. The brake booster and master cylinder are replaced with a PS and failsafe F-M (H-M and/or P-M) manifold to actuate the brakes through the EFMB or EPMB unit. It may be offered in 2012 on certain luxury models, but probably won't be offered on other vehicles because of its high cost. It may also require special OEM dealer tools and training to service this system because of its complexity [CARLEY 2004]. Automotive Mechatronics 548 Further down the road, EMB that uses no fluidics at all may probably find its way onto automotive vehicles. But don't look for this new technology to go into manufacture until the end of the next decade. Some vehicle manufacturers are using an innovative type of brake rotor made of ceramics on certain models (for example like the one on the Porsche 911). The ceramic rotor is very light mass and does not conduct heat into the hub, but it's also extremely expensive. It wears very little, but if it is damaged, it can't be resurfaced and must be replaced. It also requires a special type of high temperature friction material to withstand the heat. Some manufacturers are also using drilled and slotted rotors on their high performance models. The automotive scientists and engineers have indicated that they don't offer a significant improvement in cooling compared to a standard rotor and are used primarily to enhance the \u2018racing mage\u2019 of the vehicle. On the issue of brake life, premature pad wear and rotor wear are major customer issues with all vehicle manufacturers. The latest approach is to make the design of the brake system more robust so that the brakes last longer and run quieter. 3.10 Future Automotive BBW AWB Dispulsion Systems"
        ]
    },
    {
        "image_filename": "designv10_12_0003361_s10846-020-01178-0-Figure30-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003361_s10846-020-01178-0-Figure30-1.png",
        "caption": "Fig. 30 Representation of a two-link flexible-joint robot manipulator(minor modified according to [53])",
        "texts": [
            " Figure 29 shows that the amplitude of the control input voltage has not changed significantly in the presence of matched and mismatched uncertainties. Remark 9 Since the mass of the robot link is 100 g the external disturbance d1(t) = d2(t) is approximately equal to 80% of the mass. Therefore, the efficiency of the proposed control against this value of uncertainty is very good. In the second set of simulations, we intent to implement the proposed control on a two-link flexible-joint robot manipulator, which is similar to that of industrial robots. The general schema of an industrial robot manipulator is shown in Fig. 30. According to (1), the coefficient matrix for the equation of motion is expressed as follows [53] D \u03b8\u00f0 \u00de \u00bc m1 \u00fe m2\u00f0 \u00deL21 \u00fe m2L22 \u00fe 2m2L1L2cos\u03b82 m2L22 \u00fe m2L1L2cos\u03b82 m2L22 \u00fe m2L1L2cos\u03b82 m2L22 \u00f058a\u00de C \u03b8; \u03b8 0 \u00bc \u22122m2L1L2\u03b8 0 2sin\u03b82 \u2212m2L1L2\u03b8 0 2sin\u03b82 m2L1L2\u03b8 0 1sin\u03b82 0 \u00f058b\u00de g \u03b8\u00f0 \u00de \u00bc m1 \u00fe m2\u00f0 \u00degL1cos\u03b81 \u00fe m2gL2cos \u03b81 \u00fe \u03b82\u00f0 \u00de m2gL2cos \u03b81 \u00fe \u03b82\u00f0 \u00de \u00f058c\u00de After doing the calculations, Eq. (58) is converted into the form of (13), and the controller design can be continued. Parameters of themanipulator and themotor are given in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001045_j.triboint.2012.02.002-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001045_j.triboint.2012.02.002-Figure20-1.png",
        "caption": "Fig. 20. Operating point.",
        "texts": [
            " Initially, it seems that the same assumption has been applied in this work, which is of course true for purely hydrodynamic lubrication. However, in highly loaded regimes the lubricant film becomes stiff and thus hardly changes its thickness. Hence, little energy is dissipated with the proposed model. The oscillator is of softening type since the main resonance is bent to the left. This seems to be contrary to the stiffening effect of the lubricant (and the structure) but can be explained as follows: considering the operating point in Fig. 20 one recognises that the contact becomes harder for decreasing displacement. However, it becomes softer for increasing displacement. The latter effect is obviously the dominating one. Within this contribution the dynamic behaviour of EHL line contacts has been investigated. However, the computational costs of transient EHL problems are still challenging. For this reason a simplified model was proposed which captures the nonlinear oscillatory behaviour of EHL contacts. This simplified model is a combination of a Hertzian and a purely hydrodynamic contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.8-1.png",
        "caption": "Fig. B.8 Torques and forces acting on the spinning rotor of the carriage",
        "texts": [
            " Find the reaction force acting on the bearings when the carriage rolls on the curvilinear track. Appendix B: Applications of Gyroscopic Effects in Engineering 259 Solution The curvilinear turn of the electric motor produces the several inertial torques generated by the spinning rotor\u2019s mass. The action of the inertial and external torques produces the reactive forces on the bearings of the electric rotor\u2019s supports. The inertial torques and external loads acting on the spinning rotor around axes ox and oy, respectively, are represented by the components in Fig. B.8. The equations of inertial torques generated by the rotating mass of the rotor are represented in Table 3.1 of Chap. 3, whose components are as follows: \u2022 The resistance torques generated by the centrifugal Tct = 2\u03c02 9 J\u03c9\u03c9y and Coriolis Tcr = 8 9 J\u03c9\u03c9yforces of the spinning rotor acting around axis oy. \u2022 The precession torques generated by the change in the angular momentum Tam = J\u03c9\u03c9y of the rotor and the common inertial forces Tin = 2\u03c02 9 J\u03c9\u03c9y acting around axis ox. The curvilinear turn of the electric motor on railway generates the centrifugal forces of the centre mass acting on bearings of the electric rotor",
            " The total force acting on the bearing of the rotor along axis oy and oz is represented by the following equations with substituting of the expressions of the inertial torques and the component of the weight of the rotor: Fy = Tam l + Fw = J\u03c9\u03c9y l + mg 2 = J\u03c9\u03c9y l + mg 2 (B.8.3) Fz = m\u03c92 y L (B.8.4) where Fy and Fz are the total forces acting on the bearing of the rotor along axes oy an oz, respectively; l is the distance between the bearings symmetrical located relatively of the centre mass of the rotor. The combined load acting on the most loaded bearing of the rotor is defined by the following equation (Fig. B.8): F = \u221a F2 y + F2 z = \u221a[ J\u03c9\u03c9y l + mg 2 ]2 + (m\u03c92 y L)2 (B.8.5) where all parameters are as specified above. An electric carriage is rolling on the curvilinear rail track of radius 300mwith a linear velocity of 90.0 km/h. The motor used for traction has a rotor of mass 600 kg and a radius of gyration 300 mm. The motor shaft is parallel to the axes of the carriage\u2019s running wheels. The rotor is supported in bearings 750 mm apart symmetrically and rotates of 160.0 rad/s (Fig. B.8). Determine the combined force generated by the inertial forces of the rotor and its weight acting on the most loaded bearing. For solution is defined as the following: (a) the angular velocity of precession: \u03c9p = V/L = (90000/3600)/300 = 0.083333 rad/s where V is the linear velocity of the carriage, L is the radius of the rail curve. Appendix B: Applications of Gyroscopic Effects in Engineering 261 Fig. B.9 Torques acting on the shaft with the rotating bar and spinning disc (b) the rotor\u2019s mass moment of inertia J = mr2= 600 \u00d7 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000846_0954405411407997-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000846_0954405411407997-Figure4-1.png",
        "caption": "Fig. 4 (a) Conventional pin joint; (b) drum-shaped pin joint; (c) drum-shaped hole joint; (d) schematic of the geometric relationship",
        "texts": [
            " Such a joint also makes it easier to remove the supports within the clearance, since the joint clearances at both ends become larger. As shown in Figs 4(a) and 4(b), a conventional pin joint has a uniform joint clearance, represented by a; a drum-shaped pin joint has a clearance a at the maximum drum diameter, and a larger clearance, c, at each ends. The mobility of this redesigned joint will be maintained with a small clearance, but the pin shape will be complicated when it connects several links, because it has several corresponding drums. Another improved joint is proposed to avoid this problem, as shown in Fig. 4(c). The hole is shaped instead, so that the joint still has a small clearance a at the peak and a larger clearance c at each end. The varying clearance actually introduces an additional degree of freedom in the mechanism. Chen and Chen [15] performed a simulation to test the influence of joint clearance on the dynamic performance of a functional mechanism. The result showed that a few, suddenly raised velocity and acceleration values were observed for a drum-shaped pin joint with a minimum clearance of 0.1 mm and clearance of 0.2 mm at both ends, whereas a smooth change was observed for a conventional pin joint, assuming no clearance. As Fig. 4(d) shows, the curvature R for the drum is determined by a, c and the length of the drum, represented by l: R \u00bc c a\u00f0 \u00de2 \u00fe l=2\u00f0 \u00de2 2 c a\u00f0 \u00de \u00f04\u00de During the design, R can be obtained once the other parameters have been determined. The length of the drum can be determined by various dimensions, such as the thickness of the link, but the clearances a and c are uncertain, because they depend on several features, such as the powder material, the support structure and the process strategy, and should be determined by a series of process experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002605_01691864.2018.1556116-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002605_01691864.2018.1556116-Figure5-1.png",
        "caption": "Figure 5. The horizontal moving toward the y-direction without an inclination angle, the x-axis is perpendicular to the paper and inward.",
        "texts": [
            " \u03d5\u0308 = L Ix u2, \u03b8\u0308 = 0 \u03c8\u0308 = 0, x\u0308 = 0 y\u0308 = 2b\u03c92 m (c\u03b112s\u03d5 + s(\u03b134 + \u03d5)) z\u0308 = g \u2212 2b m + \u03c92 34 (17) The tilt angle constrain which is obtained by equating the acceleration in the y-axis, Equation (17), to zero is \u03b134 = \u2212\u03d5 + s\u22121(\u2212c\u03b112 \u00b7 s\u03d5) (18) Case (2): This case discusses the horizontal movement in the y-direction without an inclination angle. The procedure for controlling the y-position without any inclination angle are as follows: \u2022 Rotors-3, 4 will be used to produce forces along the yaxis, see Figure 5, and their tilt angles are produced from the controller and have the same value (\u03b13 = \u03b14 = \u03b134). \u2022 The other two rotors should stay vertical to avoid generating any moments or forces in the x-direction, i.e. their tilt angles\u2019 values should be equal to zero (\u03b11 = \u03b12 = 0). \u2022 To restrict the quadrotor from rotating about the zaxis, i.e. making a yaw angle, the rotational speeds of the rotors-1, 2 should have the same value (\u03c91 = \u03c92 = \u03c912) and the speeds of the rotors-3, 4 should also have the same value (\u03c93 = \u03c94 = \u03c9h); where\u03c9h denotes the hovering speed : \u03c9h = \u221a mg/4b. Assumptions of this case are given in Table 2, while Figure 5 also illustrates this case. The virtual inputs are given by u1 = 2b(\u03c92 12 + \u03c92 34 \u00b7 c\u03b134), u2 = 0 u3 = 0, u4 = 0 (19) The simplified model yields \u03d5\u0308 = 0, \u03b8\u0308 = 0 \u03c8\u0308 = 0, x\u0308 = 0 y\u0308 = 2b m \u03c92 34 \u00b7 s\u03b134 z\u0308 = g \u2212 2b m (\u03c92 12 + \u03c92 34 \u00b7 c\u03b134) (20) The prototype is capable of two flight modalities: a fixed configuration inwhich it essentially behaves as a standard underactuated quadrotor, and a variable tilt angle configuration which guarantees some degree of full actuation. This control system is designed for the second mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure4.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure4.4-1.png",
        "caption": "Fig. 4.4 Flux linkage and current distribution in a typical wound rotor machine, showing flux and current space vectors. (a) Flux linkage distribution. (b) Current distribution",
        "texts": [
            "33 Simulation results of model based synchronous current controller 92 Fig. 4.1 Symbolic and generic space vector based ITF models. (a) Symbolic model. (b) Generic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Fig. 4.2 Symbolic IRTF representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Fig. 4.3 Flux linkage and current space vector diagrams. (a) Flux linkage space vector. (b) Current space vector . . . . . . . . . . . . . . . . . . . . . 98 Fig. 4.4 Flux linkage and current distribution in a typical wound rotor machine, showing flux and current space vectors. (a) Flux linkage distribution. (b) Current distribution . . . . . . . . . . . . . . . . . 98 Fig. 4.5 Generic representations of IRTF module (for three-phase, two-pole machines). (a) IRTF-flux. (b) IRTF-current . . . . . . . . . . . . . 100 Fig. 4.6 Relationship between IRTF current/flux linkage space vectors and torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ",
            "2b) Space Vectors in the IRTF An illustration of the flux linkage seen by the rotor and stator winding is given in Fig. 4.3a. The relationship between the stator and rotor oriented flux linkage and corresponding current space vectors, as shown in Fig. 4.3, may be written as \u03c8xy m = \u03c8m e\u2212j\u03b8 (4.3a) i = ixy ej \u03b8 . (4.3b) Flux Linkage and Current Distribution in AC Machine Figure 4.3 emphasizes the fact that there is only one flux linkage and one current space vector present in the IRTF. This fact is underlined by Fig. 4.4. which shows the cross-section of a typical AC machine with a three-phase sinusoidally distributed winding on the rotor and stator. 98 4 Drive Principles During operation the three-phase flux linkage and current contributions in a typical wound rotor AC machine can be represented by a single flux linkage and two current distributions as shown in Fig. 4.4. These may in turn be represented by a space vector which for the flux is aligned with the resultant two-pole magnetic flux axis. The space vector is is aligned with the current distribution of the stator, while the space vector ir is aligned with the current distribution in the rotor bars. When considering the current vector seen by the rotor, the IRTF module uses by convention the shown vector, while in reality the current distribution in the rotor is reversed in polarity. The reason for this is that the sum of stator and rotor magneto-motive forces (MMF) approaches zero when the permeability of the magnetic material of the IRTF model is taken towards infinity and the air-gap is taken to be very small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003265_tmag.2020.3013624-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003265_tmag.2020.3013624-Figure1-1.png",
        "caption": "Fig. 1. Structures of the proposed series-parallel-connected machine. (a) Initial structure. (b) Improved structure.",
        "texts": [
            " Authorized licensed use limited to: University of Canberra. Downloaded on October 04,2020 at 14:38:56 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. > GU-03 < 2 A. Initial Structure The initial structure of the proposed hybrid-PM variableflux PMSM with series-parallel magnetic circuits is shown in fig. 1(a). The initial structure employs a V-shape layer of magnets, where red coloured ones are AlNiCo and blue coloured ones are NdFeB. NdFeB is connected with AlNiCo in series near the q-axis, and these two series-connected magnets are connected with another AlNiCo located near the d-axis in parallel. AlNiCo magnets can be magnetized or demagnetized by id pulses, and the AlNiCo near the d-axis can be forward or reversely magnetized, which greatly expands the variation range of magnetization state. The no-load flux distributions of the initial structure under different magnetization states are shown in fig",
            " So the initial structure has a wide variation range of magnetization state, similar with the parallel-connected hybrid-PM variableflux PMSMs. However, AlNiCo near the d-axis can be demagnetized by the flux-weakening current (-id) and overload current (iq), and the operating reliability of the initial structure is greatly reduced. B. Improved Structure To stabilize the working points of AlNiCo magnets, the improved structure of hybrid-PM variable-flux PMSM with series-parallel magnetic circuits is proposed. The design specifications for the improved structure are shown in Table I. As shown in fig. 1(b), two layers of magnets are placed in the proposed machine. The upper V-type layer, which is close to the air gap, is similar to the initial structure. The lower U-type layer, which is close to the rotor shaft, is composed of seriesconnected NdFeB and AlNiCo. The no-load flux and magnetic field distributions of the improved structure are shown in fig. 3. Under forward magnetization state, as shown in fig. 3(a), the flux of the lower U-type magnets flows through the upper Vtype magnets and help to stabilize the working points of upper V-type magnets, especially the AlNiCo near the d-axis, similar with the series-connected hybrid-PM variable-flux PMSMs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.2-1.png",
        "caption": "Fig. 3.2 Serial robot with six revolute joints",
        "texts": [
            "2) The matrix A12 is determined by the rotation (n, \u03d5) about 01 . The inverse equation is (premultiply by A21 = A12T and write r2 = A21r1 ) 2 2 = A21 1 1 \u2212 r2 . (3.3) It is convenient to write these equations in product form. This is achieved by adding an identity equation: [ 1 1 1 ] = [ A12 r1 0T 1 ] [ 2 2 1 ] , [ 2 2 1 ] = [ A21 \u2212r2 0T 1 ] [ 1 1 1 ] , 0 = \u23a1 \u23a3 0 0 0 \u23a4 \u23a6 . (3.4) The (4 \u00d7 4) matrices are transformation matrices. Inversion is carried out not by transposition, but by the rule shown in Eqs.(3.4). Example: In Fig. 3.2 a serial robot with six revolute joints is shown. Starting at the base the bodies and joints are labeled from 1 to 7 and from 1 to 6 , respectively. The locations of the joint axes on the bodies are specified by body-fixed vectors r2, . . . , r6 pointing from one axis to the next and by body-fixed unit vectors n1, . . . ,n6 along joint axes. The variable angle of rotation in joint i is called \u03d5i . It is the angle of body i+1 relative to body i . The vector r7 locates a specified point P on the hand of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.56-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.56-1.png",
        "caption": "Fig. 3.56 Image of a proof-of-concept automotive vehicle equipped with the RBW or XBW integrated automotive vehicle\u2019s chassis-motion mechatronic control hypersystem and ITS",
        "texts": [
            " Since the ABS entered the practical application phase in 1978, E-M friction disc, ring and drum brake mechatronic control functions have been expanding [FUJINAMI 2003]. Recently, many functions have been used in popular automotive vehicles, and some vehicle manufacturers have already started mass-producing ABSs and SCSs [UEKI ET AL. 2004]. Automotive scientists and engineers are working to develop high-performance and high-functioning mechatronic control systems for the future, and they expect these systems may lead to an RBW or XBW integrated unibody, space-chassis, skate-board-chassis or body-over -chassis mechatronic control system (see Fig. 3.56). The aim of this proof-of -concept automotive vehicle is to improve dynamics and layout [UEKI ET AL. 2004]. B.T. Fijalkowski, Automotive Mechatronics: Operational and Practical Issues, Intelligent Systems, Control and Automation: Science and Engineering 47, DOI 10.1007/978-94-007-0409-1_34, \u00a9 Springer Science+Business Media B.V. 2011 530 [Hitachi Ltd.; UEKI ET AL. 2004]. Stability Control Systems (SCS) \u2013 SCSs have appeared as the next-generation ABSs. These are designed to control vehicle dynamics by regulating the brake force on each wheel and are the basis of RBW or XBW, in terms of future chassis technologies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000412_156855309x420039-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000412_156855309x420039-Figure23-1.png",
        "caption": "Figure 23. 4.1\u20134.5\u25e6 30\u201340 s (trot gait).",
        "texts": [
            " / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 497 498 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 499 In the simulation, the slope angle was changed gradually from 4.1\u25e6 to 4.5\u25e6. Limit cycles in Fig. 19 are not clear and we cannot see what kind of gait was used. In the time interval from 10 to 20 s, limit cycles in Fig. 21 are similar to those in Fig. 15. In the time interval from 30 to 40 s, limit cycles in Fig. 23 are similar to those in Fig. 17. Figure 21 is the simulation data for a slope angle of 4.1\u25e6. Figure 23 is the simulation data for a slope angle of 4.5\u25e6. Thus, it can be said that Quartet 4 with the invariable body can change its walk gait to trot continuously when the slope angle was gradually changed from 4.1\u25e6 to 4.5\u25e6. In this way, gait transition could be considered as the transition of limit cycles. In biped passive dynamic walking, when the slope angle was gradually changed, the biped passive dynamic walker changed its gait from one-period to two-period. It is not difficult to understand the change of gait is a cascade of bifurcation in a chaotic phenomenon"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001219_s0005117913070047-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001219_s0005117913070047-Figure8-1.png",
        "caption": "Fig. 8. Proof of convexity of the function \u03c66(x) over the interval x \u2208 [0, xm).",
        "texts": [
            " We prove by contradiction that \u03c66(x) has no inflexion points over the interval x \u2208 [0, xm). We assume that on the contrary at some point xp1 < xm the function \u03c66(x) has an inflexion point. In virtue of the fact that \u03c6 \u2032\u2032 6(x) < 0 for x \u2208 [0, xp1) and at the point x = xm the function \u03c66(x) has maximum (\u03c66(xm) = 0), there must be at least one more inflexion point x = xp2 , and \u03c6 \u2032\u2032 6(x) > 0 AUTOMATION AND REMOTE CONTROL Vol. 74 No. 7 2013 for x \u2208 (xp1 , xp2) and \u03c6 \u2032\u2032 6(x) < 0 for x \u2208 (xp2 , xm) (Fig. 8). It follows from the analysis of the graph of the variable \u03c6 \u2032\u2032 5(x) that it increases over the interval x \u2208 [0, xp), xp > xm. It follows from (A.30) for the derivative \u03c6 \u2032\u2032 6(x) that over the interval x \u2208 [0, xm) the fraction numerator is the sum of two monotone functions, increasing negative function \u03c6 \u2032\u2032 5(x)[1 \u2212 ci\u03c65(x)] and decreasing positive function ci\u03c6 \u20322 5 (x). Consequently, over this interval \u03c6 \u2032\u2032 6(x) can be zero only once, that is, have only one inflexion point. The contradiction proves that \u03c6 \u2032\u2032 6(x) < 0 for x \u2208 [0, xm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.68-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.68-1.png",
        "caption": "Fig. 2.68 Cut-away section of a diesel engine \u2013 2.5 l, 5-cylinders, turbocharged mechatronically controlled [Audi; SEIFFERT AND WALZER 1991].",
        "texts": [
            " Automotive Mechatronics 222 Another method to control the M-M driveshaft torque and angular velocity is to control the timing of the ignition. The ratio between air, fuel, and compression are other parameters that can be used [HOWSTUFFWORKS.COM 2003]. The diesel engines works in a similar way, with the difference being that fuel is injected directly into the cylinder and self-ignites when heat is generated from the higher compression caused by the piston. The method of controlling the Otto engines and diesel engines also differ. The diesel engines are primary mechatronically controlled by the amount of injected fuel. In Figure 2.68 is shown a cut-away section of a diesel engine [SEIFFERT AND WALZER 1991]. Its major features are EMC, high-pressure injection and dualspring injectors with five-hole injector nozzles. The function of the dual-spring injectors is to inject the diesel-oil fuel in two stages. The supplementary progressing pressure boost in the cylinder has as a consequence a \u2018quieter\u2019 combustion process that is softer. Injection rate and timing are controlled and monitored mechatronically. This makes it possible for the diesel engine to provide high power and good economy with low exhaust emissions under all functioning circumstances and throughout its service life"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure11-1.png",
        "caption": "Fig. 11. SAW and formation of rAW for a given arrangement of UAVs.",
        "texts": [
            " In order to find the UAVs\u2019 optimal arrangement, rAW is defined as the maximum force, which a statically balanced platform with a given arrangement of the UAVs can provide in any arbitrary direction. In order to formulate rAW the following proposition is provided. Proposition 3: SAW of a point-mass robot in a given configuration of UAVs includes the force-space origin if \u2200i, dpidqi \u2265 0, where dpi and dqi are obtained from (5). In such conditions, we have rAW = min i (min{ |dpi | \u2016unulli\u2016 , |dqi | \u2016unulli\u2016 }). Proof: Consider the general SAW of Fig. 11 as a convex polytope formed by the intersection of n+m subspaces, which are arranged by n bottom and m top cables. As Fig. 11 indicates, subspacei is restricted to planepi and planeqi, which are formulated as planepi : u T nullif = dpi, planeqi : \u2212uT nullif = dqi (23) where vectors ofp\u2032i and ofq\u2032i are perpendicular to them. The force-space origin of is always between planepi and planeqi if the angle between ofp\u2032i and ofq\u2032i is \u03c0, which concludes (uT nulli ofp\u2032i)(u T nulli ofq\u2032i) \u2264 0. (24) In order to find ofp\u2032i and ofq\u2032i, the arbitrary points of p\u2032\u2032i = [fpixfpiyfpiz] T and q\u2032\u2032i = [fqixfqiyfqiz] T are considered on planepi and planeqi, which, accordingly to (23), means uT nulli [ fpixfpiyfpiz ]T = dpi,\u2212uT nulli [ fqixfqiyfqiz ]T = dqi. (25) Based on Fig. 11, we know \u2212uT nulli ofp\u2032\u2032i = ofp\u2032i,u T nulli ofq\u2032\u2032i = ofq\u2032i (26) and ofp\u2032\u2032i = [ fpixfpiyfpiz ]T , ofq\u2032\u2032i = [ fqixfqiyfqiz ]T . (27) Based on (25)\u2013(27), we have uT nulli ofp\u2032i = \u2212dpi,u T nulli ofq\u2032i = dqi (28) where replacing them in (24) gives dpidqi \u2265 0. Having ofp\u2032i and ofq\u2032i perpendicular to planepi and planeqi, the minimum radius of their corresponding SAW-surrounded sphere, centered at forcespace origin, is min{\u2016 ofp\u2032i\u2016, \u2016 ofq\u2032i\u2016}, which based on (28) is obtained as min{ |dpi | \u2016unulli\u2016 , |dqi | \u2016unulli\u2016 }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001996_s10035-018-0848-4-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001996_s10035-018-0848-4-Figure2-1.png",
        "caption": "Fig. 2 Schematic of equipment configuration for Experiment #1 (AOR)",
        "texts": [
            " Experiment #1 closely followed the setup and procedure for the standard Hall Flowmeter Funnel test [1]. In this test, 50 g of powder is first poured into a funnel and then discharged into a container below the funnel nozzle. The procedure can be used to obtain powder flow rate, apparent density, and it can be modified to obtainAOR.TheHall Flowmeter Funnel test procedure was chosen because it is a common characterization means for gas-atomized metal powders used in AM, injectionmolding, and other metallurgical applications. As shown schematically in Fig. 2, the equipment for Experiment #1 included a Hall Flowmeter, a brass collection cup (volume of 5 cm3), a high-speed camera (frame rate 1000 frame/s, shutter speed 1/2000 s, image pixilation 1024 pixel\u00d71024 pixel), and a fiber light guide and halogen illuminator. To obtain the AOR and apparent densities, the powder was poured through the Hall Flowmeter until the collection cup overflowed. An image of the resulting collection cup and pile was captured and the AOR was determined through computer-aided digital image analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003572_10775463211013245-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003572_10775463211013245-Figure1-1.png",
        "caption": "Figure 1. The rigid\u2013flexible gear.",
        "texts": [
            " A dynamic model with nine degrees of freedom considering gear backlash, bearing clearance, surface friction, meshing stiffness, as well as transmission error is established. In the dynamic model, the rigid\u2013flexible gear is composed of the ring gear and the hub. The vibration responses of the rigid\u2013flexible gear pair and the rigid gear pair are compared. Finally, the experiments are carried out to verify that the rigid\u2013flexible gear can effectively reduce the vibration. The rigid\u2013flexible gear transmission is composed of three parts as shown in Figure 1, including the ring gear 1, the metal rubber two, and the hub 3 (Wang et al., 2016, 2017a, 2017b). The rigid\u2013flexible gear can improve the performance of the meshing process by elastic deformation controlling and elastomer buffering. Because of the metal rubber, the vibration waves in high frequency of the rigid\u2013 flexible gear are filtered because of the change of the mechanical energy form and the occurrence of the micro vibration. The vibration of the hub can be reduced significantly because of the elastic deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000773_j.mechmachtheory.2009.10.006-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000773_j.mechmachtheory.2009.10.006-Figure5-1.png",
        "caption": "Fig. 5. Platform mechanism shaky to the third degree with a relative linear backlash d \u00bc 0:0005 in one of its legs.",
        "texts": [
            " For the same pose of the platform P0 as in the cases before we get with y62 \u00bc 2:6 the following three quadratic equations for the parameters: r61; r62 and y61: G6 \u00bc 2:16875\u00fe 5:03386r61 \u00fe 10:7637r62 \u00fe 5:94072y61 0:693132r61y61 2:37046r62y61 \u00bc 0; G 6 \u00bc 74:912\u00fe 30:1072r61 \u00fe 76:1826r62 \u00fe 31:7759y61 \u00fe 0:602577r61y61 20:2104r62y61 \u00bc 0; G 6 \u00bc 1521:36 185:466r61 163:706r62 332:073y61 \u00fe 142:213r61y61 51:3651r62y61 \u00bc 0: Their nontrivial solution reads: r61 \u00bc 5:53817; r62 \u00bc 0:966250; y61 \u00bc 2:04423: The set d \u00bc \u00bdr61 \u00bc 5:53817; r62 \u00bc 0:966250; y61 \u00bc 2:04423; y62 \u00bc 2:6 together with the given data set D determine a platform mechanism, which is shaky (singular) to the third degree in the position P0 (and rigid at any other pose P \u2013 P0\u00de. The length of the sixth leg in the position P0 is now given by: L6 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffi s6 s6 p \u00bc 12:7956, and if in the sixth leg there is again a small linear relative backlash d \u00bc DL6 L6 \u00bc 0:0005; then its length can freely change between L6\u00f01\u00fe d\u00de \u00bc 12:7963 and L6\u00f01 d\u00de \u00bc 12:7950, and within those limits the platform mechanism is finitely mobile with one degree of freedom. Fig. 5 shows the effect of this backlash in the platform mechanism shaky to the third degree. The lengths of the possible paths of the anchor points are approximately twice as long as in the platform mechanism that is shaky to the second degree shown in Fig. 4. In Section 4 the four position parameters of the installed sixth leg has been determined from the four conditions (21) and it has been shown that with these parameters the platform mechanism is architecturally mobile, i.e. if the platform with unlocked P-joints in the legs is brought in any geometrically possible position and the if the P-joints in this positions are locked, the platform will be mobile without any backlash \u00f0d \u00bc 0\u00de"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure8-1.png",
        "caption": "Figure 8 Rotations of two sequential points",
        "texts": [
            " In this Process planning for five-axis wire Fusheng Dai, Haiou Zhang and Runsheng Li Rapid Prototyping Journal section, we will give mathematical solutions for the calculation of five-axis transformation. Given 2 sequential points P1 and P2 on a path, fixed with vectors v1s and v2s respectively, which have been normalized. Rotating these two points around center point C(XC, YC, ZC), after the first rotation we get points P1 0 from P1, P 0 2 from P2 and vector v1t from v1s, after the second rotation we get points P 00 1 from P1 , P 00 2 from P2 and vector v2t from v2s shown in Figure 8. If the rotation is performed via two of these three vectors vx(1,0,0), vy(0,1,0) and vz(0,0,1), the question can be described as: Known P1 \u00f0XP1 ; YP1 ; ZP1\u00de, v1s Xv1s ; Yv1s ; Zv1s\u00f0 \u00de and v1t Xv1t ; Yv1t ; Zv1t\u00f0 \u00de, calculate P 0 1 XP 0 1 ; YP 0 1 ; ZP 0 1 and the rotating angles around two vectors of vx(1,0,0), vy(0,1,0) and vz(0,0,1). After the transformation, we have P 0 1 \u00bc Mst P1, whereMst is the transformation matrix. In the following, two solutions are given. Solution 1 takes no consideration of the usable axes of the five-axis platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002603_j.ifacol.2018.11.560-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002603_j.ifacol.2018.11.560-Figure5-1.png",
        "caption": "Fig. 5. Overview of the test environment.",
        "texts": [],
        "surrounding_texts": [
            "\ud835\udc35\ud835\udc35\ud835\udc62\ud835\udc62 \ud835\udc61\ud835\udc61 = \ud835\udc63\ud835\udc63(\ud835\udc61\ud835\udc61) \ud835\udc62\ud835\udc62\ud835\udc5a\ud835\udc5a\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b \u2264 \ud835\udc62\ud835\udc62 \u2264 \ud835\udc62\ud835\udc62\ud835\udc5a\ud835\udc5a\ud835\udc4e\ud835\udc4e\ud835\udc65\ud835\udc65 (11) \ud835\udc62\ud835\udc62 = \ud835\udf14\ud835\udf141 2\ud835\udf14\ud835\udf142 2\ud835\udf14\ud835\udf143 2\ud835\udf14\ud835\udf144 2\ud835\udf14\ud835\udf145 2\ud835\udf14\ud835\udf146 2 and B is the control matrix deduced from (3) \ud835\udc35\ud835\udc35 = 1 \u2212 \ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 3\ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 \u2212\ud835\udc3e\ud835\udc3e\ud835\udc61\ud835\udc61 1 \u2212\ud835\udc59\ud835\udc59\ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 0 \ud835\udc3e\ud835\udc3e\ud835\udc61\ud835\udc61 1 \u2212 \ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 \u2212 3\ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 \u2212\ud835\udc3e\ud835\udc3e\ud835\udc61\ud835\udc61 1 \ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 \u2212 3\ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 \ud835\udc3e\ud835\udc3e\ud835\udc61\ud835\udc61 1 \ud835\udc59\ud835\udc59\ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 0 \u2212\ud835\udc3e\ud835\udc3e\ud835\udc61\ud835\udc61 1 \ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 3\ud835\udc59\ud835\udc59 2 \ud835\udc3e\ud835\udc3e\ud835\udc53\ud835\udc53 \ud835\udc3e\ud835\udc3e\ud835\udc61\ud835\udc61 (12) For realizing stability while hovering, it necessary to guarantee zero moments around the three axes: \ud835\udc62\ud835\udc62\ud835\udc53\ud835\udc53 = \ud835\udc5a\ud835\udc5a\ud835\udc54\ud835\udc54, \ud835\udf0f\ud835\udf0f\ud835\udf19\ud835\udf19 = 0, \ud835\udf0f\ud835\udf0f\ud835\udf03\ud835\udf03 = 0, \ud835\udf0f\ud835\udf0f\ud835\udf13\ud835\udf13 = 0 (13) Thus the formulation of the problem becomes as follows: The control allocation aims to detect the input u that corresponds to the motors inputs given that \ud835\udc63\ud835\udc63 = [ \ud835\udc5a\ud835\udc5a\ud835\udc54\ud835\udc54 0 0 0 ]\ud835\udc47\ud835\udc47 . The constrained optimization problem is solved as follows: \ud835\udc5a\ud835\udc5a\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b 1 2 \ud835\udc62\ud835\udc62\ud835\udc47\ud835\udc47\ud835\udc62\ud835\udc62 \ud835\udc62\ud835\udc62 such that \ud835\udc62\ud835\udc62\ud835\udc5a\ud835\udc5a\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b \u2264 \ud835\udc62\ud835\udc62 \u2264 \ud835\udc62\ud835\udc62\ud835\udc5a\ud835\udc5a\ud835\udc4e\ud835\udc4e\ud835\udc65\ud835\udc65 \ud835\udc35\ud835\udc35\ud835\udc62\ud835\udc62 = \ud835\udf0f\ud835\udf0f (14) The vector umax is determined according to each fault while \ud835\udc62\ud835\udc62\ud835\udc5a\ud835\udc5a\ud835\udc56\ud835\udc56\ud835\udc5b\ud835\udc5b = 0 0 \u2026 0 \ud835\udc47\ud835\udc47 . This solution will not be optimal in every situation, but guarantees the best control allocation in IFAC SYROCO 2018 Budapest, Hungary, August 27-30, 2018 hovering flight and in small angles displacements cases. This approach offers the following advantages:  The actuators constraints, such as the limits on the motors speeds, are taken into account while solving the optimization problem using the umax parameter.  Since the system is over-actuated, multiple solutions exist such that the pre-fault performance of the faulty system is retained. These solutions can be optimized for certain objectives. In our case, the objective is to minimize energy consumption during flight.  The computational load of this method that can be estimated in function of the number of required floating-point operations is very close to the computational load in the nominal case."
        ]
    },
    {
        "image_filename": "designv10_12_0000858_978-1-4419-1126-1_8-Figure8.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000858_978-1-4419-1126-1_8-Figure8.3-1.png",
        "caption": "Fig. 8.3 Spherical mechanism \u2013 link and joint coordinate frame assignment (a) ParallelManipulator (b) Serial Manipulator",
        "texts": [
            " In the class of sphericalmechanisms, all links\u2019 rotation and translation axes intersect at a signal point or at infinity, referred to as the mechanism\u2019s remote center of rotation. Locating the remote center at the tool\u2019s point of entry to the human body through the surgical port, as typically done in minimally invasive surgery (MIS), constitutes a point in space where the surgical tool may only rotate around it but not translated with respect to it. The selected spherical mechanism has two configurations in the form of parallel (5R \u2013 Fig. 8.3a) and serial (2R \u2013 Fig. 8.3b) configurations. The parallel mechanism is composed of two serial arms: Arm 1 \u2013 Link13 and Link35 and Arm 2 \u2013 Link24 and Link46 joined by a stationary base defined by Link12 through Joints 1 and 2. The parallel chain is closed at the two collinear joints, 5 and 6. Arm 1 and 2 will be further referred to as the even and odd side of the parallel manipulator respectively. The spherical serial mechanism includes only one arm (Arm 1) with the same notation as the odd side of the parallel mechanism. By definition, the links of both mechanisms are moving along the surface of a sphere with an arbitrary radius R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002284_j.advengsoft.2018.05.005-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002284_j.advengsoft.2018.05.005-Figure2-1.png",
        "caption": "Fig. 2. (a) Main component parts of the TRB. (b) Final mesh size considered after the FE model adjustment.",
        "texts": [
            " The Jacobian factor for the entire FE models was always greater than 0.6 and for this reason, elements with zero volume were not generated. In addition, the aspect ratio, defined as the ratio between the longest edge of an element and its shortest edge, never exceeded a value of 10:1 for any of the elements. The raceways and tapered rollers were modeled with use of linear elastic and isotropic steel. The latter had a Young's modulus (E) of 208 GPa and a Poisson's ratio (\u03bd) of 0.29. The hub was modeled on the assumption that E=200 GPa and \u03bd=0.29 [17]. Fig. 2(a) shows the different component parts of the proposed TRB. Fig. 2(b) shows the final mesh size considered after the FE model adjustment. The proposed FE model was adjusted and experimentally validated so that the results obtained from it were as realistic as possible. This process were based on the adjustment of the mesh size of the pairs of contact (raceways and rollers) and on the adjustment of the relative displacements between the raceways. This process was performed using P values of 300, 400, 500, and 600 N and an Fr value of 2000 N, as in the previous work undertaken by Lostado et al",
            " The relative displacement of the inner and outer raceways was considered in validating the FE model once the mesh size had been adjusted. The relative displacement of the inner and outer raceways is used mainly to verify that there is an appropriate definition of the mesh size of the FE model, the coefficients of friction and the elastic properties (E and \u03bd). Two Red Crown comparator pencils, Fig. 3(a), are used to measure relative displacement experimentally. In the FE model, it is measured between two nodes that belong to the plane of symmetry of the model itself (Fig. 2(a)). As in the mesh size adjustment process, the P values of the loads were 300, 400, 500 and 600 N and the Fr value was 2000 N. Fr was applied to the TRB by a load cell (HBM U3 that had 5KN of capacity). The P was applied by a screw drove a steel sleeve along on the inner raceway. P loads were measured by a strain gauge affixed to a steel sleeve that pushed the inner raceway as the screw turned. Fig. 3(b) shows the differences between the relative displacements obtained from test bench and those from the FE models for various values of P and Fr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001136_1.4005462-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001136_1.4005462-Figure4-1.png",
        "caption": "Fig. 4 The 3DOF Euler pendulum has a disc-shaped foot that is tilted relative to the plane at an angle of a about the 2\u0302 axis. The vector~rp=q rotates with angular velocity _b about the 1\u0302 axis. Note that frame q is a body-fixed frame centered on the COM of the pendulum.",
        "texts": [
            " 7, APRIL 2012 Transactions of the ASME Downloaded From: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 05/05/2015 Terms of Use: http://asme.org/terms gravitational force mg term in Wight et al.\u2019s Eq. (50) should have not have been scaled by cos(h\u00fe b/2). The assumption that the contact point sticks and does not slip after contact is only valid if the ratio of the horizontal to vertical ground reaction forces does not exceed the coefficient of friction (lL) when the Euler pendulum is rolling without slipping. Note that the 2\u0302 and the r\u0302 \u00bc 2\u0302 z\u0302 (Fig. 4) axes span the horizontal plane. j~F \u00f0r\u0302\u00fe 2\u0302\u00dej ~F z\u0302 < lL (42) The expanded version of Eq. (42) has been omitted for brevity, though it can be found by substituting in Eqs. (42), (A3), (A7) and (A16). The 2D projection of Eq. (42) (achieved by setting \u20ach \u00bc _h \u00bc \u20acb \u00bc _b \u00bc 0) matches Wight et al.\u2019s Eq. (60). Now that it has been shown that foot placement can be used to stabilize a 3D inverted pendulum with a foot (in certain regions of its state-space) we will concentrate on deriving a method to find a desirable foot placement location given the state of the pendulum",
            " 3 and 4) are found by taking moments about the contact point to eliminate reaction forces. First equations for the linear and angular acceleration of the COM are kinematically derived, then substituted into the dynamic equation for angular acceleration. The dynamic equations for the COM linear acceleration are used to eliminate the unknown contact force ~F. To begin, the total angular velocity of the pendulum is composed of two components: that of a moving reference frame ~x123, and that of the pendulum relative to the reference frame xrel. ~x \u00bc ~x123 \u00fe xrel1\u0302 (A1) As shown in Fig. 4 the frame 1\u0302 2\u0302 3\u0302 rotates at _hz\u0302\u00fe _a2\u0302, ~x123 \u00bc _hz\u0302\u00fe _a2\u0302 \u00bc _h cos a1\u0302\u00fe _a2\u0302 _h sin a3\u0302 (A2) Noting that z\u0302 \u00bc cos a1\u0302 sin a3\u0302 (A3) the time derivatives of the local axes are d1\u0302 dt \u00bc ~x123 1\u0302 \u00bc _h sin a2\u0302 _a3\u0302 (A4) 021015-10 / Vol. 7, APRIL 2012 Transactions of the ASME Downloaded From: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 05/05/2015 Terms of Use: http://asme.org/terms d2\u0302 dt \u00bc ~x123 2\u0302 \u00bc _h sin a1\u0302 _h cos a3\u0302 \u00bc _hr\u0302 (A5) d3\u0302 dt \u00bc ~x123 3\u0302 \u00bc _a1\u0302\u00fe _h cos a2\u0302 (A6) Where the second horizontal unit vector r\u0302 (the first being 2\u0302) is defined by r \u00bc 2\u0302 z\u0302 \u00bc sin a1\u0302\u00fe cos a3\u0302 (A7) Thus, dr\u0302 dt \u00bc _h2\u0302 (A8) Combining Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001343_1.3663379-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001343_1.3663379-Figure2-1.png",
        "caption": "FIG. 2. Schematic of the drop deforming in a uniaxial extensional flow.",
        "texts": [
            " Thus, we describe the BI method in some detail here, based upon the equations and boundary conditions for the dynamics of a single drop in an external axisymmetric straining flow, u0 1\u00f0x0\u00de \u00bc E 1 2 x0; 1 2 y0; z0 ; (3.1) where E is the strain rate. We assume that there are two Newtonian fluids, the suspending fluid with viscosity l and the drop fluid with viscosity l\u0302, separated by a deformable interface with an interfacial tension r. A schematic of the deformable drop in a linear axisymmetric flow is shown in Fig. 2. We begin with the governing equations and boundary conditions, rendered dimensionless using the undeformed drop radius, \u2018c \u00bc a, as a characteristic length scale and uc \u00bc c=l as the characteristic velocity scale (here, c is the interfacial tension). For the characteristic time tc, pressure pc and stress sc, we use the scalings tc \u00bc al=c; pc; sc \u00bc c=a: (3.2) In the limit of very small Reynolds number, the governing equations are the creepingflow equations, Redistribution subject to SOR license or copyright; see http://scitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.13-1.png",
        "caption": "Fig. 9.13 Single roller contacting ground at P",
        "texts": [
            " In a vehicle equipped with mecanum wheels the axes of the hubs are fixed on the vehicle body. Such a vehicle can rotate on the spot and translate in any direction without slipping on the ground provided a single roller per wheel has ground contact. Vehicle motion is controlled by controlling the angular velocities of wheel hubs relative to the vehicle body. Because of their maneuverability such vehicles find applications as store trolleys, assembly platforms in factories, platforms for mobile robots etc. The following kinematics analysis was published in [13]. In Fig. 9.13 the axis of the wheel hub and a single roller contacting ground are shown. The reference basis with unit basis vectors ex , ey , ez is fixed on the vehicle. Its origin S is the center of the hub, ey is directed along the hub axis, and ez is normal to the plane on which the roller is rolling. The basis with unit basis vectors e1 , e2 , e3 is fixed on the hub. Its origin is the center S\u2217 of the roller, e2 is directed along the roller axis, and e3 is pointing towards S . Let \u03d5 be the rotation angle of the hub relative to the vehicle about ey with \u03d5 = 0 in the position e3 = ez "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure16.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure16.3-1.png",
        "caption": "Fig. 16.3 Bounce of a ball incident obliquely on a horizontal surface. 1 is the angle of incidence and 2 is the angle of reflection. N is the vertical force on the ball and F is the horizontal friction force. v1 is the incident speed and v2 is the bounce speed",
        "texts": [
            " A tennis player therefore needs to be careful, when tilting the racquet, to tilt it in the right direction. A baseball player tends to get whatever comes, unless he is skillful enough to strike the ball exactly where he wants to. We will return to this later when we examine whether a curveball (incident with topspin) can be struck farther than a fastball (incident with backspin). When a ball without spin or with topspin is incident at an oblique angle on a flat, heavy, horizontal surface, the ball will bounce with topspin, as indicated in Fig. 16.3. Provided the surface is much heavier and stiffer than the ball then motion of the surface itself can be ignored and the bounce is determined mainly by the properties of the ball. Nevertheless, there is one property of the surface that does influence the bounce, and that is the smoothness or roughness of the surface. If the surface is slippery then the friction force on the ball will be relatively small. If the surface is rough then there will be a large friction force on the ball. The friction force on the ball acts in a direction parallel to the surface and has two effects",
            " The only way to counter the hype is to take careful measurements of ball speed and spin to determine whether there is any substance to the manufacturer\u2019s claims. Some progress has been made in this direction but a lot more still needs to be done. Suppose that a ball is incident obliquely on a horizontal surface, at speed v1, and bounces at speed v2, as shown in Fig. 16.5. The horizontal components of the ball speed before and after the bounce are vx1 and vx2, respectively. The latter speeds refer to the speed of the ball center of mass (CM). Suppose also that the ball is incident with topspin and bounces with topspin, as shown in Fig. 16.3, with angular speeds !1 and !2, respectively. A point at the bottom of the ball will have a lower horizontal speed than the CM since the bottom of the ball is rotating backward. The horizontal speeds at the bottom of the ball are s1 D vx1 R!1 before the bounce and s2 D vx2 R!2 after the bounce, where R is the radius of the ball. If the contact point has a vertical speed vy1 before the bounce, and vy2 after the bounce then we define ey D vy2=vy1 as the COR in a direction perpendicular to 272 16 Ball Bounce and Spin the surface",
            " It seems that the ball surface is more elastic when the ball is relatively new and that repeated bounces act to harden the surface and to reduce its elasticity in a direction parallel to the Appendix 16.1 Ball Bounce Calculations 273 surface. The end result is that a baseball can bounce with topspin when it is incident with backspin, but only for the first few bounces. After ten or more bounces the ball tends to bounce without any spin at all when it is incident with backspin. Appendix 16.1 Ball Bounce Calculations (a) Sliding In Fig. 16.3, we show a ball incident at speed v1 and bouncing at speed v2 off a heavy surface. The horizontal component of v1 is vx1 D v1sin 1 and the vertical component is vy1 D v1cos 1. Likewise, the components of v2 are vx2 D v2sin 2 and vy2 D v2cos 2. When the ball is sliding along the surface, a friction force F D N acts on the bottom of the ball in a direction parallel to the surface. N is the normal reaction force acting on the ball in a direction perpendicular to the surface, and is the coefficient of sliding friction (COF)",
            " For a baseball on wood or aluminum, is typically about 0.4 or 0.5. If F and N are taken as average forces during the bounce, and if the ball remains in contact with the surface for a time T then the change in the horizontal and vertical components of the ball speed during the bounce are given by F D m dvx dt D m.vx1 vx2/ T (16.1) and N D m dvy dt D m.vy1 C vy2/ T ; (16.2) where m is the ball mass. To avoid complicating the issue with negative numbers and signs, we have assumed here that all quantities are positive in the direction shown in Fig. 16.3. In particular, the ball reverses direction in the y direction, but we can still take vy1 to be a positive number if we want to. If the ball is incident in the vertical direction at speed vy1 D 5 m s 1 and bounces at speed vy2 D 2 m s 1, then the change in speed is 7 m s 1, not 3 m s 1, since the ball reverses direction. If the ball bounced with vy2 D 5 m s 1, then the change in vertical speed would be 10 m s 1, not zero. The coefficient of restitution, ey , for a bounce on a heavy surface, is defined by ey D vy2 vy1 (16",
            " For a bat and ball collision, the angle of incidence is increased when the batter strikes the ball near the bottom of the ball rather than striking the middle of the ball. One way to increase ex would be to coat the bat with a soft, flexible material like rubber. In that case, extra elastic energy would be stored in the rubber and then given back to the ball, increasing the values of both ey and ex . The ball would not only bounce at higher speed but it would also spin faster. That is why table tennis bats have a rubber surface. (c) Oblique Bounce Off a Light Surface Suppose that the surface in Fig. 16.3 is only slightly heavier than the incident ball. Then the ball will bounce off the surface at reduced speed since the ball transfers some of its kinetic energy to the surface. That is essentially the situation encountered when a ball strikes a stationary bat or a tennis racquet. If the ball makes a head-on collision with the bat then conservation of momentum for the collision, plus an estimate of the COR, tells us the recoil speed of the bat. We can then proceed as in Chap. 9 to calculate the bounce speed of the ball and the recoil speed of the bat. However, if the ball does not strike the bat head-on then the ball will be deflected sideways by the curved surface of the bat, in which case we can treat the collision as an oblique bounce, as shown in Fig. 16.3. A similar situation occurs in tennis when References 277 the ball strikes the strings at an oblique angle and the racquet head recoils. Recoil motion of the bat or the racquet adds to the complexity of the problem, but there is a simple way around the problem. That is, we ignore the recoil motion and just measure what happens to the ball. We saw in Chap. 9 that it is very useful to define an apparent coefficient of restitution, eA, or bounce factor, q describing the ratio of the ball speed after the collision to that before the collision"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003254_s11431-020-1588-5-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003254_s11431-020-1588-5-Figure1-1.png",
        "caption": "Figure 1 (Color online) Different coordinate systems and legs distribution of the Hexa-XIII.",
        "texts": [
            " Besides, we present the gait switching method instructed by the stability and interference criteria. In Section 4, the simulations are performed that the Hexa-XIII robot utilized the gait switching method to generate gait sequences when climbing stairs over 45\u00b0. And the experiments validate the effectiveness of this method. Finally, we combine the results in a summary and discuss the actual applications of the proposed method in Section 5. The coordinate system (CS) and structure of the six-legged robot Hexa-XIII are illustrated in Figure 1. The legs of Hexa- XIII robot are symmetrically arranged, and each leg has corresponding hip coordinate system (HCS) located at the intersection of the motor axes. The body coordinate system (BCS) is located at the center of six HCSs, and GCS denotes the ground coordinate system when we mentioned in gait planning. The leg mechanism of Hexa-XIII is a planar parallel five-bar mechanism with 2 translational DOF at the end of the toe. To reduce the amount of actuator components, the leg mechanism removes the abduction-adduction DOF. Therefore, we design the waist mechanism to realize the robot turn. The waist mechanism consists of the waist motor and screw (see Figure 1), which connects the upper body and lower body of the robot. The legs 1, 3, 5 are fixed on the upper body, and legs 2, 4, 6 are fixed on the lower body. When changing the lengths of screw, the angle between the upper and lower body is changed. So that the Hexa-XIII robot can change locomotion direction and realize turning. The leg structure and coordinate system are illustrated in Figure 2. Two motors are fixed on the hip. Therefore, the inertia of moving parts of the leg is reduced. The leg components are illustrated in Figure 2(a)",
            " Since the robot cannot make a turn with the 2-DOF legs, so that we design the waist screw mechanism to realize turning. Before we calculate the robot kinematics, we firstly calculate the angle \u03b8w between the upper body coordinate system (UBCS) and the lower body coordinate system (LBCS). The forward solution of waist mechanism ( )FK=w wm waist can be easily derived from the rotation angle of waist motor \u03b8wm by the law of cosines. The UBCS is coincident with the BCS. And the LBCS is also concentric with BCS when all the legs are symmetric distributed (see Figure 1(a)). As aforementioned definitions of BCS, UBCS and LBCS, we can calculate homogenous transformation matrices from LBCS to BCS by eq. (6): T T R 0 0= ( ) 1 . (6)B LB B UB w (1\u00d73) Because UBCS is coincident with BCS, eq. (6) can be derived as eq. (7): T R 0 0= ( ) 1 . (7)B LB w (1\u00d73) According to the geometrical dimensions of the Hexa-XIII robot, the homogenous transformation matrices from HCSs to the LBCS/BCS can be derived as eq. (8): T R p 0 = ( ) 1 . (8)LB B Hi B Hi B Hi( ) (1\u00d73) Similarly, the homogenous transformation matricefrom robot body coordinate system to GCS is T R p 0 = ( ) 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003254_s11431-020-1588-5-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003254_s11431-020-1588-5-Figure7-1.png",
        "caption": "Figure 7 Leg swing in leg workspace.",
        "texts": [
            " If the slope criteria satisfy eq. (25), we define that the leg can swing without shin interference. The leg mechanism reciprocating swings in the workspace when the six-legged robot walking on terrains. The kinematic evaluation is based on foot tip vector Pf angle with respect to the move direction in HCS, and the foot tip po- sition constrained by critical limit positions. If the foot tip position far away from the move direction, \u03b3w<0. Therefore, the leg 1* has more swing priority than leg 2* in Figure 7. The six-legged robot Hexa-XIII evaluates the terrain conditions and calculates the constraint criteria using the method introduced in Section 3.3. Then, the legs that be constrained by stability and interference criteria are recorded. The unconstrained legs that have not swung in current gait switching cycle are available for next swing (see Figure 8). According to the swing priority of available legs, the sixlegged robot can generate stable and collision-free gaits based on the reference gait library"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003565_j.isatra.2021.04.009-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003565_j.isatra.2021.04.009-Figure2-1.png",
        "caption": "Fig. 2. Yaw motion in ship course control.",
        "texts": [
            " [57], a more realistic Norrbin nonlinar mathematical model is considered as follows: \u03a6\u0308 + \u03a6\u0307 + a\u03a6\u0307 = K (\u03b4 + \u25b3\u03b4), (35) n which T denotes the time constant, the actual ship course \u03a6 epresents the output, a is the Norrbin coefficient, \u03b4 stands for the udder angle (control input), K is the gain constant, \u25b3\u03b4 means the nput disturbance. Set x1 = \u03a6 , x2 = \u03a6\u0307 , u = \u03b4 and \u25b3u = \u25b3\u03b4, (35) can be rewritten s the following state equations. \u02d91 = x2, \u02d92 = \u2212 1 T x2 \u2212 a T x32 + K T u + K T \u25b3u, (36) For the ship steering system, we need to construct the course racking control law such that the actual course \u03a6 can asymptotcally track the desired course \u03a60. The yaw motion in ship course ontrol is illustrated in Fig. 2. Similar to Ref. [62], we set a = 0.3s2, K = 0.23s\u22121 and = 21s. Furthermore, the system parametric noises are set as \u00af = T (1 + 0.3 sin(5t)), K\u0304 = K (1 + 0.3 cos(5t)) and a\u0304 = a(1 + .1 sin(5t)). The desired course of ship and input disturbance are et as yd = \u03a60 = 30\u25e6 and \u25b3u = 0.1 sin t , respectively. In the following, the comparison of proposed control scheme nd the control scheme in Ref. [57] is made with and without ystem parametric noises, where Case 1 is the proposed control cheme and Case 2 is the control scheme in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001353_j.neucom.2014.04.023-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001353_j.neucom.2014.04.023-Figure3-1.png",
        "caption": "Fig. 3. Marine course-changing control system.",
        "texts": [
            " Simulation results To illustrate its effectiveness, the proposed control scheme is applied to a marine course-changing control system and a gyros synchronization control system shown in Figs. 3 and 4, respectively. Moreover, for comparison, simulations are performed using a wavelet adaptive backstepping control (WABC) [15] and the proposed RABC control. 5.1. Marine course-changing control system The mathematical model of a marine course-changing control system is obtained from [28] and is shown in Fig. 3. The dynamic equation of the system is \u20ac\u03c8\u00f0t\u00de\u00fe ks tm hc\u00f0 _\u03c8 \u00de \u00bc ks tm u\u00f0t\u00de \u00f055\u00de where \u03c8\u00f0t\u00de is the ship heading angle, u\u00f0t\u00de is the rudder angle, hc\u00f0 _\u03c8\u00de \u00bc n3 _\u03c8 3\u00f0t\u00de\u00fen1 _\u03c8\u00f0t\u00de is the nonlinear maneuvering characteristic, ks is a gain (1=s), and tmis a time constant (s). The parameters of the ship model are ks \u00bc 1:0 tm \u00bc 1:0, n3 \u00bc 10 2 and n1 \u00bc 10 3: The dynamic Eq. (55) can be written as \u20acx\u00f0t\u00de \u00bc \u03b1\u00f0x\u00f0t\u00de\u00de\u00fe\u03b2\u00f0x\u00f0t\u00de\u00de u\u00f0t\u00de\u00fed\u00f0t\u00de; where x\u00f0t\u00de \u00bc \u03c8\u00f0t\u00de; \u03b1\u00f0x\u00f0t\u00de\u00de \u00bc ks tm \u00f0n3 _x 3\u00f0t\u00de\u00fen1 _x\u00f0t\u00de\u00deand \u03b2\u00f0x\u00f0t\u00de\u00de \u00bc ks=tm:An external disturbance,d\u00f0t\u00de \u00bc 0:2 sin \u00f02\u03c00:1t\u00de, is considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002987_tie.2019.2949536-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002987_tie.2019.2949536-Figure1-1.png",
        "caption": "Fig. 1. The structure of a 12-8 pole DSEG.",
        "texts": [
            " The DSEG system based on the controlled rectifier and that based on the diode rectifier are compared. The APC method is analyzed. The relationship between the turn-off angle (\u03b2) and the field current (if) is studied. The DSEG is an optimized solution for harsh environment applications such as the aircraft generator. The rotor is simple and robust. The magnetic field is provided by the field windings. By regulating if, the magnetic field can be controlled. The structure of a 12-8 pole DSEG is illustrated in Fig.1. In the conventional DSEG system, as shown in Fig. 2, the 3-phase output power of the DSEG is converted to DC output by a diode rectifier. The DC-link voltage is controlled by regulating the field current. However, the inductance of the field winding is large and the electrical time constant of the field current regulation is large. The transient process is further decelerated. In the DSEG system based on the controlled rectifier, as illustrated in Fig. 3, the DSEG is connected to a controlled rectifier"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000675_sis.2009.4937849-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000675_sis.2009.4937849-Figure5-1.png",
        "caption": "Fig. 5. The sketches of an aggregate with seven robots. (a) The aggregates are assumed to form circles with a radius of Rm. When the robots are odes away from each other, we can calculate Rm with the help of circle packing theory. (b) Both growing probability for large aggregates (m > 1) and shrinking probability are calculated using the circle whose radius is odes/2 units smaller than Rm.",
        "texts": [
            " Experiments show us that the creation probability of an aggregate (Pcreate) approximately equals to the growing probability of an aggregate of size one for relatively large environments. Pcreate \u2248 Pgrow(1) (12) Calculating growing probability for larger aggregates (m > 1) requires to consider the area covered by the aggregates. For a searching robot, the probability of finding an aggregate of size m in the arena is calculated as Pgrow(m) \u2248 2(omax + Rm \u2212 (odes/2))v\u0394t Atotal , m > 1 (13) where odes is the center-to-center desired distance between robots and Rm is the approximate radius for an aggregate of size m (Figure 5-a). In this formula, the area swept by one searching robot is extended by Rm\u2212(odes/2) units (Figure 5- b) to include the regions in which the aggregate with radius Rm can be detected by the searching robot. This is depicted on Figure 6. Rm is calculated with the help of circle packing theory [6]. Circle packing is the arrangement of circles inside a given boundary such that no two overlap and have a specified pattern of tangencies. In our context, we regard robots as circles with a diameter of odes and assume the given boundary, which correspond to the area of the aggregates, has the shape of a circle. For an aggregate with radius Rm (as depicted on Figure 5-a), following relation is known to hold from the best known packings of equal circles in the unit circle [10] Rm odes/2 \u2248 amb (14) where m is the number of robots in the aggregate, a (\u223c 1.20) and b (\u223c 0.48) are constants. After some rearrangements on equation 14, we can calculate the radius of the aggregate as Rm \u2248 aodesm b 2 (15) B. Shrinking of an Aggregate (Pshrink) An aggregate of size m shrinks when one of the waiting robots belonging to this aggregate leaves from the aggregate. In previous probabilistic model studies (e",
            " Our aggregation controller which forces the robots to form compact aggregates, allows us to estimate the number of robots that can leave an aggregate. The probability of an aggregate of size m to shrink is calculated as Pshrink(m) \u2248 Np(m)Pleave (16) where Np(m) is the approximate number of robots on the periphery of the aggregate and Pleave is the leaving probability of a robot. The number of robots on the periphery of an aggregate with m robots can be estimated by finding how many robots can be placed on the circle with radius Rm \u2212 (odes/2) (Figure 5-b). This number can be found approximately by dividing the periphery of the circle to odes Np(m) \u2248 2\u03c0(Rm \u2212 (odes/2)) odes (17) When we substitute Rm with the right hand side of equation 15 and simplify the result, we obtain Np(m) as Np(m) \u2248 { \u03c0(amb \u2212 1), if m \u2265 6 m, otherwise (18) The second part of the equation is introduced for small aggregates (m < 6) where any waiting robots belonging to these aggregates can leave their aggregates. C. Iteration of the probabilistic model The model keeps an array for tracking the number of aggregates for all possible aggregate sizes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000424_ests.2009.4906554-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000424_ests.2009.4906554-Figure1-1.png",
        "caption": "Figure 1. Magnetic gear with 31 outer pole pairs and 5 inner pole pairs.",
        "texts": [
            "2 ft-lbs/lb while HTS machines were on the low end with 14.2 ft-lbs/lb. Magnetic gears have been explored more in recent years with the advent of rare-earth permanent magnets. Gears studied in [4-7] range from concentric planetary gears to newer more exotic versions such as the cycloid and harmonic gear. The torque densities for the gears studied and built range from 72 Nm/l for early prototypes all the way to 185 Nm/l for the latest prototypes, compared with 30 Nm/l for liquid-cooled electric machines. An example shown in Fig. 1 contains 31 outer pole pairs and 5 inner pole pairs. Between the magnetic rings are stator pole pieces composed of electrical steel. These stator pieces serve to modulate the flux between the permanent magnet rings. This gear is of the concentric planetary type. The advantages of using magnetic gears over traditional gearboxes include inherent overload protection. Gears which are pushed by torque transients over their torque rating will slip, instead of possibly breaking teeth. They also provide the advantage of lower acoustic noise due to the loss of mechanical contact between the teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000084_j.triboint.2005.12.005-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000084_j.triboint.2005.12.005-Figure1-1.png",
        "caption": "Fig. 1. Force equilibrium for a ball bearing: (a) the jth ball and (b) the inner ring.",
        "texts": [
            " The Nomenclature b modified exponent of the load\u2013deflection relationship di, do inner, outer raceway diameter D ball diameter exp exponential function E elastic modulus F c centrifugal force F r radial load K , K 0 load\u2013deflection factor (0: modified) of the overall bearing K i, K 0i load\u2013deflection factors (0: modified) of the inner raceway Ko, K 0o load\u2013deflection factors (0: modified) of the outer raceway ln natural logarithm function N ball number Pd diametric clearance Q contact load Qoj, Qij contact loads between ball with inner, outer raceway ri, ro groove radius of inner, outer ring u ball deformation due to contact load uij, uoj contact deformations of the jth ball relative to the inner, outer raceway ur bearing deflection urj net radial compression at angular position cj Z active ball number di, do elliptical integral of inner, outer raceway n Poisson\u2019s ratio cj angular position of the jth ball bearing deflection can be calculated quickly and accurately by using this method. This study analyzes several types of deep-groove ball bearing to determine their load\u2013deflection relationship. For two types of bearings, their three-dimensional finite element models are established, and results are calculated by using FEM, JHM and modified JHM (MJHM). All results are then compared, to verify the MJHM results. The comparisons show that the results obtained with MJHM are consistent with FEM results. When a ball bearing is subjected to a radial load F r as shown in Fig. 1, for the jth ball at the angular position cj the force equilibrium can be described by Qoj Qij F c \u00bc 0, (1) where Qoj and Qij are contact loads between the ball with inner and outer raceway, respectively, and F c is the centrifugal force as the ball rotating about the bearing center. JHM, according to Hertz contact theory, gives the ballraceway contact load Qij and Qoj which are determined by Q \u00bc Ku1:5, (2) where u is the ball deformation due to contact load, K is load\u2013deflection factor, which is denoted for both K i and Ko of the inner ring and outer ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000414_tac.2007.902750-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000414_tac.2007.902750-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " The first assertion is obvious since a closed trajectory will imply that there is a singular point at least in the inner part of '(t) (see [29, pp. 46\u201349]), which contradicts with the assumption g(x) 6= 0. Next, we use contradiction method to show that the two ends of '(t) extend to infinite. Otherwise, there exist a bounded sequence '(ti), where, without loss of generality, we assume that ti ! +1; ti+1 > ti; i = 1; 2; . . . ; n; . . .. Hence, there exists at least one accumulation point of '(ti) as shown in Fig. 1. Since g(x) 6= 0;8x 2 2; is then a regular point of the (13), and so we can make a transversal l passing the point (see [30]). By the definition of , there must exist tj > ti such '(ti) and '(tj) intersect l at P1 and P2, respectively, as shown in Fig. 1. Obviously, the finite closed arc '(t); ti t tj and the transversal between P1 and P2 form a simple closed curve C . The trajectory '(t); t > tj will stay in the inner part of C forever, because '(t); t > tj can go out from neither the transversal (since the vector field points to the inner part) and nor from '(t); ti t tj (by the uniqueness of solutions). Hence, by the Poincare-Bendixson Theorem [29], '(t) or its ! limit set is a closed curve, which imply the existence of a singular point for the (13) (see [29, pp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003066_tec.2020.3004227-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003066_tec.2020.3004227-Figure15-1.png",
        "caption": "Fig. 15. Experiment platform (a) Rotor, (b) Stator and (c) Prototype in test platform",
        "texts": [
            " NA needs 6.07 minutes to complete the iterative procedure in 28 cycles under / = 2, while FEA with 216,667 nodes and 72,040 elements needs 7.73 minutes. The difference of d-axis inductance by (55) from NA and FEA is less than 2mH. Seen from Fig. 14, PM flux linkage and d-axis inductance change very little under demagnetization state, and change greatly under magnetization state especially when . Q-axis inductance by (56) from NA and FEA is 39.7mH and 38mH respectively. VIII. EXPERIMENT VALIDATION Fig. 15 shows rotor (a), stator (b) and prototype (c) in the test platform. Self inductance from NA by (53) (for example, at = 0.1 ) is compared with that from FEA and test as shown in Fig. 16 (a). The results from NA and FEA are greater than those from test owing to ignoring end effect in NA and FEA. The maximal difference of self inductance between NA and test is 7.7mH. In test platform shown in Fig. 15 (c), the prototype serving as a generator is driven to the rating speed by a prime mover connected with a gear case. An oscilloscope tests the phase EMF shown in Fig. 16 (b). When powering a resistive load, the prototype works in a demagnetized state, viz. < 0. Because PM flux linkage and d-axis inductance in demagnetized state change very little, they are considered to be constants equal to their averages respectively. Ignoring salient pole effect and regarding d-axis inductance as synchronous inductance under different resistive load, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002596_s00170-018-2850-8-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002596_s00170-018-2850-8-Figure4-1.png",
        "caption": "Fig. 4 SLM specimen",
        "texts": [
            " The computer controls the laser beam to move in a standard alternating raster strategy at 1200 mm/s, to melt the paved powders layer by layer, as illustrated in Fig. 3. In one layer, the laser scans the powders within the contour of the model cross-section, forming a layer with bidirectional hatches. After the layer is finished, the build platform is lowered by a thickness of 40 \u03bcm and another layer of powders is spread on it. Then, the laser scan direction is rotated by 90\u00b0 to scan and melt the newly paved powders like above. This process continues until the specimen is finished. Figure 4 shows the finished SLM specimen. The SLM manufacturing parameters are presented in Table 1. An ELB N10 high-precision surface grinding machine is employed for this experiment, the spindle speed of which is up to 6000 rpm and the spindle power is 45 kW. The wheel employed in the experiment is a resin-bonded corundum wheel (grit size 50/60) with a diameter of 400 mm and a width of 40 mm. Two Inconel 718 specimens are prepared by SLM and casting, respectively, both with a dimension of 150 mm in length, 15 mm in width, and 65 mm in height"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureA.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureA.1-1.png",
        "caption": "Fig. A.1 Schematic of the spinning sphere",
        "texts": [
            "This rotationofmass elements generates the centrifugal forces acting strictly perpendicular to axis oz of the spinning sphere. The analytical approach for the modelling of the action of the centrifugal forces of the spinning sphere is similar to the spinning disc represented in Chap. 3. The rotating mass elements of the spinning sphere are located on the surface of the 2/3 sphere radius. The analysis of the acting inertial forces generated by themass element of the sphere is considered on the arbitrary planes that parallel to the plane of the maximal diameter of the sphere (Fig. A.1) that is the same as the plane of the thin disc represented in Fig. 3.2 of Chap. 3. The plane of the mass elements generates the change in the vector\u2019s components f ct.z, whose directions are parallel to the spinning sphere axle oz. The integrated product of components for the vector\u2019s change in the centrifugal forces f ct.z and their variable radius of location relative to axis ox generate the resistance torque T ct acting opposite to the external torque. The resistance torque T ct produced by the centrifugal force of the mass element of the sphere is expressed by the following equation: Tct = \u2212 fct",
            "2) where fct = mr sin \u03b1 sin \u03b2\u03c92 = [ M(2/3)R\u03c92 sin \u03b1 sin \u03b2 4\u03c0 \u03b4 ] is the centrifugal force of the mass element m; m = M 4\u03c0[(2/3)R]2 \u03b4[(2/3)R]2 = M 4\u03c0 \u03b4, M is the mass of the sphere; 4\u03c0 is the spherical angle; \u03b4 is the spherical angle of the mass element\u2019s location; r = (2/3)Rsin\u03b1sin\u03b2 is the radius of the mass elements location; R is the external radius of the sphere; \u03c9 is the constant angular velocity of the sphere; \u03b1 is the angle of the mass element\u2019s location on the plane that parallel to plane xoz; \u03b2 is the angle of the mass element\u2019s location on the plane pass axis oz; \u03b3 is the angle of turn for the sphere\u2019s plane around axis ox (sin \u03b3 = \u03b3 for the small values of the angle) (Fig. 3.2, Chap. 3). Substituting the defined parameters into Eq. (A.1.1) yields the following equation: Tct = \u2212MR\u03c92 6\u03c0 \u03b4 \u03b3 sin \u03b1 sin \u03b2 \u00d7 ym = \u2212MR\u03c92 6\u03c0 \u03b4 \u03b3 sin \u03b1 sin \u03b2 \u00d7 2 3 R sin \u03b1 sin \u03b2 = \u2212MR2\u03c92 9\u03c0 \u03b4 \u03b3 sin2 \u03b1 sin2 \u03b2 (A.1.3) where ym = (2/3)R sin \u03b1 sin \u03b2 (Fig. A.1) is the distance of the mass element\u2019s location on the sphere\u2019s plane relative to axis ox, other components are as specified above. The action of the centrifugal forces\u2019 f ct.z axial components represents the distributed load where the sphere\u2019s mass elements are located (Fig. 3.2, Chap. 3). The resultant torque is the product of the resultant centrifugal forces and the centroid at the semicircle. The location of the resultant force of the one plane is the centroid (point A, Fig. 3.2, Chap. 3) that is defined by the expression ym",
            " The mathematical models for internal torques acting on the spinning sphere are represented in Table A.1. The equations for the inertial torques acting on the spinning sphere [13] are different than for the spinning disc. Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 199 A.1.5 Working Example The sphere has a mass of 1.0 kg, a radius of 0.1 m and spinning at 3000 rpm. An external torque acts on the sphere, which rotates with an angular velocity of 0.05 rpm. It is determined by the value of the resistance and precession torques acting on the spinning sphere (Fig. A.1). Substituting the initial data into equations of Table A.1 and transforming yield the following result: \u2022 Resistance torque T r Tr = 5 18\u03c0 ( \u03c02 3 + 1 ) J\u03c9\u03c9x = 5 18\u03c0 ( \u03c02 3 + 1 ) \u00d7 2MR2 5 J\u03c9\u03c9x = 5 18\u03c0 ( \u03c02 3 + 1 ) \u00d7 2 5 \u00d7 1.0 \u00d7 0.12 \u00d7 3000\u00d72\u03c0 60 \u00d7 0.05\u00d72\u03c0 60 = 0.024632 Nm \u2022 Precession torque T p Tp = ( 5 54\u03c0 3 + 1 ) J\u03c9\u03c9x = ( 5 54\u03c0 3 + 1 )\u00d7 2 5 \u00d7 1.0 \u00d7 0.12 \u00d7 3000\u00d72\u03c0 60 \u00d7 0.05\u00d72\u03c0 60 = 0.025469 Nm where all parameters are as specified above. A.2 Inertial Forces Acting on a Spinning Circular Cone A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003289_j.rcim.2020.102055-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003289_j.rcim.2020.102055-Figure5-1.png",
        "caption": "Fig. 5. The stud welding robot. The simulated dress pack part is 1.9m and has an outer radius of 20 mm. The length density =A 1.1 kgm 1 and the effective stiffness parameters = \u00d7GA N3.4 10 ,3 = \u00d7EA N1.1 10 ,4 =EI 0.68 Nm2 and =GJ 6.3 Nm2 were used for the simulation. Models courtesy of Volvo Car Corporation [32].",
        "texts": [
            " The reasons are that these paths are relatively short, the dress pack is most strained at the start or end configuration of the path and no contacts occurs. Hence, optimization of these paths converges rapidly and only lead to minor improvements. However, a few paths ( \u2248 9%) become very problematic due to contact between the dress pack and the surrounding geometry or the robot links and stress peaks during the motion. We have generated a particularly tricky path in the same station that combines all these difficulties (Fig. 5). The robot has to move around a support pillar, causing the dress pack to be in contact with both the pillar and link 4 on the robot itself. This hard case will serve as benchmark for the forthcoming analysis and validation of the method. Contact forces are modelled between the dress pack and the robot links and an additional clearance constraint of =d 50mm on the form (11) is prescribed between the robot and the pillar. A joint coordinate restriction of \u00b1 20\u2218 is imposed on how much the interior way points can be moved from their initial configurations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001498_1.4914605-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001498_1.4914605-Figure10-1.png",
        "caption": "FIGURE 10. Metrology representation of the boroscpe boss.",
        "texts": [
            " These specimens are produced for getting material data like yield strength. Also metallographic inspection is necessary for validation of material properties. The semi-transparent 3D OT-image of a boroscope boss is shown in Fig. 9. In this case a deviation of the SLMprocess was provoked artificially in order to generate lack of fusion defects. Under normal conditions no lack of fusion defect was found in any boroscope boss. The metrology data generated by fringe pattern projection are shown in Fig. 10. In brown color the CAD geometry is represented, in grey the metrology data and in green color the comparison between the two data sets. Deviations from CAD geometry as small as 5 \u03bcm are resolvable. The boroscope bosses are now ready to be mounted on the PW1100G engine which will power the new Airbus A320NEO. The additive manufacturing technology is very powerful and useful for the aerospace and aviation industry because there is a need for the production of a lot of different complex shaped parts with lowest weight"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001946_j.matdes.2018.05.032-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001946_j.matdes.2018.05.032-Figure9-1.png",
        "caption": "Fig. 9. (a) Four {111} planes in BCC cell (b) The crystallographic relationship between the te",
        "texts": [
            " In the paper, themethod of single \u201cedge-on\u201d trace analysis is used to calculate the habit plane of \u03b1 phase as shown in Fig. 8 [38]. The specimen is tilted to the \u2329110\u232a\u03b2 direction of \u03b2 matrix as shown in Fig. 8(b), and the\u03b1 lath with [0001] \u03b1 // b110N\u03b2, as shown in Fig. 8(c), is selected to calculate the habit plane. And the result shows that the habit plane is close to (111) \u03b2-(445) \u03b2, as shown in Fig. 8(a). There are four {111} planes in a BCC cell, which forms of a tetrahedron in space, as shown in Fig. 9(a). In view of the habit plane of \u03b1 phase in titanium alloy close to the {111} plane, the crystallographic relationship between the different \u03b1 laths and BCC cell is shown as in Fig. 9(b), the \u03b1 laths are simulated as elliptical lamella in the model. So, a tetrahedral spatial distribution model of \u03b1 phase in a \u03b2 grain is put forward as shown in Fig. 9(b). And based on the tetrahedral model, the simulated 3D microstructure is simulated as in Fig. 9(c). However, this tetrahedral distribution model is an approximate model. Actually, each plane of the tetrahedron consists of several planes close to the {111} plane. Take the {334} habit plane for example, there are three planes close to the (111) plane, such as (334), (343), (433), and each habit plane corresponding to one Burgers OR. ructure in the specimen. 3.3. The model verification In order to verify the validity of themodel, themicrostructure in the different cut plane of a grain is needed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.12-1.png",
        "caption": "Fig. 17.12 The double-crank of Fig. 17.4a (a) and the crank-rocker of Fig. 17.4b (b) in the two positions with stationary values of 1/i",
        "texts": [
            " In order to determine for a given four-bar all positions with a stationary value of 1/i the four-bar and the center P12 must be drawn for a number of (monotonically increasing) angles \u03d5 over the entire possible range \u03c61 \u2264 \u03d5 \u2264 \u03c62 . A stationary value of 1/i is passed every time the moving center P12 changes its sense of direction along the \u03be -axis (jumps from \u221e to \u2212\u221e do not count as changes of sense of direction). Once a position is known approximately it can be improved by checking the angle between the lines P12P30 and P31P32 . Example: For the double-crank in Fig. 17.4a this investigation reveals that stationary values of 1/i occur in the two positions shown in Fig. 17.12a with \u03d5 \u2248 9\u25e6 and with \u03d5 \u2248 95\u25e6 . With the coordinate of P12 (17.27) yields for the position \u03d5 \u2248 9\u25e6 a maximum (1/i)max \u2248 2.7 and for the position \u03d5 \u2248 95\u25e6 a minimum (1/i)min \u2248 0.42 . For the crank-rocker of Fig. 17.4b the same investigation can be made. This is unnecessary, however, because this four-bar is obtained from the previously investigated one by interchanging the fixed link and the input link. From (17.38) it follows that two four-bars thus related have stationary values of 1/i for one and the same angles \u03d5 . Furthermore, these stationary values add up to one. If the stationary value is a maximum in one of the four-bars, it is a minimum in the other and vice versa. Hence the crank-rocker of Fig. 17.4b has at \u03d5 \u2248 9\u25e6 a minimum (1/i)min \u2248 \u22121.7 and at \u03d5 \u2248 95\u25e6 a maximum (1/i)max \u2248 0.58 . Figure 17.12b shows the crank-rocker in these positions. End of example. In what follows, two analytical methods for determining stationary values of 1/i are described. Method 1 is a direct method based on (17.35). With the abbreviation x = cos\u03d5 it is written in the form 2 i(x) = x\u2212 p1 x\u2212 p2 \u00b1 (x\u2212 p3)Q (x\u2212 p2)P , P = \u221a \u03bb2 \u2212 (x\u2212 p4)2 , Q = \u221a 1\u2212 x2 . \u23ab\u23ac \u23ad (17.42) The stationarity condition d(1/i)/dx = 0 has the form (the prime denotes the derivative with respect to x ) \u2213(p1 \u2212 p2)P 2 = (p3 \u2212 p2)PQ+ (x\u2212 p2)(x\u2212 p3)(PQ\u2032 \u2212QP \u2032) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000750_physrevlett.103.077801-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000750_physrevlett.103.077801-Figure1-1.png",
        "caption": "FIG. 1 (color online). The geometry of the scattering experiment. The incoming light ki was vertically polarized and horizontally polarized scattered light kf was detected and analyzed as a function of scattering angle and applied extension xx perpendicular to the director n. Scattering vector q \u00bc ki kf was parallel to the director (bend mode detection).",
        "texts": [
            "5 mol% concentration of a trifunctional cross-linker 1,3,5-tris-undec-10-enoxy-benzene, with the second crosslinking stage done in the isotropic phase at 80 C. It was placed in a temperature stabilized cell equipped with a force gage and a micrometer to control the stress and strain of the sample. It also allowed light scattering measurements in a range of scattering angles. The sample was well oriented as was checked by polarized microscopy. The geometry of the scattering experiments is shown in Fig. 1. The incoming light was vertically polarized, and horizontally polarized scattered light was detected and analyzed with an ALV-6010/160 photon correlator. The incoming scattering angles were chosen so that the scattering vector q was along the director n. In such geometry, a pure bend mode polarized in the x direction is observed. Figure 2 shows the ratio r \u00bc \u00f0L=Liso\u00de3 of the length of the sample to its reference length 12 K above TNI. This ratio is proportional to the nematic order parameter and is a fundamental parameter of the theory of semisoft elasticity",
            " The relaxation rate approximately linearly decreases with increasing strain and reaches a minimum at the critical strain c 1:04 at the onset of the soft plateau, so the x polarized bend mode is the soft mode of the instability associated with the semisoft response. At c stripe domains were formed, revealing the onset of director rotation. The observed critical strain is slightly lower than the strain of the beginning of the semisoft plateau in Fig. 3. This is probably due to the fact that close to the clamped edges of the sample the strain is not homogeneous (as shown in Fig. 1). This smears the onset of the plateau. Because of the scattering PRL 103, 077801 (2009) P HY S I CA L R EV I EW LE T T E R S week ending 14 AUGUST 2009 077801-2 on stripe domains, we were not able to obtain measurements above \u00bc 1:04 at 75 C and 78 C. At lower temperatures, however, we could extend our measurements slightly, revealing a \u2018\u2018V-shaped\u2019\u2019 curve of the relaxation rate at the point of the elastic instability, very similar to theoretical predictions [19]. That the internal aligning field at the critical strain becomes nearly zero is also supported by the data of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002051_tmag.2015.2436913-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002051_tmag.2015.2436913-Figure1-1.png",
        "caption": "Fig. 1. Mechanical structure of the proposed microrobot.",
        "texts": [
            " [7] proposed a spiral microrobot, which has a permanent magnet magnetized in a diagonal direction, and utilized a precessional magnetic field to perform navigating and drilling motions. However, their spiral microrobots cannot separate navigating and drilling motions, and rotating blades may damage healthy blood vessels while navigating through the blood vessel to reach the target point. In this paper, a navigating and drilling spiral microrobot actuated by a gradient and rotating uniform magnetic field is proposed to navigate through complex human blood vessels and unclog blocked human vessels. The proposed spiral microrobot, as shown in Fig. 1, consists of a cylindrical body that contains a cylindrical magnet and two spiral drilling blades on the shaft. The cylindrical magnet can rotate freely inside the magnet slot of the body and align in any direction by the application of an external uniform magnetic field. Then, several experiments are performed to demonstrate and verify the selective navigating and drilling motions of the prototyped spiral microrobot. Fig. 2(a) shows a linear motion of the spiral microrobot propelled by a magnetic gradient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003222_j.icheatmasstransfer.2020.104614-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003222_j.icheatmasstransfer.2020.104614-Figure2-1.png",
        "caption": "Fig. 2. Characteristic optical simulation with labeled parts.",
        "texts": [
            " Therefore, the lateral simulation boundaries were selected as periodic boundaries. The horizontal simulation boundaries were perfectly matched layer (PML) boundaries. These absorb all incoming radiation and best simulate the radiation propagating out to infinity which would not be reflected back into the simulation region [18]. This allows a small simulation space to behave as though there is an infinite area past the structure. An example of one of the simplified 2D simulations with the appropriate items labeled can be seen in Fig. 2. The radiation source was a plane wave which best simulated diffuse radiation from the environment. The overall intent of the simulations was to determine emissivity trends with wavelength. One assumption made was that the structure was sufficiently thick to prevent transmission of radiation. Another assumption made is that the emissivity is equal to the absorption at the surface. This assumption is made using Kirchhoff's law of thermal radiation, which states that under isothermal conditions and isolated from the environment, meaning no net heat transfer, the emissivity of a surface is equal to its absorptance [19]. Eq. 6 was used to calculate the emissivity from the measured reflection of the surface. Table 1 Emissivity regimes based on surface roughness [11]. = = \u2212 \u2212\u03b5 \u03b1 \u03c1 \u03c41 (6) where \u03b1 is the absorptance, \u03c1 is the reflectance, and \u03c4 is the transmittance of the object. To calculate the emissivity of the simulated surface geometries, the reflection and absorption were first measured. As can be seen in Fig. 2, there were two frequency-domain field power monitors. These monitors, which is the term used in Lumerical, are sensors that measure the power of all incident radiation onto them [13]. The monitor above the surface measured the radiation that was reflected by the surface. The second monitor placed below the surface measured any transmitted radiation. With both measurements and Eq. 6, the emissivity was calculated for each simulated geometry. Although the simulated radiation source, a broadband planar source, represented a spectrum of wavelengths (1 \u03bcm to 14 \u03bcm), the emissivity results were discretized to individual wavelengths for analysis",
            " In addition to these surface parameters, newly calculated surface parameters such as average peak angle, average valley angle, ratio between height and width of surface features, etc. were calculated and compared with emissivity results to observe any possible relationships. A diagram describing some of these new parameters can be seen below in Fig. 3. The focus of initial simulations was to create the fundamental surface roughness geometry to observe the effects on emissivity. The basic geometry also made the calculation of a range of surface parameters simpler. The simulation geometry and setup can be seen in Fig. 2. The simulation geometry was an isosceles triangle whose width and height were varied through the parameter sweep function. The values of these variables ranged between 1 \u03bcm and 30 \u03bcm. Surface roughness parameters were calculated for each simulation geometry and plotted against the emissivity value to observe trends. Some of these plotted trends can be seen in Fig. 4, which shows the dependence of emissivity on surface topography for the 1 \u03bcm and 14 \u03bcm wavelengths. As can be seen in the Ra plots, there is a large range seen in emissivity values for a given arithmetic surface roughness value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000630_piee.1971.0204-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000630_piee.1971.0204-Figure5-1.png",
        "caption": "Fig. 5 Arrangement of search coils",
        "texts": [
            " 2, are not zero at the ends of the rotor, as required by the boundary conditions. This is a result of the approximate nature of the solutions. A likely form of the actual distibution is also shown in Fig. 2. The errors caused by the approximations are discussed in Appendix 8. They cause negligible error in the expressions derived for the machine impedances. It is interesting to make a comparison between the distributions shown here for (f>x and <\u00a3z and those found experimentally on a slotted rotor (see Fig. 5 of Reference 9). It can by seen that the predicted and measured distributions of <f>x and <f>z are similar. The difference between the predicted distribution of radial flux and that given in Reference 9 is discussed below. PROC. 1EE, Vol. 118, No. 8, AUGUST 1971 From eqns. 4-9, the following conclusions may be drawn concerning the eddy-current distribution. All the eddy currents are concentrated close to the rotor surfaces (i.e. the airgap-rotor interface and the endfaces), the usual 'skindepth' concept being applicable",
            " Setting, in addition, y en a, gL{l + coth (aL/2)} aL{\\ + coth (aL/2)} - 2 (21) Furthermore, for machines with a high length/pole-pitch ratio, aL\\2 is large and coth (aL/2) ~ 1. F2 may then be further simplified to aL aL - 1 (22) 3 Tests of flux distribution To check the theoretical results given above, the distribution of the airgap flux was investigated in the lOkW induction motor mentioned previously. The machine was fitted with an unslotted rotor. A set of five search coils was mounted on the rotor surfaces (Fig. 5) and brought out to sliprings on the rotor shaft. Tests were carried out in two ways: (a) 3-phase slip-frequency voltages were applied to the stator terminals with the rotor at standstill. The voltages induced in the search coils were measured on a cathode-ray oscilloscope; the phase shifts between different voltages were measured by means of Lissajous figures. (b) The rotor was driven at slip s, and 50 Hz voltages were applied to the stator. The induced search-coil voltages were taken off the sliprings, passed through an active lowpass filter (which amplified the slip-frequency signal and a Magnitude b Phase 1028 Q"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003024_s00202-020-00955-2-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003024_s00202-020-00955-2-Figure3-1.png",
        "caption": "Fig. 3 Rotor of the 2.2 kW LSPMSM prototype",
        "texts": [
            " The high-power VFD and DC drive operated motors are independent of CPQI because they are isolated from the power supply. 0.5\u20133.7 kW power rating LSPMSM is the best option considering the efficiency and cost of motor [17]. Owing to the above fact, low power rating 2.2 kWmotor is considered for this study. By tuning with appropriate design parameters, it is possible to eradicate excess losses, torque ripple, abnormal noise and vibration in the LSPMSM during the design stage which is more significant in a certain application. LSPMSM is designed, optimized and prototyped for a constant load application shown in Fig. 3. Since load torque is constant, the motor was designed with 130% overload capacity. Initial dimension and design parameters are identified using a standard induction motor design procedure [18]. Based on the design parameters, motor is modeled and optimized in 2D time-stepping FEA software [19, 20]. To identify the losses and performances accurately, the properties of magnet, copper, aluminum andM43-29G are adjusted in FEA simulation software. To get accurate results, it is essential to design the motor in accordance with stator overhang and rotor end ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000885_j.mechatronics.2012.10.002-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000885_j.mechatronics.2012.10.002-Figure7-1.png",
        "caption": "Fig. 7. (a) Modular design for the whole system and (b) mechanical design.",
        "texts": [
            " (3) Motor control demonstration system (MCDS) This project is from a German company in Shanghai. The purpose is to design and build a motor control demonstrate system to make the motor control parameters visually and lively. It will be used to evaluate the motor\u2019s behavior of RPM, current, voltage, temperature with different control method, circuit structure and algorithm, thus to determine the best control method. It must be Fig. 6. (a) Models in Adams; (b) interface an with flexible connections and be easy to disassembly to change the spare parts. Based on the idea of modular design, Fig. 7a shows the concept design of the system. The preliminary CAD model is built by Solidworks modeling software (see Fig. 7b). By considering DFM guidelines, the rectangular holes in the wall for heat dissipation is hard to be processed compared to circular ones, so in the final realization they are changed to circular holes. Fig. 8 shows the design of DC/AC motor control circuits and the temperature and fan control circuits. Here bread board is used to prototyping the circuits which can be fabricated as PCB board later. The virtual instrument package LabVIEW is used to do data acquisition and control programming. The whole system (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001821_tmag.2016.2520950-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001821_tmag.2016.2520950-Figure2-1.png",
        "caption": "Fig. 2 Air gap flux density and rotor position at some time",
        "texts": [
            "html for more information. dotted line is normal rotor and its center is O1 which is the same as the center of stator. O2 is the center of dynamic eccentric rotor but rotation center is still O1. B. Dynamic UMP & Calculation of UMP Main cause for the appearance of UMP is air gap eccentricity. Due to asymmetrical air gap, magnetic reluctance of circumferential air gap is uneven. Hence, air gap flux density of opposite sides is not the same. Attraction is relevant with air gap flux density. So UMP exists. As shown in Fig. 2, radial air gap flux density at 0\u00b0 and 180\u00b0 are different. However, rotor cannot catch up with the steps of rotating stator magnetomotive. When maximum air gap flux density meets minimum or maximum air gap, UMP should be the biggest. And when zero air gap flux density meets minimum or maximum air gap, UMP should be the least. So long as there is a slip of stator magnetomotive and rotor, UMP is wavy. In this paper, we call it dynamic UMP. 02 B F A   (1) To calculate the UMP force, for limited dots, the infinitesimal UMP force formula is written as 21 0 ( 1) 2 0 1 1( ) cos[ ( )] 22 2 i i i i B B F lR i        (2) 21 90 ( 1) 2 0 1 1( ) sin[ ( )] 22 2 i i i i B B F lR i        (3) Where l is the length of rotor(silicon steel sheet) Then, resultant UMP force is written as ( 1)S i i i F F  (4) (c) In 20% DE, component resultant UMP on the direction of rotor deviation 0018-9464 (c) 2015 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003050_j.jmatprotec.2020.116745-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003050_j.jmatprotec.2020.116745-Figure11-1.png",
        "caption": "Fig. 11. (a) schematic of relative position between wire and laser beam (P=1400W, vs = 1mm/s, vf = 4mm/s, \u2212d/2<w<0) when the wire tip is placed at the leading region of the molten pool, (b) schematic of wire plunging transfer, cross-section (c) and appearance (d) of the single track.",
        "texts": [
            ", 2000), which resulted in the extensive dissolution of the ceramic particles and then a track with low retained particle content was produced. After comparing the different wire transfer behaviors under the same processing parameters but the different wire tip positions, it was best to adopt front feeding strategy which delivered a clad with a better surface quality. Although a continuous track was produced in the liquid spreading transfer, the track had a relatively low retained particle content and a large dilution ratio. Hence the liquid spreading transfer mode should be avoid by adjusting the processing parameters. As shown in Fig. 11(a), when the wire tip was placed at the leading region of the molten pool (\u2212d/2<w<0) and the No.3 parameters (in Table 3) were applied, the wire plunging transfer (Fig. 11(b)) was observed. At initial stage of laser deposition, the laser energy was used to melt the substrate and the wire tip, producing a molten pool (Fig. 12(a)). When a high wire feed rate (4 mm/s) was applied, with the accumulation of additive material in the heating area, as shown in Fig. 12(b), the molten pool was swelled up. At a high wire feeding speed, the wire was not completely melted by the laser irradiation and then could be plunged into the swollen molten pool and finally melted (Fig. 12(c), (d)) by the heat in the molten pool. With the continuously delivery of wire and relative movement between laser beam and substrate, as shown in Fig. 12(e)\u2013(i), a stable wire plunging transfer was obtained which resulted in a continuous track with a good surface shaping (Fig. 11(d), (e)). The coating cross-section showed a regular paraboloid shape (Fig. 11(c)), free from cracks and holes. Due to the improvement of additive material per unit length when the laser energy input was unchanged, only a thin layer of the substrate was melted, resulting a low level of dilution 8% and a high retained particle content When the wire plunging transfer was obtained during laser material deposition, the protective effect of the molten pool and the insertion of ceramic particles in the tubular cored wire could counteract the thermal exposure of directly irradiation of the laser beam, which effectively contributes to the decrement of the degree of ceramic particle dissolution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000288_s11071-009-9473-4-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000288_s11071-009-9473-4-Figure2-1.png",
        "caption": "Fig. 2 The parallel cube-robot",
        "texts": [
            " In conclusion, the novel matrix model may successfully be applied in forward and inverse mechanics of parallel robots, the end-effectors of which participate in a translation motion or a mixed motion. 6 Two examples 6.1 Parallel cube-robot As the first application in what follows, some recursive matrix relations for the kinematics and dynamics of a three translational DOFs parallel cube-robot are established. The concurrent actuators are arranged according to the Cartesian coordinate system with fixed orientation, which means that the actuating directions are normal to each other (Fig. 2). For this reason this type of mechanism is called a cube-robot. Explicit dynamics equations of the constrained robotic systems 225 This prototype of the robot [32] has technological advantages such as: symmetrical design, regular workspace shape properties with a bounded velocity amplification factor and low inertia effect. The mechanism input of the robot is made up of three actuated orthogonal prismatic joints. The output body is connected to the prismatic joints through a set of three identical kinematical chains (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure7-1.png",
        "caption": "Fig. 7. Contact ellipse between the conjugate surfaces.",
        "texts": [
            " (16) and (18) , the contact point of the hourglass worm drive on the right flank is derived through solving the following equations: r 1 R ( m R ) = r g R (v , t ) R ( v , t , \u03d5 1 ) = 0 (20) Similarly, the contact point of the hourglass worm drive on the left flank is represented through solving the following equations: r 1 L ( m L ) = r g L (v , t ) L ( v , t , \u03d5 1 ) = 0 (21) Eqs. (20) and (21) are considered simultaneously. The rotation angle \u03d51 is an input value. When instantaneous contact line is considered, its value is fixed. Theoretically, at each moment of the meshing of the hourglass worm drive, the two tooth surfaces are in point contact, when subjected to force, the elastic deformation of the two tooth surfaces is caused, and the initial point contact becomes instantaneous contact ellipse, as shown in Fig. 7 . According to the meshing theory of gearing [27] , the contact ellipses of hourglass worm drive are determined by the equation as: A \u03be 2 + B \u03b72 = \u00b1 (22) where, is the elastic deformation. Generally, the elastic deformation is 0.00635 mm, which is the data obtained as an experiment for light-duty gear transmissions. A and B are expressed by the following equations: A = 1 4 (( k 1 I + k 1 II ) \u2212 ( k 2 I + k 2 II ) \u2212 \u221a ( k 1 I \u2212 k 1 II )2 \u2212 2 ( k 1 I \u2212 k 1 II )( k 2 I \u2212 k 2 II ) cos \u03b812 + ( k 2 I \u2212 k 2 II )2 ) (23) B = 1 4 (( k 1 I + k 1 II ) \u2212 ( k 2 I + k 2 II ) + \u221a ( k 1 I \u2212 k 1 II )2 \u2212 2 ( k 1 I \u2212 k 1 II )( k 2 I \u2212 k 2 II ) cos \u03b812 + ( k 2 I \u2212 k 2 II )2 ) (24) Here, k i I and k i II ( i = 1, 2) are the principal curvatures of the tooth surface 1 and 2 at contact point, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.57-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.57-1.png",
        "caption": "Fig. 3.57 Outlook of the EMB (a) and EMB calliper (b)",
        "texts": [
            " To overcome this problem, EFMB BBW AWB dispulsion mechatronic control systems are used as conventional brake functions along with all the brake control functions, including ABS, ESP, BA and autonomous intelligent ACC. It may also be possible to have additional functions such as electric parking braking. There are many other advantages to the innovative system: Less space is required in the ECE or ICE and the driver\u2019s compartment; It is more environmentally-friendly because no brake fluid or air is needed; It has a potentially better pedal feel; It can be operated by means of a joystick [HONDA 2001]. Recently, all the necessary technologies for the E-M braking system, as the example shown in Figure 3.57, namely conventional disc brake technologies, electrical and electronic technologies, communication technologies, and wireharness technologies are available [ARNILD 2001; UEKI ET AL. 2004]. 3.9 Electro-Mechanical Friction Disc, Ring and Drum Brakes 531 [Siemens VDO Automotive (a), ARNOLD 2001; HITACHI LTD (B), UEKI ET AL. 2004]. A calliper regulates the deceleration of the disc fixed to the wheel by adjusting the thrust force acting on the pads via the reduction gear mechanism and the rotational-rectilinear motion conversion mechanism by controlling the current of the E-M motor stator and then the rotation of the E-M motor rotor",
            " 1996], designed by ITT Automotive, as well as (b) disc EMB and (c) ring EMB with the short-stroke linear tubular brushless DC-AC macrocommutator IPM magnetoelectrically-excited brake-force-actuator motor [FIJALKOWSKI AND KROSNICKI 1994]. 3.9 Electro-Mechanical Friction Disc, Ring and Drum Brakes 533 In these types of EMB, force is applied equally to both sides of the disc or ring rotor and braking action is achieved through the frictional action of inboard and outboard brake friction pads against the disc or ring rotor. The pads are contained within a calliper, shown in Figure 3.57, as is the wheel brake actuator. Although not a high-gain type of friction EMBs, disc or ring EMBs have the advantage of providing relatively linear braking with lower susceptibility to fading than friction drum EMBs. The E-M actuator is a disk EMB working on the calliper-principle. The E-M actuator\u2019s housing is connected firmly to the vehicle\u2019s steering knuckle. Both brake pads are fixed to the fist with one degree of freedom towards the active line of the clamping force. Figure 3.59 shows an example of a prototype of an EMB and its mounting in the vehicle [PETERSEN 2003]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000085_j.cma.2005.05.055-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000085_j.cma.2005.05.055-Figure3-1.png",
        "caption": "Fig. 3. Illustration of: (a) a single configuration; (b) and (c) discrete presentations of contacting surfaces and surface normals N1 and N2.",
        "texts": [
            " (i) Due to the effect of loading of the gear drive, the maximal transmission errors are reduced and the contact ratio is increased. (ii) Investigation of the influence of the load in a loaded gear drive requires application of a general purpose computer program [3] based on the finite element method [12]. The authors\u2019 approach allows to reduce the time of preparation of the model by the automatic generation of the finite element model [1] for each configuration of the set of applied configurations. (iii) Fig. 3 illustrates a configuration that is investigated under the load. TCA allows to determine point M of tangency of tooth surfaces R1 and R2, before the load will be applied (Fig. 3(a)), where N2 and N1 are the surface normals (Fig. 3(b) and (c)). The elastic deformations of tooth surfaces of the pinion and the gear are obtained as the result of applying the torque to the gear. The illustrations of Fig. 3(b) and (c) are based on discrete presentations of the contacting surfaces. (iv) Fig. 4 shows schematically the set of configurations in 2D space. The location of each configuration (before the elastic deformation will be applied) is determined by TCA. The described procedure is applicable for any type of a gear drive. The following is the description of the required steps: (i) The machine-tool settings applied for generation are known ahead, and then the pinion and gear tooth surfaces (including the fillet) may be determined analytically"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure9-1.png",
        "caption": "Fig. 9. (a) Solid-angle zone of two UAVs in 3-D space. (b) Dimensions of virtual cage around each UAV in 3-D space. (c) Collision-free arrangement of two solid-angle zones.",
        "texts": [
            " Line PDi is tangent to the illustrated circle only when \u2203\u03b3i \u2208 [\u03b3mini, \u03b3maxi] such that \u2220PDiBi = \u03c0/2, otherwise, variation of \u03b3i in [\u03b3mini, \u03b3maxi] provides a strictly increasing or strictly decreasing\u03b1i, which concludes \u03b1maxi = max(\u03b1i(\u03b3mini), \u03b1i(\u03b3maxi)). Proposition 2: If \u2203\u03b3i \u2208 [\u03b3mini, \u03b3maxi] such that\u2220PCiBi = \u03c0/2 then \u03b2maxi = sin\u22121( \u221a d2h + d2v/li), otherwise \u03b2maxi = max(\u03b2i(\u03b3mini), \u03b2i(\u03b3maxi)) where \u03b2i(\u03b3i) is obtained in (15). Proof: Proof of Proposition 2 is similar to proof of Proposition 1, which to avoid repetition is not provided in this article. In order to investigate the collision between the UAVs in 3-D space, a solid-angle zone, as illustrated in Fig. 9(b), is considered for each UAV, where the corresponding \u03b1i and \u03b2i are obtained as explained in the previous section. \u03b6i, as the third required angle to form the solid angle, is \u03b6i = tan\u22121( dw li ), where 2dw is the width of virtual case around each UAV as illustrated in Fig. 9(a). Moreover, the angle of line PEi with the axis x is obtained as \u03c8\u2032 i = tan\u22121 u\u2032 yi u\u2032 xi . Based on the illustrated arrangement of UAVs in Fig. 9(b), in order to prevent the collision between the UAVs and/or their connected cables, their corresponding solid angles need to have no interference. Fig. 9(c) illustrates the geometrical condition \u03bb\u2032 j \u2212 \u03b1j > \u03bb\u2032 i + \u03b2i (18) where for any value of \u03c8\u2032 i and \u03c8\u2032 j , there is no interference between the solid angles. In such configuration of the solid angles, a virtual hemisphere centered at P with an arbitrary radius r can be considered. In such hemisphere, two horizontal circles of i\u2032 and j corresponding to angles \u03bb\u2032 j \u2212 \u03b1j and \u03bb\u2032 i + \u03b2i can be considered, where as long as radius of circle j is greater than that of circle i\u2032, for any values of \u03c8\u2032 i and \u03c8\u2032 j , there is no interference between the solid angles of UAV j and i. In spite of Fig. 9(c), Fig. 10(a) shows a configuration where for some values of\u03c8\u2032 i and\u03c8\u2032 j collision between the solid-angle zones is possible. In the arrangement of Fig. 10(a), we have \u03bb\u2032 j \u2212 \u03b1j \u2264 \u03bb\u2032 i + \u03b2i, \u03bb \u2032 i + \u03b2i \u2264 \u03bb\u2032 j + \u03b2j (19) where \u03bb\u2032 i + \u03b2i is considered as the angle of collision between the solid angles, where its corresponding horizontal circle is denoted by circle Authorized licensed use limited to: University of Canberra. Downloaded on June 24,2020 at 16:03:50 UTC from IEEE Xplore. Restrictions apply"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure6-1.png",
        "caption": "Fig. 6. The coordinate systems of the force sensing mechanism.",
        "texts": [
            " 1 \u00bc JC JT 1 \u00f011\u00de The rotation transformation matrices from local to reference coordinate systems are all unit matrices because of their parallel relations, and the flexible series limb pose transformation matrices Jj (j = 1,2,. . .,5) are as follow: J1 \u00bc E S r1\u00f0 \u00deE O3 3 E ; J2 \u00bc E S r2\u00f0 \u00deE O3 3 E ; ; J5 \u00bc E S r5\u00f0 \u00deE O3 3 E \u00f012\u00de ) The simplified graphic model of the flexible ries branch f the single branch. In order to simplify the analysis, it is assumed that the moving platform and the fixed platform are equivalent to the rigid bodies with infinite stiffness, without considering the small deformation caused by the force. The establishment of the mechanism\u2019s coordinate systems is shown in Fig. 6. The reference coordinate system Opxpypzp is established at the center of the moving platform. The local coordinate system Oixiyizi (i = 1, 2, 3 . . . 8) of each flexible measuring branch is established at the center of its free-end cross-section, the xi axis coincides with the axis of the branch and points to the moving platform. R and r represent the radii of the moving platform and the fixed platform, respectively. ai is the angle between the line OpOi and the x-axis of reference coordinate, bi is the angle between the axis of the ith branch and the xaxis of reference coordinate, hi is the angle between the axis of the ith branch and the xpOpyp plane of the reference coordinate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure1.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure1.10-1.png",
        "caption": "Fig. 1.10 Rear axle seen in perspective (a) and in vertical projection (b)",
        "texts": [
            " Example: With a = 2/3 , b = 1/3 , c = 1/3 four matrices are calculated:\u23a1 \u23a2\u23a3 2 3 1 3 2 3 1 3 2 3 \u22122 3 \u22122 3 2 3 1 3 \u23a4 \u23a5\u23a6 , \u23a1 \u23a2\u23a3 2 3 1 3 \u22122 3 1 3 2 3 2 3 2 3 \u22122 3 1 3 \u23a4 \u23a5\u23a6 , \u23a1 \u23a2\u23a3 2 3 1 3 2 3 \u221211 15 2 15 2 3 2 15 \u221214 15 1 3 \u23a4 \u23a5\u23a6 , \u23a1 \u23a2\u23a3 2 3 1 3 \u22122 3 \u221211 15 2 15 \u22122 3 \u22122 15 14 15 1 3 \u23a4 \u23a5\u23a6 . (1.204) Other triples (a, b, c) resulting in rational matrix elements: ( 3 5 , 4 5 , 1 ) , ( 2 7 , 3 7 , 2 7 ) , ( 4 9 , 7 9 , 1 9 ) , ( 2 11 , 6 11 , 2 11 ) , ( 3 13 , 4 13 , 3 13 ) , ( 2 15 , 11 15 , 5 15 ) . End of example. 42 1 Rotation about a Fixed Point. Reflection in a Plane Figure 1.10a shows the simplest design of a rigid rear axle for road vehicles (Matschinsky [15]). The axle is rigidly attached to a draw-bar which is supported in the car body by the spherical joint 0 . Another spherical joint B connects the axle to a so-called sway bar or Panhard rod. The other end of this rod is supported in the car body by still another spherical joint A . The position of the axle relative to the car body is interpreted as the result of two successive rotations. Prior to the first rotation the bases e2 (fixed on the axle) and e1 (fixed in the car body) coincide. The first rotation about the line A0 (unit vector n , rotation angle \u03d51 ) carries the axle-fixed basis to the intermediate position e2 \u2217 and point B to the position B\u2217 . The second rotation is executed about the axle-fixed line B\u22170 (unit vector n\u2217 , rotation angle \u03d52 ). In Fig. 1.10b the system is shown schematically in a vertical projection in the null position \u03d51 = \u03d52 = 0 . The figure shows also basis e1 and the unit vectors n and n\u2217 along the rotation axes. It is assumed that in the null position the axle, the draw-bar and the Panhard rod are coplanar. The lengths h , a , , b are given. Point B is moving along a circular path which in the figure appears as straight line. To be determined are the coordinates in e1 of the wheel centers P1 and P2 as functions of \u03d51 and \u03d52 . Solution: The lengths h , a and determine the angle \u03b1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.15-1.png",
        "caption": "Figure 10.15. Oscillat ion of a physical pendulum.",
        "texts": [
            " Work-energy principle: The total work done over the time interval [to, t] by the externalforces and torquesacting on a rigid body about a fixed bodypoint Q or about the center ofmass, in an inertial frame <1>, is equal to the change in the total kinetic energyof the body: 11/( fK3, t) = !::>.K( fK3 , t). (10.120) Hence, the corresponding mechanicalpower is equal to the time rate ofchange in <1> of the total kinetic energy: f'i7) f17) dft/( fK3,t) dK( fK3,t) ~r (::7u , t) = dt = dt . (10.121) Example 10.13. A physical pendulum shown in Fig. 10.15 swings in its vertical plane of symmetry about a smooth, fixed axle at Q. The pendulum is released from rest at the placement eo with angular speed woo(i) Apply the workenergy principle to derive the equation of motion of the pendulum. Confirm the solution by application of Euler's equation. (ii) Describe the general solution, find 468 Chapter 10 (10.122a) the small amplitude circular frequency of the oscillation, and describe a simple pendulum having the same period. (iii) What is the mechanical power expended over the interval [0, t] as a function of ()",
            "i +M3k - mgt sin e'k , where M1 and Mz are unknown bearing reaction torque s, which are workless. Because the hinge is smooth, the bearing reaction component M3=0 and the support reaction force R is workless. Hence, with ()(O) = ()o at to = 0, 11/= t -rmg l: sin ()O dt= -rmgi:1\u00b0sin ()so.h ~ This yields the rotational work done by the applied loads as 1// = mgt (cos () - cos ()o). (10. 122b) Notice that this is just the gravitational work done: l //g = mgh = mgt (cos () - cos ()o). We choose a body frame rp = {Q; ik } in the vertical plane of symmetry, as shown in Fig. 10.15, so that k is a fixed principal axis with IR= 13~ = O. Then the first relation in (10.75) gives hrQ = I Qw = 10k, and hence the rotational kinetic energy for the body is , I \u00b7zK (f:JlJ , t) = 2w . hrQ= 2/() . (10. l 22c) With 0(0) = Wo atto = 0, the change in the kinetic energy is ~K (f:JlJ, t) = 4/[Oz - w5]; and, with (10.122b), the work-energy principle (10.118) yields mgt (cos s - cos ()o) = 4/[OZ- w6]. (10.122d) The equation for the motion () (t ) of the physical pendulum follows by differentiation of (10",
            " Then the change in the total energyofa rigid body is equal to the work done by the nonconservativepart of theforce: (10.131) This leads at once to the following useful corollary, referred to rp = {Q; ek}' Principle of conservation of energy: The total energy of a rigid body is constant if and only if the nonconservative part of the force does no work in the motion or, trivially, when the totalforce is conservative: K( [JlJ , t) + V([JlJ) = E , a constant. (10.132) Example 10.15. Apply the energy principle to derive the first integral of the equation of motion for the physical pendulum in Fig. 10.15, page 467 . Solution. The bearing reaction force R at the smooth support Q in Fig. 10.15 is workless; the bearing reaction torque J..tQ == M1i+ M2.i , because there is no rotation of the body about these directions, also is workless, in fact J..tQ= 0; and the gravitational force W is conservative with potential energy V = mgt. (1 - cos e) .Clearly, the system is conservative and (10.132) holds .The rotational kinetic energy is given by K r Q = !Iw2, where 1== IK With co = 8, (10.132) yields the first integral of the equation of motion for the physical pendulum: !I82 +mgt. (1 - cos e) = E",
            " It may be seen from this equation that the period goes to infinity when d = 0 and when d = 00, and hence there exists a value of d for which the period is least. (b) Show that this point is at a distance d = Rc from C. (c) Show that there exists another point of suspension Q on the line OC Qat b =P d from C for which the period is the same as that about O. The point Q is called the center ofoscillation. Find its distance b from C. 486 Chapter 10 10.22. A plane rigid body of mass m similar to the physical pendulum shown in Fig. 10.15, page 467, can rotate about a smooth axle at Q. The body is suspended at rest in the vertical plane, and an instantaneous impuls ive force F* is applied in the plane of the body at its boundary and in a direction perpendicular to the vertical line joining Q and the center of mass G. Find the vertical distance d from the point of support Q to the line of action of F* such that there is no impulsive reaction at Q in the direction of F*. The point at d on the vertical line QG is called the centerof percussion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.41-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.41-1.png",
        "caption": "Fig. 3.41 Fluidical mechanisation [RILEY ET AL. 2000].",
        "texts": [
            " Identical criteria are used to determine the distance to the preceding vehicle. The key objectives of ACC are improved traffic flow and increased driver comfort while reducing the driver\u2019s workload. Figure 3.40 shows the components and subsystems used to achieve ACC on a host vehicle [RILEY ET AL. 2000]. 3.7 Enhanced Adaptive Cruise 507 ACC technology is on the horizon as a convenience function especially intended to reduce the driver\u2019s workload. Considerations of moding ABS with ACC and TCS may be applied at the automotive vehicle level. Figure 3.41 depicts the fluidical mechanisation of a mechatronically controlled AC BBW AWB dispulsion mechatronic control system capable of ABS, TCS and vehicle stability enhancement (VSE). Automotive Mechatronics 508 The system performs ACC auto-braking without driver input on the braking pedal. The ABS controller signals the E-M motor in the modulator to M-F pump brake fluid or air (gas) from the master cylinder into the wheel-braking fluidical lines through the prime solenoid fluidical valves that are opened by energising their electromagnet coils [RILEY ET AL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003470_ecce44975.2020.9235826-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003470_ecce44975.2020.9235826-Figure1-1.png",
        "caption": "Fig. 1. The studied machine exploded view and 2D cross section.",
        "texts": [
            " The five subdomains consideration provides enough information for the calculation of the flux in different areas of the machine. This magnetostatics analysis addresses the difficulty of using eddy current calculation previously studied in [8] and [15]. The correct calculation of the magnetizing energy helps to estimate the machine inductances. The calculated inductances can be used in the equivalent circuit of the machine for performance parameters prediction. This model is developed based on the proposed model for the AFIMs in [13]. A 5.5kW induction motor (IM), shown in Fig. 1, is considered to verify the analytical model accuracy vs. FEA. The flux density of the machine is validated at the first step. The performance parameter results of the proposed model are compared with the FEA results. The authentic estimation of the inductances leads to accurate approximation of the copper losses. The core loss calculation which needs the flux value in iron parts of the machine is feasible using the proposed subdomain modeling. So, the efficiency can be predicted with higher accuracy in different IM geometries compared to the empirical methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.51-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.51-1.png",
        "caption": "Fig. 2.51 Physical model of the powertrain that includes: ICE, torque converter, automatic power-shift",
        "texts": [
            " Since the APT has become more common, there is an increased interest in reducing the shock during gearshifts and avoiding excessive slip that may cause unnecessary wear. Two mechatronic control objectives may be Minimise the acceleration and jerk levels to enhance ride comfort; Minimise the clutch energy dissipation to enhance the durability of frictio- nal elements. A physical model of the powertrain arrangement that includes ECE or ICE, torque converter, APT, propulsion shaft, M-M differential, and two axle shafts, is presented in Figure 2.51. Automotive Mechatronics 198 transmission (APT), driveshaft, M-M differential and two axle shafts [YANG ET AL. 1999]. The mechatronic control system is very complex and non-linear; automotive scientists and engineers may use a robust shift control strategy for an integrated engine-transmission system to overcome the non-modelled dynamics. It may be possible to incorporate modelling uncertainties directly into the mechatronic control law. Control variables for the integrated engine-transmission management controller (E-TMC) are throttle angle; spark advance and second clutch torque [YANG ET AL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002261_s12555-016-0545-1-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002261_s12555-016-0545-1-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of the model of a human lower limb wearing an exoskeleton.",
        "texts": [
            ", ch = toe, heel, med and lat), f is the vertical reaction force applied to the sensing unit, s is the coefficient relating the amplitude of the pressure (unit: kPa) to the vertical reaction force (unit: N), and c is the constant offset. The values of s and c were computed by the least-squares method and are listed in Table 1. 2.3. Mathematical formulation To estimate the active muscular torque of a user wearing an exoskeleton by the measured joint torque and vertical GRF, the inverse-dynamics based method is used in this study. The two segmental model is considered for the lower limb wearing an exoskeletal robot in the sagittal plane, as illustrated in Fig. 4. The model consists of two rigid segments (thigh and lower leg) and two pin joints (hip and knee). All parameters of the model are equal to that of the model for body-weight supported walking presented in [8] except for the vertical GRF variables (i.e., the denoted parameters in the enlarged part in Fig. 4). Each segment of the model is defined by five parameters: length (L), mass (m), the position of the center of mass in the parallel and perpendicular direction to the link (a and b, respectively), and moment of inertia (Iz). The \u03b8 is the joint angle, and positive value of \u03b8 represents the counterclockwise rotation. The subscript 1 refers to variables of the thigh segment and hip joint, and the subscript 2 refers to the shank segment and knee joint. The equation of motion for the human lower limb model is expressed as [8]: MH(\u03b8)\u03b8\u0308 +VH(\u03b8 , \u03b8\u0307)+GH(\u03b8)+P(\u03b8) = \u03c4M + \u03c4EXT , (2) where \u03b8 , \u03b8\u0307 , \u03b8\u0308 \u2208 R2 are the vector of the joint angle, angular velocity, and angular acceleration, respectively, MH(\u03b8) \u2208 R2x2 is the symmetric positive definite inertial matrix of the human limb, VH(\u03b8 , \u03b8\u0307) \u2208 R2 is the vector of the centrifugal and Coriolis torques of the human limb, GH(\u03b8) \u2208 R2 is the vector of the gravitational torques of the human limb, P(\u03b8) \u2208 R2 is the vector of the passive elastic torques of the human limb, \u03c4M \u2208R2 is the vector of the muscular torques, and \u03c4EXT \u2208 R2 is the vector of the external torques from the environment",
            ", \u03c4\u0302GRF = [ \u03c4\u0302GRF,1 \u03c4\u0302GRF,2 ] = [ Fy \u00b7 (L1 sin\u03b81 +L2 sin\u03b812 +dc) Fy \u00b7 (L2 sin\u03b812 +dc) ] , (7) where Fy is the vertical GRF computed from the measurements of the insole pressure sensors as: Fy = ftoe + flat + fmed + fheel (8) and dc is the projected distance on the x-axis from the center of rotation of the ankle to the in-shoe center of pressure (COP): dc = ftoedtoe + flatdlat + fmeddmed + fheeldheel ftoe + flat + fmed + fheel , (9) where dch is the projected distance on the x-axis from the center of rotation of the ankle to the geometric center of each air bladder (see enlarged part in Fig. 4). 3. EXPERIMENTAL VERIFICATION 3.1. Experimental procedure Experiments were performed by three healthy male subjects. The experimental procedure was approved by the Ethics Committee of Sogang University (approval number: Sogang-IRB-2014-08), and the written consent was obtained from all participants. Table 2 shows the characteristics and the body segment inertial parameters (BISPs) of the three subjects [8]. In the table, the J, X and Y represent the linear combination of inertial parameters of the link-segment model in Fig. 4 as follows: J1 = Iz1 + Iz2 +m1 ( a2 1 +b2 1 ) +m2 ( a2 2 +b2 2 ) +m2L2 1, J2 = Iz2 +m2 ( a2 2 +b2 2 ) , (10) X1 = m1a1 +m2L1, X2 = m2a2, Y1 = m1b1, Y2 = m2b2, where the mass(mi), the moment of inertia(Izi), and two elements of the center of mass location(ai and bi) are unknown. The unknown parameters J, X , and Y are identified by the least-squares method. The specification in detail can be referred to [8]. In order to proceed the experiment on over-ground walking accurately, the subjects wore the exoskeleton robot, and the link lengths of the exoskeleton were adjusted to fit each subject\u2019s leg length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003167_pi-c.1959.0034-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003167_pi-c.1959.0034-Figure7-1.png",
        "caption": "Fig. 7.\u2014Electric field on conductor surface. (a) Due to its own charge.",
        "texts": [
            " When 0 = 0 we have the position for maximum surface gradient, and the deviation from a true circle in this region is a minimum. This is a desirable feature, since the maximum electric stress is of interest to transmission engineers. (4) ELECTRIC FIELD AT CONDUCTOR SURFACE The electric field at any point on a conductor surface is influenced, not only by the charge on this conductor, but also by other charges in the bundle. In the following analysis, (4.1) Electric Field on Conductor Surface due to its own Charge [Fig. 7(a)] Let AOEQ be the electric field at Z due to the equivalent charge at Ao. Then A\u00b0Ee \u20acOrdd cos ( jS-0) This field is along the direction of A0Z and hence its normal component to the surface of the conductor, at Z, is given by q \\T- eordd = Etnr(r - 8 cos 0)/(r2 + 82 - 2rS cos 0) . (10) (4.2) Electric Field at Conductor Surface due to other Charges in the Bundle (a) n = 2 [Fig. l(b)] BE% = Electric field at Z due to the equivalent charge at Bo. *1 f\u0302 1-7 A r + (Z> + 8) cos 0 01)\"' (D + 8)2 + 2(2) + 8)r cos 0 + r2 ' ' (b) n = 3 [Fig. 7(c)]. BE% + CE$ = Electric field at Z due to equivalent charges at Bo and Co respectively. q / c o s /B0ZA COS / C0ZA\\ (b) Due to other charges in the bundle for n = 2. (c) Due to other charges in the bundle for n = 3. + 82 - r2)[lD2 + \u00b1D8 + 82 + r2 + (fD + 8)r cos 0](r2 - 2r8 cos 0 + 82)] K*(DI2 + 8)6 J (c) \u00ab = 4. 5\u00a3e + c\u00a3e + ^fe = Electric field at Z due to equivalent charges at Bo, Co and Do respectively. cos cos = +B0Z C0Z r[r + (D + 8) cos 0] A c o s /DpZAx ~ + D\u0302 Z J (D + 8)2 + 2(Z) + 8)r cos 0 + r2 + i -I r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003718_s40430-021-02834-8-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003718_s40430-021-02834-8-Figure2-1.png",
        "caption": "Fig. 2 An overview of a slider-crank mechanism",
        "texts": [
            " r1 and r2 also indicate the length of the massless virtual links related to the clearance; \u03b82 and \u03b83 represent the angles of crank and connecting rod to the horizontal axis, and 2 and 3 show the angles of the virtual massless links for joint clearance. Moreover, 2 and 3 refer to structural angles that determine the center of mass of each link. k2 and k3 similarly stand for coefficients of l2 and l3 to determine the length of structural links. Each virtual link assumed as a clearance also adds a degree of freedom to the mechanism. The examined mechanism has three degrees of freedom along 2 , 3 , and 2 given that there are two clearances. It is clear that the slider does not have angular position. Figure\u00a02 illustrates a slider-crank mechanism that clearly shows its joint clearances, and Fig.\u00a03 depicts the status of a slider-crank mechanism in vector form. Mechanism components are considered rigid and friction is ignored in this research. Considering the geometry of the mechanism, Eqs.\u00a01\u20133 represent the center of mass position of the mechanism links. (1) [ xG2 yG2 ] = k2R [ cos ( 2 + 2 ) sin ( 2 + 2 ) ] (2) [ xG3 yG3 ] = R [ cos ( 2 ) sin ( 2 ) ] + r2 [ cos ( 2 ) sin ( 2 ) ] + k3L [ cos ( 3 + 3 ) sin ( 3 + 3 ) ] (3) [ xG4 yG4 ] = R [ cos ( 2 ) sin ( 2 ) ] + r2 [ cos ( 2 ) sin ( 2 ) ] + L [ cos ( 3 ) sin ( 3 ) ] + r3 [ \u2212 cos ( 3 ) \u2212 sin ( 3 ) ] Journal of the Brazilian Society of Mechanical Sciences and Engineering (2021) 43:185 Page 5 of 18 185 Given that yG4 is always equal to zero, the angle 3 is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure4-1.png",
        "caption": "Fig. 4. Stress results of the wheel disc after the second process.",
        "texts": [],
        "surrounding_texts": [
            "The residual stress is easily produced in the surface of the wheel disc in stamping process since the recovery of plastic deformation is restricted when the external force is removed [5]. Usually this kind of residual stress caused by local plastic deformation is large and affects the stress state of the wheel disc. In this section, the residual stress of one type of wheel disc is obtained by the simulation of stamping process. There are four typical stamping processes in forming the steel wheel disc: the first three processes form different shapes of the wheel disc, while the fourth process is for outer edge flanging. In order to verify the accuracy of the simulation method, the experiments are conducted using the X-ray diffraction method."
        ]
    },
    {
        "image_filename": "designv10_12_0000414_tac.2007.902750-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000414_tac.2007.902750-Figure4-1.png",
        "caption": "Fig. 4.",
        "texts": [
            " Then, by the assumption about the control curve , we know that on hf(x) + g(x)u(t); p(x)i = [f1(x) + g1(x)u(t)]p1(x) + [f2(x) + g2(x)u(t)]p2(x) 0: Hence, by simple calculation, we have dx2 dx1 = f2(x) + g2(x)u(t) f1(x) + g1(x)u(t) d (x1) dx1 ; x 2 \\ U(x0): (17) Since the positive semitrajectory 'u(x0; t); t > 0 of (2) under control function u(t)with initial pointx0 satisfies the left-hand side (LHS) of (2), which can also be rewritten the form '(x1) in the neighborhood U(x0); '(x1) (x1); x1 2 [x01; x 1 1), where x01 < x11 (see [33]). Similarly, when f1(x 0) + g1(x 0)u(x0) < 0, according to the proof procedure above, we can also get the following result: '(x1) (x1); x1 2 (x11; x 0 1] as shown in Fig. 4, where x11 < x01. Hence, the positive semitrajectory of (2) with initial point x0 cannot go into Side-B. Case 2. det(f(x0); g(x0)) = 0. If f(x0) + g(x0)u(t0) 6= 0, then we can prove it by the same procedure as case 1. Hence, we assume that f(x0) + g(x0)u(t0) = 0. For simplicity, we suppose that g2(x) = 0;8x 2 U(x0), then the system becomes _x1 = f1(x1; x2) + g1(x1; x2)u(t) _x2 = f2(x1; x2) (18) Otherwise, we can transform g(x) into this form by a diffeomorphism as in Lemma 4.3 and the Appendix. Obviously, we have the control curve passing through x0 in U(x0) is x2 = x02, and f2(x1; x 0 2) 0;8(x1; x 0 2) T 2 U(x0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003265_tmag.2020.3013624-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003265_tmag.2020.3013624-Figure2-1.png",
        "caption": "Fig. 2. No-load flux distributions of the initial structure. (a) Forward magnetized. (b) Reversely magnetized.",
        "texts": [
            " The initial structure employs a V-shape layer of magnets, where red coloured ones are AlNiCo and blue coloured ones are NdFeB. NdFeB is connected with AlNiCo in series near the q-axis, and these two series-connected magnets are connected with another AlNiCo located near the d-axis in parallel. AlNiCo magnets can be magnetized or demagnetized by id pulses, and the AlNiCo near the d-axis can be forward or reversely magnetized, which greatly expands the variation range of magnetization state. The no-load flux distributions of the initial structure under different magnetization states are shown in fig. 2. In fig. 2(a), the AlNiCo near the d-axis is forward magnetized and provides air-gap flux together with the magnets near the q-axis. In fig. 2(b), the AlNiCo near the d-axis is reversely magnetized and most part of PM flux is short-circuited in the rotor core. So the initial structure has a wide variation range of magnetization state, similar with the parallel-connected hybrid-PM variableflux PMSMs. However, AlNiCo near the d-axis can be demagnetized by the flux-weakening current (-id) and overload current (iq), and the operating reliability of the initial structure is greatly reduced. B. Improved Structure To stabilize the working points of AlNiCo magnets, the improved structure of hybrid-PM variable-flux PMSM with series-parallel magnetic circuits is proposed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure5-1.png",
        "caption": "Fig. 5. Radial ball bearing.",
        "texts": [
            " The rolling components and the rings have the elastic properties of steel, with modulus of elasticity Eb = 2.03 \u00d7 1011N/m2 and Poisson's ratio vb = 0.3. The components of the cage are made of polyamide, with Young modulus Ec = 3.00 \u00d7 109N/m2 and Poisson's ratio vc = 0.3. Only contacts between rolling components and raceways have a non-zero friction coefficient \u03bc = 0.15. The other contacts will be considered purely as slipping. The dimensions of the bearing are given in Table 1 and ball bearing representation in Fig. 5-a and (b): where, Rout is the outer ring race radius, with Rout c the associated curvature radius, Rinn is the inner ring race radius, with Rinn c the associated curvature radius. Rb is the rolling ball radius and Rc is the ball cage radius. From the characteristics of the ball bearing defined above, the calculation of the equivalent quantities (Table 2) requested by Eqs. (6) and (7) are done below: Gb and Gc denote the shear modulus of steel and polyamide respectively. mi or mj are the mass of the ball considered (cage or rolling component), with ri and rj the associated radii"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003329_j.mechmachtheory.2019.103753-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003329_j.mechmachtheory.2019.103753-Figure15-1.png",
        "caption": "Fig. 15. The connecting of two Bricard-like mechanisms.",
        "texts": [
            " A complete inward motion and a complete outward motion are regarded as a motion cycle. A prototype of the Bricard-like mechanism is fabricated as shown in Fig. 14 . We can see from Figs. 12\u201314 that this mechanism is also an infinitely turnover mechanism. The Bricard-like mechanism discussed above can also be used as a construction unit to construct deployable mechanisms. Two identical Bricard-like mechanisms can be connected by six spherical joints, which are located at the end of the links as shown in Fig. 15 , and cooperate with each other during the movement. It is known from the research [46] that the mechanism connected by six spherical joints has the same degree of freedom of each Bricard-like mechanism, that is, this mechanism is a one degree of freedom mechanism. During the movement, the two identical Bricard-like mechanisms are mirror-symmetrical, when the first Bricard-like mechanism move inward, the second Bricard-like mechanism move outward, and vice versa. As shown in Fig. 16 , a triangular prism deployable mechanism composed of four identical Bricard-like mechanisms is design and fabricated, in which spherical joints use flexible materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure3-1.png",
        "caption": "Fig. 3. A redundantly actuated forging manipulator 2SPS+R.",
        "texts": [
            " Forging manipulators, the major ancillary equipment in hydraulic forging processes, is much powerful in improving manufacturing ability, saving material, higher precision, efficiency production, etc. [40]. Redundant actuation has been adopted in order to reinforce force capabilities, since weight of the forged piece that heavy-duty forging manipulators hold andmanipulate is very heavy. For example, two lifting hydraulic cylinders symmetrically arranged have been utilized in heavy-duty forging manipulators so as to achieve lifting motion of the forged piece [41], just as shown in Fig. 3. The redundantly actuated forging manipulator 2SPS+R is composed of a moving platform, a base, two actuated limbs, and one constrained limb. Each actuated limb connects the moving platform to the base by a S joint on the moving platform at ai(i=1, 2), an actuated P joint along the limb, and another S joint on the base at bi. Here the notations of P, S, and R denote the prismatic, spherical, and revolute joint, respectively. The constrained limb connects the moving platform to the base by only a R joint on the base at b0 coincident with a0 on the moving platform",
            " The position vector of points a1 and a2 in the coordinate frame A can be expressed as Aa1 \u00bc 0 l2 0\u00bd T Aa2 \u00bc 0 \u2212l2 0\u00bd T ) \u00f038\u00de Then, the position vector of points a1 and a2 in the coordinate frame B can be obtained as Bai \u00bc B AR Aai \u00fe BPAo ; i \u00bc 1; 2 \u00f039\u00de where BPAo represents the position vector of point o in the coordinate frame B and BPAo \u00bc l1 cos\u03b8 0\u2212 l1 sin\u03b8\u00bd T, ABR is the rotation matrix from the coordinate frame A to the coordinate frame B, which is given by B AR\u00bc cos\u03b8 0 sin\u03b8 0 1 0 \u2212 sin\u03b8 0 cos\u03b8 2 4 3 5; \u00f040\u00de where \u03b8 is the rotation angle of the moving platform measured from the x-axis to the vector a0o in the coordinate frame B. Substituting Eqs. (38) and (40) into Eq. (39) yields Ba1 \u00bc l1 cos\u03b8 l2 \u2212l1 sin\u03b8\u00bd T Ba2 \u00bc l1 cos\u03b8 \u2212l2 \u2212l1 sin\u03b8\u00bd T ) \u00f041\u00de From Fig. 3, the following equations can be obtained Ba1\u2212Bb1 \u00bc l0 \u00fe q1 Ba2\u2212Bb2 \u00bc l0 \u00fe q2 9= ;; \u00f042\u00de where q1 and q2 represent the input displacements of the two actuated P joints. Substituting Eqs. (37) and (41) into Eq. (42), solution to the inverse position of the redundantly actuated forging manipulator 2SPS+R is obtained as q1 \u00bc q2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l1 cos\u03b8\u2212l1\u00f0 \u00de2 \u00fe \u2212l1 sin\u03b8\u00fe l0\u00f0 \u00de2 q \u2212l0 \u00f043\u00de Differentiating Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.20-1.png",
        "caption": "Figure 5.20. A simple experiment demonstrating the pressure induced. friction reduction principle.",
        "texts": [
            " Applications of Coulomb 's Laws Two problems that use Coulomb 's laws in demon stration of the predicti ve value of the principles of mechanics are studied. The first example illustrates the 60 Chapter 5 phenomenon of pressure-induced friction reduction useful in a variety of engineering applications. The second example demonstrates the application of basic principles in providing the solution to a major technical problem during World WarIL 5.12.1. The Sliding Can Experiment An empty beverage can' g(j having identical top and bottom rims is shown in Fig. 5.20a. The can is placed at A on a sheet of slightly wetted glass, which is then gradually tilted until the critical angle \u00a3Xc is attained at which sliding of the can is initiated. Since the can slides on its narrow rim, the critical angle is independent of whether the open or the closed end of the can is upward . Of course , upon reaching the edge of the glass at B, the can falls off. The experiment is conducted at room temperature and the measured critical angle of friction is about 17\u00b0. Coulomb's laws hold for slightly wetted surfaces, and (5",
            " The critical angle is found to be the same as before, thus showing for this case that u. is independent of the temperature. Finally, the can is chilled to the same temperature as before and placed on the wetted surface with its open end downward. Surprisingly, the can starts to slide when the critical angle a; is only I\u00b0 or 2\u00b0; and it slides down the entire length of the glass held at this very small inclination. But it stops rather abruptly when the open end extends just beyond the edge of the sheet at B in Fig. 5.20a. \u00a7 Adapted from the article by M. K.Hubbert andW.W.Rubey cited in the chapter references . See also the related articles by M. B. Karelitz and by B. Noble reported therein. The Foundation Principles of Classical Mechanics 61 This curious phenomenon occurs because after a few seconds the cold, trapped air expands as it begins to warm, causing the internal air pressure to increase. Because the surface area of the closed end of the can is greater than that of its open end, there is a resultant uplifting, internal normal pressure on the closed end that partially supports the weight of the can, and thus reduces the normal surface reaction force between the can and the glass . The can stops suddenly at the edge of the sheet because the pressure is abruptly released. To prove this hypothesis, we analyze the phenomenon. We begin by showing in Fig. 5.20b the free body diagram of the chilled can placed on the glass with its open end downward in the inertial frame <1>. The body force is the weight W of the can. In addition to the normal and frictional contact forces N and f, there is also a resultant internal contact force P on the closed end of the can due to excess of the internal air pressure over the outside air pressure. Thus, the total force acting on the can f?!3 is F(f?!3 , t ) = W +N +f +P. (5.76a) Introducing in (5.76a) the component representations for W, N, and f given in (5",
            " Let fa be the distance moved by the center of the can from its initial rest position at x = 0 to its position at B in Fig . 5.20a, where the trapped air is released. Afterwards the can will continue to move so that it extends beyond the edge of the glass an amount say, 8, but it does not fall off. To determine the value of 8 compared with f a , we first find the speed of the can as a function of its position along the sheet. Let x* = x denote the center of mass coordinate in the inertial frame <1>, and begin with the force analysis. The free body diagram of the can is shown in Fig. 5.20b. We suppose that the internal pres sure is \"turned on\" at x = 0 when the can is placed on the glass with its open end downward, and later \"shut off\" at x = \u00a30 as the air suddenly escapes when the can reaches the edge of the sheet. Then, with the aid of the unit step function (I . I 17), we have P=[P <x-O >o-P <x-fo >O]i. (5.77a) The Foundation Principles of Classical Mechanics 63 The total force on the can throughout its motion is given by (5.76a), and hence with (5.74b) and (5.77a) , the equation of motion F(~, t) =ma* =mXiyields the scalar component relations for the sliding motion at the critical angle acd: mx = W sinacd - Idd, Nd = W cosacd - p \u00ab x - 0 > 0 - < X - \u00a30 > 0), (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001557_s12206-014-0804-0-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001557_s12206-014-0804-0-Figure6-1.png",
        "caption": "Fig. 6. Different positions of ball no. 2 relative to the outer race defect.",
        "texts": [
            " At the starting edge of the defect, ball retards due to loss of contact with the outer race and at this instant the displacement is assumed to be -1 as shown in Fig. 8. As the ball leaves the defect, it accelerates due to regaining of contact with the outer race and the displacement is assumed to be +1. Hence, the displacement law is retardation followed by acceleration. As opposed to this, in case of regular shapes, the displacements are gradual which is far from reality. As every ball establishes and breaks the contact with the defective region of the outer race shown in Fig. 6, the geometry of race movement will change. The behavior of ball establishing and breaking the contact with the race is similar to cam (follower) jump phenomenon. Essentially the ball orbiting the inner race acts as a cam and the outer race acts as the follower. For normal race contact, there is hardly any change in the geometry of the movement. During the travel of the ball in the defective region of the outer race, the locus of race center position as a function of angle q and its time derivatives are to be obtained through the mathematical modeling of the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure2.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure2.2-1.png",
        "caption": "Fig. 2.2 Sketch for calculation of the Coriolis acceleration",
        "texts": [
            " Nevertheless, Wikipedia and other encyclopaedias contain the second equation of Coriolis acceleration that presented by the following expressions: acr=V\u03c9,where all components are as specified above. This expression is not presented in textbooks but has a right for computing of Coriolis acceleration and use in engineering. Following analysis of Coriolis acceleration for different regimes of linear and angular motions of the object on a disc derived by the different methods and validated the correctness of the second expression of Coriolis acceleration. It is considered an object of the mass m that travels from the centre O towards B on the edge of a rotating disc (Fig. 2.2). The linear velocity V of the object m and angular velocity \u03c9 of the disc is uniform. The travelling from point O to B takes time t, so the distance OB = V \u00d7 t. The distance OB is calculated by the physics equations of the uniform motion, OB = V \u00d7 t. The rotation of the table in the counter-clockwise direction on the angle \u03b3 for the time t results in point B from its original position to a new position A. The angle is \u03b3 = \u03c9 t, where \u03c9 presents the constant angular velocity. However, the distance AB is calculated by the physics equations of the accelerated motion, AB= \u03b1t2/2. Finally, the Coriolis acceleration for this type of approach is depicted in Eq. (2.18). However, the following analysis of the accepted motions of the object m on a rotating disc shows the following circumstances (Fig. 2.2): (a) The motion of the object m and the rotation of the disc are independent, and no forces are acting between the object m and the disc. (b) The linearmotion of the objectm and the rotarymotion of the disc are uniformed; hence, the relative trajectory of a motionOA of the objectm on the rotating disc is the Archimedes curve. The principle of the Archimedes curve states that any point of the curve gives uniform velocities of components and without acceleration. (c) The distance AB is a result of uniform motions and calculated by the equation AB = \u03c9 \u00d7 (OB) \u00d7 t = V tB\u00d7 t,where VtB is the constant tangential velocity of point B",
            " The object, which moves on the rotating disc, can have different values of the Coriolis acceleration and a force. This study examines four types of motions: (a) a uniform motion of the object and the disc (b) a uniform motion of the object and the accelerated rotation of the disc (c) an accelerated motion of the object and the uniform rotation of the disc (d) an accelerated motion of the object and the disc The object m travels on the rotating disc and its trajectory presented by the line OA (Fig. 2.2). Rotation of the disc on the angle \u03b3 changes the vector velocity direction V of the object m on the vector velocity direction VA. The vector V \u03b3 expresses this change in the direction of the vector velocity and represents by the following equation: V\u03b3 = \u2212V sin \u03b3 V\u03b3 = \u2212V sin \u03b3 (2.19) where \u03b3 is an angle of rotation of a disc, other components are as specified above. Themagnitude of the vector velocityV \u03b3 depends on the change in the object radius location on the disc. The change in the magnitude of the velocity V \u03b3 is presented by the following equation [10]: V\u03b3 = \u2212[ V sin(\u03b3 + \u03b3 )\u2212V sin \u03b3 ] = \u2212V [ sin(\u03b3 + \u03b3 )\u2212 sin \u03b3 ] (2",
            "25) and transformation, the acceleration of the object results in the following expression: ac = \u2212V\u03c9 (2.26) Equation (2.26) is the expression of the Coriolis acceleration for uniformmotions of the object and the rotating disc. Hence, the Coriolis force will have the next equation Fc = mV\u03c9 (2.27) where all parameters are as specified above. The direction of the Coriolis force vector is opposite to the direction of the vector of acceleration. Equation (2.26) can be derived from another mathematical approach. The distances AB and OB can be calculated by the equations of AB = V \u03b3 t and OB = Vt (Fig. 2.2). The angle \u03b3 of triangle AOB is small, then AB = OB sin \u03b3 and accepted sin \u03b3 = \u03b3 . After substituting defined magnitudes of the triangle sides, the new equation has the following expression: V \u03b3 t = Vt\u03b3 which simplification yields V \u03b3 = V\u03b3 . Then, the rate change of the velocity per time represents an acceleration of the object, which expression is the same as Eqs. (2.25) and (2.26). Coriolis acceleration expressed by Eq. (2.27). These Coriolis equations are the same as presented in encyclopaedias. The method for computing of Coriolis accelerations for the combinations of the uniform and accelerated motions of the object and the disc is the same as presented in Sect. 2.2. A detailed solution for the Coriolis acceleration is described in the last paragraph of Sect. 2.2.1 after Eq. (2.24). The expressions of the equations for the motions are derived on a base of the vectorial diagram of velocities and geometrical parameters represented in Fig. 2.2. The solutions for Coriolis accelerations for each combination of motions of the object and the disc are represented in Table 2.1. Relevant equations developed for Coriolis accelerations of a moving object on a rotating disc that represented for different conditions of motions of a system. New equations consider combinations for uniform and accelerated linear and the angular velocities of a system. These equations are different from the fundamental equation of the Coriolis acceleration depicted in textbooks of physics, kinematics andmachine dynamics. In engineering, all machines work with accelerations of components that are a real condition of the functioning of any mechanism. It is very important to calculate the exact value of forces acting onmachine components. The new equations of Coriolis accelerations should be used for computing of inertial torques generated by the rotating masses of the objects for gyroscopic devices. The disc has an angular velocity of 2.0 rad/s and accelerates at the rate of 3.0 rad/s2 (Fig. 2.2.) The object of 0.1 kg mass moves with a linear velocity of 0.5 m/s and accelerates at the rate of 1.0 m/s2. Determine the values of Coriolis accelerations for four types of motions (Table 2.1) after 3.0 s of motions. The results of calculations of the Coriolis acceleration by the equations of Table textbooks of classical mechanics and encyclopaedias gives the expression of Coriolis acceleration which a result is twice bigger than represented in this chapter and known publications. Following mathematical models for the Coriolis forces, inertial torques acting on the gyroscope and equations of the gyroscope motions represented in the book take into account the expression of Coriolis acceleration that gives twice less result"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure6.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure6.7-1.png",
        "caption": "Fig. 6.7 Load angle definition (\u03c1m) in phasor diagram",
        "texts": [
            "3 Generic model of a synchronous machine which corresponds with equation set (6.1) and Eq. (6.2) . . . . . . . . . . . . . . . . . 156 Fig. 6.4 Vector diagram with direct and quadrature axis for non-salient machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Fig. 6.5 Symbolic rotor-oriented model of a non-salient machine . . . . . . . . . 159 Fig. 6.6 Generic current based rotor-oriented non-salient synchronous machine model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Fig. 6.7 Load angle definition (\u03c1m) in phasor diagram . . . . . . . . . . . . . . . . . . . . . 160 Fig. 6.8 Non-salient synchronous, phasor based machine model . . . . . . . . . . 160 Fig. 6.9 Blondel diagram of a non-salient synchronous machine . . . . . . . . . . 161 Fig. 6.10 Output power versus load angle curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Fig. 6.11 Four pole, interior permanent magnet synchronous machine, showing two-layer stator winding and rotor saliency . . . 164 Fig",
            "6) are rotating at the same speed, which is zero in dq coordinates and equals \u03c9s in stator coordinates. Therefore, the system is fully described by the relative position of the space vectors to each other and phasors (here using peak values) can be used to describe the machine variables, resulting in the following equation set: us = Rsis + j\u03c9s\u03c8 s (6.7a) 160 6 Synchronous Machine Modeling Concepts \u03c8 s = Lsis + \u03c8 f . (6.7b) The stator voltage phasor is aligned with the real axis and therefore us = u\u0302. The phasor relations are shown in Fig. 6.7. Shown in this diagram are the voltage us, the flux linkage \u03c8 f , and the current is which are linked by equation set (6.7). The complex phasor coordinate plane is shown in gray. The real axis is tied to the voltage phasor us. The load angle \u03c1m is defined as the angle between the voltage phasor us and the back-EMF phasor j\u03c9s\u03c8 f . Subsequent observation of Fig. 6.7 shows that the field flux linkage phasor \u03c8 f can be written as \u2212j\u03c8fej\u03c1m resulting in the equations us = Rsis + j\u03c9s\u03c8 s (6.8a) \u03c8 s = Lsis \u2212 j\u03c8fe j\u03c1m . (6.8b) An expression for the current phasor is can now be found by eliminating the flux linkage phasor \u03c8 s Fig. 6.8 Non-salient synchronous, phasor based machine model \u223c \u223c 6.1 Non-salient Machine 161 Expression (6.9) may also be presented by an equivalent circuit as given in Fig. 6.8. It includes two voltage sources, the supply voltage us = u\u0302s, and the back-EMF \u03c9s\u03c8 f ",
            " (6.21) The Blondel diagram for the salient machine is found by making use of the voltage equation (6.16a) and the flux linkage expression (6.21). As for the nonsalient machine both expressions are converted to their phasor form, based on the general transformation from stator to rotor coordinates Adq = Ae\u2212j\u03b8 and from phasor to space vector quantities A = Aej\u03c9st . Note that the phasors are representing sinusoidal functions in time, using peak values. Using the relationship \u03b8 \u2212 \u03c9st = \u03c1m \u2212 \u03c0/2 (cp. Fig. 6.7), this leads to the expression Adq = Ae\u2212j(\u03c1m\u2212 \u03c0 2 ). Inserting this in Eqs. (6.16a) and (6.21), we obtain the expression us = Rsis + j\u03c9s\u03c8 s (6.22a) \u03c8 s = (1 + \u03c7)Lsdis + \u03c7Lsdis \u2217ej2\u03c1m \u2212 j\u03c8fe j\u03c1m . (6.22b) Elimination of the flux linkage phasor \u03c8 s from equation set (6.22) leads to the following current phasor expression: is + [ j\u03c9sLsd\u03c7ej2\u03c1m Rs + j\u03c9s (1 + \u03c7)Lsd ] \ufe38 \ufe37\ufe37 \ufe38 K is \u2217 = u\u0302s \u2212 \u03c9s\u03c8fej\u03c1m Rs + j\u03c9s (1 + \u03c7)Lsd\ufe38 \ufe37\ufe37 \ufe38 i\u25e6s (6.23) For the non-salient case with \u03c7 = 0, Eq. (6.23) reduces to expression (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure2-1.png",
        "caption": "Fig. 2. HALF* parallel manipulators: (a) with linear actuators and (b) with revolute actuators.",
        "texts": [
            " Observing the HALF manipulator, it is not difficult to find out that, at any position (y, z) of the mobile platform, the movement of the mobile platform and the third leg is actually that of a slider-crank mechanism. If the z-coordinate of the mobile platform is specified, the shape change of the parallelogram in the third leg is just conforming to the translation along the y-axis. Then it is feasible for us to replace the third leg of the HALF parallel manipulator with a PRC (P: prismatic joint; R: revolute joint; C: cylinder joint) kinematic chain. The new manipulator, which is referred to as the HALF* parallel manipulator, is shown in Fig. 2(a). In the HALF* parallel manipulator, Legs 1 and 2 have the identical kinematic chains, i.e. PRU (U: universal) chains. Since a U joint is usually composed of two R joints. In the two U joints, the axes of two R joints that are connected to the mobile platform should be collinear. Otherwise, the mobile platform will lose 1 DOF. It is noteworthy that, due to the PRC chain of Leg 3, the two U joints can be replaced by two S (spherical joint) joints. Undoubtedly, the new manipulator also has the same mobility as that of the HALF manipulator, i",
            " It is obvious that the HALF parallel manipulator is more complex than the HALF* manipulator because of the use of a parallelogram. In a planar parallelogram, every two links should be parallel to each other. This needs approving manufacturing accuracy and increases the difficulty of link machining and assembling and the cost. Since there is no parallelogram in the third leg, the architecture of the new manipulator is simpler. The manufacturing will be easier. The cost will be accordingly decreased. As shown in Fig. 2(a), the self-calibration can be implemented by attaching the sensors to the two revolute joints and the cylinder joint that are connected to the mobile platform. Hereby, the accuracy of the HALF* parallel manipulator can be improved. Therefore, compared with the old version, the new manipulator will be more popular in practical applications. Figure 2(b) shows the HALF* parallel manipulator with revolute actuators, where the R joints fixed to the base platform are active. Notably, the actuating direction of all sliders in the HALF* parallel manipulator with prismatic actuators may be inclined at an \u03b1 angle with respect to the vertical line as shown in Fig. 3(a). Figure 3(b) illustrates a typical example when the actuating direction is horizontal. For the manipulator shown in Fig. 2(a), as previously mentioned, the collinear axes for the two revolute joints lead to the motivation of redesigning Legs 1 and 2, as shown in Fig. 4. In these two designs, the two revolute joints are combined to one revolute joint. In Fig. 4(a), the first and second legs are connected to the moving platform through one common revolute joint. In Fig. 4(b), the first and second legs have the PRR chains, which are connected to a constant orientation bar that is linked to the mobile platform by a revolute joint. If the kinematics chain for the manipulator shown in Fig. 2(a) is denoted as (2-PRU)PRC, it will be (PRR)2R-PRC for the two designs shown in Fig. 4. This modification, which has no negative influence on the kinematics and rotational capability of the manipulator, can be also extended to the HALF* parallel manipulator with revolute actuators shown in Fig. 2(b). It is noteworthy that in the HALF* parallel manipulators the universal joints connected to the mobile platform can be replaced by spherical joints. Figure 5 shows the HANA parallel manipulator introduced in ref. [15], which is also one member of the family presented in ref. [13]. In the HANA manipulator, two legs (the first and second legs) consist of parallelogram. The kinematic chain of each of the two legs is the same as that of the third leg in the HALF parallel manipulator shown in Fig",
            " For example, in the HALF* manipulators, the joints connected to the moving platform in the first and second legs can be spherical joints, in each of which there is one passive DOF. On the other hand, to decrease the operational failure, the demand on the parallelism of the C axes in the first and second legs should be very high. As mentioned in the last section, the kinematics of the new manipulators proposed in this paper will be simpler than that of the old manipulators introduced in ref. [13]. As an example, we here investigate the inverse kinematic problem of the HALF* parallel manipulator with prismatic actuators shown in Fig. 2(a). The kinematical scheme of the manipulator is shown in Fig. 9. Vertices of the mobile platform are denoted as platform joints Pi (i = 1, 2, 3); and central points of the three revolute joints attached to the sliders are denoted as Bi (i = 1, 2, 3). A fixed global reference frame O \u2212 xyz is located at the center point of the line segment ab with the z-axis normal to the plane abc and the y-axis directed along ab. Another reference frame, called the moving frame (O \u2032 \u2212 x \u2032y \u2032z\u2032), is located at the center of the side P1P2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000981_ecc.2013.6669816-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000981_ecc.2013.6669816-Figure1-1.png",
        "caption": "Fig. 1. The Quad-TiltRotor concept platform",
        "texts": [
            " Operational scenarios including search and assistance provision missions, ongoing natural disaster phenomena monitoring, border-line or power-line autonomous inspection and a multitude of similar missions, require: a) close-range inspection of small-scale areas, combined with b) highspeed surveillance of wide areas. This raises the demand for specialized UAV platforms, capable of: a) efficient and prolonged endurance flight, and b) navigating into constrained areas, while c) maintaining full operational autonomy. In this paper, a rotor-tilting convertible UAV platform, namely the Quad-TiltRotor concept shown in Figure 1, is considered. The proposed platform is capable of adjusting the orientation of its rotors concurrently with its wings\u2019 angles of attack, by rotating them relative to the fuselage axes. This 1C. Papachristos and 3A. Tzes are with the Electrical and Computer Engineering Department, University of Patras, Greece papachric(tzes)@ece.upatras.gr 2K. Alexis is with the Swiss Federal Institute of Technology (ETHZ), ASL, Tannenstrasse 3, 8092 Zuerich konstantinos.alexis@mavt.ethz.ch enables two discrete modes of operation: i) a helicopter-like Vertical Take-Off and Landing (VTOL) mode, with its rotors facing upwards, and ii) a fixed-wing aircraft-like longitudinal flight mode, with its rotors tilted forward",
            " In Section V a series of simulation studies of the proposed scheme are presented. The article is concluded in Section VI. 978-3-033-03962-9/\u00a92013 EUCA 1793 The Quad-TiltRotor\u2019s operating principles in the helicopter-like hovering mode, the fixed-wing longitudinal flight mode and the intermediate flight mode conversion phase are depicted in Figure 2. The Body-Fixed coordinates Frame (BFF) B = {Bx, By, Bz} and the North-East-Down (NED) [3] Local Tangential coordinates Plane (LTP) E = {N, E, D} are shown in Figure 1. Let \u2126 = {p, q, r} be the BFF rotational rates vector and \u0398 = {\u03c6 , \u03b8 , \u03c8} the LTP rotation angles vector. Also let U = {u, v, w} be the BFF velocity vector and XW = {xW , yW , zW} the LTP position vector. Via the Newton-Euler formulation the system\u2019s nonlinear dynamics are modeled as: FB = mU\u0307+\u2126\u00d7 (mU) MB = I\u2126\u0307+\u2126\u00d7 (I\u2126) X\u0307W = RB\u2192W U \u0398\u0307 = JB\u2192W \u2126 , (1) where FB = {Fx, Fy, Fz} the BFF total Force vector, MB = {Mx, My, Mz} the BFF total Moment vector, m the mass and I the moment of inertia matrix. Also, RB\u2192W is the BFF\u2192LTP translational velocities transformation matrix and JB\u2192W the Tait-Bryan rotational rates transformation matrix [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.2-1.png",
        "caption": "Figure 6.2. Relative motion of a crate on an accelerating truck.",
        "texts": [
            " Therefore, if the Newton-Euler law were applied in the accelerating reference frame, the operator would conclude incorrectly that a force of about 7 lb is needed, while the task actually requires nearly twice that. We thus learn that when the operator works in the accelerating vehicle, nearly twice the effort must be expended to perform the assigned task. D This example demonstrates the important role of the inertial reference frame in applications of the Newton-Euler law.The next problem concerns the prediction of relative sliding of a body in contact with an accelerating surface. Example 6.2. A truck carrying a crated load W is moving down a 15\u00b0 grade in Fig. 6.2. The driver suddenly applies the brakes and the truck decelerates at the steady rate of 4 ft/sec'' along its straight path. The coefficient of static friction between the crate and the trailer bed is J.L = 0.3. Determine for the given values of the parameters whether the crate will slide or remain stationary relative to the trailer. 100 Chapter 6 Solution. We shall assume initially that the crate does not slide relative to the truck and seek a Coulomb condition sufficient to assure this. If this condition fails for the assigned data, we then know that the crate will slide. This strategy will enable us to decide the issue. To investigate the motion of the crate C, we first draw its free body diagram in Fig. 6.2a. To simplify matters, all contact forces due to the Earth's atmosphere, including air flow effect s due to the truck 's motion and other wind effect s, are neglected. Then the total force F(C, t ) acting on C is approximated by its weight Wand the resultant normal and tangential contact force s N and f exerted by the trailer bed. The equation of motion (6.1) for C becomes F(C, t) = W + f +N = maCF , (6.7a) whereinm = m(C) is the total mass ofC and a CF is its total rectilinear acceleration in the inertial ground frame <I> = {F ; i , j , k}",
            " To determine the distance traveled by the crate on the bed, we first integrate the differential equation 8VCT /8t = aCT with the initial condition vcr(O) = 0 to obtain VCT = acrt = 4.56ti. Hence, the relative speed of C is s(t) = 4.56t; and with s(O) = 0, the distance traveled by the crate is s(t) = 2.28t 2. Therefore, after I sec the crate has moved a distance s(l) = 2.28 ft. After 2 sees, s(2) = 9.12 ft, and the crate, regardless of its physical features , slams into the cab, initially only 9 ft away in Fig. 6.2 . D 6.3.2. Intrinsic Equation of Motion for a Relativistic Particle In this section, the intrinsic equation ofmotion for a relativistic particle whose \"effective\" mass varies with its speed is derived, and the result is applied to examine the nature of a purely normal force that acts on the particle in its motion along a smooth curved path . The Newton-Euler law in the form (6.1), however, cannot be used in problems where the mass of the particle is variable; so we return to the basic law (5.34) ",
            "86e) that the damped circular frequency w is smaller than the circular frequency p for the undamped, simple harmonic case . Therefore , the effect ofdamping is to decrease the frequency ofthe oscillations compared with those of the undamped case. However, if v \u00ab p, so that the damping is very slight, the term e:\" stays close to unity for large values of t , and (6.86f) models more precisely the actual physical behavior of the ideal simple harmonic oscillator. An oscillographic recording of the motion in Fig. 6.2] may be obtained by experiment, and this graph can be used to determine the damping parameters from measurements ofany two successive amplitudes at times tn and tn+! = t\u00ab + r . Although the peak values of z(t) do not quite touch the exponential envelope lines , they often are sufficiently close for practical experimental purposes. With (6.86h) and Zn = Z(tn), we find Zn/Zn+! = evr \u2022 Thus, the natural logarithm of this ratio, called the logarithmic decrement ~, determines v and hence c in terms of measurable quantities: Zn ~ =log- = vr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure11-1.png",
        "caption": "Fig. 11. Finite element model of the steel wheel.",
        "texts": [
            " The reliability and stability of the wheel structure need to be ensured by a series of fatigue tests. The traditional fatigue tests for steel wheel of vehicle include the cornering fatigue test and radial fatigue test. In this section, the ABAQUS is used to simulate the cornering fatigue test of the steel wheel. A finite element analysis model is established using the same type of steel wheel as an example and the model is composed of disc, rim, connecting plate, bolt and moment rim according to the standard GB/T 5334-2005 [12,13]. This model is imported into the ABAQUS software, as shown in Fig. 11. All parameters in simulation are loaded strictly according to GB/T 5334-2005: the moment of 2015 Nm, the moment arm with 600 mm length, and then the concentrated force (3358.3 N) loaded on the end of the arm. The modal analysis of this finite element model shows that the first natural frequency of the steel wheel is about 275 Hz, and the corresponding rotational speed is 16,500 rpm. But in the cornering fatigue test, the steel wheel is fixed while the load rotates with the speed of 1200 rpm (far below the rotational speed corresponding to the first natural frequency), thus the dynamic rotational loading process can be converted into a static problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001527_j.mechmachtheory.2013.06.007-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001527_j.mechmachtheory.2013.06.007-Figure1-1.png",
        "caption": "Fig. 1. Gearwheel model with circumferentially moveable teeth [42].",
        "texts": [
            " All methods are realized in the commercial multi-body environment SIMPACK [5] to ensure maximum portability to other problems and reusability. For this, additional user-defined elements were developed in the programming language FORTRAN 90 and implemented. The developed element is based on the force element \u201cGear Pair\u201d [4] of the multi-body simulation software SIMPACK. This element was extended by a contact geometry calculation, flexible teeth and elastohydrodynamic lubrication at the tooth flanks. All teeth and respective contacts are treated separately. The teeth are modeled as being circumferentially movable (see Fig. 1). Each tooth has one degree of freedom: the rotation about the wheel center with the angle \u03c6Ti. During the time integration, the force element gets the actual positions and velocities of the teeth and of the two wheel bodies from the integrator of the multi-body environment. The lines of flank contact can be determined analytically because each tooth has just one rotational degree of freedom and the undeformed flank geometries are known. As a result, the distances h0i between the theoretical undeformed flanks can be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000181_ac50037a030-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000181_ac50037a030-Figure14-1.png",
        "caption": "Figure 14. Calculated percentage inhibition as a function of inhibitor concentration [I] for various enzyme activities Vm0 expressed in mol L\"s-': (a) 5 X (b) (c) 2 X (d) 3 X (e) 5 X (f) lo-', (9) 2 X lo-', (h) 3 X IO-'",
        "texts": [
            " The maximum rate Vm0 is related to the concentration of enzyme by the equation: V,\" = h,, [Elo (9) where [E]\" = [E] + [ES] + [ESI] (10) [E]\" is the concentration of active immobilized enzyme. Vm0 is then a function of the proportion of active enzymes after immobilization which depends both on binding-time (Figure 7) and cross-linking agent (Figures 5, 6). For a given binding-time and a given glutaraldehyde concentration, V,' is usually proportional to the initial amount of enzyme to be cross-linked. Figure 14 reports the percentage inhibition as a function of inhibitor concentration expressed in terms of r for various V,\". A translation to the right is observed when V,\" increases, as found in previous experimental results (Figure 4) for the urease-fluoride system. The detection limit is displaced toward high inhibitor concentration when Vmo increases. This can be explained on RECEIVED for review July 25,1978. Accepted October 12,1978."
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure5-1.png",
        "caption": "Fig. 5. The tooth profile with k1 = 0.3.",
        "texts": [],
        "surrounding_texts": [
            "Based on the analysis above, a design for an example gear drive with a variation of the parabolic parameters is taken to illustrate the proposedmethod and study the impact. The example drive has a modulus ofm = 2 mm, a transmission ratio of i = 1.2, an addendum coefficient of ha\u204e = 1, a bottom clearance of C\u204e = 0.25, and a tooth number of Z1 = 15. According to Eqs. (52) and (54), the range of the parameters k1 and k2 without undercutting and interference was calculated to be 0.2 \u2264 k1 b 0.457 and 0.2 \u2264 k2 b 0.448 respectively. 4.1. The impact of parameter k1 on the shape of the tooth profiles In order to study the influence of parameter k1 on the shape of the tooth profiles designed by the proposed method, k1 is so chosen that it varies from 0.2 to 0.4 with an increment of 0.1, while k2 is equal to 0.2. The tooth filet is an arc, whose radius is 0.38 \u2217 m, connecting the tooth profile and the root circle of a gear. The tooth profiles of the driving gear and the driven gear are established in Figs. 4, 5 and 6 corresponding to k1 = 0.2, 0.3, and 0.4, respectively. For the reason of comparison, three sets of the tooth profiles of the driving gear with different parameters of k1 and k2 are drawn in Fig. 7, while another three sets of the tooth profiles of the driven gear are shown in Fig. 8. According to the results, the following conclusions can be made: (i) The parameter k1 changes the shape of the part of the addendum of the tooth profile for the driving gear, without changing the shape of the part of the dedendum. On the contrary, as for the tooth profile of the driven gear, the parameter k1 is only relevant to the shape of the part of the dedendum. (ii) In the part of the addendum, the tooth thickness of the driving gear increases with the growth of the parameter k1, but in the part of the dedendum for the driven gear, the tooth thickness shows the opposite trend. 4.2. Impact of parameter k2 on the shape of the tooth profiles In this subsection, the effects of the parameter k2 on the shape of the tooth profile are studied. The parameter k1 is chosen as 0.2, and the parameter k2 is so chosen that it varies from 0.2 to 0.4 with an increment of 0.1, while the other parameters keep the same as example 1. The tooth profiles of the driving gear and the driven gear are shown in Figs. 4, 9 and 10 corresponding to k2 = 0.2, 0.3, 0.4, respectively. Three sets of the tooth profiles of the driving gear and driven gear with different parameters of k2 are drawn in Figs. 11 and 12, respectively. From above discussion, the following conclusions to the specified gears can be drawn: (i) In the part of the addendum of the tooth profile for the driving gear and in the part of the dedendum of the tooth profile for the driven gear, the tooth thickness will not change with the changes of the parameter k2. (ii) The tooth thickness of the part of the addendum of the tooth profile for the driven gear increases with the growth of the parameter k2, while the tooth thickness of the part of the dedendum of the tooth profile for the driving gear decreases with the growth of the parameter k2. (iii) The minimum teeth number of the proposed gear without undercutting is affected by k1 and k2, for example, according to Eq. (54), when k2 is equal to 0.2, the minimum teeth number of the driving gear is 2, which is much less than that of the involute gear."
        ]
    },
    {
        "image_filename": "designv10_12_0000377_s11740-007-0041-9-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000377_s11740-007-0041-9-Figure1-1.png",
        "caption": "Fig. 1 Cylindrical gears",
        "texts": [
            " In order to finally develop a method, which makes a sufficiently safe prognosis for the attainable gear quality possible on the basis of real process data, in the context of a interdisciplinary research project the relevant interactions of the system machine-tool-process are determined, described and modeled in suitable form. Apart from the fundamental aspects of this problem the contribution argues in particular with the problem of the influence of the interactions of the machine system on the pitch accuracy of gear teeth. Keywords Production process Gear rolling Quality estimating At the present, the production of gear teeth is still dominated by metal-removing production processes. However, forming processes are becoming increasingly important for manufacturing gear teeth (particularly spur gear teeth, Fig. 1) due to potentially excellent workpiece parameters combined with a high degree of material utilization [1]. The foremost benefits of this technology are: \u2022 Efficient material application \u2022 Short process times (6\u201312 s) \u2022 Semimachined surfaces (Ra = 0.2\u20130.4 lm, Rz = 1.0\u2013 1.4 lm) \u2022 An increase in strength in the flank zone of as much as 60% \u2022 Enhanced load-bearing capacity and smooth running from adapted fiber orientation. The following should be named as the foremost forming processes for manufacturing gear teeth: \u2022 Extruding as a cold and warm-machining process \u2022 Cold-drawing round steel via draw-die \u2022 Extruding \u2022 Precision forging and hot forging of spur gears \u2022 Longitudinal rolling of spur gear teeth \u2022 Cross rolling process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001420_s11431-013-5433-9-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001420_s11431-013-5433-9-Figure13-1.png",
        "caption": "Figure 13 3R configuration.",
        "texts": [
            " If the five-bar metamorphic linkages evolve into R phases, the reconfigurable limbs transform into configurations in Figures 9(c), 10(c), and 11(c). Each limb provides a constraint force passing through point O and parallel to axis of joint R1. A class of reconfigurable parallel mechanisms can be obtained by connecting a moving platform and a base with three identical reconfigurable limbs. Figure 12 shows the 3(R1PR1R2-5R) reconfigurable parallel mechanism constructed with three reconfigurable limbs, where number 3 denotes the number of R1PR1R2-5R limbs. When the planar five-bar metamorphic linkages evolve into R phases as shown in Figure 13, an important characteristic of the reconfigurable parallel mechanisms in this class is that all the axe of joints RC and R2 intersect at a common point O. With the planar five-bar metamorphic linkages in different phases, the parallel mechanism has various configurations. Different constraints will be exerted on the moving platform and the mechanism has different degrees of freedom. The number of the planar five-bar metamorphic linkages in source phase, in T phase, in R phase, the constraint exerted by the reconfigurable limbs, and the degrees of freedom of the parallel mechanism in corresponding configurations are listed in Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003713_tec.2021.3062501-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003713_tec.2021.3062501-Figure12-1.png",
        "caption": "Fig. 12. Prototyped motor (a) final assembly stator, (b) rotor and shaft, (c) final stator and rotor assembly. And (d) final SRM.",
        "texts": [
            " The proposed SRM shows a better dynamic performance. Table II summarizes the dynamic performance of the motors under CCC mode and a nominal speed of 1000 rpm. The turn-on and turn-off angles are 0 and 180 electrical degrees, respectively. As shown in Table II, the core losses in the proposed SRM are lower than that of the conventional SRM. Besides, the efficiency of the proposed SRM is 2.7% higher than that of the conventional SRM. To validate the predicted performances by simulation experimentally, the proposed SRM was prototyped. Fig. 12 presents the stator, rotor, cover, and finally the assembled SRM. Fig. 13 exhibits the torque-angle measurement setup for the static torque measurement between the unaligned position up to the aligned position of the rotor. Fig. 14 shows the simulated static torque by FEM, MEC model, and measured for proposed SRM and conventional SRM at four stator excitations currents. It is clear from Fig. 14 that the introduced non-linear model has good accuracy. Fig. 15 presents the simulated fluxlinkage by FEM, MEC, and measured for proposed SRM and simulated flux-linkage by FEM and MEC for conventional SRM and their good agreements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002503_sibcon.2017.7998581-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002503_sibcon.2017.7998581-Figure8-1.png",
        "caption": "Fig. 8. Pipe with two L-turns and an opening on its side and its height map; 1 \u2013 the pipe, 2 \u2013 the opening, 3 \u2013 bounding polyhedron (a prism with bases not shown), 4 \u2013 footstep sequence planned without taking into account the opening",
        "texts": [
            " The footstep planning algorithm described in this paper is designed to work with the pipes with circular cross sections, so in practice any region of the pipe\u2019s inner surface that deviates from it may be considered an obstacle. Let us assume that the obstacles on the inner surface of the pipe are represented by their vertices (in practice we can use bounding polygons or polyhedra to approximate the obstacles whose shapes that cannot be represented by a set of vertices). Then we can map these vertices onto the height map. Figure 8 shows an example of such mapping. Then we can use the algorithms presented in [19-20] to generate obstacle-free convex regions on the height map, represented by systems of linear inequalities. With this we can produce a correction procedure for every foot placement position. The procedure is implemented as the following quadratic program: j i i j s beA Wee <        +      \u03a4 \u03d5 subject to minimize , (7) where e is a displacement vector that defines where relative to the original position should the contact point be placed, jA and jb are a matrix and a vector that correspond to a linear inequality representation of a convex obstacle-free region, and W is a positive-definite weight matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001589_j.phpro.2015.11.049-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001589_j.phpro.2015.11.049-Figure1-1.png",
        "caption": "Fig. 1. 3D model of test piece used in this study.",
        "texts": [
            " This study will give the understanding of measuring dimensional accuracy of LAM pieces, and especially possibility of using CT scanning in this analysis. Test pieces in this study were pipes designed with a ~4.4 mm inner diameter, 1 mm wall thickness and length of 25 mm. For CT scanning, the wall thickness was chosen to be 1 mm due to the high absorbance of steel in the x-ray regime. The overall shape of the work piece was selected to be cylindrically symmetric due to the scanning geometry. To maximize the magnification and thus spatial resolution, the specimen was designed to be small in size. Test piece is presented in figure 1. Test piece was modelled with SolidWorks and exported to STL- file format with a resolution where the maximum deviation of the surface triangles was ~1.8 \u03bcm and angular resolution tolerance 4 degrees. Laser additive manufacturing system used in this study was modified research system representing EOS EOSINT M-series equipment. The laser beam is transferred from the laser source to Scanlab hurrySCAN 20 galvanometric scanner via optical fibre. The laser of this system produces maximum continuous power of 200 W at a wavelength of 1070 nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002407_1.4033387-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002407_1.4033387-Figure5-1.png",
        "caption": "Fig. 5 Illustration of simultaneous meshing of shaper, worm, and face-gear Fig. 6 Illustration of multistep method for grinding face-gear",
        "texts": [
            " Journal of Manufacturing Science and Engineering JULY 2016, Vol. 138 / 071013-3 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935094/ on 02/08/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 3.1 Concept of Multistep Method. According to the above analysis, when the face-gear is cut by a worm tool in some design parameters, the whole working part of the face-gear tooth surface may not covered completely. As shown in Fig. 5, the values for us of the worm to avoid singular points are in the range of [u s min\u00f0 \u00de, u s max\u00f0 \u00de], and the values for us of the worm to completely grind the face-gear should be in the range of [us min\u00f0 \u00de, us max\u00f0 \u00de]. The reason why the problem occurs, in theory, is that the value of Du s is less than the value of Dus, where Du s \u00bc ju s max\u00f0 \u00de u s min\u00f0 \u00dej and Dus \u00bc jus max\u00f0 \u00de u s min\u00f0 \u00dej. According to the principle that the worm, the shaper, and the face-gear are meshing with each other, there is a virtual internal meshing relationship between the shaper and the worm [20]",
            "asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935094/ on 02/08/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use [ ju s min\u00f0 \u00dej judj, ju s max\u00f0 \u00dej judj] (Fig. 6(b)). If the steps are superimposed together, then the final values for us of the worm will be in the range of [ ju s min\u00f0 \u00dej judj, ju s max\u00f0 \u00dej \u00fe judj]. When the final range is greater than the range of [us min\u00f0 \u00de, us max\u00f0 \u00de], the entire working part can be grinded out completely by the worm as shown in Fig. 5. Therefore, the grinding process can be divided into multiple steps which can be superimposed together to obtain the complete tooth surface of the face-gear. 3.2 Generation of Face-Gear Surface Based on Multistep Method. The coordinate systems of generating the face-gear by a worm based on the multistep method are established, as shown in Fig. 7. Coordinate systems Ow and O2 are rigidly connected to the worm and the face-gear, respectively, and Ow0, Om, Os0, Od, and O20 are fixed coordinate systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003277_tmag.2020.3020589-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003277_tmag.2020.3020589-Figure5-1.png",
        "caption": "Fig. 5. Description of the dimension parameters. (a) AFPMM. (b) Stator core.",
        "texts": [
            " (27) The AFPMM in this article is driven by three-phase sinusoidal currents and the phase currents are expressed as ia = \u221a 2Iph sin(p\u03c9t \u2212 2\u03c0/3) ib = \u221a 2Iph sin(p\u03c9t) ic = \u221a 2Iph sin(p\u03c9t + 2\u03c0/3) (28) where Iph is the rms phase current Iph = Np Ac Jc = Np k f hschc Nc Jc (29) where Np is the number of parallel paths, Ac is the crosssectional area of the copper wire, Jc is the current density of the armature winding, k f is the slot filling factor, hsc is the length of a stator core, and hc is the thickness of a winding coil. The geometric dimensions of the AFPMM can be found in Fig. 5. The electromagnetic torque can be calculated as Tem = Eaia + Ebib + Ecic \u03c9 . (30) The loss in the motor includes the copper loss in the armature winding, the iron loss in the stator cores, the loss in PMs, the iron loss in the rotor core, and the mechanical loss. The calculation of the loss in PMs, the iron loss of the rotor core, and the mechanical loss are described in detail in [26]\u2013[28]. The copper loss in the armature winding of the AFPMM is shown as PCu = 3I 2 ph Rph = 3I 2 ph Ns Nc Np \u03c1clc Ac (31) where Rph is the resistance per phase, Ns is the number of serial coils per phase, \u03c1c is the resistivity of the copper wires at the operating temperature, and lc is the length of the median line of a winding coil",
            " For the electric propulsion of underwater vehicles, the AFPMM is expected to be high both in torque density and efficiency. Therefore, in the optimization of this article, lighter motor mass and lower electromagnetic loss are taken as the optimization objective function. The optimization variables include the inner radius Ri , the outer radius Ro, the PM thickness hm , the stator core length hsc, the coil thickness hc, and the winding current density Jc. The description of geometric dimensions can be found in Fig. 5. Therefore, the optimization problem of the AFPMM can be expressed as{ min f (x) = [Loss,Mass] x = [Ri , Ro, hm, hsc, hc, Jc]T . (35) Besides the optimization variables, the structure and performance of the AFPMM also depend on the constant parameters, such as the motor speed n, the pole pair number p, the PM remanence Br , the PM relative permeability \u03bcr , the stator core number Q, the stator shoe thickness hss, and so on. The optimization constraints include the output torque Tout, the torque ripple ktr, the winding current density Jc, the stator core magnetic density Bsc, and so on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure6.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure6.12-1.png",
        "caption": "Fig. 6.12 Platform mounted on rods in positions \u03d5 = 0 (a) and \u03d5 = 0 (b)",
        "texts": [
            " The mechanism is a simple means of converting the angular velocity \u03d5\u0307 about the fixed input axis n1 into an identical angular velocity about the fixed skew output axis n2 the location of which can be freely chosen by specifying the two design parameters \u03b1 and . The mechanism is simpler and less expensive than a set of hypoid gears serving the same purpose. This is particularly true when is large. However, like the planar foldable fourbar the mechanism is not well suited for transmitting a large torque from the input to the output axis. The system shown in Fig. 6.12a consists of two parallel circular discs 1 and 2 (radii R1 and r1 = R1 arbitrary) and of n \u2265 5 rods of equal length 1 connecting the discs. The rods are generators of a frustum of a regular cone. The system is shown in two projections. The endpoints Pi and Qi of the rods i = 1, . . . , n are connected to the discs by spherical joints. Disc 1 is a fixed base. Disc 2 is referred to as platform. Every rod is free to rotate about its longitudinal axis. This degree of freedom is not of interest. Because of the symmetry of the arrangement it is obvious that the platform has a single degree of freedom. It is free to undergo a continuous screw motion about the vertical z-axis with an independent angular variable \u03d5 and with a translatory variable z which is a function z(\u03d5) . This function is obtained from Fig. 6.12b which shows the vertical projection in a position \u03d5 (arbitrary). In the x, y, zsystem the endpoints P1 and Q1 of rod 1 have the coordinates [R1 0 0] and [r1 cos\u03d5 r1 sin\u03d5 z] , respectively. The condition of constant rod length establishes between z and \u03d5 the constraint equation (r1 cos\u03d5 \u2212 R1) 2 + r21 sin 2 \u03d5+ z2 = 21 . Hence z(\u03d5) = \u221a 2R1r1 cos\u03d5+ 21 \u2212 (R2 1 + r21) . (6.93) 236 6 Overconstrained Mechanisms The same function z(\u03d5) is obtained with arbitrary parameters R , r , satisfying the conditions Rr = R1r1 , 2 = 21 \u2212 (R2 1 + r21) + (R2 + r2) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002146_1464419313519612-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002146_1464419313519612-Figure3-1.png",
        "caption": "Figure 3. Roller bearing spring mass model.",
        "texts": [],
        "surrounding_texts": [
            "Contact deformation between races and roller gives a nonlinear force deformation relation, which is derived using Hertz contact theory.16,23 In modeling as shown in Figures 2 and 3 the rolling element bearing is considered as a spring mass damper system having nonlinear spring and nonlinear damping. In this work outer race is fixed in a rigid support and inner race is held rigidly in the shaft. A constant radial load is acting on the bearing which is contact stiffness that can be calculated using Hertz theory and dissipating forces at contact point are modeled with nonlinear damping. Contact stiffness for roller bearings On inner race and on outer race localized defect is inserted with nonconventional machining processes as shown in Figure 6. Shaft is inserted in the bearing by press fit. In Figure 1, Dm is a pitch diameter of the bearing; Dr1 and Dr2 are diameters of the outer race and inner race, respectively; and Pd/4 is a radial clearance of the bearing. Palmgren24 developed empirical relation from laboratory test data which define relationship between contact force and deformation for line contact for roller bearing as \u00bc 3:84 10 5 Q0:9 l0:8 \u00f01\u00de Contact length is divided into k lamina, each lamina of width w, and rearranging the above equation to define q yields q \u00bc 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f02\u00de Edge stresses are not considered in equation (2), obtained only over small areas, here localized defect is modeled as a half sinusoidal wave, amplitude of outer race defect and inner race defect are defined as Go \u00bc A1 \u00fe Dh sin Ro DL !c\u00f0 \u00det\u00fe 2 j 1\u00f0 \u00de z \u00f03\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from Gi \u00bc A1 \u00fe Dh sin Ri DL !c !2\u00f0 \u00det\u00fe 2 \u00f0 j 1\u00de z \u00f04\u00de Roller raceway deformation considering contact deformation due to ideal normal loading, radial defection due to thrust loading, radial internal clearance, and localized defect can be given by j \u00bc j \u00fe w 1 2 j Pd 2 G0 Gi For k no. of lamina qjk \u00bc X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f05\u00de Depending on degree of loading and misalignment, all laminae in every contact may not be loaded; in equation (5), k is the number of laminae under load at roller location j. Total roller loading is given by Qj \u00bc X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 1:24 10 5 k\u00f0 \u00de0:11 w0:89 \u00f06\u00de For determining the individual roller loading, it is necessary to satisfy the requirement of static equilibrium for radial load Fr 2 Xj\u00bcZ 2\u00fe1 j\u00bc1 jQj cos j \u00bc 0 \u00f07\u00de j\u00bc angular position of the jth roller\u00bc 2 j 1\u00f0 \u00de z \u00fe !ct where j\u00bc loading zone parameter for jth rolling element j\u00bc 0.5 for j\u00bc (0, P), j\u00bc 1 for j 6\u00bc (0, P) Fr\u00bc applied radial load, substituting equation of Qj in equation (7) we get 0:62 10 5Fr w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j cos j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 \u00bc 0 \u00f08\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from For applied thrust load equilibrium equation: Fa 2 Pj\u00bcZ 2\u00fe1 j\u00bc1 jQaj \u00bc 0 Where, Qaj\u00bc total roller race way loading for length (l) for jth roller in axial direction. At each roller location, thrust couple is balanced by radial load couple caused by skewed axial load distribution. Therefore, h 2 Qaj \u00bc Qjej, where h\u00bc roller thrust couple moment arm, therefore equation becomes as Fa 2 2 h Xj\u00bcZ 2\u00fe1 j\u00bc1 jQjej \u00bc 0 \u00f09\u00de where ej is the eccentricity of the loading for jth roller and given by ej \u00bc P \u00bck \u00bc1 q j 1 2 wP \u00bck \u00bc1 q j l 2 Substituting Qj and ej in equation (9), we get 0:31 10 5Fa h w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j k0:11 X \u00bck \u00bc1 j 1:11 1 2 w ( l 2 X \u00bck \u00bc1 j 1:11) \u00bc 0 \u00f010\u00de The sum of the relative radial movements of the inner and outer rings at each roller azimuth minus the radial clearance is equal to the sum of inner and outer raceway maximum contact deformation at same azimuth a l D \u00fe r cos j Pd 2 2 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G \u00bc 0 \u00f011\u00de The set of simultaneous equations (6), (8), (10), (11) can be solved by using Newton\u2013Raphson method for solution of j, j, a, and r. The simultaneous equations are as follows f1\u00f0Dj, fj, da, dr\u00de \u00bc Qj \u00bc w0:89 1:24 10 5k0:11 X \u00bc11 \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 2 f2\u00f0Dj, fj, da, dr\u00de \u00bc 0:62 10 5Fr w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j cos j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 f3\u00f0Dj, fj, da, dr\u00de \u00bc 0:31 10 5Fa h w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11( 1 2 w l 2 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11) \u00bc 0 f4 Dj, fj, da, dr \u00bc da l D \u00fe drcosWj Pd 2 2 Xk\u00bck k\u00bc1 Dj \u00fe w k 1 2 fj Pd 2 G From the theory of Newton\u2013Raphson method, function and Jacobean matrix for nonlinear stiffness can be defined as follows F j, j, a, r \u00bc f1 j, j, a, r f2 j, j, a, r f3 j, j, a, r f4 j, j, a, r 2 66664 3 77775 \u00f012\u00de J j, j, a, r \u00bc @ @ j f1 j, j, a, r @ @ j f1 j, j, a, r @ @ a f1 j, j, a, r @ @ r f1 j, j, a, r @ @ j f2 j, j, a, r @ @ j f2 j, j, a, r @ @ a f2 j, j, a, r @ @ r f2 j, j, a, r @ @ j f3 j, j, a, r @ @ j f3 j, j, a, r @ @ a f3 j, j, a, r @ @ r f3 j, j, a, r @ @ j f4 j, j, a, r @ @ j f4 j, j, a, r @ @ a f4 j, j, a, r @ @ r f4 j, j, a, r 2 66666666664 3 77777777775 \u00f013\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from Radial contact stiffness and axial stiffness are defined as follows K\u00bcQj= j \u00bc w0:89 1:24 10 5 k\u00f0 \u00de0:11 P \u00bck \u00bc1 j\u00few 1 2 j Pd 2 G 1:11 P \u00bck \u00bc1 j\u00few 1 2 j Pd 2 G \u00f014a\u00de ka \u00bc w0:89 1:24 10 5 k\u00f0 \u00de0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 0:11 1 2 l 2 2 h \u00f014b\u00de After solving above nonlinear simultaneous equation iteratively with Newton\u2013Raphson method, program is made to calculate contact stiffness (K) in radial directions and axial direction (ka). Algorithm for n-nonlinear simultaneous equation for contact force calculations is given in Appendix 3. Nonlinear contact forces can be calculated in radial vertical and axial direction as below. Qry \u00bc XZ I\u00bc1 K x cos i\u00fe y sin i\u00f0 \u00de B\u00feAsin \u00f0 t i\u00de 1:11 sin i \u00f015\u00de Qry \u00bc XZ I\u00bc1 K x cos i\u00fe y sin i\u00f0 \u00de B\u00feAsin \u00f0 t i\u00de 1:11 cos i \u00f016\u00de Qa \u00bc 1 ka Xj\u00bcz j\u00bc1 Qaj \u00f017\u00de a\u00bc (size of local defect/raceway radius), K\u00bc contact stiffness If the defect is at inner race, t\u00bc (oc\u2013 o2)*t\u00fe 2p/z (z\u2013i), where i\u00bc 11 to 1 If the defect is at outer race, t\u00bc (oc)*t\u00fe 2p/z (z\u2013i), where i\u00bc 11 to 1 Dissipative force for roller bearing In formulation for dissipation of energy the lubrication behavior assumed in a Newtonian way and here viscous damping model is assumed in which dissipative forces are proportional to time derivative of mutual approach. According to Upadhyay et al.,17 a nonlinear damping formula, correlating the contact damping force with the equivalent contact stiffness and contact deformation rate is given by Fd \u00bc c \u00f0 \u00de _ p \u00f018\u00de where c(d) is a function of contact geometry, material properties of elastic bodies, the properties of contact surface velocities, and properties of lubricant. Hence total dissipation force can be calculated as given in Appendix 6 where c is equivalent viscous damping factor between outer race/inner race with the roller is assumed 646N s/m.15 It is assumed that equivalent viscous damping factor of roller inner race contact and roller outer race contact is equal. Fdin \u00bc Cin Keq _ in 1.11 and Fdout \u00bc Cout Keq _ ou 1.11 Fd \u00bc Qdjr \u00bc 9 19 c\u00f0 \u00de\u00f0k\u00de 19 9 \u00f0 _ \u00de1:11 Qdry \u00bc 1=z Xj\u00bcz j\u00bc1 Qdjr sin 2 \u00f0 j 1\u00de z \u00fe !c t \u00f019\u00de where \u00bc \u00f0xcos i\u00feysin i\u00de B\u00feAsin \u00f0 t i\u00de Assuming dissipative forces are similar in y and z direction, Qdry\u00bcQdrz Dynamics model of a rigid rotor system Mathematical representation for motion of rigid rotor roller bearing system is defined as \u00bdM \u20acX\u00fe \u00bdC _X\u00fe \u00bdK X \u00bc f \u00f0x, t\u00de \u00f020\u00de where [M], [C], and [K] are the mass vector of system, damping vector of system, and stiffness matrices for the system. \u20acX, _X, X refers to the acceleration, velocity, and displacement vectors, respectively, and f(t) is a force vector. Nonlinear contact stiffness and nonlinear damping between the inner race/outer race and roller is considered while modeling of equations (21) and (22). m \u20acY\u00feQry\u00feQdry\u00bcFy can be rewritten as follows m \u20acY\u00fe 1=Z XZ I\u00bc1 K \u00f0xcos i\u00fe ysin i\u00de B\u00feA sin \u00f0 t i\u00de 1:11 sin i at Purdue University on June 7, 2015pik.sagepub.comDownloaded from m \u20acZ\u00feQrz\u00feQdrz\u00bcFz can be rewritten as follows. m \u20acZ\u00fe 1=Z XZ I\u00bc1 K \u00f0x cos i\u00fe y sin i\u00de B\u00feAsin \u00f0 t i\u00de 1:11 cos i \u00fe 1=z Xj\u00bcz j\u00bc1 Qdjr sin 2 \u00f0 j 1\u00de z \u00fe!c t \u00bc Fz \u00f022\u00de where Fy is a force vector on the bearing in horizontal direction and Fz is a force vector in vertical direction, m is a mass of the rotor; Newmark-b method is used for solution of differential equations of motion and the transient responses at every time increment are obtained. Algorithm for solution of nonlinear differential equation of motion is given in Appendix 4."
        ]
    },
    {
        "image_filename": "designv10_12_0003164_1.3662578-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003164_1.3662578-Figure7-1.png",
        "caption": "Fig. 7 Free body diagram of moments acting on a ball rolling in a Vgroove",
        "texts": [
            " balls on flat surfaces and confirmed the results of Drutowski [3], Defining a rolling-friction coefficient fiR as in Fig. 4, most values of nR were in the range 10~4 \u2014\u2022 10~5. A rolling friction of this small value may be accounted for entirely by internal hysteresis or damping of the metal. Rolling friction is perhaps more realistically measured in terms of a rolling moment MR defined as in Fig. 4. A similar total moment may be calculated for balls in V-grooves if the ball diameter is replaced by the distance S as shown in Fig. 7. Fig. 5 shows a typical curve for flat-plate tests on a log-log plot. Two regions are noted: An apparently elastic region below 150-lb load and a plastic region above 150-lb load. The dividing line between the two regions occurs at a stress of about 190,000 psi for this steel. These results are not reported or analyzed in detail as they do not differ from Drutowski's work. These readings were used only to correct later readings using the V-grooves. It might be noted that in the usual range of viscosity, widely different types of oil or no oil at all gave the same force readings when used on flat plates",
            " Using this definition, a flat plate has \u00b0\u00b0 conformity while a typical ball bearing has 52 \u2014\u00bb\u2022 54 per cent conformity. Fig. 6 shows data for various configurations. All the data have been reduced to a common basis of one ball with two contact points. The rolling moment on a flat plate is almost negligible when compared to balls rolling in various types of V-grooves. This difference is attributed to the spinning action that the ball has as it rolls in the groove. A free-body diagram of a ball rolling in a V-groove may be drawn as in Fig. 7. The ball is resisted in its motion by both spinning moments Ms and rolling moments MR. The rolling moments have been determined already from the flat-plate experiments. Moment equilibrium of the ball requires Transactions of the A S M E Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use FS = 4 (J\\IS COS ~2 + MR sin 0 (2) Using this relation, the spinning moment has been determined for a variety of situations and the results are plotted in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.1-1.png",
        "caption": "Fig. B.1 Schematic of calculating of the propeller\u2019s gyroscopic bending moment",
        "texts": [
            "1 Gyroscopic Torques Acting on an Airplane Propeller The two blades propeller on an airplane has a mass of 15 kg and a radius of gyration 0.7 m about the axis of spin. The blades are mounted on the hub whose mass is 12 kg and diameter 0.2 m. The propeller is spinning at 350 rad/s in a counterclockwise direction. The airplane is travelling at 300 km/hr and enters a vertical curve having a radius of 80 m. Here is how to determine the maximal gyroscopic bending moment, which the propeller exerts on the bearings of the engine (Fig. B.1). \u00a9 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 R. Usubamatov, Theory of Gyroscopic Effects for Rotating Objects, https://doi.org/10.1007/978-981-15-6475-8 237 238 Appendix B: Applications of Gyroscopic Effects in Engineering Solution The circular motion of the f airplane manifests gyroscopic effects as the action of the inertial torques generated by the propeller. At the starting time of the airplane flight by circular trajectory, the following inertial torques are acting on the propeller (Fig. B.1). The equations of inertial torques are represented in Tables A.1 and A.2 of Appendix A, whose components are as follows: \u2022 the maximal resistance torques generated by the centrifugal Tct = \u03c0 J\u03c9\u03c9y and Coriolis Tcr = J\u03c9\u03c9y forces of the spinning propeller acting around axis oy. \u2022 themaximal precession torques generated by the change in the angularmomentum Tam = J\u03c9\u03c9yof the disc and the common inertial forces Tin = \u03c0 J\u03c9\u03c9y acting around axis oz. Thepilot has blocked the side turn of the airplane around axisoz and the turnaround axis ox",
            " The equation of the mass moment of inertia of the propeller should be rearranged and represented by the equation of the propeller\u2019s gyration radius. The mass moment of the propeller\u2019s inertia is J = Mr2g , where M is mass and rg is the radius of gyration. Then J = M(rg)2/12. The bending moments acting on the propeller are calculated by the equation of precession torque (Sect. A.4, Appendix A) and by property of deactivation of gyroscopic inertial torques. The flight trajectory of an airplane represents its rotation around one axis oy (Fig. B.1). In such condition, gyroscopic inertial torques of the propeller (T ct, T in, T cr, Fig. B.1b) are deactivated, except the change in the angular momentum T am. Then, the bending moment acting on the propeller is computed by the following equation: Tp = [J + Jh]\u03c9\u03c9y = [ 15 \u00d7 0.72/12 + 12.0 \u00d7 0.22 2 ] \u00d7 350.0 \u00d7 1.04 = 310.31Nm where T p is the precession torque, J and Jh are mass moment of inertia of the two blades propeller and the hub, respectively; \u03c9 is the angular velocity of the propeller; \u03c9y is the forced angular velocity of precession of the propeller around axis oy. Presented the example given above is typical for calculation the gyroscope effects acting on rotating shafts, discs, blades, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.18-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.18-1.png",
        "caption": "Fig. 7.18 Baseline configuration with contact surface dimensions defined",
        "texts": [
            " The intended use is for clinicians to select the desired insert configurations appropriate to the patient pathology. If the response of the implant needs to be modified due to changes in the patient pathology, then the insert can be replaced without changes to the pedicular attachment sites. Figure 7.17 displays a prototype of the insert and how it attaches to Fig. 7.17 Contact-aided attachment for baseline configuration the baseline configuration of the implant. The dimensions of the baseline configuration and the semimajor a and semiminor b axes of the elliptic surfaces are shown in Fig. 7.18. The surfaces of the insert are positioned such that the flexures come into contact with them as the device is pulled in tension (i.e., during flexion and during contralateral bending) or compressed (i.e., during extension and during ipsi- lateral bending). The elliptical geometry of the insert used in conjunction with the flexures geometry defines the stiffness of the implant. The ideal design performance of the device was evaluated using analytical modeling, finite element modeling, and benchtop testing of prototypes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003764_j.addma.2021.102070-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003764_j.addma.2021.102070-Figure19-1.png",
        "caption": "Fig. 19. CT cross sections through a) sample H2 with marked borders of adjacent stripes; enlarged cross-sectional area of samples in build plane: b)H2c) D1, d)V1; cross-sectional area of samples along build direction: e) H2, f) D1, d) V1.",
        "texts": [
            " [70] for Ti-6Al-4 V samples, and Stern et al. [71] for 316 L steel and the so-called island scan stripe strategies. For Inconel 718 processed using L-PBF, Moussaoui et al. observed characteristic pores with SEM micrographs, which were located at the melt pool boundaries and at the overlapping of layers [72]. The observed spatial distribution of pores indicates the reasons for pore formation in the tested samples. Pores occur in parallel lines and at intervals of about 10 mm, which corresponds to the distance between neighboring stripes (Fig. 19a). Thus, the number of adjacent stripes and occurring pores will be the largest for the horizontal sample, in which the melting area is the biggest. This can be seen in Fig. 19a and b\u2013d where the CT cross-sections were placed in relation to their layer orientation during the L-PBF process. Additionally, in the case of sample H2, the increased porosity is exacerbated by the temperature gradient, which for larger samples causes greater porosity. As the size of the scanned cross-section increases, a change in layer temperature in relation to the delivered same energy density (process parameters are G. Zio\u0301\u0142kowski et al. Additive Manufacturing 45 (2021) 102070 constant), make it more prone to pore formation [69]",
            " 23b), whereas for the vertically built samples, most pores had much larger diameters after the tensile test (Fig. 23c). The difference in the observed pore sizes and porosity values may result from the interaction between existing pores, microsegregation induced cracks/voids and direction of those defects in relation to the samples build direction. Vertical samples have the lowest ductility, proven by the most brittle nature of fractures. Additionally, the linearly arranged LOF pores have an unfavorable perpendicular orientation with respect to the loading direction (Fig. 19d, g). Therefore, vertical samples show the highest susceptibility to brittle cracking on defects. Contrary, for horizontal samples, the alignment of both linear LOF pores (Fig. 19b, e) and the microsegregation regions is more advantageous, because they are parallel with the loading direction. This relationship is confirmed by the obtained results regarding increase in the number and size of pores after tensile test. Newly observable pores G. Zio\u0301\u0142kowski et al. Additive Manufacturing 45 (2021) 102070 that forms on microcracks/voids in the microsegregation regions during horizontal samples tensile loading, have time to grow and can be observed using XCT. Hence the large increase in the number of previously unobserved pores with small diameters in horizontal samples occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001547_iros.2013.6696825-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001547_iros.2013.6696825-Figure3-1.png",
        "caption": "Figure 3. Structure of a peristaltic crawling robot.",
        "texts": [
            " First, the earthworm contracts an anterior segment using the longitudinal muscles. Next, this contraction is transmitted to rear segments while the anterior segments are elongated by the circular muscles simultaneously. Finally, the contraction segments generate frictional force between the segments and a surface. Because of this frictional force, a reaction force to elongate contraction segments is generated. Thus, the earthworm can move because of the repetition of thick-short and thin-long motion. Figure 3 shows the structure of a peristaltic crawling robot. As stated earlier, this robot was developed by emulating the motion of an earthworm. The robot consists of several units, each of which is equal to a segment of an earthworm. A unit consists of two flanges, a chamber, aluminum sheet, a silicon-tape-coated compression spring, and artificial muscle. When air is supplied to the chamber, the artificial muscle contracts in the axial direction and expands in the radial direction. When air is discharged from the chamber, the artificial muscle extends in the axial direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002965_j.ijheatmasstransfer.2019.118464-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002965_j.ijheatmasstransfer.2019.118464-Figure10-1.png",
        "caption": "Fig. 10. Digitized surface of a track with 0 mm edge offset (left), cross sections including model result with a temperature dependence of the surface tension according to the Eq. (10) (right).",
        "texts": [
            " r\u00f0T\u00de \u00bc 1:842 0:11 10 3\u00f0T Tmelt\u00de; \u00bdr \u00bc N m 1 \u00bc J m 2 \u00f010\u00de Under the assumptions made regarding the process parameters from Section 3, a process temperature of approximate 2000 C is reached for the quasi-stationary state (Fig. 9). On half the length of the welding track, a cross section has been created for comparison with experimental results. For the experiment and the simulation an edge offset of 0 mm has been used. Since the experimental welding track shows fluctuations, several cross sections were created along the track (Fig. 10, left) for comparison with the calculated result and these were compiled together with the model theoretical results in one diagram (Fig. 10, right). The comparison shows that the calculated crosssection forms a smaller overhang, shows a higher curvature in the area below the laser beam and shows a significantly smaller deep melting out at the vertical surface. The powder particles are typically covered with homogeneous oxide layers formed by nickel oxide/hydroxide in case of Ni-based superalloys [22]. The thickness of the oxide layers are between 1 and 4 nm, depending on alloy composition, powder manufacturing method and powder handling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000675_sis.2009.4937849-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000675_sis.2009.4937849-Figure6-1.png",
        "caption": "Fig. 6. The sketches represent the calculation of the growing probability for large aggregates. (a) An aggregate with radius Rm is detectable by a searching robot if it is located up to Rm \u2212 (odes/2) units away from the surface of the swept area of the searching robot. (b) The area obtained by extending the swept area of a searching robot by Rm \u2212 (odes/2) units: 2(omax + Rm \u2212 (odes/2))v\u0394t.",
        "texts": [
            " For a searching robot, the probability of finding an aggregate of size m in the arena is calculated as Pgrow(m) \u2248 2(omax + Rm \u2212 (odes/2))v\u0394t Atotal , m > 1 (13) where odes is the center-to-center desired distance between robots and Rm is the approximate radius for an aggregate of size m (Figure 5-a). In this formula, the area swept by one searching robot is extended by Rm\u2212(odes/2) units (Figure 5- b) to include the regions in which the aggregate with radius Rm can be detected by the searching robot. This is depicted on Figure 6. Rm is calculated with the help of circle packing theory [6]. Circle packing is the arrangement of circles inside a given boundary such that no two overlap and have a specified pattern of tangencies. In our context, we regard robots as circles with a diameter of odes and assume the given boundary, which correspond to the area of the aggregates, has the shape of a circle. For an aggregate with radius Rm (as depicted on Figure 5-a), following relation is known to hold from the best known packings of equal circles in the unit circle [10] Rm odes/2 \u2248 amb (14) where m is the number of robots in the aggregate, a (\u223c 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000994_j.mechmachtheory.2011.02.002-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000994_j.mechmachtheory.2011.02.002-Figure1-1.png",
        "caption": "Fig. 1. 3D dynamic model of the mechanism clutch\u2013helical two stage gear.",
        "texts": [
            " The differential governing equations are . All rights reserved. numerically solved from a standard Runge Kutta integration scheme. Finally, we investigate the effects of the eccentricity defect on the dynamic behavior of the system. The model of the clutch\u2013helical two stage gear system is represented by a twenty seven degrees of freedom system with dry friction path and two clearance nonlinear functions that described the clearance nonlinearity stiffness and the spline clearance nonlinearity (Fig. 1). The system is composed of four blocks. The first block contains the flywheel, the cover and the pressure plate, while the second block is composed by the friction shoes, the hub of the clutch and the gear-12. The third block is composed by a shaft and two gears. The fourth block contains a shaft, the gear-31 and the wheel-32. I1 represents the torsional inertia of flywheel and the cover. I2 is the inertia of the pressure plate. I3 and I4 are the inertia of the friction shoe and the inertia of the hub of the clutch respectively [14]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001102_0954406211403571-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001102_0954406211403571-Figure4-1.png",
        "caption": "Fig. 4 Schematic layout of the gearbox test rig",
        "texts": [
            "comDownloaded from The differential equations of motion can be expressed by equations (2) to (11) m1 \u20acy1 \u00fe c12\u00f0 _y1 _y2 r1 _ 1 \u00fe r2 _ 2\u00de \u00fe ks\u00f0 y1\u00de \u00fe k12\u00f0 y1 y2 r1 1 \u00fe r2 2\u00de \u00bc 0 \u00f02\u00de m2 \u20acy2 \u00fe c12\u00f0 _y2 _y1 r2 _ 2 \u00fe r1 _ 1\u00de \u00fe ks\u00f0 y2\u00de \u00fe k12\u00f0 y2 y1 r2 2 \u00fe r1 1\u00de \u00bc 0 \u00f03\u00de m3 \u20acy3 \u00fe c34\u00f0 _y3 _y4 \u00fe r3 _ 3 r4 _ 4\u00de \u00fe ks\u00f0 y3 y2\u00de \u00fe ks\u00f0 y3\u00de \u00fe k34\u00f0 y3 y4 \u00fe r3 3 r4 4\u00de \u00bc 0 \u00f04\u00de m4 \u20acy4 \u00fe c34\u00f0 _y4 _y3 \u00fe r4 _ 4 r3 _ 3\u00de \u00fe ks\u00f0 y4\u00de \u00fe k34\u00f0 y4 y3 \u00fe r4 4 r3 3\u00de \u00bc 0 \u00f05\u00de J1 \u20ac 1 \u00fe cc1\u00f0 _ 1 _ m\u00de \u00fe r1c12\u00f0r1 _ 1 r2 _ 2 _y1 \u00fe _y2\u00de \u00fe kc1\u00f0 1 m\u00de \u00fe r1k12\u00f0r1 1 r2 2 y1 \u00fe y2\u00de \u00bc 0 \u00f06\u00de J2 \u20ac 2 \u00fe r2c12\u00f0r2 _ 2 r1 _ 1 _y2 \u00fe _y1\u00de \u00fe kst \u00f0 2 3\u00de \u00fe r2k12\u00f0r2 2 r1 1 y2 \u00fe y1\u00de \u00bc 0 \u00f07\u00de J3 \u20ac 3 \u00fe r3c34\u00f0r3 _ 3 r4 _ 4 _y3 \u00fe _y4\u00de \u00fe kst \u00f0 3 2\u00de \u00fe r3k34\u00f0r3 3 r4 4 \u00fe y3 y4\u00de \u00bc 0 \u00f08\u00de J4 \u20ac 4 \u00fe r4c34\u00f0r4 _ 4 r3 _ 3 \u00fe _y4 _y3\u00de \u00fe kc2\u00f0 4 out\u00de \u00fe r4k34\u00f0r4 4 r3 3 \u00fe y4 y3\u00de \u00bc 0 \u00f09\u00de Jm \u20ac m \u00fe cc1\u00f0 _ m _ 1\u00de \u00fe kc1\u00f0 m 1\u00de \u00bc Tm \u00f010\u00de JL \u20ac out \u00fe cc2\u00f0 _ out _ 4\u00de \u00fe kc2\u00f0 out 4\u00de \u00bc TL \u00f011\u00de The simulation was carried out for a healthy pair of gears and a pair suffering from a tooth breakage with magnitude fault 1 (25 per cent tooth removal), fault 2 (50 per cent tooth removal), fault 3 (75 per cent tooth removal), and fault 4 (100 per cent tooth removal) of the tooth under varying loads (0, 20, 40, 60, and 80 per cent) and speeds (10, 30, 50, 70, and 90 per cent). Figure 3 shows the vibration time series for healthy gears. Each vibration signal collected from dynamic model is analysed using the procedure described in the following sections. 3 TEST RIG AND BASELINE DATA The experimental data work collected using the test rig is shown in Fig. 4. It comprises a two-stage, 11 kW, helical gearbox driven by three-phase induction motor and connected to a DC generator and adjacent resistor banks. Tests were carried out using healthy pair of gears and a pair suffering from a tooth breakage with magnitude fault 1 (25 per cent tooth removal), fault 2 (50 per cent tooth removal), fault 3 (75 per cent tooth removal), and fault 4 (100 per cent tooth removal) of the tooth under varying loads (0, 20, 40, 60, and 80 per cent) and speeds (10, 30, 50, 70, and 90 per cent); a photo of the gear with 25 per cent tooth removal is illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.1-1.png",
        "caption": "Fig. 9.1 Reference basis e1, body-fixed basis e2 and point Q in motion relative to e2",
        "texts": [
            " Wampler C W (1996) Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using soma coordinates. Mechanism Machine Theory 31:331\u2013337 11. Wittenburg J (2005) Direct kinematics of the general Stewart platform. presented at Tsinghua Univ. Beijing. (2009) Proc. Scient. Conf. BulTrans, Sozopol Chapter 9 Angular Velocity. Angular Acceleration This is the first chapter devoted not to position theory, but to continuous motion. The essential kinematical quantities are velocity, acceleration, angular velocity and angular acceleration. In Fig. 9.1 an arbitrarily moving reference basis e1 with origin 0 is shown. Relative to e1 a body is moving. The body is represented by the basis e2 rigidly attached to it. The origin A of this basis is an arbitrarily chosen point of the body. Relative to e2 a point Q is moving. The position vectors of Q in the two bases are denoted r and , respectively. The figure shows the relationship r = rA + . (9.1) In general, the velocities of Q relative to the two bases are different, and also the accelerations of Q relative to the two bases are different"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000994_j.mechmachtheory.2011.02.002-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000994_j.mechmachtheory.2011.02.002-Figure2-1.png",
        "caption": "Fig. 2. Action plan of helical gear.",
        "texts": [
            " where L\u03b41 and L\u03b42 are defined by: L\u03b41 = \u2212s1 s2 s3 s1 \u2212s2 \u2212s3 0 0 0 s4 s5 s7 s8 0 0 0 s6 s9 0 0 0\u00bd \u00f05\u00de L\u03b42 = 0 0 0 t1 \u2212t2 t3 \u2212t1 t2 \u2212t3 0 0 t4 t5 t7 t8 0 0 0 t6 t9 0\u00bd \u00f06\u00de si and ti are defined in Tables 1 and 2 respectively. where The length p1, p2, p'2 and p3 are defined by: p1 = Rb12tg\u03b11; p2 = Rb21tg\u03b11; p02 = Rb22tg\u03b12; p3 = Rb31tg\u03b12: \u00f07\u00de Rbjs are the base radius of the gear-js and \u03b1i is the pressure angle. \u03b31 and \u03b32 are the gears' location and expressed by: \u03b31 = O12O21 ! ;\u0302 X ! and \u03b32 = O22O13 ! ;\u0302 X ! : \u00f08\u00de Ojs are the geometrical centers of gears-js. l is the distance between the transverse plan and the point of contact on the line of contact. \u03b2 is the helix angle. (Fig. 2) The nonlinear dynamic model includes three types of nonlinearity: dry friction path, double stage stiffness and spline clearance. In this paragraph, the objective is to develop numerical models for the accurate and robust description of these nonlinearities. The nonlinear function describes the double stage stiffness is modeled by the expression KS f\u0303 DSS \u03b44\u00f0 \u00de. KS is the linear spring stiffness of the second stage of the clutch disk and f\u0303 DSS \u03b44\u00f0 \u00de is a nonlinear function that describes the transition between one or two springs on contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.61-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.61-1.png",
        "caption": "Fig. 2.61 Arbitrary forces acting on an automotive vehicle [GILLESPIE 1992].",
        "texts": [
            " A NSL Euler\u2013Lagrange equation of the second order can than be written for each of the three independent axis-directions (normally the auto-motive vehicle fixed axes). 2.2 Automotive Vehicle Driving Performance 213 Determining the axle loading on an automotive vehicle under arbitrary circumstances is the first simple application of NSL. It is an important first step in analysis of driving (acceleration) performance because the axle load determines the tractive effort obtainable at each axle, affecting the acceleration, gradeability, maximum value of the vehicle velocity, and drawbar effort. Consider the vehicle shown in Figure 2.61, in which most of the significant forces on it are shown. The loads carried on each axle may consist of a static component, plus the load transferred from front to rear (or vice versa) due to the other forces acting on the vehicle. The load on the front axle can be found by summing torques about the point A under the rear wheel-tyres. Presuming that the vehicle is not accelerating in pitch, the sum of the torques at point A must be zero. By the SAE convention, a clockwise torque about point A is positive, then 0cossin =\u2212+++++ rgvghhzhhxvxaazf lRhRdRhRhFhDlF \u03b8\u03b8 (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003456_j.actamat.2020.09.071-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003456_j.actamat.2020.09.071-Figure7-1.png",
        "caption": "Fig. 7. (a)-(c) Schematic representations depicting molten pool interactions in the head-to-head coalescence scenario. (d) Section of molten track produced with head-to-head coalescence.",
        "texts": [
            " In each figure, images a)\u2013(c) show a sequence of schematic diagrams for molten pool dyamics at 0, 80 and 160 \u03bcs, respectively, where t is set arbitrarily o 0 \u03bcs at the first image shown. The red dots represent the laser pots and the dark orange areas are the molten pools. Black arrows n the molten pools indicate the direction of fluid motion within. he light orange areas represent the solidified molten tracks. Subgure (d) in each figure is a confocal image that shows the periodic tructure resulting from the process depicted in (a)\u2013(c). In Fig. 7 , we present a case that we refer as head-to-head (HtH) oalescence. Such coalescence occurs at a large hatch spacing and small perpendicular offset, which means two laser beams are witched on with small temporal offset (refer to Eq. (1) ). HtH sceario can be observed in Fig. 6 where wavelengths decrease with ncreasing perpendicular offset. As shown in (a), the two laser pots are at similar positions on the y axis. Starting from an un- erged state, the two molten pools experience perturbations that c l s p t a d t a p o t a t s t F c p o i p F s ( ( t n t a t l w r ( i i o r t s r c h l t e a a c w r l 4 w a m t h o t o c a b ause them to swell and merge together"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.73-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.73-1.png",
        "caption": "Fig. 2.73 Basic mechanical layout of a simplest, early 1900s automotive vehicle\u2019s CVT [Bobbs-Merrill Co. Indianopolis, Ind.; HOMANS 1910].",
        "texts": [
            " The problem with a CVT is that the efficiency is significantly worse than in an ordinary geared transmission [LECHNER AND NAUNHEIMER 1999]. Various ratio-altering transmissions may be used. These take the form of friction drives, selective sliding gearboxes and progressive sliding gearboxes with clutches, planetary gears with brake bands, and belt systems with loose pulleys. The friction disc transmission had a large future. A simplest, early 1900s automotive vehicle\u2019s CVT is the \u2018driving-disc and driven disc\u2019 design, in which a friction driving disc rides upon the surface of a friction-driven disc (see Fig. 2.73). The simplest form had the driven disc set on a shaft at right angles to the driving disc. 2.3 M-M DBW AWD Propulsion Mechatronic Control Systems 227 The driving disc may be slid along its splinted axle to contact the driven friction discs at different distances from its centre [HOMANS 1910]. The speed ratio of such a design is simply the radius of the driving disc divided by the distance from the contact point to the centre of the driven discs. Many of the automotive vehicle manufacturers still perform research in this area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002069_1.4030242-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002069_1.4030242-Figure4-1.png",
        "caption": "Fig. 4 Sample of von Mises stress distributions at pitch point contact for: (a) l 5 0.0 case and (b) l 5 0.3 case",
        "texts": [
            " The contact stresses varied with increasing friction coefficient and helix angle of the gears. The effect of friction needs to be accounted in calculating contact stress and hence, friction factor has been found for spur and different helical gear pairs. The spur gear model was generated based on the specification as in Table 1. The static stress analysis was conducted on the spur gear model, including coefficient of friction. A comparison of the contact stress distributions in the spur gears for two example cases, frictionless and with frictional coefficient of 0.3, is shown in Fig. 4. The spur gear analysis revealed that the contact stresses increased by around 11% for a rise of coefficient of friction from zero to 0.3. Based on this contact analysis, friction factors were generated and the friction factor for pitch point contact is represented in Fig. 5. The friction factor of the spur gear is defined by a third-order polynomial equation. The function for the Kf value of the spur gear pair shown in Fig. 5 could be described with the following relation: Kf \u00bc 2:8681l3 \u00fe 2:1590l2 \u00fe 0:0036l\u00fe 0:9974 (4) Similar analysis were conducted to evaluate friction factor values for contact stresses and friction factor functions for 5 deg, 15 deg, 25 deg, and 35 deg helical gear pairs are described in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.141-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.141-1.png",
        "caption": "Fig. 2.141 HEV driving circumstances during acceleration [DRIESEN 2006] .",
        "texts": [
            " An exemplary series/parallel HEV layout with an ICE and two electrical machines is shown in Figure 2.138 [DRIESEN 2006]. In Figure 2.139 is shown the HEV driving circumstances during starting when the ICE remains off to save liquid fuel and the E-M motor drives the series/parallel HEV. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 336 In Figure 2.140 HEV driving circumstances are shown during normal driving when the ICE starts and may drive the series/parallel HEV and produce electrical energy for the E-M motor or is charging the CH-E/E-CH storage battery. In Figure 2.141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 337 In Figure 2.142 HEV driving circumstances are shown during deceleration and braking the E-M motor is turned into a M-E generator to charge the highvoltage CH-E-CH storage battery. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 338 In Figure 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000525_ichr.2010.5686851-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000525_ichr.2010.5686851-Figure2-1.png",
        "caption": "Fig. 2. Two mechanical structures for the knee. A revolute joint and a cross four-bar linkage. Absolute angles and torques.",
        "texts": [
            " Section III is devoted to the dynamic models and the resolution of the closed structure problems. The problem of trajectory optimization is presented in section IV. Numerical tests for the different bipeds are discussed in section V. Finally, section VI offers our conclusions and perspectives. To compare the performance of the planar bipedal robot in function of the knee joint, we use the same characteristics of length, mass and inertia for both bipeds. The bipedal robots are depicted in compass gait fig.1 with the two structures of the knee joint, see fig.2. Table (I) presents the physical data of the biped which are issued from the hydroid bipedal robot [18]. 978-1-4244-8690-8/10/$26.00 \u00a92010 IEEE 379 The dimensions of the four-bar structure are chosen with respect to the human characteristics measured by J. Bradley et al. by radiography in [19]. Figure 3 represents the cross four-bar knee structure. This parallel structure needs just one actuator on the drive angle \u03b11. Let us introduce \u0393m = [\u0393p1 ,\u0393p2 ,\u03931,\u03932,\u03933,\u03934] T 1 of the applied joint torques vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003237_s00170-020-05572-8-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003237_s00170-020-05572-8-Figure1-1.png",
        "caption": "Fig. 1 a Schematics of sample geometries, SLM scanning strategy, building direction, and wear test directions. b Schematic of the ball-on-disk wear test system",
        "texts": [
            " Further details of the material, including the microstructure and tensile behavior, have been reported previously by a few of the present authors in [18]. To study the anisotropy of the wear property of the SLMed SS316L samples, two types of specimens were built in different directions relative to the SLM building axis. The specimens were sliced from 20 \u00d7 20 \u00d7 100 mm blocks to achieve a thickness of 1 mm each. The wear tests were carried out in the vertical and parallel directions to the baseplate, as shown in Fig. 1. The specimens with a wear plane vertical to the building direction were designated as BD, whereas specimens with wear planes at 45\u00b0 to the laser-scanning direction were designated as 45SD. Some SLM specimens were annealed at 800 \u00b0C for 4, because SS316L is known to fully annealed at 800 \u00b0C [19, 20]. The post-heat treatment of the specimens was performed in a box-type laboratory furnace in an atmosphere. The specimens were wrapped in a protective heat treatment Parameter Setting foil to prevent oxidation of the sample surface",
            " For comparison, a commercial-grade cold-rolled SS316L plate of 3-mm thickness was also used for the wear test. Specimens with dimensions of 20 \u00d7 20 \u00d7 3 mm3 were cut from the plate for the wear tests, and these specimens were designated as CR. The chemical compositions of the SS316L powder used for the SLM and the samples CR are given in Table 2. The wear resistances of the SLM and cold-rolled specimens were evaluated using a ball-on-disk testing method (102PD, R&B Tech, Republic of Korea), as illustrated in Fig. 1. All specimens were mechanically ground with SiC papers up to 2000 grit and then wiped with alcohol prior to the wear test. The tests were conducted at 25 \u00b0C under three different normal loads of 50, 100, and 150 N and linear sliding speeds of 0.1, 0.5, and 1.0 m/s for a constant sliding distance of 200 mwith AISI 52100 high-carbon-steel balls as the counterpart material. The radius of the ball, Rb, was 12.7 mm, and the maximumHertzian contact stresses from this experimental setup were 778, 980, and 1,123 MPa for the applied normal loads of 50, 100, and 150 N, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure16.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure16.5-1.png",
        "caption": "Fig. 16.5 Watch gearing with straight-line tooth flanks inside the pitch circles",
        "texts": [
            " In well-lubricated gears (no friction force in the common tangent plane) the force transmitted by one tooth on the other has the direction of the contact normal BP12 . The periodical change of this direction is a disadvantage of cycloidal gears. Another weakness, from the point of view of bending stiffness and bending stresses, is the concave shape of the bottom parts of teeth. A favorable characteristic is the concave\u2013convex contact of teeth which reduces contact pressure as well as wear. For all these reasons cycloidal gears are used in fine precision mechanics exclusively. An example is the watch gear shown in Fig. 16.5 . In this particular example, the hypocycloids inside the pitch circles are straight lines passing through the respective centers. This indicates that the radius of the circle q equals r1/2 , and that the radius of the circle q\u2032 equals r2/2 . The large backlash of this gearing does not cause 16.1 Parallel Axes 537 problems because in watch gearings the sense of rotation does not change. Remark: All kinds of gears require a small backlash preventing teeth from having contact on both flanks simultaneously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001232_iros.2011.6094893-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001232_iros.2011.6094893-Figure2-1.png",
        "caption": "Fig. 2. Knee/orthosis model in the sagittal plane: Movements of the lower limbs are limited to flexion/extension of the knee joint.",
        "texts": [
            " The orthosis generates a torque allowing flexion and extension of the knee joint constrained by a range of motion between 0\u25e6 and 120\u25e6 in the sagittal plane. 0\u25e6 corresponds to full knee extension, 120\u25e6 corresponds to maximal knee flexion and 90\u25e6 represents the resting position. Positions of the center of mass of the lower limb and the orthosis are given by: O1G = ( K1l1cos(\u03b8),\u2212K1l1sin(\u03b8) ) (1) O1G1 = ( K2l3cos(\u03b8),\u2212K2l3sin(\u03b8) ) (2) where K1, K2 represent the coefficients of mass repartition of the shank/ lower part of the orthosis respectively (Fig.2). G and G1 represent the center of gravity of the shank/ lower part of the orthosis respectively. l1 and l3 represent respectively, the length of the shank/ foot and the length of the lower segment of the orthosis. Using the Lagrange equation, the dynamic model of the system can be written as follows (Fig.2): ( Jk + Jeqex ) \u03b8\u0308 + ( fvk + fvex ) \u03b8\u0307 \u2212 ( m1k1l1 +m3k2l3 ) g cos(\u03b8) = \u03c4ex + \u03c4k \u2212 ( fsex + fsk ) sign(\u03b8\u0307) (3) with: - m1 and Jk: mass and inertia of the shank foot - Jeqex: inertia of the lower part of the orthosis, - fvk and fvex: viscous damping coefficients of the knee joint and the actuated orthosis respectively, - fsk and fsex: solid friction coefficients of the knee joint and the actuated orthosis respectively, - (m1k1l1 +m3k2l3)gcos(\u03b8) is the gravitational torque of the knee joint-orthosis, and g is the gravitational acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001474_j.snb.2015.01.119-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001474_j.snb.2015.01.119-Figure7-1.png",
        "caption": "Fig. 7. (A\u2013C) DPASV response for analyte and interferent(s) at MIP/NIP modified sandpaper electrodes [when analyte or interferent(s) studied individually (each 400 ng mL\u22121)]: (A) NIP before washing, (B) NIP after washing, (C) MIP. (D) DPASV response on MIP modified sandpaper electrode for l-Cys (400 ng mL\u22121) present in binary mixture (1:1) w cystei ( ferent ( ation 4",
        "texts": [
            ", methinine (Met), phenylalanine (Phen), glutamic acid (Glu), d-cysteine d-Cys), glycine (Gly), hitidine (His), tyrosine (Tyr), uric acid (UA), scorbic acid (AA), tryptophan (Trp), homocysteine (Hcy), gluathione (GSH) and their clinically relevant mixture. Accordingly, IP-composite modified electrode (without washing treatment) as not responsive for any of the interferents when studied indi- idually. On the other hand, the NIP modified electrode revealed a ery feeble current response for some of the interferents (Fig. 7), hich could easily be washed away from the electrode with water 0.5 mL, n = 3). This reflects a substrate-selective imprinting effect, n this case. This means any molecule that is smaller or larger in ize than l-Cys could not be accumulated in MIP cavities and hence he non-specific binding (false-positive) was found to be practically bsent in this work. Ta b le 1 C om p ar is on S. n o. 1 2 3 4 5 6 7 8 9 10 162 B.B. Prasad, R. Singh / Sensors and Actuators B 212 (2015) 155\u2013164 t r q c c i M o s t N b s fi w r 3 e w e o p n f t s D d f T a e i b ith interferent(s) [methionine (Met), phenylalanine (Phen), glutamic acid (Glu), dAA), tryptophan (Trp), homocysteine (Hcy), glutathione (GSH), and mixture of inter 400 ng mL\u22121) present in binary mixture (1:10) with interferent(s) having concentr A study on parallel cross-reactivity (Fig. 7) was also made with he binary mixture of test analyte and interferent(s) in 1:1 and 1:10 atios. In all cases, the MIP-composite modified electrode showed a uantitative (100%) response for l-Cys; this suggests that the sensor an also be used for the quantitative analysis of l-Cys in the sample ontaining very high concentration of interferents. From this experment, it can be concluded that MIP binding sites present at the IP surface are able to recognize l-Cys molecule, in the presence f any concentration of interferent, by means of stereo chemical electivity in terms of shape, size, and chemical affinity of the funcional groups. Although the non-specific adsorption of l-Cys on IP-composite modified electrode was insignificant and that could e removed by water-washing treatment (0.5 mL, n = 3) (Fig. 7), the ame treatment is also recommended with MIP-composite modied sensor as a safe-guard in order to obtain quantitative results, ithout any non-specific contribution (false-positives) and crosseactivity. .5. Stability and reproducibility of the proposed sensor The long-term stability of sensor is an important factor, where lectrode fouling can a matter of serious concern. DPASV response as measured using a single modified electrode that was regenrated by the method of template removal using ACN and used n every alternate day, over a period of 4 weeks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002930_1.4043206-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002930_1.4043206-Figure6-1.png",
        "caption": "Fig. 6 Coordinate system Sg e(e g 1 , e g 2 , ng) at the contact point on the gear tooth surface",
        "texts": [
            " Error sensitivity of the moving velocity of the contact point is defined as J(vr , \u03c3) = dvr d\u03c3 (15) where vr is the moving velocity of the contact point and \u03c3 is the composition of misalignments that can be represented as [24] \u03c3 = (E \u00b7 apg \u2212 P \u00b7 ap + G \u00b7 ag)2 \u221a (16) in which E is the offset of the pinion, P and ap are the axial displacement and the unit vector along the rotation axis of the pinion, respectively, G and ag are the axial displacement and the unit vector along the rotation axis of the gear, respectively, and apg= (ap\u00d7 ag)/sin \u03a3 with \u03a3 being the shaft angle, as shown in Fig. 5. A coordinate system Sge (e g 1, e g 2, ng) is used to describe the position of the contact point on the gear tooth surface \u03a3g, as shown in Fig. 6. Unit tangent vectors along two principal directions are denoted by eg1 and eg2. Projections of the moving velocity vrg of the contact point in the two principal directions eg1 and eg2 are denoted by vr1g and vr2g , respectively. Likewise, a coordinate system Spe (e p 1, e p 2, np) is used to describe the position of the contact point on the pinion ease-off tooth surface \u03a3p. Projections of the moving velocity vrp of the contact point in two principal directions ep1 and ep2 are denoted by vr1p and vr2p , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.4-1.png",
        "caption": "Fig. 13.4 Exploded view of Fenyi\u2019s joint",
        "texts": [
            "1 the angle of rotation \u03c81 of the cross relative to shaft 1 is determined as function of \u03d51 . Arbitrarily, \u03c81 = 0 is associated with \u03d51 = 0 . From (13.12) and (13.13) it follows that d\u03c81 d\u03d51 = sin\u03b1 cos\u03b1 cos\u03d51 1\u2212 sin2 \u03b1 cos2 \u03d51 . (13.19) With the new variable z = tan\u03d51/2 and with the constant k2 = (1 \u2212 sin\u03b1)/(1 + sin\u03b1) this takes the form \u03c81 = 2 tan\u03b1 \u222b 1\u2212 z2 (1 + k2z2)(1 + z2/k2) dz = 2 tan\u03b1 k2 \u2212 1 [ k2 \u222b dz 1 + k2z2 \u2212 \u222b dz 1 + z2/k2 ] = tan\u22121(z/k)\u2212 tan\u22121(kz) = tan\u22121(tan\u03b1 sin\u03d51) . (13.20) Hence tan\u03c81 = tan\u03b1 sin\u03d51 . (13.21) This equation is the second Eq.(10.10). Figure 13.4 is the exploded view of a shaft coupling brought to the author\u2019s attention by Fenyi2. The coupled shafts 1 and 2 are skew. They are mounted in frame-fixed bearings not shown in the figure. Let e\u030212 and e\u0302 2 2 be dual unit vectors along the shaft axes, and let, furthermore, \u03b1\u0302 = \u03b1 + \u03b5 be the constant dual screw angle displacing e\u030212 into the position e\u0302 2 2 . The projected angle \u03b1 and the length of the common perpendicular of the two shaft axes are the only parameters of the joint. To each shaft and at right angles to the shaft two collinear trunnions are rigidly attached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000221_s0006-3495(83)84406-3-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000221_s0006-3495(83)84406-3-Figure2-1.png",
        "caption": "FIGURE 2 The central pair and the ith outer doublet of an axoneme are shown relative to a fixed coordinate system, XYZ. The body coordinate axis is tangent to the central pair (strictly, the neutral axis) at arc length position s, and Li(s) is perpendicular to the tangent and has a fixed length.",
        "texts": [
            " (4) Because dr/ds = T in body coordinates is z, then the position vector, r, to the flagellum at position s from an origin at s = 0 is 7(s) = A(0, s')zds'. (5) Thus in fixed coordinates the X, Y, and Z components of the position vector are X(s) = f A13(0,s')ds' Y(s) = f A23(0,s')ds' Z(s) = A33(0,s')ds'. (6) II. SLIDING FILAMENT MODEL The position vector of the ith doublet of the axoneme can be written formally as ri(si) = 7(s) + Li(s), (7) where 7 refers to the position vector of the central pair of microtubules (Fig. 2). The sliding filament model is expressed succinctly merely by requiring that Li, a vector from the central pair to the ith outer doublet, be a constant vector in body coordinates. We choose Li normal to the central pair tangent vector. (For convenience Li may be thought of as directed along an undistorted radial link.) This formalism then specifies that the normal distance between the central pair and any of the outer doublets is fixed, but allows the axoneme as a whole to bend and twist in three dimensions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002940_j.engappai.2019.03.025-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002940_j.engappai.2019.03.025-Figure2-1.png",
        "caption": "Fig. 2. The inertial and body frames of the quadrotor system.",
        "texts": [
            " It is proven that a unique \ud835\udf06 can be found by solving the following equation: \ud835\udf06 + 1 = \ud835\udc5b \u220f \ud835\udc56=1 (1 + \ud835\udf06\ud835\udf07\ud835\udc56), \u22121 < \ud835\udf06 <\u221e, \ud835\udf06 \u2260 0 (9) where \ud835\udf07\ud835\udc56 = \ud835\udf07 { \ud835\udc65\ud835\udc56 } . Thus, the \ud835\udc5b densities determine the 2\ud835\udc5b values of fuzzy measures. The modeling of a quadrotor system requires careful considerations of the various engineering aspects involved and their affecting factors such as aerodynamic, and inertial counter torques, frictions, as well as gyroscopic and gravitational effects. The quadcopter structure is presented in Fig. 2 along with the corresponding angular velocities, torques and forces created by the four rotors, while Fig. 3 shows a schematic of the quadrotor body structure and corresponding masses. In this section, we present the general descriptions of the quadrotor\u2019s model while the modeling details about the structure, dynamics, motor model and aerodynamics of the quadrotor are thoroughly described in Appendices A\u2013D. The complete quadrotor\u2019s equations of motion taking into account all the aforementioned forces and moments can be expressed as follows: \ud835\udc3c\ud835\udc65\ud835\udc65",
            " Table 2 shows the best-constrained PSO parameters used in the proposed detailed design method and Table 3 shows the constrained handling penalty coefficients, described in Eq. (21), for different groups of design constraint functions. Moreover, to model the interactions and relative importance of criteria involved in the detailed design, we need to specify the fuzzy measures and indices based on the method described in Section 4. The mechanism used to assign the fuzzy measures to each criterion and subcriterion from various domains has been depicted in Fig. 2. Table 4 shows the results of the identification of fuzzy measures based on the Sugeno \ud835\udf06-method, where: [ \ud835\udf07\ud835\udc60\ud835\udc61\ud835\udc5f\ud835\udc62\ud835\udc50\ud835\udc61\ud835\udc62\ud835\udc5f\ud835\udc52, \ud835\udf07\ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc61\ud835\udc5f\ud835\udc5c\ud835\udc59 , \ud835\udf07\ud835\udc4e\ud835\udc52\ud835\udc5f\ud835\udc5c, \ud835\udf07\ud835\udc63\ud835\udc56\ud835\udc60\ud835\udc62\ud835\udc4e\ud835\udc59 , \ud835\udf07\ud835\udc60\ud835\udc66\ud835\udc60\ud835\udc59\ud835\udc52\ud835\udc63\ud835\udc52\ud835\udc59 ] = [ \ud835\udf071, \ud835\udf072, \ud835\udf073, \ud835\udf074, \ud835\udf075 ] . Tables 5\u20137 present the fuzzy measures for the objective functions for each subsystem. Based on the fuzzy measures obtained using the identification algorithm, we attain the following resulting interaction and importance indices: \ud835\udc3c = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udf191 \ud835\udc3c12 \ud835\udc3c13 \ud835\udc3c14 \ud835\udc3c15 \ud835\udc3c21 \ud835\udf192 \ud835\udc3c23 \ud835\udc3c24 \ud835\udc3c25 \ud835\udc3c31 \ud835\udc3c32 \ud835\udf193 \ud835\udc3c34 \ud835\udc3c35 \ud835\udc3c41 \ud835\udc3c42 \ud835\udc3c43 \ud835\udf194 \ud835\udc3c45 \ud835\udc3c51 \ud835\udc3c52 \ud835\udc3c53 \ud835\udc3c54 \ud835\udf195 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003778_j.mechmachtheory.2021.104407-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003778_j.mechmachtheory.2021.104407-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of external loads on five DOFs ( \u03b4x , \u03b4y , \u03b3 x , \u03b3 y , \u03b3 z ) of the RLMG.",
        "texts": [
            " Finally, the results of the proposed approach are compared with the results of other theoretical models and published experimental results. RLMGs assembled with a block, a rail, a cage structure, and a number of rollers are widely used in heavy-load mechanical systems due to their high carrying capacity and less friction [1] . To determine the static and dynamic performances of heavyload mechanical systems assembled with RLMGs, it is necessary to analyze the non-uniform load distribution and stiffness characteristics of the RLMG. Fig. 1 presents the geometry of the RLMG featuring five loading conditions in a referential coordinate system ( O-xyz ). The five DOFs respectively represent the displacements of the block in the x - and y -directions ( \u03b4x and \u03b4y ), and the angular displacements around the x -, y -, and z -directions ( \u03b3 x , \u03b3 y , and \u03b3 z ). The origin O lies at the center of the RLMG, while the cross-section of the plane ( x i O i z i ) passes through the centers of rollers located at the position of z i along the negative z -direction",
            " In this study, following the contact analysis method proposed by Kwon [22] , the effect length of the roller and the axial contact position along the roller contact surface are considered to have major influences on the contact compression. Thus, the effect of the structure of the circular arc transition is neglected. When various loading conditions are applied to the block of the RLMG, the force vector can be expressed as follows: { F } T = { F x F y M x M y M z } . (1) The displacement vector in response to each load state can then be given as follows: { \u03b4 }T = { \u03b4x \u03b4y \u03b3x \u03b3y \u03b3z } . (2) As shown in Fig. 1 , the location of z i along the z -direction can be calculated by z i = l N 2 \u2212 ( i \u2212 1 ) l N N \u2212 1 , (3) where l N and N are the effective contact length of the roller and block and the effective number of rollers on each raceway, respectively, and i is the roller index, i = 1, \u2026, N . In this study, to analyze the non-uniform load distribution and stiffness characteristics of the RLMG, the variation of the contact angle of each roller is investigated while considering the initial contact angle, preload, and block flexibility",
            " 4 , where \u03b10,ij is the initial contact angle, l is an independent variable along the x ij -axis, and the points A ij and B ij represent the initial corner points before loading. When applying an external load, the initial contact angle \u03b10,ij will be shifted to a new position angle \u03b1ij . Moreover, the initial corner points A ij and B ij will be moved to new points A \u2032 i j and B \u2032 i j , which will result in a variation of the contact line \u03c8 i j (l) between the roller and block. According to the global coordinate system shown in Fig. 1 and the geometric relationships shown in Fig. 4 , the block cross-section of the plane ( x i O i y i ) passes through the center of each roller located at the position z i along the positive and negative z -directions. Then, the displacement vector { u } between the roller and block in the cross-section along the z -direction can be written as Eq. (8) : { u } = ( { u } zn \u2212\u2212 { u } zp ) , (8) where { u } zp and { u } zn represent the displacement vectors along the positive and negative z -directions, respectively, and can be expressed as follows: { u } zn T = { u ( i j ) x u ( i j ) y } , ( i = 1 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001692_s1068366615020038-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001692_s1068366615020038-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the sliding bearing.",
        "texts": [
            "63 INTRODUCTION The use of sliding bearings, as one of the wide spread friction unit (Fig. 1), remains sufficiently sig nificant at the present time where it is impossible or unreasonable to use rolling bearings. The range of their use in engineering is rather various: at loads from 1 to 20 \u00d7 106 N, with shaft diameters from 10\u20132 to 103 mm, with a speed of 105 rpm, and a width from 10\u23af2 to 102 and more mm. They operate under various conditions at not only fluid (gas), but boundary and dry friction as well. Therefore, calculating an estimate of their bearing capacity, wear, and service life is the actual problem at the design stage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001487_gt2013-95878-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001487_gt2013-95878-Figure2-1.png",
        "caption": "Figure 2. Nomenclature for the specimen orientation during SLM manufacturing. nr indicates the build direction.",
        "texts": [
            " After finalization, the remaining loose powder is removed and the component is cut off from the build platform. Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 3 Copyright \u00a9 2013 by ASME In the current project, specimen manufacturing was performed in an EOS EOSINT M270 machine. Specimens for tensile and fatigue testing were manufactured from cylindrical bars produced with the SLM process, where the bars were built in different directions relative to the build direction, see Figure 2. The material is supplied by EOS and is, in principle, conforming to the composition of Haynes International Hastelloy X, see Table 1. nr Table 1. Nominal composition of Hastelloy X, developed by Haynes International. SLM material in principle conforming to the specification. Ni Cr Fe Mo Co Si Mn W Bal. 22 18 9 1.5 <1 <1 0.6 Tensile testing has been performed in an electromechanical test rig (Instron 8862) equipped with a high temperature extensometer (Instron 2632-055) and a chamber furnace (Instron SF-1594)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000241_j.ijfatigue.2007.02.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000241_j.ijfatigue.2007.02.003-Figure1-1.png",
        "caption": "Fig. 1. Elements of rotational connections.",
        "texts": [
            " The paper presents the material model, numerical analysis of the actual carrying capacity of the rolling contact in single-row ball bearings and the verification of the numerical material model with experimental results of low cycle carrying capacity. 2007 Elsevier Ltd. All rights reserved. Keywords: Rotational connections; Low cycle fatigue; Cyclic plasticity; Damage Large rolling bearings can be classified among the most frequently used machine elements in machine engineering and mobile techniques (Fig. 1). Owing to their multiple use, the requirements which bearings should meet are highly diverse. Bearing usage ranges from applications in which a bearing collapse does not constitute a major problem, to the applications in which the collapse of a bearing could lead to enormous economic damage and potential disastrous consequences for the users. It is therefore understandable that a bearing composition must be specifically designed to suit a particular application and the operation of a rotational connection should be carefully controlled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002006_j.aej.2018.12.010-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002006_j.aej.2018.12.010-Figure5-1.png",
        "caption": "Fig. 5 Nodal Temperature (NT11) distribution, in Kelvin, half way during the deposition of the first layer.",
        "texts": [
            " (4), where P refers to the laser power, r is the laser beam radius (1.25 mm in the current case), and g represents the absorption coefficient that was found to be 0.4 for the current conditions based on the experimental results of Liu [9]. I \u00bc g P p r2 \u00f04\u00de The Abaqus user subroutine DFLUX was used in order to implement the laser heating effects in terms of a surface heat flux (Eq. (4)). A zigzag pattern was followed, as shown in art distortion calculation in selective laser melting, Alexandria Eng. J. (2018), Fig. 4, between subsequent layers. Fig. 5 shows the temperature distribution half way through the deposition of the first layer, as an example. The user subroutine FILM was used to simulate the heat loss, via convection and radiation, to the surroundings. An empirical equation, Eq. (5) [9], was used to represent the combined effect of both mechanisms. In Eq. (5), h represents the overall heat transfer coefficient (W/m2 K) and e refers to emissivity, which was assumed to be 0.9 based on the work of Liu [9]. h \u00bc 2:41 10 3eT1:61 \u00f05\u00de In addition, following the same procedure used by Alimardani et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002965_j.ijheatmasstransfer.2019.118464-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002965_j.ijheatmasstransfer.2019.118464-Figure7-1.png",
        "caption": "Fig. 7. With triangles meshed surface of the component including the normal vectors in the edge area.",
        "texts": [
            " Elements which are included by the track geometry during simulation are then activated. But in contrast to the death/ birth methodology, the current track geometry is not represented by the activated elements, but by a free form surface of its own, which is introduced to it and represents the same. For this purpose, the surface of the component is first derived from the 3D hexahedral element mesh. The resulting 2d finite elements mesh consists of quadrilateral elements that are transformed into a triangle mesh (Fig. 7) with which it is easier to reconnect and thus regularize curvilinear limited areas. This triangular mesh is divided into a part on which the welding tracks are built up (yellow, Fig. 7) and a part that remains unchanged during the process. Normal vectors are derived on the yellowmarked area at the nodes (Fig. 7). For the calculation of the melt pool surface, each node is allowed a degree of freedom of movement in the direction of the normal one (see Fig. 8). With respect to these degrees of freedom, the melt pool surface is calculated at a certain point in time as the minimum of the surface energy. The time dependent three-phase line is given as a Dirichlet condition and the variation of the melt volume is taken into account as a constraint. If the surface of the component does not correspond to one of the three Cartesian planes in all surface areas, it is possible to t) and mesh extension for model-theoretical coverage of track formation (right)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.9-1.png",
        "caption": "Fig. 13.9 Hebson coupling (a) and Tracta coupling (b)",
        "texts": [
            " Every one of the eight mechanisms has been used in patented shaft couplings. Detailed documentations see in Kutzbach [10, 11], Duditza [5] and Seherr-Thoss/Schmelz/Aucktor [17]. In most engineering realizations adjacent joint axes are either parallel or at right angles. This is not a necessary condition. The only necessary condition, in addition to symmetry, is that the shafts must have the freedom to rotate full cycle. A homokinetic coupling based on the chain RSR was shown in Fig. 4.11. A coupling based on the chain CRC is shown schematically in Fig. 13.9a . It was known to Koenigs [9] already. The patented engineering realization is known as Hebson coupling. A single chain CRC suffices. The second chain CRC is added in order to diminish dynamical unbalance (total balance is achieved when shafts 1 and 2 are collinear). In a Hebson coupling a larger number of chains is evenly distributed around the cylinders. The joints R in these chains may be replaced by spherical joints since the additional degrees of freedom thus introduced are passive. With this coupling inclination angles up to 90\u25e6 are possible. The so-called Tracta coupling shown schematically in Fig. 13.9b is based on the chain RER . The chain is encapsulated in two concentric spherical shells which together represent the spherical joint connecting shafts 1 and 2 . The axes of both revolutes R are in the plane E . Each revolute axis intersects one shaft axis orthogonally. Rotations in these revolutes keep plane E normal to plane \u03a3 independent of the angular position \u03d5 of the shafts. In the figure plane E is shown in the positions \u03d5 = 0, \u03c0 and \u03d5 = \u00b1\u03c0/2 . The Tracta coupling is widely used in the automotive field because of the following properties: Inclination angles up to 50\u25e6 ; compact form; simple assembly; no loss of lubrication; large wear-resistant contact surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.28-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.28-1.png",
        "caption": "Figure 6.28. Motion of a particle relative to the Earth.",
        "texts": [
            "107) yields (6.1 12k) derived earlier for the free fall case in which terms of order Q2 were neglected. 6.18.1. First Order Vector Solution for Projectile Motion The approximate solution (6.l14f) for the motion of a particle under a constant force is applied to investigate the Coriolis effect on the motion of a projectile P fired at Xo = 0 with a relative muzzle velocity Vo = V(cosai + cos,8j + cos yk) . (6.1l5a) Here a, ,8, yare the direction angles of the gun in theframe rp = {o; i, j, k} defined in Fig. 6.28 . The usual extraneous effects are neglected. Then only the body force f=g= -gk per unit mass acts on P. We thus recall (6.107) and (6.115a) to derive from (6.114f) the following estimate for the projectile's motion relative to the Earth: x(P, t) = Vt(cos a +Qt cos,8 sin A)i [ Qg~ ]+Vt cos,8 - Qt(cos y cos A+cos a sin A)+ ]V cos A j + Vt (COSY + QtcOS,8COSA - :~) k. (6.115b) Example 6.16. Determine the Coriolis deflection of a projectile fired eastward at latitude A. Derive the classical relations for the motion and the range when the Earth's rotation is neglected. Dynamics of a Particle 191 Solution. Since the projectile is fired due east (the j direction in Fig. 6.28), the angle of elevation is {3. Then a = n /2, y = 1- - (3, and (6.115b) becomes xC?, t) = QVt2 cos {3 sin Ai ( Qgt2 )+ V t cos {3 - Qt sin {3 cos A+ 3V cos A j ( . gt)+ V t SIn {3 + Qt cos (3 cos A - 2V k. (6.1 16a) (6.116b) First consider the case when the Earth 's rotation is neglected. With Q = 0, (6.116a) reduces to the classical elementary solution for projectile motion: xC?, t) = Vt cos{3j + Vt (sin{3 - :~ ) k. The time of flight t * = (2V sin (3)/g for which z(t*) =\u00b0is then used to find the projectile's range r == y (t* ), namely, V2 r = -sin2{3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002618_b978-0-12-814062-8.00015-7-Figure13.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002618_b978-0-12-814062-8.00015-7-Figure13.1-1.png",
        "caption": "Figure 13.1 Schematic drawings of SLM specimens with surfaces of different orientations to the build platform. For inclined surface ((A) up-skin and (B) down-skin surfaces), an inclination angle \u03b8 is used to describe the orientation. SLM, Selective laser melting.",
        "texts": [
            " One advantage of the SLM process is the ability to manufacture geometrically complex structures with high resolution. However, the surface roughness of SLMed parts remains a drawback of the SLM process for applications in the aerospace industry where the parts are subject to fluid flow [2] or cyclic loading [3]. In general, surfaces of different orientations can be classified into horizontal (top) surfaces, vertical (side) surfaces, upward-facing surfaces (up-skin), and downward-facing surfaces (down-skin) (refer to Fig. 13.1 for illustration). The processing conditions of SLM process has a significant influence on the roughness on horizontal and vertical planes of SLMed metallic parts. The effects of layer thickness and laser scan speed on the side surface of a one-pass thin wall sample were explored experimentally [4], a low-speed and a small-layer thickness produced rough side surface due to excess heat input; on the other hand, surface become porous when scan speed and layer thickness exceeded a certain value. In another study of one-pass thin-wall sample [5], the optimum linear energy density Additive Manufacturing for the Aerospace Industry",
            " Three sets of pre-developed SLM parameters termed as \u201cPerformance,\u201d \u201cIntermediate,\u201d and \u201cSpeed\u201d were applied to make the samples [27] (Table 13.1). \u201cPerformance\u201d parameter set was designed for making parts with maximum relative density; \u201cSpeed\u201d parameter set aimed to build parts with highest feasible production rate; \u201cIntermediate\u201d parameter set was a balance of the former two. To study the effect of different inclination angle on surface roughness, cuboid samples with two parallel inclined surfaces to the substrate were fabricated. Each sample possesses a pair of up-skin and down-skin surfaces with the same \u03b8 angle to the substrate (Fig. 13.1). As a means to improve surface finish and dimensional accuracy, a contour scan over the edge of the scan area was performed for each layer after the laser exposure of the core area (Fig. 13.2). Same contour parameters were applied for \u201cPerformance\u201d and \u201cIntermediate\u201d samples because these two groups shared the same layer thickness (Table 13.2). A Mitutoyo Surftest SJ410 machine was used to conduct the surface roughness measurements by stylus contact method. The stylus traverse direction was set to be perpendicular to the layer boundaries for all the measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.124-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.124-1.png",
        "caption": "Fig. 2.124 Tandem E-M motor [Fichtel and Sachs].",
        "texts": [
            " Tandem E-M Motor - The part to be subsequently explained is the tandem E-M motor that is composed of two separate brushless DC-AC macrocommutator IPM magnetoelectrically-excited synchronous motors installed on one flange and driving the rear or front wheels in absolute autonomy. Similar to the on-board M-E generator, it is an outer rotor structure. The tandem E-M motor may have 2 \u00d7 27 kW constant power output and 2 \u00d7 30 k W peak power output (delta connected). The electrical machines and their ASIM AC-DC/DC-AC macrocommutator may be water-cooled. The tandem E-M motor torque control is also affected by means of a CAN-bus interface. Figure 2.124 shows the tandem E-M motor. Automotive Mechatronics 318 CH-E/E-CH Storage Battery -- A NiMH storage battery may be used as an electrical energy store (EES) and as a shock absorber between the ESU and traction tandem E-M motors, To cut off the storage battery from the transitional circuit, a main switch is used that has been installed into a switch cupboard. The high-performance, all-round energy-efficient, mechatronically-controlled trimode HEV, termed the \u2018Poly-Supercar\u2019, shown in Figure 2.125, may be an advanced ultra-light hybrid that means it will be electrically-powered by a highdensity mechanical energy-storing, high-angular-velocity M&GF pack that is backed up by primary energy sources (PES), a small hydrogen (metal-hydrate) combustion gas turbine-generator/motor (GT-G/M) that is based on the Fijalkowski turbine boosting (FTB) system, or the Fijalkowski enginegenerator/motor -(FE-G/M) and electrified highway or powered roadway designed to extend the HEV\u2019s range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.27-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.27-1.png",
        "caption": "Fig. 17.27 Four-bar generating a coupler curve with symmetry axis y",
        "texts": [
            " The figure shows also one of the cognate four-bars which, according to the Roberts-Tschebychev theorem, generate the same coupler curve. The third four-bar is the reflection of the second in the midnormal of the base A0B0 . The parameters of the second four-bar are denoted r\u20321 , a \u2032 , r\u20322 , b \u2032 1 , b \u2032 2 . They satisfy the condition r\u20322 = b\u20322 = a\u2032 . Hence also this is a sufficient condition for the coupler curve to be symmetric. The symmetry axis passes through C0 , and its inclination angle against the base line C0A0 is \u03b2/2 . The angle at C is \u03b2\u2032 = \u03c0/2\u2212\u03b2/2 . In Fig. 17.27 this kind of four-bar A0A1B1B0 with coupler point C is shown again, but this time with the usual notation, i.e., r2 = b2 = a instead of r\u20322 = b\u20322 = a\u2032 and \u03b2 instead of \u03b2\u2032 . The length of the input link is r . The symmetry axis of the coupler curve passes through B0 under the angle \u03c0/2\u2212 \u03b2 against the base line. The symmetry axis is made the y -axis of an x, y -system with origin B0 . At B1 the transmission angle 2\u03b1 is shown. It is convenient to use \u03b1 as independent variable for the x, y-coordinates of C ",
            "140) the function \u0394n is replaced by \u03bb\u0394n with an arbitrary constant \u03bb , the solutions for p0 , . . . , pn , x1 , . . . , xn+2 remain unaltered, but D is replaced by \u03bbD . Now back to straight-line approximations. In [40] p.51 Tschebychev investigated the family of coupler curves which are symmetric with respect to the midnormal of the base A0B0 and among these coupler curves those which approximate a straight line parallel to the base. Roberts\u2019 coupler curve belongs to this family. Watt\u2019s does not. For the family of symmetric coupler curves the parameter Eqs.(17.104), (17.105) based on Fig. 17.27 are used11: y(\u03b1) = 1 2 [ 4a2(cos\u03b2 sin\u03b1 cos\u03b1+ sin\u03b2 sin2 \u03b1) + ( 2 \u2212 r2)(sin\u03b2 + cos\u03b2 cot\u03b1) ] , x(\u03b1) = \u00b1\u221a4a2 cos2(\u03b1\u2212 \u03b2)\u2212 y2 . \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad (17.143) The symmetry-axis is the y -axis. The constant parameters of the four-bar are , r , a , \u03b2 , and the free parameter is the angle \u03b1 . Intersection points of the coupler curve with the y -axis are associated with one of the angles (see (17.106)) sin\u03b1 = \u2213 r 2a . (17.144) 11 The four-bar analyzed in [40] p.51 is the one with symmetries r1 = r2 and b1 = b2 . Only later Tschebychev [40] p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000412_156855309x420039-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000412_156855309x420039-Figure19-1.png",
        "caption": "Figure 19. 4.1\u20134.5\u25e6 (walk to trot).",
        "texts": [
            " 15, there is a remarkable difference in hind leg motion. 494 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 495 496 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 497 498 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 499 In the simulation, the slope angle was changed gradually from 4.1\u25e6 to 4.5\u25e6. Limit cycles in Fig. 19 are not clear and we cannot see what kind of gait was used. In the time interval from 10 to 20 s, limit cycles in Fig. 21 are similar to those in Fig. 15. In the time interval from 30 to 40 s, limit cycles in Fig. 23 are similar to those in Fig. 17. Figure 21 is the simulation data for a slope angle of 4.1\u25e6. Figure 23 is the simulation data for a slope angle of 4.5\u25e6. Thus, it can be said that Quartet 4 with the invariable body can change its walk gait to trot continuously when the slope angle was gradually changed from 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure6-1.png",
        "caption": "Fig. 6. Geometry of medium gear and IHB gear.",
        "texts": [
            " 5 (a) and (b), the contact line L I between the IHB gear and the medium gear, and the contact line L II between the OPE hourglass worm and the medium gear are simultaneously present on the medium gear tooth surface. These contact lines do not coincide but intersect each other. Therefore, after the medium gear is removed, the meshing between the OPE hourglass worm and the IHB gear is in-point contact, as shown in Fig. 5 (c). The contact line between the IHB gear and the medium gear in coordinate system \u03c3 1 is shown in Fig. 6 (a). The IHB gear tooth surface and contact line L I are projected onto the plane x 1 o 1 y 1 , as shown in Fig. 6 (b). The cross section tooth profile of IHB gear is an involute curve, and the cross section tooth profile of medium gear is a beeline, as well as the geometry relationship of cross section tooth profile is illustrated in Fig. 6 (b). In coordinate system \u03c3 1 , the unit normal vector of the IHB gear surface 1 is given as follows: n R 1 ( u , \u03b8 ) = [ \u2212 sin ( \u03b4\u2212\u03b8\u2212u ) \u221a 1+ cos 2 \u03b1tan 2 \u03b2R \u2212 cos ( \u03b4\u2212\u03b8\u2212u ) \u221a 1+ cos 2 \u03b1tan 2 \u03b2R cos \u03b1 tan \u03b2R \u221a 1+ cos 2 \u03b1tan 2 \u03b2R ] T (13) In coordinate system \u03c3 1 , the unit normal vector of the medium gear surface g is given as follows: n R 1g = M R 1g M R ga n R a (14) Where M R 1 g = [ cos (\u03b4 \u2212 \u03b8 \u2212 u ) sin (\u03b4 \u2212 \u03b8 \u2212 u ) 0 \u2212 sin (\u03b4 \u2212 \u03b8 \u2212 u ) cos (\u03b4 \u2212 \u03b8 \u2212 u ) 0 0 0 1 ] , M R ga = [ 1 0 0 0 sin \u03b2bR \u2212 cos \u03b2bR 0 cos \u03b2bR sin \u03b2bR ] Using Eqs. (13) and (14) , the relationship between unit normal vector n R 1 and n R 1 g is described as: n R 1 = kn R 1 g (15) Where, k is a constant. Hence the medium gear tooth surface is tangent to the IHB gear tooth surface in contact position. In Fig. 6 , point P 1 and P 2 are the contact point of involute curve and straight on IHB gear end-face. Based on the forma- tion method of helical gear tooth surface, the connection of point P 1 and P 2 is the contact line L I . Therefore, on the tooth surface g of right flank, the contact line L I can be described as: r R I ( m R ) = [ x I 1 R y I 1 R z I 1 R ]T = \u23a1 \u23a3 r b cos ( \u03b4 \u2212 \u03b80 R \u2212 u ) \u2212 r b m R sin ( \u03b4 \u2212 \u03b80 R \u2212 u ) \u2212r b sin ( \u03b4 \u2212 \u03b80 R \u2212 u ) \u2212 r b m R cos ( \u03b4 \u2212 \u03b80 R \u2212 u ) r b ( m R \u2212 u ) / tan \u03b2bR \u23a4 \u23a6 (16) In the same way, the contact line can be described on the tooth surface g of left flank as follows: r L I ( m L ) = [ x I 1 L y I 1 L z I 1 L ]T = \u23a1 \u23a3 r b cos( \u03b4 \u2212 u ) \u2212 r b m L sin( \u03b4 \u2212 u ) r b sin( \u03b4 \u2212 u )+ r b m L cos ( \u03b4 \u2212 u ) r b ( m L \u2212 u ) / tan \u03b2bL \u23a4 \u23a6 (17) Where, m and m are the line parameters of L I on the right flank and the left flank, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000549_j.engappai.2008.12.005-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000549_j.engappai.2008.12.005-Figure2-1.png",
        "caption": "Fig. 2. ANM fully connected structure with NIN+NOUT neurons, NIN inputs Ui and NOUT outputs Y\u0302j.",
        "texts": [
            " Let us define NIN and NOut, respectively, as the number of plant inputs and outputs and assume that NIN \u00bc NOut, where IN and OUT represent the set of input and output indexes. The autonomous evolution of ANM and NC starts from zero values. It results in a compact IDNC structure with a small number of nodes. For ANM, the total number of neurons Nm, is chosen equal to NIN+NOUT, so that any node is either an input node or an output node but not both at same time, in order to avoid perturbing any output signal with input ones (Fig. 2). Additional nodes are useless (Leclercq et al., 2005). For NC, the total number of neurons Nc is chosen equal to 2NOUT, the NC inputs are the NOUT plant desired outputs and the NOUT output error functions (Fig. 3). Both adapting processes (ANM, NC) act synchronously and there is not any pre-training or post-training phase but only an online updating of the weights, time parameters and adaptation parameters. Inputs and outputs signals of ANM, NC and plant are normalized in the range of [ 1, 1]. Let us define t \u00bc kDT where DT is a sampling period and k an integer",
            " The real-time adaptation provides an efficient compensation of the unpredictable process disturbances and sensor noises. Let us notice that the aim of ANM is not to provide a complete dynamical model of the process but to obtain an estimation of the process output for a short time window. It is not our intention to memorize the dynamics of the controlled system, but just to estimate the instantaneous output which will be used to update the controller parameters. Consequently, the complexity of ANM is reduced to a small number of neurons and parameters. The ANM shown in Fig. 2 is developed with fully connected recurrent neural networks (Leclercq et al., 2005). The dynamics of the Nm neurons take the following form in continuous time: 1 jtm\u00f0t\u00dej dY\u0302i\u00f0t\u00de dt \u00bc Y\u0302 i\u00f0t\u00de \u00fe tanh XNm j\u00bc1 Wij\u00f0t\u00deY\u0302 j\u00f0t\u00de \u00fe Xi\u00f0t\u00de 0 @ 1 A (1) with Xi(t) \u00bc Ui(t) if iAIN and Xi(t) \u00bc 0 if iAOUT. Y\u0302i(t), Wij, 1/tm(t) and Ui(t) represent, respectively, the ith neuron state, the ANM weight from jth neuron to ith neuron, the ANM adaptive time parameter and the NC output. Let us define Y\u0302(k) \u00bc (Y\u0302i(k)), iAOUT, as the estimated output vector of the plant at time t \u00bc kDT"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002632_j.optlastec.2019.05.008-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002632_j.optlastec.2019.05.008-Figure10-1.png",
        "caption": "Fig. 10. Schematic diagram of powder fusion spreading process: (a) low laser power; (b) high laser power.",
        "texts": [
            " After the powder melted to form a melt pool, the absorption of the laser by liquid metal significantly improved. Therefore, the penetration of the single track increased linearly with an increase in the laser power. Since the diameter of the laser spot was 100 \u03bcm, the width increase of the single track was limited when the width was significantly larger than 100 \u03bcm. The line energy density had less influence on the width than that of the penetration of the single track. The melt pool shape and schematic diagram of powder fusion spreading process are shown in Fig. 10. According to Eq. (1), at a constant powder thickness and scanning speed, the line energy density was controlled by the laser power. The line energy density had a direct influence on the size of the melt pool and the spreading properties of liquid metals. At a low laser power, the melt mode was laser thermal conductivity welding. The size of the melt pool was small, and the spreadability was poor. The hole and balling defects formed easily at the surface of the single track. At a high laser power, the welding mode was laser deep penetration welding, and the keyhole formed during the SLM process [25]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.7-1.png",
        "caption": "Figure 7.7. Spring deflection due to impact by a falling body.",
        "texts": [
            " The first integral of the equation of motion ms = d(!mIs2) /ds = -vmg yields the general form of work-energy equation: (7.41b) When s = e, Is = 0, we obtain (7.41a). Conversely, differentiation of the workenergy equation (7.41b) with respect to either s or t yields the equivalent equation of motion . D Example 7.7. A mass m is dropped from a height h onto a linear spring of constant stiffness k and negligible mass. Determine the maximum deflection 8 of the spring, and compare this value with the static spring deflection 8s produced by m, See Fig. 7.7. Assume that m maintains contact with the spring in its motion following the impact. Solution. Since the velocity of m is zero at both its initial and terminal states at 1 and 3 in Fig. 7.7, the change in its kinetic energy on the path {i' is zero. Because the mass of the spring is negligible , its kinetic energy may be ignored . Moreover, all the forces that act on m are constant, workless, or vary only with the particle's position on f!i. Therefore, the work-energy principle may be applied . Momentum, Work, and Energy 239 (7.42a) The total work done by the forces acting on m from its initial position I to its final position 3 on (\u00a7 is determined by (7.21) in which {i = {it U {i2.We note that the instantaneous impulsive force of the spring does no work on m. The free body diagrams in Fig. 7.7 show that the force acting on m over {it is F 1 =mgi and over (\u00a72 is F2 = (mg - kx2)i. Hence, I f/ = { F\u00b7 dx+ I.F\u00b7 dx = {h mgdx, + {8(mg - kx2 )dx2 .le, e2 10 10 The work-energy equation (7.36) thus yields I f/ = mgh + mg8 - ~k82 = /)\"K = 0, which determines the following deflection of the spring: mg J(mg)2 2mgh8=-+ - +--. k k k (7.42b) (7.42c) (7.42d) The static deflection that would result from the weight alone is 8s = mg]k. Use of this relation in (7.42c) gives 8 = 8s +J8~ + 28sh :::: 28s\u00b7 This formula shows that the dynamic deflection 8 is not less than twice the static deflection 8s",
            "76), that R\u00a2 = s is the tangential component of the acceleration, and W cos \u00a2 = F, is the conservative tangential component of the total force F = W +N acting on m in Fig. 7.9, whose workless normal component is Fn = N - W sin \u00a2 . 0 Let the reader consider the following example . Exercise 7.10. Apply the principle of conservation of energy to solve Example 7.7, page 238. Derive the equation for the maximum spring deflection resulting from the impact by a mass m falling through a height h shown in Fig. 7.7. 0 The centripetal acceleration of a particle in a moving frame tp = {O ; ek} gives rise to a central directed, apparent centrifugal force P(x, t)= -mw X (w X x). So, consider a radial motion with x = re, in tp and wet) = w(t)ez = cae., say, then P(x , t) =mrw2er in a cylindrical reference basis . Notice that this force has a potentialfunction r ex, t) = -!mr2w2,suchthatP = -V r(x, t) = -a r jarer = mrw2er \u2022But this is not a conservative force, because the potential function r ex, t) varies with both position and time, indeed, with w = at , a r jat = -mr2a2t"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.9-1.png",
        "caption": "Fig. 14.9 Resultants SC (a) and CS (b) . Pole P and angle \u03d5 of the rotation C , line of reflection g , line g\u2032 and translation t of the resultant glide reflection",
        "texts": [
            " In this case, \u03d5 = \u03c0 , and the pole P is midpoint between A1 and A\u2032 1 and also midpoint between A2 and A\u2032 2 . End of proof. The resultants SC and CS : Both resultants are glide reflections. For both resultants the line of reflection and the translation along this line are constructed geometrically by displacing an isosceles triangle from an initial position 1 via an intermediate position 2 into the final position 3 . This geometrical approach is simpler than the analytical approach by means of complex numbers. First, the resultant SC is considered. In Fig. 14.9a the point P is the pole of the rotation C , and g is the reflecting line of the subsequent reflection S . Let \u03d5 be the angle of the rotation C (positive counterclockwise). In the intermediate position 2 following the rotation the triangle has the apex P , the apex angle \u03d5 and the base on g . From this position 2 422 14 Displacements in a Plane the initial position 1 is obtained by the inverse of the rotation C , i.e., by clockwise rotation through \u03d5 about P . The final position 3 is the result of reflecting position 2 in the line g ",
            " In position 3 these points assume the positions A\u2032 1 , A\u2032 2 , A\u2032 3 . The desired line g\u2032 of the glide reflection is the line passing through the midpoints between Ai and A\u2032 i (i = 1, 2, 3). Two of these midpoints coincide. The line g\u2032 makes the angle \u03d5/2 with g . It is orthogonal to the lines A1A \u2032 2 and A\u2032 1A \u2032 3 . Hence the distance between these two lines is the translation of the glide reflection along g\u2032 . In terms of the distance h of P from g this translation t is 2h sin\u03d5/2 in the direction shown by the arrow. Next, the resultant CS is considered (Fig. 14.9b). The pole P and the angle \u03d5 of the rotation C as well as the line g of the reflection S are as before. Positions 1 and 2 of the triangle before and after the reflection and the final position 3 after the rotation are as shown. The points initially located at A1 , A2 , A3 assume the final positions A\u2032 1 , A \u2032 2 , A \u2032 3 . The line g\u2032 of the glide reflection is determined as before. Again, two of the midpoints between Ai and A\u2032 i (i = 1, 2, 3) coincide. The line g\u2032 makes the angle \u03d5/2 with g , but this time to the other side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003251_s12540-020-00793-8-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003251_s12540-020-00793-8-Figure2-1.png",
        "caption": "Fig. 2 Extraction areas of horizontal and vertical a wear samples b tensile samples",
        "texts": [
            " All the layers in the CW wall were built on each other using the mentioned process. Also, a manually operated hydraulic press was utilized to deform the layers. To investigate the effects of cold working on the walls\u2019 mechanical properties and isotropy of tensile properties in vertical and horizontal directions, both AD and CW walls 1 3 were machined in the same dimensions. Then, the tensile test samples were prepared in accordance with the process described in the following. As can be seen in Fig.\u00a02a, vertical (V) and horizontal (H) tensile test samples were extracted from the top (HT), middle (HM), and bottom (HB) of the walls in the determined areas. For the repeatability of the tensile test results, three tensile samples were taken from each of the mentioned areas (V, HT, HM, HB). The tensile samples were prepared in the dimensions of 100 mm \u00d7 10 mm \u00d7 6 mm according to ASTM E 8M standard. All the tensile tests were carried out at room temperature with the strain rate of 0.15 mm/mm/min. Table\u00a01 presents the specifications of the tensile and wear samples. The samples for microstructural investigation were cut from the middle of the AD and CW walls, perpendicular to the layers. Then, they were polished and etched in an electrolyte solution containing 40 ml H2O and 60 ml HNO3 at a voltage of 1.1 V for 120 s. The samples were characterized using optical microscopy (OM) and the scanning electron microscopy (SEM). As can be seen in Fig.\u00a02b, vertical (V) and horizontal (H) wear test samples were extracted from both AD and CW walls. The pin-on-disk wear tests were carried out at the ambient temperature in dry sliding conditions, in accordance with ASTM-G99-05 standard [16]. Before the test, the entire surface of the samples was prepared by emery cloths No. 80 to 2000 and polished using a 0.3 \u00b5m Alumina solution. The samples were ultrasonically washed in an alcohol-acetone solution before and after the test. Next, they were weighed using the A&D scale N92 with an accuracy of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000717_s12541-010-0076-2-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000717_s12541-010-0076-2-Figure2-1.png",
        "caption": "Fig. 2 Kinematic relationship between a grinding wheel and a screw rotor",
        "texts": [
            " The grinding wheel is considered to be at rest in the process of generation and the rotor being generated performs the screw motion around its axis with the screw parameter ,p where / 2 ;p H \u03c0= the axes of the grinding wheel and the rotor are crossed forming the mounting angle .\u03a3 Figure 1 shows the geometry relationship between a grinding wheel and a screw rotor. In the process of grinding, the grinding wheel performs rotation around its axis but this is related to the velocity of grinding only and may be ignored when the mathematical aspects of rotor generation are considered. The radii of a contact point M in coordinate systems 1 ,\u03c3 u \u03c3 are ,r , u r respectively. Figure 2 shows the kinematic relationships between a grinding wheel and a screw rotor. The CBN wheel is a surface of revolution. Therefore, the shape of the CBN wheel will be known if the axial section of the surface of revolution is given. According to Figure 1 and Figure 2, the radii of a contact point M in coordinate system 1 \u03c3 and u \u03c3 can be expressed as Eq. (1): 1 1 1 1 1 1 1 u u u u u u u r x i y j z k r x i y j z k  = + +  = + + (1) Eq. (1) can be transformed as seen in Fig. 2(b): 1 ( ) ( ) u u u r r p k xi yj z p k r r A i x A i yj zk \u03d5 \u03d5 = \u2212 = + + \u2212  = \u2212 = \u2212 + + (2) The angular and the velocity of the contact point M in the 1 \u03c3 and u \u03c3 can be deduced as followings, respectively: 1 1 1 0 1 1 1 1 1 1 1 1 1 1 ( ) k v r v y i x j pk \u03c9 \u03c9 \u03c9 \u03c9  =  = \u00d7 + = \u2212 + + (3) 0 ( ) u u u u u u u u u u u u k v r v y i x j \u03c9 \u03c9 \u03c9 \u03c9  =  = \u00d7 + = \u2212 + (4) Then transforming Eq. (3) and Eq. (4) into the fixed coordinate system \u03c3 : 1 1 1 1 ( ) k v yi xj pk \u03c9 \u03c9 \u03c9  =  = \u2212 + + (5) ( sin cos ) [( sin cos ) ( )cos ( )sin ] u u u u u u j k v z y i x A j x A k \u03c9 \u03c9 \u03c9  = \u2212 \u03a3 + \u03a3  = \u2212 \u03a3 \u2212 \u03a3  + \u2212 \u03a3 + \u2212 \u03a3 (6) Substituting 1 v and u v into 1 1 ,u u v v v= \u2212 the relative speed 1u v of the contact point M can be given by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001614_rnc.3788-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001614_rnc.3788-Figure1-1.png",
        "caption": "Figure 1. Diagram of the simulated truck-trailer model.",
        "texts": [
            "tk/ is projected in the interval \u0152 ; . That is to say, \u0131V .tk/ 6 0 for all s.tk/ \u00a4 0 can be achieved, and the sliding mode is enforced in finite time, as well as the overall system in (2) is asymptotically convergent. This completes the proof. Copyright \u00a9 2017 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control (2017) DOI: 10.1002/rnc In this section, a truck-trailer model [41] is exploited to test and verify the availability of the sliding mode fault-tolerant control scheme presented in the proposed results. Figure 1 shows the model diagram. The state space equation of the truck-trailer model is expressed in (29).8\u0302\u0302< \u02c6\u0302: Px1 D v Nt LNt0 x1 C v Nt l Nt0 u; Px2 D v Nt Lt0 x2; Px3 D v Nt Nt0 sin. v Nt LNt0 x1 C x2/; (29) where x1, x2, and x3 are respectively the angle difference between truck and trailer, the angle of trailer, and the vertical position of rear end of trailer. L D 5:5m, l D 2:8m, v D 1:0m/s, Nt D 2:0 s, and Nt0 D 0:5 s. Under the sampling period T D 0:02 s, the discreted system in \u0131-domain from (29) is obtained as follows: \u0131x"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.71-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.71-1.png",
        "caption": "Fig. 2.71 Contemporary four-velocity automatic transmission with fluidodynamical M-M torque converter (CT) and human driver-selected operating modes [Renault and Volkswagen ; SEIFFERT AND WALZER 1991].",
        "texts": [
            " At present, a computer controls the transmissions; the automotive vehicle can agree with the driver\u2019s agility and change gear. The system can also be tuned for economic, sporty, or winter characteristics. In some automotive vehicles, a choice can be made between manual and automatic transmissions. When driving with manual shift, the transmission\u2019s computer betters the driver if she/he tries to shift in a less suitable situation. The computer may make the shift as soon as the situation is considered suitable. In Figure 2.71, as an example of this development, a mechatronically controlled four-speed automatic transmission with driver-selected operating modes is shown. This automatic transmission uses a torque converter (TC) that allows the ECE or ICE to spin somewhat independently of the transmission. The torque converter (TC) with its connections to the ECE or ICE and the transmission is shown in Figure 2.72. The M-F pump inside a TC is a type of centrifugal M-F pump. As fluid is flung to the outside, a vacuum is created that draws more fluid in at the centre"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001848_s1061830916060097-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001848_s1061830916060097-Figure2-1.png",
        "caption": "Fig. 2. A flowchart of the selective laser melting system.",
        "texts": [
            " Samples were manufactured with a 280 HL selective laser melting system (SLM Solution GmbH SLM) that is shown in Fig. 1. The system is equipped with two ytterbium fiber lasers with powers of 400 and 1000 W, a characteristic wavelength of 1070 nm, and the maximum scanning speed up to 15 m/s. The maximum dimensions of products (280 \u00d7 280 \u00d7 350 mm) are limited by the system\u2019s working chamber. Products are constructed in an inert-gas atmosphere (nitrogen or argon). A flowchart of the selective laser melting system is presented in Fig. 2. A detailed description of the SLM process for manufacturing of articles can be found in [3, 4]. A LASER ULTRASONIC TECHNIQUE FOR STUDYING THE PROPERTIES 305 The powder of an Inconel 718 heat-resisting alloy that was supplied by the manufacturer of the SLM system was used as a raw material. The chemical composition of the Inconel 718 alloy is listed in Table 1. The laser-ultrasonic method, in which characteristics of ultrasonic waves are registered in a test object, was used as a nondestructive testing method in this article"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.47-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.47-1.png",
        "caption": "Fig. 3.47 Structural and functional block diagram of the BBW AWB dispulsion mechatronic control system [Freescale Semiconductor Inc. \u2013 Flex Ray\u2122; FREESCALE 2004, 2005B].",
        "texts": [
            " A BBW AWB dispulsion mechatronic control system uses electrical connections to connect the four braking \u2018corners\u2019 to the brake-pedal and to each other. This system provides better control of brake pedal stiffness, traction control, vehicle stability, and brake-force distribution. A BBW AWB dispulsion mechatronic control system requires high-performance control architecture, for example, such as the one offered by the MPC500/MPC5500 microcontroller family from Freescale Semiconductor Inc., shown in Figure 3.47 [FREESCALE 2004, 2005A]. Automotive Mechatronics 518 Furthermore, high-speed protocol networks that are deterministic, faulttolerant, and capable of supporting distributed control systems are necessary. FlexRay provides these capabilities and more [FREESCALE 2004, 2005A]. Consequently, a change is afoot, and the FlexRay is an innovative communications protocol designed for the high data transmission rates required by advanced automotive mechatronic control systems. These are the same mechatronic control systems that, in the next few years, are expected to replace nearly every fluidical or pneumatical line and mechanical cable in most recent automotive vehicles with electrical or optical wire-based networks, sensors, and actuators [FREESCALE 2004, 2005A]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000268_tmag.2008.921097-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000268_tmag.2008.921097-Figure1-1.png",
        "caption": "Fig. 1. Static eccentricity: (a) cross section of stator and rotor positions, (b) static degree definition.",
        "texts": [
            "5, a two-dimensional (2-D) finite-element-analysis (FEA) software package, is employed to obtain mutual fluxes and mutual voltages in both healthy and faulty SRMs. Different types of the eccentricities are static eccentricity, dynamic eccentricity, and mixed eccentricity. In static eccentricity, the rotor rotation axis coincides with its symmetry axis but displaces from the stator symmetry axis. In this case, air gap distribution around the rotor loses its uniformity but it is not time-variant. The static eccentricity degree, , is defined [Fig. 1(b)] as follows: (1) 0018-9464/$25.00 \u00a9 2008 IEEE where is the radial air gap length in the case of uniform air gap or with no eccentricity, is the stator symmetry center, is the rotor symmetry center, and is the rotor rotation center. and are called the initial static eccentricity angle and static transfer vector, respectively. This vector is constant for all rotor angular positions. In Fig. 1(a), shows the circle which is surrounding the outer faces of the rotor poles, while is inscribed in the stator and is surrounded by the outer faces of stator poles. Due to the fabrication tolerances, a relative eccentricity between the stator and rotor axes of 10% is very common. Also eccentricity degrees larger than 30% will not be considered in this paper. The proposed SRM is a 4-phase 8/6 motor, as illustrated in Fig. 2. Details of machine dimensions and material are given in Table I. Pole windings belong to each phase are connected in series"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.142-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.142-1.png",
        "caption": "Fig. 2.142 HEV driving circumstances during deceleration and braking [DRIESEN 2006].",
        "texts": [
            " Automotive Mechatronics 336 In Figure 2.140 HEV driving circumstances are shown during normal driving when the ICE starts and may drive the series/parallel HEV and produce electrical energy for the E-M motor or is charging the CH-E/E-CH storage battery. In Figure 2.141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 337 In Figure 2.142 HEV driving circumstances are shown during deceleration and braking the E-M motor is turned into a M-E generator to charge the highvoltage CH-E-CH storage battery. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 338 In Figure 2.143 HEV driving circumstances are shown during charging when the CH-E/E-CH storage battery gets low and the ICE may automatically start to recharge it. In Figure 2.144 HEV driving circumstances are shown during stopping when the ICE automatically shuts off when the series/ parallel HEV is stopped"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000773_j.mechmachtheory.2009.10.006-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000773_j.mechmachtheory.2009.10.006-Figure1-1.png",
        "caption": "Fig. 1. Geometry of the platform mechanism.",
        "texts": [
            " Evidently, at a certain degree of shakiness any construction will become finitely mobile even with zero backlashes. We are going to show that a double planar platform mechanism is mobile if in a general position it is shaky up to the fourth degree. Moreover, the platform is then architecturally mobile, i.e. it is mobile if we start with locked actuators from any architecturally possible position. Two Cartesian coordinate systems fO; E1; E2; E3g and fo; e1; e2; e3g help to describe the relative position of the platform with regard to the basis of the mechanism (Fig. 1). The first is fixed in the basis, the second in the platform. The points of attachment of the telescoping legs are located in the space spanned by the vectors E1 and E2 or the space spanned by e1 and e2 respectively: ya \u00bc ya1E1 \u00fe ya2E2; ra \u00bc ra1e1 \u00fe ra2e2; a \u00bc 1 6: \u00f01\u00de If we take the two Cartesian coordinate systems coinciding at the start, the positions of the anchors in the platform are given by: ra0 \u00bc ra1E1 \u00fe ra2E2: With Rodriquez0 pseudo vector w \u00bc n tan u 2 \u00f02\u00de the rotation tensor is given by R \u00bc I \u00fe 2 1\u00few w \u00bd\u00f0w \u00de \u00fe \u00f0w \u00de \u00f0w \u00de : \u00f03\u00de The components of the unit tensor I, the pseudo vector w and the tensor \u00f0w \u00de read in matrix form: I \u00bc 1 0 0 0 1 0 0 0 1 2 64 3 75; w \u00bc w1 w2 w3 2 64 3 75; \u00f0w \u00de \u00bc 0 w3 w2 w3 0 w1 w2 w1 0 2 64 3 75: \u00f04\u00de If the two Cartesian coordinate systems coincide at the starting point, the translation vector f \u00bc f1E1 \u00fe f2E2 \u00fe f3E3 \u00f05\u00de and the rotation tensor R transport the point with the position vector ra0 into the position: xa \u00bc f \u00fe R ra0: \u00f06\u00de If the platform is mobile and f and R are functions of time t for the velocity of the point with the position vector xa we obtain: x a dxa dt \u00bc va \u00bc f \u00fe R ra0 \u00bc f \u00fe \u00f0R RT\u00de ra \u00bc f \u00fex ra va \u00bc f \u00fex \u00f0xa f \u00de: \u00f07\u00de If instead of f we choose the position vector x0 leading to the point 0 of the platform which at the moment passes the origin O of the coordinate system in the base x0 \u00bc 0 E1 \u00fe 0 E2 \u00fe 0 E3 \u00f08\u00de we, by exchanging f $ x0 in (7), obtain for the velocity and its time derivatives: va \u00bc v0 \u00fex \u00f0xa x0\u00de; \u00f09:1\u00de v a \u00bc v 0 \u00fex \u00f0xa x0\u00de \u00fex \u00f0va v0\u00de; \u00f09:2\u00de v a \u00bc v 0 \u00fex \u00f0xa x0\u00de \u00fe 2x \u00f0va v0\u00de \u00fex \u00f0v a v 0\u00de; \u00f09:3\u00de v a \u00bc v 0 \u00fex \u00f0xa x0\u00de \u00fe 3x \u00f0va v0\u00de \u00fe 3x \u00f0v a v 0\u00de \u00fex \u00f0v a v 0\u00de: \u00f09:4\u00de It is worth noting that, although x0 is a zero vector at time t, it has non-vanishing time derivatives: x 0 \u00bc v0 \u00bc dx0 dt ; x 0 \u00bc a0 \u00bc d2x0 dt2 ; "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002576_j.promfg.2018.07.118-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002576_j.promfg.2018.07.118-Figure1-1.png",
        "caption": "Fig. 1. Experimental set up.",
        "texts": [
            " Laser deposition process For this experimental study, a DMG MORI LaserTec 65 3D\u2014a hybrid additive and subtractive five-axis machine tool\u2014was used. The machine includes a direct diode laser with a maximum power of 2,500 W at a wavelength of 1,020 nm. The beam is focused by a lens with a 200 mm focal length to a 3 mm spot size. Gas atomized super alloy INCONEL 718 powder of particle size 50-150 \u00b5m was used. Argon gas with a flow rate of 7 L/min was used as the shield gas and the conveying gas to deliver the powder coaxially to the melt pool. A schematic of the experimental configuration is shown in Fig. 1. Fig. 1. Experimental set up. An IN718 thin wall was deposited on a stainless steel 304 substrate. The wall was 120 mm in length, 60 mm in height, and one track thick, or approximately 3 mm. A thin wall was chosen so that temperature can be assumed constant through the wall thickness. The programmed layer height was 0.5 mm. The wall was created using a zig-zag tool path with no dwell between layers. Between layers, the laser was off while the motion system traversed vertically to the next layer. The laser tool path was reversed at the end of the substrate, so acceleration and deceleration occurred within the tool path during the process",
            " Laser deposition process For this experimental study, a DMG MORI LaserTec 65 3D\u2014a hybrid additive and subtractive five-axis machine tool\u2014was used. The machine includes a direct diode laser with a maximum power of 2,500 W at a wavelength of 1,020 nm. The beam is focused by a lens with a 200 mm focal length to a 3 mm spot size. Gas atomized super alloy INCONEL 718 powder of particle size 50-150 \u00b5m was used. Argon gas with a flow rate of 7 L/min was used as the shield gas and the conveying gas to deliver the powder coaxially to the melt pool. A schematic of the experimental configuration is shown in Fig. 1. An IN718 thin wall was deposited on a stainless steel 304 substrate. The wall was 120 mm in length, 60 mm in height, and one track thick, or approximately 3 mm. A thin wall was chosen so that temperature can be assumed constant through the wall thickness. The programmed layer height was 0.5 mm. The wall was created using a zig-zag tool path with no dwell between layers. Between layers, the laser was off while the motion system traversed vertically to the next layer. The laser tool path was reversed at the end of the substrate, so acceleration and deceleration occurred within the tool path during the process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001900_s11661-017-4219-2-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001900_s11661-017-4219-2-Figure1-1.png",
        "caption": "Fig. 1\u2014Schematic of the EBF3 build color coded with the three planes investigated in this study (a), IPF orientation maps of the alpha-phase and calculated prior-beta phase Z dir: jj ND\u00f0 \u00de, captured from the \u2018\u2018plan-view\u2019\u2019 XY plane of the substrate prior to deposition (b), (c), respectively, and the corresponding discrete pole figures Z dir: jj ND\u00f0 \u00de from the prior-beta phase (d).",
        "texts": [
            " A Ti-6Al-4V plate was heat treated above the beta transus temperature for twodays to intentionally produce large prior-beta grains. A rectangular parallelepiped with dimensions 109 59 5 mm3 that was contained within a single prior-beta grain was removed from the plate by wire electric discharge machining (EDM). The 109 5 mm2 face, which was parallel to {112}b, was polished and subjected to deposition using EBF3 with ~1.6 mm Ti-6Al-4V wire at NASA Langley Research Center. A schematic of the build is shown in Figure 1(a), with the build direction jj Z. The small single crystal sample was low temperature brazed onto a sacrificial Ti-6Al-4V plate along with run-on/off tabs to accommodate the start and stop positions of the deposit and leaves only steady-state deposit material on the single crystal. Fifteen layers were sequentially deposited along the same direction (X direction in Figure 1(a)) onto the substrate to create a simple two-dimensional wall shape. The deposited sample was sectioned parallel to the substrate surface at approximately the tenth layer. It was also sectioned transverse to the layer direction. Specimens were polished using standard metallographic techniques. Final polishing was performed on a vibratory polisher using 0.05-lm, non-crystallizing colloidal silica. The alpha-phase textures of the substrate and build were determined via electron backscatter diffraction (EBSD) in a PHILIPS/FEI XL-30 SEM (FEI Company, Hillsboro, OR) equipped with a field emission source",
            "[37] Using this approach, each a-phase montage was inverted to its respective prior b-phase EBSD map using the commercial software \u2018\u2018TiBOR\u2019\u2019 (Materials Resources LLC, Dayton, OH). This inversion code utilizes the equations from the work of Glavicic et al.,[34,35] but employs the quaternion parameterization of orientation space and examines average colony orientations, as opposed to using rotation matrices and Monte Carlo methods.[36,38] Prior to deposition, the initial texture of the substrate was verified. EBSD data were collected from the entire substrate deposition face in plan view (XY plane), as colored green in Figure 1(a). Figures 1(b) and (c) show Z-dir. IPF maps of the a-phase and calculated prior b-phase captured from this region. These data show that the entire build face was indeed a single orientation and that it was closely aligned with the {112}b. This is further illustrated by the discrete pole figures in Figure 1(d) where the projection normal is aligned with the build direction. In order to examine the development of texture in the build and the degree of epitaxial growth from the substrate, EBSD scans were collected in cross-section (YZ plane), as indicated by the blue plane in Figure 1(a). Figures 2(a) and (b) show montage X-dir. IPF maps of the a-phase and calculated prior b-phase captured from this orientation. Due to the geometry and size of the melt pool, a distinct region of ~1 mm maximum depth was observed between the build and the substrate. The corresponding textures in this region and adjacent regions were not found to be significantly different. A periodic horizontal banding was also observed near each concave layer boundary, shown most prominently in the alpha IPF map, Figure 2(a), and represents the beta transus boundary and the associated microstructural scale difference on either side of the boundary",
            "[30] on laser-remelted (011)-oriented CMSX-4 single crystals. In region 2, the (001)b pole figure (Figure 3(d)) revealed three principal intensities suggesting a \u2018\u2018smearing\u2019\u2019 of orientation about a near-cube texture component. In the Y\u2013Z cross-section, a preference to nearly align h001i with the deposition direction is observed. The relatively few grains in the Y\u2013Z cross-section preclude a clear view of the texture in region 2 and hence an additional scan was performed on top of the build in the XY plane indicated by the red plane in Figure 1(a). The Z-direction IPF map of the prior-b phase and the corresponding pole figures (Figure 4) were similar to those in region 2 (Figures 2(b) and 3(d)) with a near-cube preference 16.6 times random. In this case, however, the greater number of grains sampled clearly revealed the trend toward the formation of a h001i-fiber texture. Furthermore, the fiber axis was confirmed to be inclined relative to the build direction, leaning in the same direction of the overall build as was evident in the Y\u2013Z cross-section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003709_tec.2021.3052365-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003709_tec.2021.3052365-Figure9-1.png",
        "caption": "Fig. 9. Experiment platform.",
        "texts": [
            " Pir represents the iron loss generated by each harmonic of airgap magnetic flux density, and pcage represents the rotor cage loss generated by each harmonic of airgap magnetic flux density. According to (42), the stray load loss calculated by the main space harmonics of the airgap magnetic flux density obtained by the GAFMT is 43.15 W. IV. TEST VERIFICATION In order to verify the accuracy of the proposed model, the experiment platform is built for no load and rated load experiments on the SCIM shown in Fig. 9. The tested IM is with skewed cast aluminum bar cages. The rated power is 5.5 kW and the rated speed is1440 r/min, and the thermal sensor is inserted in the stator slot. The test facilities and instruments used in the tests are conformed to the IEEE 112-B standard requirements. The procedures of no load tests and variable load tests comply with the IEEE 112 standard requirements. The motor temperature is stable, and it is possible to perform several measurements for each load torque. In particular, the tested IM has been supplied with a 15kVA three-phase variac"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure9.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure9.7-1.png",
        "caption": "Fig. 9.7 Model where ball consists of two masses m1 and m2 and two springs, S1 and S2. The dashpot in parallel with S2 accounts for energy losses in the ball. The ball is incident normally at speed v1 and rebounds at speed v2 < v1. During a time t , m1 moves a distance x1 and m2 moves through a distance x2",
        "texts": [
            " The region of maximum stress in a bouncing ball is known to be confined to a volume of radius approximately a, where a is the radius of the circular contact area between the ball and the surface with which it contacts [5]. Nevertheless, the rest of the ball is connected elastically to the contact volume and will compress and expand via this elastic connection. To model this situation, and to distinguish between actual ball compression and displacement of the ball CM, we can assume that the ball consists of two connected parts, one of mass m1 in contact with the surface and one of mass m2 which acts on m1 via a damped spring S2. The situation is shown in Fig. 9.7. The elastic properties of m1 are represented by a nonlinear 9.6 Two-Part Ball Model 149 spring, S1, obeying a force law F D k1xn 1 where x1 is the compression of S1, taken to be equal to the displacement of the CM of m1. To account for possible energy loss in S1 we can allow the spring to expand according to the relation F D k3x p 1 where p > n and where k3x p 1 D k1xn 1 at maximum compression. To account for energy loss in spring S2, one could assume that this spring also obeys a different power law during its expansion, but such an approach does not yield any information on the energy loss mechanism or its time history",
            " The integral R y 0 F dy is the total work done on the spring to arrive at a compression y, regardless of whether the spring is compressing or expanding at that point. The component k2y2=2 represents the stored elastic energy, and the component R kD.dy=dt/ dy represents the energy dissipated in S2. In the present context, the physical mechanism responsible for damping within the ball is unknown, but the damping model assumed here provides very good agreement with the experimental data, as shown in Fig. 9.8. It is relatively easy to set up and solve the equations describing the model in Fig. 9.7, as described in Appendix 9.2. Typical numerical solutions are shown in Fig. 9.8 for a case where the ball is incident at speed v1 D 5:02 ms 1. An excellent fit to the experimental F vs. t waveform is obtained with m2=m1 D 10, n D 1:8, p D 2:8, k1 D 2:6 108, k2 D 0 and kD D 2;080 Nsm 1. The k values are quoted here in SI units. The ball bounces, when F D 0 and x1 D 0, at a time when it is still compressed. The ball remains compressed well after the bounce in this case since the numerical solution was obtained with k2 D 0",
            " 1 for the baseball and k D 9;04 lb in. 1 for the softball. A bell-shape force waveform, like that in Fig. 9.4, can be described by F D 1 C 4t to 3t2 t2 o Fot 2to ; which also has the property that F D Fo and dF=dt D 0 at t D to. For this waveform, R F dt D 13Foto=24 Dmvo in which case the peak force is given by Fo D 24mvo=.13to/, and xo D 0:677voto, both being slightly larger than the values obtained for a sinusoidal force waveform. 152 9 Ball Hysteresis Appendix 9.2 Equations Describing the Two-Part Ball in Fig. 9.7 The two-part ball model shown in Fig. 9.7 requires some damping to prevent the ball vibrating during and after the bounce. If kD D 0 it is found that m1 and m2 undergo undamped, large amplitude oscillations after the ball bounces, which is not consistent with experimental observations. Rather, baseballs and softballs behave as strongly damped springs, consistent with the fact that they don\u2019t bounce very well. The results of the model calculations do not depend significantly on the value of k2 or whether S2 is linear, as assumed, or nonlinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.4-1.png",
        "caption": "Fig. 2.4 Principle layout of the RBW or XBW integrated unibody or chassis motion mechatronic control system, integrating DBW AWD propulsion, BBW AWB dispulsion, SBW AWS conversion and ABW AWA suspension mechatronic control systems [PEIT 2004].",
        "texts": [
            " For instance, the technical objective of a powertrain equipped with intelligent technologies (PEIT) project [PEIT 2004] might be thus to build up an integrated self-stabilising powertrain that provides an interface to add all accident prevention and driver assistance functions of the vehicle. The powertrain interface may make it possible to integrate DBW AWD propulsion, BBW AWB dispulsion, ABW AWA suspension, and SBW AWS conversion mechatronic control systems and fail operative energy management into the RBW or XBW integrated unibody or chassis motion mechatronic control system, for example as shown in Figure 2.4 [PEIT 2004] 2.1 Introduction 153 To connect the functionalities and their mechatronically controlled devices, a failure tolerant system architecture is developed with two or even three central electronic control units (ECU) derived from the avionics industry co-ordinating the powertrain functions. Thus, only a single input, the motion vector providing the information of vector length and vector angle for acceleration/deceleration and yaw angle, respectively, vehicle body sideslip angle, may be necessary to control the whole motion task"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure6.20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure6.20-1.png",
        "caption": "Fig. 6.20 Universal joint with nonorthogonal axes",
        "texts": [
            " The vectors n1 and n2 are fixed in basis e . The constant angle \u03b1 between them is determined by cos\u03b1 = n1 \u00b7n2 . The coordinates ( \u221a 3/3)[1 1 1] of n1 and ( \u221a 3/3)[1 \u2212 1 1] of n2 determine cos\u03b1 = 1/3 (\u03b1 \u2248 70.5\u25e6) . The vector n2+n1 and, therefore, also \u03a921 is directed along the bisector of this angle. Hence the joint connecting faces 1 and 2 is a two-degree-of-freedom joint with an axis of rotation 1 fixed on face 1 in the direction of n1 and with an axis of rotation 2 fixed on face 2 in the direction of n2 (see Fig. 6.20). This joint is a universal joint with nonorthogonal axes intersecting at P1 . Faces 7 and 6 are separated from face 1 by two and by three joints, respectively. Let \u03a971 and \u03a961 be their angular velocities relative to face 1 . These angular velocities are \u03a971 = \u03d5\u03077n7 \u2212 \u03d5\u03071n1 = \u03d5\u03071(n7 \u2212 n1) and \u03a961 = \u03d5\u03076n6\u2212 \u03d5\u03071n1 \u2261 0 . The latter formula reconfirms that face 6 is in pure translation relative to face 1 . The former can be written in the alternative forms \u03a971 = \u03d5\u03071(n7 + n6) = \u03a976 and \u03a971 = \u2212\u03d5\u03071(n4 + n1) = \u2212\u03a941 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure16.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure16.7-1.png",
        "caption": "Fig. 16.7 Frame-fixed x0, y0-system and wheel-fixed x, y- and \u03be, \u03b7-systems for external gearing (a) and for internal gearing (b). Flank f1 with coordinates x(u) , y(u) . Contact point B with normal passing through P12",
        "texts": [
            " In this way the contact point B and the initial positions of B2 and B2N2 of flank f2 are determined for each pair ( B1 , B1N1 ) of flank f1 . It may happen that flank f1 is intersecting f2 at some point while it is in contact at another point. This phenomenon is called undercutting. It restricts the freedom in choosing flank f1 . The geometric locus of all contact points B is the line of contact (see the example in Fig. 16.4 where the line of contact is the arc sequence A1-P12-A2 ). Analytically, the condition in Theorem 16.1 is formulated as follows. The x0, y0-system shown in Fig. 16.7a is frame-fixed. Against this x0, y0-system the x, y-system fixed on wheel 1 and the \u03be, \u03b7-system fixed on wheel 2 are rotated through the angles \u03d51 (arbitrary) counterclockwise and \u03d52 = \u03bc\u03d51 = (n2/n1)\u03d51 clockwise, respectively. The following transformation equations are deduced from the figure: x0 = x cos\u03d51 \u2212 y sin\u03d51 \u2212 r1 , y0 = x sin\u03d51 + y cos\u03d51 , } (16.19) \u03be = \u2212x cos(\u03d51 + \u03d52) + y sin(\u03d51 + \u03d52) + (r1 + r2) cos\u03d52 , \u03b7 = x sin(\u03d51 + \u03d52) + y cos(\u03d51 + \u03d52)\u2212 (r1 + r2) sin\u03d52 . } (16.20) Flank f1 is assumed to be given in the x, y-system in the form x(u) , y(u) with a parameter u ",
            " From this it follows that the line of contact has, in the frame-fixed x0, y0-system, the parameter equations x0B(u) = x(u) cos\u03d51(u)\u2212 y(u) sin\u03d51(u)\u2212 r1 , y0B(u) = x(u) sin\u03d51(u) + y(u) cos\u03d51(u) . } (16.25) Equations (16.20) determine the \u03be, \u03b7-coordinates of flank f2 : \u03be(u) = \u2212x(u) cos[\u03d51(u) + \u03d52(u)] + y(u) sin[\u03d51(u) + \u03d52(u)] + (r1 + r2) cos\u03d52(u) , \u03b7(u) = x(u) sin[\u03d51(u) + \u03d52(u)] + y(u) cos[\u03d51(u) + \u03d52(u)]\u2212 (r1 + r2) sin\u03d52(u) . } (16.26) These equations represent a mapping of flank f1 into flank f2 . This ends the solution of the problem for external gearing. 540 16 Theory of Gearing In the case of internal gearing, Fig. 16.7b replaces Fig. 16.7a . Deliberately, the inner wheel is given the label 2 in contrast to the labeling in Figs. 16.1b and 16.2 . The x0, y0-system and the x, y-system are located as before. This has the consequence that (16.19) and (16.22) \u2013 (16.25) remain valid. The line of contact is the same for external and for internal gearing. Equations (16.26) for flank f2 are replaced by \u03be(u) = x(u) cos[\u03d52(u)\u2212 \u03d51(u)] + y(u) sin[\u03d52(u)\u2212 \u03d51(u)]\u2212 (r1 \u2212 r2) cos\u03d52(u) , \u03b7(u) = \u2212x(u) sin[\u03d52(u)\u2212 \u03d51(u)] + y(u) cos[\u03d52(u)\u2212 \u03d51(u)] + (r1 \u2212 r2) sin\u03d52(u) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.4-1.png",
        "caption": "Figure 6.4. Projectile motion in an inertial reference frame without friction.",
        "texts": [
            " Afterwards, a fascinating technological application of a controlled projectile motion is studied. In addition to earlier assumptions, frictional effects arc ignored. Example 6.9. Percy Panther is snoozing in an open-top artillery truck when he senses the presence of the mischievous Arnold Aardvark lurking beneath. He Dynamics of a Particle .I 113 quietly releases the handbrake to escape down the hill inclined at an angle a . Arnold Aardvark having quietly rigged a remote trigger, immediately fires the gun, launching a shell of mass m straight up from the truck, as shown in Fig. 6.4. The gun has a muzzle velocity vo, and the total mass of the truck and its strange driver is M. Determine the time and the location at which the shell impacts the ground, and find the location of Percy Panther at that time. Solution. First, we determine the motion of the shell S, whose free body diagram is shown in Fig. 6.4. The total force acting on S is its weight Ws = mg. Thus, in the inertial frame <P = {F ; id fixed in the ground , the constant force in (6.22) and (6.23) is Fo = Ws = mg(sin ai- cos aj); and with Vo = voj and Xo = 0 initially, we obtain, in evident notation , vs(t ) = voj + gt(sin ai- cos oj), xs(t) = ~gt2sinai+ (vot - ~gt2cosa)j. (6.26a) (6.26b) Let the reader derive these results starting from (6.1), determine the maximum height reached by S, and show that its trajectory is a parabola. The shell returns to the ground after a time t* when xs(t*) = ri in Fig. 6.4, and hence by (6.26b) , Ir = _gt*2 sin a2 ' * 2vot =-- g cos o (6.26c) The results are independent of the mass or any other property of the shell. Elimination of t* from the first of (6.26c) yields the impact range r in terms of the muzzle 114 Chapter 6 (6.26d) speed Vo and the angle a that the gun makes with the vertical axis of g: 2v5tanar = ---''--- gcosa Now consider the free body diagram of the truck in Fig. 6.4. The total force FT acting on the truck is its total weight WT and the normal surface reaction force N. Without frictional effects, (6.1) becomes FT = N +WT = Nj +Mg(sinai- cos oj) = MaT . (6.26e) Since the truck accelerates along the i direction, N =Mg cos a and aT = g sin ai. Hence, two easy integrations with Vo = 0 and Xo = 0 yield VT(t) = gt sin cd, (6.26f) ( ) I 2\u00b7 \u2022 (626 )XT t = \"2gt smm, . g Comparison of the i components in (6.26b) and (6.26g) parallel to the truck's motion reveals that the shell at each instant is directly above the truck, now coasting toward the ultimate surprise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000733_0022-2569(71)90002-4-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000733_0022-2569(71)90002-4-Figure6-1.png",
        "caption": "Figure 6. Closed equiangular chord polygon of a circle.",
        "texts": [
            " Let us investigate a convex curve c whose isoptic curve for a certain view angle r r - - y is a circle o; this means that the pair of tangent lines p./5 issued from any point P \u00a2 o to c forms always the constant angle ~_pPp = rr-- y. Starting from an arbitrary tangent p to c with intersection points P0. P~ on o we may construct an equiangular p o l y g o n . . . P-~PoP~P,,_ \u2022 . . inscribed in the circle o and having at each corner the interior angle r r - y . Such a chord polygon of o has periodic structure and in general sides of only two different lengths P _ I P o = P , P2 = . . . and P o P , = P2P3 = - . - (Fig. 6). All sides must touch the curve c. This polygon is closed if and only if the fraction 7r/y is rational. Otherwise the polygon is infinite and its sides are alternatively touching two circles k,k concentric with o. As the points of contact form two everywhere dense sets on k and/~, we see, by reasons of continuity, that there exists, for irrational 7fly, only the trivial solution c = k = ~: (qJ = const). Non-trivial cam mechanisms of the kind in question therefore are possible only for rational values of ~' /y > 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002102_s00170-015-6915-7-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002102_s00170-015-6915-7-Figure3-1.png",
        "caption": "Fig. 3 Tooth surface envelope",
        "texts": [
            " The feed displacements of the grinding disk in axesX and Z are dx \u00bc a\u00fe rps\u2212ha \u2212 rw\u2212rps cos\u03c6B \u00fe bsin\u03c6B dz \u00bc \u2212 rw\u2212rps sin\u03c6B \u00fe bcos\u03c6B \u00f03\u00de When machining the face gear, axis B should be taken as the main control axis, and the other axes move along with axis B by Eq. (3). And, The rotation angle of A axis should be determined by Eq. (4) because of meshing relation between the shaper and face gear. \u03c6A \u00bc Ns N 2 \u03c6B \u00f04\u00de where Ns and N2 are the tooth numbers of the virtual shaper and the face gear, respectively. The feed move in axis Yof the grinding disk does not affect the generation relationship between the face gear and grinding disk, so the control equation of Sy is not necessary. 3.1 Definition of envelope residual As shown in Fig. 3, \u03a31 and \u03a32 are two instantaneous surfaces of the shaper in the coordinate system S2, and \u0393e is the intersection of \u03a31 and \u03a32. The distance \u0394 between \u0393e and the theoretic tooth surface of the face gear is called envelope residual. Envelope residual is an important indicator of gear precision which influences surface finish, so it must be strictly controlled. In order to ensure machining accuracy, the minimum envelope times should be calculated before processing, to determine the tool\u2019s feeding magnitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000208_j.arcontrol.2008.08.003-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000208_j.arcontrol.2008.08.003-Figure10-1.png",
        "caption": "Fig. 10. Trajectory of the aircraft.",
        "texts": [
            " The purpose of the simulations is to verify the asymptotic tracking properties of the controller, both during standard demonstration manoeuvres (climb, steady turn, dive), and non-standard ones (such as a 1808 roll). The flight plan includes the following sectors. (1) I nitial speed 26 m/s. Climb from 30 m to 60 m at a rate of 12 m/s. (2) A ccelerate to 42 m/s. (3) P erform a 1808 turn of radius 200 m (at roll angle 438). (4) P erform a 1808 roll. (5) P erform a 1808 turn of radius 200 m (at roll angle 1378). (6) R esume level flight. (7) P erform two successive 2708 turns of radius 110 m (at roll angle 608). The trajectory of the aircraft is shown in Fig. 10. The aircraft follows the desired trajectory with zero tracking error for the airspeed and attitude and zero steady-state error for the altitude, despite the lack of information on the aerodynamics and despite the fact that we have used a simplified aerodynamic model for the design. Adaptive control of linear time invariant systems is a wellestablished discipline whose major theoretical issues have been fully sorted out and the main plant structural obstacles clearly identified. Many successful applications of adaptive control for linear plants have also been reported in the literature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure5-1.png",
        "caption": "Fig. 5. Stress results of the wheel disc after the third process.",
        "texts": [
            " Another set of data is selected according to the traditional experience: the fatigue life is 1000 revolutions when the equivalent stress amplitude is 0:9rb. Two sets of data are introduced into Eq. (16), then the fatigue limit (the corresponding fatigue life is 107) and the parameter m are calculated as r1l \u00bc 268:084 MPa \u00bc 0:394rb and m1 \u00bc 11:1582, respectively. In this section, the effects of the residual stress are included. The residual stresses of point A are acquired from the stress contour (Fig. 5) as rx \u00bc 135:057 MPa and ry \u00bc 131:152 MPa. Considering the reduction of the residual stress from the natural aging, the residual stress are recalculated as r0 x \u00bc 121:551 MPa and r0 y \u00bc 118:037 MPa with the subtractive ratio of 10%. The angle between the Y-axis and the line connecting the bolt hole center and point A is 22.5 deg. The coordinate system in point A is x0oy0 while it is xoy in ABAQUS software, and the angle between x-axis and x0-axis is 22.5 deg (a \u00bc 22:5 ), as shown in Fig. 17. Therefore, the residual stress in the coordinate system of point A needs to be transformed into the coordinate system of the ABAQUS software using following equations [11]: s0 \u00bc rx ry 2 sin 2a\u00fe sxy cos 2a r0 x \u00bc rx\u00fery 2 \u00fe rx ry 2 cos 2a sxy sin 2a r0 y \u00bc rx\u00fery 2 rx ry 2 cos 2a\u00fe sxy sin 2a 8>< >: \u00f017\u00de The stresses of point A are calculated after introducing the residual stresses, and the third invariant of the stress deviator is used to judge the deformation state of the point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001866_s00170-017-9988-7-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001866_s00170-017-9988-7-Figure2-1.png",
        "caption": "Fig. 2 Calculation of tooth profile deviation",
        "texts": [
            " Thus, the constraint of the cutting edge enveloping the tooth flank of the workpiece can be determined by the following equation f u;\u03c6c\u00f0 \u00de \u00bc t 2\u00f0 \u00de c v 2\u00f0 \u00de d \u22c5v 2\u00f0 \u00de cw \u00bc 0 \u00f020\u00de Themeshing point in S2 can fulfill Eqs. (15) and (20), and it will be a tooth flank point of the workpiece if transformed into the workpiece coordinate system Sw. The tooth profile deviation can be obtained by comparing the transverse tooth profile of the workpiece tooth flank with the standard involute tooth profile [19, 20]. Point A\u2032 is on the actual tooth profile which intersects with the standard involute tooth profile at point B on the base circle of the workpiece as shown in Fig. 2. Line A\u2032C is the tangent line of the base circle, which intersects with the involute tooth profile at point A. As shown in Fig. 2,Q is the generating angle of point A on the standard involute tooth profile, which can be expressed as: Q \u00bc Q1 \u00fe Q2 \u00bc arccos r 0 w\u22c5\u039f\u0392 r0 w \u22c5 \u039f\u0392j j ! \u00fe arccos rbffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x02 w \u00fe y02 w q 0 B@ 1 CA \u00f021\u00de The coordinates of point A can be obtained by using the angle Q and the involute tooth profile equations [21], then the tooth profile deviation can be expressed as the distance between the point A\u2032 and the point A: d \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x0 w\u2212xw 2 \u00fe y0 w\u2212yw 2q \u00f022\u00de A numerical example of tooth profile deviation calculation is carried out, which is aimed at analyzing the influences on the gear tooth profile deviation of the tool position and orientation errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure23-1.png",
        "caption": "Figure 23 Path planning on conical surfaces",
        "texts": [
            " This component was fabricated separately, with its shell manufactured on a plane substrate by conventional 2D slicing, and with its blades manufactured on the rod-like substrate by our surface slicing and five-axis algorithm. The top of the rod-like substrate has the same dimension with the spindle of the blades, and its bottom is welded on the flat substrate (Figure 22). To enhance the connection, another four stiffeners were welded between the bottom and the flat substrate. The flat substrate was fixed on the rotary table with bolts and nuts through the four through-holes of the flat substrate, and four clamps on the rim. Our path planning method was used to generate the tool-paths of the blades, shown in Figure 23, including the following steps: Knowing the radius (R = 60) and the height (H = 200) of Process planning for five-axis wire Fusheng Dai, Haiou Zhang and Runsheng Li Rapid Prototyping Journal A set of equidistant conical surfaces, in which the radius and height of the ith surface were Ri \u00bc 601 ffiffiffiffiffiffi 109 p 10 d i; Hi \u00bc 2001 ffiffiffiffiffiffi 109 p 3 d i, were generated and used to carry out (b) (c) (d) and (e); Finally, we got all the tool-paths. The blades of the underwater thruster (Figure 21) were fabricated by manufacturing a blank in our method and postprocessing in CNC milling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.32-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.32-1.png",
        "caption": "Fig. 3.32 Simplified solenoid fluidic valve anti-lock 4WB BBW dispulsion mechatronic control system\u2019s principle layout and schematic diagram [AMISEMICONDUCTOR 2004 \u2013 left image; CAGE 1994 \u2013 right image].",
        "texts": [
            " A variety of active sensor technologies, including the Hall or Wiegand effect and magnetoresistive, may be used in applications requiring very low angular velocity sensing and in applications where an appropriate signal level cannot be achieved with conventional variable reluctance sensors. Anti-lock Fluidic or Pneumatic Modulators - Anti-lock fluidic modulators typically take two forms in production anti-lock BBW AWB dispulsion mechatronic control systems: solenoid fluidical valves and E-M motors. A simplified solenoid fluidical valve anti-lock BBW AWB dispulsion mechatronic control system\u2019s principle layout and schematic diagram are shown in Figure 3.32 [CAGE 1994; AMISEMICONDUCTOR 2004]. In this BBW AWB dispulsion system, if the solenoid fluidical valves are de-energised, fluid or air is free to flow between the master cylinder and the brakes. 3.5 Anti-Lock EFMB 489 If too much fluid or air pressure is presented to the brakes and wheel lock is imminent, the anti-lock BBW AWB dispulsion mechatronic control system may actuate a solenoid fluidical valve and energise the E-M-F pump or E-M-P compressor. Actuation of the solenoid fluidic valve allows fluid or air pressure to decrease from the brake through the fluidical valve to a low-pressure fluidical accumulator/sump"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000427_elt.2008.104-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000427_elt.2008.104-Figure4-1.png",
        "caption": "Figure 4. Photograph of the rotor position detector.",
        "texts": [
            " There is a centrailzed coil wound on each stator tooth, and there are four coils in each phase, so that the A phase winding could be made up of the coils \u201c1\u201d, \u201c4\u201d, \u201c7\u201d and \u201c10\u201d, the B phase winding could be made up of the coils \u201c2\u201d, \u201c5\u201d, \u201c8\u201d and \u201c11\u201d, and the C phase could be made up of the coils \u201c3\u201d, \u201c6\u201d, \u201c9\u201d and \u201c12\u201d. By taking A phase winding for an example, the four coils- \u201c1\u201d, \u201c4\u201d, \u201c7\u201d and \u201c10\u201d, could be connected in series to form the winding of the phase A, which is shown in Fig. 3. The four coils in phase B and C could also be connected in series. There are no brushes, no magnets and no windings on the rotor. The rotor position detector is installed on the no shaft extension of the generator, which is shown in Fig. 4. It is made up of three photoelectric transducers and a slotted disk. There are eight teeth with 22.50 widths per tooth and eight slots with 22.50 widths per slot on the slotted disk, which is fixed on the same shaft of the rotor. The three photoelectric transducers SP, SQ and SR , are fixed on the end shield of the generator in a 600 interval. When the rotor of the generator rotates, the three photoelectric transducers produce square wave signals, which represent the rotor position information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure2-1.png",
        "caption": "Fig. 2. An actuation wrench and the resultant elastic deformation along the axis of the actuation wrench.",
        "texts": [
            " As a result of the actuation wrench $a,i applied on the centroid C of the cross section of the supporting limb, the supporting limb undergoes an elastic deformation which is considered to be small. Note that the shape of the cross section is arbitrary. Since the actuation wrench is restricted to pure force or pure couple, it can be decomposed into three parts along the x1-, y1-, and z1-axis, respectively, where z1-axis represents axial direction of the supporting limb, x1- and y1-axis represent principal axes of the cross section, as shown in Fig. 2. Then the deformation along the x1-, y1-, and z1-axis can be obtained as da;ix \u00bc wix=ka;ix da;iy \u00bc wiy=ka;iy da;iz \u00bc wiz=ka;iz ) ; \u00f08\u00de where ka, ix, ka, iy, and ka, iz represent translational or rotational stiffness of the supporting limb along the x1-, y1-, and z1-axis, respectively, wix, wiy and wiz are x1-, y1-, and z1-component of wi, respectively. The total elastic deformation of the supporting limb as a result of the actuation wrench $a,i can then be yielded as da;i \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi da;ix 2 \u00fe da;iy 2 \u00fe da;iz 2 q \u00f09\u00de The component of the total deformation along the axis of the actuation wrench $a,i can be derived as dea;i \u00bc wix 2 =ka;ix \u00fewiy 2 =ka;iy \u00fewiz 2 =ka;iz wi \u00bc wi=k e a;i; \u00f010\u00de where ka, i e is defined as the stiffness of the actuation wrench $a,i, given by kea;i \u00bc wi 2 wix 2=ka;ix \u00fewiy 2=ka;iy \u00fewiz 2=ka;iz ; \u00f011\u00de which is related to not only the stiffness of the corresponding supporting limb but also the axis of the actuation wrench applied on the supporting limb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001619_s11666-017-0554-5-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001619_s11666-017-0554-5-Figure1-1.png",
        "caption": "Fig. 1 Schematic of powder flowing process and its interaction with laser beam",
        "texts": [
            " The reason for the early instability of the building process without any temperature control unit is constructed, and the effect of parameters such as laser power, deposition velocity and laser beam deposition pattern on the evolving temperature field is interpreted. The applied deposition parameters are derived from experimental investigation with optimized vertical wall manufacturing. In the coaxial LMD, laser irradiates vertically downward through the middle channel of the powder-feed nozzle. Driven by carrier gas and gravity, powder particles flow down through the powder-feed channel of the nozzle, which is angled with an inclination of 17 with respect to vertical direction (shown in Fig. 1). Both powder stream and laser beam are focused on the substrate surface. Before the powder reaches the substrate, the laser briefly interacts with the flowing powder. During vertical thin wall building, the nozzle moves along X-axial, and the laser irradiates the surface of the substrate. Due to the dropping of powder and the consequent increase in depth of the molten pool, molten metal in the melting pool solidifies rapidly and a cladding track with a certain height, length and width forms after the laser beam moves",
            " In this region, shielding gas interacts with substrate, which causes a strong upward pressure performed on powder particle close to the substrate, consequently the shielding gas can protect the cladding track from contaminant from oxidation and nitridation during laser cladding, finally powder particles are decelerated again. Although powder particles experience phases of acceleration and deceleration in the flowing process many times, they ultimately reach the surface of the substrate as converged powder stream of optimized parameters of carrier gas and shielding gas (shown in Fig. 1). The process of acceleration and deceleration for powder particles and their peak flowing velocity are in agreement with that in Ref 17 and 19. The computation domain is composed of a thin wall and a substrate, both are in solid phases. The substrate in the simulations used in this paper is 60 9 20 9 2 mm3 in X, Y, and Z direction, where a vertical thin wall with 3D-size of 40 9 1 9 3 mm3 is built (shown in Fig. 4). At the start of calculation, there is only the substrate, the clad track will be formed on the substrate surface once deposition begins"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.5-1.png",
        "caption": "Fig. 7.5 The pseudo-rigid-body model of the compliant parallel-guiding mechanism consists of appropriately located pin joints and torsional springs. (This device is a building block of other devices, such as the folded-beam suspension)",
        "texts": [
            " The pseudo-rigid-body model is used to model compliant mechanisms as traditional rigid-body mechanisms, which opens up the possibility of using the design and analysis methods developed for rigid-body mechanisms in the design of compliant mechanisms [10]. With the pseudo-rigid-body model approach, flexible parts are modeled as rigid links connected at appropriately placed pins, with springs to represent the compliant mechanisms resistance to motion. Extensive work has been done to develop pseudo-rigid-body models for a wide range of geometries and loading conditions. Consider a simple example. The mechanism shown in Fig. 7.5 has a rigid shuttle that is guided by two flexible legs. (Note that the folded-beam suspension in Fig. 7.2 has four of these devices connected in series and parallel.) The pseudo-rigid-body model of the mechanism models the flexible legs as rigid links connected at pin joints with torsional springs. Using appropriately located joints and appropriately sized springs, this model is very accurate well into the nonlinear range. For example, if the flexible legs are single walled carbon nanotubes, comparisons to molecular simulations have shown the pseudo-rigid-body model to provide accurate results [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001827_1350650116649889-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001827_1350650116649889-Figure3-1.png",
        "caption": "Figure 3. Local roller consideration: (a) Local roller at angle position ; (b) roller\u2013raceways contact geometry.",
        "texts": [
            " The outer race was assumed to be stationary, while the inner race could freely rotate around the bearing axis. The external load vector of the inner ring was assumed to be unchanged, and given by Ff gT \u00bc Fx,Fy,Fz,Mx,My \u00f02\u00de Even though the external load Ff g was a timeindependent vector, the inner ring displacements varied with time because of the error in roller diameter and the varied number of rollers under load. Upon equilibrium of the inner ring at a certain time t, the instantaneous inner ring displacement vector was represented by f gT \u00bc x, y, z, x, y \u00f03\u00de For an arbitrary roller shown in Figure 3(a), the angle t\u00f0 \u00de of the roller is calculated as t\u00f0 \u00de \u00bc 2 j 1\u00f0 \u00de z \u00fe !ct \u00f04\u00de where j and z are the roller index and number of rollers, respectively, and !c denotes the angular speed of the cage, or orbital speed of roller. Assuming that only pure rolling occurs at the roller\u2013raceways contact, !c is calculated by27 !c \u00bc ra dm ! \u00f05\u00de where dm is the bearing pitch diameter, ! is the angular speed of inner ring, and ra is the radius of inner contact point on the diameter passing through the roller center of gravity C as shown in Figure 3(b). A cross-sectional view of the TRB over the roller at location angle t\u00f0 \u00de is shown in Figure 3(b). at Middle East Technical Univ on May 18, 2016pij.sagepub.comDownloaded from The contact forces and moments between the roller and inner and outer raceways are Qa and Ma, where a \u00bc i, e indicates the inner and outer raceways, respectively. In order to determine the roller contact loads, the contact regions were divided into s slices of equal length l. The contact compression k between the roller and raceways at the kth slice was determined, taking into account the roller diameter error D as k \u00bc 0 \u00fe lk hk \u00fe D \u00f06\u00de where 0 and are the contact compression due to the translation motion and the relative misalignment angle between the roller and raceway. The crown drop hk resulted from the modified roller and/or raceways profiles. The contact force over a slice qk was estimated to give total contact forces and moments as qk \u00bc c 10=9k l \u00f07\u00de Qa \u00bc Ps k\u00bc1 qk; a \u00bc i, e\u00f0 \u00de \u00f08\u00de Ma \u00bc Xs k\u00bc1 qklk \u00f09\u00de where c is the contact constant depending on the contact geometry and material,28 and lk is the axial position of the kth slice (Figure 3(b)). Having obtained roller contact loads, the equilibrium equation of roller was derived, taking into account the effect of inertial loading such as centrifugal force and gyroscopic moment. After the equilibrium equations of all rollers were solved, global equilibrium equations were solved to provide the bearing displacement and stiffness matrix. In this study, the TRB model was capable of providing a fully populated (5 5) stiffness matrix, which was calculated using the Jacobian of bearing external load vector Ff g with respect to displacement vector f g as26 k\u00bd \u00bc @ Ff g @ f gT \u00bc kxx kxy kxz kx y kx z kyx kyy kyz ky y ky z kzx kzy kzz kz y kz z k yx k yy k yz k y y k y z k zx k zy k zz k z y k z z 2 6666664 3 7777775 \u00f010\u00de Detailed descriptions for roller and global equilibrium equations of TRB and bearing stiffness matrix formulations are well documented in the literature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003220_j.addma.2020.101174-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003220_j.addma.2020.101174-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the C(T) specimen and FCG test apparatus.",
        "texts": [
            " The electron backscattered diffraction (EBSD) results revealed that the microtexture and orientation of the columnar grains were responsible for the difference in the FCG rate in different columnar grains, and the orientation of the columnar grains also determined the extent of the difference. The material used in this work and its manufacturing process are the same as those in our previous work, and the detailed information, such as chemical composition of the powder, the DED parameters and the heat treatment method, can be found in the literature [9]. A Ti-6.5Al-2Zr-Mo-V bulk sample was produced by DED and then machined into C(T) specimens in three sampling directions, as shown in Fig. 1. Fig. 2 shows a schematic diagram of the C(T) specimen with W = 60 mm, B = 13 mm and a0 = 27 mm. The specimen is thick because the length of the columnar grains is long. Two specimens were tested in each sampling directions. The details of six specimens are shown in Table 1. The FCG test was carried out on an INSTRON 8801\u2212100 kN electrohydraulic servo fatigue test machine under atmospheric conditions at room temperature and in accordance with the ASTM-E647 [23]. The load is a sine-wave constant-amplitude (CA) stress with a stress ratio R of 0.1. A clevis and pin assembly was used at both the top and bottom of the specimen, as shown in Fig. 2. The crack length was measured during the FCG test using a visual measurement system with an accuracy of 0.01 mm. The system consisted of an electric controller, an OISC0033 stepper motor, a microscopic observation device (charge-coupled device (CCD) camera and magnifier) and a ring light, as shown in Fig. 3. The lengths of the cracks on the front and back surfaces were periodically observed during the test. A step-down method was used for precracking. The reduction in Pmax between the steps was 15 %, and the extension of the crack during any step was approximately 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002133_s11771-015-2967-y-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002133_s11771-015-2967-y-Figure3-1.png",
        "caption": "Fig. 3 LOS guidance schematics for bottom-following in Serret-Frenet frame",
        "texts": [
            " (3) Corollary of Barbalat\u2019s lemma (CBL) [18]: If f(t) is a double differentiable function such that f(t) is finite as t goes to \u221e, and such that ( )f t exists and is bounded, then ( )f t tends to 0 as t tends to \u221e. (4) LaSalle\u2019s invariance principle [18]: let \u2126 be a positively invariant set of the system described in (1) and (3). Suppose that every solution starting in \u2126 converges to a set E   and let M be the largest invariant set contained in E. Then every bounded solution starting in \u2126 converges to M as t tends to \u221e. 3) The tracking differentiator for surge velocity is introduced to avoid setpoint jump. In the bottom-following, the intuitive explanation of the LOS guidance principle is shown in Fig. 3. In the Serret-Frenet frame {F} with respect to the reference point P, the point T is chosen as the next reference point, and its coordinate is T[ , 0]Fx  , where the diving law tuning parameter \u0394>0 denotes the lookahead distance. This parameter usually takes values between 1.5 and 2.5 times of the vehicle total length [5]. However, in order to adapt to the curvature changes of the bottom profile, the parameter \u0394>0 is considered as a function of the curvature \u03ba(s) at the point P. The LOS angle is familiarly defined as los e LOS arctan( ) arctan( ) z z z        (23) However, in the subsequent derivation, the aforementioned definition Eq. (23) is replaced with its arcsine form: LOS e LOS 2 2 e arcsin( ) k z z     (24) where LOSk R is tuning parameter. The parameter \u0394 is chosen as c2 sat( ( ) ),l l k s   where kc>0, sat(\u00b7) denotes saturation function, and l is the vehicle total length. According to the geometric relationship in Fig. 3, the pitch angle error \u03b8e is equal to the LOS angle \u03b8LOS in an ideal situation. J. Cent. South Univ. (2015) 22: 4193\u22124204 4198 Consider the following control Lyapunov function (CLF) 2 kin1 e LOS1/ 2( ) .V    It is straightforward to indicate the desired pitch angular velocity: LOS e LOS( ) ( )q qs s k           (25) makes 2 kin1 e LOS kin1( ) 2 0q qV k k V       with kq arbitrary positive gain. Therefore, the CLF Vkin1 is a positive and monotonically decreasing function. And then, the limit value of Vkin1(t) as t goes to \u221e exists and is bounded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000137_j.automatica.2007.07.002-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000137_j.automatica.2007.07.002-Figure3-1.png",
        "caption": "Fig. 3. Active magnetic bearing.",
        "texts": [
            " We will also earn one additional relative degree from P0(s). The optimal performance for P( ) can be obtained by application of Corollary 9, i.e., E\u2217 =E\u2217 d/T . Then it is easy to show that limT \u21920E \u2217 = E\u2217 . In this section we implement our results to study the performance limitations in a magnetic bearing system, which has been widely investigated, see Thibeault and Smith, R. (2001), Thibeault and Smith, R. S. (2001), and Maslen, Montie, and Iwasaki (2006). We consider a simple active magnetic bearing (AMB) depicted in Fig. 3. AMBs suspend the levitated object (generally, a rotor) of mass M by forces of two opposing magnetic attractions which are supplied by power switching amplifiers of voltages V1, V2 and currents I1, I2. AMBs use actively controlled electromagnetic forces to control the position of the rotor or other ferromagnetic body in air which has nominal air gap g0. If we assume that the state variable can be forced to track some constant trajectory 0 by appropriate choice of control input u, then a linearizing model may be realized as follows (Maslen et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002001_icstc.2018.8528714-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002001_icstc.2018.8528714-Figure4-1.png",
        "caption": "Fig. 4. Geometric assembly based on analytical results.",
        "texts": [
            " RESULTS AND DISCUSSION Because geometric dimension is related to the experimental site, Table 1 shows the results of (1) to (9) with experimental site conditions of 0.041 m3/s for discharge, water depth height (d) of 0.164 m, and width of blade (W) of 0.25 m. Thus, the power potential was calculated at 20.5 W with the inlet velocity (u) of 1 m/s. Due to variable inlet velocity, the power potential also varied. For inlet velocity (u) of 3 m/s, the potential power was 184.5 W and for u of 5 m/s, the potential power was 512.5 W. The geometric dimensions obtained from the analytical results are illustrated in Fig. 4. The turbulence model independency was calculated to find out which model was the best fit to represent the fluid pattern. As shown in Fig. 5, the standard k-\u03b5 with scalable wall functions model was almost precise because the result was not very different from RNG k-\u03b5 with scalable wall functions, with a difference 11.12%. In addition, standard k-\u03b5 was not used because the study by Nishi, Inagaki, Li, and Hatano [10], which adopted standard k-\u03b5, showed a relatively high error value. Thus, standard k-\u03b5 with scalable wall functions model was chosen in this study because it enables solutions on arbitrarily fine near-wall grids, which is a significant improvement over standard wall functions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000872_1.4002077-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000872_1.4002077-Figure1-1.png",
        "caption": "Fig. 1 A quadratic spherical parallel manipulator",
        "texts": [
            " Inspired by the above advances on the FDA of quadratic parallel manipulators, in this paper, we will present a formula that produces a unique current solution to the FDA of the Agile Eye for a given set of inputs. This paper is organized as follows: in Sec. 2, the geometric description of the Agile Eye is presented and an alternative formulation of the kinematic equations is proposed. In Sec. 3, the singularity analysis of the Agile Eye is performed. In Sec. 4, the FDA of the Agile Eye is dealt with and a formula that produces the current solution to the FDA is presented. Finally, conclusions are drawn. 2 Geometric Description of the Agile Eye The Agile Eye 1 Fig. 1 is a specific case of the 3-R RR spherical parallel manipulator. Here and throughout this paper, R and R denote, respectively, revolute joints and actuated revolute joints. It is composed of a base and a moving platform connected with three RRR legs. To facilitate the analysis, two coordinate systems, O\u2212XYZ and O\u2212XPYPZP, are set up in a similar way as in Ref. 5 . The X-, Y-, and Z-axes are along the axes of the three R joints on the base. The XP-, YP-, and ZP-axes are along the axes of the three R joints on the moving platform. The unit vectors along the joint axes of joints in leg i i=1, 2, and 3 starting from the base are denoted by ui, wi, and vi. We have u1= 1 0 0 T, u2= 0 1 0 T, and u3= 0 0 1 T. In O\u2212XPYPZP, the unit vectors along the three R joints on the moving platform are v1 = 0 \u22121 0 T, v2 = 0 0 \u22121 T, and v3 = \u22121 0 0 T. In the reference configuration Fig. 1 , O\u2212XPYPZP coincides with O\u2212XYZ. The unit vectors along the three intermediate R joints are w10= 0 0 1 T, w20= 1 0 0 T, and w30= 0 1 0 T. Let 1, 2, and 3 denote the joint variables of the three actuated joints and 3 and \u2212 2 denote the joint variables of the two passive joints in leg 1. In the reference configuration, we have 1=0, 3=0, and 2=0. From leg 1, the rotation matrix of the moving platform is R = Rx 1 Rz 3 R\u2212y \u2212 2 1 where Rx, Ry, and Rz denote the rotation matrix about the X-, Y-, and Z-axes, respectively",
            " Therefore, 2 of the current olution to the FDA is C 2 = sign C 3 abs b1 / a1 2 + b1 2 1/2 S 2 = \u2212 a1C 2/b1 25 Table 1 The relation among the four nontri No. Solution to FDA J1 1 v10, v20, and v30 J10 2 v10, \u2212v20, and \u2212v30 J10 3 \u2212v10, v20, and \u2212v30 \u2212J1 4 \u2212v10, \u2212v20, and v30 \u2212J1 able 2 The working modes of the four solutions to the FDA within the input-space c2>0\u2026 No. Working modes 1 +++ 2 +\u2212\u2212 3 \u2212+\u2212 4 \u2212\u2212+ ournal of Mechanisms and Robotics om: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/16/2 Equations 24 and 25 are the formulas of the current solution to the FDA of the Agile Eye. 4.3 Numerical Example. For the Agile Eye Fig. 1 , a set of inputs is 1=30 deg, 2=30 deg, and 3=30 deg. Using Eqs. 24 and 25 , we obtain its current solution as 3=17.58 deg and 2=30 deg. The configuration of the Agile Eye is shown in Fig. 2. 4.4 Input Space. Except in the lock-up configurations\u2014the four trivial solutions to the FDA\u2014the entire input-space is divided into two regions 7 : a c2 0 and b c2 0 by the singularity surface Eq. 13 . To simplify the control, it might be useful to confine the inputs into the maximum cube containing the reference configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003365_tmrb.2020.2988462-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003365_tmrb.2020.2988462-Figure5-1.png",
        "caption": "Fig. 5. A four coil array was printed from ULTEM 1010 (Stratasys Direct) and coils were directly wound onto the printed form. The interior surface of the printed form was coated with a waterproof resin sealant to prevent water leaking into the sample region of interest. Here, an inserted sample dish and pegs for purse string suture pattern are shown.",
        "texts": [
            " In this work, the measured penetration forces from the NdFeB needle were used to design the electromagnetic array in order to generate sufficient magnetic force for rat intestine tissue penetration according to Equation (1). We propose a cube-shaped magnetic work space greater than 90 mm \u00d7 90 mm with the ability to generate sufficient force on a NdFeB needle to demonstrate tissue penetration. In particular, we created an electromagnetic coil array containing four coils, each coil having an outer diameter of 98 mm. The coils are orthogonally arranged along the X and Y axes with an optional insertable soft iron core to enhance the magnetic field. A picture of the coil array is shown in Fig. 5. Coils were wound on a 3D printed ULTEM 1010 frame (Stratasys Direct; www.stratasysdirect.com), ULTEM 1010 being chosen for its comparatively high heat deflection temperature (217 \u25e6C). Coils were wound using AWG 16 polyimide-coated copper wire (MWS Wire Industries, Inc.; www.mwswire.com) and had lengths of 60 mm, inner diameters of 85 mm, and outer diameters of 98 mm, as shown in Fig. 6. Each coil had 54 turns per layer, 12 layers, and a total resistance \u22482.7 . The iron cores for each coil, when used, were identical as well, having diameters of 50"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002203_j.cirpj.2016.11.002-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002203_j.cirpj.2016.11.002-Figure3-1.png",
        "caption": "Fig. 3. FEM-simulation of the hobbing process.",
        "texts": [
            " Depending on the generating position the chip and the tool load are different. To identify differences between the tool profiles and to match wear phenomena with simulated tool loads the chip removal of wear critical generating cuts has to be simulated. Therefore, the chip formation and the load on the rake face was FEM-simulated for the generating position with the largest chip volume in full cut for most of the cases of gearing tested. The general set-up of the FEMsimulation and several additional aspects are illustrated in Fig. 3. In adaption of the fly cutting analogy test only one tooth of a hob is cutting and the chip removal of only one generating position of one gap is being simulated. All previous generating cuts were performed within the CAD-system. The FEM-simulation was performed for the reference cutting parameters of both investigated moduli. Using AdvantEdge1 for simulation of the chip formation, standard material models of the software regarding workpiece (case hardening steel, 20NiCrMo22) and tool (HSS, ASP2052) were used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001678_978-3-319-09411-3-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001678_978-3-319-09411-3-Figure11-1.png",
        "caption": "Fig. 11 Differences between experimental and theoretical values for the cam follower displacement of Fig. 10",
        "texts": [
            " 9 Measurement of cams profiles Machine and Mechanism Design at UMinho\u2026 885 Figure 10 represents the experimental data versus the theoretical values for the cam follower displacement, as obtained with the set-up shown in Fig. 8. It can be concluded that, in general, the experimental results follow the theoretical values for the modified sine equation. However, looking at the results with more detail, there are some visible differences between the experimental and theoretical values, as shown in Fig. 11. These visible differences in the follower movements (rise and return), happened, approximately, between 0\u00b0 and 90\u00b0, which can be linked to measuring errors due to the curvature of the follower\u2019s surface and consequently, perpendicularity loss 886 M. Lima et al. between the laser beam and the measured surface, existence of clearances in joints and differences between designed and real cam profiles, originating a different follower displacement. It can also be observed that, approximately between 0\u00b0 and 90\u00b0 the experimental data are greater than the expected theoretical values, which may be due to existent clearances in joints and geometric differences in the kinematic chain, besides the ones existing in the follower shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002637_13621718.2019.1629379-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002637_13621718.2019.1629379-Figure1-1.png",
        "caption": "Figure 1. Schematic diagrams: (a) the sampling positions, (b) the dimensions of tensile specimens, and (c) the test samples.",
        "texts": [
            " For sample 2, 25 layers of Al alloy were deposited on a 6061 Al alloy substrate, and 15 layers of Ti alloy layers were deposited on the Al alloy layer. During the WAAM process, the time interval between adjacent layers was 2min. Droplet transfer pictures were obtained with a high-speed CCD camera at a frame rate of 2000 frames per second. Metallographic samples with the dimensions of 20\u00d7 5\u00d7 10mm of the Al and Ti alloys were cut and polished, and then etched for 1min using a standard Keller solution. A schematic of the sampling positions is shown in Figure 1(a). The observed surfaces of the metallographic samples were parallel to the y\u2013z surface. The microstructures of the metallographic samples were observed via scanning electron microscopy (SEM), coupled with energy dispersive spectroscopy (EDS) and transmission electron microscopy (TEM). Tensile tests were carried out at ambient temperature using an electro-mechanical universal testing machine. Three specimens of each sample were loaded at a constant displacement rate of 0.5mmmin\u20131 for tensile testing. The dimensions of the tensile specimens are shown in Figure 1(b). To evaluate the tensile strength of the samples accurately, the tensile specimens were cut and polished as shown in Figure 1(c). Figure 2 shows the fabricated components. As shown in Figure 2(a), for sample 1, a Ti/Al dissimilar alloy component was obtained with the Ti alloy deposited first. The length, height, and thickness of sample 1 were \u223c150, 130, and 6mm, respectively. No obvious defects were found on the component surface. The Al side of the component was flat and smooth with a metallic lustre. However, grooves had formed between the Figure 2. Components: (a) sample 1; (b) sample 2, and (c) voids in sample 2. Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000565_j.talanta.2010.11.070-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000565_j.talanta.2010.11.070-Figure1-1.png",
        "caption": "Fig. 1. (A) Details of the flow cell employed in this study: (a) electrode body (Teflon); (b) metallic rod; (c) epoxy resin body; (d) Plexiglas cell body; (e) steel tube (auxiliary e (i) OP c njecto c",
        "texts": [
            " mperometric measurements were performed using a -Autolab ype III potentiostat (Eco Chemie) connected to a microcomputer nd controlled by Autolab GPES v. 4.8 software. A conventional hree-electrode cell, consisting of a pyrolytic carbon electrode, platinum wire and a calomel electrode was employed for the oltammetric measurements. The working electrode was contructed using a pyrolytic graphite rod (length 8 mm, diameter mm Union Carbide Co., Cleveland, Ohio, USA), embedded in epoxy esin. For the flow injection analysis experiments, a simple flow cell as built in our laboratory (Fig. 1A) in such a way as to fit the same yrolytic carbon electrode previously employed in the voltametric experiments. A miniaturized Ag/AgCl/KClsat electrode was onstructed in the laboratory for use in the same flow cell [20]. .3. Electrode preparation Prior to modification, the basal plane of the ordinary pyrolytic raphite electrode (OPG) was polished with 2000 grit emery paper, ashed with deionized water, than transferred to a beaker con- G rod; (j) Teflon tape, B) flow injection manifold used for NAC determinations: (a) r; (e) sample reservoir (f) flow cell (detailed on the left side); (g) potentiostat; (h) taining deionized water and sonicated for 2 min. After cleaning, the electrode was immersed for 20 min in a 1 \u00d7 10\u22123 mol L\u22121 CoPc dimethylsulfoxide solution. Finally, it was washed with purified water, dried and it was then ready to use. 2.4. Flow analysis The flow measurements employed a single channel manifold (Fig. 1B) connected to the homemade wall-jet flow cell. A peristaltic pump (Model 78016-30, Ismatec S/A) was used to propel the carrier solutions. A manually operated rotary valve was used to introduce the standards and samples into the flow stream. The carrier solution was 0.1 mol L\u22121 NaOH. This electrolyte was selected based on the voltammetric experiments undertaken previously. Polyethylene tubes (0.8 mm i.d.) were used to connect all parts of the system. All experiments were carried out at room temperature (23 \u00b1 3 \u25e6C)",
            " This suggests that this technique should be uitable for the quantification of NAC in many different pharmaeutical products. .3. Flow injection analysis (FIA) of NAC The high current density observed in the previous experiments as a result of the strong catalysis achieved at the OPG\u2013CoPc interace of the modified electrode. These results suggested that the ensor could also be effective for the quantification of NAC by mperometry in a flow analysis system. To investigate this possibilty, a new wall-jet cell (shown in Fig. 1) was built in our laboratory nd a flow system was assembled. Since the previous experiments ad shown that the best results were obtained when 0.1 mol L\u22121 aOH was used as the supporting electrolyte, the same solution was sed here as the carrier solution and to prepare the NAC solutions. Optimization of the FIA method involved consideration of the nfluences of flow rate, sample volume and the distance between he nozzle and the detector. A solution of the NAC (5 \u00d7 10\u22124 mol L\u22121) n 0.10 mol L\u22121 NaOH was monitored at 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003265_tmag.2020.3013624-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003265_tmag.2020.3013624-Figure3-1.png",
        "caption": "Fig. 3. No-load flux and magnetic field distributions of the improved structure. (a) Forward magnetized. (b) Reversely magnetized.",
        "texts": [
            " Improved Structure To stabilize the working points of AlNiCo magnets, the improved structure of hybrid-PM variable-flux PMSM with series-parallel magnetic circuits is proposed. The design specifications for the improved structure are shown in Table I. As shown in fig. 1(b), two layers of magnets are placed in the proposed machine. The upper V-type layer, which is close to the air gap, is similar to the initial structure. The lower U-type layer, which is close to the rotor shaft, is composed of seriesconnected NdFeB and AlNiCo. The no-load flux and magnetic field distributions of the improved structure are shown in fig. 3. Under forward magnetization state, as shown in fig. 3(a), the flux of the lower U-type magnets flows through the upper Vtype magnets and help to stabilize the working points of upper V-type magnets, especially the AlNiCo near the d-axis, similar with the series-connected hybrid-PM variable-flux PMSMs. Under reverse magnetization state, as shown in fig. 3(b), the AlNiCo near the d-axis in the V-type layer is reversely magnetized by -id pulses, and the other AlNiCo is demagnetized but not reversely magnetized for the influence of series-connected NdFeB. Most flux of V-type magnets is short-circuited in the rotor core. And part of the U-type magnets\u2019 flux flows into the air gap through the magnetic bridges. The improved structure also has a wide magnetization state variation range, similar with the parallel-connected hybrid-PM variable-flux PMSMs. The torque density and power density are 8",
            " So Lq is lower than that in the forward magnetization state. When the flux-weakening current angle decreases, negative d-axis current increases and q-axis current decreases. The magnetic saturation along the q-axis is reduced, so Lq increases, which is similar with the variation laws under forward magnetization state. And the difference of Lq under two magnetization states is nearly zero when the fluxweakening current angle is small enough. While Ld decreases, which is different from the variation law mentioned above. As shown in fig. 3(b), the AlNiCo magnets along the d-axis magnetic circuit are reversely magnetized. So the direction of the magnetic field generated by flux-weakening current is identical to the magnetization direction of the magnets along the d-axis. The magnetic saturation along the d-axis Authorized licensed use limited to: University of Canberra. Downloaded on October 04,2020 at 14:38:56 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002858_j.prostr.2019.08.112-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002858_j.prostr.2019.08.112-Figure5-1.png",
        "caption": "Fig. 5. Component test: (a) experimental setup, (b) raw velocity signal, (c) filtered signals, (d) relative amplitude.",
        "texts": [
            " This is also shown by the impact tests at low temperatures (-20 \u00b0C and -50 \u00b0C). At low temperatures, body-centered cubic (bcc) materials break more brittle, which causes the energy absorbed to drop. The aged samples are not affected by the low temperatures. Again, there is no difference between the building directions and wrought material. 848 Thomas Simson et al. / Procedia Structural Integrity 17 (2019) 843\u2013849 6 Author name / Structural Integrity Procedia 00 (2019) 000\u2013000 For the test of ball joints for attaching headlamps a test setup was realized (Fig. 5a)). To connect them, a prototype frame made by LPBF was used. For testing automotive headlamps, frequency ranges of excitation from low (5-10 Hz) to high (200-1000 Hz) are typically used for multi-hour tests. The typical acceleration is about 1 to 3 g (RMS) at resonant frequencies in the range of 30 to 50 Hz. The tests are carried out in the low frequency range of 5-50 Hz, in which the resonance frequency of the headlamp is to be expected. Fig. 5a) shows the experimental setup. In the experimental setup, 6 points for measurement and one point on the excitation plate are defined as reference. Points 1-3 are on the metal frame produced by LPBF , and points 4-6 refer to the aluminum weights. The experiment was repeated several times, tightening of plastic ball joints and other joints for better results. The measurement itself was first performed for discrete frequencies (5, 10, 15-50 Hz) and later with continuous increment of frequency from 5-50 Hz. For each test, 6 points were measured on the frame and aluminum weights and one point on the excitation source (to calculate the relative amplitude). The measured signal has the lowest noise on the clean reflective aluminum surface of the excitation plate. Higher noise is measured on the AM frame, possibly due to the surface roughness. The measured time-dependent velocity signal from excitation plate is shown Fig. 5b) (top) and from point 2 of the frame with noise (bottom). The noise was then removed by the digital filtering before analysis. The measured signals were filtered and then the accelerations calculated by numeric method. The calculated accelerations of the frame points 1, 2, 3 are shown in Fig. 5c) (green, blue, magenta). It is obvious that we achieve resonant frequency. The time in second is plotted on the x-axis of the signal (measurement with continuous frequency increase). The x-axis was then converted to the corresponding frequency, the acceleration amplitude was divided by amplitude of point 0 (excitation frequency) and resulting relative amplitude is shown in Fig. 5d). Through data analysis, a range of 30-35 Hz for the resonant frequency could be determined. This is a typical result for car headlamps. The resonant frequency range is a parameter for tightening the ball joints. However, it has been stated that the frame produced by LPBF does not give different results than a conventionally produced frame. This shows that AM components can be used for prototype testing. Thomas Simson et al. / Procedia Structural Integrity 17 (2019) 843\u2013849 849 Author name / Structural Integrity Procedia 00 (2019) 000\u2013000 7 The results demonstrated that the high-strength MAR 300 which was comparable to the wrought material could be produced by LPBF and subsequent solution annealing heat treatments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001285_bf00818317-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001285_bf00818317-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of thehorizontal-plane fr ict ion tes ter .",
        "texts": [
            " To exper imenta l ly evaluate the ha rdness dependence of the total coefficient of f r ic t ion, we c a r r i e d out expe r imen t s in which a spher ica l indenter g razed polished fiat su r faces of copper samples . These flat s amples were made f rom the s ame types of copper as the samples for which the ha rdness dependence of the adhesive component of the coeff icient of f r ic t ion was studied. The indenter , 2 m m in d iamete r , was made f r o m ShKh-15 s teel . The expe r imen t s were c a r r i e d out on a hor izonta l -p lane f r ic t ion t e s t e r , shown s c h e - ma t i ca l ly in Fig. 4. F la t sample 2 is p laced on ca r r i age 1 which is connected to hydraul ic cyl inder 4 by a push rod. The c a r r i a g e can slide along guides with r e spec t to the indenter , which is connected by rod 5 to e las t ic e lement 6, to which r e s i s t a n c e pickups a re cemented. The s ignals f rom the pickups are amplif ied by ampl i f i e r 7 and detected by osc i l loscope 8. The load is produced by a se t of weights 9. The e las t ic e l e - ments a re ca l ib ra ted beforehand by a f i lament through a block mounted on a base and by weights"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.41-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.41-1.png",
        "caption": "Fig. 17.41 Pole quadrilateral with four circle points and center point Q0",
        "texts": [
            " The pole curve is the geometric locus of all points from which opposite sides of a pole quadrilateral are seen under angles which are either identical or which add up to \u03c0 . The present problem is to determine all four-tuples of homologous points Q1 , Q2 , Q3 , Q4 which are located on a circle and for each circle the center point Q0 . Following Burmester the geometric locus of all center points thus defined is called center point curve. Proposition: The center point curve is the pole curve. Proof: Figure 17.41 shows four homologous points Q1 , Q2 , Q3 , Q4 on a circle with center Q0 . Homologous means that the poles of the pole quadrilateral (P12,P23,P34,P41) are located somewhere on the dashed bisectors of the angles of rotation \u03d5ij = (QiPijQj) (i, j = 1, 2, 3, 4 different). From Q0 the opposite sides P12P23 and P34P41 are seen under the angles 1 2 (\u03b212 + \u03b223) and 1 2 (\u03b234 + \u03b241) , respectively. Since \u03b212 + \u03b223 + \u03b234 + \u03b241 = 2\u03c0 , these angles add up to \u03c0 . If a pole, say P41 , is located on the other side of Q0 , the two opposite sides of the pole quadrilateral are seen under identical angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001293_0954406214543490-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001293_0954406214543490-Figure2-1.png",
        "caption": "Figure 2. Parameters definition for the misalignment error.",
        "texts": [
            " Then, the transmission error of gear pair on every transverse cross section, mesh stiffness of external and internal gear pairs and dynamic and static model of planetary gear set are given in the second section. A numerical method solving contact problem is presented in the third section. The numerical solution is obtained and the analysis on the characteristic of misalignment error of carrier is presented in the fourth section. Conclusions are given in the final section. Figure 1 shows the scheme of the carrier and the planets and a three-dimensional coordinate system wherein the shaft axis of the carrier coincides with the Z-axis. The parameter definitions of misalignment are shown in Figure 2 where OG is the shaft axis of carrier with misalignment. The axis of the carrier is tilting around the point O where O is in the end face of the carrier. Here, it needs to be noted that the point O stays stationary. The deviation of point O is not discussed as it will give rise to change of relative position of sun\u2013planet and ring\u2013planet. Then, the load sharing between planets will become uneven. The characteristic of planetary gear system due to pinhole position error has been investigated sufficiently.13\u201316 So, this paper focuses on the characteristic analysis on the tilting of carrier with point O fixed. For the point E on the line OG in Figure 2, with z coordinate z0, the x and y coordinate values are x0 \u00bc z0 tan y0 \u00bc z0 tan = cos \u00f01\u00de at UNIV CALIFORNIA SAN DIEGO on February 16, 2016pic.sagepub.comDownloaded from Perfect pinion-sun mesh when there is no misalignment error is shown in Figure 3(a). Each contact line in the base plane is discretized into several potential contact points. As the carrier is titling, all planets are assumed to incline in the same degree regardless of the effect of the bearing clearance as shown in Figure 3(b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000230_j.jweia.2007.06.031-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000230_j.jweia.2007.06.031-Figure3-1.png",
        "caption": "Fig. 3. Support arrangement. (a) rear support, (b) lower support, (c) upper support, (d) side support.",
        "texts": [
            " value of the fluctuating pressure Dp \u00f0\u00bc ffiffiffiffiffiffi p02 q \u00de on the surface of the plane was measured using a semi-conductor pressure sensor. The lift and drag coefficients were obtained by integrating the pressure distribution. The fluctuating velocity was measured using an I-type hot wire anemometer, and the vortex shedding frequency from the sphere was obtained by analyzing the fluctuating velocity of the wake. In order to avoid support effects, the sphere was variously supported from the rear, from the side, from below and from above, as shown in Fig. 3, depending on the area being investigated. For instance, when the pressure on the top half of the sphere was measured, the sphere was supported from below. ARTICLE IN PRESS T. Tsutsui / J. Wind Eng. Ind. Aerodyn. 96 (2008) 779\u2013792782 Figs. 4(a)\u2013(g) are photographs showing the flow visualization of the sphere for d/d \u00bc 0.46 and S/d \u00bc 0\u20130.526. The smoke wire (0.1mm) was placed centrally (Y \u00bc 0) upstream of the sphere. For S/d \u00bc 0, 0.026, 0.053 and 0.088, arch vortices were formed downstream of the sphere and the separated shear layer from the top surface of the sphere reattaches at its rear surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002979_lra.2019.2945468-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002979_lra.2019.2945468-Figure2-1.png",
        "caption": "Fig. 2: C-drive supplied with a SWG (for scale, ballscrews are 60 mm long)",
        "texts": [
            " Simulation results based on a dynamics model are reported. Experimental data are also provided and discussed. Finally, some practical insights are given, for further development. The two C-drive architectures are tested in conjunction with the PMC. These two mechanisms were initially designed to overcome issues related to bending moments on the rotary coupling in the architecture proposed by Harada et al. [22]. The first, a cable-driven architecture, as shown in Fig. 1, is tested. The second, a strain-wave gear (SWG) speed reducer, shown in Fig. 2, is used as a replacement of the cable-driven mechanism. Kinematically, both alternatives are equivalent. 3strain-wave gear The main difference resides in the high speed-reduction ratio G in the CSWG-drive4. These two versions of the C-drive were proposed in an earlier paper [23] and tested with an external load generated by a mass of 0.5 kg. In this letter, each drive is mounted on the PMC to compare their performance w.r.t. PPOs. The complete kinematic chain of the PMC is illustrated in Fig. 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003706_j.wear.2021.203687-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003706_j.wear.2021.203687-Figure2-1.png",
        "caption": "Fig. 2. Rotation direction of driving worm and driven worm gear.",
        "texts": [
            " A schematic diagram of an experimental worm gear test rig under controlled testing conditions was designed and then manufactured to carry out the series of tests as shown in Figs. 1 and 2. The test rig consists of a pair of worm gears. A driving brass worm is directly driven by a 150 W DC motor. This provides the test rig to have a power of 0.20 hp and maximum speed at 12,000 rpm. A simple bicycle disc brake is used as an applied torque loading system. The applied resisting torques in this particular work are set at 0.03 and 0.09 Nm. Direction of the driving worm is CCW and the driven worm gear is CCW at 90\u25e6 perpendicular to the driving worm axis, as shown in Fig. 2. A small size pocket of fixed volume grease of 2 cc is accommodated between the brass worm and steel worm gear contact as shown in Fig. 3. A typical view of the worm gear test rig is illustrated in Fig. 4. Table 1 provides JIS C2200 brass worm and DIN 17100 St37 steel worm gear specimen properties. Fig. 5 shows typical images of both steel worm gear and brass worm used in this work. In the case of worm gear three body abrasive wear tests, silicon dioxide particles (SiO2) at a mean particle size range between 50 and 75 \u03bcm as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001782_1.4031792-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001782_1.4031792-Figure1-1.png",
        "caption": "Fig. 1 Methods of modifying the cage [13,14]",
        "texts": [
            " In all these simulations, cage stability is evaluated by analyzing the cage center whirl, as it allows to distinguish between stable and unstable cage movements. Additionally, experimental studies were conducted, investigating the cage whirl and slip of bearing components. References [3] and [4] were among the first identifying the cage instability as a critical factor for bearings. The majority of experiments regarding cage whirl used metal cages or were conducted by modifying the bearing to make the cage motion visible. In the latter case, either metal tapes are added on the cage [13] or the cage geometry is modified [14], see Fig. 1. Other authors added foil, with black and white barcode, on the cage to detect slip, e.g., see Ref. [15]. Measuring the movements of the components is very challenging due 1Corresponding author. Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 19, 2015; final manuscript received October 5, 2015; published online November 9, 2015. Assoc. Editor: Xiaolan Ai. Journal of Tribology APRIL 2016, Vol. 138 / 021105-1Copyright VC 2016 by ASME Downloaded From: http://tribology",
            "org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use to the fact that high-precision angular contact ball bearings for motor spindles typically are hybrid bearings consisting of ceramic rolling elements and polyamide or phenolic cages. Moreover, any changes to the cage mentioned above influence the cage properties and thereby the results. On the other hand, radial cage movements in spindle bearings cannot be detected without changing the bearing rings to attach sensors, as shown in Fig. 1. Additionally, detecting the movements of bearing components made from ceramic or phenolic materials is challenging because the typically utilized inductive sensors can only be used with metal materials. Hence, investigating bearings with an image evaluation approach is very interesting and promising for optimizing cage geometries regarding the cage movements because it allows to observe unmodified bearings under realistic operating conditions. In order to investigate the bearing behavior without changing the properties of its components, a test rig was built as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure12.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure12.3-1.png",
        "caption": "Fig. 12.3 The first two bending modes of a baseball bat. At one instant of time, the bat is bent in the shape of the solid curve. A short time later, the bat is completely straight but it shoots past the straight position and bends the other way, as indicated by the dashed curve. The handle is more flexible and bends farther than the barrel",
        "texts": [
            " The strings of a racquet act as a trampoline when they eject the ball, and they vibrate for a second or so afterward with an audible ping sound. Bats can vibrate in several different ways. The low frequency, barely audible vibrations correspond to a back and forth bending of the bat along its whole length. The bat bends into a banana or C shape, first in one direction and then in the opposite direction, at about 170 times per second or 170 Hz. The bat can also vibrate simultaneously at a higher frequency, around 530 Hz, by bending back and forth into an S shape. Both modes of vibration are shown in Fig. 12.3 for a wood bat. Different parts of the bat vibrate with different amplitude. For the 167 Hz mode, the ends and the middle section of the bat vibrate the most. There are two spots about 6.5 in. in from each end that don\u2019t vibrate at all. These spots are node points. For the 530 Hz mode there are three node points, one of them being about 5 in. from the barrel end, one being about 3 in. from the knob end and one near the middle of 12.7 Bat Vibrations 211 the bat. The 167 Hz mode is called the fundamental mode, meaning that it is the mode with the lowest vibration frequency",
            "5) Consequently, high frequency waves propagate at a higher speed than low frequency waves. The velocity is high for stiff beams (with a large value of EI ) and for light beams (with a low value of A). For a freely supported, uniform beam of length L, standing waves exist when D 1:328L (for the fundamental mode) or when D 0:800L (for the second mode) corresponding to k D 4:730=L and k D 7:853=L, respectively. The fundamental mode for a uniform beam has a node at x D 0:22L and another node at x D 0:78L, similar to the situation shown in Fig. 12.3 for a freely supported bat. Solutions of the beam equation are shown in Fig. 12.8 for a uniform beam of mass 0.885 kg and length 0.84 m, similar in mass and length to a real bat, for impacts near the tip, sweet spot and middle of the beam. The beam was initially stationary and was impacted with a baseball of mass 0.145 kg and stiffness 1,000 kN m 1, exciting both the fundamental and second bending modes. The behavior of the beam is very similar to that of a real bat [3] and it exhibits many of the features that we have previously described"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002085_tec.2014.2326301-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002085_tec.2014.2326301-Figure5-1.png",
        "caption": "Fig. 5. Geometry of the permanent-magnet machine.",
        "texts": [
            " With motion at this level constrained along partition boundaries, no motion can take place within these partitions or within their children. When these partitions are also magnetically linear, their Jacobian matrices will remain constant as the device moves from one position to the next. The Jacobian matrices of partitions nearer the root, which contain motion, must be recomputed but their dimensions are only that of the number of boundary nodes of their children. A permanent-magnet synchronous machine, as shown in Fig. 5, operating below saturation provides a convenient practical example of this type of scenario. By partitioning the rotor and stator of this machine as separate children of the global domain, the relative motion between them is constrained to the root partition. The nodes of this root partition consist only of the 360 nodes centered in the air-gap along the boundary separating the rotor from the stator. The subsequent partitioning of the stator and rotor regions follows the hierarchical strategy set forth in Section IV and is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure10-1.png",
        "caption": "Fig. 10. The 2T1R + 1-DOF parallel manipulators: (a) type 3 (b) type 4.",
        "texts": [
            " For the 2T1R + 1-DOF parallel manipulators with planar four-bar platforms, two L 1 F 1 C -limbs are constructed. The constraint-forces are parallel, while the constraint-couples are linearly dependent. In the wrench system, a constraint-couple is generated by two parallel constraint-forces. And the orientation of the caused constraint-couple is vertical to the platform. As a result, the 2T1R parallel manipulators that can output 1-DOF internal mobility within the configurable platform are de- rived, as drawn in Fig. 10 . When the 6R closed-loop linkage is mounted on the end of connected limbs, the 2T1R + 1-DOF parallel manipulators with the 6R configurable platforms are derived. Two L 1 F 1 C -limbs are used to construct 2T1R + 1-DOF parallel mechanisms. The constraint-forces are parallel, while the constraint-couples are linearly dependent. The constraint-forces generate an additional constraint-couple which is vertical to the platform. Therefore, the 2T1R + 1-DOF parallel manipulator with two working phases is constructed, as shown in Fig",
            " For the Bennett platform, the motion of two end-effectors can be taken as a rotation. The axis of the rotation is passing through the intersecting point O . It is perpendicular to the plane determined by E 1 , E 2 , and O . It is noteworthy that there is a dependent translation between E 1 E 2 and E 3 E 4 , and the direction is parallel to OO \u0301. Similarly, the relation motion between the end-effectors of other single-loop platforms can be obtained in the following Table 6 [28] . Taking the type 4 parallel manipulator shown in Fig. 10 (b) as an example, the qualified actuators of the bottom mecha- nism n a1 equals to 3. The dimension of the screw system for the single-loop mechanism is 1. Then the number of actuators ( n a1 + n a2 ) is matched. When all actuators are locked, the mechanism is transformed into a five-bar structure. And the DOF of the derived structure is zero. Therefore, the deployment of driving motors for this manipulator is reasonable. For the 2T3R + 1DOF mechanism shown in Fig. 16 (b), the equation ( n a1 + n a2 ) = 6 is carried out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001565_0954406214562632-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001565_0954406214562632-Figure10-1.png",
        "caption": "Figure 10. The uneven tooth surface of gear.",
        "texts": [],
        "surrounding_texts": [
            "Make use of Matlab to program and calculate the machining adjustment parameters of gear and pinion, then put in the above parameters to get their tooth surface discrete points cloud, and output the points cloud data documents as shown in Figure 5. Sample 12,445 discrete points of gear and 24,644 of pinion, which is adequate for the precision of modeling and processing such gears with geometry specification. Based on the design parameters of gear set shown in Table 1, the adjustment parameters can be calculated through Matlab program. Tables 2 and 3 indicate the calculated adjustment parameters for gear and pinion, respectively. Ru, g, P!2, and ! are the cutter parameters for gear; Rp, p, and f are the cutter parameters for pinion; Sr2, q2, Em2, XB2, XD2, and m2 are the gear machine-tool settings; Sr1, q1, Em1, XB1, XD1, and m1 are the pinion machine-tool settings; m1c (m2c) is the ratio of instantaneous angular velocities of the pinion (gear) and the cradle; C and D are the modified roll coefficients for calculating rotation angle. Digital true tooth surface modeling The curved surface reconstructed in the 3D software (SolidWorks) via leading points cloud documents by means of reverse engineering, is not smooth but stitched by many small curved surfaces, as shown in Figures 6 to 12. A crack seems to be in the middle of the curved surface, which not only influences the visual effects, but also prevents contact analysis and xm1 ym1 zm1 ya1 oa1 za1 xa1 yb1 y1 o1 (ob1) x1 xb1 z1 (zb1) \u0394Em1 \u0394X B1 \u0394X D1 m 2 \u03a6 1 om1 \u03b3 Figure 4. Workpiece coordinate system for pinion. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from solution in FEA, and even contact setting. Therefore, it is necessary to adopt other methods or approaches to deal with the reconstruction. The uneven tooth surface is modeled via the function of \u2018\u2018Scan To 3D.\u2019\u2019 Points cloud can almost automatically form the curved surface in software only by simple operations, at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from in no need of many man-made operations. However, by use of \u2018\u2018Scan To 3D,\u2019\u2019 some points cannot be scanned and thus ignored. Moreover, as the sequence and path of scan cannot be controlled, the surfaces do not look smooth with numerous cracks. In order to solve these problems, the method of \u2018\u2018Lofted Surface\u2019\u2019 is adopted to create the surface. Firstly, all the points make up lines in order. Secondly, use the function of \u2018\u2018Lofted Surface\u2019\u2019 to select the lines in sequence. Thirdly, form the smooth surfaces. Finally, by means of \u2018\u2018Clipping,\u2019\u2019 \u2018\u2018Array,\u2019\u2019 and other operations, model smooth spiral bevel gear and pinion. The digitized and high-precision true tooth surfaces under the study of this paper are shown in Figures 13 and 14. Smooth tooth surface can also reduce model errors and lay a foundation for high precision machining and FEA. Gear cutting and contact pattern experiments To verify the technical advancement and practicability in engineering digitized true tooth surface of spiral bevel gear based on machining adjustment parameters, this study gets the NC codes via NC process simulation software from 3D model with machining adjustment parameters and then inputs the codes to five-axis NC machine tools to conduct gear cutting experiments. Figures 15 and 16 show the processing of gear cutting in YH606 CNC Curved Tooth Bevel Gear Generator made by Tianjin Jing Cheng Machine Co., Ltd of China. The gear and pinion after processing are as shown in Figures 17 and 18, which completely meet the required design precision. Figure 13. The smooth tooth surface. Figure 12. The uneven assembly drawing of spiral bevel gear. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from To better illustrate the problem, other related experiments have also been conducted. The illustration of VHG is shown in Figure 19. H is the movement along the pinion axis, while G is the movement along the gear axis, and V is the offset of the gear set. When doing the experiments of contact pattern for spiral bevel gear set, keep the offset (V) at the value of 0, and the true backlash for the gear is set at 0.22mm. Each time, only change the value of H from 0.2 to \u00fe0.2. In this way, three experiments have been done, setting the value of H as \u00fe0.2, 0, and 0.2, respectively. The transmitted torque of contact patterns experiment was 20Nm according to at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from some standard; Figures 20 to 22 show the results of contact pattern experiments of three complete teeth in gear, without use of any correction in the tooth surfaces of pinion, from which it can be told that the contact pattern for the gear set is not bad, for it satisfies all the requirements of engineering. The gear cutting experiment can prove the validity of the precise modeling method of spiral bevel gear true tooth surface, which can be used in mechanical engineering, besides theoretical research. Breaking the blockade on Gleason technology, the spiral bevel gear true tooth modeling method, without any Gleason at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from software, can calculate the machining adjustment parameters. General NC machine can also be used to process spiral bevel gear, needless of special purpose machine for Gleason spiral bevel gear and Gleason software. This is the contribution of this research, other method cannot processing spiral bevel gear in general NC machine, the special purpose machine of spiral bevel gear and Gleason software are needed. The gear contact pattern experiments are the test method for the rotating gear pair. From the contact spot, vibration and noise of gear pair can be assessed in the same case. The use of standard spherical involute 3D model has no meaning in engineering, for it fails to get good contact pattern. In fact, spiral bevel gear is not the standard spherical involute, but just a modified spherical involute. It is the value and the reason why to use machining adjustment parameters to get the true tooth surface precise modeling processed in NC machine."
        ]
    },
    {
        "image_filename": "designv10_12_0001593_10671188.1963.10613232-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001593_10671188.1963.10613232-Figure1-1.png",
        "caption": "FIGURE 1. Ballistic pendulum.",
        "texts": [
            " In order that there be no impulsive jar on the suspension, it is desirable that the path of the projectile should pass through what is known as the center of percussion (10). This condition is satisfied if h(c-k) = k2, where k is the radius of gyration about the mass center. The ballistic pendulum used for the tests was designed so that the center of percussion was in the center of the target board, which means that the point of impact of a puck was usu ally fairly close to the center of percussion. The striking area of the ballistic pendulum was 2-ft. square (Figure 1). Its surface was painted black and lined horizontally at Lin, intervals. Light chalk dust was evenly spread over the surface for each trial so that the point ~ n AXIS AT or i,.-POINTER D ow nl oa de d by [ U ni ve rs ity o f O ta go ] at 2 0: 54 2 1 D ec em be r 20 14 262 The Research Quarterly, Vol. 34, No.3 of contact of puck and pendulum could be measured by observing the point of disturbance of the chalk dust. Measurements were made from the hot tom edge of the pendulum to the centre of the impact point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001654_s00170-017-1048-9-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001654_s00170-017-1048-9-Figure11-1.png",
        "caption": "Fig. 11 Interaction of feed rate and spindle speed on average roughness (a, b) and mean roughness depth (c, d) using ANN and Poisson statistical analyses",
        "texts": [
            " Also, the lag angle is close to zero and the immersion angle has the highest value so the dynamic of the metal cutting process is similar to turning (single point/continues cutting), and based on Eqs. 16 and 29, an increase in cutting force is observed. By taking into account the low elastic modulus for titanium and high springback effect, the values of vibration and surface roughness increase. Figure 9a\u2013d shows that rougher surfaces were obtained when using the helical tool path [39, 41, 43\u201345]. Figure 10 also shows that using the linear tool path results in better surface quality associated with the movement of a cutting point on the cutter. Figure 11 shows that the surface roughness decreases by increasing the spindle speed, and this trend is proved by using both ANN and Poisson regression methods. In the machining of titanium, thermal softening initiation occurs in the range of 300\u2013500 \u00b0C. Also, titanium has high tendency to react with most of the cutting tools and this phenomenon leads to losing sharp edges, and the cutting area is moved toward the second position (Fig. 10b). Therefore, the cutting force, the chance of chip welding to the cutting edge and roughness increase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002383_1.4035079-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002383_1.4035079-Figure1-1.png",
        "caption": "Fig. 1 The lengthwise curve and profile of a tooth surface",
        "texts": [
            " Subsequently, the tool path planning is implemented for five-axis flank milling in Sec. 4. Furthermore, the closed-form representation of the simulate machined tooth surface is obtained in Sec. 5. The discussion is conducted in Sec. 6. Finally, conclusions are given. 2.1 Tooth Surface Design of Spiral Bevel Gears. Tooth surface geometry is the fundamental factor to determine the contact and transmission of spiral bevel gears. It is usually described with a lengthwise curve and a series of profiles, as shown in Fig. 1. The lengthwise curve is a curve defined on the pitch cone of the spiral bevel gear. Assuming that q is a point on the lengthwise curve, the profile corresponding to q is defined as the intersection of the tooth surface with a plane Q . Q is the plane passing through q and perpendicular to the radial direction ogq in which og is the pitch cone apex. Generally, any reasonable shape can be chosen for both the lengthwise curve and profile [43]. Since the working part of the tooth surface generated from some conventional approaches is close to a ruled surface, we proposed a new ruled tooth surface design for the benefits of five-axis flank milling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001132_10402004.2011.648825-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001132_10402004.2011.648825-Figure1-1.png",
        "caption": "Fig. 1\u2014Transmission system of the test rig and the specimen configuration.",
        "texts": [
            " Previous research has mainly focused on a single sample of the triboparts. This study investigates the differences between the damage modes of the two surfaces of M50 steel tribo-parts and explores the regularity of surface damage under the extreme conditions experienced by aircraft bearings. The results provide design data and evaluation standards for the development of new tribomaterials and lubricants and surface treatments that can prolong bearing life. A two-disc test rig was employed in the experiments; the transmission system is shown in Fig. 1. One disc is a cylinder and the other has a crowned profile in the circumferential direction. The shape of the two discs was designed to investigate the wear characteristics of the elliptical contact, which is usually the contact pattern of the counterpart in bearings (Martin, et al. (5); Patching, et al. (6)). Both of the discs are made of M50 steel, and the heat treatment and surface finish of the tribo-parts were consistent with those of the ball bearings in aircraft engines; the material properties of the discs were nearly identical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram for each coordinate system of the flexible spherical joint.",
        "texts": [
            " Ct \u00bc K 1 t \u00bc EA L 0 0 0 0 0 0 12EIZ L3 1\u00feUy\u00f0 \u00de 0 0 0 6EIz L2 1\u00feUy\u00f0 \u00de 0 0 12EIy L3 1\u00feUz\u00f0 \u00de 0 6EIy L2 1\u00feUz\u00f0 \u00de 0 0 0 0 GIp L 0 0 0 0 6EIy L2 1\u00feUz\u00f0 \u00de 0 4\u00feUz\u00f0 \u00deEIy L 1\u00feUz\u00f0 \u00de 0 0 6EIz L2 1\u00feUy\u00f0 \u00de 0 0 0 4\u00feUz\u00f0 \u00deEIy L 1\u00feUz\u00f0 \u00de 2 66666666666664 3 77777777777775 1 \u00f01\u00de where L is the length of the beam and A is the cross-section area of the beam; Iy,Iz are the moment of inertia of the cross-section, and Iy \u00bc b3h 12 ; Iz \u00bc bh3 12 ; Ip is the polar moment of inertia of the crosssection, Ip \u00bc Iy \u00fe Iz; E and G are the modulus of elasticity and shear modulus of the material, respectively; Uy \u00bc 12EIz GAyL2 \u00bc 12EIzky GAL2 , Uz \u00bc 12EIy GAzL2 \u00bc 12EIykz GAL2 , ky \u00bc kz \u00bc 5\u00fe5v 6\u00fe5v, v is Poisson\u2019s ratio. The straight circular flexible spherical joint is shown in Fig. 3. According to reference [18], flexibility matrix of the straight circular flexible spherical joint is as follow: C \u00bc c1 0 0 0 0 0 0 c2 0 0 0 c3 0 0 c2 0 c3 0 0 0 0 c4 0 0 0 0 c3 0 c5 0 0 c3 0 0 0 c5 2 666666664 3 777777775 \u00f02\u00de where c1 c5 are expressed respectively as follows: c1 \u00bc 4I1 pE c2 \u00bc 64I3 pE \u00fe 2\u00f0j \u00fe v\u00deI1 pG c3 \u00bc 64rI2 pE c4 \u00bc 64 1\u00fe m\u00f0 \u00deI2 pE c5 \u00bc 64I2 pE \u00f03\u00de where k = 1 represents the average shear stress, m is the Poisson\u2019s ratio of the material, I1; I2; I3 are intermediate variables and expressed respectively as follows: I1 \u00bc 1 2r 1 n\u00f0n\u00fe2\u00de \u00fe 2 n\u00f0n\u00fe2\u00de\u00f0 \u00de\u00f03=2\u00de arctan ffiffiffiffiffiffi n\u00fe2 n q n o I2 \u00bc 8 pr3E n\u00f0n\u00fe2\u00de\u00f0 \u00de3 6n5\u00fe30n4\u00fe70n3\u00fe90n2\u00fe59n\u00fe15 6\u00f0n\u00fe1\u00de3 \u00fe 4n2\u00fe8n\u00fe5ffiffiffiffiffiffiffiffiffiffi n\u00f0n\u00fe2\u00de p arctan ffiffiffiffiffiffi n\u00fe2 n q I3 \u00bc 1 8r n\u00f0n\u00fe2\u00de\u00f0 \u00de3 8n4\u00fe32n3\u00fe57n2\u00fe50n\u00fe15 6\u00f0n\u00fe1\u00de2 \u00fe 5\u00f0n\u00fe1\u00de2ffiffiffiffiffiffiffiffiffiffi n\u00f0n\u00fe2\u00de p arctan ffiffiffiffiffiffi n\u00fe2 n q \u00f04\u00de The load-bearing branch can be considered as a beam model, whose stiffness matrix can be obtained from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.5-1.png",
        "caption": "Fig. B.5 Torques acting on the ship",
        "texts": [
            "1) where T is the total moment of action the forces about the point o; W =Mg is the weight of the flywheel; Scg = S \u2212 h ( 1 \u2212 R1 R2+R1 ) is the length of axle (distanced from the point o to the centre of gravity) [Appendix A]; Tp = J\u03c9\u03c9pis the precession torque generated by the rotating flywheel (Eq. 3.43); J = 3 10 M(R5 2\u2212R5 1 ) (R3 2\u2212R3 1 ) is the mass moment of inertia of the flywheel [1, 4, 6, 9];\u03c9 is the angular velocity of the flywheel; \u03c9p is the angular velocity of the precession of the flywheel around the vertical axis O; other components are specified above and in Fig. B.5. \u03c9p = \u03c0 rad/s = 3.141 rad/s (B.3.2) Since by hypothesis the flywheel does not slip on the plate of the pan, the angular velocity of the flywheel rotation is defined by its tangential velocity. The average tangential velocity of the rotation the flywheel about axis of the pane is as follows V = 2\u03c0nS = 2\u03c0 \u00d7 30 60 \u00d7 0.6 = 1.885m/s (B.3.3) The angular velocity of the flywheel is as follows \u03c9 = 2\u03c0n/60 = 2\u03c0 \u00d7 30/60 = 3.141 rad/s (B.3.4) The mass moment of the flywheel inertia is (Sect. A.2, Appendix A) J = 3 10 M(R5 2 \u2212 R5 1) (R3 2 \u2212 R3 1) = 3 10 \u00d7 1000 \u2217 (0",
            "9) Substituting defined expression and initial data into Eq. (B.4.2) and transforming yield the following: 0.5 = (4\u03c02 + 17)(296.471397 \u2212 1317.650653b), which sowing yields the following result: b = 0.225m The location of the counterweight from the pivot should be 225 mm that supports constant precession around axis oy, which is \u03c9y = 0.5 rad/s. B.5 Gyroscopic Torques Acting on a Ship The ship equipped with the turbine engine which rotating masses (spinning rotor) are horizontal and across the breadth of the ship (Fig. B.5). The direction of the angular velocity of the rotor in the clockwise direction when viewed from the tip of the ox axis. During the motion in the sea, the ship can get the steering to the left and right side around axis oz, pitching on the limited angle of motion about the transverse axis oy and rolling on the limited angle of motion about the longitudinal axis ox. The terms of the ship components, acting torques and motions are represented in Fig. B.5. Gyroscope torques act during steering. When the ship turns left by the action of the torque Tl, the angular momentum of the spinning turbine changes from H to Hl. The spinning turbine produces the following torques: Appendix B: Applications of Gyroscopic Effects in Engineering 249 \u2013 the resulting precession torque generated by the inertial forces T in, the rate change in the angular momentum T am and the resistance torque of Coriolis forces tend to raise the bow and lower the stern; \u2013 the resulting resistance torque generated by the centrifugal T ct and Coriolis forces T cr and the change in the angular momentum T am counteracts on the left turn (Fig. B.5). \u2013 The huge mass of the ship is many times bigger than the mass of the turbine. This is the reason that the ship does not demonstrate the sensitive raise of the bow, i.e. no pitching around axis oy. This situation means all inertial torques generated by the rotating mass of the turbine are deactivated and the ship turns only under the action of the steering torque. The steering process of the ship\u2019s turn is manifested by the action of the inertial torques of the change in the angular momentum of the turbine. The rolling of the ship does not relate to gyroscopic inertial torques. The axes of the rolling of the ship and the spinning turbine are parallel, and there is no precession of the spin axis and thus no gyroscopic effects. Example. The turbine rotor of the ship has a mass of 3.0 tonnes, length of 3 m and rotates 2000 rpm in the clockwise direction (Fig. B.5). The radius of gyration of the turbine rotor is 0.4 m. The mass and size of the ship are many times bigger than the turbine. Determine the maximal force acting on the supports of the turbine when the ship turns left at the radius of 200 m with a speed of 30.0 km/h and the steering torque applied on the ship is 130 kNm. Solution The ship turns left under the action of the external torque. At the starting condition of the turn, the rotating turbine generates the resistance and precession inertial torques produced by the centrifugal, common inertial and Coriolis forces and the change in the angular momentum acting around axis oz and oy. The action of the resulting precession torque at the starting condition manifests the minor pitching of the ship that can be neglected. Then, it is accepted the absence of the pitching, and hence, deactivation of the gyroscopic inertial torques accepts the change in the angular momentum of the turbine. The latter acting around axis oy on the supports of the turbine. The components of the turbine weight act on the supports along the axis oz (Fig. B.5). The force acting on one support of the turbine due to the action of the change in the angular momentum is as follows: Fy = Ty a = J\u03c9\u03c9z 3.0 = 240 \u00d7 209.439510239 \u00d7 0.041666666 3.0 = 698.13058N where a is the length of the turbine or distance between its supports, and other components are as specified above. The force acting on one support of the turbine due to the action of is weight is as follows: 250 Appendix B: Applications of Gyroscopic Effects in Engineering Fz = Mg a/2 = 3000 \u00d7 9.81 3.0/2 = 19620N where M is the mass of the turbine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002443_j.ifacol.2016.07.769-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002443_j.ifacol.2016.07.769-Figure1-1.png",
        "caption": "Fig. 1. Finite Element Model of PMSM and the mesh division.",
        "texts": [
            " This modeling approach is able to obtain an accurate and a complete description of an electrical machine. The magnetic circuit is modeled by a mesh of small elements. There field values are assumed to be a simple function of position within these elements, enabling interpolation of results (Prasad and Ram [2013]). Maxwell 14 that is one of the Ansoft software well known for FEM modeling. This software solves complex electromagnetic field problems and it considers the non-linearity of the study domain (Diga et al. [2014]). Tab.1. Fig. 1 shows the geometrical 2D model of the PMSM and the mesh division of the model. In this section, the principle diagram of the FEM cosimulation is proposed using Ansys Maxwell and Ansys Simplorer. The main circuit of PWM inverter shown in Fig. 3, is built by the circuit component module in Simplorer. There are six IGBTs switches and six stream diode modules. The PWM inverter control circuit, TRIANG module serve as a carrier wave generator and SINE module serve as a modulation wave generator. Each sinusoidal signal is shifted by 120 degrees based on a same frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000085_j.cma.2005.05.055-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000085_j.cma.2005.05.055-Figure13-1.png",
        "caption": "Fig. 13. Function of transmission errors of Example 4 with error Dc = 3 0 for: (a) unloaded gear drive; (b) loaded gear drive with torque 250 N m.",
        "texts": [
            " The formation of the bearing contact for the loaded gear drive is shown in Fig. 11. The drawings of Fig. 11 confirm that the edge contact is eliminated. Contact and bending stresses are shown in Fig. 12. Reduction of stresses is confirmed (Fig. 12). (iv) Example 4: A standard misaligned helical gear drive is considered. The purpose of the example is to demonstrate the disadvantage of a design wherein modification of geometry and a predesigned parabolic function of transmission errors are not applied. Fig. 13(a) shows the function of transmission errors D/2(/1) for an unloaded misaligned gear drive with error Dc = 3 0. The shape of function D/2(/1) confirms that the tooth surfaces of the pinion and gear are not conjugated, and edge contact exists. Fig. 13(b) shows the function of transmission errors D/2,t(/1) for a loaded gear drive, by application of a torque of 250 N m. The influence of load on transmission errors is favorable, since the magnitude of function of transmission errors is reduced. However, it cannot compensate the defects of non-conjugation (see Figs. 14 and 15). The drawings of Fig. 14 confirm existence of edge contact. Fig. 15 shows that the stresses are much higher in comparison with the design based on double-crowning or even profile crowning (see Examples 3 and 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000189_1.2805429-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000189_1.2805429-Figure5-1.png",
        "caption": "Fig. 5 Pressure and film thickness for a he when the bump is located at the center of the",
        "texts": [
            " As the bump moves into the contact region, pressure spikes develop due to solid contact. Since the height of the bump is almost five times the central film thickness, solid contact occurs even before the bump enters into the contact zone. Due to insufficient lubrication at the trailing edge of the contact, the pressures there drop to zero. As the bump exits the contact, steady state conditions are restored and the pressure and the film thickness are the same as those in the absence of the bump. Figure 5 illustrates the 3D pressure and film thickness distributions and contours at the instance when the herical bump under pure rolling condition at isp bump is located at the center of the contact zone. Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use a u o a i h t c s o 3 F b J Downloaded Fr Figure 6 depicts the variation of contact load ratio and contact rea ratio for the case of the hemispherical bump described above nder pure sliding condition. The contact load ratio is the fraction f the total applied load carried by solid contact while the contact rea ratio indicates the fraction of the total Hertzian area, which is n solid contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001401_imece2012-87675-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001401_imece2012-87675-Figure1-1.png",
        "caption": "FIGURE 1. CABLE-DRIVEN MANIPULATOR STRUCTURE",
        "texts": [
            " 1 1 r r r r j j j j n i in i q q q q q q               (3) n j n j j j j j q q q q W                   r P r P 1 1 (4) In order for Eq. 4 to remain equal to zero regardless of the variation in generalized coordinate, the coefficients must equal zero, as shown in Eq. 5. These are the governing equations for the static equilibrium. Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 3 Copyright \u00a9 2012 by ASME 0 r P j j j iq     (5) In this paper, the mechanics of a cable-driven manipulator with an elastic core are considered. Figure 1 illustrates the typical structure of such a manipulator, based on an implementation by Rucker and Webster [7]. Rigid disks are mounted along an elastic core, and flexible cables transmit actuation along the length of the manipulator. A frictionless interaction is assumed along the length of the cable, resulting in a constant tension along the length of the cable. This assumption is common in the literature during early-stage investigations into continuum robot mechanics [7] and may be validated by selecting low friction materials for the disk and cable (such as Teflon-filled plastic and Teflon-coated thread)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002646_j.anucene.2019.07.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002646_j.anucene.2019.07.003-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the reactor core, the OTSG and their connections.",
        "texts": [
            " In addition, the robustness of the proposed BLSMC control system is also analyzed. This paper is constructed as follows. The nonlinear MHTGR model is presented in Section 2. TS fuzzy control system is introduced, and the proposed BLSMC controller is developed in Section 3. Simulations where the CSMC controller is design for comparisons are conducted and discussed in Section 4. Finally, Section 5 concludes this paper. In MHTGRs, the output power of the reactor is regulated by moving the control rod. As shown in Fig. 1, the reactor is connected with the once-through steam generator (OTSG) by a horizontal coaxial hot gas duct. Helium that is served as the coolant circulates between the reactor and the OTSG, and the heat produced in the reactor core is taken away simultaneously. Considering reactor kinetics based on one equivalent delayed neutron group, temperature feedback and reactivity feedback determined by the pebblebed/reflector community, the dynamic model of the MHTGRs can be described as (Dong, 2014a,b,c; Zhe, 2015): nr \u00bc qr b K nr \u00fe b K cr \u00fe aR K \u00f0TR TR;m\u00denr cr \u00bc k\u00f0nr cr\u00de TR \u00bc XP lR \u00f0TR TH\u00de \u00fe P0 lR nr TH \u00bc XP lH \u00f0TR TH\u00de XS lH \u00f0TH TS\u00de qr \u00bc Grv r 8>>>>>< >>>>>: \u00f01\u00de Remark 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003255_s00170-020-05766-0-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003255_s00170-020-05766-0-Figure1-1.png",
        "caption": "Fig. 1 The slicing diagram of a STL model. a Intersection points solving. b Linear equation solving",
        "texts": [
            " The core of discretization is the slicing process, which slices the target model into certain layers along the forming direction. The essence of the slicing process is to solve the intersection points of triangular patches and tangent planes. The core of accumulation is to fill the outline polygons layer by layer and the filling effect depends on the accuracy and stability of the slicing process [12, 22]. In this section, an optimized slicing algorithm that improves the efficiency and practicability of the slicing process is proposed. As shown in Fig. 1, the slicing process of a STL model is to solve the intersection points of the spatial triangle and certain plane (height Z = C). The triangle V1V2V3 intersects the planes Z1, Z2, and Z3 at a vertex, a vertex and a side, and two sides, respectively. The linear equation of any side of the triangle can be calculated by the coordinates of the triangle vertices, and its calculation formula is as follows (1): x1\u2212xv1 xv2\u2212xv1 \u00bc y1\u2212yv1 yv2\u2212yv1 \u00bc z1\u2212zv1 zv2\u2212zv1 x2\u2212xv2 xv2\u2212xv3 \u00bc y2\u2212yv2 yv2\u2212yv3 \u00bc z2\u2212zv2 zv2\u2212zv3 x3\u2212xv1 xv3\u2212xv1 \u00bc y3\u2212yv1 yv3\u2212yv1 \u00bc z3\u2212zv1 zv3\u2212zv1 8>>>< >>>: \u00f01\u00de where x1, y1, and z1 represent the linear equation of the segment v1v2; x2, y2, and z2 represent the linear equation of the segment v2v3; x3, y3, and z3 represent the linear equation of the segment v1v3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure2-1.png",
        "caption": "Fig. 2. Machine tool setting for pinion teeth finishing.",
        "texts": [
            " A hypoid gear pair with the generated pinion and the non-generated gear is treated (Fig. 1). The pinion is the driving member. In order to reduce the sensitivity of the gear pair to errors in teeth surfaces and to the mutual position of the mating members appropriately chosen modifications are introduced into the teeth of the pinion. As a result of these modifications theoretically point contact of the meshed teeth surfaces appears instead of linear contact. The machine tool setting for pinion teeth finishing is shown in Fig. 2. The concave side of pinion teeth is in the coordinate system K1 (attached to the pinion) defined by the following system of equations: ~r\u00f01\u00de1 \u00bcMp4 Mp3 Mp2 Mp1 ~r\u00f0T1\u00de T1 ; \u00f01:1\u00de ~v\u00f0T1 ;1\u00de 0 ~e\u00f0T\u00de0 \u00bc 0; \u00f01:2\u00de where~r\u00f0T1\u00de T1 is the radius vector of tool surface points, matrices Mp1, Mp2, Mp3 and Mp4 provide the coordinate transformations from system KT1 (rigidly connected to the cradle and head-cutter T1) to system K1 (rigidly connected to the being generated pinion). Eq. (1.2) describes mathematically the generation of pinion tooth surface by the head-cutter [43]. The matrices and vectors of system of Eq. (1)are defined as it follows: The surface of the tool used for the generation of pinion teeth is in the coordinate system KT1 (attached to tool T1) defined by the following equation (based on Fig. 2): ~r\u00f0T1\u00de T1 \u00f0u; h\u00de \u00bc u \u00f0rt1 \u00fe u tga1\u00de cos h \u00f0rt1 \u00fe u tga1\u00de sin h 1 2 6664 3 7775: \u00f02\u00de On the basis of Fig. 2. and Eq. (2), for the relative velocity vector~v\u00f0T1 ;1\u00de 0 of tool T1 to the pinion and for the unit normal vector of the tool surface ~e\u00f0T1\u00de 0 , it follows ~v\u00f0T1 ;1\u00de 0 \u00bc x\u00f0T\u00de ig \u00f0z\u00f0T1\u00de 0 \u00fe g\u00de cos c1 z\u00f0T1\u00de 0 ig \u00f0z\u00f0T1\u00de 0 \u00fe g\u00de sin c1 ig \u00bdy\u00f0T1\u00de 0 sin c1 \u00f0x \u00f0T1\u00de 0 c\u00de cos c1 y\u00f0T1\u00de 0 2 664 3 775; \u00f03\u00de ~e\u00f0T1\u00de 0 \u00bcMp2 Mp1 ~e\u00f0T1\u00de T1 \u00bcMp2 Mp1 sin a1 cos a1 cos h cos a1 sin h 0 2 6664 3 7775; \u00f04\u00de where ~r\u00f0T1\u00de 0 \u00bcMp2 Mp1 ~r\u00f0T\u00deT1 : \u00f05\u00de Matrices Mp1 Mp4 contain the machine tool setting parameters and are defined by the following equations (on the basis of Fig. 2): ~rT0 \u00bcMp1 ~rT1 \u00bc cos b sin b 0 0 cos d sin b cos d cos b sin d 0 sin d sin b sin d cos b cos d 0 0 0 0 1 2 6664 3 7775 ~rT1; \u00f06\u00de ~r0 \u00bcMp2 ~rT0 \u00bc 1 0 0 0 0 sin w cos w e cos w 0 cos w sin w e sin w 0 0 0 1 2 6664 3 7775 ~rT0; \u00f07\u00de ~r01 \u00bcMp3 ~r0 \u00bc cos c1 sin c1 0 c cos c1 sin c1 cos c1 0 f c sin c1 0 0 1 g 0 0 0 1 2 6664 3 7775 ~r0; \u00f08\u00de ~r1 \u00bcMp4 ~r01 \u00bc cos w1 0 sin w1 0 0 1 0 p sin w1 0 cos w1 0 0 0 0 1 2 6664 3 7775 ~r01; \u00f09\u00de while w1 = ig w. The pertinent equations governing the pressure and temperature distributions and the oil film shape are the Reynolds, elasticity, energy, and Laplace\u2019s equations",
            " The systems of linear equations, obtained by using finite difference approximation of the Reynolds, elasticity, energy, and Laplace\u2019s equations, are solved by the successive-over-relaxation method. The details of the presented theoretical background are described in Ref. [9]. On the basis of the presented theoretical background a computer program has been developed. By using this program, the influence of machine settings for pinion finishing as are: the sliding base setting (c), basic radial (e), basic offset setting (g), basic tilt angle (b), basic swivel angle (d), machine root angle (c1), velocity ratio in the kinematic scheme of machine tool (ig) and basic cradle angle (w0) (Fig. 2), on maximum oil film pressure (pmax) and temperature (Tmax), EHD load carrying capacity (W), and on power losses in the oil film (fT) was investigated. In this paper, the term of \u2018\u2018EHD load carrying capacity\u201d is used for the load calculated by Eq. (17) for a prescribed value of the minimum oil film thickness. The investigation was carried out for the hypoid gear pair of the design data given in Table 1. The starting machine tool setting parameters for the generation of pinion tooth blanks are given in Table 2, and the lubricant characteristics and operating parameters in Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000632_s10846-010-9445-4-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000632_s10846-010-9445-4-Figure23-1.png",
        "caption": "Fig. 23 Kadet senior ARF used for the UAV implementation",
        "texts": [
            " The robostix gives access to the different PWMs, A/D with a 10-bit resolution, eight analog I/O pins, three UARTS and gives access to the STUART of the verdex-XM4. The microcontroller and the motherboard are connected thru a Hirose 60-pin connector and it uses i2c to communicate. Figure 22 shows the Verdex XM4 and the Robostix card. The sensors used were a GPS module with a LEA-5H chip with an accuracy of 2.5 m CEP. The IMU has an orientation accuracy of \u00b12.0\u25e6. For data communication the Maxstream 2.4 GHz modem was used, with a range of 10 miles. A camera and a separate modem were used for video transmission. Figure 23 shows the UAV used for experimental verification, while Table 4 gives its specifications. As it was mentioned the Kadet Senior ARF is the model airplane (see Fig. 23) used for the UAV control implementation. The airplane\u2019s flight dynamic rotations (Yaw, Pitch and Roll) are controlled by servos connected to rudder, elevators and ailerons respectively. The airplane\u2019s propeller is powered by a glow engine. The main advantage of a glow engine is the higher power to weight ratio than a comparable electric motor. The actual payload capacity allows for the installation of sensors needed for the implementation of the proposed control algorithm. The long range operation will allow the airplane cover a wide area, without having to land and refuel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003491_j.jsv.2020.115919-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003491_j.jsv.2020.115919-Figure1-1.png",
        "caption": "Fig. 1. Planetary gear system with a single planet gear.",
        "texts": [
            " The remaining sections of this article are organized as follows: Section 2 provides a brief introduction of traditional modeling for background knowledge; Section 3 identifies the problems encountered in traditional modeling; Section 4 reexamines the relationship between transfer effects and phases to form an improved model. The reason for spectrum asymmetry is also revealed; Simulation and experimental studies are conducted in Section 5 and 6 ; finally, Section 7 concludes the article. The traditional modeling process usually analyzes the system, including a single planet gear for simplicity, then extends to multiple planet gears. Gear meshing processes and transfer effects are the two main factors that must be introduced. The schematic of a planetary gear system with one planet gear is shown in Fig. 1 . Fig. 1 shows a planetary gear system with a sun gear, a ring gear, and a planet gear. The ring gear is fixed, and the sun gear rotates on its own; the planet gear not only rotates on its own but also rotates around the sun gear. \u03d5 \u2208 [0 , 2 \u03c0) , represents the phase angle between the planet gear and the sensor. The meshing vibration originates from the planet gear meshing with the sun gear and the ring gear, simultaneity. Due to the sensor\u2019s placement in close proximity to the ring gear, the original vibration captured by the sensor is the meshing of the planet gear with the ring gear because of its directly transmitted route [16] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000733_0022-2569(71)90002-4-Figure16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000733_0022-2569(71)90002-4-Figure16-1.png",
        "caption": "Figure 16. Single-cam mechanism with two oscillating roller followers joined by a coupler link.",
        "texts": [
            "3) The pitch profile c (6.3) is convex ifb >= 2e > 0. A numerical investigation of the errors occurring would be desirable. A new kind of single-cam mechanism was recently proposed by Jackowski and Dubil[5]: Two oscillating followers PA and QB of equal length L and with equal end rollers (centers A and B, common radius a) are operated by a cam disk c whose center O is the mid-point of the segment PQ = 2ljoining the follower pivots P and Q. A supplementary coupler link with joints in A and B connects the two followers (Fig. 16). This m e c h a n i s m - w h o s e possibility is not sufficiently c la r i f ied-cons is t s of five links: Frame Eo ( P Q ) , cam Y~ (~-), followers E,, ( PA ) and E3 (QB), and coupler E4 (AB). The existence of double cam mechanisms of this kind is evident, even in the case of different follower lengths, unequal roller radii and arbitrarily arranged pivots. In the course of the relative motion Ea/Et which has to be considered, the point A ~ Y.a is led around a curve c in E, parallel to the (given) cam profile 6",
            " The shape of c may be deter- mined by a prescribed law \u00a2(\u00a2) defining the advance motion of the follower PA from t0min to qJmax' Thus the return motion is already determined; it is equivalent to the movement of the follower QB during the advance motion of PA. In Fig. 18 the part A3Bo of the arc AoB0 was chosen as a circle quadrant with center O to get a dwell mechanism; consequently the corresponding part B3.40 of the complementary arc BoAo is also a circle quadrant with center O. The working profile of the definite cam disk consists of curves ~', d parallel to the pitch arcs c and d at a distance a equal to the roller radius (Fig. 16). When the cam is driven in the opposite sense the characters of the forward and return motions will be interchanged. It is improbable that there exist closed algebraic or analytic cam profiles for this single-disk mechanism. 20 R e f e r e n c e s [l] G O L D B E R G M. Rotors in polygons and polyhedra. ),l~lr/t. C(,mp,f . 14. 229-239 ( 19601. [2] G R E E N J. W. Sets subtending a constant angle on a ciccle. Dt,&e 5[citJt. d. 17. 263-267 11951)). [3] H A G E D O R N L. Z,aanglLiufiges Fr~.isen yon Kurvensche iben t~r torm>:h/Jssige Kurvengetrieb\u00a2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002873_j.mechmachtheory.2019.103669-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002873_j.mechmachtheory.2019.103669-Figure3-1.png",
        "caption": "Fig. 3. The elementary friction force on the contact ellipse in the rolling direction [24].",
        "texts": [
            " The tangential speeds of a point from the ball vbi,o are: vbi,o(y,\u03c9b) = \u03c9b \u00b7 Ai,o(y) (10) In the contact ellipses of an ACBB, two angular pivoting speeds \u03c9so,i can be expressed using the following equations [24]: \u03c9so(no,\u03c9c) = \u03c9o(no,\u03c9c) \u00b7 sin (\u03b1) (11) \u03c9si(no,\u03c9c) = \u2212\u03c9i(no,\u03c9c) \u00b7 sin (\u03b1) (12) The total sliding speeds in the rolling directions vti and vto, are computed with the following equations: \u03c5ti(y, no,\u03c9b,\u03c9c) = \u03c5si(y, no,\u03c9b,\u03c9c) + \u03c9si(no,\u03c9c) \u00b7 y (13) \u03c5to(y, no,\u03c9b,\u03c9c) = \u03c5so(y, no,\u03c9b,\u03c9c) + \u03c9so(no,\u03c9c) \u00b7 y (14) The sliding speed in the rolling direction on an elementary slice of width dy as shown in Fig. 3, generates an elementary friction force dFs. Using on the contact ellipse a constant coefficient of friction (COF) \u03bc, Houpert [19] developed the following relation for dFs: dFs = \u00b13 4 \u00b7 \u03bc \u00b7 Q \u00b7 ( 1 \u2212 Y 2 ) \u00b7 dY (15) where Y= y/a and the sign (+) or (\u2212) is the sign of the sliding speed vt in the coordinate system attached to contact ellipse (Fig. 3). Eq. (15) can be expressed for inner and outer contact ellipses according to the following relations [19]: dFsi,o = \u00b13 4 \u00b7 \u03bc \u00b7 Q ai,o \u00b7 ( 1 \u2212 ( y ai,o )2 ) \u00b7 dy (16) For an ACBB operating at low speed, Houpert [19] analytically calculated the locations of the two pure rolling lines on contact ellipses (a1 and a2) using the ball\u2019s forces and moments equilibrium and considering a constant friction coefficient on ball-race contacts. Also, using some geometrical considerations, the locations of the two pure rolling lines are linked via a geometrical parameter E and the following equation [19]: a1 a + a2 a + E = 0 (17) where the parameter E is given by the following approximate equation: E \u2248 2 \u00b7 ( Ra a ) \u00b7 db \u00b7 sin (\u03b1) dm (18) The elementary forces dFsi,o were integrated by Houpert [19] who obtained the following general relations for the friction forces Fsi,o on the ball-races ellipses: Fsi,o = \u03bc \u00b7 Q \u00b7 [ 1 \u2212 3 2 \u00b7 ( 2 \u00b7 a2i,o ai,o + Ei,o ) + 1 2 \u00b7 [ ( a2i,o ai,o ) 3 + ( a2i,o ai,o + Ei,o) 3 ]] (19) If the geometrical parameter E > 1, only one rolling line location positioned at distance a2 from the center of contact ellipse can be found in the contact because a1/a < \u22121"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001883_s00170-017-0363-5-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001883_s00170-017-0363-5-Figure4-1.png",
        "caption": "Fig. 4 Coordinate systems of the gear",
        "texts": [
            " According to the predesigned TE function, there exists only one point with 0TE on each modified tooth surface of the visual generating rack cutter, as shown in Fig. 1. Set Xc = 0; the processing pinion rotation angle \u03c6p can be obtained by \u03c6p \u00bc ycncx\u2212xcncy rpncx \u00f015\u00de The position vector and the unit normal vector of the generated pinion tooth surface \u03a3p can be represented as rp uc; lc;\u03c6p \u00bc Mpc \u03c6p rc uc; lc\u00f0 \u00de \u00f016\u00de np uc;\u03c6p \u00bc Lpc \u03c6p nc uc\u00f0 \u00de \u00f017\u00de respectively, where Mpc and Lpc are transformation matrices from Sc to Sp for the position vector and the unit normal vector, respectively. As shown in Fig. 4, when the pinion rotates by the angle \u03c6p, the gear is constrained to rotate by the angle\u03c6g. With Eqs. (11) and (15), \u03c6g can be obtained by \u03c6g \u03b5; \u03b4;\u03bb; T ; \u03be\u00f0 \u00de \u00bc A\u22121BYT \u00fe zp zg ycncx\u2212xcncy rpncx \u00f018\u00de Pinion tooth surfaces are regarded as generating surfaces of gear tooth surfaces. In the coordinate system Sg, gear tooth surfaces can be generated by envelopes of pinion tooth surfaces. The position vector and the unit normal vector of the generated gear tooth surface \u03a3g can be represented as rg uc; lc;\u03c6g \u00bc Mgc \u03c6g rc uc; lc\u00f0 \u00de \u00f019\u00de ng uc;\u03c6g \u00bc Lgc \u03c6g nc uc\u00f0 \u00de \u00f020\u00de where Mgc and Lgc are transformation matrices form Sc to Sg for the position vector and the unit normal vector, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001102_0954406211403571-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001102_0954406211403571-Figure5-1.png",
        "caption": "Fig. 5 25 per cent tooth removal",
        "texts": [
            " It comprises a two-stage, 11 kW, helical gearbox driven by three-phase induction motor and connected to a DC generator and adjacent resistor banks. Tests were carried out using healthy pair of gears and a pair suffering from a tooth breakage with magnitude fault 1 (25 per cent tooth removal), fault 2 (50 per cent tooth removal), fault 3 (75 per cent tooth removal), and fault 4 (100 per cent tooth removal) of the tooth under varying loads (0, 20, 40, 60, and 80 per cent) and speeds (10, 30, 50, 70, and 90 per cent); a photo of the gear with 25 per cent tooth removal is illustrated in Fig. 5. The drive pinion at the first stage had 34 teeth meshing with a 70-tooth wheel. The pinion gear at the second stage had 29 teeth meshing with 52-tooth wheel. The vibration signals were collected using an accelerometer mounted vertically on the gearbox housing. The accelerometers were B&K type 4371 with sensitivity of 10 mV/g and suitable for vibration measurements within a range of 1 Hz to 12 kHz. The sampling frequency was set to 50 kHz. Before the accelerometer signals were fed to the analogueto-digital converter NI USB 9233 card, they passed through a B&K type 2635 charge amplifier to condition the signal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure6-1.png",
        "caption": "Fig. 6. The tooth profile with k1 = 0.4.",
        "texts": [],
        "surrounding_texts": [
            "Based on the analysis above, a design for an example gear drive with a variation of the parabolic parameters is taken to illustrate the proposedmethod and study the impact. The example drive has a modulus ofm = 2 mm, a transmission ratio of i = 1.2, an addendum coefficient of ha\u204e = 1, a bottom clearance of C\u204e = 0.25, and a tooth number of Z1 = 15. According to Eqs. (52) and (54), the range of the parameters k1 and k2 without undercutting and interference was calculated to be 0.2 \u2264 k1 b 0.457 and 0.2 \u2264 k2 b 0.448 respectively. 4.1. The impact of parameter k1 on the shape of the tooth profiles In order to study the influence of parameter k1 on the shape of the tooth profiles designed by the proposed method, k1 is so chosen that it varies from 0.2 to 0.4 with an increment of 0.1, while k2 is equal to 0.2. The tooth filet is an arc, whose radius is 0.38 \u2217 m, connecting the tooth profile and the root circle of a gear. The tooth profiles of the driving gear and the driven gear are established in Figs. 4, 5 and 6 corresponding to k1 = 0.2, 0.3, and 0.4, respectively. For the reason of comparison, three sets of the tooth profiles of the driving gear with different parameters of k1 and k2 are drawn in Fig. 7, while another three sets of the tooth profiles of the driven gear are shown in Fig. 8. According to the results, the following conclusions can be made: (i) The parameter k1 changes the shape of the part of the addendum of the tooth profile for the driving gear, without changing the shape of the part of the dedendum. On the contrary, as for the tooth profile of the driven gear, the parameter k1 is only relevant to the shape of the part of the dedendum. (ii) In the part of the addendum, the tooth thickness of the driving gear increases with the growth of the parameter k1, but in the part of the dedendum for the driven gear, the tooth thickness shows the opposite trend. 4.2. Impact of parameter k2 on the shape of the tooth profiles In this subsection, the effects of the parameter k2 on the shape of the tooth profile are studied. The parameter k1 is chosen as 0.2, and the parameter k2 is so chosen that it varies from 0.2 to 0.4 with an increment of 0.1, while the other parameters keep the same as example 1. The tooth profiles of the driving gear and the driven gear are shown in Figs. 4, 9 and 10 corresponding to k2 = 0.2, 0.3, 0.4, respectively. Three sets of the tooth profiles of the driving gear and driven gear with different parameters of k2 are drawn in Figs. 11 and 12, respectively. From above discussion, the following conclusions to the specified gears can be drawn: (i) In the part of the addendum of the tooth profile for the driving gear and in the part of the dedendum of the tooth profile for the driven gear, the tooth thickness will not change with the changes of the parameter k2. (ii) The tooth thickness of the part of the addendum of the tooth profile for the driven gear increases with the growth of the parameter k2, while the tooth thickness of the part of the dedendum of the tooth profile for the driving gear decreases with the growth of the parameter k2. (iii) The minimum teeth number of the proposed gear without undercutting is affected by k1 and k2, for example, according to Eq. (54), when k2 is equal to 0.2, the minimum teeth number of the driving gear is 2, which is much less than that of the involute gear."
        ]
    },
    {
        "image_filename": "designv10_12_0000188_s00170-008-1785-x-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000188_s00170-008-1785-x-Figure5-1.png",
        "caption": "Fig. 5 Simulation scene for laser-repairing",
        "texts": [
            " Material is pure nickel and adopts the thermal physical parameters recommended values [19] given by graphs shown in Fig. 4a\u2013c. The model allows for the non-linear behaviour of thermal conductivity, density and specific heat due to temperature changes and phase transformations. Laser-processing parameters are set: laser power is 800 W; scanning velocity is 300 mm/min; laser beam diameter is 0.6 mm; spectral absorptivity of nickel is 0.15\u20130.35. In this study, 0.25 is adopted. 4.1 Temperature profiles It is seen from Fig. 5 that only the laser-passed elements are activated to the repaired layers. At the same time, the gap elements are endued with corresponding thermal conductivity, and the heat transfer diffuses in the big substrate. In the laser-applied neighbouring region, a great temperature gradient is formed. The temperature history of node A in layer 1 (shown in Fig. 2) is illustrated in Fig. 6; there are a total of eight peak values. The maximum value appears at the location where the laser is just applied. The second peak value appears at the time where the laser passes the neighbourhood second line path, and the temperature decrease is much more compared with the first peak"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002506_j.jsv.2017.08.029-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002506_j.jsv.2017.08.029-Figure4-1.png",
        "caption": "Fig. 4. Forces acting on the jth ball.",
        "texts": [
            " The dynamic differential equations can be shown as XN j\u00bc1 PRhj \u00fe Qcxj \u00bc mc \u20acxc (9) XN j\u00bc1 Qcyj PRxj cos fj Fcy \u00bc mc \u20acyc (10) XN j\u00bc1 Qczj \u00fe PRxj sin fj Fcz \u00bc mc\u20aczc (11) XN j\u00bc1 PRxj$ DW 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q2 cyj \u00fe Q2 czj q dm 2 \u00feMcx \u00bc Icx _ucx Icy Icz ucyucz (12) XN j\u00bc1 PRhj \u00fe Qcxj $ dm 2 sin fj \u00bc Icy _ucy \u00f0Icz Icx\u00deuczucx (13) XN j\u00bc1 PRhj \u00fe Qcxj $ dm 2 cos fj \u00bc Icz _ucz Icx Icy ucxucy (14) wheremc is the mass of cage, xc, yc, zc are the accelerations of cage.Mcx is the external load, Icx, Icy, Icz aremoments of inertia of cage, ucx,ucy,ucz are angular velocities of cage, _ucx, _ucy and _ucz are angular accelerations of cage. The directions of the quantities are along the axes of coordinate {Oc;Xc,Yc,Zc}. As key components in the bearing, the balls have contact with the inner ring, the cage and the outer ring, and the forces acting on the ball is shown in Fig. 4. In Fig. 4, Gzj and Gyj show the decomposition components of the gravity of the jth ball along axes of ObjZbj and ObjYbj, respectively, meeting that Gyj \u00bc mbgcos 4j Gzj \u00bc mbgsin 4j (15) Q'cxj, Q'cyj and Q'czj are the projection of Qcxj, Qcyj and Qczj on coordinate {Ob;Xb,Yb,Zb} and can be obtained through coordinates transformation that 8< : Q 0 cxj \u00bc Qcxj Q 0 cyj \u00bc Qczj cos fj \u00fe Qcyj sin fj Q 0 czj \u00bc Qczj sin fj Qcyj cos fj (16) Fbx, Fby and Fbz are the hydrodynamic forces acting on the mass center of the ball, PRhj and PRxj are frictional forces between the cage and the ball acting on the surface of the ball, and the dynamic differential equations of the jth ball can be expressed as Fbx \u00fe FRhoj cos aoj FRhij cos aij Qoj sin aoj \u00fe Qij sin aij \u00fe Q 0 cxy \u00fe PRhj \u00bc mb \u20acxbj (17) Fby \u00fe Gyj \u00fe Q 0 cyj \u00fe FRxij Txij FRxoj \u00bc mb \u20acybj (18) Qij cos aij Qoj cos aoj \u00fe FRhij sin aij FRhoj sin aoj \u00fe Fbz Gzj PRxj \u00bc mb\u20aczbj (19) Txij FRxoj FRxij \u00fe PRxj $ DW 2 \u00bc Ib _ubxj \u00fe Jx _uxj (20) FRhij \u00fe FRhoj \u00fe PRhj $ DW 2 \u00bc Ibubyj \u00fe Jyuyj \u00fe Ibubzj _qbj (21) PRhj$ DW 2 \u00bc Ibubzj Ibuyj _qbj \u00fe Jz _uzj (22) wheremb is the mass of the ball, \u20acxbj, \u20acybj and \u20aczbj are accelerations along axes ObjXbj, ObjYbj and ObjZbj"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure1.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure1.3-1.png",
        "caption": "Fig. 1.3 Ride-by-wire (RBW) or x-by-wire (XBW) integrated unibody motion mechatronic control hypersystem",
        "texts": [
            " Automotive Mechatronics 10 The intention of this chapter is to give to the interested reader the background for presentation of safety-related fault-tolerant (FT) mechatronic control systems without mechanical backup in automotive vehicles (so-termed \u2018RBW or XBW integrated unibody, space-chassis, skateboard-chassis or body-over-chassis motion mechatronic control hypersystems\u2019). The \u2018R\u2019 or \u2018X\u2019 in \u2018RBW\u2019 or \u2018XBW\u2019, respectively, represents the basis of any safety-related FT longitudinal x axis (Roll), lateral y axis (Pitch) and vertical z axis (Yaw) mechatronic control system application, such as DBW AWD propulsion and BBW AWB dispulsion, SBW AWS conversion, as well as ABW AWA suspension mechatronic control systems (Fig. 1.3). [Continental Automotive Systems; RIETH 2006]. These applications may greatly increase overall vehicle safety by releasing the driver from routine tasks and assisting it in finding solutions in critical circumstances. Highly sophisticated future vehicle applications, such as driver assistance or autonomous driving, necessitated computerised mechatronic control of the driving dynamics. This entails that the driver requirement be sensed and interpreted appropriately so as to take proper account of the existing driving circumstances and environmental influences"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.31-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.31-1.png",
        "caption": "Fig. 3.31: Components in the Robert Bosch Corporation ESP system",
        "texts": [
            "29 is shown an actual implementation of the EMB AWD DBW dispulsion mechatronic control system with the single-sense of a direction vector redundant ring structure that contains the following components and/or responsibilities [CADENCE 2003]: Two travel sensors and one force sensor to determine driver intent (each sensor connected to a different wheel node); Sensor values communicated over the network \u2192 consistency checks; Wheel node calculates the actuation commands for all four wheels; Commands communicated by means of network \u2192 each of the four wheel nodes compares its own actuation commands with those calculated by the other wheel nodes; Voting mechanism in the network layer of each wheel node can then disable the power to individual actuators in the case of a fault; If a node needs to be shut down, the brake force is redistributed to prevent the ehicle from yawing; The advanced brake functions (ABS) are executed in two front-wheel nodes; If the front-wheel nodes do not calculate the same output commands for these advanced brake functions, the function may be deactivated; this provides fail-safe operation; redundant power supply. Automotive Mechatronics 486 In Figure 3.30, as an example solution, a Robert Bosch Corporation ESP system is shown [ROMANO 2000]. In Figure 3.31 the components in the Robert Bosch Corporation ESP system are presented. They include (A) active wheel angular velocity (speed) sensors; (B) steering angle sensor; (C) combined yaw rate sensor/lateral accelerometer; (D) attached ECU; (E) E-M motor; (F) pressure sensor, and (G) fluidical (hydraulical) unit. Some ESP system use ride height sensors [ROMANO 2000]. [Robert Bosh Corporation; ROMANO 2000]. The objectives of anti-lock BBW AWB dispulsion mechatronic control systems are three fold: To reduce stopping distances; To better stability in automotive vehicle handling; ; To better steerability during braking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002814_j.mechmachtheory.2019.03.022-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002814_j.mechmachtheory.2019.03.022-Figure2-1.png",
        "caption": "Fig. 2. Screw with reference systems and applied torques.",
        "texts": [
            " where the subscripts i refers to the two contact points between the nut, the sphere and the screw, while the subscript j distinguishes the two nuts. The angles \u03b2A, j and \u03b2B, j between the segment identified by contact points and the sphere\u2019s centre are the contact angles ( Fig. 3 ); in this analysis, they are supposed to be constant and both equal to the most common literature value of 45 \u00b0. This means that the line which connects the two contact points identifies the direction along which forces are transmitted. The rotational matrices between these reference frames are computed in [38] . Fig. 2 depicts the torques acting on the screw, which compose its dynamic equilibrium equation: C m \u2212 C f \u2212 C V \u2212 I S \u0308 = 0 (1) where C m is the input torque from the motor, C f is the friction torque and C V is the torque obtained from the sum of all reaction forces from the spheres to the screw groove. It can be expressed as: C V = Z \u2211 j [ F V, j + H B, j cos ( \u03b1\u2032 )][ r m \u2212 r b cos ( \u03b2B ) ] (2) where H B, j is the tangential friction force, along the t axis, from the spheres belonging to the j-th nut (\u00a73"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001562_j.conengprac.2013.12.004-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001562_j.conengprac.2013.12.004-Figure2-1.png",
        "caption": "Fig. 2. Variables in the body-fixed frame of the helicopter.",
        "texts": [
            " The rigid body dynamics of such a vehicle are described by Newton\u2013Euler equations of motion: _u _v _w 2 64 3 75\u00bc 1 m F p q r 2 64 3 75 u v w 2 64 3 75 \u00f01\u00de _p _q _r 2 64 3 75\u00bc I 1 M p q r 2 64 3 75 I p q r 2 64 3 75 0 B@ 1 CA \u00f02\u00de where F and M denote the external forces and moments acting on the center of gravity of the helicopter, respectively, m is the mass, I\u00bc diagfIxx; Iyy; Izzg is the inertial matrix with respect to the bodyfixed reference frame, \u00bdu; v;w T and \u00bdp; q; r T are the translational and rotational velocities in the body-fixed reference frame, respectively. In a helicopter system, external forces and moments are produced by the main and tail rotors, gravity, and the aerodynamic forces of the fuselage. Fig. 2 shows the variables in the body-fixed reference frame. Control forces and moments originate mainly from the main and tail rotors, controlled by four inputs: lateral and longitudinal cyclic rotor controls \u03b4lat, \u03b4lon; collective pitch input \u03b4col; and tail rotor collective input \u03b4ped. \u03b4lat and \u03b4lon are used to control roll and pitch motions through swashplate tilting. The rotation speed of the main rotor is controlled by an engine governor and it is not considered. The magnitude of the thrust is controlled by changing the collective pitch angle of the main blades through \u03b4col"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002506_j.jsv.2017.08.029-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002506_j.jsv.2017.08.029-Figure6-1.png",
        "caption": "Fig. 6. Schematic diagram of the experiment.",
        "texts": [
            " The radiation noise decreases subsequently, and the variance ratio of the radiation noise curve changes at 20000r min 1, 28000r min 1 and 30000r min 1. It seems that the bearing reaches a critical speed near 28000r min 1, and the radiation noise decreases rapidly after the critical speed. More detailed information need to be tested and verified through experiments. 3. Experimental verification The experimental system is carried out on the ceramicmotorized spindle test rig, the schematic diagram of the experiment is shown in Fig. 6. In Fig. 6, the spindle is placed on a special support, the shaft and bearings of the spindle are made of ceramic. The shaft is driven by the motor inside, and the motor is controlled by a control cabinet. High-speed angular contact ball bearings are installed at both ends, and the bearings applied on the spindle are of the same structural parameters with 7009C. The air compressor and oil lubrication system are used for lubrication of the whole ceramic motorized spindle system, and the lubrication parameters can be adjusted manually"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000039_nme.1990-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000039_nme.1990-Figure3-1.png",
        "caption": "Figure 3. Comparison of projection vector: (a) orthogonal projection under the norm \u2016\u00b7\u20162C and (b) orthogonal projection under the Euclidean norm.",
        "texts": [
            " This result indicates that the presented wrinkle model gives the similar elastic strain energy density to one in Reference [22], in which rigours treatment of wrinkling is discussed within a context of applied mathematics. In this paper, the wrinkle-mode deformation vector ew given in (19) is considered as the orthogonal projection of e onto the direction s2 under the norm \u2016\u00b7\u20162C, and then, the classical strain energy density (0) is replaced by the minimized strain energy density (\u0304) given by the solution Copyright q 2007 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 71:1231\u20131259 DOI: 10.1002/nme of (23). For better understanding of the projection, we illustrate in Figure 3 the comparison between the orthogonal projection under the norm \u2016\u00b7\u20162C and the well-known orthogonal projection under the Euclidean norm in the least-squares problem. The modified elasticity matrix that relates e to rt in the wrinkled membrane can be systematically derived by projection operator. It is easily proven that Equation (19) can be rewritten as ew = sT2Ce sT2Cs2 \u00b7 s2 =Qe (28) where Q= s2sT2C sT2Cs2 (29) is the projection matrix that maps ew to itself and ee to zero as follows: Qew = 2w \u00b7 s2(s T 2Cs2) (sT2Cs2) = ew (30) Qee =Q(e\u2212 ew) = 0 (31) Moreover, substituting (28) into (15) yields ee = e\u2212 Qe=Pe (32) where P= I \u2212 Q= I \u2212 s2sT2C sT2Cs2 (33) and I is 3\u00d7 3 identity matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure6-1.png",
        "caption": "Fig. 6. HANA* parallel manipulators: (a) with linear actuators and (b) with revolute actuators.",
        "texts": [
            " It is noteworthy that in the HALF* parallel manipulators the universal joints connected to the mobile platform can be replaced by spherical joints. Figure 5 shows the HANA parallel manipulator introduced in ref. [15], which is also one member of the family presented in ref. [13]. In the HANA manipulator, two legs (the first and second legs) consist of parallelogram. The kinematic chain of each of the two legs is the same as that of the third leg in the HALF parallel manipulator shown in Fig. 1. Therefore, the two legs can be also replaced by the PRC chain. The new version of the HANA parallel manipulator is illustrated in Fig. 6(a), which is referred to as the HANA* parallel manipulator where the P joints are actuated. The new manipulator with revolute actuators is shown in Fig. 6(b), where the R joints fixed to the base platform are active. Then, as shown in Fig. 6(a), the mobile platform of the HANA* manipulator is connected to the base by a PRU or PRS chain (Leg 3) and two PRC chains (Legs 1 and 2). It is noteworthy that the axes of the two C joints in Legs 1 and 2 must be parallel to each other. If Leg 3 uses the PRU chain, the axes must also be parallel to the R joint of the U joint that is connected to the mobile platform. Due to the arrangement of links and joints of the manipulator, the combination of the three legs constrains the rotation of the moving platform with respect to the y- and z-axes and the translation along the y-axis, leaving the manipulator with two translational DOFs in the O\u2013xz plane and one rotational DOF about the axis parallel to the x-axis",
            " Table II shows the Note: P: prismatic joint; R: revolute joint; C: cylinder joint; T: translation; RO: rotation, in each of which the subscript stands for the DOF. description about the mobility of the manipulator. One may see that the HALF* and HANA* have the same mobility. However, there is a remarkable difference between these two manipulators in terms of the rotational DOF. The rotational DOF of HANA* is implemented with the combination of Legs 1 and 2 with the PRC chain. This situation is same to the HANA* with revolute actuators shown in Fig. 6(b). In the HALF*, the rotational DOF is reached by actuating only one leg, i.e. Leg 3. Similarly, the actuating direction of all sliders in the HANA* parallel manipulator with prismatic actuators may be inclined at an \u03b1 angle with respect to the vertical line as shown in Fig. 7(a). Figure 7(b) illustrates a typical example when the actuating direction is horizontal. They have the same mobility as that of the manipulator shown in Fig. 6. It is not difficult to find out that, compared with the HANA manipulators, the HANA* parallel manipulators introduced here also have the advantages in kinematics, architecture, manufacturing, energy cost, accuracy, and assembling for the similar reasons described in Section 2.1. Since there is no planar parallelogram in each manipulator of the new family, every leg can be designed as a telescopic link. For example, the HALF* and HANA* parallel manipulators with such links are shown in Fig. 8(a) and (b), respectively",
            " R1 = R - r, there are z1 = \u00b1 \u221a R2 2 \u2212 (R1 + y)2 + z (13) z2 = \u00b1 \u221a R2 2 \u2212 (R1 \u2212 y)2 + z (14) from which we may see that the inverse kinematic problem of the first and second legs are actually that of the PRRRP symmetrical parallel manipulator,17 which is kinematically a planar parallel mechanism. If the position of point O \u2032 is specified, the kinematic Eq. (6) is actually that of a slidercrank mechanism.18 Therefore, in the design process, the manipulator can be considered as the combination of a PRRRP parallel manipulator and a slider-crank mechanism. Observing the HANA* manipulator shown in Fig. 6(a), we will see that, it can be thought of as the combination of a slider-crank mechanism and a PRRP four-bar mechanism. Therefore, compared with those of the manipulators in ref. [13], the kinematics and design of some new manipulators proposed in this paper will become accordingly simpler. Actually, the design of most spatial manipulators in the new family can be divided into two parts, i.e. those of two simple mechanisms. By replacing the kinematic chain of the leg consisting of a parallelogram of the manipulator family introduced in ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003182_10426914.2020.1726947-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003182_10426914.2020.1726947-Figure1-1.png",
        "caption": "Figure 1. Schematic of double-arc additive manufacturing equipment.",
        "texts": [
            " Specifically, the appearance, efficiency, grain type and size, and material properties of single- and double-arc deposited samples are compared. The results suggest that double-arc additive manufacturing is efficient and offers good performance. This study lays a foundation for further research and applications of the twin-wire double-arc welding process for highly efficient additive manufacturing. Two 1.2 mm diameter of SS316L stainless-steel wires whose composition is shown in Table 1, and a sheet of 250 mm long, 100 mm wide and 5 mm thick were selected in this study. The double-arc AM system displayed in Fig. 1 consisted of two Lorch S3 Robot MIG XT welding power supplies, two wire feeders, a M-10ia robot and a control cabinet of FANUC. The deposition parameters of single- and double-arc additive manufacturing are listed in Table 2. The 99.999% pure argon with the flow of 25 L/min was chosen as the shielding gas. Twin-wire extension and wire spacing were all 12 mm. The electrodes using the same current phase were tilted inward by 17 degree.[14] A 160 mm long weld was deposited to perform 30-layer part and the odd layers were deposited in the opposite direction to the even layers[15], the welding torch was raised by 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000846_0954405411407997-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000846_0954405411407997-Figure8-1.png",
        "caption": "Fig. 8 A fabricated revolute joint: (a) fabrication direction; (b) design dimensions; (c) revolute joint after polishing",
        "texts": [
            " The part by fabricated SLM has improved mechanical properties, which implies that the fabricated nonassembly mechanisms can be useful for practical applications. Two joints have been fabricated using the Dimetal280 SLM machine. The material was 316L stainless steel spherical powder with an average particle size of 17 mm and maximum particle size of about 35 mm. The process parameters were laser power 150 W, track spacing 0.12 mm, powder thickness 0.035 mm, and scanning speed 600 mm/s. All joints were produced without requiring assembly. A revolute joint was fabricated, shown in Fig. 8. The ring hole was designed to the drum shape; the clearance at both ends of the ring was 0.5 mm, and that at the peak was 0.2 mm. The vertical display was preferred, since the horizontal display led to too many overhangs. Figure 8(c) shows that the actual fabricated rings can rotate freely. In Fig. 9 the 3D model together with the build position and direction of a universal joint are shown. The joint consists of two yokes and a connecting cross hub. The hub was designed to the drum shape. The clearance at the peak was 0.2 mm and that at both ends was 0.4 mm. The assembly angle was adjusted to reduce overhang surface. Some supports were still needed within the clearances at this configuration, and were removed when the fabrication was done"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure17-1.png",
        "caption": "Fig. 17. Simulated no-load magnetic flux density distributions of the motors with different rotors. (a) 2605SA1. (b) 10JNEX900.",
        "texts": [
            " In this case, the torque and power densities will be correspondingly decreased. As this article is not focused on solving the degradation problems of 2605SA1 rotor and the goal of the article is to study whether 10JNEX900 is feasible for the proposed high-speed IPM rotor, the problems of 2605SA1 rotor are not further discussed. The electromagnetic performances of the two motors are predicted with the assistance of a finite element analysis (FEA) software Flux 2D. The no-load magnetic flux density distributions of the two motors are compared in Fig. 17. It clearly shows that the magnetic flux density at the flux bridge regions of HR is slightly higher than that of AR. This is because the saturation flux density of 10JNEX900 is higher than that of 2605SA1. Furthermore, the magnetic flux density of the shaft of HR is much lower than that of AR. Because the flux leakage of HR is higher than that of AR, the air-gap PM excitation magnetic flux density of the former is lower than that of the latter as can be seen in Fig. 18. When the amplitude of phase current is 50 A, the torque of the two motors is around 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure14-1.png",
        "caption": "Figure 14 The magnetic field and electromagnetic forces around the arc",
        "texts": [
            " The magnetic field is generated not only from the wire and arc, but also from the welding bead. When the fusion model is completely symmetric, the center current has no lateral deflection, so the axial electromagnetic force is zero (Xie et al., 2015). When the fusion model is asymmetric, the magnetic field is in asymmetric distribution around the arc, where the magnetic induction linear density is smaller in the inner side and larger in the outer side. Thus, the center current has some lateral deflection to the outer side. Figure 14 shows the electromagnetic forces FL and FR generated by the magnetic fields on both sides. The magnetic bias forces the arc to deflect. To avoid interfering factors, we set the shielding gas flow rate at 18 L/min, the gun plate spacing at 10mm and the wire feeding speed at 6.5m/min, and keep the gun vertical to the plate. To investigate the influence of the curvature on the welding appearance, specifically, the width and height, we have acquired welding beads with different curvatures and travel speeds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002952_s12555-018-0400-7-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002952_s12555-018-0400-7-Figure2-1.png",
        "caption": "Fig. 2. Curved beam model of continuum robot ( signifies the coordinate frame).",
        "texts": [
            " 1 can be simplified by applying the following common static boundary conditions: 1) constant external force; 2) the components at all interfaces are rigid; and 3) the effect of friction on the structure is negligible. To satisfy the above conditions, we assume that the four wires are rigid and there is no clearance in any element constituting the continuum robot. In addition, the continuum robot can be assumed to be a single body because it is a hyper-redundant type robot in which multiple joints make one movement through a wire [18]. With these assumptions, the robot shown in Fig. 1 can be considered to be a curved beam with an arbitrary curvature, as shown in Fig. 2. It is also assumed that the robot body is made of the same material. The static analysis of this curved beam has been well established in a previous study [29]; however, the static analysis in this section is specifically carried out for a continuum mechanism. When an external force F is applied at the end of the robot along the z\u0302E direction, twist torque T and deformation \u03a8 are generated at the end of the robot, as shown in Fig. 2. If F is the vertical force applied to the robot when lifting or pushing a tissue, the ith element of the robot body has moments mxi, myi, and mzi and shear forces fxi, fyi, and fzi along the axial direction of x\u0302i, y\u0302i, and z\u0302i, respectively. From Fig. 2, we can obtain the moment equilibrium equations as follows: dmxi ds \u2212\u03bamyi \u2212 fyid\u03d5i = 0, (1) \u03bamxi + dmyi ds \u2212 fxid\u03d5i = fzi, (2) where ds is the length of the element, \u03ba is the curvature of the curved beam (ds= d\u03b8 \u03ba ), and \u03b8i is the angle about the y\u0302 axis. Equations (1) and (2) represent the momentbalancing equations obtained by considering the axial and radial directions, respectively. The curvature of a robot driven by four wires is obtained from the general kinematics of the continuum robot pro- posed by Webster and Jones [14], as follows: \u03ba = (l4 \u22123l1 + l2 + l3) \u221a (l3 \u2212 l1)2 +(l2 \u2212 l4)2 r(l1 + l2 + l3 + l4)(l3 \u2212 l1) , (3) where li is the length of each wire for i = 1, 2, \u00b7 \u00b7 \u00b7 , 4 and r is the radius of the curved beam",
            " (5) The moments about x\u0302i and y\u0302i are obtained from the differential equations given in (4) and (5) in terms of the bending angle of the curved beam \u03b8 : mxi = B_1 cos\u03b8i +B2 sin\u03b8i \u2212 cos\u03b8i \u222b \u03b8i 0 fzi sin\u03b8 \u03ba d\u03b8 + sin\u03b8i \u222b \u03b8i 0 fzi cos\u03b8 \u03ba d\u03b8 , (6) myi =\u2212B_1 sin\u03b8i +B2 cos\u03b8i + sin\u03b8i \u222b \u03b8i 0 fzi sin\u03b8 \u03ba d\u03b8 + cos\u03b8i \u222b \u03b8i 0 fzi cos\u03b8 \u03ba d\u03b8 . (7) The integration constants B1 and B2 are obtained from the boundary conditions, mxE = 0 and myE = 0. Assuming that the curved beam moves on the x \u2212 y plane with respect to {0}, as shown in Fig. 2, the positions of the element at frame {i} and the shear force at the end-effector are obtained as follows: pxi = 1 \u03ba \u222b \u03b8i 0 cos\u03b8d\u03b8 , pyi = 1 \u03ba \u222b \u03b8i 0 sin\u03b8d\u03b8 , fzi =\u2212F, (8) where pxi and pyi are the positions of x and y, respectively at frame {i}. Finally, we can represent the moments about x\u0302i and y\u0302i using the combination of (6), (7), and (8), as follows: mxi = F sin\u03b8i(pxE \u2212 pxi)\u2212F cos\u03b8i(pyE \u2212 pyi), (9) myi = F cos\u03b8i(pxE \u2212 pxi)+F sin\u03b8i(pyE \u2212 pyi). (10) The deformations of the elements that depend on the moments are expressed using the material properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.5-1.png",
        "caption": "Fig. 3.5 Three special cases of Roth\u2019 theorem",
        "texts": [
            "24) Except for a single case these formulas define three points and, hence, a plane. The single case is a pure rotation about an axis not passing through P . It is characterized by s = 0 and R,\u03d5 = 0 . The corresponding solutions \u03bb = \u03bc = \u03bd = 0 define only the point 0 . However, even in this case, a body-fixed plane with the required property exists. Without calculation it is obvious that the plane contains the rotation axis. In the initial position it is rotated against the line P0 through \u2212\u03d5/2 and in the final position through +\u03d5/2 . In Fig. 3.5a the points P and 0 and the two positions of the plane are shown in the projection along the rotation axis n . Thus, it is proved that Roth\u2019 Theorem is valid without any exception. In what follows, three more special cases are considered in which the body-fixed plane is predictable without the above analysis. 1. The special case R = 0 , \u03d5, s = 0 (screw displacement with a screw axis passing through P ): Without calculation it is obvious that the plane is normal to the screw axis. The perpendicular from P onto the plane is \u2212(s/2)n in the initial position and +(s/2)n in the final position of the body (Fig. 3.5b). The plane is defined by Eqs.(3.24) which, in this case, yield \u03bb = \u2212s/2 and \u03bc, \u03bd \u2192 \u221e . A point A in this plane is displaced to A\u2032 . 2. The special case \u03d5 = 0 , s = 0 , R unspecified (pure translation sn): Without calculation it is obvious that Fig. 3.5b applies also to this case. As before, Eqs.(3.24) yield \u03bb = \u2212s/2 and \u03bc, \u03bd \u2192 \u221e . 3. The special case \u03d5 = \u03c0 , R , s = 0 (screw displacement with 180\u25e6- turn): Equations (3.24) yield \u03bb = \u2212s/2 , \u03bc = s2/(4R) and \u03bd \u2192 \u221e . These results indicate that the line n \u00d7 e is parallel to the plane. In Fig. 3.5c the two positions of the plane are shown in the projection along n\u00d7 e . The points with position vectors r1 , r \u2032 1 and r2 , r \u2032 2 in Eqs.(3.22) and (3.23) are marked A , A\u2032 and B , B\u2032 , respectively. In this case, the solution is less 3.5 Screw Displacement Determined from Displacements of Three Body Points 93 obvious than in the previous cases, but it is still predictable without analysis. In all other cases \u03bb , \u03bc and \u03bd are finite and different from zero. Problem: For three noncollinear body-fixed points P1 , P2 , P3 the position vectors zi before and z\u2032i after a displacement, respectively, are given (i = 1, 2, 3) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002672_j.measurement.2019.107096-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002672_j.measurement.2019.107096-Figure3-1.png",
        "caption": "Fig. 3. Lumped mass model of planetary subsystem.",
        "texts": [
            " The nodes on the bearing housing surface are coupled to the center of the housing to obtain the external nodes, and the remaining finite element nodes are internal nodes. The mass and stiffness parameters of the box could be extracted to condense internal nodes to external nodes by the sub-structure method. On the basis of reference [9], a lumped mass parametric analytical model of single-stage planetary subsystem is proposed by considering the influence of internal excitation factors. As shown in Fig. 3, an OXY fixed coordinate system and an Onfngn follow-up coordinate system are respectively established. The components were simplified into different lumped mass in planetary subsystem. The ring gear and the sun gear are respectively connected to the planetary gears through springs. The supporting and torsional stiffness of the bearings are considered, respectively. Relative displacement of external and internal meshing gears are respectively dsn and drn in the planetary subsystem. The relative displacement between the planetary carrier and planetary gear are respectively dfn and dgn in the orthogonal direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000905_02640414.2011.553963-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000905_02640414.2011.553963-Figure2-1.png",
        "caption": "Figure 2. Definition of the global and local reference frames. RG is the global reference frame, and RH is the hand reference frame.",
        "texts": [
            " Euler 3, 2, 1 rotation angles were used to define the angular orientations. The first rotation about the ZG axis leads to the RH 0 (xH 0yH 0zH 0) reference frames. The second rotation about the yH 0 axis leads to the RH 00 (xH 00yH 00zH 00) reference frames. The third rotation about the xH 00 axis leads to the RH 000 (xH 000yH 000zH 000) reference frames. The angles of the hand direction are designated right/left rotation, right/left sideways, and backward/forward tilts for the first, second, and third rotations, respectively (Figure 2). The shoulder is defined by Euler rotation angles in accordance with the ISB standard (Wu et al., 2005). The angles of the shoulder joint are designated as horizontal adduction/abduction, abduction/adduction, and internal/external rotation for the first, second, and third rotation, respectively. The velocities of the wrist joint centre and third metacarpal joint centre were determined using the three-point central difference method. The instants of maximum velocity of the wrist and third metacarpal joint centre are represented by WVmax and MPVmax, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.94-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.94-1.png",
        "caption": "Fig. 2.94 Dead axle and axleless transmission arrangement",
        "texts": [
            " Because there is an attenuation in the angular velocities of the road wheels due to the different dimensions of the chain sprocket and chain wheel, either a smaller attenuation is necessary in the final drive gear or, for example, in heavy-duty automotive vehicles, a particularly large complete attenuation can be attain-ed. Comparative movement between the axle and the frame, as the road springs bend, is assisted by the rotary motion of the loops of the chains about the axes of the chain wheels and sprockets. One more, and normally employed, dead-axle M-M transmission arrangement is that used by the de Dion automotive vehicles, as shown in Figure 2.94 [NEWTON ET AL. 1989]. for the M-M DBW 2WD propulsion mechatronic control system [NEWTON ET AL. 1989]. As a rule, it is accepted for low automotive vehicles with unalterable suspension, and thus is preferred by some racing car manufacturers. This is partially due to its intrinsic suspension features and practically for the reason that it is more acceptable for restricted manufacture than admittedly enhanced, separate rear suspension systems. The transmission arrangements for the de Dion axle layout and for the axleless systems with separate suspension are analogous"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001533_j.automatica.2014.06.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001533_j.automatica.2014.06.003-Figure1-1.png",
        "caption": "Fig. 1. Coordinate frames, positions and orientations of an AUV.",
        "texts": [
            " Section 3 states the output feedback controller design procedure, and in Section 4 the stability analysis is discussed. In Section 5, the performance of the proposed control algorithm is evaluated using computer simulations and real seabed data. Section 6 contains concluding remarks. Part of thisworkwas presented in preliminary form in Adhami-Mirhosseini, Aguiar, and Yazdanpanah (2011). This section describes the AUV equations of motion used for control design and formulates the bottom-following problem. Fig. 1 illustrates the AUV coordinate frames, position and orientation variables. In general, the motion of an AUV can be described using six degrees of freedom (DOF) differential equations of motion, which can be highly nonlinear and coupled, see e.g., Fossen (1994). In practice, the procedure adopted to simplify the controller design, is to split the equations into two noninteracting models for the vertical and horizontal planes, Jalving (1994). For the bottom-following case and for control design, we are concerned with the vertical plane and we follow the model simplification strategy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001911_iet-cta.2017.0584-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001911_iet-cta.2017.0584-Figure1-1.png",
        "caption": "Fig. 1 Quadrotor coordinate frames, rotation speed of rotors, thrust forces, and torques generated by propellers",
        "texts": [
            " Unlike the FLC, the proposed FPC is simple enough to be implemented on the on-board electronics of the quadrotor. Flight experiments in hovering conditions are given to demonstrate the effectiveness of the FPC. The rest of this paper is organised as follows: Section 2 presents the non-linear mathematical model of the quadrotor. Section 3 describes the design procedure of the FLC and FPC with the stability analysis. In Section 4, the FLC is compared with the FPC using simulations. Experimental results are shown in Section 5. Concluding remarks are given in Section 6. As depicted in Fig. 1, the rotation speed of each rotor is presented by \u03a9i \u2265 0, where i = 1, 2, 3, 4. The thrust force (Fi) and the torque (Ti) generated by each propeller can be obtained by Fi = cF\u03a9i 2 and Ti = cT\u03a9i 2, where cF > 0 and cT > 0 are the force and torque coefficients, respectively. I = XI, YI, ZI denotes an earth-fixed inertial frame and B = XB, YB, ZB defines a body-fixed frame with the origin located at the quadrotor centre of mass. Let r = x, y, z T represent the position of the origin of the frame B with respect to the inertial coordinate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003114_j.engfailanal.2020.105005-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003114_j.engfailanal.2020.105005-Figure7-1.png",
        "caption": "Figure 7 The hardness and the tensile strength curves",
        "texts": [],
        "surrounding_texts": [
            "The case hardening layer is gradually formed during gear carburizing, and the hardness declines remarkably from the gear case to the core of the material within the hardening layer due to the characteristics of the carburizing processes. The hardness varies from 670 HV at the gear case to 420 HV at the core. The effective case depth is 2.2 mm, which is the depth where the hardness value equals to 550 HV. The measured hardness data agrees well with the characteristics of the Thomas empirical method [37]. The hardness gradient, together with other mechanical properties such as the tensile strength, is expected to result in obvious discrepancies of the fatigue resistance of material points at different depth consequently. Therefore, the variations of these mechanical properties should be considered in the analysis of the gear contact fatigue behavior. The details of the Vickers hardness test have been mentioned in the former work [38]. The combination of the residual stress and the load-induced stresses has a direct impact on the gear contact fatigue behavior [28], which needs to be considered in cyclic damage evaluation. The X-ray diffraction method was chosen to characterize the normal residual stress component along the tooth profile direction ( ). The electro-polishing technique was employed to measure the residual r, x stress gradient, which might lead to a somewhat stress relaxation. The magnitude of the compressive residual stress on the surface is around 100 MPa, while the maximum amplitude of the compressive residual stress is around 200 MPa and appears at the depth of 0.7 mm. Then its magnitude decreases gradually as the depth increases. Detailed measurement process can be found in the former investigations [28, 32]. Figure 6 shows the calculation procedures of the hardness and residual gradients during the damage and fatigue life estimation. Figure 6 Schematic diagram of calculations of case carburized properties 6 Based upon the studies about the significant effects of the compressive mean stress on the high-cycle life, this term should be taken into account while applying the Basquin equation [40]. Considering the complicated multiaxial contact stress condition in gears, the original stress amplitude 7 in the Basquin equation should be replaced by the Dang Van equivalent stress [11]. a Dang Van Therefore, the characteristics of the chosen Dang Van criterion can be implicitly considered during evaluation. The modified Basquin equation reads [40]: (4)Dang Van ( ) (2 N )b b m f     where is the magnitude of the mean normal stress. In this work, this modified Basquin equation is m adopted for the gear contact fatigue life estimation."
        ]
    },
    {
        "image_filename": "designv10_12_0003131_0309524x20968816-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003131_0309524x20968816-Figure1-1.png",
        "caption": "Figure 1. System of systems model for electrical generator.",
        "texts": [
            "enerator, manufacturing, wind turbine, strand tilt, windings Losses in the generator system have been already widely discussed in previous researches, for example, iron loss, eddy loss, copper loss, windage loss. In this research, system of three-phase windings is considered as a system of three systems. Each phase is further considered as a system of several stator bar systems. Stator bar is considered a single system that is made up of several interacting and interdependent components that is, copper strands. System as presented in Figure 1 generates a different level of understanding, that is, how an individual interconnected and interdependent component of the system is contributing towards the generator system\u2019s overall performance. Each system of stator bar is a collection of several layers of mutually transposed and conducting strands. Eddy current losses can be minimized by such arrangement (Fujita et al., 2005). In Figure 1, each stator bar is represented as a system made up of several interdependent strands. The collaborative effect of all component gives rise to improve the functionality of the whole generator system. There are three main issues due to strand tilt that is voids leading to partial discharge, strand to strand short and the effect on the magnitude of slot induced eddy voltage. The analysis confirmed that if the tilt is uniform across the stator bar, then the eddy voltage of all the strands relative to the hypothetical strand along the bottom of the stator bar side will be equal (but will change in magnitude)",
            " On the other hand, if the system and sub-system contributing towards the overall goals, then it directly will be reflected in the AEP or generator efficiency. The benefit of this system approach is that it makes it possible to evaluate the performance of the overall system concerning components coordination. If the system is not performing as expected, then it gives the opportunity to check and correct the system orientation at the production level. If the system Efficiency is not as expected, then eddy current losses, or short circuit might be the leading cause. The full representation of the generator system is shown in Figure 1. Figure 3 presenting the dissection of ideal stator bar. For the demonstration purpose, the possible location of the voids has been shown. Strand tilt could lead to the possible void between main insulation and turn to turn insulation. Void free insulation is a challenging task, and Danikas and Sarathi (2014) presented the details of electrical machine insulation and related issues . New capacitances are created between the insulation layers due to the voids, which leads to lower breakdown voltage",
            " Two shorted strand form one strand loop, and magnetic flux circulation will be affected. Induced current will lead to a higher winding temperature, affecting the lifetime of the insulation system. Yaghobi et al. (2014) study show turn to turn insulation fault detection through total harmonic distribution. The reason behind making several thin strands inside the stator bar is to reduce eddy losses. This is done by the linkage flux with the contours inside the conductors. In order to make the current distribution, equal strands are transposed in a certain way. Figure 1 represents how the strands are stacked together and transposed along with the machine. This process is called roebelling, and the formed bar is called roebel stator bar (Robel, 1915). Eddy current losses and the effects can be minimized and canceled by forming a perfect stator bar, through the correct transposition of the strands. This can be achieved if every single strand for the equal axial length occupies every radial position. Maintaining the symmetry concerning constant axial and radial ends region flux various transposition methods like 540-degree transposition in the slot and 180-degree transposition, the end part can be used (Neidhofe, 1970)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000507_tcst.2009.2014876-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000507_tcst.2009.2014876-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems.",
        "texts": [
            " Combining the designed observers and state feedback SPA stabilizing controllers, we design output feedback SPA stabilizing controllers. We first introduce the following notations to describe the equation of motion of a ship. Let , , and be the North and the East positions of a ship and the yaw angle (orientation) of a ship, respectively, in the Earth-fixed coordinate system and let , and be linear velocities in surge, sway and the angular velocity in yaw, i.e., , respectively, decomposed 1063-6536/$26.00 \u00a9 2009 IEEE in the body-fixed coordinate system. Let and (see Fig. 1). In DP problems, the speed of a ship is quite small ( , , ) and we can assume that the damping forces are linear [3]. Hence, the equation of motion of a dynamically positioned ship can be written as (1) where , , and is the rotation matrix in yaw, is the inertia matrix including hydrodynamic added inertia, is the damping matrix and the control forces and moment are provided by thrusters. Note that and is bounded for any . Let be a sampling period, and . If we set , , then the exact discrete-time model of (1) is given by and the Euler approximate model of (1) is given by (2) where , , , and again to avoid the complexity of notations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000733_0022-2569(71)90002-4-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000733_0022-2569(71)90002-4-Figure4-1.png",
        "caption": "Figure 4. Double-cam mechanism with two rigidly connected oscillating flat-faced followers.",
        "texts": [
            " - - - - \" / ' H B * A * parallel to c at the distance a and appropriate to work with a follower line/511 p that is offset from P by the distance a (see Fig. I 1). 2. Double-Disk Cams with Flat-Faced Followers The cam disk c operating the straight-line follower p is well able to achieve the forward motion. To avoid springs or other elastic links maintaining the contact o f p and c during the return motion, we may arrange a second straight-line follower # rigidly connected with p and forming in P a constant angle ,-r - 3' with p (Fig. 4). This line p belonging also to the system ~2. generates in E1 a second cam profile ( which is appropriate to produce the return motion of the oscillating follower, provided the cam center O remains in the interior of the moving angle ~ # p = r e - 7 . The point of contact, C, o f # and ~ is found in the same way as before by issuing the normal It~ _L # form the instant center I. The corresponding center of curvature, ,4-*, may be added again by aid of the construction of Bobillier using the centrode tangent t. Both of the centers A* and A~\" are situated, as all points related to points at infinity,t on the so-called \"cusp circle\" which touches the centrode in l . t Thus the center of curvature A* can simply be found by intersecting the normal IC with the cusp circle determined by I, t andA * (Fig. 4). #The cusp circle, to be considered as a locus in the fixed plane, is analogous to the well-known \"inflection circle\" of the moving plane; it is identical with the inflection circle of the inverted motion. The cusp circle comprises all cusps which at the moment may appear at envelopes generated by moving straight lines: these lines form a pencil. The characterist ic function for the motion o f p is described by From this relation the support function o(~) of the second cam profile d can be derived by analogy to (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.6-1.png",
        "caption": "Fig. 17.6 (a) Foldable four-bar of first kind: r1+a = r2+ ( = 4 , r1 = 6 , a = 1 , r2 = 3 ). (b) Foldable four-bar of second kind: r1+r2 = a+ ( = 6 , r1 = 4 , a = 1 , r2 = 3 ). Instantaneous centers of rotation P1 and P2 of the coupler tend toward M1 and M2 when the four-bar is folding",
        "texts": [
            " Depending on whether the shortest link is the fixed link or the input link or the coupler the four-bar is either a double-crank or a crank-rocker or a double-rocker of first kind, respectively (compare Figs. 17.4a, b, c). In this respect there is no difference to the general case of fourbars satisfying the inequality condition min + max < \u2032 + \u2032\u2032 . The equality min + max = \u2032 + \u2032\u2032 has the consequence that the four-bar is foldable. In a folded position all four links are collinear. Two different kinds of foldable four-bars have to be distinguished: - first kind: r1 + a = r2 + (Fig. 17.6a) - second kind: r1 + r2 = a+ (Fig. 17.6b). With link lengths (1, 3, 4, 6) the following foldable four-bars ( , r1, a, r2) can be formed: Foldable four-bars of first kind: Two double-cranks (1, 3, 4, 6), (1, 4, 3, 6); four crank-rockers (4, 1, 6, 3), (3, 1, 6, 4), (6, 1, 4, 3), (6, 1, 3, 4); two double-rockers of first kind (4, 6, 1, 3), (3, 6, 1, 4) ; Foldable four-bars of second kind: One double-crank (1, 3, 6, 4); two crank-rockers (3, 1, 4, 6), (4, 1, 3, 6); one double-rocker of first kind (6, 4, 1, 3). Example: The foldable four-bar of first kind in Fig. 17.6a is the doublerocker with ( , r1, a, r2) = (4, 6, 1, 3) , and the foldable four-bar of second kind in Fig. 17.6b is the double-rocker with ( , r1, a, r2) = (6, 4, 1, 3) . For a single angle \u03d5 of the input link the two associated positions of coupler and output link are shown. The points P1 and P2 are the instantaneous centers of rotation of the coupler in these positions. Let x be the coordinate of P1 or P2. In positions sufficiently close to the folded position (\u03d5 = \u03c8 = 0 in Fig. 17.6a and \u03d5 = \u03c0 \u2212 \u03c8 = 0 in Fig. 17.6b) the following approximations are valid: 17.2 Transfer Function 573 x tan\u03d5 \u2248 { (x\u2212 ) tan\u03c8 (foldable four-bars of first kind) ( \u2212 x) tan(\u03c0 \u2212 \u03c8) (foldable four-bars of second kind). (17.5) In Sect. 17.2 these approximations are used for determining instantaneous centers of rotation of the coupler in folded positions when intersection points P1 and P2 do not exist. End of example. In the folded position motion is possible in two ways with either \u03c8\u0307/\u03d5\u0307 > 0 or \u03c8\u0307/\u03d5\u0307 < 0 . In engineering applications of foldable four-bars provisions must be made either to avoid the folded position or to pass through it with prescribed sense of rotation",
            " The solutions \u03bb1,2 and the associated coordinates x1,2 of M1 and M2 are \u03bb1,2 = r1r2 \u00b1 \u221a r1r2a r2(r2 \u2212 a) , x1,2 = \u03bb1,2 \u03bb1,2 \u2212 1 . (17.18) The solution for foldable four-bars of second kind is obtained in a similar way. In (17.9) the substitutions \u03c8 = \u03c0 \u2212 \u03b1 and = r1 + r2 \u2212 a are made. Following this, a Taylor expansion up to second-order terms is made. The result is a quadratic equation for \u03bb = \u03b1/\u03d5 = x/( \u2212 x) . The solutions \u03bb1,2 are identical with those in (17.18): \u03bb1,2 = r1r2 \u00b1 \u221a r1r2a r2(r2 \u2212 a) , x1,2 = \u03bb1,2 \u03bb1,2 + 1 . (17.19) Examples: The link lengths of Fig. 17.6a yield x1 \u2248 5.17 , x2 \u2248 10.8 and those of Fig. 17.6b yield x1 \u2248 4.64 , x2 \u2248 2.21 . These are the points M1 and M2 shown in the figure. End of examples. 576 17 Planar Four-Bar Mechanism In Fig. 17.8 the four-bar A0ABB0 with link lengths , r1 , a , r2 is called four-bar F . Dashed lines parallel to the fixed link and to the input link define the point P . The quadrilateral B0PAB is drawn one more time in dotted lines. The dotted quadrilateral is called four-bar F\u2217 . Its fixed link has length r1 , and its input link has length . Both four-bars have the same coupler and the same output link"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001460_tmag.2013.2239271-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001460_tmag.2013.2239271-Figure6-1.png",
        "caption": "Fig. 6. N-I curve ( A).",
        "texts": [],
        "surrounding_texts": [
            "The target -axis current ( A) was given so that the high-speed rotor will not slip. The N-T curve with A is shown in Fig. 8. It was observed that the high-speed rotor does not slip. Therefore the current limiting can prevent the high-speed rotor from slipping."
        ]
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.11-1.png",
        "caption": "Fig. 17.11 Two four-bars in positions when P12P30 is orthogonal to the coupler",
        "texts": [
            " Whenever it has zero velocity, the ratio 1/i attains a stationary value. This is a consequence of the monotonicity property of the function 1/i(\u03be) shown in the figure. The velocity of P12 is zero if and only if the couplerfixed point momentarily coinciding with P12 has a velocity in the direction of the coupler (labeled body 3 ). Then the center P30 of the coupler lies on the normal to the coupler erected in P12 . In other words: In positions of the four-bar with a stationary value of 1/i the lines P12P30 and P31P32 are mutually orthogonal2. Figure 17.11 shows two different four-bars in such positions. If a stationary value occurs at \u03d5 = 0 or at \u03d5 = \u03c0 , P12 and P30 are located on the base line, and the coupler is orthogonal to the base line. Then the parameters satisfy the condition 2 In Bobillier\u2019s Theorem 15.6 the line P12P30 was shown to play another important role (line h in Fig. 15.19) 582 17 Planar Four-Bar Mechanism stationary value at \u03d5 = 0 : ( \u2212 r1) 2 + a2 = r22 , stationary value at \u03d5 = \u03c0 : ( + r1) 2 + a2 = r22 . } (17.41) In the vicinity of an angle \u03d5 for which 1/i has a stationary value the angle between the lines P12P30 and P31P32 is very sensitive to changes of \u03d5 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002994_j.mechmachtheory.2019.103679-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002994_j.mechmachtheory.2019.103679-Figure4-1.png",
        "caption": "Fig. 4. Relationship between bearing displacement and roller deformation.",
        "texts": [
            " To avoid parameters in the scale model being out of range, the fundamental scaling parameter should be the one with the smallest range of variation in all the parameters related to dynamic characteristics. As stiffness of bearings can only be settled with finite standard values, the bearing radial stiffness is regarded as the fundamental scaling parameter in this study. The bearing radial stiffness can be expressed as r K = F r \u03b4r (10) where F r is the radial force on the bearing and \u03b4r is the radial displacement between its inner and outer raceways. \u03b4r is mainly caused by the contact deformation between rollers and raceways, as shown in Fig. 4 . The relationship between \u03b4r and the contact deformation \u03b4g 0 of the roller at the bottom of the bearing can be expressed as \u03b4r = \u03b4g0 cos \u03b1 (11) where \u03b1 is the bearing contact angle. \u03b4g 0 can be further expressed as \u03b4g0 = i \u03b4g0 + o \u03b4g0 (12) where i \u03b4g 0 is the contact deformation between the roller and inner raceway and o \u03b4g 0 is the contact deformation between the roller and outer raceway. Assuming that the bearing is well lubricated, the relationship between F r and load on roller Q g 0 can be written as F r = \u03b3 ( Z ) Q g0 cos \u03b1 (13) where \u03b3 ( Z ) is a nonlinear function of roller amount Z "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure25-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure25-1.png",
        "caption": "Fig. 25. Manufacturing processes of the proposed IPM rotor made from 2605SA1.",
        "texts": [
            " Because the losses of copper windings close to the air gap are higher than those at the bottom of slots and the cooling condition at the bottom is better, the windings close to the air gap is much hotter than the bottom windings. The maximum temperatures of each component of the two motors are listed and compared in Table IV. It is found that the HM has lower temperature than the AM. IV. VERIFICATION BY TESTING OF A PROTOTYPE To verify the FEA and CFD analysis results, the tested results of a prototype made from 2605SA1 are compared with the simulated results. The manufacturing processes of the proposed IPM rotor made from 2605SA1 are illustrated in Fig. 25. 2605SA1 ribbons are first stacked and solidified and then are cut by wire electrical discharge machining method. When 10JNEX900 is used, the same methods can be used. Alternatively, 10JNEX900 core can be cut by laser. The hollow shaft is first welded by friction and then is slotted. The manufactured rotor is about 200 g while the whole motor is about 2.8 kg in weight. The test bench of the designed high-speed IPM motors is shown in Fig. 26. Two prototypes are directly connected through a coupling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.63-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.63-1.png",
        "caption": "Fig. 3.63 Cross-section diagrams of a friction drum EMB (a) with the conventional rotating brushed DC-AC mechanocommutator electromagnetically-excited brake-force-actuator motor, developed by Delphi for the BBW AWB dispulsion mechatronic control system known as Galileo and (b) with a novel short-stroke linear tubular brushless DC-AC macrocommutator IPM magnetoelectrically-excited brake-force-actuator motor, which have been conceived and developed by the Cracow University of Technology's Automotive Mechatronics Institution, Poland [(a) WELLS AND MILLER 1993; (b) FIJALKOWSKI AND KROSNICKI 1994]",
        "texts": [
            "30) where k - constant coefficient, depending on a construction of the short- stroke linear tubular brushless DC-AC macrocommutator IPM brake-force-actuator motor; i - brake application armature current of the short-stroke linear tubular brushless DC-AC macrocommutator IPM magneto-electrically-excited brake-force-actuator motor; E - effectiveness factor (ratio of the disc or ring rubbing surface to the input force on the shoes); R - brake radius. Brake force applied to the disc rotor by the pads is a function of the brake application armature current in the BBW dispulsion sphere and the constant coefficient of the wheel brake-force-actuator E-M motor. The static brake force Fcan is calculated with the following relationship: F = T/r, where r is the wheel-tyre rolling radius. Automotive Mechatronics 536 Figure 3.63 depicts the layout of a friction drum EMB: (a) with a conventional rotating brushed DC-AC mechanocommutator electromagneticallyexcited brake-force-actuator motor, developed by Delphi Corporation for the BBW AWB dispulsion mechatronic control system known as Galileo [WELLS AND MILLER 1993, SCARLETT 1996] and (b) with a novel short-stroke linear tubular brushless DC-AC macrocommutator IPM electromagnetically-excited brake-force-actuator motor [FIJALKOWSKI AND KROSNICKI 1994]. In friction drum EMBs, force is applied to a pair of brake shoes in a variety of configurations, including leading trailing shoe (simplex), duo-duplex, and duo-servo"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000675_sis.2009.4937849-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000675_sis.2009.4937849-Figure4-1.png",
        "caption": "Fig. 4. The sketch representing the movement of a searching robot with an average speed (v) for a duration of a simulation step (\u0394t) where omax is the sensing range from center of a robot to the center of another robot. The searching robot sweeps an area of size 2omaxv\u0394t (shown in gray). The waiting robots whose center is inside the swept area are detected by the searching robot. While robot A, whose center is outside the swept area, will not be detected by the searching robot; robot B, whose center is on the surface of the swept area, will be detected by the searching robot. The center of robots are indicated by cross signs.",
        "texts": [
            " Growing and Creation of an Aggregate (Pgrow and Pcreate) An aggregate of size m grows when one searching robot finds this aggregate in the environment. The simplest form of this event is growing of an aggregate of size one. The growing probability for an aggregate of size one is calculated as Pgrow(1) \u2248 2(omax)v\u0394t Atotal (11) where Atotal is the area of the arena, v is the average speed of an individual, omax is the sensing range of an individual and \u0394t is the time discretization of the system. The derivation of this equation is depicted on Figure 4. The figure shows the change of the position of a searching robot at one time step (\u0394t) in an environment of size Atotal. The area swept by the searching robot at that time step equals to 2omaxv\u0394t. omax is the sensing range from center of a robot to the center of another robot. Defining omax in this way allows us to consider the aggregate of size one as a point in the environment. Since the searching robot can only detect the aggregate if the aggregate is inside the swept region, the growing probability equals to the probability of having a randomly selected point inside the swept area which is the ratio of the swept area to the total area of the environment (Equation 11)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure11-1.png",
        "caption": "Fig. 11. The 2T1R + 1-DOF parallel manipulator: (a) configuration 1 (b) configuration 2.",
        "texts": [
            " When the 6R closed-loop linkage is mounted on the end of connected limbs, the 2T1R + 1-DOF parallel manipulators with the 6R configurable platforms are derived. Two L 1 F 1 C -limbs are used to construct 2T1R + 1-DOF parallel mechanisms. The constraint-forces are parallel, while the constraint-couples are linearly dependent. The constraint-forces generate an additional constraint-couple which is vertical to the platform. Therefore, the 2T1R + 1-DOF parallel manipulator with two working phases is constructed, as shown in Fig. 11 . Different from the Bennett platform, the distance between the intersect- ing point and the end-effectors is constant. The 1-DOF Bricard linkage can also serve as the configurable platform. The parallel manipulator with the Bricard linkage has two configurations, i.e., intersecting and parallel working modes. It should be mentioned that the intersecting point is moving relative to the platform. To realize the symmetrical structure of the manipulator as much as possible, three limbs are connected to the end moving platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001153_1077546312474679-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001153_1077546312474679-Figure3-1.png",
        "caption": "Figure 3. Schematic diagram and relations of displacement of angular contact ball bearing: (a) Sketch of ball bearing, (b) Relations of centers.",
        "texts": [
            " The dynamic model of the disk is formulated as follows: Md \u20acXd \u00fe Gd _Xd \u00bc Fd \u00f06\u00de where Md is the mass matrix of the disk, Gd is the gyroscopic matrices of the disk, Fd is unbalance on the disc and Xd is the displacement vector of the disc. The dynamic model of the coupling is given as follows: Mc \u20acXc \u00fe KcXc \u00bc Fc \u00f07\u00de where Mc is the mass matrix of the coupling, Kc is the stiffness matrices of the coupling, Xc is the displacement vector of the coupling and Fc is the external load vector. A schematic diagram of an angular contact ball bearing is shown in Figure 3(a), where oxyz is the coordinate system of the outer ring and o2x2y2z2, objxbjybjzbj are coordinate systems of the inner ring and jth ball. Dw, D1, D2 are diameters of the ball, outer ring and inner ring, respectively. f1 and f2 are curvatures of the outer and inner ring. Rc1 and Rc2 are curvature centers of the outer and inner ring. It is assumed that the center of curvature of the outer ring is fixed and those of the inner ring and balls of bearing are free. The bearing is modeled as a 5-DOF bearing. The displacement vectors of the inner ring are assumed as xi, yi, zi, yi, zi , which can be obtained by the displacement of the ith node of the shaft element. Relations of displacement and deflection in the ball bearing under arbitrary loads are shown in Figure 3(b), where, obj and o 0 bj are the original and the new locations of the center of the jth ball, R 0 c2 is the new location of the curvature center of the inner ring, 0 is the initial contact angle, 1j is the new contact angle between the jth ball and the outer ring and 2j is that of the jth ball and the inner ring. The angular location of the jth ball is assumed to be j, which can be written as j \u00bc 2 j 1\u00f0 \u00de=n\u00fe !ct \u00f08\u00de where !c \u00bc 1 2! 1\u00fe 2Dw= D1 \u00feD2\u00f0 \u00de\u00f0 \u00de, !c is the rotating speed of the cage, ! is the rotating speed of the rotor and n is number of the balls"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000846_0954405411407997-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000846_0954405411407997-Figure2-1.png",
        "caption": "Fig. 2 Display positions and fabrication direction: (a) horizontal display; (b) vertical display; (c) tilted display",
        "texts": [
            " Support structures are often needed to support overhangs of the part and provide a starting point for the overhangs. The supports are removed when the fabrication process is complete. Metallic support structures are often less easy to remove than polymer ones. The removal of too many supports may destroy the part surface. Furthermore, too many overhangs will affect the quality of fabrication, since they often lead to undesirable defects, such as warping. A reasonable fabrication direction is important. As shown in Fig. 2(a), for a horizontal stretched joint, the overhang surface needs to be supported by adding support structures, and the surface quality may be poor after the supports are removed. Making the joint vertical, as shown in Fig. 2(b), can reduce the area of overhang surface, as well as the number of supports needed. However the height h of the joint is a limiting factor, because it may exceed the maximum stroke of the build platform. A tilted display (Fig. 2 (c)) is proposed when the angle a between the under-surface of the joint and the horizontal plane is larger than the critical angle of fabrication, because in this case support structures are not Proc. IMechE Vol. 225 Part B: J. Engineering Manufacture needed. In this building orientation, a \u2018staircase\u2019 effect appears, caused by using a discrete set of thin layers to approximate a continuous curved or slanted surface in the vertical direction. To obtain good fabrication quality, thinner layers are needed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.5-1.png",
        "caption": "Figure 8.5. Momentof momentum of a systemof antennacoils referred to a moving frame.",
        "texts": [
            " To find the moment about C of the momentum relative to the origin in <l> , we shall need the total velocity of each particle in the inertial frame <l> , namely, Xk = Vo + Pk. Then, with (8A8a) and (8A8b), (8.19) gives hc = PI x ml(vO + PI) + pz x mz(vo + pz) = 2pI x mlPl = hrc , in agreement with the general rule (8.22): hc = hrc = 2mdzwk. Notice in passing that the velocity of the center of mass v* = va does not affect the final result. In view of (5.6), the term (mlPl +mzpz) x va == O. 0 316 ChapterS Example 8.4. The antenna coil system in the previous example has an additional angular velocity n normal to the plane of i' and k in Fig. 8.5, and relative to its initially oriented shaft frame 1 = tp = {C; id, which is turning with angular velocity W relative to the ground frame 0 = <l> = {F;Id at the instant shown. Find the applied torque about the center of mass required to sustain the motion of the system referred to the shaft frame 2 = tp' = {C ; i~} . Ignore the mass of the control shaft. Solution. The torque about C is given by (8.45), so we must first find he in (8.22) referred to the moving frame . The total angular velocity of the moving frame 2 = tp' = [c, i~} fixed in the control shaft is W f == Wzo = WZI +WIO = n +w. Hence, with reference to Fig. 8.5, referred to ip', W f = -r.lj' + w(sin ei'+ cos ek'). (8.49a) The velocity of each coil relative to C is /Jk = (-l)k v +W f X Pk, where we recall (8.48a) in which i ~ i'. Specifically, PI = -pz = -vi' + cod cos ej' + r.ldk'. Then (8.22) yields he = 2pI x mp, = 2mdz(-r.lj ' + to cos ek'). (8.49b) (8.49c) When e= 0 and r.l= 0, we recover (8.48c) . The total torque about C required to sustain the motion of the system is determined by (8.45) for he given in (8.49c). But he is a vector referred to a moving reference frame, so we shall need to apply (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure2-1.png",
        "caption": "Fig. 2. The prototype of the mechanism.",
        "texts": [
            " Considering the complexity of the force sensing mechanism structure, the traditional processing method is hard to achieve the accuracy requirement. In this paper, the flexible parallel sixcomponent force sensing mechanism is manufactured by means of 3-D printing rapid prototyping technology which keeps high manufacturing accuracy. The material is made of titanium alloy and after manufacturing, the proposed mechanism is only 180 mm in diameter and 17 mm in height. The manufactured prototype of the force sensing mechanism is shown in Fig. 2. The size and bearing capacity of some parallel six-component force sensing mechanism are shown in Table 1. Compared with the same type of force sensing mechanisms, the force measuring element and the load-bearing element are designed separately in this paper and combined in parallel. Finally, a spoke configuration with hybrid branches is formed. The structure proposed in this paper has certain advantages in terms of size and bearing capacity which can provide a new design idea for the heavy load six component force sensing mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure1-1.png",
        "caption": "Fig. 1. The HALF parallel manipulator presented in ref. [12].",
        "texts": [
            " A family of spatial 3-DOF fully parallel manipulators was introduced in ref. [13]. In this family, all manipulators consist of at least one parallelogram in their architectures. The parallelogram will eventually result in the difficulty of manufacturing and assembling. This will affect the accuracy and application of the manipulators. This motivates us to find a solution to overcome it. As analyzed in ref. [13], the use of a parallelogram in each manipulator of the family guarantees the unique rotational DOF of the mobile platform. For example, as shown in Fig. 1, the parallelogram in the HALF manipulator can restrict the rotations about the z- and x-axes.12 The translation in the O\u2013yz plane of the mobile platform is actually implemented by actuating the sliders of the two legs (denoted as the first and second legs) with identical kinematic chains. The two legs are in a same plane, i.e. the O\u2013yz plane. Therefore, the leg with a parallelogram (referred to as the third leg) acts the role of providing the mobile platform with the active rotation about the axis parallel to the y-axis and the passive translations along the x-, y-, and z-axes",
            " 2(b). It is noteworthy that in the HALF* parallel manipulators the universal joints connected to the mobile platform can be replaced by spherical joints. Figure 5 shows the HANA parallel manipulator introduced in ref. [15], which is also one member of the family presented in ref. [13]. In the HANA manipulator, two legs (the first and second legs) consist of parallelogram. The kinematic chain of each of the two legs is the same as that of the third leg in the HALF parallel manipulator shown in Fig. 1. Therefore, the two legs can be also replaced by the PRC chain. The new version of the HANA parallel manipulator is illustrated in Fig. 6(a), which is referred to as the HANA* parallel manipulator where the P joints are actuated. The new manipulator with revolute actuators is shown in Fig. 6(b), where the R joints fixed to the base platform are active. Then, as shown in Fig. 6(a), the mobile platform of the HANA* manipulator is connected to the base by a PRU or PRS chain (Leg 3) and two PRC chains (Legs 1 and 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002146_1464419313519612-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002146_1464419313519612-Figure4-1.png",
        "caption": "Figure 4. (a) Model of inner race defect, (b) model of inner race defect.",
        "texts": [],
        "surrounding_texts": [
            "Contact deformation between races and roller gives a nonlinear force deformation relation, which is derived using Hertz contact theory.16,23 In modeling as shown in Figures 2 and 3 the rolling element bearing is considered as a spring mass damper system having nonlinear spring and nonlinear damping. In this work outer race is fixed in a rigid support and inner race is held rigidly in the shaft. A constant radial load is acting on the bearing which is contact stiffness that can be calculated using Hertz theory and dissipating forces at contact point are modeled with nonlinear damping. Contact stiffness for roller bearings On inner race and on outer race localized defect is inserted with nonconventional machining processes as shown in Figure 6. Shaft is inserted in the bearing by press fit. In Figure 1, Dm is a pitch diameter of the bearing; Dr1 and Dr2 are diameters of the outer race and inner race, respectively; and Pd/4 is a radial clearance of the bearing. Palmgren24 developed empirical relation from laboratory test data which define relationship between contact force and deformation for line contact for roller bearing as \u00bc 3:84 10 5 Q0:9 l0:8 \u00f01\u00de Contact length is divided into k lamina, each lamina of width w, and rearranging the above equation to define q yields q \u00bc 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f02\u00de Edge stresses are not considered in equation (2), obtained only over small areas, here localized defect is modeled as a half sinusoidal wave, amplitude of outer race defect and inner race defect are defined as Go \u00bc A1 \u00fe Dh sin Ro DL !c\u00f0 \u00det\u00fe 2 j 1\u00f0 \u00de z \u00f03\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from Gi \u00bc A1 \u00fe Dh sin Ri DL !c !2\u00f0 \u00det\u00fe 2 \u00f0 j 1\u00de z \u00f04\u00de Roller raceway deformation considering contact deformation due to ideal normal loading, radial defection due to thrust loading, radial internal clearance, and localized defect can be given by j \u00bc j \u00fe w 1 2 j Pd 2 G0 Gi For k no. of lamina qjk \u00bc X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f05\u00de Depending on degree of loading and misalignment, all laminae in every contact may not be loaded; in equation (5), k is the number of laminae under load at roller location j. Total roller loading is given by Qj \u00bc X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 1:24 10 5 k\u00f0 \u00de0:11 w0:89 \u00f06\u00de For determining the individual roller loading, it is necessary to satisfy the requirement of static equilibrium for radial load Fr 2 Xj\u00bcZ 2\u00fe1 j\u00bc1 jQj cos j \u00bc 0 \u00f07\u00de j\u00bc angular position of the jth roller\u00bc 2 j 1\u00f0 \u00de z \u00fe !ct where j\u00bc loading zone parameter for jth rolling element j\u00bc 0.5 for j\u00bc (0, P), j\u00bc 1 for j 6\u00bc (0, P) Fr\u00bc applied radial load, substituting equation of Qj in equation (7) we get 0:62 10 5Fr w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j cos j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 \u00bc 0 \u00f08\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from For applied thrust load equilibrium equation: Fa 2 Pj\u00bcZ 2\u00fe1 j\u00bc1 jQaj \u00bc 0 Where, Qaj\u00bc total roller race way loading for length (l) for jth roller in axial direction. At each roller location, thrust couple is balanced by radial load couple caused by skewed axial load distribution. Therefore, h 2 Qaj \u00bc Qjej, where h\u00bc roller thrust couple moment arm, therefore equation becomes as Fa 2 2 h Xj\u00bcZ 2\u00fe1 j\u00bc1 jQjej \u00bc 0 \u00f09\u00de where ej is the eccentricity of the loading for jth roller and given by ej \u00bc P \u00bck \u00bc1 q j 1 2 wP \u00bck \u00bc1 q j l 2 Substituting Qj and ej in equation (9), we get 0:31 10 5Fa h w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j k0:11 X \u00bck \u00bc1 j 1:11 1 2 w ( l 2 X \u00bck \u00bc1 j 1:11) \u00bc 0 \u00f010\u00de The sum of the relative radial movements of the inner and outer rings at each roller azimuth minus the radial clearance is equal to the sum of inner and outer raceway maximum contact deformation at same azimuth a l D \u00fe r cos j Pd 2 2 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G \u00bc 0 \u00f011\u00de The set of simultaneous equations (6), (8), (10), (11) can be solved by using Newton\u2013Raphson method for solution of j, j, a, and r. The simultaneous equations are as follows f1\u00f0Dj, fj, da, dr\u00de \u00bc Qj \u00bc w0:89 1:24 10 5k0:11 X \u00bc11 \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 2 f2\u00f0Dj, fj, da, dr\u00de \u00bc 0:62 10 5Fr w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j cos j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 f3\u00f0Dj, fj, da, dr\u00de \u00bc 0:31 10 5Fa h w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11( 1 2 w l 2 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11) \u00bc 0 f4 Dj, fj, da, dr \u00bc da l D \u00fe drcosWj Pd 2 2 Xk\u00bck k\u00bc1 Dj \u00fe w k 1 2 fj Pd 2 G From the theory of Newton\u2013Raphson method, function and Jacobean matrix for nonlinear stiffness can be defined as follows F j, j, a, r \u00bc f1 j, j, a, r f2 j, j, a, r f3 j, j, a, r f4 j, j, a, r 2 66664 3 77775 \u00f012\u00de J j, j, a, r \u00bc @ @ j f1 j, j, a, r @ @ j f1 j, j, a, r @ @ a f1 j, j, a, r @ @ r f1 j, j, a, r @ @ j f2 j, j, a, r @ @ j f2 j, j, a, r @ @ a f2 j, j, a, r @ @ r f2 j, j, a, r @ @ j f3 j, j, a, r @ @ j f3 j, j, a, r @ @ a f3 j, j, a, r @ @ r f3 j, j, a, r @ @ j f4 j, j, a, r @ @ j f4 j, j, a, r @ @ a f4 j, j, a, r @ @ r f4 j, j, a, r 2 66666666664 3 77777777775 \u00f013\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from Radial contact stiffness and axial stiffness are defined as follows K\u00bcQj= j \u00bc w0:89 1:24 10 5 k\u00f0 \u00de0:11 P \u00bck \u00bc1 j\u00few 1 2 j Pd 2 G 1:11 P \u00bck \u00bc1 j\u00few 1 2 j Pd 2 G \u00f014a\u00de ka \u00bc w0:89 1:24 10 5 k\u00f0 \u00de0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 0:11 1 2 l 2 2 h \u00f014b\u00de After solving above nonlinear simultaneous equation iteratively with Newton\u2013Raphson method, program is made to calculate contact stiffness (K) in radial directions and axial direction (ka). Algorithm for n-nonlinear simultaneous equation for contact force calculations is given in Appendix 3. Nonlinear contact forces can be calculated in radial vertical and axial direction as below. Qry \u00bc XZ I\u00bc1 K x cos i\u00fe y sin i\u00f0 \u00de B\u00feAsin \u00f0 t i\u00de 1:11 sin i \u00f015\u00de Qry \u00bc XZ I\u00bc1 K x cos i\u00fe y sin i\u00f0 \u00de B\u00feAsin \u00f0 t i\u00de 1:11 cos i \u00f016\u00de Qa \u00bc 1 ka Xj\u00bcz j\u00bc1 Qaj \u00f017\u00de a\u00bc (size of local defect/raceway radius), K\u00bc contact stiffness If the defect is at inner race, t\u00bc (oc\u2013 o2)*t\u00fe 2p/z (z\u2013i), where i\u00bc 11 to 1 If the defect is at outer race, t\u00bc (oc)*t\u00fe 2p/z (z\u2013i), where i\u00bc 11 to 1 Dissipative force for roller bearing In formulation for dissipation of energy the lubrication behavior assumed in a Newtonian way and here viscous damping model is assumed in which dissipative forces are proportional to time derivative of mutual approach. According to Upadhyay et al.,17 a nonlinear damping formula, correlating the contact damping force with the equivalent contact stiffness and contact deformation rate is given by Fd \u00bc c \u00f0 \u00de _ p \u00f018\u00de where c(d) is a function of contact geometry, material properties of elastic bodies, the properties of contact surface velocities, and properties of lubricant. Hence total dissipation force can be calculated as given in Appendix 6 where c is equivalent viscous damping factor between outer race/inner race with the roller is assumed 646N s/m.15 It is assumed that equivalent viscous damping factor of roller inner race contact and roller outer race contact is equal. Fdin \u00bc Cin Keq _ in 1.11 and Fdout \u00bc Cout Keq _ ou 1.11 Fd \u00bc Qdjr \u00bc 9 19 c\u00f0 \u00de\u00f0k\u00de 19 9 \u00f0 _ \u00de1:11 Qdry \u00bc 1=z Xj\u00bcz j\u00bc1 Qdjr sin 2 \u00f0 j 1\u00de z \u00fe !c t \u00f019\u00de where \u00bc \u00f0xcos i\u00feysin i\u00de B\u00feAsin \u00f0 t i\u00de Assuming dissipative forces are similar in y and z direction, Qdry\u00bcQdrz Dynamics model of a rigid rotor system Mathematical representation for motion of rigid rotor roller bearing system is defined as \u00bdM \u20acX\u00fe \u00bdC _X\u00fe \u00bdK X \u00bc f \u00f0x, t\u00de \u00f020\u00de where [M], [C], and [K] are the mass vector of system, damping vector of system, and stiffness matrices for the system. \u20acX, _X, X refers to the acceleration, velocity, and displacement vectors, respectively, and f(t) is a force vector. Nonlinear contact stiffness and nonlinear damping between the inner race/outer race and roller is considered while modeling of equations (21) and (22). m \u20acY\u00feQry\u00feQdry\u00bcFy can be rewritten as follows m \u20acY\u00fe 1=Z XZ I\u00bc1 K \u00f0xcos i\u00fe ysin i\u00de B\u00feA sin \u00f0 t i\u00de 1:11 sin i at Purdue University on June 7, 2015pik.sagepub.comDownloaded from m \u20acZ\u00feQrz\u00feQdrz\u00bcFz can be rewritten as follows. m \u20acZ\u00fe 1=Z XZ I\u00bc1 K \u00f0x cos i\u00fe y sin i\u00de B\u00feAsin \u00f0 t i\u00de 1:11 cos i \u00fe 1=z Xj\u00bcz j\u00bc1 Qdjr sin 2 \u00f0 j 1\u00de z \u00fe!c t \u00bc Fz \u00f022\u00de where Fy is a force vector on the bearing in horizontal direction and Fz is a force vector in vertical direction, m is a mass of the rotor; Newmark-b method is used for solution of differential equations of motion and the transient responses at every time increment are obtained. Algorithm for solution of nonlinear differential equation of motion is given in Appendix 4."
        ]
    },
    {
        "image_filename": "designv10_12_0001821_tmag.2016.2520950-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001821_tmag.2016.2520950-Figure3-1.png",
        "caption": "Fig. 3 Calculation of UMP including UMP0 and UMP90 Stator\u2019s attraction to rotor is expressed in (1) and B is radial air gap flux density, \u03bc0 is magnetic permeability of vacuum, A is the cross section perpendicular to radial air gap flux density. 2",
        "texts": [],
        "surrounding_texts": [
            "(c) In 20% DE, component resultant UMP on the direction of rotor deviation 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. To obviously display UMP, this paper uses a high power motor-1200kw, 6kv, 4-pole model to simulate. 20%, 40%, 60% dynamic eccentricity of UMP0, UMP90, resultant UMP and component resultant UMP on the direction of rotor deviation will be compared below. (c) In 40% DE, component resultant UMP on the direction of rotor deviation What needs to be explained is that eccentric direction of rotor is at position 180\u00b0. As shown in (a), UMP0 at previous time is negative. This model is simulated under the method of full-voltage start-up in consideration of common operating condition. UMP at position 0\u00b0 and position 90\u00b0 are calculated (c) In 60% DE, component resultant UMP on the direction of rotor deviation 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. because the direction of resultant UMP on rotor is changing. According to UMP0 and UMP90, the direction and magnitude of resultant UMP will be known. From (b) in Fig. 4, 5, 6, it is clear to see that resultant UMP at range 0~300 ms(start-up) is about three times as much as that at range 300~500ms(steady). Along with rising eccentricity ratio, resultant UMP increases accordingly. On account of maximum deflection, component resultant UMP on eccentric direction is calculated separately. In Fig. 4, 5, 6(c), Fmax is nearly alternating up and down in equiamplitude. Its magnitude is bigger at previous time than at rear time and frequency is lower. What\u2019s more, the frequency is becoming higher at previous time. Interestingly, Fmax is not a sine wave but a triangular wave. From Fig. 7, rotor accelerates at the beginning and then slows down to steady speed. Difference of rotor and UMP position curve is similar to rotor position curve. Table I lists the root mean square of dynamic UMP at startup and steady state under 20%, 40%, 60% DE respectively. Fmax caused by full voltage start is much bigger so that Fmax should get enough attention for further study later."
        ]
    },
    {
        "image_filename": "designv10_12_0003771_00207179.2021.1941264-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003771_00207179.2021.1941264-Figure3-1.png",
        "caption": "Figure 3. Underactuated ship coordinate frames. Adapted from Fu et al. (2018).",
        "texts": [
            " In this section, two numerical examples are provided to illustrate the effectiveness of the proposed state estimation-based control scheme using flat inputs derived in the above section. The first one demonstrates that the proposed approach is a suitable choice for observable non-differentially flat nonlinear systems. The second example illustrates that our formulation is equally well suited for controlling differentially flat nonlinear systems whose flat output vector is not a measurable variable. The underactuated ship (see Figure 3) is an example of a nondifferentially flat nonlinear system and can be described by the following mathematical model (Sira-Ram\u00edrez, 1999):\u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 x\u0307 = u cos(\u03c8)\u2212 v sin(\u03c8), y\u0307 = u sin(\u03c8)+ v cos(\u03c8), \u03c8\u0307 = r, v\u0307 = \u2212\u03b7ur \u2212 \u03b2v, (16) where x, y and \u03c8 determine the position and orientation of the ship in the Earth-fixed frame, which are the only measurable state variables of the system. The state variable v represents the sway velocity in the Body-fixed reference frame. The constants \u03b7 and \u03b2 are strictly positive constants that depend on the structural characteristics of the system (see Fossen, 2011 for more details)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001626_978-3-319-55372-6_19-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001626_978-3-319-55372-6_19-Figure2-1.png",
        "caption": "Fig. 2 Vessel variables. The superscripts (\u00b7)n and (\u00b7)b denote the NED and body-frames [7], respectively. The variables N , E , and \u03c8 are the vessel pose, u, v, and r are the vessel velocity and U is the vessel speed over ground. The course \u03c7 is the sum of the heading \u03c8 and the sideslip \u03b2",
        "texts": [
            " Chapter 4 describes the four controllers which are considered in the paper, while Chap. 5 presents the results from the motion control experiments. Finally, Chap.6 concludes the paper. The vast majority of surface vessel models are based on the 3DOF model [7]: \u03b7\u0307 = R(\u03c8)\u03bd (1a) M \u03bd\u0307 + C RB(\u03bd) + C A(\u03bdr )\u03bdr + D(\u03bdr )\u03bdr = \u03c4 + \u03c4wind + \u03c4wave, (1b) where \u03b7 = [ N E \u03c8 ]T \u2208 R 2 \u00d7 S1 is the vessel pose, \u03bd = [ u v r ]T \u2208 R 3 is the vessel velocity and \u03bdr denotes the relative velocity between the vessel and the water, see Fig. 2. The terms \u03c4 , \u03c4wind, \u03c4wave \u2208 R 3 represent the control input, wind, and wave environmental disturbances, respectively. The matrix R(\u03c8) is the rotation matrix about the z-axis, the inertia matrix is M = M RB + M A where M RB is the rigidbody mass and M A is the added mass caused by the moving mass of water. The matrices C RB(\u03bd) and C A(\u03bdr ) represent the rigid-body and hydrodynamic Coriolis and centripetal effects, respectively, while D(\u03bdr ) captures the hydrodynamic damping of the vessel. An important limitation of (1b) is that it can be challenging to use for vessels operating outside of the displacement region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.149-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.149-1.png",
        "caption": "Fig. 2.149 TTR HE transmission arrangement for the HEV Polski FIAT 125p \u2013 TETROTA [FIJALKOWSKI 1985B]",
        "texts": [
            " Locating the E-M/M-E motor/generator at the axle not driven by the ECE or ICE can also make available a DBW AWD propulsion mechatronic control system, while reducing mass and inertia by removing the power take-off unit and propulsion shaft indispensable in conventional DBW AWD propulsion mechatronic control systems. Experimental Proof-of-Concept TTR HE Transmission Arrangement for HEV \u2013 TETROTA - In the HEV field, an example study may be represented by the experimental proof-of-concept TTR HE transmission arrangement for the HEV with a 4 \u00d7 2B + 2E wheel arrangement conceived by the author named TETROTA. Figure 2.149 is a simplified representation of the overall TTR HE transmission arrangement [FIJALKOWSKI 1985B]. Automotive Mechatronics 344 As shown, it may be designed for HEVs and the highest, in order of importance, components of split HE transmission arrangements are: ECE or ICE and M-M transmission for a RWD HEV (for example, Polski FIAT 126p) \u2013 drive is taken from the M-M clutch by an overhead shaft in the M-M transaxle unit to the MT gear trains, then forward to the finaldrive unit; this is coupled to the wheel hubs through jointed drive shafts; similar M-M transmission arrangements are used in front ECE or ICE-ed automotive vehicles; AC-DC/DC-AC macrocommutator-based M-E/E-M dynamotorized transaxle - A brushless AC-DC/DC-AC macrocommutator hyposynchronous (induction) squirrel-cage-rotor M-E/E-M dynamotor with an integratedmatrixer macrocommutator, microprocessor-based lower-level macrocommutator controller, and higher-level propulsion controller, and limited-slip M-M differential in the common case, on the same axis as the drive wheels and having a single oil system for cooling and lubrication; Vehicular controller (VC) - An on-board microprocessor-based highestlevel HEV controller i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001640_1.4037548-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001640_1.4037548-Figure5-1.png",
        "caption": "Fig. 5 Generation of third type of available 5-DoF open-loop limb",
        "texts": [
            " 4 Generation of second type of available 5-DoF open-loop limb Acc ep te d Man us cr ip t N ot C op ye di te d Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 08/14/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 7 Paper No.: JMR-17-1055 Corresponding Author: Sun By the same way, three types of available 5-DoF open-loop limbs are obtained. As shown in Fig. 3 and Fig. 4, the first and second type are obtained by adding one finite rotation along 4Dr axis and at the intersection point of R 2,M,4Du and R 3,M,4Du of 4-DoF limbs respectively. As shown in Fig. 5, the third type is derived by adding one rotation with fixed angle before the whole finite motions of the second type of 5-DoFopen-loop limbs. And their motions are described as    3 ,5D ,5D R 1,5D ,M,5D 1 5 ,5D ,5D R R ,M,5D 1,5D ,M,5D 4 c s 2 2 c s 2 2 i i i i i i i i i                         M u I u I r u e (16)       1,5D 1,5D R 2,5D 1,M,5D 4 ,5D ,5D R R ,M,5D S ,M,5D 2 5,5D 5,5D R R 5,M,5D 2,5D 5,M,5D c s 2 2 c s 2 2 c s 2 2 i i i i i                                        M u I u I r u e u I r u e (17)          1,5D 1,5D R R 3,5D 1,M,5D 1,M,5D 4 ,5D ,5D R R ,M,5D S ,M,5D 2 5,5D 5,5D R R 5,M,5D 3,5D 5,M,5D c s 2 2 c s 2 2 c s 2 2 b i i i i i                                            M u I r u e u I r u e u I r u e (18) Acc ep te d Man us cr ip t N ot C Downloaded From: http://mechanismsrobotics",
            " In order to generate all possible topological structures of open-loop limbs, we need to match each part of finite motions of limbs with articulated joints, and assemble the matched joints following the sequence of the corresponding parts in finite motion of limbs. Since finite motions can be identically transformed into another format, all topological structures can be generated by equally transforming finite motions of open-loop limbs and rerun the above steps. For simplicity, only R, U and S joints are used in this paper. All topological structures of open-loop limbs are generated and listed in Table 2. Typical structures of 5-DoF limbs are shown in Fig. 3(b), Fig. 4(b) and Fig. 5(c). Herein, (UR)R(RU) means distal axis of (UR), proximal axis of (RU) and axis of R joint intersect at a point. U(URU)U indicates axis of R joint passes through centers of both U joints. (RU) and (UR) mean that axis of R joints passed through center of next and last U joint, respectively. (RRR)PL means three R joint parallel with each other. Ro and (UR)o means that axis of R joint and proximal axis of (UR) pass through origin of coordinate frame. Table 2 Topological structures of available open-loop limbs DoF Finite motion Topological structures 4 4DM RRRR 5 1,5DM U(URU)U, SU, RRRU, RUU, SRR, RRRRR, RURR, US, RRS, URRR, UUR 5 2,5DM RoSR, (UR)oR(RU), (RoRR)PLR(RRR)PL 5 3,5DM RSR, R(RU)UR, RU(UR)R, (UR)R(RU), (RRR)PLR(RRR)PL 5",
            " Acc ep te d Man us cr ip t N ot C op ye di te d Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 08/14/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 12 Paper No.: JMR-17-1055 Corresponding Author: Sun Figure Captions List Fig. 1 General finite motion of arbitrary rigid body Fig. 2 Generation of available 4-DoF open-loop limb Fig. 3 Generation of first type of available 5-DoF open-loop limb Fig. 4 Generation of second type of available 5-DoF open-loop limb Fig. 5 Generation of third type of available 5-DoF open-loop limb Fig. 6 Typical topological structures of parallel tracking mechanisms with varied axes \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Acc ep te d Man us cr ip t N ot C op ye di te d Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 08/14/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 13 Paper No.: JMR-17-1055 Corresponding Author: Sun Table Caption List Table 1 Finite motions of articulated joints Table 2 Topological structures of available open-loop limbs Table 3 Suitable combinations of available open-loop limbs \u00a0 \u00a0 \u00a0 \u00a0 Acc ep te d Man us cr ip t N ot C op ye di te d Downloaded From: http://mechanismsrobotics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002671_b978-0-12-814245-5.00029-3-Figure29.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002671_b978-0-12-814245-5.00029-3-Figure29.8-1.png",
        "caption": "FIGURE 29.8 Prototypes of the stereo cameras and their feasibility as an imaging system for knee arthroscopy. The NanEye stereo module is shown in (A). Its miniature dimension is ideal for arthroscopy; however, it suffers from a low image resolution and unreliable performance. The second prototype (B) is based on pairing two mcU103A cameras.",
        "texts": [
            " Three-dimensional reconstruction using stereo image pairs requires identification of image pixels that correspond to the same point in a physical scene that is being observed by the two cameras. Two prototypes of arthroscopes have been developed at Queensland University of Technology for achieving this aim: (1) NanEye stereo camera (each with 2503 250 pixels) mounted on a 3D printed head and (2) a pair of muC103A cameras (each with 4003 400 pixels) assembled as a stereo pair and mounted on a 3D printed head. The images of arthroscope prototypes are shown in Fig. 29.8. In comparison to prototype 1, substantial improvements have been achieved using prototype 2, in terms of image resolution and reliability of the camera during the recordings. However, there is room for further improvements in physical characteristics of the camera such as adding LED illuminators and having a multibaseline stereo arrangement. Fig. 29.9 shows a set of stereo images acquired by arthroscope prototype 1. It is evident that despite the stereo camera having an image resolution of 2503 250 only the amount of detail present in these images is more informative than that provided by traditional oblique-view arthroscopes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.49-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.49-1.png",
        "caption": "Fig. 15.49 Domains \u0393 \u2032 1, . . . \u0393 \u2032 5 (\u0393 \u2032 2 , \u0393 \u2032 4 shaded) for \u03b1 = 40\u25e6 . When P0 is point A , the rectangle of maximum width is in contact with P0 in three positions occurring in phases 2, 3 and 4 . Two positions are shown",
        "texts": [
            " The solution for, say \u03d52 , must be calculated numerically. For reasons of symmetry it suffices to consider the interval \u03c0/2\u2212 \u03b1 \u2264 \u03d53 \u2264 (\u03c0 \u2212 \u03b1)/2 . For every pair of values (\u03d52, \u03d53) the corresponding quantities x , y and b are calculated from (15.181). From b the angle \u03d50 of Eq.(15.171) is calculated. If the condition \u03d50 \u2264 \u03d52 \u2264 \u03c0/2 \u2212 \u03b1 is satisfied, x and y 526 15 Plane Motion are the coordinates of a point of G23 . Figure 15.48 shows the curve G23 calculated for the angle \u03b1 = 40\u25e6 . Reflection of G21 and G23 on g produces G45 and G43 , respectively. Figure 15.49 displays the curves Gij (i, j = 1, . . . , 5 ; j = i ) . Together with g1 and g2 they divide the sector between g1 and g2 into the domains \u0393 \u2032 1, . . . \u0393 \u2032 5 . The domain boundaries G31 and G35 shown as dashed lines are irrelevant. Finally, an equation determining bmin is formulated for the case when P0 is located in \u0393 \u2032 2 . Equations (15.174) determine b and \u03d5 if x = x0 and y = y0 is substituted. The second equation is solved for b and then this expression is substituted into the first equation",
            " The result is the 6th-order equation for u (with abbreviations s = sin\u03b1 , c = cos\u03b1 ) References 527 b6u 6 + b5u 5 + b4u 4 + b3u 3 + b2u 2 + b1u+ b0 = 0 , b6 = \u2212(y0 + s) , b5 = 2s(sx0 \u2212 cy0) + 4c , b0 = y0 \u2212 s , b1 = 2s(sx0 \u2212 cy0)\u2212 4c , b4 = \u22128s(cx0 + sy0) + 3y0 + 5s\u2212 4/s , b3 = 12c(cx0 + sy0)\u2212 4x0 , b2 = 8s(cx0 + sy0)\u2212 3y0 + 5s\u2212 4/s . \u23ab\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23ad (15.187) Every real solution u determines an angle \u03d5 = 2 tan\u22121 u . If this angle satisfies the condition \u03d50 \u2264 \u03d5 \u2264 \u03c0/2 \u2212 \u03b1 , the corresponding width b(\u03d5) is calculated from (15.185). The smallest of all widths thus determined is the desired solution Bmax . In Fig. 15.49 point A belongs to the three domains \u0393 \u2032 2 , \u0393 \u2032 3 and \u0393 \u2032 4 . When P0 is at A , the rectangle of maximum width is in contact with P0 in three positions. The two positions in phases 2 and 3 are shown. The coordinates of A , the associated maximum width b and the associated angle \u03d5 in phase 2 are determined as follows. The coordinates in phase 2 as functions of b and \u03d5 are given in (15.174). The coordinates in phase 3 are (see Fig. 15.49) x = y cot \u03b1 2 = cos \u03b1 2 ( 1 2 cot \u03b1 2 + b ) , y = 1 2 cos \u03b1 2 + b sin \u03b1 2 . (15.188) Equating the two yields two equations for the unknowns b and \u03d5 . Elimination of b leads to an equation for \u03d5 . It can only be solved numerically since it contains as highest-order term cos3 \u03d5 . 1. Bereis R (1951) Aufbau einer Theorie der ebenen Bewegung mit Verwendung komplexer Zahlen. O\u0308sterr.Ing.-Arch. 5:246\u2013266 2. Besicovitch A S (1928) On Kakeya\u2019s problem and a similar one. Mathematische Zeitschrift 27:312\u2013320 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.7-1.png",
        "caption": "Fig. 2.7 Principle layout of a unique sidestick (joystick) [DaimlerChrysler].",
        "texts": [
            " What appears to be a kind of video game to a conventional driver is actually a unique innovation based on a revolutionary concept known as \u2018DBW AWD\u2019. This new system not only offers improved safety, comfort, and ergonomics, but also provides extra advantages in terms of vehicle design and production. It\u2019s all made possible by a mechatronic control system that replaces the mechanical and fluidical connections linking the steering wheel and pedals with the steering, drive, and brakes. Designed so that it can only be moved to the left or right, a unique sidestick (see Fig. 2.7) enables drivers to steer with high precision. Automotive Mechatronics 158 At the same time, an integrated E-M motor gives them a more realistic feeling of steering resistance. A two-dimensional force-measuring sensor that reacts to forward or backward hand pressure, registers commands to accelerate or brake. The DBW AWD propulsion mechatronic control system takes over control of the ECE or ICE plus the braking and steering functions. In this manner, it can control the automotive vehicle as the driver would wish, even in a situation where the driver might not be able to react in time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.4-1.png",
        "caption": "Fig. 3.4 Axes and quantities R , \u03bb , \u03bc , \u03bd in the context of Roth\u2019 theorem",
        "texts": [
            " Four noncoplanar body-fixed points satisfying (3.21) cannot exist since otherwise the displacement of the body would be a rotation about P contrary to the assumption. In the general case, the displacement of the body is a screw displacement. Define (n, \u03d5) to be the rotation, R \u2265 0 the distance of P from the screw axis, e a unit vector through P normal to the screw axis (in the case R > 0 , the vector Re is the perpendicular from P onto the screw axis). Finally, let s be the translation along the screw axis (see Fig. 3.4). The special cases of pure translation ( s = 0 , \u03d5 = 0 ) and of pure rotation ( s = 0 , \u03d5 = 0 ) are not excluded. Three distinguished points of the unknown body-fixed plane 92 3 Finite Screw Displacement are its intersections with the line Pe , with the screw axis and with the line perpendicular to both screw axis and line Pe . The vectors ri (i = 1, 2, 3) from P to these points in the initial position have, with unknown quantities \u03bb , \u03bc and \u03bd of dimension length, the forms r1 = Re+ \u03bbn , r2 = (R+ \u03bc)e , r3 = Re+ \u03bdn\u00d7 e . (3.22) In the final position after the screw displacement the position vectors are found by simple inspection from Fig. 3.4 : r\u20321 = Re+ (s+ \u03bb)n , r\u20322 = sn+ (R+ \u03bc cos\u03d5)e+ \u03bc sin\u03d5 n\u00d7 e , r\u20323 = sn+ (R\u2212 \u03bd sin\u03d5)e+ \u03bd cos\u03d5 n\u00d7 e . } (3.23) Substitution into (3.21) yields for the unknowns the expressions \u03bb = \u2212s 2 , \u03bc = s2 2R(1\u2212 cos\u03d5) , \u03bd = s2 2R sin\u03d5 . (3.24) Except for a single case these formulas define three points and, hence, a plane. The single case is a pure rotation about an axis not passing through P . It is characterized by s = 0 and R,\u03d5 = 0 . The corresponding solutions \u03bb = \u03bc = \u03bd = 0 define only the point 0 . However, even in this case, a body-fixed plane with the required property exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001224_icra.2011.5980498-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001224_icra.2011.5980498-Figure2-1.png",
        "caption": "Fig. 2. Human-like foot mechanism with the medial longitudinal arch.",
        "texts": [],
        "surrounding_texts": [
            "Turning motion by utilizing the slip between the feet and the ground is classified into two groups; i) turn with one foot and ii) turn with both feet. The toe joint of the human-like foot system [3] is a passive joint as shown in Fig, 2, and it is difficult for a robot to stand on the tiptoes with one foot. Therefore in this research, we focus on the turning motion with both feet. Considering the contact conditions between the feet and the ground, the turning motion with both feet is also classified into the following three groups: \u2022 Heel contact \u2013 Heel contact \u2022 Toe contact \u2013 Heel contact \u2022 Toe contact \u2013 Toe contact In this research, we target at the turning motion with \u201ctoe contact \u2013 heel contact\u201d because a larger support polygon can be formed and a robot can maintain the stability during turning even if the toe is a passive joint. In case of \u201ctoe contact \u2013 toe contact\u201d, the toe joint should be actuated to maintain a robot\u2019s stability. In particular, we focus on the turning motion to rotate 90 degrees by rotating each foot around the toe and the heel as shown in Fig. 3. We measured a human\u2019s turning motion by a motion capture system and force plate to generate a robot\u2019s motion. We measured a human\u2019s turn not only by slipping motion but also by stepping motion. Fig. 4 shows a transition of each foot\u2019s CoP (Center of Pressure) during slipping motion. We found that a human rotate the foot standing on the tiptoe around the metacarpophalangeal joint of the forefinger and rotate the foot standing on the heel around the heel. We also compared the travel distance of CoP of slipping turn with that of stepping turn (see Fig. 5). The travel distance of slipping turn is about 40% shorter than that of stepping turn, so the reduction of energy consumption is expected by utilizing the slip between the feet and the ground. Fig. 6 (a) illustrates a human\u2019s toe trajectory during slipping turn with both feet. The origin of this figure is the CoM of the subject, and the direction of the X axis signifies the frontal direction of the subject\u2019s waist. We can find that a human moves its feet along an arc trajectory when turning by using slipping motion with both feet. Based on the anthropometric data, a turning motion is generated to rotate each foot around the toe and the heel. Fig. 6 (b) illustrates a robot\u2019s toe trajectory of a turning pattern generated. The origin of this figure is the moving coordinate system fixed to the robot\u2019s waist, and the direction of the X axis signifies the frontal direction of the robot\u2019s waist. Fig. 6 (b) is similar to the human\u2019s toe trajectory. Reference ZMP is fixed at the midpoint between the toe and the heel during turning as shown in Fig. 7. Fig. 8 shows a turning simulation. But if the turning pattern is output to a robot, the robot falls down during turning due to a model error of the robot. So, we have developed a turning stability control as described in the following chapter."
        ]
    },
    {
        "image_filename": "designv10_12_0003106_aris50834.2020.9205794-Figure17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003106_aris50834.2020.9205794-Figure17-1.png",
        "caption": "Figure 17. Design and fabrication of unmanned surface vehicle.",
        "texts": [
            " This module use aerial robots for face recognition and tracking [10] as shown in Figure 15, to assist search and rescue for shortening the search time and reduce the search area. The workflow is illustrated in Figure 16. V. SURFACE MODULE Aerial robot often cannot stay in the air for a long time because of the limited energy carried, and the communication range is limited. Therefore, this module proposes the concept of UAV-based offshore platform. A surface robot is designed and fabricated to perform forward, backward, and steering movements as shown in Figure 17. Robot with sensors perceive the environment for their position and orientation, find the target, and plan and execute motion. Single propeller generates the propulsion. Propeller rotate clockwise or counterclockwise generate the forward or backward motion respectively. A steering rudder is Authorized licensed use limited to: University of New South Wales. Downloaded on October 01,2020 at 18:21:43 UTC from IEEE Xplore. Restrictions apply. connected with a servo motor which control the direction of propeller\u2019s propulsion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000423_tmag.2009.2012540-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000423_tmag.2009.2012540-Figure4-1.png",
        "caption": "Fig. 4. Stator core mesh includes: 67 388 tetrahedral elements, 16 142 boundary elements and 2982 edge elements.",
        "texts": [
            "4, it is possible to represent an accurate 3-D geometry with its real complexity and to find more exact solution of the electromagnetic field even in the vicinity of the end core region. An application example is given, referring to a 200 MW turbine generator. The 3-D geometry of the machine is presented in Fig. 2 showing the stator and the rotor core with the rotor end windings. The complete model of the machine end zone is shown in Fig. 3. Because of the whole model complexity and especially the too large number of elements in the whole domain, in Fig. 4 is presented the stator core mesh only. There are described the number and the kinds of the elements for the stator core discretization. The technical characteristics of the investigated object are presented by its specification in Table I. The force densities are calculated using Maxwell stress tensor. The force distribution is determined outside the stator and the rotor cores. This study shows that as the temperature and the temperature gradient fields [8] the force density distribution closely depends on the working mode of the machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.40-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.40-1.png",
        "caption": "Fig. 3.40 The components and subsystems of the enhanced ACC BBW AWB dispulsion mechatronic control system [RILEY ET AL. 2000].",
        "texts": [
            " 2011 506 ACC is an extension of the existing cruise control feature that links together a forward obstacle detection system for monitoring traffic directly in front of the vehicle, the cruise control system (throttle valve), the braking system, and the driver\u2019s input as to the desired cruise-control set vehicle velocity. Identical criteria are used to determine the distance to the preceding vehicle. The key objectives of ACC are improved traffic flow and increased driver comfort while reducing the driver\u2019s workload. Figure 3.40 shows the components and subsystems used to achieve ACC on a host vehicle [RILEY ET AL. 2000]. 3.7 Enhanced Adaptive Cruise 507 ACC technology is on the horizon as a convenience function especially intended to reduce the driver\u2019s workload. Considerations of moding ABS with ACC and TCS may be applied at the automotive vehicle level. Figure 3.41 depicts the fluidical mechanisation of a mechatronically controlled AC BBW AWB dispulsion mechatronic control system capable of ABS, TCS and vehicle stability enhancement (VSE)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.8-1.png",
        "caption": "Fig. 15.8 Limac\u0327ons of Pascal with double point A (a), with a cusp (cardioid (b)), with inflection points (c) and without inflection points (d)",
        "texts": [
            " Since H lies on the fixed circle (xH \u2212 )2 + y2H = R2 , point K lies on the fixed circle (xK\u2212 /2)2+y2K = (R/2)2 . This is the circle k shown in Fig. 15.7a . It is concentric with k2 , and its radius is R/2 . These facts are summarized in the statement that q is enveloped by all circles centered on k and passing through A . This is demonstrated in Fig. 15.7b in which A and the circle k are copied from Fig. 15.7a . Next, the polar-coordinate equation (15.12) is considered again: r(\u03d5) = cos\u03d5 + R . In the case R < , the function r(\u03d5) has two roots. They are associated with the double point A of q (Fig. 15.8a). In the case R = , r(\u03d5) has a double root. In this case, q has a cusp at A (Fig. 15.8b). This curve is called cardioid. In the case < R < 2 , shapes with inflection points result (Fig. 15.8c), and in the case R > 2 , shapes without inflection points (Fig. 15.8d). In the case R > , the fixed point A is an isolated point which is not part of the trajectory traced by Q . Equation (15.14) is satisfied by the coordinates x = y = 0 of A independent of R , whereas the polarcoordinate equation r(\u03d5) = cos\u03d5+ R shows that r = 0 is possible if and only if R \u2264 . 15.1 Instantaneous Center of Rotation. Centrodes 461 The generation of ellipses and of limac\u0327ons of Pascal by means of an elliptic trammel is made use of in many engineering apparatuses (examples see in Wunderlich [30])",
            " The similarity of the triangles (B,P\u2217,C) and (D,B0,C) establishes the equation (R+ )/r = /a . Hence R = (r/a \u2212 1) . Setting the square of this expression equal to the previous expression for R2 results in the polar-coordinate equation for the fixed centrode kf : r = 2 a 2 \u2212 a2 ( + a cos\u03d5) . (15.28) Comparison with (15.12) shows that kf is a limac\u0327on of Pascal and, because of > a , one without double point. Its line of symmetry is A0B0 . The constant coefficients depending on and a determine the quantities and R of Fig. 15.8. An equation for the moving centrode km is obtained as follows. In the coupler-fixed system the pole P has the polar coordinates \u03d5 = (ABB0) and r\u2032 =BP= \u2212R and with the above expression for R r\u2032 = (2\u2212 r/a) . Hence r = a(2 \u2212 r\u2032/ ) . Substitution into (15.28) results in the desired equation for km : r\u2032 = 2 a a2 \u2212 2 (a+ cos\u03d5) . (15.29) This is a limac\u0327on of Pascal with the double point B and with the line of symmetry BA . The equation is obtained directly from (15.28) by interchanging and a . Example 6 : Door mechanism In Fig",
            " The curvature of trochoids was the subject of the example illustrating Fig. 15.21. 15.5 Trochoids 497 From the elliptic trammel in Fig. 15.4 the following results are known about wheels having the ratio 1 : 2 of radii with the small wheel being inside the larger wheel. If the small wheel is the planetary wheel 1 , trochoids are diameters of wheel 0 if C is located on the circumference of wheel 1 and ellipses otherwise. If the large wheel is the planetary wheel 1 , trochoids are limac\u0327ons of Pascal (Fig. 15.8). Three parameters suffice if the radii r0 and r1 of the wheels and the radius b of point C on wheel 1 are defined as quantities which may be positive or negative. These definitions are given next. In Figs. 15.26 and 15.27 the poles P20 , P12 and P10 are shown. The tangent to the trochoid is the normal to the line P10C . The position of C is specified by the complex number z in the complex plane with origin P20 . A system has several, possibly even infinitely many so-called straight-line positions",
            "29) or in both mechanisms from the inside (Fig. 15.30). Trochoids generated by mechanisms of the former type are called epitrochoids, and trochoids generated by mechanisms of the latter type are called hypotrochoids. Epitrochoids and hypotrochoids alike are divided into three families: 1. Trochoids have double points if in the first generation the generating point C is outside the circle of wheel 1 , i.e., if |b/r1| > 1 . Such trochoids are called curtate trochoids (Fig. 15.26 and the limac\u0327on of Pascal in Fig. 15.8a ). 2. Trochoids have cusps on the circumference of wheel 1 if the generating point C is located on the circumference of wheel 1 (in both generations; |b/r1| = 1 ). Such trochoids are called cycloids (either epicycloids or hypocycloids). 3. Trochoids have neither double points nor cusps if in the first generation point C is inside of wheel 1 , i.e., if |b/r1| < 1 . Such trochoids are called prolate trochoids (Fig. 15.28 and the limac\u0327ons of Pascal in Figs. 15.8c,d ). Example: In the system shown in Fig",
            "121) yields v2 = |z\u0307|2 = \u03d5\u03072 1r 2 1[(cos\u03d52 \u2212 cos\u03d51) 2 + (sin\u03d52 \u2212 sin\u03d51) 2] = 2\u03d5\u03072 1r 2 1 [ 1\u2212 (cos\u03d52 cos\u03d51 + sin\u03d52 sin\u03d51) ] = 2\u03d5\u03072 1r 2 1[1\u2212 cos(\u03d51 \u2212 \u03d52)] = 4\u03d5\u03072 1r 2 1 sin 2 \u03d51 \u2212 \u03d52 2 . (15.128) This complicated calculation is of course unnecessary. In the resulting formula v = \u03d5\u030712r1 sin 1 2 (\u03d51 \u2212 \u03d52) the factor of \u03d5\u03071 is the distance of C from the instantaneous center of velocity P10 . The maximum velocity occurs in the vertices of the trajectory: vmax = 2r1\u03d5\u03071 . End of example. Both generating mechanisms of a cycloid share the same sunwheel 0 and, furthermore, cusps occur on the sunwheel. An example is the cardioid shown in Fig. 15.8b . It is an epitrochoid with the two generations according to Fig. 15.32. Hypocycloids of particular interest are Steiner\u2019s hypocycloid in Fig. 15.33b and the astroid in Fig. 15.33c . A special case belonging to this family is the system shown in Fig. 15.33a . It is known from the elliptic trammel. This particular hypocycloid is a diameter of the sunwheel. Equation (15.119) for the astroid is simplest when as straight-line position \u03d51 = \u03d52 = 0 not the position shown in Fig. 15.33c is chosen, but the position when P10 is a cusp of the astroid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002873_j.mechmachtheory.2019.103669-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002873_j.mechmachtheory.2019.103669-Figure8-1.png",
        "caption": "Fig. 8. View of the sections through 7205B M-ACBB assemblies loaded with Fa = 5 N and Fa = 15 N.",
        "texts": [
            " For both simulated conditions, a linear variation of the total friction torque T with the friction coefficient is observed. These two linear dependencies between total friction torque and friction coefficient can be considered as a real possibility to evaluate the friction coefficient in ball-race contacts by means of M-ACBB with three balls and without cage. The experimental methodology for the friction torque evaluation in 7205B M-ACBB is presented in detail in reference [26]. The schematic view of 7205B M-ACBB with the two axially loads is presented in Fig. 8. The inner ring is mounted on the rotating table and the outer ring is initially stationary. Two steel cylinders are mounted on the outer ring. They define, with the outer race, the axial load of 5 N and 15 N. The corresponding inertia moment J are 4.354.10\u22124 kgm2 and 9.98.10\u22124 kgm2, respectively. The geometrical parameters of 7205B M-ACBB were presented in the Table 1. The tests are based on spin \u2013 down method and similar tests realized with modified thrust ball bearings in various lubrication regimes have been presented in references [21\u201323]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure17.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure17.12-1.png",
        "caption": "Fig. 17.12 A ball of radius r falls vertically at speed v1 onto a stationary bat of radius R, and bounces at speed v2. The ball is scattered through an angle A. The horizontal distance between the ball center and the bat center is E . We can model the collision as an oblique bounce off a flat surface that is inclined at an angle parallel to the dashed tangent line",
        "texts": [
            " This result is similar to that for a rolling ball but it is not exactly the same since the bat itself rotates and translates after the collision. A ball that rolls along a stationary surface does so with vx D R! but if it continues to do so while the surface itself is moving then the bottom of the ball actually slides along the surface. That is what happens when a ball bounces off a bat. The ball grips the bat, both are set in motion and then the ball slides backwards along the surface before finally bouncing off the bat with eT D 0. A model of the scattering process is shown in Fig. 17.12. A ball of radius r falls vertically onto a stationary bat of radius R. At least, this was the situation in the experiment described above. Once we determine the basic physics of the scattering process in this case, then it is relatively easy to consider a more realistic case where a bat and ball approach each other in a horizontal direction or in some other direction. As shown in Fig. 17.12, the horizontal distance between the bat and ball centers is denoted by E . That distance is commonly called the impact parameter in scattering experiments. The line joining the ball centers is inclined at an angle \u02c7 to the horizontal, where cos \u02c7 D E=.r C R/. The ball is incident an an angle 1 D 90 \u02c7 to the line joining the ball centers and rebounds at angle 2. The ball is, therefore, scattered through an angle A D 1 C 2. Despite the curvature of the bat, we can model the collision as one where the ball bounces off a flat surface inclined at an angle parallel to the tangent line shown in Fig. 17.12. We can even choose to ignore motion of the bat. Suppose that the bat recoils at speed Vy in a direction perpendicular to the surface. Then the coefficient of restitution (COR) in the y direction is defined by ey D .vy2 C Vy/ vy1 (17.1) We can ignore motion of the bat in the y direction by defining an apparent coefficient of restitution, eA D vy2=vy1, which is defined purely in terms of the ball speed in the y direction. Similarly, we can ignore motion of the bat in the x direction by defining an apparent tangential coefficient of restitution, eT , considering only the tangential velocity of the contact point on the ball, given by vx r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure13-1.png",
        "caption": "Fig. 13. Contact ratio of the gear drive.",
        "texts": [
            " (iii) The minimum teeth number of the proposed gear without undercutting is affected by k1 and k2, for example, according to Eq. (54), when k2 is equal to 0.2, the minimum teeth number of the driving gear is 2, which is much less than that of the involute gear. The contact ratio can be defined as the average number of teeth of each gear in contact. It can also be defined as the ratio of the angle rotated by the gear between starting and end points of contact to the angle between two adjacent teeth which (the latter angle) is equal to 2\u03c0 divided by the number of teeth [19]. As illustrated in Fig. 13, B presents the intersection point between the line of action and the addendum circle of the driven gear and C is the intersection point between the line of action and the addendum circle of the driving gear. Assuming that the driving gear rotates in a clockwise direction, two gears would firstly engage at B, and finally separate at C. The contact ratio of the gear drive can be expressed as where \u03b5 \u00bc \u03a8 2\u03c0=z1 \u00f055\u00de \u03a8 denotes the angle between O1B and O1C . The parameters are set with the same values as those in examples 1 and 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure16.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure16.14-1.png",
        "caption": "Fig. 16.14 Wheel 2 with internal gearing meshing with wheel 1 with external gearing",
        "texts": [
            "62) determine \u03b1\u2032 and e1 + e2 . This section is closed with a formula for the tooth thickness d(ra) at the tip of a tooth in the case of zero addendum modification. With (16.46) the tip radius is ra = r +m = r(1 + 2/n) . Hence with (16.53) and (16.54) d(ra) = r ( 1 + 2 n )[\u03c0 n + 2(inv\u03b1\u2212 inv\u03c8) ] , cos\u03c8 = cos\u03b1 1 + 2 n . (16.66) With \u03b1 = 20\u25e6 this formula yields d(ra) \u2248 0.076r for n = 18 and d(ra) \u2248 0.032r for n = 48 . These very reasonable figures show that the engineering standard addendum is well chosen. Figure 16.14 differs from Fig. 16.10 in that the pitch circle p1 of wheel 1 with radius r1 is inside wheel 2 . The outer wheel has internal gearing, whereas the inner wheel has external gearing as before. As in Fig. 16.10 the common normal en to the involutes f1 and f2 at the point of contact B is tangent to the base circles c1 and c2 . Equation (16.17) is satisfied with a = r2 \u2212 r1 , b = r1 , \u03bc = b/(a + b) = r1/r2 , en \u00b7 b = \u2212r1 sin\u03b1 , 2 \u2212 1 = A1A2 = (r2 \u2212 r1) sin\u03b1 , 1 \u2212 r = r1 sin\u03b1 and 2 \u2212 r = r2 sin\u03b1 . This suffices as proof for the involutes being conjugate tooth flanks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002661_s10010-019-00354-5-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002661_s10010-019-00354-5-Figure2-1.png",
        "caption": "Fig. 2 Test gear: POM spur gear",
        "texts": [
            " Until now, there are no studies on which working condition is reasonable for plastic POM gear in endurance test. In this study, we attempt an unchanged testing condition with 7Nm of torque and 1000rpm of rotational speed, in which a test POM gear can work approximately 5h in an endurance test. \u2466 is an angular velocity sensor for the driven shaft. \u2467 is the high-speed camera, which can capture images of teeth of plastic gears from the lateral side. In this study, the analysis object is POM (Polyoxymethylene) spur gears. The driven test gear is shown in Fig. 2. The module is 1.0, and the number of teeth is 48. In addition, a steel spur gear is used as the driving side gear. The number of teeth of the driving gear is 67. A data acquisition system developed in the previous study [3] was used to collect vibration and image data. The automatic data acquisition system consists of the acceleration sensor, high-speed camera, angular velocity sensor and a relay circuit. The flow chart of the data acquisition is shown in Fig. 3. A signal from a PC controls the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001523_tmag.2014.2364264-Figure25-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001523_tmag.2014.2364264-Figure25-1.png",
        "caption": "Fig. 25, in which the parameters are same as shown in Table I. Fig. 26 shows the measured and predicted phase backEMFs at two different field currents (half and full rated DC currents as shown in Table I) when the speed is 400rpm. Fig.",
        "texts": [],
        "surrounding_texts": [
            "In order to validate the foregoing analyses, two prototype machines, 1\u00d76/7 stator/rotor pole single-tooth VFRM and 4\u00d76/25 stator/rotor pole 4-tooth VFRM are made and shown in 0.0 0.4 0.8 1.2 1.6 0 60 120 180 240 300 360 T or qu e( N m ) Rotor position (elec.deg) 4\u00d76S/22R 4\u00d76S/23R 4\u00d76S/25R 4\u00d76S/26R 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 27 shows the variation of static torque with the rotor position at four different field and armature currents combinations, i.e. 25%, 50%, 75% and 100% of rated DC current with pf = pa (If = 0.707Ia). Based on Fig. 27, the variation of the static torque at 270\u00b0 rotor position with the total copper loss is obtained and shown in Fig. 28. Overall, the measured and FE predicted results match well, especially for phase back-EMF waveforms. The differences between the measured and FE predicted results of static torque under higher current (copper loss) are due to the increased influence of end-effect."
        ]
    },
    {
        "image_filename": "designv10_12_0000440_978-1-4020-8829-2_2-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000440_978-1-4020-8829-2_2-Figure1-1.png",
        "caption": "Fig. 1. Peasgood et al.\u2019s seven segment, nine degree of freedom, planar gait model with a 2-point continuous foot contact model",
        "texts": [
            " Originally the 1,000 gait simulations took 10 days to perform on a single computer using the popular mechanical modeling package MSC.Adams [21]. DynaFlexPro [9], another modeling package, developed since Peasgood et al.\u2019s work, offers substantial performance advantages over Adams: the updated version of Peasgood et al.\u2019s predictive system now takes only 8 hours to run. Peasgood et al.\u2019s work was taken, carefully examined, analyzed, improved and implemented in DynaFlexPro. Peasgood et al. developed a predictive gait simulation using a 2D, seven segment, nine degree of freedom (dof), anthropomorphic model shown in Fig. 1 with a continuous foot contact model. This is a fairly standard model topology for gait studies. The upper body is simplified into a single body representing the head, arms and trunk (HAT); the thigh and shank are each one segment, as is the foot [1, 3, 13]. An additional simplification has been made in this model by fusing the HAT to the pelvis. There was an unintended error in Peasgood et al.\u2019s original model: there was an extra body attached to the foot that had a moment of inertia of 1.5 kg m2, which is comparable to the HAT segment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003464_j.addma.2020.101657-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003464_j.addma.2020.101657-Figure1-1.png",
        "caption": "Fig. 1. Built pre-forms (AM) on the wrought Ti-6Al-4V substrate plate (top) and an illustration of the pre-forms overlaid with the specimens before postprocessing (bottom).",
        "texts": [
            " Both the powder and build plate were used in their virgin form i.e. have not experienced any prior heat cycle. The process parameters are given in Table 1. The substrate material for the hybrid specimens manufacturing was wrought chosen to be Ti-6Al-4V cold-rolled plate purchased from TITANIUM INTERNATIONAL GROUP SRL. No support structures were used in the building process to facilitate the mechanical evaluation of the hybrid material. The various pre-forms used for this study and their designation are given in Fig. 1 along with an illustration of the tensile and compacttension fracture specimens overlaid on the pre-forms. Following the SLM process pre-forms were carefully machined out of the substrate plate and AM material. The pre-forms from the three groups (i.e. hybrid, AM and wrought) were heat-treated following two commonly used stress-release procedures for AM Ti-6Al-4V, namely: 650 \u25e6C for 3 h or 800 \u25e6C for 4 h. Both heat treatments were held and cooled in vacuumed furnace. Finally, the pre-forms were machined into tensile specimens (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003097_j.rcim.2020.102053-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003097_j.rcim.2020.102053-Figure12-1.png",
        "caption": "Fig. 12. Screenshots of results of EA with Individual Count (IC)=200 in Production Scenario. Red line shows best path and black lines show more solution candidates of the population.",
        "texts": [
            " 11 and 12 show the screenshots of the planning results with the shortest path lengths from all runs. Both for IC=100 and for IC=200 the path points are distributed at the height of the table and the tool shape, which leads to a very direct movement of the robots. If more intermediate points are used to calculate the path, they appear to be less angular at first glance; this leads to a softer robot movement. At second glance, however, it can be seen that this can lead to zigzag movements, like in Fig. 11c when entering the tool shape or in Fig. 12c after being picked up above the table. In summary, it can be said that with EA surprisingly good paths can be found in a relatively short time. During the experiments it was also shown that it is not necessary to make the fitness function very complex. Complex in this context means that only the three parameters number of collisions, euclidean path length and axis movement are enough to build a fitness values which is able to make a good indication of the quality of a chromosome. In this paper we presented an implementation of a genetic algorithm capable of calculating paths for 6-DOF industrial robots in a single robot scenario and with 14-DOF in a scenario with cooperating robots on a common linear track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002102_s00170-015-6915-7-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002102_s00170-015-6915-7-Figure1-1.png",
        "caption": "Fig. 1 Grinding of face gear by a disk",
        "texts": [
            " In this paper, a grinding method for face gears on a general CNC machine with only five degrees of freedom is proposed, and the interpolation formulas are deduced. An envelope residual model for grinding face gears is developed for determining the maximal feed value. Numerical results such as envelope residual lines for a specific pair of face gear are analyzed and comparedwith experimental data to demonstrate the effectiveness of the proposed model. 2 CNC machining method with grinding disk 2.1 Machining principle As illustrated in Fig. 1, machining of face gear can be accomplished by a grinding disk simulating the movement of an involute cylindrical gear (shaper). Figure 1 presents the grinding disk at two different positions. The cross profile of the grinding disk is identical with the tooth profile of the pinion meshing with the face gear. The rotating grinding disk swings around the axis of the virtual shaper and meanwhile moves along the gear tooth width. Therefore, this complexmovement of grinding disk forms a rotating virtual shaper. Face gear must also rotate around axis A for the corresponding rotation according to gear ratio. According to this machining principle, face gears can be grinded on a machine tool with 5 degrees of freedom, and the axes of A, B, X, and Z must be linked"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.24-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.24-1.png",
        "caption": "Fig. 5.24. For equilibrium of P relative to the oblate spheroidal Earth, (5.89) now yields",
        "texts": [
            "88), however, suggests that the problem is more subtle than the possibility of error introduced by our treating the Earth, the Sun, and the Moon as particles separated by great distances and neglecting small terms in mfm s , Suppose, on the other hand, that the gravitational force in (5.89) must have a small tangenti al component that balances the tangential centrifugal force component in (5.90). Though this correction addresses objections raised here, it implies that our spherical model of the Earth is inaccurate. Let us consider the revised model shown in Fig. 5.24. Suppose that the attractive force mg3 of the Earth on P has a small northerly directed , tangential component -mg3 sinat to balance the tangential centrifugal force component mr2Q sin Bcos f3t shown in Fig. 5.24a. If the gravitational force exerted by the Earth is directed toward its center C , while Fa is normal to its surface, as shown in Fig. 5.24, then the Earth must flatten somewhat at the poles and bulge slightly at the equator. In fact, geophysical theory and measurements show that the Earth is an oblate spheroid with a mean equatori al radius re =3963 mile (6378 km) and a smaller mean polar radius rp = 3950 mile (6357 km), approximately. The accepted international value for the amount of flattening at the pole is fL == (rE - rp)lrE = 1/297. The centrifugal force arising from the Earth's rotation thus produces a measurable equatorial bulge of the Earth",
            " To account for polar flattening, let us suppose that the direction of the actual gravitational force mg3 due to the Earth is still directed toward its center C in The Foundation Principles of Classical Mechanics 75 In this equation, 13 is the geograph ical colatitude angle, the angle between the polar axis of rotation and the outward, normal vector to the surface; () is the geocentric colatitude angle, the angle between the polar axis and the radial line through the Earth 's center; and a == () - 13 is their angle of deviation. (See Fig. 5.24.) Thus, the normal reaction force F0 in (5.89) balances the apparent weight mg of P , which varies slightly over the surface of the Earth . That is, F 0 +mg = 0, wherein the apparent gravitational fie ld strength g is defined by g == g3 - 0 x (0 x r) . (5.92) This rule shows the effect of the Earth 's rotation on the real gravitational field strength g3. The tangential component of g vanishes in accordance with (5.91): -g3 sin o + rQ 2sin e cos\u00ab() - a ) = 0; (5.93) and (5.92) becomes g = gn = (g3cos a - rQ2sin() sin\u00ab() - a\u00bb) n , (5.94) in which n is the inward directed unit normal vector to the Earth 's surface. (See Fig. 5.24a.) This is named the apparent acceleration of gravity ; it is the 76 Chapter 5 gravitational field strength apparent to an observer stationed at a point on the surface of the Earth at the geographic colatitude f3 = () - a. The apparentaccelerationofgravity is always perpendicular to the Earth's surface. This is the direction n along which a plumb bob is attracted when freely suspended by a string . In this case, F 0 is the tension in the line. The angle a of the plumb line's deviation from 'the direction of the real gravitational vector g3 in Fig "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000555_j.cclet.2010.07.026-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000555_j.cclet.2010.07.026-Figure1-1.png",
        "caption": "Fig. 1. CVs of 0.25 mmol/L AA at the (b) bare CPE, (d) TN-CPE, (e) BBNBH-CPE and (f) BBNBH/TN-CPE. (a) and (c) show the CVs of blank solution at the bare CPE and BBNBH/TN-CPE, respectively. Electrolyte: 0.1 mmol/L phosphate buffer solution (pH 8.0), scan rate: 10 mV/s.",
        "texts": [
            " The apparent charge transfer rate constant, ks, and the charge transfer coefficient, a, of a surfaceconfined redox couple can be evaluated from cyclic voltammetric experiments and by using the variation of anodic and cathodic peak potentials with logarithm of scan rate, according to the procedure of Laviron [14]. We found that the value for the anodic (aa) and cathodic (ac) transfer coefficients are 0.35 and 0.65 respectively and the value of ks is 13.0 0.6 s 1. The cyclic voltammetric responses from the electrochemical oxidation of 0.25 mM AA at the BBNBH/TN-CPE (curve f), BBNBH modified CPE (BBNBH-CPE) (curve e), TiO2 nanoparticles CPE (TN-CPE) (curve d), and unmodified CPE (curve b) shown in Fig. 1. As shown, the anodic peak potential for AA oxidation at the BBNBH/TNCPE (curve f) and BBNBH-CPE (curve e) was about 180 mV, while at the TNCPE (curve d), the peak potential was about 430 mV. At the unmodified CPE, the peak potential was about 510 mV of AA (curve b). From these results, it was concluded that the best electrocatalytic effect for AA oxidation was observed at the BBNBH/TN-CPE (curve f). For example, results show that the peak potential of AA oxidation at the BBNBH/TN-CPE (curve f) shifted by about 250 and 330 mV toward negative values when compared with that at the TNCPE (curve d) and unmodified carbon paste electrode (curve b), respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000267_t-pas.1977.32431-FigureI-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000267_t-pas.1977.32431-FigureI-1.png",
        "caption": "Figure I - Phasor diagram of rotating flux waves.",
        "texts": [
            " 2nfo , radiuslsecond magnitude of flux due to V I magnitude of flux due to V2 total magnitude of flux due to PI and P2 All quantities are per unit, unless otherwise stated. A rigorous analysis of motor performance for two frequency operation would require a numerical solution of general machine equations for currents, torque and speed. 5 However, a basic understanding of the alternating motor-generator operation is possible by analyzing the flux wave. For sinusoidalvoltages, flux equals voltage divided by frequency, if all quantitiesare per unit. With two voltages in series, the total flux would be the sum of two flux waves of different magnitude and frequency. Figure I shows these vectors rotating a t different angular velocity. Resolving them into components and combining terms, the magnitude and angle of the sum is: Here, V I and V 2and w1 and w2are the per unit voltage and angular frequency respectively, of the two sources in series with the motor. The base quantities are rated phase voltage and frequency so W1 will be one, and VI will be nearly one during test. Differentiating 6 with respect to time, and simplifying both expressions yields: These equations represent a flux wave that varies in magnitude and angular velocity as a function of time, supply voltages and frequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000415_chem.200901046-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000415_chem.200901046-Figure6-1.png",
        "caption": "Figure 6. Influence of two ILs on the conductivity of a 100 mmol L 1 phosphate buffer pH 8. For each IL an addition of 2, 4, 6, 8 and 10 vol % of IL were investigated and these results are grouped together (from left to right). The dashed line represents the conductivity of the pure bufferACHTUNGTRENNUNG(~16.2 mS cm 1).",
        "texts": [
            " However the half life reached was higher than for the [MDEGSO4] IL. For [MMIM] ACHTUNGTRENNUNG[MeSO4], [EMIM]ACHTUNGTRENNUNG[Et2PO4] and [MMIM] ACHTUNGTRENNUNG[Me2PO4] a contrary trend was observed; the stability increased with increased amount of IL. Generally, the enzyme was more stable in these ILs than in pure buffer. Since it was only possible to obtain a sufficient compromise for activity and stability with [EMIM] ACHTUNGTRENNUNG[Et2PO4] and [MMIM] ACHTUNGTRENNUNG[Me2PO4] conductivity measurements were carried out for these two ILs. Figure 6 summarises the findings. It can clearly be seen, that [MMIM] ACHTUNGTRENNUNG[Me2PO4] has a stronger influence on the conductivity. With addition of 10 vol% the conductivity was almost doubled. Therefore it was obvious that [MMIM] ACHTUNGTRENNUNG[Me2PO4] showed the best compromise in terms of enzyme performance and conductivity. Thus, batch electrolyses were carried out in presence of different amounts of this IL and compared with the results obtained in pure buffer solution (see Figure 7). In pure buffer the STY was approximately 18 gL 1 d 1 and the TOFFcCOOH for the ferrocene carboxylic acid was 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureA.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureA.2-1.png",
        "caption": "Fig. A.2 Schematic of the spinning cone",
        "texts": [
            " The analytical approach for the modelling of the action of the centrifugal forces generated by themass elements of the spinning cone is the same as represented for the spinning disc in Sect. 3.1, Chap. 3. The rotating mass elements of the spinning cone are located on the cone surface which maximal radius is the 2/3 radius of the base of the cone. The analysis of the acting inertial forces generated by the mass element of the cone is considered on the arbitrary planes that parallel to the plane of the base of 200 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects the cone (Fig. A.2) that is the same as the plane of the thin disc represented in Fig. 3.2 of Chap. 3. Similar resistance torques are generated by the mass elements located on the planes of the cone that parallel to the plane xoy. The resistance torque T ct produced by the centrifugal force of the mass element is expressed by the following equation: Tct = fct.z ym (A.2.1) where is f ct.z is the axial component of the centrifugal force; ym = (2/3)(2/3)R sin\u03b1 = (4/9)R sin\u03b1 is the distance of the location of the cone\u2019s plane of the centre mass and mass element along axis oz and relatively to axis ox",
            "2) where fct = mr sin \u03b1\u03c92 is the centrifugal force of the mass element m; m = (M/2\u03c0b) \u03b4 b,M is the mass of the cone; b = [(2/3)R]/sin\u03b2 is the line that forms the cone surface of the mass element\u2019s location, R and L is the radius and height of the cone, respectively, \u03b4 is the sector\u2019s angle of the mass element\u2019s location on the plane that parallel to the plane xoy; b = r/sin\u03b2 is the line part of the mass element\u2019s location, r is the radius of the arbitrary circle plane of the cone where the mass elements located; \u03c9 is the constant angular velocity of the cone; \u03b2 is the angle of the mass element\u2019s location on the cone forming line (Fig. A.2); \u03b3 is the angle of turn for the cone\u2019s plane around axis ox (sin \u03b3 = \u03b3 for the small values of the angle). Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 201 Substituting the defined parameters into Eq. (A.2.2) yields the following equation: fct.z = [ Mr\u03c92R sin \u03b2 sin \u03b1 2\u03c0(2/3)R sin \u03b2 ] r \u03b4 \u03b3 = 3M\u03c92 4\u03c0R \u03b4 \u03b3 r r sin \u03b1 (A.2.3) where all components are as specified above. Equation (A.2.3) contains variable parameters whose incremental components are independent and represented by different symbols",
            " Analysis of the inertial torques acting on the spinning cone demonstrates differences in the results compare with other spinning objects. 206 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects A.2.5 Working Example The cone has a mass of 1.0 kg; a radius of 0.1 m at about the spin axis and spinning at 3000 rpm. External torque acts on the cone, which rotates with an angular velocity of 0.05 rpm. It is determined by the value of the resistance and precession torques generated by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum of the spinning cone (Fig. A.2). The value of the resistance and precession torques acting on the spinning cone is defined by equations of Table A.2. Substituting the initial data into defined equations and transforming yield the following result: Tr = Tct + Tcr = 20 81 ( \u03c02 + 2 ) J\u03c9\u03c9x = 20 81 ( \u03c02 + 2 )3MR2 10 \u03c9\u03c9x = 20 81 ( \u03c02 + 2 )\u00d7 3.0 \u00d7 1.0 \u00d7 0.12 10 \u00d7 3000 \u00d7 2\u03c0 60 \u00d7 0.05 \u00d7 2\u03c0 60 = 0.0144627 Nm Tp = Tin + Tam = ( 20 81 \u03c02 + 1 ) J\u03c9\u03c9x = ( 20 81 \u03c02 + 1 ) 3MR2 10 \u03c9\u03c9x = ( 20 81 \u03c02 + 1 ) \u00d7 3.0 \u00d7 1.0 \u00d7 0.12 10 \u00d7 3000 \u00d7 2\u03c0 60 \u00d7 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002786_s12206-018-1216-3-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002786_s12206-018-1216-3-Figure23-1.png",
        "caption": "Fig. 23. Diagnosis results of the experiment signal 1: (a) Kurtgram; (b) ES of the signal corresponding to node (2, 2) in (a).",
        "texts": [
            " The experiment fault signal is processed by EEMD-ICA method. Table 6 presents the correlation coefficient of each IMF component of initial signal. The IMF1\u2013IMF6 components are used as the input parameter for ICA algorithm. Fig. 22 displays the diagnosis results. The ES of IC1 and IC2 shows that the ORFF fo and its doubling frequency 2fo- 4fo is more obvious, and the IRFF fi is relatively weak. That is to say, the IRFF fi is usually ignored. The experiment fault signal is processed by WPT-SK method. Fig. 23(a) displays that the node (2, 2) has the maximum kurtosis value. Fig. 23(b) illustrates the ES of the fre- quency band signal corresponding to node (2, 2). As seen, the ORFF fo and its doubling frequency 2fo - 4fo are identified productively whereas the IRFF fi cannot be extracted. The experiment fault signal is processed by E-Kurtogram method. Fig. 24(a) displays that the node (3, 3) has the maximum kurtosis value. Fig. 24(b) illustrates the ES of the frequency band signal corresponding to node (3, 3). As seen, the ORFF fo and its doubling frequency 2fo - 4fo are identified productively whereas the IRFF fi cannot be extracted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000972_978-3-642-22164-4_2-Figure2.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000972_978-3-642-22164-4_2-Figure2.7-1.png",
        "caption": "Fig. 2.7 5th order differentiation",
        "texts": [
            " Following is the 5th order differentiator: z\u03070 = v0,v0 =\u22128L1/6|z0 \u2212 f (t)|5/6sign(z0 \u2212 f (t))+ z1, z\u03071 = v1,v1 =\u22125L1/5|z1 \u2212 v0|4/5sign(z1 \u2212 v0)+ z2, z\u03072 = v2,v2 =\u22123L1/4|z2 \u2212 v1|4/5sign(z2 \u2212 v1)+ z3, z\u03073 = v3,v3 =\u22122L1/3|z3 \u2212 v2|4/5sign(z3 \u2212 v2)+ z4, z\u03074 = v4,v4 =\u22121L1/2|z4 \u2212 v3|4/5sign(z4 \u2212 v3)+ z5, z\u03075 =\u22121.1Lsign(z5 \u2212 v4); f (6) \u2264 L. It is applied with L = 1 for the differentiation of the function f (t) = sin 0.5t + cos0.5t, | f (6)| \u2264 L = 1. The initial values of the differentiator variables are taken zero. In practice it is reasonable to take the initial value of z0 equal to the current sampled value of f (t), significantly shortening the transient. Convergence of the differentiator is demonstrated in Fig. 2.7. The 5th derivative is not exact due to the software restrictions (insufficient number of valuable digits within the long double precision format). Higher order differentiation requires special software to be used. Differentiation with Variable Parameter L. Consider a differential equation y(4) + ... y + y\u0308+ y\u0307 = (cos0.5t + 0.5sint + 0.5)( ... y \u22122y\u0307+ y) with initial values y(0) = 55, y\u0307(0) =\u2212100, y\u0308(0) =\u221225, ... y (0) = 1000. The measured output is y(t), the parametric function L(t) = 3(y2 + y\u03072 + y\u03082 + "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure11.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure11.2-1.png",
        "caption": "Fig. 11.2 Joint i connecting bodies i and b(i) . Articulation point Pi with position vectors cii in basis ei and cb(i)i in basis eb(i) . Position vectors ri and rb(i) in basis e",
        "texts": [
            " , n the position vector ri , the velocity r\u0307i and the acceleration r\u0308i of 0i relative to the common reference basis e , the direction cosine matrix Ai defined by the equation e = Aie i , the angular velocity \u03c9i and the angular acceleration \u03c9\u0307i relative to basis e . For body 0 these six quantities are, by assumption, prescribed functions of time r0(t) , r\u03070(t) , r\u03080(t) , A0(t) , \u03c90(t) and \u03c9\u03070(t) . The solution to the problem is given in Sect. 11.2 . It is based on the kinematics of individual joints which is treated first. In Fig. 11.2 a single joint i of unspecified nature connecting two bodies i and b(i) is shown. The reference bases fixed on these bodies are ei and eb(i) , respectively. Let q i be the column matrix of joint variables qi1, . . . , qifi . The problem of joint kinematics is stated as follows. Determine as functions of the variables q i and of their time derivatives the following six quantities: The position vector cb(i)i , the velocity vi and the acceleration ai relative to eb(i) of a single point Pi fixed in ei , the direction cosine matrix Gi defined by the equation eb(i) = Gie i , the angular velocity \u03a9i and the angular acceleration \u03b5i of ei relative to eb(i) ",
            " , n the position vector ri , the velocity r\u0307i and the acceleration r\u0308i of 0i relative to the common reference basis e , the direction cosine matrix Ai defined by the equation e = Aie i , the angular velocity \u03c9i and the angular acceleration \u03c9\u0307i relative to basis e . Solutions are formulated in different forms for different purposes. For the purpose of minimizing computation time in numerical evaluations a 354 11 Direct Kinematics of Tree-Structured Systems set of recursive equations is developed. For applications in analytical investigations the solutions are expressed in explicit form. Figure 11.2 yields for the direction cosine matrix Ai , for the angular velocity \u03c9i and for the position vector ri the recursion formulas Ai = Ab(i)Gi , \u03c9i = \u03c9b(i) +\u03a9i , ri = rb(i) + cb(i)i \u2212 cii \u23ab\u23aa\u23ac \u23aa\u23ad (i = 1, . . . , n) . (11.10) Recursion formulas for \u03c9\u0307i , r\u0307i and r\u0308i are obtained by differentiating \u03c9i and ri with respect to time. According to Eq.(9.9) in which e1 and e2 are now identified with e and eb(i) , respectively, the results are \u03c9\u0307i = \u03c9\u0307b(i) + \u03b5i + \u03c9b(i) \u00d7\u03a9i , r\u0307i = r\u0307b(i) + vi + \u03c9b(i) \u00d7 cb(i)i \u2212 \u03c9i \u00d7 cii , r\u0308i = r\u0308b(i) + ai + \u03c9\u0307b(i) \u00d7 cb(i)i \u2212 \u03c9\u0307i \u00d7 cii + hi , hi = \u03c9b(i) \u00d7 (\u03c9b(i) \u00d7 cb(i)i)\u2212 \u03c9i \u00d7 (\u03c9i \u00d7 cii) + 2\u03c9b(i) \u00d7 vi \u23ab\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23ad (11",
            " Since the bodies are assumed rigid, it is impossible to determine the distribution of constraint forces. Only an equivalent force system can be determined which consists of a single force and a single torque. The torque depends upon the choice of the point at which the single force is thought to be acting. It is natural to choose for each joint i the articulation point located on body i . Let Xi and Yi be the constraint force and the constraint torque, respectively, thus defined for joint i . More precisely, +Xi and +Yi are acting on body b(i) , and \u2212Xi and \u2212Yi are acting on body i (see Fig. 11.2). In order to express whether a given constraint force is applied to a given body with positive or with negative sign or not at all numbers Sji are defined as follows: Sji = \u23a7\u23a8 \u23a9 \u22121 (j=i) +1 (j=b(i)) 0 (else) (j, i = 1, . . . , n) . (19.35) The first index refers to a body and the second to a joint. With this definition the resultant of all constraint forces and the resultant of all constraint torques applied to body j (arbitrary) are the sums (summation over all joints) n\u2211 i=1 SjiXi , n\u2211 i=1 Sji(cji \u00d7Xi +Yi) (j = 1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure5.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure5.8-1.png",
        "caption": "Fig. 5.8 Location of the gyroscope suspended from the flexible cord",
        "texts": [
            " \u2022 A similar value of the resulting reactive force acting on the support along with axis ox, where the gyroscope precession torque is the load torque acting around axis oy. Described gyroscope property of the action of the inertial torques should be taken into account for calculations of the gyroscopic forces and motions for different gyroscopicmechanisms and devices. The action of the inertial torques is manifesting only in the process of gyroscope motions and disappearing in case of the absent one. The gyroscope suspended from the flexible cord about point B represents the movable system with free motion on the horizontal plane xoz (Fig. 5.8). At the starting condition, the action of the gyroscope weight and the resistance inertial torques turn the gyroscope around axis ox and oy. The free horizontal location of the one side support of the suspended gyroscope is having several peculiarities. The resulting torques acting around axis oy are shifting the centre of gravity of the gyroscope about point B of the cord (Fig. 5.8). The location of the gyroscope relative to the centre axis of system oxyz is defined by the action of the gyroscope weight and the inertial torques. The resulting inertial torque acting around axis oy shifts the flexible cord and turns the gyroscope on the angle \u03b2 relative to its centre of gravity A. The end of the gyroscope shaft is shifted on distance b, and the end of the cord o is turned around point B of the suspension on the angle \u03d5. The angles \u03d5 and \u03b2 are restricted by balancing of the force F1 of the component of the resulting torque acting on the gyroscope around axis ox and by the component force of the gyroscope weight acting around axis oy",
            " The centrifugal force Fz generated by the rotating gyroscope centre mass around axis oy shifts the end of the gyroscope shaft o on the distance a, and the flexible cord d turns on the angle\u03c8 around point B of the suspension. The angle\u03c8 is restricted by balancing of the force F2 of the component of resulting torque and by the component force of the gyroscope weight acting around point B. The measurement of the small value of the resulting torques acting on the movable gyroscope suspended on the flexible cord is problematic (Fig. 5.8). The new location for the end o1 of gyroscope shaft is defined by the angles \u03b2, \u03d5 and \u03c8 and by the linear parameter a and b.All these parameters are calculated based on the values of the acting forces and the geometrical parameters of the gyroscope with one side free support. The value of the force F i is defined by the formula F1 = Ty/l, where l is the overhang of the gyroscope\u2019s centre of gravity from the free support o. The value of the force F2 is defined by the formula F2 = Ml\u03c92 y , M is the gyroscope mass, \u03c9y is the angular velocity of precession around axis oy, other components are as specified above. The angles \u03d5 and \u03c8 are defined by the following formula: sin \u03d5 = F1/Fm and sin \u03c8 = F2/Fm, (Fig. 5.8). The angle \u03b2 is calculated by the formula: sin \u03b2 = b/l, where b = d sin \u03d5 and d is the length of the flexible cord. The angle \u03c8 is calculated by the formula: sin \u03c8 = a/d. The new location of the end of the flexible cord o1 relative to the point B of the suspension is natural for the gyroscope with one side free support. The shifted location of the gyroscope relatively to point B does not have any influence on the formulation of the gyroscope motions. The gyroscope does not manifest the motions of a swinging pendulum",
            " The action of the precession and resistance torques represents the gyroscope as an overdamped or critically damped non-oscillating system. This statement is considered in Chap. 7. The forces acting on the gyroscope support (point o) are defined by the following scheme. The action of the force Fx, which is a component of the resulting inertial torques Ty acting around axis oy, shifts the end of the flexible cord o on the angle \u03b2 around the gyroscope centre of gravity A on the horizontal plane xoz and on the angle \u03d5 around point B of the suspension (Fig. 5.8). The reactive force Fm and the gyroscopeweightW produce the forceF1 that counteracts to the action of the reactive force FX (Eq. 5.55, Sect. 5.3.1). The balance of the action of two forces (F1 = Fx and F2 = Fz) enables the angular location \u03d5 and \u03c8 about the vertical of the gyroscope to be defined by the following solution: sin \u03d5 = F1 Fm = 2.589667650 \u00d7 10\u22125 0.146 \u00d7 9.81 = 1.808098843 \u00d7 10\u22125 that giving rise to the following \u03d5 = 0.00103\u25e6 (5.56) The angle \u03d5 enables for defining the angle \u03b2 by the following expressions: sin \u03d5 = b d , sin \u03b2 = b l (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000480_j.ijnonlinmec.2010.12.010-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000480_j.ijnonlinmec.2010.12.010-Figure2-1.png",
        "caption": "Fig. 2. The treadmilling swimmer problem [14]: a circular swimmer, of radius r, translating with complex speed Uu and rotating with angular velocity Ou near a no-slip wall actuated by a surface treadmilling action but experiencing no net force or torque. There is a distinguished diameter making an angle y to the wall direction.",
        "texts": [
            " WhenO\u00bc 0 and U \u00bc U so the motion is away from the wall then Fd \u00bc U 2\u00f01 r2\u00de=\u00f01\u00fer2\u00de\u00fe logr2 : \u00f051\u00de Hence the force on the cylinder is Fx\u00fe iFy \u00bc 8pmFd \u00bc 4pmU \u00f01 r2\u00de=\u00f01\u00fer2\u00de\u00fe logr \u00f052\u00de or, on making use of the relationships betweenr, a and d found earlier, Fx\u00fe iFy \u00bc 4pmU log\u00f01=r\u00de \u00f01 r2\u00de=\u00f01\u00fer2\u00de \u00bc 4pmU log\u00f0\u00f0d\u00fea\u00de=r\u00de \u00f0a=d\u00de , \u00f053\u00de which is purely imaginary (the force is perpendicular to the wall) and is again in agreement with [14]. We now describe the same treadmilling swimmer studied by Crowdy and Or [9]. Assume a circular swimmer centred at zd \u00bc x\u00fe id has radius r and is positioned in the fluid region above a no-slip wall. It is rotating with angular velocityOu and travelling with velocity \u00f0U u,Vu\u00de where these velocities are to be determined by the conditions that the swimmer is force-free and torque-free. Fig. 2 shows a schematic. On its surface a tangential velocity having magnitude 2V sin\u00f02\u00f0f y\u00de\u00de is imposed where V is a characteristic velocity which sets the timescale of the motion while y is a distinguished angle. Physically, the angle y might correspond to the direction of the swimmer\u2019s head, for example. The angle f is the angular position around the circular boundary measured from the direction of the positive real axis. In standard index notation the fluid velocity on the swimmer surface is Uui\u00feeimnXum\u00f0xn xdn\u00de\u00feUsi, \u00f054\u00de where Uui are components of the swimmer\u2019s rigid body displacement velocity, i",
            " (86) can be used to check if the simple model system (92) gives good qualitative agreement with the actual swimmer dynamics near a wall when ra0. This is found to be the case. Fig. 3 shows the integral curves of y against y for the system (86) when r\u00bc0.2. Note that it is enough to plot results for y in the range p=2ryrp=2 because the system (86) only depends on the quantity 2y. Fig. 3 is qualitatively similar to Fig. 4 of Crowdy and Or [9] where the integral curves of the approximate model are plotted. It also closely resembles a similar phase diagram featured in Fig. 2(b) of Or and Murray [22] obtained by using the Swan\u2013Brady mobility tensors to compute the dynamics of model swimmers comprising systems of rotating spheres attached together by rods (see also Fig. 2(a) of the experimental paper by Zhang et al. [37]). Note, however, that unlike the swimmers considered here those analyzed in [37] can undergo a displacement even in the absence of a wall. The model of [9] also gives reasonably good quantitative agreement with the unapproximated dynamics found here. It is clear from (86) that if we make the choice y\u00bc p=4 then dy=dt\u00bc 0 which implies that y, and hence r, is constant. The choice r2 \u00bc 1=3 means that dy=dt \u00bc 0 so y, and hence c, are also constant. The swimmer then travels at a constant distance from the wall given by y\u00bc r 2r \u00f01\u00fer2\u00de \u00bc 2rffiffiffi 3 p 1:155r \u00f096\u00de and at constant horizontal speed given by dx dt \u00bc 4 3 ffiffiffi 3 p r 0:770 r , \u00f097\u00de where we have taken Vr\u00bc1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000221_s0006-3495(83)84406-3-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000221_s0006-3495(83)84406-3-Figure7-1.png",
        "caption": "FIGURE 7 Twist due to an external force and an asymmetric bending resistance. A filament is bent by the action of an external force (left panel, arrows) so that the tangent at the distal end is normal to the fixed Z-axis. The external force applied at the distal end is at all times normal to the tangent. Bending resistances of the thin and thick axes were 25 and 100 pN ,um2, respectively, and twisting resistance was 54 pN giM2. The direction and relative magnitude of normal force which caused the distal end tangent to be 00, 450, and 900 from the fixed Y-axis and normal to the Z-axis are shown as arrows. At 00 and 900 the external force is in the negative Z direction. It takes four times the force to bend the filament along the thick axis and there is no twist. At 450 the external force is not in the Z direction and the twist is 280. The right-hand panel shows total twist at the distal end as a function of the angle of the distal end-tangent from the Y-axis for thick axis bending resistances of 50, 100, and 200 pN gm2. The 200 pN gim2 filament displays very complex behavior at large angles and only the linear portion is plotted. The dotted line is for thick axis bending and twisting resistances of 100 pN gM2 each.",
        "texts": [
            " At the kth iterative step the linear variation of each nonlinear term, say Wj, with respect to the variable x, is computed numerically as W(xk) = W(xk ') + [W(xk + h) - W(xk -)] (xk xk ')/h (44) where h is a small number. The resulting linear equations are solved by Gaussian elimination. The iterations are performed until the difference between the values of the sum of the variable differences between the kth and k - 1th iterations is <10-4. Effect of Asymmetrical Bend Resistance on Twist In the absence of internal shear forces, twisting may arise if an external force that is not along either the thick or the thin axis of the central pair is applied to an initially straight flagellum. Fig. 7 (left panel) illustrates this for a normal force applied at the distal end to bend the flagellum by 900. The amount of twist depends on the plane of the bend relative to the central pair, the magnitude of the twist resistance, and the ratio of the thick and thin axis bending resistances. As shown in the right-hand panel, the amount of twist is small even for a thick-to-thin axis bendresistance ratio of 2, i.e., 50 vs. 25 pN Aim2. For a real flagellum the ratio between thick and thin axis bending resistances is close to unity (see section III) so that application of an external force in the absence of shear resistance would not cause appreciable twist"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001366_1.4745081-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001366_1.4745081-Figure13-1.png",
        "caption": "FIG. 13. Newly developed zoom-optics for adaptive LMD, manual version (left) and automatic, NC controlled version (right) (Fraunhofer ILT & LLT, RWTH Aachen University & reis Lasertec).",
        "texts": [
            " In the specific case of the additive BLISK manufacture, an average deposition rate of 2450 mm3/min for a near-net shape build-up of a single blade mock-up could be realized that results in an overall powder consumption of 4.31 kg for all 76 blades. This means an increase in the deposition rate by a factor of approximately 12\u201313 compared with the reference. The average deposition rate cannot be higher due to the ambivalent objective of an accurate near-net-shape build-up with a constant oversize of less than 1 mm for the final machining. In turn, this requirement necessitates the use of a newly developed zoom-optic (Fig. 13) which guarantees a part adapted constant oversize due to an numerical control (NC) controlled manipulation of the melt pool width via the laser beam diameter on the work piece surface. The corresponding processing parameters such as the laser power (to keep, e.g., the intensity constant), the velocity, and the powder mass flow are automatically adapted by the NC control, accordingly. Laser additive manufacturing with its two processes LMD and SLM and other\u2014subtractive\u2014laser material processing techniques such as in-volume selective laser etching that is used for in-volume structuring of transparent dielectrics offer unique opportunities to overcome the traditional technological obsolescence of the ambivalence between \u2022 the value-/planning-orientation on the one hand and \u2022 the scale/scope dilemma on the other hand"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003214_j.measurement.2020.107897-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003214_j.measurement.2020.107897-Figure3-1.png",
        "caption": "Fig. 3. Resulted propagating distances between the fault meshing position and sensor: (a) Closest position; (b) Farthest position; (c) Possible position 1; (d) Possible position 2.",
        "texts": [
            " 2, the transfer path 2 (yellow dashed line) and transfer path 3 (blue dashed line) do not time-varying [16, 27]; therefore, the attenuation effects through these two transfer paths can be identically deemed for all the meshing positions. The attenuation effect of the remaining transfer path 1 (black dashed line), which relies on the positions of fault-meshing, should be mainly focused. Some possible fault-meshing positions (solid dot) and their corresponded propagating distances through transfer path 1 to the fixed sensor are shown in Fig. 3. The fault-meshing positions, as were displayed in Fig. 3 (a) and (d), exhibits the sun gear\u2019s faulty tooth meshing with a planet gear that is located closest and farthest in line to the sensor, respectively. Fig. 3 (b) and (c) are two possible fault-meshing positions, neither farthest nor closest. We use d t\u00f0 \u00de to represent the distance between the fault-meshing positions and the fixed sensor. Relative to different fault-meshing positions in Fig. 3, d t\u00f0 \u00de can be represented in Fig. 4. Postulating that each time the fault meshing will generate the same original amplitude, then the fault-induced vibration will transmit through a length of d t\u00f0 \u00de to the sensor. The measured fault amplitude, therefore, should be the product after attenuation effect through d t\u00f0 \u00de: Asun t\u00f0 \u00de \u00bc Ase nd t\u00f0 \u00de v ; \u00f02:1\u00de where Asun t\u00f0 \u00de is the measured fault-induced amplitude, As is the original fault-induced amplitude, v is the transmission speed of the vibration, and n represents the attenuation coefficient which depends on the material characteristic of the system; d t\u00f0 \u00de v means the attenuate time duration to the sensor. For a tested planetary gear system, n is constant; meanwhile, v is also constant. Eq. (2.1) reveals that Asun t\u00f0 \u00de only depends on the value of d t\u00f0 \u00de. In such a scenario, Asun t\u00f0 \u00de will reach a maximum or minimum corresponding to the positions in Fig. 3 (a) and (d). The amplitudes should fall between these two extreme values for other possible fault meshing positions, such as in Fig. 3 (b) and (c). These time-varying captured amplitudes of fault induced vibrations, characterizing modulation effects to the perceived signals, are valuable fault-related features. Though it is difficult to exactly determine every fault meshing position, these fault meshing positions should follow a certain pattern and repeat thereafter. As a result, d t\u00f0 \u00de and Asun t\u00f0 \u00de will also follow this certain pattern. Consequently, the motion pattern of the fault meshing position should be revealed as the prior knowledge so that the fault characterization could be further revealed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure2-1.png",
        "caption": "Fig. 2. Parabolic curve at the first quadrant.",
        "texts": [
            " (21) yields 1\u00fe i\u00f0 \u00dex0 \u03b8\u00f0 \u00dex\u20320 \u03b8\u00f0 \u00de \u00fe a\u00fe 1\u00fe i\u00f0 \u00dey0 \u03b8\u00f0 \u00de\u00bd y\u20320 \u03b8\u00f0 \u00de \u00bc 0: \u00f022\u00de Similarly, the sliding velocity of the contact point on the tooth profile of the driven gear can be expressed as V r2 \u00bc dr2 d\u03b8 \u22c5d\u03b8 dt : \u00f023\u00de Using the same method, the condition of undercutting of the tooth profile of the driven gear can be derived as 1\u00fe i\u00f0 \u00dex0 \u03b8\u00f0 \u00dex\u20320 \u03b8\u00f0 \u00de \u00fe y0 \u03b8\u00f0 \u00de \u00fe i y0 \u03b8\u00f0 \u00de\u2212a\u00bd f gy\u20320 \u03b8\u00f0 \u00de \u00bc 0: \u00f024\u00de Firstly, we look at a parabola which is assumed to act as the line of action in the first quadrant. As shown in Fig. 2, supposing that the vertex of the parabola is located at (0,0) and its focus F at (0, p1/2), the equation of the parabolic curve in the first quadrant can be described as x0 \u00bc 2p1t y0 \u00bc 2p1t 2 p1 > 0; t\u22650 \u00f025\u00de t is a parameter of the parabolic curve. where Assuming that \u03b1 denotes the angle between x0-axis and the line that connects the point O0 and a point M on the parabolic curve, Eq. (25) can be rewritten as x0 \u00bc 2p1cot\u03b1 y0 \u00bc 2p1 cot\u03b1\u00f0 \u00de2 0b\u03b1 b \u03c0 2 : \u00f026\u00de When \u03b1 = 0, the following relationship exists: x0 \u00bc 0 y0 \u00bc 0 : \u00f027\u00de Supposing that the parameter r\u2032 is a non-dimensional parameter, which can be described as r\u2032 \u00bc p1 2 \u00bc k1r2, the following equation exists: k1 \u00bc p1 2r2 \u00f028\u00de k1 is the ratio of r\u2032 to r2, r2 is the radius of the pitch circle of the driven gear. Hence, k1 can be interpreted as the ratio of the where size (or shape) of the parabola used against the size of the driven gear. According to the geometry of the triangle O0MF in Fig. 2, we have O0M sin\u03b8\u00bcMF sin \u03c0 2\u2212\u03b1\u00f0 \u00de \u00f029\u00de O0M represents the distance between point M on the parabola and the center point O0;MF denotes the distance between where point M on the parabola and the focus of the parabola F. According to the characteristic of the parabola, O0M and MF can be expressed respectively as follows. O0M \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x20 \u00fe y20 q \u00f030\u00de MF \u00bc y0 \u00fe p1 2 \u00f031\u00de (x0, y0) denotes the coordinate values of point M in the coordinate system \u03a30 (O0, x0, y0)",
            " (iii) Parameters k1 and k2 affect the shape of the parabola and the tooth profile, the shape of the tooth profile can therefore be controlled by choosing the values of k1 and k2 based on the gear meshing theory. Substituting Eq. (33) into Eq. (24), the critical condition of the undercutting of the tooth profile of the driven gear can be given as \u03b8 \u00bc sin\u22121 2ai\u22122p1\u22122p1i 2ai\u2212p1\u2212p1i : \u00f046\u00de Substituting Eq. (28) into Eq. (46), yields \u03b8 \u00bc sin\u22121 1\u22122k1 1\u2212k1 : \u00f047\u00de According to the gear meshing theory, the contact ratio should be greater than 1 in a gear drive for smooth transmission. When the contact point is located in the first quadrant as shown in Fig. 2, the angle \u03b2 should be greater than the angle corresponding to a quarter of a tooth of the driven gear. The range of the angle \u03b2 can be expressed as 0b \u03c0 2z2 b\u03b2\u2264\u03b8b\u03c0: \u00f048\u00de According to Fig. 2, the following equations can be obtained. MF sin\u03b2\u00bcO2M sin \u03c0\u2212\u03b8\u00f0 \u00de \u00f049\u00de O2M \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x20 \u00fe y0\u2212r2\u00f0 \u00de2 q : \u00f050\u00de Substituting Eqs. (31), (33) and (50) into Eq. (49) yields \u03b2 \u00bc sin\u22121 1\u22122k1\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k1 1\u2212k1\u00f0 \u00dep 2k1 1\u2212k1\u00f0 \u00de : \u00f051\u00de Substituting Eq. (51) into Eq. (48), the range of the parameter k1 without undercutting and interference can be yield. sin \u03c0 2z2 b 1\u22122k1\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k1 1\u2212k1\u00f0 \u00dep 2k1 1\u2212k1\u00f0 \u00de \u22641\u22122k1 1\u2212k1 : \u00f052\u00de Similarly, substituting Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001827_1350650116649889-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001827_1350650116649889-Figure2-1.png",
        "caption": "Figure 2. TRB geometry with loading and displacements.",
        "texts": [
            " The other geometric parameters of the TRBs were selected from the standard bearing. TRB dynamic model with roller diameter error Several authors25,26 outlined a quasi-static bearing model. Tong and Hong15 developed a model for calculating time-varying stiffness of TRBs having out-ofroundness inner and outer races. The accuracy of their TRB model was confirmed by experimental measurements and a commercial code. This study adopted the same analytical approach for TRB equilibrium as that used in Tong and Hong,15 but modified it to include the error in roller diameter. Figure 2 shows a general 5-DOF bearing model in the global coordinate system, including external loads and displacements. A global Cartesian coordinate system Oxyz was chosen whose origin point was fixed at the inner ring center. The outer race was assumed to be stationary, while the inner race could freely rotate around the bearing axis. The external load vector of the inner ring was assumed to be unchanged, and given by Ff gT \u00bc Fx,Fy,Fz,Mx,My \u00f02\u00de Even though the external load Ff g was a timeindependent vector, the inner ring displacements varied with time because of the error in roller diameter and the varied number of rollers under load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002991_s0263574719001620-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002991_s0263574719001620-Figure2-1.png",
        "caption": "Fig. 2. Representation of submechanism m1.",
        "texts": [],
        "surrounding_texts": [
            "Moreover, fuzzy SMC has used the dubious neuron and neural network for solving the optimization problems. Thus the proposed model has attained the optimal point that converges fast with the adopted control strategy.\nIn 2015, Fang et al.5 controlled the single-phase active power filter (APF) using the model reference adaptive sliding mode (MRASMC) based on neural network and radial basis function (RBF). The symphonic current in APF system was removed by combing the adaptive control technique with the neural network. This model has attained the asymptotic stability of the system by tuning the weight of the neural network online. Finally, the proposed model has provided better performance by enhancing the performance of DC side voltage in the case of tracking.\nWith the best performance in the thermal regulation of the quick thermal processing (RTP) system, the SMC can control the uncertainties of the system. In 2016, Xiao et al.6 used the assertive modes to design the RTP system by SMC. Here, the parabolic partial differential equation was used to formulate the temperature dynamics of the system. Further, the dominant modes of the system were extracted by the eigenfunctions, which in turn have determined the assertive dynamics of the system. Subsequently, Galerkin\u2019s method was adopted to frame the diminished model of the dominant modes. Later, the compensation of the nonlinear uncertainty of SMC was achieved by the nonlinear finitedimensional reduced model.\nIn 2016, Zhang et al.7 used the mismatched and matched disturbances to search the disturbance rejection control problem for Markovian jump linear systems (MJLSs). Concurrently, current state and the disturbances were authorized by the continuous and discontinuous extended SMC. Hence the existing disturbances were effectively denied by the design of composite controllers.\n1.1.2. Review. The methods such as composite controllers and probabilistic models fall off in computational efficiency and capricious problem domains. Thus, methods based on intelligent schemes include fuzzy sets and neural networks, that provide good performance for SMC on the robotic system,1 process control millng head reference,37 etc. is attained by the neural network, on comparing diverse, intelligent controllers. In fact, the primary benefit of the neural network is learning with the lack of prior knowledge, integrity and achievable for real-time systems. However, it suffers from some issues such as reduced probability of adapting precise weight functions, regularization problem, and model gap between the problem space and characteristics of the system. Moreover, those problems are highly proportional to each other. The learning knowledge of the network is enhanced by adapting the weight functions. Since the accessible updating model in ref. [1] was a function of derivation, it cannot be improved substantially. As a result, it generates the incremented margin among the actual data of the system and function of the sliding mode, the third problem as described earlier. Therefore, the margin can be reduced by the weight functions and leads to accurate prediction. However, the problem of overfitting requires a suitable regularization function. Thus the improvement is mainly needed for contributions to the conventional neural networks for facilitating the sliding mode function and tuning of design variables.1 However, the reported literature does not show the contributions on precise selection of such design variables. In addition, the neural network-based SMC still needs additional improvements in terms of current system models, though it outperforms the SMC.\nThe locomotion pattern of inchworm robot is constructed per Fig. 1, to derive the dynamic relations. This pattern comprises a sequence of connected joints that take the forward locomotion. According to the locomotion of the robot, the distance crossed by the robot per complete cycle can be determined using Eq. (1), where \u03c8 indicates the gait angle of the robot and L indicates the length of the arm. The architecture model is illustrated in Fig. 4.\nD = 2L (1 \u2212 cos\u03c8) (1)\nSubsequently, the categorized submechanisms associated with the motion pattern are denoted as m1,m2,m3, and m4, where the representations of m1 and m2 are shown in Figs. 2 and 3, respectively. One or more links remain static in the submechanism (which are marked in blue color in Fig. 1)\nhttps://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574719001620 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 18 Nov 2019 at 20:24:57, subject to the Cambridge Core terms of use, available at",
            "due to sufficient friction acting on the links. The remaining submechanisms such as m3 and m4 are defined based on contrary trajectory orientation. A local coordinate system is used to map the angles associated with these models. As the entire submechanisms are solved, the angles are transformed into a global coordinate system.\nEq. (2) depicts the geometries\u2019 constraint of the system, where \u03d5m represents the angle of the mth link due to the positive direction of the horizontal axes \u03c6m = \u03c6m\u22121 + \u03b8m, n refers to the number of joints and \u03b8m indicates the joint angles, respectively.\nn\u2211 m=1 sin \u03d5m = 0 (2)\nhttps://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574719001620 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 18 Nov 2019 at 20:24:57, subject to the Cambridge Core terms of use, available at",
            "This section obtains the dynamic equation of the submechanism m1. The manipulator is considered to act in the vertical plane x \u2212 y as shown in Figs. 2 and 3. The velocity and position of the origin of the mth link are denoted as Vi and Pi. According to ref. [1], the velocity centroid of the ith link is represented in Eq. (3), and its square is represented in Eq. (4), where, \u03c6\u0307i denotes the derivative form of \u03c6i and Lm indicates the length of the mth link; definitions of Cmn and Smn are given in Eq. (5a) and (b).\nV\u0302i = Vi + Li 2 \u03c6\u0307i (\u2212 sin \u03c6im\u0302 + cos \u03c6in\u0302 ) (3)\nV\u03022 i = L2 p\n4 \u03c6\u03072\ni + i\u2211\nm=1 i\u22121\u2211 n=1 LmLn\u03c6\u0307m\u03c6\u0307nCmn (4)\nCmn = cos (\u03c6m \u2212 \u03c6n) (5a)\nSmn = sin (\u03c6m \u2212 \u03c6n) (5b)\nMoreover, Eq. (6) depicts the height of the ith link.\nH\u0302i = Pi+1.n\u0302 \u2212 1\n2 Li sin \u03c6i = i\u2211 n=1 (Ln sin \u03c6n)\u2212 Li 2 sin \u03c6i (6)\nThe total kinetic energy is expressed in Eq. (7) followed by Eq. (8), where Ii specifies the moment of inertia and mi indicates the mass of the ith link, respectively.\nKe = 1\n2 3\u2211 i=1 ( miV\u0302 2 i + Ii\u03c6 2 i ) (7)\nKe = 1\n24 mL2\n( 28\u03c6\u03072\n1 + 16\u03c6\u03072 2 + 4\u03c6\u03072 3 + 36\u03c6\u03071\u03c6\u03072c12 + 12\u03c6\u03072\u03c6\u03073c23 + 12\u03c6\u03073\u03c6\u03071c31 )\n(8)\nIn addition, Eq. (9) provides the total gravitational potential energy.\nGe = 3\u2211\ni=1\nmigH\u0302i (9)\nGe = 1\n2 mgL (5 sin \u03c61 + 3 sin \u03c62 + sin \u03c61) (10)\nAs per the model of Coulomb friction, Eq. (13) defines the virtual works associated with the applications of entire non-consecutive forces in the system. Here, \u03c4\u0307 indicates the joint torques applied to the link, Ri indicates the non-consecutive forces, and Ff specifies the frictional forces exerted on the edge of the link. Moreover, \u03c7i = Li ( cos \u03c6i + \u03bc\u0302 sin \u03c6i ) , \u03bc\u0302=\u03bcsgn (et.\u03bdt), and \u03c1 denotes the Kronecker delta factor.\n\u2202w = \u03c4\u0307 .\u2202\u03b8 + ( Ff m\u0302 + Mn\u0302 ) .\u2202Pi+1 (11)\n\u2202w = 3\u2211\ni=1\n\u03c4\u0307i\u03c1 (\u03c6i \u2212 \u03c6i\u22121)+ M ( \u03bc\u0302\n3\u2211 i=1 Li sin \u03c6i\u03c1\u03c6i + 3\u2211 i=1 Li cos \u03c6i\u03c1\u03c6i\n) (12)\n\u2202w = 3\u2211\ni=1\n(\u03c4\u0307i \u2212 \u03c4\u0307i\u22121 + \u03c7iM) \u03c1\u03c6i = 3\u2211\ni=1\nRi\u03c1\u03c6i (13)\nThe relationship of the Euler and Lagrange contributes the equation of motion that is represented in Eq. (14).\nRj = d\ndt\n( \u2202Ke\n\u2202\u03c6\u0307j\n) \u2212 \u2202Ke\n\u2202\u03c6j + \u2202Ge \u2202\u03c6\u0307j (14)\nhttps://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574719001620 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 18 Nov 2019 at 20:24:57, subject to the Cambridge Core terms of use, available at"
        ]
    },
    {
        "image_filename": "designv10_12_0001948_1.4040324-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001948_1.4040324-Figure1-1.png",
        "caption": "Fig. 1 Experimental apparatus developed for l-PTAPD process (a) schematic view and (b) photograph",
        "texts": [
            " Therefore, objectives of the present work are: (i) identifying feasible values of six most important process parameters of l-PTAPD process (l-plasma power, flow rate of powder, travel speed of the deposition head, shielding gas flow rate, plasma gas flow rate and stand-off distance) for single-layer deposition of Ti\u20136Al\u20134V through pilot experiments; (ii) study of deposition characteristics and energy consumption aspects using 27 main experiments to identify optimum values of the l-plasma power, flow rate of powder and travel speed of the developed powder deposition head for multilayer deposition of Ti\u20136Al\u20134V; and (iii) study of the multilayer deposition characteristics (i.e., total wall width (TWW), effective wall width (EWW), deposition efficiency and surface straightness), microstructure, lamellae widths, tensile properties (i.e., yield strength, ultimate strength and strain), fractography of tensile specimen, wear characteristics (i.e., wear volume and coefficient of sliding friction), wear mechanism, and microhardness of Ti\u20136Al\u20134V in continuous and dwell-time mode multilayer deposition. 2.1 Development of the Experimental Apparatus. Figure 1 depicts schematic diagram (Fig. 1(a)) and photograph (Fig. 1(b)) of the l-PTAPD experimental apparatus. It was developed by integrating (i) 440 W capacity of power supply system; (ii) lplasma torch; (iii) powder feeding system; (iv) deposition head; and (v) three-axis Arduino based controller. The power supply system had a provision to vary current from 0.1 to 20 A with an increment of 0.1 A. The powder feeding system was designed and developed to ensure an uninterrupted supply of the powder deposition material for particle size in a range from 20 to 200 lm from the hopper to the deposition head by means of the pressurized carrier gas (argon) supplied at a constant flow rate of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003449_tmag.2020.3022844-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003449_tmag.2020.3022844-Figure11-1.png",
        "caption": "Fig. 11. Stator tooth shape of the proposed model",
        "texts": [
            " The target function was selected to reduce the electromagnetic vibration by more than 10%, torque by more than 3.3N\u2219m, and torque ripple by less than 6.5%. A graph of the total value of vibration velocity is shown in Fig. 9, and a graph of the torque and torque ripple were shown in Fig. 10. Each model refers to the model in Table 4, and the 0th model in Figs. 9 and 10 refers to the conventional model. Model3 was selected as the proposed model satisfying the target specifications, and the shape of Model3 is shown in Fig. 11. As can be seen from Table 4, in the conventional model, all variables are equal to 0 mm, and the proposed model has a shape in which LB has a value of 0.9 mm and all the other variables are equal to 0 mm. The performances of the target functions of the conventional and proposed models are compared in Table 5. AND PROPOSED MODEL Model Vibration velocity [mm/s] Torque [N\u2219m] Torque ripple [%] Conventional model 0.0587 3.50 7.79 Proposed model 0.0516 3.34 6.11 In the proposed model, the torque decreased by 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000418_1.2742383-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000418_1.2742383-Figure2-1.png",
        "caption": "FIG. 2. Geometry of the static shear deformation investigated in the text. The bulk volume element of the nematic SCLSCE is oriented such that n\u03020 x\u0302. The shear is applied within the x-z plane as indicated by the arrows.",
        "texts": [
            " As already discussed in the Introduction relative rotations play a role of major importance in a continuum model of SCLSCEs see, e.g., Ref. 16 . Up to now various unique effects of SCLSCEs have been characterized in a linear macroscopic description that directly result from relative rotations and cannot be explained without these.9\u201311,16\u201318 In this section we want to demonstrate that also qualitatively different nonlinear effects have to be attributed solely to relative rotations. For this purpose we investigate the case of a nematic SCLSCE under a static shear deformation. The geometry we have in mind is depicted in Fig. 2. In the ground state the nematic elastomer is oriented such that the mesogenic units are aligned on average parallel to the x\u0302 axis. Thus the director in its ground state conformation reads n\u03020 = 1,0,0 . 19 This conformation is spatially homogeneous and we do not have to explicitly account for an a r dependence of n\u03020 according to Eq. 1 , which simplifies the problem. In order to This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation",
            " On the one hand these are the explicitly nonlinear cubic terms in Eq. 21 . On the other hand, the quadratic terms contain nonlinear contributions because the nonlinear expression for and the new nonlinear expression for \u0303 derived in the preceding section must be inserted in these terms. That is the reason why the material parameters c1, D1, and D2 will significantly contribute to the nonlinear results listed later on. We now want to analyze the consequences of a shear deformation of the bulk of the nematic SCLSCE, as indicated in Fig. 2. Denoting the shear amplitude by A0 and looking only for homogeneous solutions due to the reasons elucidated above we make the Ans\u00e4tze This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 134.124.28.17 On: Tue, 11 Aug 2015 09:10:19 ux r = A0z + A1x , 22 uy r = B1y , 23 uz r = C1z , 24 ny r = ny , 25 nz r = nz. 26 If we assume the system to be incompressible, which is a good approximation for the elastomers under investigation, we obtain B1 = A1C1 \u2212 A1 \u2212 C1 1 + A1C1 \u2212 A1 \u2212 C1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure2-1.png",
        "caption": "Fig. 2. Geometrical relation in the axial section of grinding wheel.",
        "texts": [
            " Based on the theory, the effects of the technological parameters on the meshing behavior of a DTT worm set are also studied in detail by means of a computerized simulation approach. The theoretical researches reported in this study will lay a foundation for designing and manufacturing this new type of hourglass worm set. Of course, the basic theory developed herein is easy to be extended to other types of the hourglass worm pair. The generation process of a DTT worm helicoid is usually called the first enveloping. The coordinate system (Oa; x, y) lies in an axial section of a grinding wheel as shown in Fig. 2. Axis x lies in the mid-plane and axis y is along the axial cord. The axial section of the grindingwheel intersects its generating torus along the arc working profile AB. The coordinates of point A are xA= rd and yA=sa/2. Meanwhile, considering the relative position of the grinding wheel and the worm rough after installing on the machine tool, the abscissa of point B is xB=rd\u2212hf\u2212r2(1\u2212cos\u03c80). In Fig. 2, point O(p, q) is the center of the arc working profile AB and point C is the middle point of chord AB. Based on the geometric relation, the equations of straight lines BO and CO can be represented as x\u2212ytan\u03b1d\u2212xB + yBtan\u03b1d = 0;8 rd\u2212xB\u00f0 \u00dex\u22124 2yB\u2212sa\u00f0 \u00dey\u2212s2a + 4x2 B + 4y2 B\u22124r 2d = 0; \u00f01\u00de yB is the ordinate of point B. where By solving linear Eq. (1) in unknowns (x,y), the coordinates of point O can be expressed in the form of p and q as p = s2atan\u03b1d + P1sa + P2 4 sa\u22122xBtan\u03b1d\u22122yB + 2rdtan\u03b1d\u00f0 \u00de ;q = s2a + Q 4 sa\u22122xBtan\u03b1d\u22122yB + 2rdtan\u03b1d\u00f0 \u00de \u00f02\u00de P1=4(xB\u2212yB tan \u03b1d), P2=\u22124xB2 tan \u03b1d+4yB2 tan \u03b1d\u22128xByB+4rd2 tan \u03b1d, Q=4xB2\u22124yB2\u22128xByB tan \u03b1d\u22128rdxB+8rdyB where tan \u03b1d+4 rd 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002226_tie.2017.2714148-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002226_tie.2017.2714148-Figure1-1.png",
        "caption": "Fig. 1. Virtual Simulated MAV System.",
        "texts": [
            " In view of (47), we can see that if \u03b5l \u2192 0 and \u03b5a \u2192 0, then the bounds of the states S under output feedback based design (30)-(33) can converge to the bounds achieved with state feedback based design (14)-(19). Now, using similar analysis, we can also simplify V\u0307 for the smooth input (34) to (36) as V\u0307 \u2264 \u2212\u03bbmin(k)\u2016S\u20162 2 + k\u03b5\u03b5. This implies that the output feedback based design (34)-(36) can also recover the performance achieve with algorithm (14), (16), (24)-(25) as \u03b5l \u2192 0 and \u03b5a \u2192 0. Let us now evaluate the proposed design on a miniature unmanned quadrotor aerial vehicle as shown in Fig. 1. The proposed state and output feedback design is tested on Hardware in the loop simulation on virtual environment created by ROS and Gazebo simulator [25], [26]. Due to page constraint, we present the results with output feedback method. In hardware in the loop simulation, the controller embedded with on board PX4 autopilot that connected to the simulator. The proposed algorithm runs on the on board autopilot. For real-time application, the proposed hardware in the loop simulation method has the benefit of testing in actual flight code on the real processor for real-time experiment in straight forward manner"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003379_j.ijmecsci.2020.105709-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003379_j.ijmecsci.2020.105709-Figure9-1.png",
        "caption": "Fig. 9. Different actuation schemes which are respectively (a) Situation A by three linear actuators and (b) Situation B by three rotational actuators.",
        "texts": [
            " (43) F p \ud835\udf53 T c s p S d o a p S t c r a t k n 4 a S \ud835\udefc w t q t w i t a \ud835\udc1d w b \ud835\udc02 old angles of hinges 2, 3, and 4 of the two configurations can be comuted using Eq. (4) and respectively are 0 = \u23a1 \u23a2 \u23a2 \u23a3 \u22123 . 1416 3 . 1416 0 \u23a4 \u23a5 \u23a5 \u23a6 and \ud835\udf53\ud835\udc61 = \u23a1 \u23a2 \u23a2 \u23a3 \u22123 . 1289 3 . 1163 0 . 0232 \u23a4 \u23a5 \u23a5 \u23a6 . (44) here are an infinite number of kinematic paths connecting the two onfigurations. As an illustrative example, this subsection generates two uitable paths based on two different user preferences. Consider two user references correspondingly in Situation A and B , as shown in Fig. 9 . In ituation A (shown in Fig. 9 (a)), the deployment is actuated by three isplacement-controlled linear actuators, which can be by mechanical r electromechanical actuators. The requirement is to coordinate actutor lengths l 1 , l 2 , and l 3 in a way that the deployment process is comatible and relatively fast. Generating the corresponding path employs cheme A that is introduced in Section 4.1.2 . In Situation B ( Fig. 9 (b)), he deployment is facilitated by the rotation-controlled actuation, which an be by stepper motors or servomotors, at hinges 2, 3, and 4. The corespondingly suitable path, which coordinates actuator angles \ud835\udf191 , \ud835\udf192 , nd \ud835\udf193 in a way that the deployment process is compatible and relaively fast, is computed based on Scheme B in Section 4.1.3 . Different inematic paths are expected from the two schemes. Displacements of odes 1 and 5 are removed in the following analysis. .1.2. Scheme A: employing three linear actuators It is equivalent to try to move nodes 2, 3, and 4 to target positions in compatible and locally fastest way, which is described in Section 3",
            " Then x 0,3 is regarded as xtension-free and assigned as x 2 . Repeating incrementation and corection steps until \ud835\udc31 \ud835\udc61 \u2212 \ud835\udc31 \ud835\udc56 \u2225< \ud835\udf16\ud835\udc61 = 0 . 02 . (60) t results in a set of compatible configuration points, noted as \ud835\udc31 0 \ud835\udc34 , \u2026 , \ud835\udc31 160 \ud835\udc34 ] , where the subscript A is added to represent Scheme A. his forms a kinematic path which is noted as Path A , and it can be arameterized also in terms of [ l 1 , l 2 , l 3 ] (computed by the distance forula) and [ \ud835\udf191 , \ud835\udf192 , \ud835\udf193 ] (computed by Eq. (4) ) respectively as in Fig. 9 , nd correspondingly gives [ \ud835\udc25 0 \ud835\udc34 , \u2026 , \ud835\udc25 160 \ud835\udc34 ] and [ \ud835\udf530 \ud835\udc34 , \u2026 , \ud835\udf53160 \ud835\udc34 ] . .1.3. Scheme B: employing three rotational actuators As the preference is to approach the target configuration fastest in erms of hinge rotations, the method presented in Section 3.3 is emloyed. The target rotation for the initial step is \ud835\udc61 \u2212 \ud835\udf530 = \u23a1 \u23a2 \u23a2 \u23a3 3 . 9397 \u22121 . 9452 0 . 7981 \u23a4 \u23a5 \u23a5 \u23a6 . (61) he compatibility matrix for rotational hinges based on Eq. (13) is given s \ud835\udc5f\u210e |0 = \u23a1 \u23a2 \u23a2 \u23a3 0 0 0 1 0 0 0 1 0 0 0 \u22121 0 0 0 \u22121 0 2 \u23a4 \u23a5 \u23a5 \u23a6 ",
            " To conclude the plots: \u2022 different kinematic paths can be found using the shooting method employing different target functions based on user preferences; \u2022 a relatively shorter path (not necessarily the shortest) is found in the specific parametric space in which the shooting target is assigned, while it appears to be relatively longer in other parametric spaces; \u2022 the kinematic manifold of a mechanism that employs revolute joints has a simpler/smoother structure in the space parameterized by angles than in the space parameterized by coordinates or distances. Implications for practical actuations from the result of this analysis re: \u2022 if three displacement-controlled linear actuators are employed as in Fig. 9 (a), controlling the actuators\u2019 lengths ([ l 1 , l 2 , l 3 ]) according to path \ud835\udc25 \ud835\udc56 \ud835\udc34 in Fig. 11 gives a compatible and faster actuation process (than \ud835\udc25 \ud835\udc56 \ud835\udc35 ); \u2022 if three angle-controlled rotational actuators are used as in Fig. 9 (b), controlling the actuators\u2019 angles ([ \ud835\udf191 , \ud835\udf192 , \ud835\udf193 ]) according to path \ud835\udf53\ud835\udc56 \ud835\udc35 in Fig. 12 gives a compatible and faster actuation process (than \ud835\udf53\ud835\udc56 \ud835\udc34 ). .2. Folding paths of a multi-DOF origami mechanism To demonstrate the generality of the method, a more complex examle, for which the analytical kinematic relationship is not available, is emonstrated in this subsection. The triangular Ron Resch\u2019s pattern has ulti-DOF behavior. It can be folded from a completely flat geometry nto a spherical shape and then further into a fully folded flat configuraion, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003479_j.eml.2020.101114-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003479_j.eml.2020.101114-Figure1-1.png",
        "caption": "Fig. 1. Two representative functional 3D ribbon mesostructures and the evolution of deformed configurations under the out-of-plane compression. (a) A colorized SEM image of the ultralow-stiffness PVDF mesostructure consisting of serpentine curves and two bridge-shaped supporting ribbons. Scale bar, 500 \u00b5m. Reprinted ith permission from Han et al. (2019), Copyright 2019, Macmillan Publishers Ltd. (b) Uncompressed (top) and compressed (bottom) configurations of the 3D PVDF esostructure based on finite element analyses (FEA). (c) Evolution of the deformed configuration for a bridge-shaped supporting ribbon. (d) An optical image of the lexible health monitoring device consisting of multiple helical coils. Scale bar, 5 mm. Reprinted with permission from Jang et al. (2017), Copyright 2017, Macmillan ublishers Ltd. (e) Uncompressed (top) and compressed (bottom) configurations of four helical coils interconnecting two electronic chips based on FEA. (f) Evolution f the deformed configuration for a helical coil.",
        "texts": [
            " For example, ecent studies established the mechanically-guided 3D assembly hrough controlled, compressive buckling as a versatile route o 3D flexible electronics that can offer new functionalities and nprecedented mechanical/electrical performances, while posess precisely tailored 3D geometries [28\u201332]. Those 3D flexible lectronics, usually composed of ribbon-shaped mesostructures, ould undergo the out-of-plane compression in many scenarios f practical operations [33\u201339], with two representative examples llustrated in Fig. 1. Fig. 1a shows a 3D piezoelectric polymer \u2217 Corresponding author. E-mail address: yihuizhang@tsinghua.edu.cn (Y. Zhang). ttps://doi.org/10.1016/j.eml.2020.101114 352-4316/\u00a9 2020 Elsevier Ltd. All rights reserved. microsystem consisting of two bridge-shaped supporting ribbons and two suspended serpentine wires, which can be implanted into the hind leg of a mouse to harvest low frequency vibrational energy of muscular movement [8]. In these biointegrated applications, the ribbon-shaped mesostructures inevitably undergo the out-of-plane compression (Fig. 1b), due to the mechanical interactions with the adjacent bones/organs [8,40]. Fig. 1c shows the configuration evolutions of the bridge-shaped supporting ribbon simulated by FEA, where the buckled straight ribbon transforms to the flattened state with two free S-shaped segments at high levels of compressions. Fig. 1d shows a flexible health monitoring electronic device built with 3D interconnected network of helical coils and \u223c50 chip components, which is capable of physiological tatus monitoring (e.g., respiration rate, three-axis acceleration nd electrophysiological signals), while maintaining exceptionally igh levels of stretchability [41]. The skin integration represents major application scenario of these devices, where the helical oils could be pressed by fingers or tight clothes [41,42]. Fig. 1e w m f P o a t d a n c i o f b a b l r f b 6 m t t v r m a i c 6 m a r s t c a t s s o t g m w c i b l g c B a c t H m t p a nd f shows a schematic illustration of the configuration evoluions associated with the helical ribbons, which exhibit a distinct eformation mode from that of bridge-shaped ribbons. Generally, the compressive deformations of mechanicallyssembled complex 3D mesostructures could involve intricate onlinear behaviors (e.g., multiple deformation modes and bifurations [43\u201353]), and an in-depth understanding of these behavors could offer important guidelines for the engineering design f 3D flexible electronic devices",
            " By incorporating the continuity conditions and boundary onditions of bridge-shaped mesostructures under compression, e determine three representative deformation modes and a critcal mode transition state in Section 2.2. Section 2.3 illustrates the alidation of the developed model by experiments and FEA. The ffects of asymmetric deformations and interfacial friction on the hase diagram and mode transition are analyzed in Sections 2.4 nd 2.5. .1. Basic equations Consider an elastic beam that deforms in the x \u2212 z plane (Fig. 1a), where the left end is clamped and the right end is subjected o a concentrated force (FI ). Due to the slender geometry of ribbon mesostructures, the axial deformations (e.g., axial tension and compression) are usually negligible such that the arc length of the beam does not change after deformation. Then the equilibrium equation of a micro-element (ds) in the beam can be given by dM ds + Fx sin \u03b8 \u2212 Fz cos \u03b8 = 0, (1) where Fx and Fz are the reaction force components along the x and z directions at the left end of the beam, respectively; and \u03b8 and M are the rotation angle and the bending moment, respectively",
            ", MO2 = 0), as laborated subsequently. .2.2. Configuration of the face-contact mode (FC) With the vanishing of the internal bending moment (MO2) at he contact line, a face-contact (FC) deformation mode develops, here the flattened region spreads as the out-of-plane compresive strain (\u03b5z) increases. As a result, the arc lengths of the two ree folds (i.e., segments O2I1O3 and O5I2O4) decrease, as shown n Fig. 2b. Considering the symmetry of the free folds, we focus n analyzing a half of the free fold, e.g., segment O2I1 (see Fig. 1c for details). According to Eqs. (3), (5) and (6), and MO2 = 0, wo important equations, \u03c60 = \u2212 \u03c0 2 and \u03b1 = 2\u03b2 , can be deduced. Substitution of these two equations into Eq. (7) then gives the arc length (sI1) and coordinates (xI1, zI1) at the inflection point (I1) of the segment O2I1 as in Box III. The loading conditions and geometric constraints for the facecontact deformation mode are written as [sI1 xI1 zI1 ] = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 L0 \u2212 a \u2212 b \u2212 c 4 L0 (1 \u2212 \u03b5x) \u2212 a \u2212 b \u2212 c 4 H(1 \u2212 \u03b5z) 2 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 . (12) With the aid of the defined relation (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003478_d0sm01162b-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003478_d0sm01162b-Figure8-1.png",
        "caption": "Fig. 8 Collective dynamics of sparsely packed filaments. (a) Kymograph of the end\u2013end length Lee in a system of N = 300 clamped filaments for the spacing parameter d = 11 with b = 384. Videos of corresponding simulation trajectories are shown in Movie-3 in the ESI.\u2020 The 0 on the y-axis corresponds to the left end of the filament array. The thin, slanted patterns correspond to fast-moving waves translating in both the directions. A blown-up version of the kymograph is shown on the right. (b) Snapshot of a section of filament array, indicating a phase-lag synchronization. (c) Individual filament oscillation frequencies in a sparsely packed carpet d = 11 (red) and for isolated filaments d c dmax.",
        "texts": [
            " The lack of coordination results from irregularities in the beating patterns of individual filaments induced by interactions with their neighbors (Fig. 7(b)). Thus, the disappearance of coordinated beating at intermediate filament separations described above for N = 3 extends to large systems with N c 1. When the inter-filament spacing is further increased (d4 dmax/ 2), the contact interaction becomes \u2018pulse\u2019-like and the individual filaments beat with a higher frequency, close to that of an isolated filament. Interestingly, we observe the reemergence of waves at these large separations (Fig. 8 and ESI\u2020 Movie-2). However, the wave propagation is qualitatively different than observed for tightly packed filaments, where filaments are in continuous contact with their neighbors. At large separations, the filaments which are initially oscillating independently, coordinate their oscillatory phase through the \u2018pulse\u2019-like interactions. This results in nucleation of independent waves moving in either directions, at different regions in the array of filaments. Two oppositely moving waves meet at a \u2018node\u2019 where they annihilate (cf. Fig. 8(a)), leading to a saw-tooth pattern in the kymograph. Also, the speed of wave propagation, which is closely linked to the individual filament beating frequency, is higher compared to the tightly packed filaments. A closer examination of the configuration (Fig. 8(b) and Movie-3, ESI\u2020) indicates that the filaments exhibit a phaselagged synchronization, with a much larger phase difference compared to d C 1. Analysis of the frequency spectrum of Lee oscillations identifies multiple harmonics in the oscillation waveform (Fig. 8(c)). However, the oscillation frequency of individual filaments at this separation closely matches with that of an isolated filament (Fig. 8(c)). The previous section discusses the collective dynamics of active filaments for which the individual beads have an effective interaction diameter s = 4c0 that is larger than the equilibrium separation between neighboring beads c0. This arrangement ensures relatively low resistance to tangential sliding between adjacent filaments in tightly packed configurations and mimics steric interactions between brush-grafted filaments as in the Fig. 7 (a) Kymograph of the end\u2013end length Lee in system of N = 300 clamped filaments for the spacing parameter d = 5 with b = 384"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000007_978-1-4613-2811-7_7-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000007_978-1-4613-2811-7_7-Figure9-1.png",
        "caption": "Figure 9. MBB test piece after rough machining.",
        "texts": [],
        "surrounding_texts": [
            "generating a contouring cut to remove cusps, followed by a final finishing cut."
        ]
    },
    {
        "image_filename": "designv10_12_0002383_1.4035079-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002383_1.4035079-Figure13-1.png",
        "caption": "Fig. 13 The assembly of gear and pinion models",
        "texts": [
            " When the gear tooth surface is given, the pinion tooth surface can be derived to mesh with the gear as a pair [10]. For the aforementioned example, the tooth surface of a pinion model is generated according to the simulate machined tooth surface of the gear. The parameters and machine setting related to the pinion are given in Table 4. Correspondingly, the pinion tooth surface can be represented according to these parameters and machine settings [38]. Subsequently, the pinion is modeled and assembled with the simulate machined gear in CATIA V5, as shown in Fig. 13. With both tooth surfaces of the pinion and gear, TCA can be implemented [10,49]. As shown in Fig. 14, the results of TCA are good. Hence, the proposed method is effective. A new approach to designing and modeling the tooth surface is proposed for the five-axis flank milling of spiral bevel gears. Several features of this new approach are summarized as follows: (1) Five-axis flank milling is introduced to machine spiral bevel gears. Compared to the previous researches about five-axis flank milling, a new tool path planning strategy is proposed by considering the work performances of spiral bevel gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.143-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.143-1.png",
        "caption": "Fig. 2.143 HEV driving circumstances during charging [DRIESEN 2006].",
        "texts": [
            "141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 337 In Figure 2.142 HEV driving circumstances are shown during deceleration and braking the E-M motor is turned into a M-E generator to charge the highvoltage CH-E-CH storage battery. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 338 In Figure 2.143 HEV driving circumstances are shown during charging when the CH-E/E-CH storage battery gets low and the ICE may automatically start to recharge it. In Figure 2.144 HEV driving circumstances are shown during stopping when the ICE automatically shuts off when the series/ parallel HEV is stopped. Further optimising of the ICE operating range is necessary so as to achieve optimum hybrid system energy efficiency. As a result, fuel economy during medium- and high-velocity constant running, in particular, could be improved",
            " The automotive ECE or ICE and the auxiliary EEBs are mounted on separate power trains, but are mechanically connected to each other, to the output traction by means of the power-splitting natural track, that is, the road or ground surface. The auxiliary EEBs are always rotating when the HEV is running (excluding EEBs connected to the retracted axles that are lifted). They recover most of the excessive power from the ECE or ICE powertrain, thus increasing efficiency, power, and torque multiplication at low values of vehicle velocity. For application where high stall torque is not required, the multi-power train split HE transmission arrangement (Figure 2.143) can be converted to a simplest dualor single-powertrain split HE transmission arrangement by the omission or exchange of some of the parts or components in a modular HE transmission arrangement. Locating the E-M/M-E motor/generator at the axle not driven by the ECE or ICE can also make available a DBW AWD propulsion mechatronic control system, while reducing mass and inertia by removing the power take-off unit and propulsion shaft indispensable in conventional DBW AWD propulsion mechatronic control systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure16-1.png",
        "caption": "Fig. 16. The 2T2R + 1-DOF parallel manipulator: (a) configuration 1 (b) configuration 2.",
        "texts": [
            " Taking the type 4 parallel manipulator shown in Fig. 10 (b) as an example, the qualified actuators of the bottom mecha- nism n a1 equals to 3. The dimension of the screw system for the single-loop mechanism is 1. Then the number of actuators ( n a1 + n a2 ) is matched. When all actuators are locked, the mechanism is transformed into a five-bar structure. And the DOF of the derived structure is zero. Therefore, the deployment of driving motors for this manipulator is reasonable. For the 2T3R + 1DOF mechanism shown in Fig. 16 (b), the equation ( n a1 + n a2 ) = 6 is carried out. When all actuators are locked, the mechanism is transformed into a five-bar rigid structure. As a result, the driving scheme of the manipulator is valid. The driving schemes of other manipulators can be analyzed in the same way. Consequently, the driving schemes of manipulators shown in Figs. 9\u201312 , 13 (b), 14 (a), 15 and 16 are reasonable. The multi-drive hybrid limbs have the potential to avoid the limbs\u2019 interference to enlarge the workspace of the manip- ulators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000739_iros.2010.5651324-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000739_iros.2010.5651324-Figure5-1.png",
        "caption": "Fig. 5. Right leg of segment i in swing phase: The leg tip stays at the midair point Pup, and approaches the next contact point Pnewi by the control mode 3.",
        "texts": [
            " In this phase, the desired motor angle \u03b8\u0302m in (1) is calculated from inverse kinematics of Pup. Pup) In the swing phase 2, the leg tip stays at the midair point Pup. This control is being activated until the leg tip of fore leg i\u22121 enters into Area 1 of leg i (see section IV for details). The desired motor angle \u03b8\u0302m of (1) is calculated from inverse kinematics of Pup as same as the control mode 1. In the swing phase 3, the leg tip leaves the midair point Pup and approaches to the next contact point Pnewi (Fig. 5). The position of the next contact point Pnewi, except for the first legs (i = 1), is calculated based on the contact point of the fore leg Pi\u22121 in the left and right legs respectively as follows (s \u2208 {l, r}, double-sign corresponds): P s newi = R1(i)R s 2(i)w s(i) + bs(i), (2) R1(i) = \u23a1 \u23a3 c\u03c6i \u2212s\u03c6i 0 s\u03c6i c\u03c6i 0 0 0 1 \u23a4 \u23a6 , R2(i) = \u23a1 \u23a3 c\u03c8i 0 \u2213s\u03c8i 0 1 0 \u00b1s\u03c8i 0 c\u03c8i \u23a4 \u23a6 , (3) w(i) = \u23a1 \u23a3 xsi\u22121 \u2213 2R\u00b1 L ysi\u22121 +W zsi\u22121 \u23a4 \u23a6 , b(i) = \u23a1 \u23a3 \u00b1L \u2212W 0 \u23a4 \u23a6 (4) where P s newi = (xsnewi, y s newi, z s newi) T and P s i\u22121 = (xsi\u22121, y s i\u22121, z s i\u22121) T , c\u03b7 \u2261 cos \u03b7 and s\u03b7 \u2261 sin \u03b7, \u03c6i and \u03c8i are respectively the yaw and pitch angles of the intersegment joint between trunks i\u22121 and i, 2W , L and R are the width of trunk, the distance between the joint center and the trunk center, and the radius of leg tip, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.9-1.png",
        "caption": "Fig. 9.9 Domains with three eigenvectors (shaded) and with a single eigenvector",
        "texts": [
            " Real solutions exist only for 0 < \u03bc2 \u2264 1/3 and for 0 < | cos\u03b1| \u2264 1/3 . In a diagram with axes cos\u03b1 and \u03bc the curve D = 0 separates the domain D < 0 with three real eigenvectors from the domain D > 0 with a single real eigenvector. At the point \u03bc2 = 1/3 , cos\u03b1 = 1/3 the curve has a cusp. With these parameter values the characteristic Eq.(9.92) has the form (\u03bb + 2/3)3 = 0 . 312 9 Angular Velocity. Angular Acceleration The triple eigenvalue \u03bb = \u22122/3 is associated with the single eigenvector = [ 1/ \u221a 2 1/ \u221a 6 1/ \u221a 3 ]T . In Fig. 9.9 the curve D = 0 is shown not in the cos\u03b1, \u03bc-diagram, but in a diagram with axes \u03bc sin\u03b1 and \u03bc cos\u03b1 . According to (9.85) these are the coordinates of the vector \u03c9\u0307/\u03c92 in the plane of \u03c9 and \u03c9\u0307 . The unit vector \u03c9/|\u03c9| is directed along the \u03bc cos\u03b1-axis (see (9.85)). Three real eigenvectors exist if the vector \u03c9\u0307/\u03c92 terminates in the shaded domain D < 0 . Three real eigenvectors are not mutually orthogonal. Let \u03b2i be the angle between the eigenvector i and \u03c9 . With the coordinates i1 , i2 , i3 of i cos2 \u03b2i = 2i3 2i1 + 2i2 + 2i3 (i = 1, 2, 3) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002672_j.measurement.2019.107096-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002672_j.measurement.2019.107096-Figure4-1.png",
        "caption": "Fig. 4. Finite element substructure model of the box.",
        "texts": [
            " sym 2 66666666664 Fp1 t\u00f0 \u00de \u00bc P kpn efn coswn egn sinwn P kpn efn sinwn \u00fe egn coswn P kpnegnP krnern sinwrn P krnern coswrnP krnernP ksnesn sinwsn P ksnesn coswsn P ksnesn .. . ksnesn sinas \u00fe krnern sinar ksnesn cosas \u00fe krnern cosar ksnesn \u00fe krnern 2 6666666666666666666666666664 3 7777777777777777777777777775 \u00f010\u00de Fp2 t\u00f0 \u00de \u00bc 0 0 Tc rc 0 0 0 0 0 Ts rs 0 0 0 0 0 0 h iT \u00f011\u00de In order to realize the dynamic modeling of coupled system between the transmission and the box, the static substructure method is used to extract the dynamic model parameters of the box by using ANSYS software with reference to [22\u201324]. Fig. 4 is the finite element substructure model of the box. The box nodes are divided into internal nodes and external nodes. The nodes on the bearing housing surface are the external nodes, and the other finite element nodes are the internal node. The mass and stiffness parameters of the box could be extracted by the substructure Kn c2 Kn r2 Kn s2 0 .. . Kn c3 \u00fe Kn r3 \u00fe Kn s3 3 77777777775 \u00f09\u00de method after the internal nodes are condensed to the external nodes. The external nodes of the box are divided into main nodes and slave nodes. As shown in Fig. 4, the main nodes are established at the center of the bearing housing on the box, and the slave nodes are established on the surface of the bearing housing. The rigid region is established between the main nodes and the slave nodes, and the mass matrix and stiffness matrix are extracted at the main nodes. Obviously, the substructure method can avoid the introduction of large-scale finite element stiffness and mass matrix, and box substructure model could be easily coupled with the dynamic model of the transmission system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001749_s12239-014-0053-3-Figure17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001749_s12239-014-0053-3-Figure17-1.png",
        "caption": "Figure 17. Evolution of wear amount distribution: (a) 1st, (b) 10th, (c) 20th and (d) 32nd sub-phase.",
        "texts": [
            " Meanwhile, the wear grooves seem to be slightly oblique to the axial direction of tire. Furthermore, if figure 14 is reflected horizontaly, a Vpatern wear can be observed (figure 16), which agrees with the reported polygonal wear phenomenon described above. mj 2\u03c0 Aj\u03bdrim 3600\u03c9rim -------= Alignment 0o 0.16o 3500 N 110 km/h 0.28 MPa Table 4. Wear prediction information of the 1st sub-phase. Max. size of geometric update 0.30 mm Max. wear amount 1.3326\u00d710-7 mm Extrapolation factor 2.2512\u00d7106 Mileage 4.4038\u00d7103 km Figure 13. Wear amount distrbution countour of the 1st sub-phase. Figure 17 shows the evolution of wear amount distribution. There is no regular patern in the circumferential direction during 1st and 10th sub-phase. The polygonal patern is not formed gradualy until 20th sub-phase and the wear grooves come into being during the final stage. Figure 18 presents the same process in a phase plane curve. The extrapolation factor fluctuates substantialy during the whole process, shown in figure 19, but its trend reduces with the sum of mileage, which implies that the wear efect is intensified"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002596_s00170-018-2850-8-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002596_s00170-018-2850-8-Figure9-1.png",
        "caption": "Fig. 9 Metallographic structure of SLM Inconel 718: a Z-plane, b X-plane, c representative crosssection of a single melt pool, and d melt pool superposition \u201ctrace by trace\u201d and \u201clayer by layer\u201d",
        "texts": [
            " The mechanical properties of SLM/casting Inconel 718 are measured through tensile test by an electronic universal testing machine (WDW-100E) according to GB/T228.1-2010. The samples are made into bars with circular cross-section according to GB/T 2975. The loading rate is 2 mm/min. Table 5 presents the mechanical properties of SLM/casting Inconel 718. Figure 8a shows the tensile fracture surface of SLM Inconel 718. There exist some internal defects such as unmelted powders (Fig. 8b) and micropores (Fig. 8c), which will probably reduce the mechanical strength, i.e., yield strength and tensile strength. The metallographic structures shown in Fig. 9a and b are for Z- and X-planes of SLM Inconel 718. The strips in Fig. 9a are the longitudinal sections of the melt pools, whereas the cross-sections of the melt pools in Fig. 9b are arc-shaped, due to the Gaussian distribution of laser beam energy and wetting characteristics of the liquidsolid interface. Boundaries between the melt pools in the same layer are called \u201ctrace-trace\u201d boundary, whereas the boundaries between the layers are called \u201clayer-layer\u201d boundary, which can be observed clearly after corrosion. The melt pool width is observed to vary from 70 to 100 \u03bcm, while the layer thickness is from 30 to 50 \u03bcm. Additionally, some micropores can be observed existing in the metallographic structure. They are mainly attributed to the small voids among powers, which are not fully filled because of rapid cooling during solidification of the material. It can be illustrated through the topological structure of the specimen cross-section. Figure 9c shows the representative cross-section of a single melt pool, the upper and lower profiles of which are all curved, due to the Gaussian distribution of laser beam energy and surface tension of liquid. However, as the size of the powder is not exactly the same and the powders are randomly distributed in the space, the melt pools formed by the powders are also not the same. The cross-section of the specimen is formed by superposing these irregular \u201ccross-sections\u201d trace by trace and layer by layer, as shown in Fig. 9d. The area that is not covered will form a void, that is, the micropore in the part. Different from SLM Inconel 718, there are no layered structures or micropores in the metallographic structure of casting Inconel 718, as shown in Fig. 10 [38]. Copying method is adopted to measure the wheel wear. By measuring the height difference between two adjacent steps on the graphite sheet corresponding to the grinding radial wear, the cumulative wheel wear after each grinding step can be obtained, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001796_s12541-015-0346-0-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001796_s12541-015-0346-0-Figure3-1.png",
        "caption": "Fig. 3 TRB inner and outer races with out-of-roundness errors",
        "texts": [
            " 2(a) shows a cross section of the bearing at a particular roller. Because the inner race cross section and the roller are displaced from their original positions by {u\u03ba} = {u\u03be, u\u03b6, \u03b8}T and {v\u03ba} = {v\u03be, v\u03b6, \u03c8}T, respectively, contact forces between the roller and races are generated. Fig. 2(b) shows the free body diagram of a roller, where Qf, Fc, and Mg are the flange force, centrifugal force, and gyroscopic moment, respectively. Qi,e and Mi,e denote the contact forces and moments, respectively, between the roller and the inner and outer races. Fig. 3 shows cross sections in the yz plane of the inner and outer races with out-of-roundness errors. The inner and outer race errors ei and eo shown in Fig. 3 are defined as negative values in this study, though these errors may be positive or negative. Because of the out-ofroundness errors of the bearing races, the contact forces between the roller and races must be modified. Fig. 4 shows the contact geometry between a roller and the inner race. The roller-inner race contact force and moment can be calculated using the well-known slicing technique,17,24 as (1) , (2) where c is the contact constant; ns is the total number of slices; and \u0394lk and \u03b4k are the slice length and the contact compression, respectively, of slice k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002407_1.4033387-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002407_1.4033387-Figure1-1.png",
        "caption": "Fig. 1 (a) Meshing of shaper, worm, and face-gear, (b) coordinate systems applied for the generation of worm surface, and (c) involute profiles of shaper",
        "texts": [
            " Moreover, the relative position of the worm and the face-gear stock is changeable to different processing area. The machining simulation is also used to verify the feasibility and correctness of the multistep method in the VERICUT software. 2.1 Meshing Process of Generating Face-Gear by Worm. According to the principle of face-gear manufacturing process [20], the worm, the shaper, and the face-gear are meshing with each other, and there is a virtual internal meshing relationship between the shaper and the worm, as shown in Fig. 1(a). By taking the shaper as a medium, the kinematic relationship between the worm and the face-gear is described as shown in Figs. 1(a) and 1(b). The movable coordinate systems O2;Ow;Os are rigidly connected to the face-gear, the worm, and the shaper, respectively. As shown in Fig. 1(b), O20; Ow0; Os0 are fixed coordinate systems. u2; uw; us are the rotation angles of the face-gear, worm, and shaper, respectively. Figure 1(c) is the shaper with a standard involute profile, and it will be used as the fundamental element to derive the models of face-gear and worm. Based on the standard involute, the shaper surface is written in Os as [20] Rs us; hs\u00f0 \u00de \u00bc rb sin hs \u00fe hs0\u00f0 \u00de hs cos hs \u00fe hs0\u00f0 \u00de\u00bd rb cos hs \u00fe hs0\u00f0 \u00de \u00fe hs sin hs \u00fe hs0\u00f0 \u00de\u00bd us 1 2 66664 3 77775 (1) Manuscript received June 9, 2014; final manuscript received April 5, 2016; published online May 25, 2016. Assoc. Editor: Allen Y. Yi. Journal of Manufacturing Science and Engineering JULY 2016, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.13-1.png",
        "caption": "Fig. 3.13 Screw axes with reference basis e1,2,3 on the common perpendicular",
        "texts": [
            "5 states that the same equations are valid when vectors n of rotation axes are replaced by dual vectors n\u0302 = n + \u03b5w of screw axes and rotation angles \u03d5 by dual screw angles \u03d5\u0302 = \u03d5 + \u03b5s . The angle \u03b1 between intersecting rotation axes is replaced by the dual angle \u03b1\u0302 = \u03b1 + \u03b5 of the screw displacement which carries n\u03021 into n\u03022 (this means that , positive or negative, is the length of the common perpendicular of the two screw axes). For making (3.107) with n\u03021,2 and \u03b1\u0302 valid the origin 0 of the basis e1,2,3 of Fig. 1.4 must be the midpoint of the common perpendicular (see Fig. 3.13). The primary parts of the dualized equations are Eqs.(3.108) and (3.109). The dual parts are sres sin \u03d5res 2 = s1 ( sin \u03d51 2 cos \u03d52 2 + cos \u03d51 2 sin \u03d52 2 cos\u03b1 ) +s2 ( cos \u03d51 2 sin \u03d52 2 + sin \u03d51 2 cos \u03d52 2 cos\u03b1 ) \u22122 sin \u03d51 2 sin \u03d52 2 sin\u03b1 , (3.110) 114 3 Finite Screw Displacement nressres cos \u03d5res 2 + 2wres sin \u03d5res 2 = e1 [ (s1 + s2) cos \u03d51 + \u03d52 2 cos \u03b1 2 \u2212 sin \u03d51 + \u03d52 2 sin \u03b1 2 ] \u2212e2 [ (s1 \u2212 s2) cos \u03d51 \u2212 \u03d52 2 sin \u03b1 2 + sin \u03d51 \u2212 \u03d52 2 cos \u03b1 2 ] \u2212e3 [( s1 cos \u03d51 2 sin \u03d52 2 + s2 sin \u03d51 2 cos \u03d52 2 ) sin\u03b1 +2 sin \u03d51 2 sin \u03d52 2 cos\u03b1 ] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002979_lra.2019.2945468-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002979_lra.2019.2945468-Figure3-1.png",
        "caption": "Fig. 3: PMC mechanism, a CRRHHRRC kinematic chain",
        "texts": [
            " The second, a strain-wave gear (SWG) speed reducer, shown in Fig. 2, is used as a replacement of the cable-driven mechanism. Kinematically, both alternatives are equivalent. 3strain-wave gear The main difference resides in the high speed-reduction ratio G in the CSWG-drive4. These two versions of the C-drive were proposed in an earlier paper [23] and tested with an external load generated by a mass of 0.5 kg. In this letter, each drive is mounted on the PMC to compare their performance w.r.t. PPOs. The complete kinematic chain of the PMC is illustrated in Fig. 3. The relationships between the homogeneous variables defining the displacement array \u03c3 of the collar of each Cdrive, and the angular-displacement array \u03c8 of the actuators are expressed via the \u201cJacobian\u201d5 matrix Jh: \u03c3 = Jh\u03c8, (1) with \u03c3 =   \u03c31 \u03c32 \u03c33 \u03c34   =   u1 Gp\u03b81/(2\u03c0) u2 Gp\u03b82/(2\u03c0)   and \u03c8 =   \u03c81L \u03c81R \u03c82L \u03c82R   (2a) 4The SWG we used features a speed reduction of 22.5:1. 5The quotation marks indicate that the putative \u201cJacobian\u201d is, actually, a constant, posture-independent coefficient matrix. 2377-3766 (c) 2019 IEEE",
            " Jh = p 4\u03c0   1 \u22121 0 0 1 1 0 0 0 0 1 \u22121 0 0 1 1   (2b) where ui and \u03b8i are the position and angle of the ith Cdrive arm, p is the pitch of the C-drive screws, one right-, one left-hand, and G is the gear reduction ratio of the Cdrive (1 for the cable-driven mechanism, 22.5 for its SWGdriven version). The subscripts iL and iR refer, respectively, to the motor coupled to the left-hand screw and right-hand screw of the ith C-drive. The pitch of C-drive ballscrews is 60 mm. Originally, these motors were also physically located at each end of the C-drive [22]. The Jacobian matrix Jh is dimensionally homogenous, with units of m. The pose of the \u201cmoving platform\u201d6, the gripper in Fig. 3, is defined by the vector x = [xc yc zc \u03c6]T , whose components can be used to compute \u03c3:   \u03c31 \u03c32 \u03c33 \u03c34   =   xc (\u03b11 + \u03b21)Gp/(2\u03c0) yc (2\u03c0 \u2212 \u03b12 \u2212 \u03b22)Gp/(2\u03c0)   (3) with \u03b11 \u2261 arctan(h1/yc), \u03b12 \u2261 arctan(h2/xc) (4a) \u03b2i \u2261 arccos r2 \u2212 l2 \u2212 k2i 2rki (4b) k1 \u2261 \u221a y2c + h21, k2 \u2261 \u221a x2c + h22 (4c) hi \u2261 zi(\u22121)iq\u03c6/(2\u03c0) (4d) The geometric parameters are illustrated in Fig. 3. 6The quotation marks indicate that what plays the role of the moving platform in a PKM is, in fact, a rod-like link, as per Fig. 3 The inverse-dynamics model of the PMC, as reported elsewhere7 [24], is used to determine the torques required from the actuators, a key issue in the design of the C-drives. This model was obtained by means of the natural orthogonal complement [25]. For completeness, the inverse-dynamics model is briefly recalled below: \u03c4 = I\u03c8\u0308 + C\u03c8\u0307 \u2212 \u03b3 \u2212 \u03b7 \u2212 \u03b4 (5a) where \u03c4 \u2261 [ \u03c41L \u03c41R \u03c42L \u03c42R ]T , I \u2261 11\u2211 i=1 Ti T MiTi (5b) C \u2261 11\u2211 i=1 (Ti T MiT\u0307i + Ti T WiMiTi) (5c) \u03b3 + \u03b7 + \u03b4 \u2261 11\u2211 i=1 Ti T (wG i + wE i + wD i ) (5d) , Mi \u2261 [ Ii O O mi1 ] , Wi \u2261 [ \u2126i O O O ] , Ti \u2261 \u2202ti \u2202\u03c8\u0307 (5e) Matrices Ii, Mi, 1 and O denote, respectively: the inertia tensor, the inertia dyad, both at the c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003592_j.oceaneng.2021.109186-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003592_j.oceaneng.2021.109186-Figure2-1.png",
        "caption": "Fig. 2. The process of tracking the trajectory.",
        "texts": [
            " The rudder forces (moment) XR, YR and NR are given by {XR = \u2212 (1 \u2212 tR)FNsin\u03b4 YR = \u2212 (1 + aH)FNcos\u03b4 NR = \u2212 (xR + aHxH)FNcos\u03b4 (3) where, tR is the number of rudder resistance deductions; FN is the rudder positive pressure; \u03b1H is the ratio of the hull\u2019s additional lateral force to the rudder lateral force caused by steering; xR is the longitudinal position of the rudder; xH is the distance from the steering induced hull lateral force center to the ship\u2019s center of gravity. The control inputs of the MMG are the propeller revolution n and rudder angle \u03b4. The process of tracking the trajectory is shown in Fig. 2. where, xe is the along-track error and is controlled directly by (Shen et al., 2017) n; ye is the cross-track error and is controlled indirectly by \u03b4, which uses \u03d5 as the virtual control objective; Pd (xd, yd) is the reference Z. Li and R. Bu Ocean Engineering 233 (2021) 109186 trajectory; \u03b8 = arctan (\u1e8fd/\u1e8bd) is the angle of L1; L1 is the reference trajectory tangent line, and k1 = tan(\u03b8), b1 = yd-k1xd; L2 is the reference trajectory normal line, and k2 = \u2212 1/k1, b2 = yd-k2xd; In this paper, the objective is to design the control inputs n and \u03b4 to let xe and ye tend to 0, respectively",
            " So, to illustrate some parameters clearly, its characteristic is shown in Fig. 5. where, c1 and c2 are the positive parameters. We can see that the hyperbolic tangent function is a bounded odd function, and c1 could adjust the amplitude limit range, c2 can adjust the amplitude variation range. In this section, the backstepping algorithm is used to design the virtual control laws, so that trajectory tracking is converted into the heading control and surge velocity control. Firstly, according to Fig. 2 and the distance theorem from a point to a line, the track errors xe and ye are computed xe = A2x + B2y + C2 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 A2 2 + B2 2 \u221a , ye = A1x + B1y + C1 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 A2 1 + B2 1 \u221a (7) where, xe is computed by the ship position P (x, y) and line L2 in Fig. 2; A2 = k2, B2 = \u2212 1, C2 = b2 are the parameters of L2; ye is computed by P (x, y) and line L1; A1 = k1, B2 = \u2212 1, C1 = b1 are the parameters of L1. Substituting k1 = tan(\u03b8) into above equation and transforming the trigonometric function, we have { xe = \u2212 x cos \u03b8 \u2212 y sin \u03b8 + xd cos \u03b8 + yd sin \u03b8 ye = x sin \u03b8 \u2212 y cos \u03b8 \u2212 xd sin \u03b8 + yd cos \u03b8 (8) Differentiating xe and ye with respect to time, we have \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 x\u0307e = \u2212 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 u2 + v2 \u221a cos(\u03d5 + \u03b2 \u2212 \u03b8) + hx y\u0307e = \u2212 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 u2 + v2 \u221a sin(\u03d5 + \u03b2 \u2212 \u03b8) + hy hx = \u03b8\u0307(x sin \u03b8 \u2212 y cos \u03b8 \u2212 xd sin \u03b8 + yd cos \u03b8) + x\u0307d cos \u03b8 + y\u0307d sin \u03b8 hy = \u03b8\u0307(x cos \u03b8 + y sin \u03b8 \u2212 xd cos \u03b8 \u2212 yd sin \u03b8) \u2212 x\u0307d sin \u03b8 + y\u0307d cos \u03b8 (9) Finally, the virtual reference surge velocity ud and virtual reference heading \u03d5d will be designed by letting \u1e8be = -kx1tanh (kx2xe) and \u1e8fe = -ky1tanh (ky2ye) \u23a7 \u23aa\u23a8 \u23aa\u23a9 ud = \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 ( kx1 tanh(kx2xe) + hx cos(\u03d5 + \u03b2 \u2212 \u03b8) )2 \u2212 v2 \u221a \u03d5d = arcsin (( ky1 tanh ( ky2ye ) + hy )/ \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 u2 + v2 \u221a + \u03b8 \u2212 \u03b2 ) (10) where, the positive parameters kx1 and ky1 are used to adjust the ranges of ud and \u03d5d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003764_j.addma.2021.102070-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003764_j.addma.2021.102070-Figure2-1.png",
        "caption": "Fig. 2. Manufacturing strategy (a) and build orientation (b) of the DIN 50125 sample.",
        "texts": [
            " The main goals of the strategy are to: \u201cbreak\u201d the columnar grains and minimize the anisotropy of the material (rotation of the scan vectors by 67\u25e6), reduce the residual stresses (short hatch vectors \u2013 7 mm stripes) and surface roughness control (by directing the spatter and fumes to the areas that have already been scanned \u2013 scan vector rotation limitation window). The manufacturing is as follows: (1) depositing a thin layer of IN718 powder with a roller, (2) melting the IN718 powder with the laser beam in accordance with the shape of the layer, (3) shifting the manufacturing plate down by the thickness of one layer for a new deposit of powder and its melting. The process is repeated until the finished elements are produced (Fig. 2a). The samples were manufactured in the form of cylinders with a diameter of 9 mm and a height of 82 mm (Fig. 2b) in three orientations relative to the working platform: vertically (V), diagonally at an angle of 45\u25e6 (D), and horizontally (H). In total, 6 samples were produced from each test series as part of one production process. After manufacturing, a three-stage heat treatment was applied, which included stress relief annealing before cutting the samples from the build platform and subsequent solution annealing and double aging according to ASTM F3055\u201314a (Table 3). Tensile specimens (Fig. 2c) were machined from prefabricated cylinders in accordance with the DIN 50125 standard. A standard procedure for microstructure observation was used to examine the material properties of the IN718. Examinations were carried out on longitudinal polished sections of the control specimens. The specimens were etched with 87 Glyceregia (ASTM E 407, 3:2:1 \u2013 HCl, Glycerol and HNO3). The etchant was used fresh a maximum of 15 min after preparation. The Olympus LEXT OLS4000 optical microscope (OM) Table 1 Chemical composition of the IN718 powder used in the study according to the ASTM B637 standard (wt%)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.103-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.103-1.png",
        "caption": "Fig. 2.103 Principle layout of the HF transmission arrangement for The HF DBW AWD propulsion mechatronic control system [Valentin Technologies Inc. (USA)].",
        "texts": [
            " The infinite adjustability of the wheel-hub F-M motors is mechatronically controlled by the E-TMC ECU or CPC, giving the HF transmission a variety of additional functions, such as Anti-locking brake system (ABS); Anti-slip brake system; DBW AWD propulsion mechatronic control system; Locked M-M or F-M differentials. The fluidostatic principle allows additional features that further improve the functionality and use of energy: constant or variable velocity drive for auxiliary power units as needed, for example, M-E generator, M-F pumps, and comfort fluidics, namely, active suspension, park-automatic, and so on, as shown in Figure 2.103 [VALENTIN TECHNOLOGIES INC., USA]. Automotive Mechatronics 280 The mass distribution for the passenger vehicle is assumed to be 50 : 50% under static and 75 : 25% under maximum dynamic (braking) conditions. The size of the in-wheel-hub F-M motors is based on the maximum torque requirements under dynamic conditions such as braking under full load. The maximum value of fluidic pressure of the fluidostatic circuit is 41 MPa (6,000 psi). The size of the M-F pump on the ECE or ICE is based on the use of nearly full ECE or ICE power at constant velocity of 403 rad/s (3,850 rpm) and a fluidostatic circuit pressure of 17 MPa (2,500 psi)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure6.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure6.2-1.png",
        "caption": "Fig. 6.2 Sketch of the gyroscope test stand",
        "texts": [
            "5) where \u03c9y is the angular velocity of the gyroscope around axis oy and other components are as specified above. (c) The centrifugal force of the rotating gyroscope centremass around axis ox acting along the gyroscope axle (Fig. 6.3) Fz.ct.x = Ml\u03c92 x (6.6) where \u03c9x is the angular velocity of the gyroscope around axis. (d) The frictional torques acting on the supports B and D are represented by the following equation: T f.x = T f.x .E .x + T f.x .cr.y + +T f.z.ct.x + T f.x .ct.y (6.7) where: (e) The frictional torque acting on the supports B and D (Fig. 6.2) in the clockwise direction around axis oy generated by the centrifugal force of the rotating gyroscope centre mass around axis oy: T f.x .ct.y = Ml cos \u03b3\u03c92 y ( d f 2 cos \u03b4 ) (6.8) where d is the diameter of the centre beam; f is the frictional sliding coefficient; \u03b4 = 45o is the angle of the cone of sliding bearing of the supports (Fig. 6.2), and other components are as specified above. (f) The frictional torque acting on the supports B and D in the clockwise direction around axis ox generated by the centrifugal force of the rotating gyroscope centre mass around axis ox: T f.x .ct.x = Ml\u03c92 x ( d f 2 cos \u03b4 ) (6.9) where all components are as specified above. (g) The frictional torque acting on the supports B and D in the clockwise direction around axis ox generated by the Coriolis force of the rotating gyroscope centre mass around axes oy and ox: T f.x .cr.y = Ml\u03c9y\u03c9x sin \u03b3 [ l h d f 2 cos(\u03b4 \u2212 \u03c4) ] (6.10) where h = 56.925 mm is the distance between the centre of the gyroscope and the support (Fig. 6.2); \u03c4 = arctan[l/(c/2)]= 38.581o is the angle of the action of Coriolis force on the sliding bearing, and other components are as specified above. (h) The frictional torque acting on the sliding bearing of the supports B and D in the clockwise direction around axis ox generated by the gyroscope weight with the centre beam E: T f.x .E .x = (Eg sin \u03b3 + Ml\u03c92 x) d f 2 cos \u03b4 (6.11) (i) where E is the mass of the gyroscope with the centre beam (Table 6.1), Fy.ct.x = Ml\u03c92 x is the centrifugal force of the rotating gyroscope centre mass around axis ox acting along axis oy (Fig",
            "x = Eg sin \u03b3 d f 2 cos \u03b4 + Ml\u03c92 x d f 2 cos \u03b4 + Ml\u03c9y\u03c9x (sin \u03b3 ) l h d f 2 cos(\u03b4 \u2212 \u03c4) + Ml\u03c92 y cos \u03b3 d f 2 cos \u03b4 (6.12) The torque generated by Coriolis force of the rotating gyroscope centre mass around axes oy and ox and acting in the clockwise direction around axis oy: Ty.cr.y = (Ml\u03c9y sin \u03b3 )(\u03c9x l sin \u03b3 ) = M\u03c9y\u03c9x (l sin \u03b3 )2 (6.13) where all components are as specified above. The frictional torques acting on the pivot C are represented by the following equation: T f.y = T f.y.F.y + T f.y.cr.y + T f.y.ct.y + T f.y.ct.x (6.14) where: (j) The frictional torque acting on the pivot C (Fig. 6.2) in the clockwise direction generated by the centrifugal force of the rotating gyroscope centre mass around axis oy: T f.y.ct.y = Ml\u03c92 y cos \u03b3 ( dc fc 2 ) (6.15) where dc is the diameter of the pivot; f c is the frictional sliding coefficient, and other components are as specified above. (k) The frictional torque acting on the pivot C in the clockwise direction around axis oy generated by the centrifugal force of the rotating gyroscope centre mass around axis ox and acting along axis oz: T f.z.ct",
            "26)) is substituted into Eq. (6.24), and transformation yields the following: JEy d\u03c9y dt = 8 9 ( 4\u03c02 + 17 ) J\u03c9\u03c9x \u2212 Ag ( de + dc 4 ) fc \u2212 Ml\u03c92 x dc fc 2 \u2212 Ml\u03c92 y dc fc 2 \u2212 8 9 J\u03c9\u03c9y (6.27) where \u03c9x is represented by Eq. (6.25), other components are as specified above. Equation (6.27) can be used for the direct computing of the angular velocity of the gyroscope motion around axis oy. Themathematicalmodel formotions of the gyroscopewith the action of the frictional torques is considered on the test stand (Fig. 6.2). The practice tests conducted for the horizontal location of the gyroscope spinning axle. The coefficients of the sliding friction of supports and pivots defined empirically f = 0.1, f c = 0.3. The speed of the gyroscope\u2019s rotor for the tests is accepted 10,000 rpm. The velocity of the spinning rotor measured by the Optical Multimeter Tachoprobe Model 2108/LSR Compact Instrument Ltd. with a range of measurement 0 \u2026 60,000.00 rpm. The spinning rotor demonstrated the permanent drop of 67 revolutions per second",
            " The measurements of the angular location for the gyroscope axlewere conducted optically by the angular template with accuracy \u00b11.0\u00b0. The time of the gyroscope motions around axesmeasured by the stopwatch ofModel SKUSW01with resolution 1/100 s. The results of practical tests are represented by the following average data. The time spent on one revolution around axis oy is ty = 3.86 s, and then, the angular velocity is \u03c9y= 360\u00b0/3.86 s = 93.860\u00b0/s. The time spent on the gyroscope turn of angular velocity is \u03c9y = 20\u00b0/13.9 s = 1.43\u00b0/s. The numerical solution of the case study. The gyroscope parameters (Table 6.1, Fig. 6.2) and Eq. (4.6), Chap. 4 are substituted into Eq. (6.23), and transformation yields the following equation of the gyroscope motion around axis ox. JEx d\u03c9x dt = Mgl + Ag9 ( 4\u03c02 + 17 2\u03c02 + 9 )( de + dc 4 ) fc \u2212 ( 38\u03c02 + 161 9 ) J\u03c9\u03c9x + [ 9 ( 4\u03c02 + 17 2\u03c02 + 9 ) dc fc \u2212 d f cos \u03b4 ][ 1 + (4\u03c02 + 17)2 2 ] Ml\u03c92 x 2.286976 \u00d7 10\u22124 d\u03c9x dt = 0.146 \u00d7 9.81 \u00d7 0.0355 + 0.259 \u00d7 9.81 \u00d7 9 \u00d7 ( 4\u03c02 + 17 2\u03c02 + 9 )( 0.012 + 0.006 4 ) \u00d7 0.3 \u2212 ( 38\u03c02 + 161 9 ) \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10000 \u00d7 (2\u03c0/60)\u03c9x \u2212 [ 9 ( 4\u03c02 + 17 2\u03c02 + 9 ) \u00d7 0",
            "33) gives the equations of the angular velocity for the gyroscope around axis ox and oy as the result of the action of the gyroscope weight and the frictional torques. \u03c9x = 0.031114426 rad/s = 1.782725291\u25e6/s (6.34) \u03c9y = (4\u03c02 + 17) \u00d7 0.031114426 rad/s = 100.685503501\u25e6/s (6.35) The time of one revolution around axis oy is t = 360\u25e6/\u03c9y = 360\u25e6/100.685503501\u25e6/s = 3.575s (6.36) The angular velocity of the precession around axis oy can be defined by Eq. (6.27). Numerical solution of Eq. (6.27) is similar as for Eq. (6.23), and all comments are omitted. Substituting initial data (Table 6.1, Fig. 6.2) and Eq. (6.25) into Eq. (6.27) yields the following differential equation: JEy d\u03c9y dt = 8 9 ( 4\u03c02 + 17 ) J\u03c9\u03c9x \u2212 Ag ( de + dc 4 ) fc \u2212 Ml\u03c92 x dc fc 2 \u2212 Ml\u03c92 y dc fc 2 \u2212 8 9 J\u03c9\u03c9y (6.37) where \u03c9x is computed by Eq. (6.25) 120 6 Mathematical Models for Motions of a Gyroscope \u2026 \u03c9x = ( 38\u03c02+161 9 ) \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10000 \u00d7 (2\u03c0/60) 2 [ 9 ( 4\u03c02+17 2\u03c02+9 ) 0.006\u00d70.3 2 \u2212 0.00424\u00d70.1 2 cos \u03b4 ] [1 + (4\u03c02 + 17)2] \u00d7 0.146 \u00d7 0.0355 \u2212 \u221a\u221a \u221a\u221a \u221a \u23a7 \u23a8 \u23a9 ( 38\u03c02+161 9 ) \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10000 \u00d7 (2\u03c0/60) 2 [ 9 ( 4\u03c02+17 2\u03c02+9 ) 0",
            "52) is removed because themodified precession torque Tp.y contains it, other components are as specified above. The gyroscope with one side support and horizontal location (\u03b3 = 0\u00b0) turns under the action of the two external torques Ty and T, which act around axes oy and ox, respectively. The value of the first torque Ty is half of the value of torque T (i.e. Ty=0.05 Wgl). The actions of the torques and motions are presented in Fig. 6.4. The technical data related to the gyroscope are presented in Table 6.1 and Fig. 6.2. The angular velocity of the sinning rotor is 10,000 rpm. All Eqs. (6.52)\u2013(6.55) are modified because \u03b3 = 0\u00b0. Equation (6.55) expresses the gyroscope motion around axis ox. Substituting the initial data of the gyroscope (Table 6.1) into Eq. (6.55) for horizontal location of the gyroscope yields the following equation: 3.38437 \u00d7 10\u22124 d\u03c9x dt = \u22128 ( 4\u03c02 + 17 38\u03c02 + 161 ) [ 0.05 + 9 \u00d7 ( 4\u03c02 + 17 2\u03c02 + 9 ) \u00d7 0.146 \u00d7 9.81 \u00d7 0.0355 ] + ( 8 9 ) \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10000 \u00d7 (2\u03c0/60)\u03c9x (6.56) Equation (6.56) is simplified and yields the following: 0",
            "66) Jx d\u03c9x dt = 8 ( 4\u03c02 + 17 38\u03c02 + 161 )[ Ty \u2212 9 ( 4\u03c02 + 17 2\u03c02 + 9 ) Mgl ] \u2212 ( 8 9 ) J\u03c9\u03c9x (6.67) where the torque of the gyroscope weight (Eq. 6.64) is removed because themodified precession torque Tp.y contains it, other components are as specified above. Equation (6.65) can be used for the direct computing of the angular velocity of the gyroscope motion down around axis ox. The motions of the gyroscope with one side support are conducted under the clockwise action of the load torqueTy around axisoy. The sketch of the action of the torques and motions is represented in Fig. 6.2. Equation (6.67) represents the gyroscope motion around axis oy. The angular velocities of precessions around two axes should be defined. Substituting the initial data of the gyroscope represented in Sect. 6.3.1.1 into Eq. (6.67) and making transformations yields the following equation: 3.38437 \u00d7 10\u22124 d\u03c9x dt = 8 ( 4\u03c02 + 17 38\u03c02 + 161 ) [ 0.05 \u2212 9(4\u03c02 + 17) 2\u03c02 + 9 \u00d7 0.146 \u00d7 9.81 \u00d7 0.0355 ] \u2212 ( 8 9 ) \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10000 \u00d7 (2\u03c0/60)\u03c9y (6.68) Equation (6.68) is simplified. Then, the steps of solutions similar to the steps presented in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001264_we.1530-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001264_we.1530-Figure12-1.png",
        "caption": "Figure 12. Result comparison among models. FR\u2013M plane.",
        "texts": [],
        "surrounding_texts": [
            "This work presents a theoretical method to arrange the general static load capacity of four contact-point slewing bearings, which takes into account the load-dependent contact angle variability in the ball\u2013raceway contacts. Wind Energ. (2012) \u00a9 2012 John Wiley & Sons, Ltd. DOI: 10.1002/we The method is a further step of previous work published by the authors, where the contact angle was assumed to be constant.3 The results of the present method (variable contact angle) and the ones of the previous method (constant contact angle) have been compared with the results provided by an FE model developed by the authors in another work,11 and it has been proven that the new model presented in this work is more realistic. It is also pointed out that the stiffness of the rings plays an important role in the static load-carrying capacity of the bearings, but it has been verified that the method leads to conservative results. Besides, several normalized curves for different combinations of the osculation ratio s and the initial contact angle \u02db0 are also provided. The authors believe that the acceptance curves derived from this work can be used for the initial selection of yaw and blade bearings at the initial stage of the design of WTGs."
        ]
    },
    {
        "image_filename": "designv10_12_0003006_j.ijfatigue.2020.105483-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003006_j.ijfatigue.2020.105483-Figure1-1.png",
        "caption": "Fig. 1. Qualitative dependence of roughness on surface inclination [29].",
        "texts": [
            " The magnitude of the surface roughness is dependent on melting energy, powder size distribution, the thickness of each built layer [1,2]. Layer thickness selection depends on the machine capability. On the other hand, discrete layer thickness and build direction have an effect on sloped or freeform features of the part [27,28]. PBF-process-dependent factors affecting the final surface quality of a curved surface are therefore introduced here with the dual aim of (i) defining an interpretative framework of the notch fatigue behavior and (ii) motivating the fatigue testing of directional specimens containing notches. Fig. 1 qualitatively shows the roughness variation in dependence of the flat surface orientation with respect to the build platform [29]. Two parameters, \u03b4 and \u03c5, are defined in Fig. 1 and used to characterize the surface orientation as either up-skin (i.e. 0 < \u03c5 < 90) or as down-skin (angle 0 < \u03b4 < 90). A vertical surface (i.e. \u03b4 = \u03c5 = 90\u00b0) has the lowest roughness. The roughness of a tilted surface is the result of two contributions the segmentation of the nominally flat surface layer-bylayer (i.e. also termed stair-case effect [28]) and the local solidification of the contour with adhesion occurring between loose and melted powder. Down-skin surfaces are considerably rougher than the up-skin counterparts due to the presence of dross [28]",
            " 2 is approximated by the actual stair-stepped profile due to segmentation. The stepped profile depends on the \u03bb/R ratio where \u03bb is the layer thickness and R is the radius of curvature. The stair stepping severity depends on the local position with respect to the build direction defined by angle \u03b8: the actual surface is markedly stair-stepped when \u03b8 is close to 0\u00b0 while it merges to the nominal geometry when \u03b8 is close to 90\u00b0. Surface orientation with respect to build. According to the previous definition of Fig. 1, the curved geometry of Fig. 2 is associated to the down-skin surface orientation. Therefore, in addition to the local severe stair stepping, dross formation is expected during PBF fabrication of the surface for \u2212 45\u00b0 < \u03b8 < 45\u00b0 because the metal powder does not support the melted layer during solidification. If the radius R is relatively large, support structures of the surface are required to guarantee an acceptable final geometry. The surface quality of the notch would be considerably different if the same geometry of Fig",
            " The images confirm the strong dependence of the surface quality on the fabrication parameters and notch orientation. Adherence to the nominal CAD geometry is clearly dependent on specimen type: Type B specimens reveal accurate semicircular and semi elliptical notches, respectively, while Type Aspecimens present large deviation of the actual notches from the design intent. Type C specimens show notches that are nonsymmetrical with respect to the notch center line as the left side was oriented up-skin and the right side oriented down- according to the definition of Fig. 1. Stresses used to plot the fatigue data were always calculated assuming the nominal minimum cross-section of the notched specimens, namely 5 \u00d7 5 mm2, and therefore a section modulus W = 20.8 mm3. Inspection of Fig. 11 shows that the majority of the notches confirm the nominal notch depth of 2 mm. The deviation of the actual notch geometry from the design intent is possibly critical only for the sharp notch of the Type A- specimens. Down-skin fabrication of the narrow semielliptical notches reduces considerably the actual maximum notch depth because of dross formation and lack of support of the melt pool by the powder below"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001861_s40516-016-0033-8-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001861_s40516-016-0033-8-Figure13-1.png",
        "caption": "Fig. 13 Future aims of the repair process at different areas of the turbine blade",
        "texts": [
            " 11c shows a homogeneous orientation since the misoriented area at the top of the clad is removed during post-processing. The cladding of notched substrates with and without preheating showed different results. The substrates on which cladding was performed without preheating showed cracks and pores on their surface, similar to the results shown in Fig. 8. Those substrates that were preheated showed a crack-free, directionally oriented surface. The result of a cladded notch is shown in Fig. 12 and the parameters of this process are listed in table 1 (Fig. 13). There are no macroscopic cracks visible on the surface (Fig. 12b) and the micrograph (Fig. 12c) and EBSD analysis (Fig. 12d) shows a mainly well-oriented clad. In the middle of the clad, the formation of grains is visible. This formation could be caused by an oxide on the surface before starting the cladding process. The rest of the clad shows a well oriented microstructure up to the top of the clad. The figures show that for notched substrates, a preheating of the substrate that allows for the directional solidification of the material in a crack-free manner"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001488_s00604-014-1444-x-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001488_s00604-014-1444-x-Figure1-1.png",
        "caption": "Fig. 1 Configuration of the disposable screen\u2212printed electrode device",
        "texts": [
            " Cyclic voltammetric experiments were carried out in quiescent solutions with a scan rate of 50 mV s\u22121. Fabrication of the screen\u2014printed working electrode CNTs were pretreated as described previously [22]. 1.5 mL cyclohexane, 1.0 mL acetone, 90 mg cellulose acetate (CA) and 150 mg CNTs were mixed adequately to prepare CNTs ink. The electrode strip designed presented was fabricated by thick-film technology [23]. A manual stainless-steel pattern (140\u00d7180 mm, 200 \u03bcm thick) was utilized to produce thickfilm electrodes. A group of 10 electrodes, each of them corresponding to the pattern shown in Fig. 1, was printed on a clear epoxy substrate (40\u00d7100 mm\u00d7500 \u03bcm) by forcing the CNTs ink to penetrate through the mask of screen stencil using a rubber squeegee. After each printing, the printed film was allowed to dry at 60 \u00b0C for 1 h. Once dry, the individual electrode was cut from the epoxy film to each electrode unit. The resulted electrode strips were stored in refrigeratory at 4 \u00b0C when not in use. Fabrication of disposable biosensor HRP was immobilized on SPCNTE based on the crosslinking reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001763_tmag.2013.2278837-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001763_tmag.2013.2278837-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the pump with a magnetic bearing: (a) basic configuration of the pump; (b) pump with magnetic bearings using a magnet array\u201414 magnet pieces are attached in a circular arrangement at the top and bottom of the pump; and (c) simulation result for the distribution of magnetic flux density on the single magnet array. White arrows denote the direction of magnetization.",
        "texts": [
            " In addition, the axial coupling had both nonstep and step-up speed control of the impeller, whereas the radial coupling allowed only the step-up speed control. Thus, the axial coupling exhibited higher controllability. We investigated magnetic properties of the magnetic bearing through simulation and experimental analysis. In addition, we verified the enhanced performance of the pump using the proposed mechanisms through the performance evaluation. 1) Structure and Property of Magnetic Bearings: We developed a magnetic bearing using a magnet array consisting of 14 permanent magnetic pieces in a circular arrangement, as shown in Fig. 1. Each single magnet in the bearing was a rectangular Nd-Fe-B magnet ( mm) and the magnet strength was 340 mT. The length and maximum outer diameter of the pump is 34 and 27 mm, respectively. Fig. 1(a) shows the basic configuration of the magnetic wireless pump. The fully magnetic impeller (FMI) consisted of two magnetic cylinder parts and five stages of blade parts. In addition, the FMI had a radial direction of magnetization and we used a magnetic impeller with two poles or four poles. Because of the radial magnetization of the magnetic impeller, the axial coupling force was lower than the radial coupling force. Thus, we considered magnetic bearing using the magnet array to improve the driving conditions. The positions of the two magnet arrays were equivalent to the sections of the two magnetic cylinders, as shown in Fig. 1(b). Furthermore, for the magnetic levitation of the FMI, the magnetic poles of the arranged magnetic pieces at array_1 and array_2 were in the opposite direction. Then, a circular arrangement for the magnetic bearing generated a regular magnetic field inside the arrangement, as shown in Fig. 1(c). We investigated the basic magnetic properties of themagnetic bearing (array) through a magnetic simulation. Fig. 2 represents the distribution of the magnetic flux density in both the vertical and horizontal direction with an air-gap of 3.5 mm from one 0018-9464 \u00a9 2013 IEEE of the magnetic pieces because distance between FMI and the magnetic arrays is 3.5 mm. The vertical magnetic flux density from the center of the magnet surface to the air-gap of 3.5 mm was found to be from full 336 to 54"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002205_c6nr08255f-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002205_c6nr08255f-Figure5-1.png",
        "caption": "Fig. 5 Formation of wrinkles on air plasma oxidised/UVO oxidised PDMS bilayers. A neat PDMS specimen is pre-strained uniaxially by \u03b5 prestrain, then exposed to UVO for tUVO, leading to the formation of a layer with plane elastic modulus E\u0304 f 1 , followed by air plasma exposure for tplasma (MHz, p = 7.16W, P = 1mbar) resulting in the formation of a second layer with plane modulus E\u0304 f 2. Henceforth the strain is removed and sinusoidal wrinkling patterns with sub-100 nm \u03bb are observed.",
        "texts": [
            " Plasma oxidation results in the formation of a thinner, stiffer oxide layer compared to UVO, which leads to gradient layers 38. The differences in layer elastic moduli and thicknesses justify the different pattern dimensions attainable with the two processes. Encouraged by the \u03bbmin reduction afforded by the increase in E\u0304s, we explore whether the thick oxide layer resulting from UVO treatment, can serve as a substrate and be further oxidised via plasma treatment to obtain a trilayer on which wrinkling can be induced. The process is depicted in Figure 5. XRR experiments on PDMS treated with UVO followed by air plasma oxidation confirmed the formation of two layers, with mismatching SLDs, and hence mechanical properties, as shown in Figure 6. Since hplasma << hUVO << PDMS thickness, we expect wrin- kling at each interface to be decoupled. Under these circumstances, two critical strains can be defined, \u03b5c1 between PDMS and the UVO skin, and \u03b5c2 between the upper plasma skin and UVO layer. Upon strain relaxation, we expect wrinkling from the top bilayer alone provided that \u03b5c1 < \u03b5prestrain < \u03b5c2, with \u03b5c1 = 1 4 ( 3E\u0304PDMS E\u0304 f 1 ) 2 3 (6) \u03b5c2 = 1 4 ( 3E\u0304 f 1 E\u0304 f 2 ) 2 3 (7) with no wrinkling arising from the intermediate UVO layer and PDMS substrate",
            " X-ray and neutron reflectivity experiments on oxidised PDMS provided insight into the mechanism of film for- Journal Name, [year], [vol.], 1\u20138 | 5 N an os ca le A cc ep te d M an us cr ip t Pu bl is he d on 1 3 Ja nu ar y 20 17 . D ow nl oa de d by U ni ve rs ity o f N ew ca st le o n 14 /0 1/ 20 17 0 8: 43 :2 9. Fig. 6 a) XRR measurements on PDMS specimens treated with subsequent UVO (tUVO = 3600 s) and air plasma oxidation (tplasma = 1800 s, P = 1 mbar, p = 7.16 W) according to the process in Figure 5. Normalised scattered intensity is plotted as a function of Q. Both experimental data (scatter) and the corresponding fitting (black line, resulting from the assumption of a bilayer model) using RasCal are presented. b) XRR scattering length density profiles obtained from the reflectivity curves fitting. Two distinct layers could be identified, of thicknesses hUVO and hplasma, resulting from the subsequent oxidative processes. mation and densification. Analyses of scattering length density (SLD) profiles confirmed the existence of a critical exposure time tc that must be overcome in order to yield glassy films with sufficient conversion, guaranteeing the modulus mismatch required for wrinkling (at finite \u03b5)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001278_j.engfailanal.2013.02.030-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001278_j.engfailanal.2013.02.030-Figure4-1.png",
        "caption": "Fig. 4. \u00bd Symmetry FEM-model of a three-row roller slewing bearing: external loads, support and couplings (a), detail of the bearing FEM-model with visible mesh and 1D connectors (b).",
        "texts": [
            " frame structures [8,18]) or/and the companion structure with some initial deflection which can result an initial deformation of the bearing ring when mounted. Therefore, slewing bearing manufacturers prescribe allowable mounting structure deviations and required stiffness [18]. Furthermore, as a result of manufacturing process and mounting, an unwanted clearance can be present in slewing bearings. All these factors can influence the internal contact force distribution and are the object of the presented study. In presented study a simplified \u00bd symmetry 3D FEM-model of the whole three-row roller slewing bearing is generated (Fig. 4a). As the numerical model of the bearing consists of a large number of features (geometrical sections, sets, surfaces and connectors), manual creation of all these would be cumbersome. Because of that, the Abaqus software\u2019s scripting language Python [19] is employed in order to automatize this procedure. Both, the inner and the outer ring (Fig. 4b), are meshed using 8-node linear brick elements (C3D8, full integration), with consideration of elastic material properties of steel 42CrMo4. The outer ring of the analysed bearing is considered fixed and it is resting on a number of independent supports, that can be individually modified, by which different ring support deformation can be applied. The translation/rotation of the inner (movable) ring is governed by a reference point, which is coupled (constrained degrees of freedom) with the mounting plane of the inner ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000372_s12206-008-0427-4-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000372_s12206-008-0427-4-Figure9-1.png",
        "caption": "Fig. 9. Ultra light-weight Amtec arm, a seven degree of freedom arm and its kinematics structure.",
        "texts": [
            " Although the initial configuration of robot is close to a singularity, our method still guarantees the quality of damped and keeps the error minimum. The smooth transition of error velocity of our approach is shown in Fig. 7. The algorithm also shows a good performance in keeping small Cartesian error due to DLS as shown in Fig. 8. Our algorithm is also applied to a redundant robot, ultra light-weight Amtec, a seven degree of freedom manipulator which has a kinematic structure like the human arm. The manipulator and its kinematic structure are given in Fig. 9 and its Denavit Hartenberg is given in Table 3. The genetic algorithm in this case also uses parameters given in table 1. The maximum end effector translational velocities and rotational velocities are set 28 cm and 16 degrees per second respectively. Maximum allowable velocity in this redundant case is set at 0.6 rad/s. Trajectory 1: In Fig. 10, manipulator encounters both a singularity in the second joint and wrist singularity around step 40. The init ial configurat ion (0 0.349 0 1.396 0 0.96 0)T initialq = \u2212 and final configuration (0 / 6 0 / 2 0 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.11-1.png",
        "caption": "Figure 7.11. Satellite motion under a central force, and the orbital area swept out by the radius vector in an infinitesimal time.",
        "texts": [
            "71), valid for all time in the motion , differs from our earlier conservation rule (7.20) for a system of two particles whose moment of momentum is constant only during the impulsive instant. A classical application of our conservation law follows . Example 7.11. Central Force Motion and Kepler's Second Law.A force directed invariably along a line through a fixed point is called a central force. A familiar example of a central force is the tension in a pendulum string; another is the gravitational force exerted by the Earth on a satellite shown in Fig. 7.11. Derive Kepler's second law: Aparticle inmotionunderacentralforce alonemustmove in aplane; and if its path is not a straightline throughthefixed centralpointO, itsposition vectorfrom thefixed point sweepsout equal areas in equal intervalsoftime. Solution. Consider a central force F directed through the fixed origin 0 of an inertial frame <p = (0 ; ek) in Fig. 7.11. Then the moment of F about 0 is zero: M o = x x F = 0, wherein x = re. : and the moment of momentum principle (6.79) shows that the moment of momentum about 0 is a constant vector : ho = x x mv, a constant. (7.72a) It follows that ho =0 if and only if the position vector x is parallel to the velocity: v = kx, where k is a constant. In this instance the motion x(t)= xoekt , with Xo = x(O) initially, is along a straight line through O. Otherwise, when 252 Chapter 7 (7 .72b) ho =j:. 0, both X and v are always perpendicular to the constant vector ho, and hence the particle must move in a plane whose vector equation is (7",
            " This has the geometrical interpretation that the radius vector of P sweeps out the same area in equal time intervals, the second of three laws deduced empirically by the German astronomer and mathematician Johannes Kepler (1571-1630) based on preciseastronomicalobservationsof thepositionsofstarsandplanetsby theDanish astronomer TychoBrahe (1546-1601), Kepler's mentor. More than half a century later, Kepler's lawswere deduced by Newton (1642-1727) from his mathematical theory of planetary motion. Here we determine the motion of an orbital body, characterize its path, and derive Kepler's first and third laws of planetary motion. 7.12.1. Equation of the Path We introduce cylindrical coordinates identified in Fig. 7.11, page 252, with origin at 0 in the inertial frame qJ = {O; e., e\",} and with respect to which the polar coordinate equation of the path of a particle P is described by r = r(\u00a2). The only force acting on P is the conservativegravitationalforce with potential energy given in (7.62). The constant Va = 0 may be chosen so that V -+ 0 when r -+ 00, and hence V = - um / r, where the constant /l == GM. The kinetic energy of P is given by K = ~m(r2 + r 2\u00a2 2). The energy principle together with (7.72b) yields "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.14-1.png",
        "caption": "Fig. 3.14 Parallel screw axes n1 = n2 ; \u03d52 = \u2212\u03d51 (a) and \u03d52 = \u2212\u03d51 (b)",
        "texts": [
            " This general case is considered first. Equations (3.108) \u2013 (3.112) reduce to \u03d5res = \u03d51 + \u03d52 = 0 , sres = s1 + s2 , nres = n1 = n2 , (3.126) u sin \u03d51 + \u03d52 2 = ( e2 sin \u03d51 2 sin \u03d52 2 \u2212 e3 1 2 sin \u03d51 \u2212 \u03d52 2 ) . (3.127) The last equation is rewritten in the form 118 3 Finite Screw Displacement 2 e3 + u = ( e2 sin \u03d51 2 + e3 cos \u03d51 2 ) sin \u03d52 2 sin \u03d51+\u03d52 2 . (3.128) This equation proves that the parallel screw axes n1 , n2 and nres , seen in projection along the axes, form the triangle (P1,P2,P3) shown in Fig. 3.14a . It has internal angles \u03d51/2 and \u03d52/2 at P1 and P2 , respectively, and the external angle \u03d5res/2 at P3 . The vector ( /2)e3 + u is \u2212\u2212\u2212\u2192 P1P3 , and (e2 sin \u03d51 2 + e3 cos \u03d51 2 ) is the unit vector in the direction of \u2212\u2212\u2212\u2192 P1P3 . The equation expresses the sine law in the triangle. In the special case \u03d52 = \u2212\u03d51 , (3.108) yields \u03d5res = 0 . This indicates that the resultant of the two screw displacements is a translation. No further information is obtained from (3.109) \u2013 (3.112). Both magnitude and direction of the translation are obtained from Fig. 3.7. In the case of parallel screw axes n1 = n2 and with \u03d52 = \u2212\u03d51 , the lines g2 and g3 are parallel. In Fig. 3.14b the screw axes and the lines are shown in projection along the axes as in Fig. 3.14a . The component (s1+s2)e1 of the displacement is normal to the plane. The in-plane component is illustrated by the displacement of the point which prior to the first screw displacement is located at A . It is displaced via B to C . The total translatory displacement vector is sres = (s1+s2)e1+ \u2212\u2192 AC = (s1+s2)e1+ [\u2212 sin\u03d51 e2+(1\u2212cos\u03d51)e3] . (3.129) Equations (3.126) \u2013 (3.129) remain valid in the case s1 = s2 = 0 . In this case, the equations determine the resultant of two rotations about parallel axes",
            "173) These equations show that the resultant screw axis has the direction of n1 , and that it intersects the e3-axis orthogonally at the point u = \u03bc sin\u03b1 . Special case \u03b1 = 0 (parallel screw axes) and \u03d52 = \u2212\u03d51 : Equations (3.126) become (with a Taylor series expansion for u ) \u03d5 = \u03d51 + \u03d52 = 0 , p = p1 + p2 , n = n1 = n2 , u = \u2212e3 2 \u03d51 \u2212 \u03d52 \u03d51 + \u03d52 . \u23ab\u23ac \u23ad (3.174) This means that the resultant screw axis intersects the e3-axis orthogonally at a point u which depends on the ratio \u03d52/\u03d51 . The points P1 , P2 and P3 in Fig. 3.14a are collinear. Special case \u03b1 = 0 (parallel screw axes) and \u03d52 = \u2212\u03d51 : According to (3.129) the resultant displacement is a pure translation s . With s1 = p1\u03d51 and s2 = p2\u03d52 = \u2212p2\u03d51 it is s = [(p1 \u2212 p2)e1 \u2212 e2]\u03d51 . (3.175) This displacement is normal to e3 . In Fig. 3.17 two skew lines are defined by their unit line vectors r\u03021 and r\u03022 . The line vector r\u03022 is produced from r\u03021 by the screw displacement (n\u03023, \u03b1\u0302) with the dual unit vector n\u03023 along the common perpendicular and with the dual screw angle \u03b1\u0302 = \u03b1+\u03b5 between the two lines",
            "23) yields the relationship between the final position z\u2032 and the initial position z in the form 424 14 Displacements in a Plane z\u2032 = p2 + w2[p1 + w1(z \u2212 p1)\u2212 p2] , wi = ei\u03d5i (i = 1, 2) . (14.39) In the special case \u03d52 = \u2212\u03d51 , which means w1w2 = 1 , the resultant is a translation, because the equation then reads z\u2032 = z + t with t = (1\u2212w2)(p2 \u2212 p1) = (1\u2212 cos\u03d51 + i sin\u03d51)(p2 \u2212 p1) . (14.40) This is, with a different notation, the special case s1 = s2 = 0 of (3.129). The translation t is the complex number equivalent to the vector \u2212\u2192 AC in Fig. 3.14b . In the general case \u03d52 = \u2212\u03d51 , the resultant C2C1 is a rotation. Equation (14.39) has the form z\u2032 = p+ w1w2(z \u2212 p) with p = p1 + (p2 \u2212 p1) 1\u2212 w2 1\u2212 w1w2 . (14.41) The factor w2w1 shows that the angle of the resultant rotation is \u03d5res = \u03d51 + \u03d52 . (14.42) From the formula for p and from (14.26) it follows that p\u2212 p1 = (p2 \u2212 p1) exp ( \u2212 i \u03d51 2 ) sin \u03d52 2 sin \u03d51+\u03d52 2 . (14.43) Except for differences of notation, the last two equations are identical with (3.126) and (3.128). The geometrical interpretation was given in Fig. 3.14a . The poles identified by p1 , p2 and p define a triangle (P1,P2,P3) with internal angles \u03d51/2 and \u03d52/2 at P1 and P2 , respectively, and with the external angle \u03d5res/2 at P3 . Equations (14.39) and (14.43) show that the resultant displacement C2C1 is commutative only in the case when the poles P1 and P2 coincide. Table 14.1 summarizes the commutativity conditions found for the various resultant displacements. The resultant T2T1 is the only resultant which is unconditionally commutative, and reflection is the only displacement which can be commutative in the product with all three elementary displacements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001470_0016-0032(65)90310-8-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001470_0016-0032(65)90310-8-Figure7-1.png",
        "caption": "FIG. 7. Misalignment of rotation",
        "texts": [
            " (13) The subscript m Stands for the indicated value of the accelerometers. Comparing Eq. 13 to Eq. 11 the error is only in the measured linear accelerations A,~. The data obtained on angular velocities remains unchanged. R o t a t i o n Axes off the Disc Misa l igned w i t h the Vehicular Axes The rotation axes of the discs make small angles A0~ with the vehicular axes V~. The projections of the angular velocity vectors ~/ on the VjVk planes make angles of ~b~ with the vehicular axes Vi. A one dimensional model is presented in Fig. 7. Assuming that the accelerometers arc aligned with the rotation axes of the discs, the accelerometer measurements are oh- Fro. 6. Displacement of the center of rotation of disc. axis of disc. 3 1 2 Journal of The Franklin I n s t i t u t e ruined from a knowledge of the accelerations of the points L~. By making small angle approximations for 50~, the following vector equations can be written for ~ /and i~: ~Il~ ___= o~/~l,~ + lij~v~'~JAO~ cos ~ b ~ j + likL.k + oJyA0i sin \u00a2i~k} ( i j k ) = (123), (231), (312)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001209_imece2012-86513-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001209_imece2012-86513-Figure5-1.png",
        "caption": "FIGURE 5. SCHEMA OF CALCULATION OF TOOTH FORM FACTOR.",
        "texts": [
            " The bending stress has hence been determined by means of Equation 3, obtained adapting the ISO formula of the nominal tooth root stress (\u03c3F0) (defined in Clause 5.2.2 of [7]). Method B (described in [7]) has been adopted to determine the relevant factors. The nominal stress can be determined by means of Equation 3, since Y\u03b2 (helix angle factor), YB (rim thickness factor) and YDT (deep tooth factor) are all equal to one. The tooth form factor and stress correction factor have been determined applying the load at its actual radius (RR or RL). The geometric entities corresponding to the symbols are shown in Figure 5. Load (F) is normal to tooth flank and it is applied at radius RL or RR (determined by means of Equations 2), depending on the considered tooth. Table 2 lists the values of these parameters for each specimen family. \u03c3F0 = Ft b \u00b7m \u00b7YF \u00b7YS (3) 4 Copyright c\u20dd 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 10001-A 10002-E High 10002-E Low hF [mm] 10.811 11.006 8.054 lx [mm] 9.886 10.049 7.522 \u03b1Fen [deg] 23"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002789_tec.2019.2898640-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002789_tec.2019.2898640-Figure8-1.png",
        "caption": "Fig. 8. Distribution of the rotor ohmic-loss density. (a) Machine A at t1. (b) Machine B at t2. (c) Machine C at t3 at 50 kr/min calculated by FEM.",
        "texts": [
            "html for more information. > IEEE PES Transactions on Energy Conversion< 7 are compared. According to the parameters of Table I and the winding arrangements of Fig. 4, the 2D finite element model is established. The time-varying phase currents shown in Fig. 5 are injected into the windings and the rotors are set to rotate synchronously with respect to the fundamental MMF in which k = 1 and v = 1. Meanwhile, the magnets are not magnetized. Therefore, the harmonic eddy-current losses can be calculated. Fig. 8 presents the distribution of the ohmic-loss densities of the machines at the time instants of t1, t2 and t3, respectively. At these time instants indicated in Fig. 5, the currents change abruptly, causing large ohmic-losses in the rotors. It can be observed from Fig. 8 that the area with high ohmic-loss density in the rotor of machine B is greatly reduced compared with machine A or machine C. Fig. 9 depicts the comparison of the harmonic eddy-current losses of the sleeves and the magnets of the three machines at the speed of 50 000 r/min, as well as the total harmonic eddy-current losses. It can be observed that the harmonic eddy-current losses from the analytical method agree closely with those obtained from FEM. The total harmonic eddy-current loss of machine B at 50 000 r/min calculated by using the analytical method is 55"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003780_j.jmrt.2021.05.039-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003780_j.jmrt.2021.05.039-Figure2-1.png",
        "caption": "Fig. 2 e (a) Schematic of laser metal deposition using a coaxial powder feeder and (b) scanning procedure for the repair.",
        "texts": [
            " Both the heat treatments were conducted with the rate of temperature increase of 15 C/min. For the SA, the sample wasmaintained at 1040 C for 1 h, which was followed by quenching using a nitrogen-gas. Meanwhile, for the PH, the sample was maintained at 480 C for 4 h followed by aircooling. The equipment used for heat treatment was Retort furnace NRA 25/09 (Nabertherm Co., Germany). Hereinafter, the solution-annealed sample is referred to as the \u201cSA sample,\u201d and the sample subjected to SA followed by PH heat treatment is referred to as the \u201cSA \u00fe PH sample.\u201d The diagram in Fig. 2.(a) introduces the principles of the DED process. A high-power laser beam irradiates the powder as it is supplied to the substrate surface, and a melt pool forms. After the beam passes, the melt pool solidifies rapidly and forms a deposition bead. This process repeats until a layer of deposited material is formed. Figure 2.(b) shows the scanning procedure. To form each layer, deposition was first performed around the perimeter (\u201ccontour\u201d) of the area to be repaired. This was followed by deposition in the inner region (\u201cpocket\u201d) using a bidirectional deposition pattern, which enabled the beads to overlap by 0.5 mm. The deposition direction of each subsequent layer was transposed, and the process continued layer-by-layer until the repair was complete. In this study, a direct metal tooling (DMT) device (MX3, Insstek Co"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure23-1.png",
        "caption": "Fig. 23. Stress results of wheel 2 under the load applied at 0-deg.",
        "texts": [
            " A comparison of the operating stress in one cycle before and after the superposition of the residual stress is shown in Fig. 21. The corresponding fatigue life is estimated by Eq. (16), as shown in Table 7. The experimental fatigue life of this steel wheel on the fatigue test machine is 1.79 million revolutions and the cracking position is consistent with the simulation results, as shown in Fig. 22. The model of wheel 2 is 14 5 J with four bolt holes, and the stress distributions of wheel 2 is shown in Fig. 23 under the load applied at 0-deg, in which the dangerous area locates at the connecting position between the bolt hole and the strengthening rib, as shown in Fig. 24. One typical point in this position (Point C) is also selected to calculate the operating stress. A comparison of the operating stress before and after superposing the residual stress in one cycle is shown in Fig. 25, and the corresponding fatigue life of the wheel is estimated and shown in Table 8. The experimental fatigue life of this steel wheel on the fatigue test machine is 550,401 revolutions and the cracking position is also consistent with the simulation results, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002381_j.measurement.2015.12.006-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002381_j.measurement.2015.12.006-Figure4-1.png",
        "caption": "Fig. 4. Definition of pitch deviation of curve-face gear.",
        "texts": [
            " However, there isn\u2019t any special measuring instrument about the angular error detection. And the general measurement methods are meshing with standard gear or measuring its absolute coordinates by the coordinate measuring machine. Similarly, for curve-face gear there is no practical possibility for a reliable metrological traceability to national or international measurement standards can be provided. Thus, this paper defines that the pitch of curve-face gear is the arc length of the pitch curve between two adjacent corresponding flanks (see Fig. 4). These experiments use the contour scanning software of the German Klingelnberg P26 automatic CNC controlled gear measuring center to measure the coordinates of the gear pair (see Figs. 5 and 6). The main work flow is shown in Fig. 7. During the experiments, the following rules must be conformed 1. In order to avoid the probe intervenes with the under test or the adjacent flanks, the probe must be chosen appropriately, i.e. the intersection angle of the probe and the intersecting line which was formed of the tangent plane and pitch plane at the measuring point must be greater than zero, moreover, be small as far as possible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003640_j.mechmachtheory.2021.104532-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003640_j.mechmachtheory.2021.104532-Figure2-1.png",
        "caption": "Fig. 2. Body-fixed joint frames of the UPR and the RPS limbs.",
        "texts": [
            " Similarly, the joint twist screws of a RPS limb can be expressed as \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa\u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa\u23a9 $;ta,1,i = [ s1,i; rO\u2032 Ai \u00d7 s1,i ] $;ta,2,i = [ 03\u00d71; s2,i ] $;ta,3,i = [ s3,i; rO\u2032 Bi \u00d7 s3,i ] $;ta,4,i = [ s4,i; rO\u2032 Bi \u00d7 s4,i ] $;ta,5,i = [ s5,i; rO\u2032 Bi \u00d7 s5,i ] (i= 2, 4) (5) Thus, the constraint wrench and actuation wrench are derived as $\u0302;wc,i = [ s1,i; rO\u2032 Bi \u00d7 s1,i ] (i= 2, 4) (6) $\u0302;wa,i = [ s3,i; rO\u2032 Bi \u00d7 s3,i ] (i= 2, 4) (7) where $\u0302;wc,i denotes a constraint force limiting translation along s1,i; $\u0302;wa,i denotes an actuation force along s3,i (i = 2, 4). After the screw and wrench analysis of the limbs, it can be found that the four limbs produce 4 actuation wrenches and 6 constraint wrenches working on the moving platform. Based on the above kinematic formulation, the subsequent error modeling is conducted. For the convenience of error modeling, Fig. 2 shows all the body-fixed joint frames in the UPR and the RPS limbs, respectively. As shown in Fig. 2, Oj,i \u2212 xj,iyj,izj,i is defined as the body-fixed frame of the jth 1-DOF joint in the ith limb. Herein, zj,i axis coincides with the joint axis; xj,i axis coincides with the common normal of the zj,i axis and the zj+1,i axis; Oj,i is the intersection of zj,i axis and xj,i axis. In addition, yj,i axis is defined by the right hand rule. Specially, for each limb, the global frame O \u2212 xyz is viewed as the 0th joint frame; the body-fixed frame O\u2032 \u2212 uvw is viewed as the last joint frame; the point Ai coincides with O1,i; the point Bi coincides with O4,i(i= 1,3) or O5,i(i = 2,4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure7.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure7.4-1.png",
        "caption": "Fig. 7.4 Vectors u , a , v and ri locating the origin of basis e2 in e0",
        "texts": [
            "25) determine the sines and cosines of the variable angles \u03d51 and \u03d52 compiled in Table 7.1. End of example. Skew Joint Axes From the principle of transference it follows that the number of positions which can be prescribed for the terminal body of a chain with skew joint axes cannot be larger than for a chain with intersecting axes. Skew joint axes have a common perpendicular of length = 0 . This length and the angle \u03b1 are the Denavit-Hartenberg parameters of body 1 . The unit vector along the common perpendicular is called a (Fig 7.4). The origin 00 of e0 is no longer located on the axis of joint 1 nor is the origin 02 of e2 located on the axis of joint 2 . The origins are defined by the vector u from 00 to the foot P1 and by the vector v from the foot P2 of the common perpendicular to 02 . Furthermore, the bases e0 and e2 are fixed on their respective bodies such that they are aligned parallel in the position \u03c8 = \u03b8 = \u03d51 = \u03b1 = \u03d52 = 0 . As before, the basis vector e22 is aligned parallel to the axis of joint 2 , so that in position i the unit vector a has in e2 the coordinate matrix [ cos\u03d5i 2 0 sin\u03d5i 2 ) = [ ci2 0 si2 ] T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.59-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.59-1.png",
        "caption": "Fig. 3.59 Outlook of the exemplary EMB [PETERSEN 2003].",
        "texts": [
            " The pads are contained within a calliper, shown in Figure 3.57, as is the wheel brake actuator. Although not a high-gain type of friction EMBs, disc or ring EMBs have the advantage of providing relatively linear braking with lower susceptibility to fading than friction drum EMBs. The E-M actuator is a disk EMB working on the calliper-principle. The E-M actuator\u2019s housing is connected firmly to the vehicle\u2019s steering knuckle. Both brake pads are fixed to the fist with one degree of freedom towards the active line of the clamping force. Figure 3.59 shows an example of a prototype of an EMB and its mounting in the vehicle [PETERSEN 2003]. Figures 3.58a and 3.60 show a cross-section diagram of an example of a prototype of the EMB actuator E-M motor. The E-M actuator is a conventional rotary brushless DC-AC mechanocommutator brake-force-actuator motor. The rotor gear forms the sun wheel of the planetary gear at the pad-sided end. The planet wheels of the planetary gear are in mesh with the internal-geared wheel, bolted in the brake cabinet, and power the planet carrier",
            " Integral to the drum EMB is a rotating brushed DC-AC mechanocommutator electromagnetically-excited brake-force-actuator motor, gear train, and ball screw/nut mechanism [CHEW 1996] or a short-stroke linear tubular brushless DC-AC macrocommutator IPM magnetoelectrically-excited brake-forceactuator motor only [FIJALKOWSKI AND KROSNICKI 1994]. In the first case, the ball-screw converts rotary-motion torque to linearmotion force. This in turn actuates a conventional friction surface drum EMB mechanism through a system of apply and motionless levers. The friction drum EMB, as shown in Figure 3.59, must have the ability to mechanically reduce braking to an acceptable level upon the withdrawal of electrical energy. It must not remain energised in cases of electrical energy interruption during braking. This requires a highly efficient system with a return spring mechanism to \u2018astern-drive\u2019 the friction drum EMBs without the assistance of electrical energy. The \u2018astern-drive\u2019 capability needs a separate parking-brake latch mechanism. Thus, the ability to automatically release the braking torque during an electrical energy interruption demands the use of a highly efficient brake-apply-lever actuator and separate parking brakeholding latch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.5-1.png",
        "caption": "Figure 6.5. An unusual lesson on projectile motion .",
        "texts": [
            " But a few tenths of a second before the impending catastrophe, Percy Panther spots the converging shell and slams on the brakes. The shell explodes violently in front ofthe truck, destroying it. Through the smoky haze, Arnold Aardvark spies the black, whisker-singed and disheveled driver crawling safely away to seek revenge another day. D Example 6.10. Arnold Aardvark is sunbathing on a lookout platform at Xo = ai + bj in the frame <I> = {O; ik } when he spots Percy Panther at 0 preparing to fire an artillery gun pointed directly toward the platform, as shown in Fig. 6.5. The gun has a muzzle velocity Vo and the tower is well within its range r . At the moment the gun is fired, Arnold Aardvark, sensing impending danger, grabs his umbrella, steps through a hole in the platform, and falls freely in pursuit of safety toward the ground. Determine the distance d that separates Arnold Aardvark and the shell at the instant t\" when it crosses his line of fall. Solution. The free body diagrams of the shell S and Arnold Aardvark Bare shown in Fig . 6.5, in which W s = msg and W B = mBg denote their respective weights"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.4-1.png",
        "caption": "Fig. 17.4 Four-bars with different distributions of the link lengths (3, 5, 6, 7). Doublecrank (a) with all links fully rotating. Crank-rocker (b) with fully rotating input crank. Double-rocker of first kind with fully rotating coupler (c)",
        "texts": [
            " Depending on the behavior of input link and output link a four-bar is either a double-crank or a crank-rocker or a double-rocker. It is obvious that a fourbar not satisfying Grashof\u2019s condition is a double-rocker. On the other hand, a four-bar satisfying Grashof\u2019s condition may be either a double-crank or a crank-rocker or a double-rocker. Details are worked out in what follows. Four-Bars Satisfying Grashof\u2019s Inequality Condition min + max < \u2032 + \u2032\u2032 . For demonstration the link lengths (3, 5, 6, 7) are used which satisfy Grashof\u2019s condition (3 + 7 < 5 + 6) . In Fig. 17.4a the fixed link is the shortest link. This link (and only this link) is fully rotating relative to all other links. In other words: The input link, the output link and the coupler are fully rotating relative to the fixed link. Hence the four-bar is a double-crank. For a single input angle the two existing positions of the four-bar are shown (one of them with dashed lines). In Fig. 17.4b the input link is the shortest link. Only this link is fully rotating relative to all other links. Hence the four-bar is a crank-rocker. The four-bar is shown in all four limit positions of the rocker. The angular range of the rocker consists of two sectors < 180\u25e6 which are arranged symmetrically to the base line. The base line is outside these sectors. For a single input angle the two existing positions of the four-bar are shown (one of them with 17.1 Grashof Condition 571 dashed lines). In these two positions the output link is located on opposite sides of the base line. Figure 17.4c differs from Fig. 17.4a in that the fixed link and the coupler are interchanged. The coupler is the shortest link. Only the coupler is fully rotating relative to all other links. The four-bar is referred to as double-rocker of first kind. The figure shows the limit positions of both rockers. The angular range of each rocker is a single sector. The sectors of both rockers are on one and the same side of the base line. For a single input angle the two existing positions of the four-bar are shown (one of them with dashed lines)",
            " Its fixed link has length r1 , and its input link has length . Both four-bars have the same coupler and the same output link. If F is a foldable four-bar, also F\u2217 is foldable. If F is a double-rocker of first kind (of second kind), also F\u2217 is a double-rocker of first kind (of second kind). If F is a double-crank, F\u2217 is either a double-crank or a crank-rocker. If F is a crank-rocker, F\u2217 is either a double-crank (if fixed link and crank are interchanged) or a crank-rocker (if fixed link and rocker are interchanged). Example: Let F be the crank-rocker in Fig. 17.4b . Interchange of fixed link and crank produces the double-crank of Fig. 17.4a . In Fig. 17.8 F and F\u2217 have one and the same input angle \u03d5 . The relation between the output angles \u03c8 and \u03c8\u2217 is seen to be \u03c8 + \u03c8\u2217 \u2261 \u03d5+ \u03c0 . (17.20) For a given angle \u03d5 Eqs.(17.12) determine in the four-bar F two angles \u03c81 and \u03c82 and in the four-bar F\u2217 with coefficients A\u2217 = 2r2(r1 \u2212 cos\u03d5) , B\u2217 = \u22122 r2 sin\u03d5 , C\u2217 = C two angles \u03c8\u2217 1 and \u03c8\u2217 2 . The coordination of the pairs of angles is as follows: \u03c81+\u03c8\u2217 2 \u2261 \u03d5+\u03c0 . This is verified by substituting 17.4 Inclination Angle of the Coupler. Transmission Angle 577 A , B ,C and A\u2217 , B\u2217 , C\u2217 into the equation cos\u03c81 cos\u03c8 \u2217 2 \u2212 sin\u03c81 sin\u03c8 \u2217 2 \u2261 \u2212 cos\u03d5 ",
            "9 : cos\u03d5\u221e = 2 \u2212 a2 + (r1 \u2213 r2) 2 2 (r1 \u2213 r2) , cos\u03c7stat = 2 + a2 \u2212 (r1 \u2213 r2) 2 2a . (17.24) The angles \u03d5\u221e have a kinematical interpretation. They determine the directions of asymptotes of the fixed centrode of the coupler. The centrode has no asymptotes if both cosines have absolute values > 1 , i.e., if the conditions ( \u2212 a)2 > (r1 \u2212 r2) 2 and ( + a)2 < (r1 + r2) 2 are satisfied. This is the 578 17 Planar Four-Bar Mechanism case if and only if the coupler is fully rotating. These four-bars are either double-cranks (Fig. 17.4a) or double-rockers of first kind (Fig. 17.4c). In Ex. 6 of Sect. 15.1.2 centrodes of couplers of four-bars with special link lengths were investigated. In Fig. 17.7 the transmission angle \u03bc of a four-bar is defined. Its dependency on \u03d5 is obtained as follows. The length of the diagonal starting from A is expressed by means of the cosine law once in terms of cos\u03d5 and once in terms of cos\u03bc . The identity of these expressions results in cos\u03bc = 2r1 cos\u03d5\u2212 (r21 + 2) + r22 + a2 2r2a . (17.25) Extremal values of \u03bc are obtained from (17.1) by interchanging (r1, ) and (r2, a) : cos\u03bcstat = r22 + a2 \u2212 ( \u2213 r1) 2 2r2a ",
            " In order to determine for a given four-bar all positions with a stationary value of 1/i the four-bar and the center P12 must be drawn for a number of (monotonically increasing) angles \u03d5 over the entire possible range \u03c61 \u2264 \u03d5 \u2264 \u03c62 . A stationary value of 1/i is passed every time the moving center P12 changes its sense of direction along the \u03be -axis (jumps from \u221e to \u2212\u221e do not count as changes of sense of direction). Once a position is known approximately it can be improved by checking the angle between the lines P12P30 and P31P32 . Example: For the double-crank in Fig. 17.4a this investigation reveals that stationary values of 1/i occur in the two positions shown in Fig. 17.12a with \u03d5 \u2248 9\u25e6 and with \u03d5 \u2248 95\u25e6 . With the coordinate of P12 (17.27) yields for the position \u03d5 \u2248 9\u25e6 a maximum (1/i)max \u2248 2.7 and for the position \u03d5 \u2248 95\u25e6 a minimum (1/i)min \u2248 0.42 . For the crank-rocker of Fig. 17.4b the same investigation can be made. This is unnecessary, however, because this four-bar is obtained from the previously investigated one by interchanging the fixed link and the input link. From (17.38) it follows that two four-bars thus related have stationary values of 1/i for one and the same angles \u03d5 . Furthermore, these stationary values add up to one. If the stationary value is a maximum in one of the four-bars, it is a minimum in the other and vice versa. Hence the crank-rocker of Fig. 17.4b has at \u03d5 \u2248 9\u25e6 a minimum (1/i)min \u2248 \u22121.7 and at \u03d5 \u2248 95\u25e6 a maximum (1/i)max \u2248 0.58 . Figure 17.12b shows the crank-rocker in these positions. End of example. In what follows, two analytical methods for determining stationary values of 1/i are described. Method 1 is a direct method based on (17.35). With the abbreviation x = cos\u03d5 it is written in the form 2 i(x) = x\u2212 p1 x\u2212 p2 \u00b1 (x\u2212 p3)Q (x\u2212 p2)P , P = \u221a \u03bb2 \u2212 (x\u2212 p4)2 , Q = \u221a 1\u2212 x2 . \u23ab\u23ac \u23ad (17.42) The stationarity condition d(1/i)/dx = 0 has the form (the prime denotes the derivative with respect to x ) \u2213(p1 \u2212 p2)P 2 = (p3 \u2212 p2)PQ+ (x\u2212 p2)(x\u2212 p3)(PQ\u2032 \u2212QP \u2032) ",
            "49) yields the desired sixthorder equation (x2\u22121)[(x\u2212p4) 2\u2212\u03bb2][K3x 2+(x+p2)(K2+p2K3)+K1]\u2212[F (x)]2 = 0 . (17.51) The coefficient of x6 is K3 \u2212 p24 = (p1 \u2212 p2) 2 \u2212 (p3 \u2212 p2 \u2212 p4) 2 = ( 2 \u2212 a2)(a2 \u2212 r21) (r1 )2 . (17.52) The equation is of fifth order if a = and/or a = r1 . Only real roots |x| \u2264 1 are significant. For every such root it is checked to which sign in (17.44) the root belongs. With the same sign (17.42) and (17.12) determine the corresponding stationary value of 1/i and the angle \u03c8 . Example: With the parameters of the double-crank in Fig. 17.4a as well as with those of the crank-rocker in Fig. 17.4b (17.51) has the four real roots x = cos\u03d5 \u2248 \u22120.084 , 0.9882 , 1.11 and 4.02 . The first two roots determine the angles \u03d5 \u2248 94.8\u25e6 and \u03d5 \u2248 8.8\u25e6 , respectively. These are the angles shown in Figs. 17.12a and b . End of example. The second (historically the first) analytical method for determining stationary values of 1/i is due to Freudenstein [14]. Also this method leads to a sixth-order equation. The method starts out from Fig. 17.10 and from the coupler curve traced by a point C fixed on the coupler line P31P32 ",
            "74) This is the desired parameter representation of the coupler curve. For cos\u03c7 and sin\u03c7 the expressions from (17.23) are substituted: cos\u03c7k = A\u0304C\u0304 \u2212 (\u22121)kB\u0304 \u221a A\u03042 + B\u03042 \u2212 C\u03042 A\u03042 + B\u03042 , sin\u03c7k = B\u0304C\u0304 + (\u22121)kA\u0304 \u221a A\u03042 + B\u03042 \u2212 C\u03042 A\u03042 + B\u03042 , \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (k = 1, 2) , (17.75) A\u0304 = \u22122a( \u2212r1 cos\u03d5) , B\u0304 = 2r1a sin\u03d5 , C\u0304 = 2r1 cos\u03d5\u2212(r21+ 2+a2\u2212r22) . (17.76) Every input angle \u03d5 determines two positions of the four-bar and, hence, two positions of the coupler point C . From Sect. 17.1 it is known that doublerockers of first kind (Fig. 17.4c) and of second kind (Figs. 17.5a,b,c) have the property that the two positions can be reached one from the other by a continuous motion. Hence these four-bars have the property that the coupler curve is unicursal (a single closed curve). In contrast, double-cranks and crank-rockers have the property that the two positions associated with a single input angle cannot be reached one from the other by a continuous motion, but only by disconnection and reassembly (see Figs. 17.4a and b). This has the consequence that coupler curves of such four-bars are bicursal (two closed branches)",
            " Identical senses of all three circle point triangles are achieved with a set of points Q0 which is either a single section or the union of several nonneighboring sections. In what follows, the set is denoted \u03c3c. Example: In Fig. 14.22 the sense of the three circle point triangles is clockwise for points Q0 in the unbounded section to the right of \u03a012 and in the section \u03a014-\u03a6-\u03a034 . It is counterclockwise in the unbounded section to the left of \u03a023 . Thus, the set \u03c3c of admissible crank centers is the union of these three sections. From Fig. 17.4b the following properties of crank-rockers are known. A four-bar is a crank-rocker if (a) Grashof\u2019s inequality condition min + max \u2264 \u2032 + \u2032\u2032 is satisfied and if, in addition, (b) the crank has the minimal length min . The angular range of a rocker consists of two disconnected sectors < 180\u25e6 which are arranged symmetrically with respect to the base line. For being an admissible crank-rocker a Burmester solution must satisfy condition (c) all four circle points of the rocker must be on one and the same side of the base line, for otherwise the four prescribed positions could not be produced without disconnecting and reassembling the crank-rocker"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure5.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure5.5-1.png",
        "caption": "FIGURE 5.5. Radial Mode and the First Three Thickness Modes, n = 0.",
        "texts": [],
        "surrounding_texts": [
            "Axially symmetric vibration occurs only in breathing mode with radial displacement (Markus 1988). Longitudinal modes occur with axial displacement, and torsional modes with transverse displacement around the circumference of the cross section. Figures 5.4 through 5.6 depict the three axisymmetric modes associated with the corresponding first three thickness modes of vibrations."
        ]
    },
    {
        "image_filename": "designv10_12_0003581_tec.2021.3087831-Figure16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003581_tec.2021.3087831-Figure16-1.png",
        "caption": "Fig. 16 shows the effective domain of the PMSM electro-mechanical energy conversion. Point O is close to the non-fan side and the shaft. Fig. 17 shows the temperature distribution of the effective domain (non-end domain) of the electromechanical energy conversion when the inlet air flow velocity is 25m/s. It can be seen from Fig. 18 that in the PMSM straight section domain, the winding in the slot acts as a heat source. Under different air flow velocity, the highest temperature appears in the upper winding.",
        "texts": [],
        "surrounding_texts": [
            "To study the cooling effect of different air flow speed on non-fan side end windings and end insulation, the armature winding current of the PMSM is set to 799A. The temperature trends of the armature winding and the end insulation are studied when the fan inlet air flow speed is set to 0m/s, 5m/s, 10m/s, 15m/s, 20m/s, 25m/s respectively. Fig. 10 shows the axial cross-sectional velocity distribution of the air at the end of the non-fan side at different air flow velocity. It can be seen from Fig. 10 that the air-fluid at the non-fan end is in an irregular turbulent state. The cooling air flows from the stator Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 04:38:51 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. >IEEE Transactions on Energy Conversion < 7 yoke air passage into the end air domain on the non-fan side. Part of the air flows out of the PMSM directly through the air outlet. The other part of the cooling air forms a circulation M and a circulation N on both sides of the end insulation. The circulation M is on the rotor side and the circulation N is on the water channel side. To study the flow velocity of air circulation M and N on the end insulation surface, Fig. 11 shows the specific positions of points A-J in the axial section of the end insulation. Among them, GH and JI are the edges of the end insulation on the rotor side and the water channel side respectively, and HI is the edge of the end insulation on the air outlet side. In Fig. 12, on the whole, the air flow speed along AB and FE increases first and then decreases as the axial distance increases. The maximum air flow velocity along AB and FE are located at the axial distances of 31.75mm and 36.52mm, respectively. When the air flow speed is 0m/s, 5m/s, 10m/s, 15m/s, 20m/s, 25m/s, the average air flow velocity is 0.89m/s, 1.85m/s, 2.75m/s, 3.93m/s, 5.01m/s along FE respectively, which are higher than the average air flow velocity of AB. This is because the ventilation channel of the stator yoke is closer to the water channel side insulation FE. When the air flowing out of the ventilation duct passes through the insulating FE, the fluid loss is smaller than that of AB. Therefore, the average air flow velocity of AB is lower than that of FE. To further study the influence of different inlet air flow speed on the temperature of the non-fan side end insulation and end windings, Fig. 13 shows the axial cross-sectional temperature distribution of the PMSM at different inlet air flow velocity. When the inlet air flow speed is 0m/s, 5m/s, 10m/s, 15m/s, 20m/s, 25m/s, the maximum temperature of the end windings is 131.87\u00b0C, 122.02\u00b0C, 117.03\u00b0C, 113.00\u00b0C, 110.13\u00b0C, 107.89\u00b0C, respectively. As the inlet air flow velocity increases, the temperature of the end insulation and the temperature of the end winding decrease significantly on the non-fan side. Fig. 14 shows the temperature distribution of end insulation GH and JI under different inlet air flow velocity. M N M N M N M N M N insulation vent ventilation duct G H IJ G H IJ G H IJ G H IJ G H IJ m/s ventilation duct ventilation duct ventilation duct ventilation duct vent vent vent vent (a) (b) (c) (d) (e) Fig.10. Air velocity distribution at the non-fan end of the PMSM under different air flow velocity. (a) 5m/s. (b) 10m/s. (c) 15m/s. (d) 20m/s. (e) 25m/s. Radial Axial insulation Winding rotor side waterway side 1mm 1mm 1mm A B C D FG J E H I Fig.11. The specific location of insulation point A-J at the non-fan side. Fig.12. Air flow velocity changes of AB and FE under different Inlet air flow velocity. It can be seen from Fig. 14 that when the inlet velocity is 0m/s, GH and JI have the same temperature at the same axial distance. When the inlet air flow velocity is in the range of 5m/s-25m/s and the axial distance is in the range of 0mm-16mm, the temperature of JI is higher than that of GH. In the range of 16mm-77.8mm axial distance, the average temperature of JI is lower than the average temperature of GH. This is because the air is sufficiently cooled by the water. In the range of the axial distance from 16 mm to 77.8 mm, the cooling air flows directly from the stator yoke ventilation channel to the JI through a short path. While the boundary GH is on the other side of the insulation, when the cooling air flows to GH, the kinetic energy is reduced, the cooling effect of cooling air on GH is less than that on JI. In the range of 0mm-16mm axial distance, although the average air flow velocity along FE is higher than AB under the same inlet air flow velocity, the air flow velocity at point A is higher than the air flow velocity at point F. This is because the air flows out of the air-gap and rotor holes into the end air domain. A part of the air forms a circulation M, and the other part enters the other side of the insulation through the gap between the stator and the end insulation. The cooling effect of air on the upper winding is stronger than the lower winding. Therefore, in the range of 0mm-16mm axial distance, the temperature along GH is lower 0 20 40 60 80 0 2 4 6 8 10 12 14 W in d s p ee d \uff08 m /s \uff09 Axial distance\uff08mm\uff09 AB_5 AB_10 AB_15 AB_20 AB_25 FE_5 FE_10 FE_15 FE_20 FE_25 Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 04:38:51 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. >IEEE Transactions on Energy Conversion < 8 than the temperature along boundary JI. When the inlet air flow velocity reaches 25m/s, the average temperature of end insulation GH is 53.22\u00b0C, and the average temperature of JI is 50.02\u00b0C. In general, the end insulation and windings on the side of the water channel can be better cooled by the cooling air. Temperature\uff08 \uff09 \uff08a\uff09 C\u00b0 C\u00b0 Temperature\uff08 \uff09 \uff08b\uff09 Temperature\uff08 \uff09 \uff08c\uff09 C\u00b0 C\u00b0Temperature\uff08 \uff09 (d) Temperature\uff08 \uff09 \uff08e\uff09 C\u00b0 C\u00b0Temperature\uff08 \uff09 \uff08f\uff09 Fig.13. Axial section temperature distribution of end insulation and winding. (a)0m/s. (b)5m/s. (c)10m/s. (d)15m/s. (e)20m/s. (f)25m/s. 80 60 40 20 0 30 40 50 60 70 80 90 100 110 G H _ 0 J I _ 0 G H _ 5 J I _ 5 G H _ 1 0 J I _ 1 0 G H _ 1 5 J I_ 1 5 G H _ 2 0 J I_20 G H _25 JI_25 T em p er a tu re /\u00b0 C Axial d ista nce\uff08 mm\uff09 GH_0m/s JI_0m/s GH_5m/s JI_5m/s GH_10m/s JI_10m/s GH_15m/s JI_15m/s GH_20m/s JI_20m/s GH_25m/s JI_25m/s Fig.14. Temperature of end insulation GH and JI with different inlet air flow velocity. 0 10 20 30 40 50 40 60 80 100 120 140 Radial distance\uff08mm\uff09 T em p er a tu re \uff08 \u00b0C \uff09 Radial distance\uff08mm\uff09 0m/s 5m/s 10m/s 15m/s 20m/s 25m/s 0 20 40 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 W in d s p ee d \uff08 m /s \uff09 Fig.15. Air flow velocity along end insulation CD and temperature distribution at HI. Fig.15 shows the distribution of fluid velocity at CD and temperature at HI. The end insulation HI temperature first increases and then decreases along the radial direction. The temperature reaches the maximum at a radial distance of 26.42mm. The temperature along HI is affected by the shape of the end windings. At the radial distance of 26.42mm, the axial distance between HI and the heat source winding is the closest. When the inlet air flow velocity is 0m/s, the maximum temperature on boundary HI is 108.72\u00b0C. When the inlet air flow velocity increases from 0m/s to 25m/s by 5m/s, the maximum HI temperature will decrease by 21.73\u00b0C, 14.72\u00b0C, 8.79\u00b0C, 5.45\u00b0C, 4.15\u00b0C. This is because as the inlet air flow velocity further increases, the cooling effect of the fluid on the HI gradually reaches saturation. On the whole, as the radial distance increases, the air flow velocity flowing through CD first increase and then decrease. CD reaches its maximum air flow velocity at a radial distance of 20mm, while the HI reaches its maximum temperature at a radial distance of 26.42mm. This is because the temperature of the HI is not only affected by the fluid flow rate, but also by the insulation and winding shape. To study the temperature of the straight section of the PMSM, The maximum temperature point coordinates are located at a radial distance of 0.062mm and an axial distance of 0.297mm. This is because the air from the end of the fan side has little cooling effect on the upper straight winding. From the general trend, the temperature of the straight section decreases in the radial direction from the winding to the air-gap and the stator core. The end air has a cooling effect on the straight section of PMSM. Therefore, the temperature in the axial middle of each structural member is relatively high. When the inlet air flow velocity is increased, the cooling effect of the cooling air on the winding in the slot is enhanced. When the inlet air flow velocity Authorized licensed use limited to: National University of Singapore. Downloaded on July 04,2021 at 04:38:51 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. >IEEE Transactions on Energy Conversion < 9 increases from 5m/s to 25m/s, the maximum temperature of the winding in the slot decreases from 107.70\u00b0C to 97.19\u00b0C."
        ]
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure9-1.png",
        "caption": "Fig. 9. The 2T1R + 1-DOF parallel manipulators: (a) type 1 (b) type 2.",
        "texts": [
            " Two parallel constraint-forces generate a constraint-couple with the direction vertical to the plane defined by the constraints. Three spatial parallel constraint-forces can provide two constraint-couples. The orientations of the constraint- couples are normal to constraint-forces. The probable combination of two L 1 F 1 C -limbs is selected to form the 2T1R + 1-DOF parallel manipulators with the Bennett platform. The constraint-forces are collinear, and the constraint-couples are linearly independent. Then the 2T1R + 1-DOF parallel mechanisms with configurable platforms are obtained, as drawn in Fig. 9 . For the 2T1R + 1-DOF parallel manipulators with planar four-bar platforms, two L 1 F 1 C -limbs are constructed. The constraint-forces are parallel, while the constraint-couples are linearly dependent. In the wrench system, a constraint-couple is generated by two parallel constraint-forces. And the orientation of the caused constraint-couple is vertical to the platform. As a result, the 2T1R parallel manipulators that can output 1-DOF internal mobility within the configurable platform are de- rived, as drawn in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure16.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure16.1-1.png",
        "caption": "Fig. 16.1 Cylindrical friction wheels in rolling contact with opposite (a) and with equal senses of rotation (b)",
        "texts": [
            " Transmission of rotation from one shaft to another parallel shaft is possible by means of two cylindrical friction wheels which are rolling one on the other without slipping. In Figs. 16.1a and b cross sections of the two possible arrangements of wheels are shown. The radii are r1 and r2 . The circles p1 and p2 rolling one on the other are the centrodes of the wheels. The point of rolling is the center of relative rotation P12 . In the theory of gearing the centrodes are referred to as pitch circles and P12 as pitch point. The wheels in Fig. 16.1a are rotating relative to the fixed frame with opposite senses of direction whereas those in Fig. 16.1b are rotating with equal senses of direction. If in both cases \u03c91 and \u03c92 are the magnitudes of the angular velocities relative to the frame, in both cases the rolling condition is \u03c91r1 = \u03c92r2 or \u03bc = \u03c92 \u03c91 = r1 r2 . (16.2) If the wheels are gears, the centrodes exist only virtually. As is indicated in the figures on parts of the circumferences the centrodes are replaced by teeth. These teeth must have shapes which ensure that the gear ratio \u03c92/\u03c91 is constant throughout the motion. Necessary conditions are formulated further below. In Fig. 16.1a both wheels have external gearing whereas in Fig. 16.1b the larger external wheel has internal gearing. Equations (16.1) and (16.2) establish between angular velocities, radii of pitch circles and numbers of teeth the relationship \u03bc = \u03c92 \u03c91 = r1 r2 = n1 n2 . (16.3) A cylindrical gear \u2013 with external or internal gearing \u2013 is called spur gear if the teeth are parallel to the gear axis. Such gears are treated first. Spur gears have line contact. This has the consequence that unavoidable misalignment 16.1 Parallel Axes 531 of wheel axes results in edge contact leading to rapid destruction of teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003024_s00202-020-00955-2-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003024_s00202-020-00955-2-Figure1-1.png",
        "caption": "Fig. 1 LSPMSM construction",
        "texts": [
            " High-efficiency electrical motors significantly reduce the operating cost for industry. Super premium efficiency (IE4) line-start permanent magnet synchronous motor (LSPMSM) is one of the good alternatives to SCIM, particularly in line-start applications [1\u20133]. Recent research also proved the viability of LSPMSM for the power range of 30\u2013250 hp which would make the industry evince more interest in this motor [4]. Construction of LSPMSM is similar to that of SCIM apart from permanent magnet in the rotor as shown in Fig. 1. LSPMSM starts like an SCIM and in a steady state; it operates like a permanent magnet synchronous motor (PMSM). This synchronous behavior makes the relative speed difference between stator rotating magnetic field and rotor to zero, so the rotor losses are reduced to a great extent [5]. A loss in the motor is further influenced by the customary power quality indices (CPQI) like voltage harmonic distortion (VHD), voltage unbalance factor (VUF) and longduration voltage variation (LDVV). So, studying the behavior of LSPMSM under CPQI is necessary to satisfy the load and productivity of industry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.89-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.89-1.png",
        "caption": "Fig. 2.89 Rear ICE, M-M clutch, MT and live-axle transmission arrangement for the M-M DBW 2WD propulsion mechatronic control system [NEWTON ET AL., 1989].",
        "texts": [
            " Encompassing a multitude of features, the horizontally-opposed ICE is an engineering triumph that makes the symmetrical M-M DBW 4WD propulsion possible. 2.4 M-M Transmission Arrangement Requirements 257 2.4.7 Rear ECE or ICE, M-M Clutch, MT or SAT or FAT or CVT and Live-Axle M-M Transmission Arrangements for the M-M DBW 2WD Propulsion Mechatronic Control System The rear ECE or ICE and live axle M-M transmission arrangement has advantages for buses and coaches, primarily because it allows the floor to be put at a low level and be flat and clear right through practically the entire length of the chassis. In Figure 2.89, the ECE or ICE and MT (gearbox) are constructing as a single unit that is fixed transversely behind the rear axle. The M-M clutch is inserted between the ECE or ICE and MT, while at the other end of this box is a bevel gear pair termed the \u2018transfer drive\u2019 [NEWTON ET AL. 1989]. To transfer the drive to the rear axle, the driven gear of the bevel gear pair is joined by a FJ, UJ or CVJ to a reasonably short propeller shaft that is also joined at its other end to the pinion shaft of the final drive unit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001772_1.4027166-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001772_1.4027166-Figure3-1.png",
        "caption": "Fig. 3 Definition of axes on a gear hobbing machine of SIEMENS",
        "texts": [
            " (1)\u2013(5), the locus and unit normal of the right-hand side rack cutter can be attained as r3 \u00bc \u00bdx3\u00f0u1; v1;w1\u00de; y3\u00f0u1; v1;w1\u00de; z3\u00f0u1; v1;w1\u00de; 1 T (6) and n3 \u00bc \u00bdnx3\u00f0u1; v1;w1\u00de; ny3\u00f0u1; v1;w1\u00de; nz3\u00f0u1; v1;w1\u00de T (7) where u1 \u00bc sin aon\u00f0 ro1w1 \u00fe v1 sin bo1\u00de cos bo1 (8) x3 \u00bc \u00f0ro1 \u00fe u1 cos aon\u00de cos w1 \u00fe \u00f0ro1w1 \u00fe u1 cos bo1 sin aon v1 sin bo1\u00de sin w1 (9) y3 \u00bc \u00f0ro1 \u00fe u1 cos aon\u00de sin w1 \u00fe \u00f0 ro1w1 u1 cos bo1 sin aon \u00fe v1 sin bo1\u00de cos w1 (10) z3 \u00bc v1 cos bo1 \u00fe u1 sin bo1 sin aon (11) nx3 \u00bc sin aon cos w1 cos aon cos bo1 sin w1 (12) ny3 \u00bc cos aon cos bo1 cos w1 \u00fe sin aon sin w1 (13) and nz3 \u00bc cos aon sin bo1 (14) The tooth profile and its unit normal of the standard involute helical gear (i.e., standard hob) are defined by considering Eqs. (5), (6) and (7), simultaneously. The definitions of axes on a gear hobbing machine are shown in Fig. 3. The coordinate systems for the hobbing of helical gears with longitudinal crowning teeth are shown in Fig. 4, where coordinate systems S1\u00f0x1; y1; z1\u00de and S2\u00f0x2; y2; z2\u00de are rigidly connected to the hob and work gear, respectively, while the coordinate system Sa\u00f0xa; ya; za\u00de is rigidly connected to the frame of hobbing machine, and Sb\u00f0xb; yb; zb\u00de, Sc\u00f0xc; yc; zc\u00de, Sd\u00f0xd; yd; zd\u00de, Se\u00f0xe; ye; ze\u00de, and Sf \u00f0xf ; yf ; zf \u00de are auxiliary coordinate systems. On a modern gear hobbing machine, there are three hob\u2019s movements: traverse movement along the axis of the work gear za(t) (i.e., Z-axis movement, as shown in Fig. 3), diagonal feed along the axis of hob zs(t) (i.e., Y-axis movement, as shown in Fig. 3), and radial feed-in Eo along the center distance between the hob and work gear (i.e., X-axis movement, as shown in Fig. 3), and there are two rotary motions: rotation of work piece table (i.e., C axis motion, as shown in Fig. 3) and rotation of hobbing cutter (i.e., B\u00bc axis motion, as shown in Fig. 3). The crossed angle c of the hob and work gear axes is usually a machine-tool setting. According to the literatures [1,9], it can be expressed as follows: Journal of Mechanical Design JUNE 2014, Vol. 136 / 061007-3 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use c \u00bc bo16bo2 (15) where the \u201c6\u201d sign indicates the same/opposite direction of helices between the hob cutter and work gear. The crossed angle of the hob and work gear is usually fixed during the gear\u2019s hobbing process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003426_s00170-020-05707-x-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003426_s00170-020-05707-x-Figure5-1.png",
        "caption": "Fig. 5 Application of symmetry and boundary conditions for the macroscale model (used with permission from [113])",
        "texts": [
            " [112] proposed an adaptive meshing scheme in the FEM model for a selective laser melting process to enhance the computational efficiency with moderate accuracy. Moreover, the application of symmetry in part scale model is frequently applied to reduce computational cost in additive manufacturing. A single cantilever is modeled for residual stress and distortion evaluation using symmetrical geometry configuration instead of a full model for double cantilever proposed by Li. C et al. [113] and demonstrated in (Fig. 5). Modeling approaches may be classified as macroscopic, mesoscopic, or microscopic based on the process. Macroscopic modeling treats powder material as a homogenized continuum throughout the process. Typically, the spatial temperature distribution, part scale residual stress, and geometrical inaccuracy are primarily examined through such constitutive models. Microscopic modeling stipulates metallurgical and microstructural ambiguities [114]. As far as the mesoscopic model is concerned, it covers melting pool dynamics, adhesion, and defects in the powder bed fusion process [95]",
            " The expression for hc is proposed below, and T and Ta are the surface and ambient temperature, as stated in the earlier equation. hc \u00bc Nukf L \u00f039\u00de where Nu is the Nusselt number, L is specimen length, and kf stands for the fluid thermal conductivity in the above equation for powder bed additive manufacturing [118]. Another thermal boundary condition is imposed, which specifies no heat exchange from the bottom surface of the powder bed. \u2212\u03bb \u2202T \u2202z z\u00bcbottom surface \u00bc 0 \u00f040\u00de A detailed illustration of thermal and mechanical boundary conditions for part scale simulation is shown in Fig. 5. Nonlinear mechanical analysis in the FEM simulation can be regarded as a quasi-static incremental analysis, and the corresponding governing equation can be treated as [40]: \u2207:\u03c3 \u00bc 0 \u00f041\u00de where \u03c3 is the second-order stress tensor following the laws of material behavior. Considering the elastoplastic behavior of the material, the strain, and stress can be demonstrated as: \u03c3 \u00bc C\u03b5e \u00f042\u00de where C is the fourth-order material stiffness tensor and \u03b5e is a second-order elastic strain tensor. Global strain tensor \u03b5 consists of the elastic strain \u03b5e, plastic strain \u03b5p, and thermal strain \u03b5th, respectively [119]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001176_robio.2012.6490977-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001176_robio.2012.6490977-Figure2-1.png",
        "caption": "Fig. 2. Swing leg control. (A) Sequence of natural control tasks for reaching a target placement while guaranteeing foot ground clearance. (B) Functional relationship between \u03b1 and \u03c6h and \u03c6k . With \u03b3 = 90 \u2212 \u03c6k 2 and \u03b2 = 180\u2212 \u03b3 \u2212 \u03c6h, \u03b1 relates to \u03c6h and \u03c6k as \u03b1 = \u03c6h \u2212 \u03c6k 2 .",
        "texts": [
            "2Nmrad\u22121) and accounts for hip translational accelerations (ax, ay) in later comparisons to human swing phases in steady walking and running (Sec. IV). In addition to the fundamental goal of placing the foot into target points, the swing leg motion is subject to the constraint that the foot point needs to clear the ground or an obstacle. We represent both, the placement goal and the clearance constraint, by two control variables, the target leg angle \u03b1tgt and the clearance leg length lclr, respectively (Fig. 2A). Assuming equal segment lengths lt = ls (good approximation for human legs) in the remainder of this paper, the leg angle is given by \u03b1 = \u03c6h \u2212 \u03c6k 2 and the leg length resolves to l = 2lt sin \u03c6k 2 (Fig. 2B). Figure 2A outlines a natural sequence of three control tasks which reflects the objective and constraint. First, starting at the ground level from an initial leg angle \u03b10, the clearance constraint requires the leg to flex to at least the clearance length lclr (reached at P). Second, the control focus shifts to advancing the swing leg to the target angle \u03b1tgt (reached at Q). And the final task is to extend the leg until ground contact. Although this sequence of control tasks can be strictly enforced with classical state feedback control, we avoid tracking predefined trajectories for two reasons",
            " In addition to the angle control, the hip control receives a second input \u03c4 iiih from the knee control, \u03c4h = \u03c4\u03b1h + \u03c4 iiih , (5) during the last, leg extension stage in the control sequence (after reaching Q). We detail the purpose of \u03c4 iiih in the next section on knee control. It is the only crossover input between the joints. The knee control\u2019s primary function is to regulate leg length. However, due to the influence of the knee angle on both, leg length and leg angle, the control is more involved. We separate it into the three natural control tasks outlined before (Fig. 2A). To accomplish the first control task of reaching a minimum clearance lclr in the initial swing, we take advantage of the passive swing leg dynamics. Equation 2 shows that while the Coriolis, centrifugal and gravitational terms always tend to extend the knee, a negative hip acceleration tends to flex the knee. The hip control (Eq. 4) generates negative hip acceleration initially to drive the leg into the target angle. The resulting passive, negative knee acceleration sufficiently overcomes the opposing Coriolis, centrifugal and gravitational accelerations as long as the leg angle \u03b1 increases, \u03b1\u0307 > 0 or equivalently \u03c6\u0307k < 2\u03c6\u0307h (backward motion of foot point)",
            " Once the leg length has shortened past the clearance length, l < lclr, the knee control switches to the second task of holding the knee so that the leg angle control by the hip can take full effect (Eq. 4). We realize this task with a damping input \u03c4 iik = \u23a7\u23aa\u23a8 \u23aa\u23a9 \u2212kii\u03c6\u0307k, \u03c6\u0307k \u2264 0 \u2212kii\u03c6\u0307k(\u03b1\u2212 \u03b1tgt)(\u03c6\u0307k + \u03b1\u0307), \u03c6\u0307k > 0 & \u03c6\u0307k > \u2212\u03b1\u0307 0, otherwise (7) that is pure when the knee flexes (\u03c6\u0307k \u2264 0) and modulated when it extends (\u03c6\u0307k > 0), with a proportional gain of kii. The implementation avoids the large torques that a precise tracking of l = lclr would incur fighting the passive swing leg dynamics (Fig. 2A). In particular, when the hip control stops pulling forward, all interaction terms in equation 2 create passive knee extension. The first modulation term (\u03b1\u2212\u03b1tgt), enables this passive extension when \u03b1 approaches its target, easing the third control task. However, when the leg swings faster at higher speeds, passive knee extension amplifies markedly due mainly to the Coriolis acceleration lt sin\u03c6k\u03c6\u0307 2 h, and the second modulation term (\u03c6\u0307k + \u03b1\u0307), prevents a premature landing of the leg. This term compares the knee extension velocity to the approach velocity \u03b1\u0307 (negative when moving forward)",
            " The model shows an elevating response for the early disturbance and a premature landing for the late disturbance. Both responses are observed in human locomotion and often assumed to reflect two explicit control strategies [26]. By contrast, the model shows these two behaviors as inherent outcomes of its placement control. We developed a control for swing leg placement. The control is structured around a sequence of three tasks that include flexing the leg into a clearance length, advancing the leg into a target angle, and extending it until ground contact (Fig. 2). Although this sequence can be enforced with strict trajectory tracking, we target energy efficient and modular artificial legs in rehabilitation robotics and developed the control to take advantage of passive swing leg dynamics and to modularize the individual hip and knee controls. Our results suggest that the identified control can achieve swing leg placement into a large range of targets for a wide range of walking and running speeds with robustness to disturbances in initial conditions and to sudden changes in the placement target during swing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure13-1.png",
        "caption": "Fig. 13. The contour of third invariant under the load applied at 0-deg.",
        "texts": [
            " To simulate the cornering fatigue test, the load is respectively applied on the end of the moment arm at every 22.5 deg. The stress distribution of the wheel under the load applied at 0-deg position is shown in Fig. 12. There are large operating stresses around the area (dangerous position) between the bolt hole and the bump ring (shown in Fig. 14). Each point of the wheel is in different deformation conditions, which can be determined by the third invariant of the stress deviator [14], as shown in Fig. 13. One dangerous point is selected and defined as point A in Fig. 14 to research its stress state in the following investigation. Fig. 15 is a stress curve from the data of the cornering stress of point A (Fig. 14) obtained in 16 simulations. This point suffers the tension/compression stress states for 16 different load positions, eventually leading to fatigue crack after certain cycles because of the high stress amplitude. The residual stresses in two directions on the surface are measured by X-ray diffraction method in Section 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000412_156855309x420039-Figure21-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000412_156855309x420039-Figure21-1.png",
        "caption": "Figure 21. 4.1\u20134.5\u25e6, 10\u201320 s (walk gait).",
        "texts": [
            " / Advanced Robotics 23 (2009) 483\u2013501 495 496 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 497 498 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 499 In the simulation, the slope angle was changed gradually from 4.1\u25e6 to 4.5\u25e6. Limit cycles in Fig. 19 are not clear and we cannot see what kind of gait was used. In the time interval from 10 to 20 s, limit cycles in Fig. 21 are similar to those in Fig. 15. In the time interval from 30 to 40 s, limit cycles in Fig. 23 are similar to those in Fig. 17. Figure 21 is the simulation data for a slope angle of 4.1\u25e6. Figure 23 is the simulation data for a slope angle of 4.5\u25e6. Thus, it can be said that Quartet 4 with the invariable body can change its walk gait to trot continuously when the slope angle was gradually changed from 4.1\u25e6 to 4.5\u25e6. In this way, gait transition could be considered as the transition of limit cycles. In biped passive dynamic walking, when the slope angle was gradually changed, the biped passive dynamic walker changed its gait from one-period to two-period"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure6.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure6.11-1.png",
        "caption": "Fig. 6.11 4R-P mechanism projected along the z-axis (a) and along the x-axis (b)",
        "texts": [
            " As output the translatory variable in the prismatic joint P is chosen. Let this be the coordinate x of r . From the orthogonality condition n2 \u00b7 r = 0 it follows that x = tan\u03b1 sin\u03d51 . (6.92) Rotation with constant angular velocity \u03d5\u03071 = \u03c9 is converted into oscillatory translation x(t) = tan\u03b1 sin\u03c9t . The mechanism was used in a pneumatic saw (see Design and development/scanning the field for ideas, Sept.1964, p.158 ). See also Altmann [2, 1]. 234 6 Overconstrained Mechanisms In the fixed x, y, z-system of Fig. 6.11a two skew lines n1 and n2 are fixed. Their common perpendicular of length lies in the z-axis. This axis is intersected by n1 at z = /2 (point A1 ) and by n2 at z = \u2212 /2 (point A2 ). The projected angle \u03b1 between the lines is bisected by the y-axis. The lines n1 and n2 are the axes of two cylinders 1 and 2 of equal radius r . Points denoted B1 and B2 are fixed on the cylinders. More precisely, Bi (i = 1, 2) is fixed on cylinder i such that the line AiBi is orthogonal to both ni and z-axis, and that, furthermore, B1 and B2 are, in the projection shown, on a line parallel to the y-axis and at equal distances from the xaxis",
            " Imagine now that both cylinders are rotated about their axes through identical angles \u03d5 (arbitrary). This causes B1 and B2 to move on their respective circles to new positions B\u2032 1 , B \u2032 2 . The displacements in z-direction are identical, namely, u = r sin\u03d5 , and also the displacements in x-direction are identical, namely, r(1 \u2212 cos\u03d5 ) . In the projection shown the distance between B\u2032 1 and B\u2032 2 is \u03b4 = 2r cos\u03d5 sin\u03b1/2 . The generator of cylinder i passing through B\u2032 i is called n\u2032i (i = 1, 2). In Fig. 6.11b the essential points and lines are shown in the projection along the x-axis. In this projection, the axes and generators of the cylinders are shown as lines parallel to the y-axis. Through B\u2032 1 and B\u2032 2 lines B\u2032 1C1 and B\u2032 2C2 of equal lengths /2 are drawn parallel to the z-axis. The line p through C1 and C2 is (not only in this projection) parallel to the y-axis. Imagine now that A1A2 , A1B \u2032 1 , A2B \u2032 2 , B\u2032 1C1 and B\u2032 2C2 are rigid links which are interconnected by four revolute joints with pairwise parallel axes n1 , n\u20321 and n2 , n\u20322 and by a prismatic joint with the axis p "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003228_j.procir.2020.03.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003228_j.procir.2020.03.003-Figure1-1.png",
        "caption": "Fig. 1. Corrosion-fatigue set-up and C-ring specimen specifications.",
        "texts": [
            " Experimental setup The corrosion-fatigue behaviour of maraging steel 18NiC300 C-ring specimens was investigated with the aid of an appropriate, fully automated, corrosion-fatigue set-up presented in [11,12]. This device allows the conduct of fatigue experiments by the oscillation of a piston at the desired frequency and load, offering also the opportunity to concurrently engage a corrosive environment to explore the synergistic effect of fatigue and corrosion, by adding a corrosive solution in the can (see Figure 1). Apart from the frequency and loading profile that prescribe the applied strain rate, it is also possible to define the loading mode, i.e. displacement-constraint or force-constraint. \u0399n the experiments that were performed both in a corrosion-free and corrosion environment, the applied force was in the range between 400 \u039d and 700 N with fatigue stress ratio R=0 and a frequency of 40 Hz at ambient temperature. For fabricating the standardized by ASTM G38 C-rings specimens, two different manufacturing approaches were considered, (i) machining the parts conventionally from a rolled bar and (ii) by additive manufacturing. The maraging steel 18Ni-C300 round bar (see Table 1 for chemical composition) was received in a solution annealed state according to the standard AMS 6514 and ground to a diameter of 19 mm. Then, the as received bar was machined by turning and drilling to achieve the dimensions of the specimen presented in Figure 1. AM specimens were fabricated with the aid of an EOS M280 SLM machine. The specifications of the applied powder are also shown in Table 1. The applied layer size by the SLM process was 20 \u03bcm and the recoater positioning speed amounted to 80 mm/s. Subsequently, some of the AM specimens were glass-blasted for improving surface integrity. Table 1. Chemical composition of maraging steel 18Ni-C300 in rolled bar stock and powder for AM. Alloying elements (wt %) Bar stock Powder Fe Balance Ni 18.3 17.0 - 19",
            " Experimental setup The corrosion-fatigue behaviour of maraging steel 18NiC300 C-ring specimens was investigated with the aid of an appropriate, fully automated, corrosion-fatigue set-up presented in [11,12]. This device allows the conduct of fatigue experiments by the oscillation of a piston at the desired frequency and load, offering also the opportunity to concurrently engage a corrosive environment to explore the synergistic effect of fatigue and corrosion, by adding a corrosive solution in the can (see Figure 1). Apart from the frequency and loading profile that prescribe the applied strain rate, it is also possible to define the loading mode, i.e. displacement-constraint or force-constraint. \u0399n the experiments that were performed both in a corrosion-free and corrosion environment, the applied force was in the range between 400 \u039d and 700 N with fatigue stress ratio R=0 and a frequency of 40 Hz at ambient temperature. For fabricating the standardized by ASTM G38 C-rings specimens, two different manufacturing approaches were considered, (i) machining the parts conventionally from a rolled bar and (ii) by additive manufacturing. The maraging steel 18Ni-C300 round bar (see Table 1 for chemical composition) was received in a solution annealed state according to the standard AMS 6514 and ground to a diameter of 19 mm. Then, the as received bar was machined by turning and drilling to achieve the dimensions of the specimen presented in Figure 1. AM specimens were fabricated with the aid of an EOS M280 SLM machine. The specifications of the applied powder are also shown in Table 1. The applied layer size by the SLM process was 20 \u03bcm and the recoater positioning speed amounted to 80 mm/s. Subsequently, some of the AM specimens were glass-blasted for improving surface integrity. Table 1. Chemical composition of maraging steel 18Ni-C300 in rolled bar stock and powder for AM. Alloying elements (wt %) Bar stock Powder Fe Balance Ni 18.3 17.0 - 19",
            "01 Among the various treatments available to modify the surface characteristics of the specimens [13], glass-blasting was selected as one of the most commonly applied in AM parts. The blasting was conducted with glass grit of average diameter close to 100 \u03bcm at an air pressure of 3.5 bar, for a duration of 30 s and at 25 cm nozzle standoff distance to the target surface. For examining the surface characteristics of the specimens, a STIL MicroMesure 2 optical system was employed, enabling the visualisation of the 3D micro-topography with high-resolution and without any filtering. Fig. 1. Corrosion-fatigue set-up and C-ring specimen specifications. 3. Results and discussion All samples were metallographically prepared and observed through a Leica DM4000M optical microscope to assess their microstructure in solutionized state. Figure 2 presents micrographs of the wrought and SLM material. The latter was investigated both in its cross and longitudinal sections to better visualize the diversity of microstructure obtained during the evolution of layers. In general, SLM material features a finer cellular-dendritic structure compared to the wrought one and possesses a higher Rockwell C hardness, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002605_01691864.2018.1556116-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002605_01691864.2018.1556116-Figure2-1.png",
        "caption": "Figure 2. Quad-tilt-rotor with earth, body and additional new frames.",
        "texts": [
            " The benefits are to increase the degrees of freedom and improve the hovering of the quadrotor as well. One of the endeavors that is for improving the hover of the quadrotor without touching the issue of underactuation is inward tilting of the four rotors with a fixed angle. That mimics the dihedral angle in the fixed wing airplanes (see Figure 1). Hence, replacing the fixed dihedral angle with a varying one will add potential to the quadrotor to perfectly face more stability problems as recommended in the future work of the aforementioned work (see Figure 2). Thus, considering different tilting axes with changeable values is to trend the designmodification to servemore than one idea, i.e. increasing the DOFs and improving the hover. Furthermore, this thrust vectoring may be subjected to transform the quadrotor to a hybrid vehicle which can move onto surfaces using horizontal thrust force components (see Figure 3). For the proposed design, it is needed to make a slight change in the conventional configuration which maintains the moment balanced. This different configuration is to make the front and left propellers rotate clockwise while back and right ones rotate counterclockwise as in Figure 1(c)",
            " u1 m (6) Equations (4) and (6) represent the mathematical model of the conventional design of the quadrotor. More details about the conventional mathematical model derivation are given in [11\u201314]. In the next section, themodification supposed in this paper and the associated mathematical model will be described. The main modification of the quadrotor/quadcopter model is to permit every rotor to make a tilt angle about the axes perpendicular to its arm. Note that the rotational speed directions taken are as shown in Figure 2. Additional frames should be considered together with the main two frames, namely, the body and the earth frame. As a certain result from these additional frames, each frame should has its own rotationmatrix to the body frame and the earth frame. As shown in Figure 2 all the additional frames have the same orientation of the body frame. Thus the new rotationmatrices will be standard rotationmatrices about the y-axis for the left and right propellers and about the x-axis for the front and back propellers. The following equations represent the four additional rotation matrices as a function of the tilted angle (\u03b1i). Note that these relations are similar for the other two rotors while tilting is about the y-axis for rotors-1, 2 and about the x-axis for rotors-3, 4: Rb n1 = Ry,\u03b11 = Ry1 Rb n3 = Rx,\u03b13 = Rx3 Using thesematrices the thrust force andmoment vectors can be calculated in the body fixed frame as follows: (a) The thrust force vectors: Fbth1 = Ry1 \u00b7 Fth1 = \u23a1 \u23a2\u23a3 \u2212b\u03c92 1 \u00b7 s\u03b11 0 \u2212b\u03c92 1 \u00b7 c\u03b11 \u23a4 \u23a5\u23a6 Fbth2 = Ry2 \u00b7 Fth2 = \u23a1 \u23a2\u23a3 \u2212b\u03c92 2 \u00b7 s\u03b12 0 \u2212b\u03c92 2 \u00b7 c\u03b12 \u23a4 \u23a5\u23a6 Fbth3 = Rx3 \u00b7 Fth3 = \u23a1 \u23a2\u23a3 0 b\u03c92 3 \u00b7 s\u03b13 \u2212b\u03c92 3 \u00b7 c\u03b13 \u23a4 \u23a5\u23a6 Fbth4 = Rx4 \u00b7 Fth4 = \u23a1 \u23a2\u23a3 0 b\u03c92 4 \u00b7 s\u03b14 \u2212b\u03c92 4 \u00b7 c\u03b14 \u23a4 \u23a5\u23a6 (7) (b) The moment vectors: Mb 1 = Ry1 \u00b7 M1 = \u23a1 \u23a2\u23a3 \u2212d\u03c92 1 \u00b7 s\u03b11 0 \u2212d\u03c92 1 \u00b7 c\u03b11 \u23a4 \u23a5\u23a6 Mb 2 = Ry2 \u00b7 M2 = \u23a1 \u23a2\u23a3 d\u03c92 2 \u00b7 s\u03b12 0 d\u03c92 2 \u00b7 c\u03b12 \u23a4 \u23a5\u23a6 Mb 3 = Rx3 \u00b7 M3 = \u23a1 \u23a2\u23a3 0 \u2212d\u03c92 3 \u00b7 s\u03b13 d\u03c92 3 \u00b7 c\u03b13 \u23a4 \u23a5\u23a6 Mb 4 = Rx4 \u00b7 M4 = \u23a1 \u23a2\u23a3 0 d\u03c92 4 \u00b7 s\u03b14 \u2212d\u03c92 4 \u00b7 c\u03b14 \u23a4 \u23a5\u23a6 (8) From the thrust force vectors in Equation (7) and the drag moment vectors in Equation (8), it can be observed that the virtual inputs to the system will take a different form as follows: u1 = b\u03c92 1 \u00b7 c\u03b11 + b\u03c92 2 \u00b7 c\u03b12 + b\u03c92 3 \u00b7 c\u03b13 + b\u03c92 4 \u00b7 c\u03b14 u2 = b\u03c92 3 \u00b7 c\u03b13 \u2212 b\u03c92 4 \u00b7 c\u03b14 \u2212 d L \u03c92 1 \u00b7 s\u03b11 + d L \u03c92 2 \u00b7 c\u03b12 u3 = b\u03c92 1 \u00b7 c\u03b11 \u2212 b\u03c92 2 \u00b7 c\u03b12 \u2212 d L \u03c92 3 \u00b7 s\u03b13 + d L \u03c92 4 \u00b7 s\u03b14 u4 = \u2212d\u03c92 1 \u00b7 c\u03b11 + d\u03c92 2 \u00b7 c\u03b12 + d\u03c92 3 \u00b7 c\u03b13 \u2212 d\u03c92 4 \u00b7 c\u03b14 (9) Again, by using the Euler andNewton equations, the final form of the model will be given as \u03d5\u0308 = \u03b8\u0307 \u03c8\u0307 (Iy \u2212 Iz) Ix + IR Ix (\u2212\u03b8\u0307g\u03c93 + \u03c8\u0307g\u03c92)+ L Ix u2 (10) \u03b8\u0308 = \u03d5\u0307\u03c8\u0307 (Iz \u2212 Ix) Iy + IR Iy (\u2212\u03d5\u0307g\u03c93 + \u03c8\u0307g\u03c91)+ L Iy u3 (11) \u03c8\u0308 = \u03d5\u0307\u03b8\u0307 (Ix \u2212 Iy) Iz + IR Iz (\u2212\u03d5\u0307g\u03c92 + \u03b8\u0307g\u03c91)+ u4 Iz (12) mx\u0308 = \u2212b\u03c92 1(s\u03b11c\u03c8c\u03b8)\u2212 b\u03c92 2(s\u03b12c\u03c8c\u03b8) + b\u03c92 3(s\u03b13c\u03c8s\u03b8s\u03d5)\u2212 b\u03c92 3(s\u03b13s\u03c8c\u03d5) + b\u03c92 4(s\u03b14c\u03c8s\u03b8s\u03d5)\u2212 b\u03c92 4(s\u03b14s\u03c8c\u03d5) + (\u2212c\u03c8s\u03b8c\u03d5 \u2212 s\u03c8s\u03d5)u1 (13) my\u0308 = \u2212b\u03c92 1(s\u03b11s\u03c8c\u03b8)\u2212 b\u03c92 2(s\u03b12s\u03c8c\u03b8) + b\u03c92 3(s\u03b13s\u03c8s\u03b8s\u03d5) + b\u03c92 3(s\u03b13c\u03c8c\u03d5)+ b\u03c92 4(s\u03b14s\u03c8s\u03b8s\u03d5) + b\u03c92 4(s\u03b14c\u03c8c\u03d5)+ (\u2212s\u03c8s\u03b8c\u03d5 + c\u03c8s\u03d5)u1 (14) mz\u0308 = mg + b\u03c92 1(s\u03b11s\u03b8)+ b\u03c92 2(s\u03b12s\u03b8)+ b\u03c92 3(s\u03b13c\u03b8s\u03d5) + b\u03c92 4(s\u03b14s\u03c8s\u03b8s\u03d5)+ b\u03c92 4(s\u03b14c\u03b8s\u03d5)+(\u2212c\u03b8c\u03d5)u1 (15) While gw1 = (w1 \u00b7 s\u03b11 \u2212 w2 \u00b7 s\u03b12) gw2 = (w3 \u00b7 s\u03b13 \u2212 w4 \u00b7 s\u03b14) gw3 = (w1 \u00b7 c\u03b11 \u2212 w2 \u00b7 c\u03b12 \u2212 w3 \u00b7 c\u03b13 \u2212 w4 \u00b7 c\u03b14) This designmodification grants a total of 8 control inputs (4 propeller spinning velocities and 4 tilting angle) and makes it possible to obtain complete controllability over the main body 6 DOFs configuration thus rendering the quadrotor UAV an overactuated flying vehicle [3]",
            " curve which is under the horizontal axis represents the period in which the propellers\u2019 rotating speeds have not reached yet to the hover speed value. Figure 17(c) proves the decoupling between the roll angle and displacement in the y-direction where there is no motion in the ydirection, although the roll angle has a nonzero value. The other state variables of the quadrotor are maintained at zero value. Figure 18(a) shows the change of\u03b11 for both trajectories of the roll angle (\u03d5). The trend of \u03b12 change will be the same as \u03b11 but in the opposite direction (see Figure 2). The tilt angle \u03b134 is realized in Figure 18(b) where it settled at the value of (\u22122\u03d5ref .) just when the value of (\u03b112) went back to zero, the same result might be obtained from Equation (18). Referring to Figure 4, as the roll angle increases, the need for more thrust force increases to make its vertical component opposes the weight, this is obvious in Figure 18(c). Because of using Ix and Iy with the same values, the performance with a Figure 18. The response of the other variables in the system in case (1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001525_j.mechmachtheory.2013.04.001-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001525_j.mechmachtheory.2013.04.001-Figure11-1.png",
        "caption": "Fig. 11. 3D modal.",
        "texts": [
            " The planar internal gear intermittent rotates about axes zg with the rotating angle \u03c6g2 every time. Based on the tooth profile of planar internal gear, the kinematics relation can be represented as: vxg \u00fe vzg \u22c5vzg vxg \u00fe vzgjjvzg \u00bc cos \u03b2 \u03c6g2 \u00bc 2\u03c0 Z2 : 8>>>< >>>: \u00f018\u00de A planar internal gear with the major design parameters of example B,is machined by a milling machine. And the milling process is shown in Fig. 10. The 3D model of planar internal gear single-enveloping crown worm drive is built as shown in Fig. 11. The physical prototype of this novel drive is assembled with the machined crown worm and planar internal gear, as shown in Fig. 12. Compared with the traditional toroidal worm drive with the same gearing ratio and the samemodule [6], the center distance of this novel worm drive shortens 41.2%, the volume reduces about 12.1% and the weight decreases about 7.4%. To confirm the practical use of this novel worm drive, the following performance tests are carried out: running in of the drive, checking the temperature of oil and the efficiency of the drive [16]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002724_j.ymssp.2015.04.033-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002724_j.ymssp.2015.04.033-Figure1-1.png",
        "caption": "Fig. 1. Concept (a) and overview (b) of the presented test rig. The test bearing is mounted on a spindle and driven by an electric motor. The actuators apply a radial force (Fr) and an axial force (Fa) on the test bearing.",
        "texts": [
            ", The influence of external dynamic loads on the lifetime of rolling element bearings: Experimental analysis of the lubricant film and surface wear, Mech. Syst. Signal Process. (2015), http://dx.doi. org/10.1016/j.ymssp.2015.04.033i This section introduces the test rig used in the current study. Both the test rig design and measurements are discussed. Only the aspects which are relevant for this study are described. A full review of the test rig can be found in an earlier publication of the authors [11]. The main concept and overview of the test rig are outlined in Fig. 1. An electric motor drives a shaft through a flexible coupling. The shaft is supported by two bearings, forming a rigid spindle. At the end of the shaft, a third bearing is mounted. This is the test bearing. The load is directly applied on the stationary outer ring of the test bearing. The test rig allows applying a radial and axial load on different types and sizes of test bearings. The design is optimised to analyse the dynamic behaviour of the test bearing in a wide frequency range. The test rig allows mounting different types of bearings (such as deep groove ball bearings, angular contact ball bearings and tapered roller bearings) and different sizes of bearings (with an inner bore diameter varying from 10 to 19 mm, an outer diameter varying from 20 to 52 mm and a width varying from 5 to 15 mm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000280_s0076-6879(76)44043-0-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000280_s0076-6879(76)44043-0-Figure7-1.png",
        "caption": "FIG. 7. An Aminco filter fluorometer equipped with a cell and cell holder.",
        "texts": [
            " Each possible combination of pad color and filter was examined, and it was found that the most accurate results could be obtained if a gray silicone-rubber pad were used (Table III) . The silicone materials can retain a reactant film on their surfaces for an indefinite time and permit the direct measurement of fluorescence from their surface when an appropriate second reagent solution is applied onto the first reactant film. Background interference due to light scattering and nonspecific fluorescence is minimal compared to other materials. An Aminco filter fluorometer, set on its end (Fig. 7) and equipped with the cell and cell holder described below {Fig. 8), was used for all the fluorometric measurements. The fluorometer was supported by two wooden blocks placed parallel to the primary filter holder to prevent electric FTo. 8. The cell (lower drawing) is constructed of a cylindrical aluminum rod with a slot, approximately twice the length of the pad, located toward the end of the rod. The cell holder (top drawing) consists of an Aminco cuvette adapter with water circulating around it to maintain constant temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.10-1.png",
        "caption": "Figure 2.10. CAD model of a reactionless planar 3-dof mechanism",
        "texts": [
            " The individual balancing of the legs is justified by the fact that dynamic balancing is a property associated with the moving masses and inertia. The three point masses being equivalent to the platform, balancing will be achieved. Although the reaction forces and moments on the base of each leg may not be zero in the real system with the solid platform because of the distribution of the internal forces, the net reactions on the base will be equal to zero. A reactionless planar 3-dof mechanism is shown in Figure 2.10. The mechanism has been obtained using the synthesis approach described above and each of the 2- dof legs has been optimised (including a point mass) using the approach presented in the preceding section. Similarly, a reactionless spatial 3-dof mechanism is shown in Figure 2.11. In this case the three 2-dof legs are mounted in different planes and attached to a common platform through spherical joints. The platform, therefore, has three degrees of freedom in space. In both of the above cases, dynamic simulations were performed and the results obtained confirmed the reactionless property"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure1-1.png",
        "caption": "Fig. 1 Detailed component view of a typical railroad taperedroller bearing",
        "texts": [
            " The finite element (FE) model was used to simulate different heating scenarios with the purpose of obtaining the temperatures of internal components of the bearing assembly, as well as the heat generation rates and the bearing cup surface temperature. The results showed that, even though some rollers can reach unsafe operating temperatures, the bearing cup surface temperature does not exhibit levels that would trigger HBD alarms. [DOI: 10.1115/1.4006273] Keywords: railroad bearing thermal modeling, tapered-roller bearing heating, internal bearing temperatures, discolored rollers, excessive roller heating, thermal finite element analysis Tapered-roller bearings (see Fig. 1) are the most widely used bearings in railroad cars. When operated under satisfactory load, alignment, and contaminant free conditions, the service life is exceptionally long. As a general rule, bearings will outlast the wheel life, and survive several reconditioning cycles prior to being retired. At the end of their life, bearings will initiate fatigue, particularly subsurface fatigue, rather than wearing out due to surface abrasion. Fatigue failures, or spalling, can lead to material removal at the raceway surface which in turn will cause grease contamination and increased friction that manifests itself as heat within the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure4.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure4.3-1.png",
        "caption": "Fig. 4.3 Five-point wheel suspension system",
        "texts": [
            "6) is the quantity determining the degree of freedom f = 1 + d of the joint. An engineering realization of the constraint of a body to five surfaces is shown in Fig. 4.2 . The body, now called platform, is connected to a frame by five rods with spherical joints at both ends. Each surface is a sphere with the rod length as radius. The axes of the five rods are the complex lines. The platform on five rods finds an important engineering application in the fivepoint wheel suspension system for cars shown in Fig. 4.3 . The platform is the 142 4 Degree of Freedom of a Mechanism carrier of the wheel, and the frame is the car body. A single spherical joint on the car body is operated by the steering mechanism. When the steering is held fixed, the carrier has a single degree of freedom. Springs connecting the carrier with the car body allow small carrier displacements only. These displacements are screw displacements. The screw displacement of a platform can be made visible by the following experiment. Instead of mounting the platform on rigid rods it is suspended by five mutually skew inextensible strings in such a way that an equilibrium position exists in which the weight of the platform keeps all strings tight"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure7-1.png",
        "caption": "Figure 7 Five-axis transformation",
        "texts": [
            " The contours are filled with parallel contours as shown in Figure 6(a) or parallel lines as shown in Figure 6(b). For better continuity, the filling paths can be linked with short arcs or lines, thus generating a consecutive spiral line as shown in Figure 6(c) or zigzag line as shown in Figure 6(d). The five-axis process can be realized by rotating the part via two-axis turntable to orientate the surface normal toward the weld torch. During the rotation, any point P1 on the original too-paths will get to a new position P1 0 (Figure 7). In this Process planning for five-axis wire Fusheng Dai, Haiou Zhang and Runsheng Li Rapid Prototyping Journal section, we will give mathematical solutions for the calculation of five-axis transformation. Given 2 sequential points P1 and P2 on a path, fixed with vectors v1s and v2s respectively, which have been normalized. Rotating these two points around center point C(XC, YC, ZC), after the first rotation we get points P1 0 from P1, P 0 2 from P2 and vector v1t from v1s, after the second rotation we get points P 00 1 from P1 , P 00 2 from P2 and vector v2t from v2s shown in Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002338_icuas.2015.7152364-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002338_icuas.2015.7152364-Figure1-1.png",
        "caption": "Fig. 1. Definitions of state and control input",
        "texts": [
            " Therefore, the system may become unstable during the transition flight. We propose the flight control system without switching controller gains and a dynamical model. The dynamic inversion method, which is a linearization method without an approximation algorithm, is applied to a control problem of the UAV[4]. The validity of the proposed control system is verified through numerical simulation and experiment. II. DYNAMICS A. Parameter definitions State variables and control inputs of a QTW-UAV are defined as shown Fig.1. An inertial coordinate system is fixed by earth\u2019s surface. The origin of the body-fixed coordinate system coincides with the center of mass of the QTW-UAV. QTW-UAV can achieve vertical takeoff, landing and hovering flight, and high cruising speed by using two tilt wings. \ud835\udc48, \ud835\udc49 and \ud835\udc4a represent velocities of the UAV along \ud835\udc65\ud835\udc35 , \ud835\udc66\ud835\udc35 , and \ud835\udc67\ud835\udc35 axes, respectively.\ud835\udc43 , \ud835\udc44 , and \ud835\udc45 denote the angular velocities around each axis. The position and attitude of QTW-UAV is controlled by thrust \ud835\udc47 that is generated by propeller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001380_j.proeng.2013.08.229-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001380_j.proeng.2013.08.229-Figure2-1.png",
        "caption": "Fig. 2. (a) B axis movements scheme; (b) Clads deposition strategies top view.",
        "texts": [
            " In this case, the substrate material is a structural steel AISI 1045, whereas a stainless steel AISI 316L whose particle size is +45 -150 \u03bcm has been used for the deposited material. The chemical composition of both, substrate and deposited material, are shown in Table 1. Secondly, both, the carrier and protection gas are high purity Argon (99,999%) with a volumetric flow of 13 and 5.5 l/min, respectively. The optimization test piece geometry is based on a semi-sphere that has been turned out of an AISI 1045 bar. The strategies developed for this geometry require the B axis to rotate from 0 to 90\u00ba (Fig. 2a) according to the laser requirement of constant perpendicularity between the laser and the surface. In addition, in order to introduce a rotary movement in the C axis too, a slightly inclination of 5\u00ba in relation to the sphere generatrix has been given to the clad deposition strategies. Thereby there is a clad every 13\u00ba up to an amount of 27 clads (Fig. 2b). First of all, optimal values of power, feed and mass flow are selected for the test geometry, need to be selected. For that purpose, the different values vary according to the process window shown in Table 2. Once the tests are carried out, the clad geometry is measured with a LEICA DMC 3D optical profilometer. Both, the height and width of the clad are measured in three different sections of the clad, and, these measurements determine the geometrical parameters of the clad. deposition rate (DR), considered as an indicative of the process productivity, is calculated multiplying the midsection of the clad by the process feed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003348_j.matpr.2020.01.519-Figure1.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003348_j.matpr.2020.01.519-Figure1.1-1.png",
        "caption": "Fig. 1.1. Composition of the direct laser growth plant based on a robotic arm, where 1-powder feeder, 2-cladding head, 3-robot, 4-shielding gas (Ar), 5-laser source, 6- work table [1].",
        "texts": [
            " It is shown that by changing such process parameters as laser power, powder feed rate, head lift and hatch distance, it is possible to improve the quality of the cladding and substantially reduce the process-induced defects. 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry. Direct laser deposition (DLD) technology allows to grow large scale 3D-printed products from metal alloys [1]. A typical DLD installation scheme based on a 5-axis robot is shown in Fig. 1.1. It should be noted that most DLD setups, in addition to the shown components, also have a protective chamber, which allows to manufacture products in an inert environment. The main working part of the setup is a cladding head with 3 powder feed nozzles (see Fig. 1.2). There are a number of process parameters that directly affect the microstructure and quality of the final additively manufactured product. The main adjustable parameters in the setup shown in Fig. 1.1 are presented in Table 1.1. Due to a large a set of parameters, it is not always possible to correctly determine the source of a process-induced defect. In additive technologies the main focus is studying the structure of the material and obtaining optimal mechanical properties [2\u20137]. The quality and methods of obtaining powders for additive technologies are also studied [8\u201310]. For the practical application of the DLD method and its introduction into the industry, it is necessary to pay attention to the analysis and classification of the main defects formed during the cladding process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.3-1.png",
        "caption": "Figure 2.3. Schematic representation of a spatial 6-dof parallel mechanism with revolute actuators",
        "texts": [
            " The Cartesian coordinates of the platform are given by the position of point O' with respect to the fixed frame, noted p = [x, y, z]T and the orientation of the platform (orientation of frame O'-x'y'z' with respect to the fixed frame), represented by matrix Q, which can be written as 333231 232221 131211 qqq qqq qqq Q (2.12) where the entries can be expressed as functions of Euler angles, quadratic invariants, linear invariants or any other representation. Finally, the coordinates of centre points Pi (Figure 2.3) of the S-joints relative to the moving coordinate frame of the platform are noted (ai, bi, ci) with i = 1, \u2026, 6. A reference frame noted Oi1-xi yi zi is attached to the first link of the ith leg. Point Oi1 is located at the centre of the first revolute joint. The coordinates of point Oi1 expressed in the base coordinate frame are (xio, yio, zio), where i = 1, \u2026, 6. Moreover, the unit vectors defined in the direction of axes xi, yi and zi are denoted xi1, yi1 and zi1, respectively. Vector zi1 is defined along the axis directed from point Oi1 toward point Oi2 while vector xi1 is defined along the direction of the first revolute joint axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003097_j.rcim.2020.102053-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003097_j.rcim.2020.102053-Figure2-1.png",
        "caption": "Fig. 2. Screenshots of the single-robot validation scenario.",
        "texts": [
            " In the second step, the determined parameters were validated in Production Scenario with cooperating robots. The practice of EA involves the tuning of many parameters, such as population size, crossover and mutation rates. Section 5 shows an overview of the parameters which where examined in this work. Since computing time in a reduced scenario with one robot is considerably shorter than for the later application with cooperating robots, considerably more combinations of settings could be validated in a shorter time. Fig. 2 shows the validation scenario. It consists of a series of obstacles in blue, which severely restrict the robot\u2019s freedom of movement. The red box on the left side marks the starting point of the path, the green box on the right side the goal. The gray floor, the yellow ceiling and the wall are further obstacles. The wall position was chosen so close to the robot that it is forced to move the TCP in the front below the right blue obstacle to avoid a collision with axis 3. The presented system was also evaluated in a production scenario of an Airbus A320 fuselage section with a diameter of 1977 mm and a length of 2000 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.21-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.21-1.png",
        "caption": "Fig. 15.21 Points Q and M on a line e and centrodes k1 , k2 together with their centers of curvature Mp 1 , Mp 2",
        "texts": [
            " End of proof. Once the tangent to the centrodes is known, the theorem can be used for constructing the center of curvature M3 associated with an arbitrarily chosen point Q3 . This is done in the following steps. 15.3 Curvature of Plane Trajectories 485 1. Draw the line h\u2032 through P1 under the angle \u03b11 (known by now) against the line P1Q3 . 2. Construct the point A\u2032 as point of intersection of h\u2032 with the line Q1Q3 . 3. The desired point M3 is the point of intersection of the lines M1A \u2032 and P1Q3 . In Fig. 15.21 the points Q and M on an arbitrary line e are those of Fig. 15.18. In the figure also the centrode k2 fixed in \u03a32 and the centrode k1 fixed in \u03a31 together with their point P1 of rolling contact are shown. The centers of curvature of the centrodes at P1 are denoted Mp 1 and Mp 2 , respectively. They are located on the common normal to the centrodes. Let en be the unit vector directed from P1 toward Mp 2 . The radii of curvature 1 and 2 are defined by expressing the vector from P1 to Mp i (i = 1, 2) in the form ien ",
            "74) shows that the relationship between Mp 1 and Mp 2 is the same as the relationship between associated points M and Q on the line en . Equation (15.75) establishes between 1 , 2 and the radii R , r of any pair of associated points M and Q the relationship( 1 r \u2212 1 R ) sin\u03b1 = 1 2 \u2212 1 1 . (15.90) When 1 and 2 are known, this equation determines the center of curvature M for every point Q in the entire plane. Euler showed that this analytical solution is equivalent to the following geometrical solution. Construct in Fig. 15.21 the point B as point of intersection of the line QMp 2 with the perpendicular to e through P1 . Proposition: The center of curvature M lies at the intersection of e and BMp 1 . Proof: As auxiliary quantity the length b = BP1 is introduced. Similar triangles yield R b = R\u2212 1 sin\u03b1 1 cos\u03b1 , r b = r \u2212 2 sin\u03b1 2 cos\u03b1 . (15.91) Elimination of b produces (15.90). End of proof. Note: Unlike (15.90), the geometrical construction fails when Q and M are located on the normal en . Example: Equation (15.90) and the alternative geometrical construction of M are of particular interest in the case when the centrode k2 is materialized as circular wheel rolling on the inside or outside of another circular wheel k1 . Trajectories of points Q fixed in the plane of k2 are called trochoids. They are the subject of Sect. 15.5. For every position of Q the associated center of curvature is determined. Consider, for example, the special case when k1 is a straight line (a wheel of infinite radius 1 ) and when Q is a point on the circumference of k2 . The trajectory is the cusped cycloid b shown in Fig. 15.38 where the points Q and P1 are denoted C and P , respectively. In this case, the rule of construction in Fig. 15.21 shows that P is the midpoint between the generating point C and the center of curvature M . End of example. Equation (15.89) shows that the normal poles P1 and P2 do not suffice for determining 1 and 2 . In addition, also P3 must be known. An expression for 1 in terms of the coordinates of these three poles is found as follows. The circle of curvature with radius 1 has the equation x2 + y2 \u2212 2 1y = 0 . Hence 1 \u2261 (x2 + y2)/(2y) and 15.3 Curvature of Plane Trajectories 487 1 = lim x\u21920 x2 2y . (15",
            " Depending on the arrangement of the wheels and on the location of C on wheel 1 trochoids come in many different shapes. This makes them interesting for engineering applications. Mathematical investigations of trochoids started very early because of their role in the explanation of orbits of solar planets by cycles and epicycles (de la Hire [14], J. Bernoulli). The crank 2 connecting the centers of the wheels has no influence on the shape of trochoids. Its only purpose is to keep the wheels in touch and to make wheel 1 rolling. The curvature of trochoids was the subject of the example illustrating Fig. 15.21. 15.5 Trochoids 497 From the elliptic trammel in Fig. 15.4 the following results are known about wheels having the ratio 1 : 2 of radii with the small wheel being inside the larger wheel. If the small wheel is the planetary wheel 1 , trochoids are diameters of wheel 0 if C is located on the circumference of wheel 1 and ellipses otherwise. If the large wheel is the planetary wheel 1 , trochoids are limac\u0327ons of Pascal (Fig. 15.8). Three parameters suffice if the radii r0 and r1 of the wheels and the radius b of point C on wheel 1 are defined as quantities which may be positive or negative",
            " This yields for the x, y-coordinates of C and for their time derivatives the expressions x = r\u03d5\u2212 b sin\u03d5 , y = r \u2212 b cos\u03d5 , x\u0307 = \u03d5\u0307(r \u2212 b cos\u03d5) , y\u0307 = \u03d5\u0307b sin\u03d5 , x\u0308 = \u03d5\u0308(r \u2212 b cos\u03d5) + \u03d5\u03072b sin\u03d5 , y\u0308 = b(\u03d5\u0308 sin\u03d5+ \u03d5\u03072 cos\u03d5) . \u23ab\u23aa\u23ac \u23aa\u23ad (15.133) Depending on whether b < r or b = r or b > r ordinary cycloids are either curtate or cusped or prolate (Fig. 15.38). By the conventions of Sect. 15.5.2 only the cusped cycloids should be called cycloids. The indiscriminate name ordinary cycloid is much older than this convention. The cusped ordinary cycloid has in the cusps the acceleration coordinates x\u0308 = 0 , y\u0308 = r\u03d5\u03072 . (15.134) Another property was shown in the example illustrating Fig. 15.21: In every position \u03d5 the point of rolling P is midpoint between the generating point C and the center of curvature M . The inverse motion of a circle rolling along a straight line is the rolling of a straight line g on a fixed circle k of radius r0 . This is the situation when in Fig. 15.26 r1 is infinite. In Fig. 15.39 the line g is tangent to k at point A . To be investigated are the trajectories traced by the point B fixed on g and by the point P rigidly attached to g at the distance h on the perpendicular 508 15 Plane Motion through B "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.133-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.133-1.png",
        "caption": "Fig. 2.133 Parallel HE transmission arrangement for the HEV VW Golf II [VW-Bosch-LUK; SEIFFERT AND WALZER 1991].",
        "texts": [
            "8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 331 The supplementary electrical machinery is completed with little loss of comfort or luggage space of the vehicle. Embedded in place of the conventional ICE\u2019s flywheel is a compact DC-AC macrocommutator hyposynchronous squirrel-cage-rotor flywheel E-M motor. On the side to the ICE, as well as on the side to the MT or SAT or CVT, mechatronically activated M-M clutches are installed. The E-TMC system operates as stop-start (SS) clutches. Figure 2.132 shows the drive E-M motor and Figure 2.133 illustrates the operating rule arrangement. Only if the M-M clutch to the ICE is not turned on, the HEV is driven electrically, and during regenerative braking, electrical energy is being supplied to the CH-E/E-CH storage battery. If an ICE is propelling the vehicle, the M-M clutch on the ICE side is turned on; the squirrel-cage rotor of the DC-AC macrocommutator asynchronous squirrel-cage-rotor flywheel motor may then function as a flywheel. Besides, this electric drive unit acts as a starter E-M motor and as an onboard M-E generator [SEIFFERT AND WALZER 1991]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure2.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure2.4-1.png",
        "caption": "FIGURE 2.4. An Element in Cylindrical Coordinates.",
        "texts": [
            " Governing Equations from which the direct stress in the radial direction is determined to be: \u03c3rr = \u03bdE (1\u2212 2\u03bd) (1 + \u03bd) \u03b5+ E 1 + \u03bd err (2.20) Now using the definitions of the shear modulus and Lame\u2019s elastic constant, the direct radial stress is presented as: \u03c3rr = \u03bb\u03b5+ 2Gerr (2.21) In a similar procedure, the direct circumferential stress and the direct axial stress are represented in terms of the volumetric strain, Lame\u2019s elastic constant, the shear modulus, and the appropriate direct strains are presented in the following equations. \u03c3\u03b8\u03b8 = \u03bb\u03b5+ 2Ge\u03b8\u03b8 (2.22) \u03c3zz = \u03bb\u03b5+ 2Gezz (2.23) 2.4 Strain-Displacement Relationships In Figure 2.4, a small element of an elastic homogenous and isotropic medium is represented in cylindrical coordinates. The element contains the point A, which represents a given point having the coordinates of (r, \u03b8, z) and the point F , an infinitesimal distance away, having the coordinates (r + \u03b4r, \u03b8 + \u03b4\u03b8, z + \u03b4z). In this figure, the angle \u03b8 may be measured from any arbitrary coordinate direction such as x. A typical small linear deformation of this element is depicted in Figure 2.5 where displacement and the distorted shape of the enlarged element is outlined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure18.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure18.2-1.png",
        "caption": "Fig. 18.2 Examples of the Magnus force acting on (a) a spinning paper cylinder and (b) a spinning balloon",
        "texts": [
            " A baseball or softball pitched with spin about its vertical axis curves either to the left or right, depending on the direction of spin, while a baseball or softball spinning rapidly about a horizontal axis can curve up like a golf ball or down like a tennis ball, depending on the amount and direction of spin. If a ball is spinning slowly about a 296 18 Bat and Ball Projects horizontal axis, then it will curve down due to gravity regardless of the spin direction since the Magnus force is then much smaller than the gravitational force. A simple demonstration of the Magnus effect is shown in Fig. 18.2a. The object here is a paper cylinder constructed from half an ordinary sheet of writing paper with one edge joined to the opposite edge with adhesive tape. If the cylinder is rolled down a flat, inclined sheet of cardboard or a plank of wood, then the cylinder will spin through the air after it rolls off the bottom end. One would normally expect that the cylinder would fall to the floor and land a few feet beyond the bottom end of the incline. Instead, the cylinder curves back underneath the incline due to the Magnus force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003544_j.jmapro.2021.02.002-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003544_j.jmapro.2021.02.002-Figure2-1.png",
        "caption": "Fig. 2. Edge welding of the nickel alloy foil pair (unit: mm).",
        "texts": [
            " The length and width of the foil were cut to 100 mm and 25 mm, individually. The chemical composition of the foil was tested by an X Ray Fluorescence, shown in Table 1. It was reported that Inconel 718 alloy was a kind of Fe-Ni alloy that was able to serve under high temperature less than 650 \u25e6C. Its base microstructure is Fe-Ni austenite. Al, Ti and Nb were added to form some intermetallic compounds with Ni for strengthening. And the carbides were also able to strengthen the alloy. In order of simplification a straight edge joint shown in Fig. 2(a) was designed to simulate the forming of the edge joint of the ring, shown in Fig. 1. A pair of foil whose thickness was 0.2 mm were welded at their edge without any filling. A welding fixture was designed shown in Fig. 2 (b). The moving precision of the fixture was 0.01 mm. And the extension of the foil before welding was able to be controlled by the fixture. A laser beam whose power was able to be controlled precisely by a computer system was applied on the foil pair for joining shown in Fig. 2 (a). The wave length of the laser beam was 1060 nm and the spot diameter was 0.3 mm. The moving path of the laser beam was led by an ABB robot. The continuous and pulsed laser beams were both tried to join the foil pair, respectively. The welding parameters including laser power, welding speed and duty ratio were all considered to evaluate the effect of heat input on the joint geometry and hot cracking of the edge joint. Table 1 Chemical composition of Inconel 718 alloy (mass fraction/%). Element Ni Cr Co Mo Nb Ti Al C Mn Si Cu Fe Ratio 50"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure6.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure6.4-1.png",
        "caption": "Fig. 6.4 Motion of a bat subject to various forces",
        "texts": [
            " In fact, the swing was almost a carbon copy of the one analyzed in considerable detail by Adair in his book [3]. The question we now ask is, what does a batter actually do when he swings a bat? A batter grabs hold of the bat handle with both hands. What force does he apply to the handle with each hand, and in what direction do those forces act? To work out the forces on a bat, it will help to first consider the effect of forces in a more general way. Figure 6.3 shows the effect of a vertical force on a baseball and the effect of horizontal forces on a block of wood. Figure 6.4 shows the effect of various forces on a bat. If a ball is held at rest in the hand and then dropped vertically, the force of gravity acts in a vertical direction through the middle of the ball, and the ball falls vertically in a straight line, as shown in Fig. 6.3a. In Fig. 6.3b, the ball is thrown horizontally and follows a curved path, despite the fact that the same force of gravity acts on the ball as in Fig. 6.3a. In Fig. 6.3b, the ball travels at constant speed in the horizontal direction since there is no horizontal force on the ball (apart from the small horizontal force due to air resistance)",
            " If F1 is bigger than F2 then the block will move to the right, but if F1 is smaller than F2 then the block will move to the left. The block also rotates. There is a torque F1d1 which, on its own, would cause the block to rotate counter-clockwise. The torque F2d2, on its own, would cause the block to rotate clockwise. The final result depends on the total torque F1d1 F2d2 which could be positive or negative or zero depending on the values of the F \u2019s and the d \u2019s. The block will rotate in a clockwise direction if F2d2 is larger than F1d1. Figure 6.4 shows the results of applying various forces to a bat. The centre of mass of the bat is shown by a black dot, and it is located about 10 in. from the end of the barrel. Figure 6.4a shows the effect of applying a force F at right angles to a bat, in line with its center of mass (CM). If the mass of the bat is m then the acceleration of the bat is given by F D ma or a D F=m. If the bat is initially at rest then the whole bat accelerates to the left without rotating. You can try this yourself by pushing a ruler (or a pencil) along a table. In that case, the CM of the ruler is probably in the middle, so you will need to push in the middle to avoid any rotation. Actually, you might need to cheat a little and push with two fingers, since friction with the table might cause one end to get stuck and then the ruler will rotate, which will ruin the whole experiment. Physics experiments are often like that. Scientists set out to observe or measure something and might discover that something else is just as important if not more so. That is how things often get discovered but it can be frustrating for a beginner. Figure 6.4b shows the effect of applying a force at right angles to the handle, using both hands. One hand exerts a force F1 to the right and the other exerts a force F2 to the left. Provided that F2 is larger than F1 then the whole bat will accelerate to the left. But how do we make sure that the bat also rotates counter-clockwise, as shown in Fig. 6.4b? Given that F2 is larger than F1, won\u2019t the bat rotate clockwise, in the wrong direction? To ensure that the bat rotates in the correct direction, the torque due to F1 must be bigger than the torque due to F2. Such a result will be achieved if F2 is only slightly bigger than F1 and if F2 acts along a line that is closer to the bat CM than F1. You can try this with a pencil or a ruler on a table. Your brain will tell you what to do without even thinking about the physics of it. You don\u2019t need two hands to rotate a pencil or a ruler in the manner shown in Fig. 6.4b. You can rotate a pencil or a ruler using just one hand, swinging it through the air like a small table-tennis bat. In that case, the two separate forces are supplied by different parts of the same hand. The part of the hand near the index finger supplies the force F2 and the part closest to the little finger supplies the force F1. Alternatively, you can push and rotate a ruler on the table using just the thumb and the index finger of the same hand. 92 6 Swinging a Bat Figure 6.4c shows a situation where the bat CM is moving in a curved path at speed v, and the whole bat is simultaneously rotating counter-clockwise about an axis through the CM. To move in a curved path like this, there must be a force on the bat acting at right angles to the curved path, similar to the situation shown in Fig. 6.3b for the curved ball path. In Fig. 6.4c, the force F on the handle acts in a direction that is almost along the handle but it is at a slight angle to the handle. That is exactly what the batter needs to do to hit the ball as fast and as far as possible. The force is directed towards the batter\u2019s body and causes the bat CM to follow a curved path. In addition, the force generates a torque on the bat causing the whole bat to rotate in such a way that the barrel speeds up as it approaches the ball. Simultaneously, the handle slows down. Near the end of the swing, the bat rotates so fast that the handle pushes backward against the hands, causing the forearms to slow down",
            " The batter starts the swing with the knob pointing roughly toward first base or even further around toward the catcher. Contact with the ball is made when the bat is aligned at right angles to path of the ball. To rotate the bat in this manner, the batter also needs to exert a torque on the handle. There are two ways that a batter can exert a torque on the bat, and both of them are used to swing the bat at different stages of the swing. One way is to push with one hand and pull with the other, as shown in Fig. 6.4b. The other way is to pull with both hands at a slight angle to the bat, as shown in Fig. 6.4c. The situation in Fig. 6.4b is used at the start of the swing and the situation in Fig. 6.4c is used near the end of the swing. There is a great deal of information contained in Figs. 6.5 and 6.6, and it allows us to determine the forces and torques acting on the bat, at least in the horizontal plane. Batters normally swing a bat in a plane that is inclined to the horizontal, given that the tip of the bat starts at a point above the shoulders and drops to about waist level when the bat collides with the ball. To obtain the results in Figs. 6.1, 6.5, and 6.6, the batter was asked to swing in a horizontal plane, although he started off with the bat near shoulder height, a bit closer to the camera",
            " The object of the exercise, assuming the batter wants to hit the ball at high speed, is to allow the bat to line up almost at right angles to the path of the incoming ball at a time when the impact point on the barrel is traveling at maximum speed. The forces shown in Figs. 6.7 and 6.8 are not the only forces acting on the bat. In addition, the batter exerts a torque on the bat to make it rotate. If the batter exerts equal and opposite forces on the handle, using both hands, then those forces will have no effect on the motion of the bat CM but they will cause the bat to rotate, as indicated in Fig. 6.4b. In Fig. 6.4b, we show the two forces as F1 and F2. If these two forces are equal and opposite then there is no net force on the bat but there is still a torque or turning force. Two equal and opposite forces acting in this way are known as a \u201ccouple.\u201d The rate of rotation of the bat is determined by the total torque acting on the bat. That torque can conveniently be regarded as consisting of three separate parts that all add up to give the total torque. The batter just does what he needs to do, so the three separate parts are not part of three separate actions",
            " The value of B remains negative throughout the swing, meaning that the force component M dV=dt acts in the correct direction to accelerate the bat, but it acts in 98 6 Swinging a Bat the \u201cwrong\u201d direction in terms of bat rotation. It is for that reason that the batter must apply a small positive couple near the start of the swing to make sure the bat rotates in the correct direction. He does that by keeping his wrists locked so that barrel of the bat does not get left behind when he first applies a force to the handle. The situation near the start of the swing can be explained with reference to Fig. 6.4b. If F1 D 0 then the force F2 would cause the bat CM to move and accelerate to the left, but the torque due to F2 would cause the bat to rotate in the wrong (clockwise) direction and the tip of the barrel would move to the right. To overcome this problem, the batter needs to apply an additional force F1. The combined effect of F1 and F2 can be described as a net force F D F2 F1 acting to the left plus a couple that is large enough to rotate the bat in the correct (counterclockwise) direction. As the bat accelerates, the couple required to rotate the bat in the correct direction decreases, because the torque due to the centripetal force increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001565_0954406214562632-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001565_0954406214562632-Figure11-1.png",
        "caption": "Figure 11. The uneven tooth surface of pinion.",
        "texts": [],
        "surrounding_texts": [
            "Make use of Matlab to program and calculate the machining adjustment parameters of gear and pinion, then put in the above parameters to get their tooth surface discrete points cloud, and output the points cloud data documents as shown in Figure 5. Sample 12,445 discrete points of gear and 24,644 of pinion, which is adequate for the precision of modeling and processing such gears with geometry specification. Based on the design parameters of gear set shown in Table 1, the adjustment parameters can be calculated through Matlab program. Tables 2 and 3 indicate the calculated adjustment parameters for gear and pinion, respectively. Ru, g, P!2, and ! are the cutter parameters for gear; Rp, p, and f are the cutter parameters for pinion; Sr2, q2, Em2, XB2, XD2, and m2 are the gear machine-tool settings; Sr1, q1, Em1, XB1, XD1, and m1 are the pinion machine-tool settings; m1c (m2c) is the ratio of instantaneous angular velocities of the pinion (gear) and the cradle; C and D are the modified roll coefficients for calculating rotation angle. Digital true tooth surface modeling The curved surface reconstructed in the 3D software (SolidWorks) via leading points cloud documents by means of reverse engineering, is not smooth but stitched by many small curved surfaces, as shown in Figures 6 to 12. A crack seems to be in the middle of the curved surface, which not only influences the visual effects, but also prevents contact analysis and xm1 ym1 zm1 ya1 oa1 za1 xa1 yb1 y1 o1 (ob1) x1 xb1 z1 (zb1) \u0394Em1 \u0394X B1 \u0394X D1 m 2 \u03a6 1 om1 \u03b3 Figure 4. Workpiece coordinate system for pinion. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from solution in FEA, and even contact setting. Therefore, it is necessary to adopt other methods or approaches to deal with the reconstruction. The uneven tooth surface is modeled via the function of \u2018\u2018Scan To 3D.\u2019\u2019 Points cloud can almost automatically form the curved surface in software only by simple operations, at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from in no need of many man-made operations. However, by use of \u2018\u2018Scan To 3D,\u2019\u2019 some points cannot be scanned and thus ignored. Moreover, as the sequence and path of scan cannot be controlled, the surfaces do not look smooth with numerous cracks. In order to solve these problems, the method of \u2018\u2018Lofted Surface\u2019\u2019 is adopted to create the surface. Firstly, all the points make up lines in order. Secondly, use the function of \u2018\u2018Lofted Surface\u2019\u2019 to select the lines in sequence. Thirdly, form the smooth surfaces. Finally, by means of \u2018\u2018Clipping,\u2019\u2019 \u2018\u2018Array,\u2019\u2019 and other operations, model smooth spiral bevel gear and pinion. The digitized and high-precision true tooth surfaces under the study of this paper are shown in Figures 13 and 14. Smooth tooth surface can also reduce model errors and lay a foundation for high precision machining and FEA. Gear cutting and contact pattern experiments To verify the technical advancement and practicability in engineering digitized true tooth surface of spiral bevel gear based on machining adjustment parameters, this study gets the NC codes via NC process simulation software from 3D model with machining adjustment parameters and then inputs the codes to five-axis NC machine tools to conduct gear cutting experiments. Figures 15 and 16 show the processing of gear cutting in YH606 CNC Curved Tooth Bevel Gear Generator made by Tianjin Jing Cheng Machine Co., Ltd of China. The gear and pinion after processing are as shown in Figures 17 and 18, which completely meet the required design precision. Figure 13. The smooth tooth surface. Figure 12. The uneven assembly drawing of spiral bevel gear. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from To better illustrate the problem, other related experiments have also been conducted. The illustration of VHG is shown in Figure 19. H is the movement along the pinion axis, while G is the movement along the gear axis, and V is the offset of the gear set. When doing the experiments of contact pattern for spiral bevel gear set, keep the offset (V) at the value of 0, and the true backlash for the gear is set at 0.22mm. Each time, only change the value of H from 0.2 to \u00fe0.2. In this way, three experiments have been done, setting the value of H as \u00fe0.2, 0, and 0.2, respectively. The transmitted torque of contact patterns experiment was 20Nm according to at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from some standard; Figures 20 to 22 show the results of contact pattern experiments of three complete teeth in gear, without use of any correction in the tooth surfaces of pinion, from which it can be told that the contact pattern for the gear set is not bad, for it satisfies all the requirements of engineering. The gear cutting experiment can prove the validity of the precise modeling method of spiral bevel gear true tooth surface, which can be used in mechanical engineering, besides theoretical research. Breaking the blockade on Gleason technology, the spiral bevel gear true tooth modeling method, without any Gleason at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from software, can calculate the machining adjustment parameters. General NC machine can also be used to process spiral bevel gear, needless of special purpose machine for Gleason spiral bevel gear and Gleason software. This is the contribution of this research, other method cannot processing spiral bevel gear in general NC machine, the special purpose machine of spiral bevel gear and Gleason software are needed. The gear contact pattern experiments are the test method for the rotating gear pair. From the contact spot, vibration and noise of gear pair can be assessed in the same case. The use of standard spherical involute 3D model has no meaning in engineering, for it fails to get good contact pattern. In fact, spiral bevel gear is not the standard spherical involute, but just a modified spherical involute. It is the value and the reason why to use machining adjustment parameters to get the true tooth surface precise modeling processed in NC machine."
        ]
    },
    {
        "image_filename": "designv10_12_0000444_s12206-008-0110-9-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000444_s12206-008-0110-9-Figure11-1.png",
        "caption": "Fig. 11. Photograph of acoustic modal test setup.",
        "texts": [
            " A structural modal test was performed by random excitation with a shaker to examine the structural frequency response of the motor and its test setup is shown in Fig. 9. The frequency response function of the motor is shown in Fig. 10, where no resonance is observed near 650 Hz. Therefore, the noise component of 650 Hz seems not to be related to the mechanical resonance. To examine the acoustic characteristics of the motor internal airspace, white noise excitation by a horn driver is applied to the motor at standstill through a 25 mm diameter hole introduced on the rotor frame, and the noise is measured by a microphone as shown in Fig. 11. The acoustic frequency response function is shown in Fig. 12 where acoustic resonance is observed near 650Hz. In many cases, noise independent of the motor RPM can be regarded as structural resonance. However, for the test motor, acoustic resonance seems to be more dominant than structural resonance. To confirm the existence of acoustic resonance near 650Hz, acoustic mode analysis is performed with commercial FEM software Sysnoise to consider complexity of the motor internal geometry.[14,15] The internal airspace of the motor is modeled by using 39,288 elements and 29,088 nodes as shown Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure3-1.png",
        "caption": "Fig. 3. Contact modeling.",
        "texts": [
            " The designation \u201cdiscrete element\u201d recalls that the model comes from granular media [6]. The ball bearing is considered as a ball chain. By using the DEM, the contact forces between particles are described with a contact model depending on elastic force displacement law, Coulomb friction and viscous damping coefficient. The principle of the calculation is based on dynamic considerations. If contact is detected, so \u03b4n = Rij \u2212 Ri \u2212 Rj b 0, the springs are activated; here \u03b4n denotes the normal overlap, as suggested by Fig. 2. The equivalent model of the contact is given by Fig. 3, where 4 parameters and \u03bc, the dry friction coefficient, are introduced. Kn and Kt respectively represent the normal stiffness and the tangential stiffness. Nevertheless, stiffnesses are not sufficient to describe the contact correctly, and a viscous damping force is also considered. To dissipate energy and move towards a steady state system, dampers are introduced in the normal direction, Cn and in the tangential direction, Ct. The force F ! i between particles includes the inter-particle interaction forces F ! i j and the external forces F ! ext;i F ! i \u00bc X j\u2260i F ! i j \u00fe F ! ext;i \u00f01\u00de F ! i j is the force exerted by particle j on particle i. F ! ext;i are the external forces acting on particle i (gravity, loading\u2026). The contact force F ! i j depends on the model chosen. As shown in Fig. 3, this model included a normal component and a tangential component, F ! i j is then decomposed as follows: F ! i j \u00bc Fn n !\u00fe Ft t ! : \u00f02\u00de Fn is the contact force in the normal direction and Ft is the contact force in the tangential direction. In order to describe the interactions, expressions are available to calculate the parameters Kn, Cn, Kt and Ct. Usually, these parameters are related to each other. Whatever the choice of the stiffness/damper expression, the force components at the contact can be written as follows: Fn \u00bc Kn \u03b4n \u00fe Cn v"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.4-1.png",
        "caption": "Fig. 15.4 Orthogonal (a) and nonorthogonal (b) guides for points A and B . Fixed centrode k1 and moving centrode k2 . Elliptical trajectory of Q fixed in \u03a32 (c)",
        "texts": [
            " There, it is shown that the motion of the central cross in a Hooke\u2019s joint is the inverse of the motion studied here. A plane normal to the body-fixed line 0P2 intersects the moving cone in the circle (x = x\u2032/ cos\u03b1 ) (x\u2032 \u2212 1 2 sin\u03b1) 2 + y2 = ( 12 sin\u03b1) 2 . (10.20) 10.3 Bryan Angles 333 In the case \u03b1 1 both cones are circular cones with the curves (x\u2212 \u03b1 2 ) 2 + y2 = (\u03b12 ) 2 , X2 + Y 2 = \u03b12 . (10.21) The smaller circle is rolling inside the fixed circle which is twice as big. These circles are met again in Sect. 15.1.2 (Fig. 15.4a). End of example. Figure 1.1a yields for the angular velocity vector \u03c9 the expression \u03c9 = \u03c8\u0307e13 + \u03b8\u0307e2 \u2032 1 + \u03c6\u0307e23 . (10.22) The vectors are decomposed in basis e2 . With the help of (1.26) this results in the coordinate equations\u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 = \u23a1 \u23a3 sin \u03b8 sin\u03c6 cos\u03c6 0 sin \u03b8 cos\u03c6 \u2212 sin\u03c6 0 cos \u03b8 0 1 \u23a4 \u23a6 \u23a1 \u23a3 \u03c8\u0307 \u03b8\u0307 \u03c6\u0307 \u23a4 \u23a6 . (10.23) Inversion yields the desired differential equations:\u23a1 \u23a3 \u03c8\u0307 \u03b8\u0307 \u03c6\u0307 \u23a4 \u23a6 = \u23a1 \u23a3 sin\u03c6/ sin \u03b8 cos\u03c6/ sin \u03b8 0 cos\u03c6 \u2212 sin\u03c6 0 \u2212 sin\u03c6 cot \u03b8 \u2212 cos\u03c6 cot \u03b8 1 \u23a4 \u23a6 \u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 . (10",
            " The associated points of the centrode have the coordinates [x = 0 , y = \u2212(a2 \u2212 b2)/ \u221a a2 + b2 ] , [x = 0 , y = 0 ] and [x = (a2 \u2212 b2)/ \u221a a2 + b2 , y = 0 ] , respectively. The entire centrode is obtained by reflecting the curved segment connecting these three points in the x-axis and in the y-axis. The centrode has the form of a rosette with four leaves of equal length (one pair of leaves different in shape from the other). Similar arguments lead to equations for the centrode fixed on the follower. This centrode is an oval with a single axis of symmetry along the bisector of the right angle. Example 2 : Elliptic trammel In Fig. 15.4a a rod of length is shown the endpoints A and B of which move along mutually orthogonal guides. These guides define the plane \u03a31 . The rod is part of the infinitely extended plane \u03a32 . The instantaneous center P is the intersection point of the perpendiculars drawn as dashed lines. In 456 15 Plane Motion every position of the rod its distances from M and from the midpoint C of the rod are and /2 , respectively. From this it follows that the circles shown in the figure are the centrodes. Theorem 15",
            "1 the motion of a body with a fixed point 0 was investigated two points P1 and P2 of which are constrained to two mutually orthogonal fixed planes E1 and E2 , respectively. In the projection along the line of intersection of E1 and E2 these planes are mutually orthogonal guides for the projections of P1 and P2 . When the apex angle \u03b1 in the triangle (P1,0,P2) is very small, the polhode cone and the herpolhode cone have the circular cross sections described by Eqs.(10.21). These are the circles shown in Fig. 15.4a where the two points are called A and B . End of remark. Obviously, not only the points A and B on the circumference of k2 , but every point on this circumference moves along a straight line through M . Hence two wheels having the diameter ratio 1 : 2 can be used for guiding the endpoints of a rod along two lines under an arbitrary angle \u03b1 (see Fig. 15.4b). If is again the rod length, the radius of the small wheel is /(2 sin\u03b1 ) . This follows from the theorem that in the small circle the central angle subtended by the chord equals 2\u03b1 . During two full revolutions of k2 the rod moves through all four quadrants of k1 . From an engineering point of view the generation of this motion by means of two toothed wheels is better than by sliding two points along straight guides. The simplest possible forms of toothed wheels are shown in Fig. 15.5 . On the small wheel cylinders of arbitrary diameter are fixed with their centers on the circumference of k2 . Every cylinder is moving in a slot cut into the big wheel. The cylinders and the slots are the flanks of the teeth. The minimum number of teeth is two. Pins, as the cylinders are called, are the historically oldest forms of teeth. See also Sec. 16.1.5 . 15.1 Instantaneous Center of Rotation. Centrodes 457 In what follows, the trajectory of an arbitrary point Q fixed in \u03a32 is investigated. The straight line passing through Q and C intersects k2 at two points A and B (see Fig. 15.4c). After what has been said these points move along mutually orthogonal straight lines passing through M . These lines fixed in \u03a31 constitute the x, y-system best suited for the description of the trajectory of Q . With r denoting the radius of the small circle and with the distance R of Q from C the x, y-coordinates of Q are x = (r \u2212R) cos\u03d5 , y = (r +R) sin\u03d5 . (15.8) In the special cases R = r and R = \u2212r , these are the equations of the straight lines x \u2261 0 and y \u2261 0 , respectively. In all other cases, the constraint equation cos2 \u03d5+ sin2 \u03d5 = 1 produces the equation of an ellipse: x2 (r \u2212R)2 + y2 (r +R)2 = 1 ",
            " Hence the conclusion: A rod with endpoints moving along straight guides as well as a set of gear wheels having the diameter ratio 1 : 2 is capable of generating elliptical trajectories with arbitrary ratio of principal axes. For this reason both systems are referred to as elliptic trammel. Darboux Motion Before continuing with plane motion a harmonic translation along the axial z-axis is superimposed on the rolling motion. Let z(\u03d5) = a sin\u03d5 with arbitrary amplitude a be the displacement when the radius MC is under the angle \u03d5 against the x-axis as shown in Fig. 15.4c . In this so-called Darboux motion the circles k1 and k2 are the cross sections of raccording cylinders. Proposition: The trajectory of every body-fixed point is located in a plane (every point in its own plane) and, furthermore, these trajectories are either ellipses or straight-line segments. Proof: As representative point the point is chosen which has in the position \u03d5 = 0 the coordinates x = (r \u2212 R) cos\u03d50 , y = (r + R) sin\u03d50 , z = z0 458 15 Plane Motion with arbitrary constants R , \u03d50 , z0 ",
            "10) It is satisfied by F = a sin\u03d50 r \u2212R G = \u2212a cos\u03d50 r +R K = \u2212z0 . (15.11) This proves that the trajectory is planar. That it is either an ellipse or a straight-line segment follows from the fact that its projection onto the x, yplane is described by (15.9). End of proof. Darboux [7] showed that this special motion is the only nonplanar motion (planar in the narrower sense defined following (15.1)) having the property that every body-fixed point is moving in a plane (see also Bottema/Roth [4]). After this digression the plane motion shown in Fig. 15.4a is considered again. In what follows, the inverse motion is investigated. This means that the small circle k2 is stationary. The large circle k1 is rolling on k2 . Every diameter of k1 is sliding through a fixed point on k2 . This is shown in Fig. 15.6a . The two mutually perpendicular diameters of k1 which up to now were fixed guides for moving points A and B are now moving lines g1 and g2 which are guided through fixed points A and B , respectively. An engineering realization is the Oldham coupling of which an exploded view is shown in Fig. 15.6b . The fixed points A and B are located on the axes of two parallel shafts with discs 1 and 2 . Grooves on these discs are guides for the lines g1 and g2 which are materialized as rails on the central disc 3 . The Oldham coupling transmits the angular velocity of one shaft to the other. 15.1 Instantaneous Center of Rotation. Centrodes 459 Figure 15.7a shows the circle k1 rolling on the fixed circle k2 . As in Fig. 15.4a the radii are denoted for k1 and /2 for k2 . Also the notations P and M for the instantaneous center of rotation and for the center of k1 are the same. To be investigated is the trajectory of an arbitrary point Q fixed on k1 at the radius R (R < or R = or R > ). This point Q determines two mutually perpendicular diameters fixed on k1 which are sliding through fixed points A and B on the circumference of k2 . The trajectory of Q , from now on abbreviated q , is most easily described in the x, y-system with origin A and with the x-axis along the diameter AB of k2 ",
            " Next, the motion of \u03a32 is again interpreted as rolling motion of the centrode fixed in \u03a32 on the centrode fixed in \u03a31 . The point of rolling contact is P . The point of \u03a32 coinciding with P has, instantaneously, zero velocity and the acceleration a0 in y -direction. From this it follows that its trajectory has a cusp in P . The trajectory into and out of P is tangent to the y -axis. This means that the y -axis is the common normal of both centrodes, and the x -axis is the common tangent. Example: In the elliptic trammel shown in Fig. 15.4a the circle k2 is the moving centrode. It was shown that all points of k2 move on straight lines. From this it follows that k2 is also the inflection circle. The second Bresse circle has its center on the tangent to the inflection circle in P . Its radius depends on \u03d5\u0308 . End of example. The inverse of the motion of \u03a32 relative to \u03a31 is the motion of \u03a31 relative to \u03a32 . For angular velocity and angular acceleration of \u03a31 and for velocities and accelerations of points fixed in \u03a31 (9.17), (9.18) and (9",
            " With the additional abbreviation r1 \u2212 r0 = a the complex numbers are rA = aei\u03bb\u03d5 , r = aei\u03bb\u03d5 + bei\u03d5 . (15.63) The n th derivative of r is 478 15 Plane Motion r(n) = in(\u03bbnaei\u03bb\u03d5 + bei\u03d5) = in[r \u2212 a(1\u2212 \u03bbn)ei\u03bb\u03d5] . (15.64) With this expression Eq.(15.57) for the normal pole Pn becomes rPn = a(1\u2212 \u03bbn)ei\u03bb\u03d5 = (1\u2212 \u03bbn)rA (n \u2265 1) . (15.65) Hence rPn \u2212 rA = \u2212\u03bbnrA . This shows that the normal poles are located on the normal to the centrodes, and that their distances from the center of the planetary wheel form a geometric series. The elliptic trammel in Fig. 15.4 is the planetary gear with \u03bb = \u22121 . In this special case, the normal poles coalesce alternatingly with P1 and with the center of the planetary wheel. End of example. Let P\u2217 n be the n th-order normal pole of the inverse motion (motion of \u03a31 relative to \u03a32 ). From Sect. 15.1 it is known that P\u2217 1 =P1 . Furthermore, from Fig. 15.17 it is known that P\u2217 2 and P2 are located symmetrically to P1 on the normal to the centrode. With (15.53) P\u2217 n (n \u2265 1 arbitrary) is expressed in terms of P1, . . . ,Pn as follows",
            " This makes them interesting for engineering applications. Mathematical investigations of trochoids started very early because of their role in the explanation of orbits of solar planets by cycles and epicycles (de la Hire [14], J. Bernoulli). The crank 2 connecting the centers of the wheels has no influence on the shape of trochoids. Its only purpose is to keep the wheels in touch and to make wheel 1 rolling. The curvature of trochoids was the subject of the example illustrating Fig. 15.21. 15.5 Trochoids 497 From the elliptic trammel in Fig. 15.4 the following results are known about wheels having the ratio 1 : 2 of radii with the small wheel being inside the larger wheel. If the small wheel is the planetary wheel 1 , trochoids are diameters of wheel 0 if C is located on the circumference of wheel 1 and ellipses otherwise. If the large wheel is the planetary wheel 1 , trochoids are limac\u0327ons of Pascal (Fig. 15.8). Three parameters suffice if the radii r0 and r1 of the wheels and the radius b of point C on wheel 1 are defined as quantities which may be positive or negative",
            " Two arbitrarily chosen n -tuples of this kind define two suitable cranks and, thus, a four-bar. Whether a four-bar thus determined produces the prescribed positions in the prescribed order remains to be seen. The problem of order is the subject of Sect. 17.14.4 . In what follows, n homologous points on a circle are called circle points, and the center of the circle is called center point. The slider-crank mechanism in Fig. 17.29a is a degenerate four-bar in that one center point Q0 is at infinity. The circle is a straight line. The elliptic trammel in Fig. 15.4 has two sliders. In the inverted slider-crank mechanism in Fig. 17.29b and in the inverted elliptic trammel the sliders are pivoted at center points Q0 fixed in \u03a30 . The associated circle points Q1, . . . ,Qn are at infinity. In the mechanism shown in Fig.15.9 one slider is pivoted in the frame \u03a30 and the other in the coupler \u03a3 . This mechanism equals its inverse. Three prescribed positions can be generated by four-bars of all types including the previously listed degenerate forms. Three prescribed positions determine a pole triangle (P12 ,P23 ,P31 )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003408_tmag.2020.3007203-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003408_tmag.2020.3007203-Figure3-1.png",
        "caption": "Fig. 3. DS-PMVMs: (a) Case I. (b) Case II.",
        "texts": [
            " Then, the q-axis inductance of the singleturn inner and outer stator windings can be can be calculated from the abc\u2192dq transformation [16]. Step 6: With the help of Lagrange multiplier method and MATLAB, ni and no which make Y minimum can be obtained from (5). This means that the optimal turn-numbers assignment of the inner and outer stator windings to maximize the PF as well as to reach target torque are determined. And the maximum PF can be calculated by (5) and (2). III. VERIFICATION As shown in Fig. 3, two 3-phase DS-PMVMs respectively corresponding to Case I and Case II are taken as two representative examples in order to verify the theoretical Authorized licensed use limited to: UNIVERSITY OF WESTERN ONTARIO. Downloaded on July 27,2020 at 04:17:09 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information",
            " It should be noted that: 1) the inner and outer stators of Case I adopt the straight-teeth stators; both inner and outer rotor PMs are surface-mounted magnetic-poles; the numbers of inner and outer stator slots and PPNs of inner and outer stator windings are the same; the inductances of single-turn inner and outer stator windings are approximately equal; 2) for Case II, the outer stator adopts the straight-teeth stator, while the inner stator adopts the split-teeth stator; the outer rotor PMs are surface-mounted magnetic-poles, while the inner rotor PMs are consequent-poles; the numbers of inner and outer stator slots are different, the inductances of single-turn inner and outer stator windings are not equal, but PPNs of inner and outer stator windings are the same; 3) the two DS-PMVMs in Fig. 3 respectively correspond to the case with equal and unequal inductances, and the two DS-PMVMs are only used to verify the principle to maximize the PF with consideration on turn-number assignment, not to compare their performance. Fig. 4 illustrates the stator slots and winding connections of the two DS-PMVMs. Note that the locations of No. 1 stator slots in Fig. 4 are marked with green color in Fig. 3. According to the flowchart in Fig. 2, Table I and (6)-(8), we can complete step 1 to step 4 at the beginning. Then, we can get i1, o1, the phase self- and mutual inductances of the single-turn inner and outer stator windings by using 2D FEM. According to the abc\u2192dq transformation, 1 i q L and 1 o q L can be obtained from the phase self- and mutual inductances. Fig. 5 gives the waveforms of 1 i q L , 1 o q L , i1 and o1. This means that step 5 has been completed. Finally, with the help of Lagrange multiplier method and MATLAB, we can complete step 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.162-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.162-1.png",
        "caption": "Fig. 2.162 Principle layout of the direct diesel fuel-to-electrical energy solid oxide fuel cell (SOFC) and proton exchange membrane fuel cell (PEMFC) generators [Office of Naval Research; NICKENS 2004 -- Top image; PSA \u2013 Bottom image].",
        "texts": [
            " An alternative to petrol is methanol that can be effortlessly processed into a hydrogen-rich gas using steam or autothermal reforming, but it too suffers from a sulphur content dilemma and its carbon monoxide contaminates must be eliminated. An alternative dilemma is that the world\u2019s methanol infrastructure only produces the equivalent of 6% of the petrol consumption. Substantial savings would be necessitated to produce and distribute methanol [MADER AND GERTH 2004]. Besides, a direct electro-mechanical oxidation (DECO) technology may be used for direct diesel fuel-to-electrical energy (electricity) SOFCs and PEMFCs as is shown in Figure 2.162 [NICKENS 2004]. 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 363 SOFC Generator PEMFC Generator In summary, the dilemma in emergent and promotion FCEVs is not only contingent upon inventing inexpensive, durable, more efficient FCs and realising a suitable storage medium, but also on the evolution of a hydrogen-based economy. Although some automotive manufacturers have presumed that onboard reforming of petrol or diesel fuels is not feasible, it is maybe too premature in FC technology research to eliminate this"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.19-1.png",
        "caption": "Fig. 15.19 Four-bar M1Q1Q2M2 , inflection circle of the coupler-fixed plane and angles \u03b11 = \u03b22 , \u03b12 = \u03b21 of Bobillier\u2019s theorem",
        "texts": [
            " The same equation then determines for every point Q on this line the associated point M . Likewise, a second pair of points Q2 ,M2 on another line e2 determines s2 on this line and then for every point Q on this line the associated point M . Subsequently, Fayet\u2019s Eq.(15.77) determines the constant s3 on any third line e3 specified by the angular difference \u03b13 \u2212 \u03b11 and, consequently, the center of curvature M for every point Q on this line. Example: These analytical methods find an important application in the theory of the four-bar mechanism (see the four-bar M1Q1Q2M2 in Fig. 15.19). 482 15 Plane Motion The moving plane \u03a32 under investigation is the plane fixed to the coupler Q1Q2 . When the four-bar is moving, every point Q fixed in \u03a32 moves along a trajectory referred to as coupler curve. Properties of coupler curves are the subject of Sect. 17.8. The Euler-Savary equation determines the center of curvature of the coupler curve in an instantaneous position of Q . The pole P1 of \u03a32 lies at the intersection of the cranks. On the lines e1 and e2 the fixed points M1 and M2 are the centers of curvature associated with Q1 and Q2 , respectively",
            " Lines P\u2217M and P\u2217P1 are drawn and parallel to these lines the lines g1 through P1 and g2 through W . Proposition: The point of intersection W \u2217 of g1 and g2 lies on the line P\u2217Q . Proof: The triangles (Q,M,P\u2217) and (Q,P1,W \u2217 ) are similar, and the triangles (Q,P1,P \u2217) and (Q,W,W\u2217 ) are similar. Therefore, QP\u2217 : QW\u2217 equals : r as well as r : (rW \u2212 r) . Hence (rW \u2212 r) = r2 . This is Eq.(15.80). End of proof. The name sawtooth construction refers to the shape of the figure. If P1 and any two of the points Q , M and W are given, the missing third point is determined. Example: In Fig. 15.19 the points W1 ,W2 can be constructed by two sawtooth constructions applied to the lines e1 and e2 (preferably, both with one and the same auxiliary point P\u2217 ). Following this, the normal pole P2 is constructed graphically as point of intersection of two perpendiculars. Any third line e3 intersects the circle in a point W3 . For an arbitrary point Q on this line the associated point M can be constructed by one more sawtooth construction. End of example. Bobillier showed that the tangent to the centrodes (the x-axis) can be constructed without constructing the inflection circle (see Fig. 15.19). It suffices to draw the line h through P1 and the point A at the intersection of the 484 15 Plane Motion lines M1M2 and Q1Q2 (when the quadrilateral M1Q1Q2M2 is interpreted as four-bar, A is the instantaneous center of rotation of the two cranks relative to each other). The lines e1 , e2 and h define the angles \u03b21 and \u03b22 . Bobillier is author of Theorem 15.6. \u03b11 = \u03b22 , \u03b12 = \u03b21 . (15.81) Proof (Husty[17]): According to (15.75)( 1 r1 \u2212 1 R1 ) sin\u03b11 = ( 1 r2 \u2212 1 R2 ) sin\u03b12 . (15.82) Consider the triangles (A,P1,M1) and (A,P1,Q1) located to the right of line e1 ",
            "101) the following special formulas are obtained5. The equation of the asymptote parallel to the line \u03bbx+ \u03bcy = 0 is \u03bbx+ \u03bcy + \u03bb\u03bc \u03bb2 + \u03bc2 = 0 . (15.106) The cardinal point H and the focus \u03a6 have the coordinates xH = \u2212\u03bb \u03bb\u03bc \u03bb4 \u2212 \u03bc4 , yH = \u03bc \u03bb\u03bc \u03bb4 \u2212 \u03bc4 , x\u03a6 = \u03bc 2(\u03bb2 + \u03bc2) , y\u03a6 = \u03bb 2(\u03bb2 + \u03bc2) . \u23ab\u23aa\u23ac \u23aa\u23ad (15.107) From these equations it follows that P1 lies halfway between the asymptote and the line parallel to the asymptote and passing through \u03a6 . Example: The coupler of the four-bar mechanism shown in Fig. 15.19 is considered again. The points Q1 and Q2 are both vertices because every point of a circular trajectory is a vertex. Hence the x, y-coordinates of these points determine the parameters \u03bb and \u03bc , the cubic of stationary curvature, its asymptote, the normal pole P3 , the radii of curvature of the centrodes and the points H and \u03a6 of the coupler in the instantaneous position shown. In Fig. 15.22 the cubic of stationary curvature, its asymptote and the points H and \u03a6 are shown together with various other lines and points which are explained later",
            " Then the center P30 of the coupler lies on the normal to the coupler erected in P12 . In other words: In positions of the four-bar with a stationary value of 1/i the lines P12P30 and P31P32 are mutually orthogonal2. Figure 17.11 shows two different four-bars in such positions. If a stationary value occurs at \u03d5 = 0 or at \u03d5 = \u03c0 , P12 and P30 are located on the base line, and the coupler is orthogonal to the base line. Then the parameters satisfy the condition 2 In Bobillier\u2019s Theorem 15.6 the line P12P30 was shown to play another important role (line h in Fig. 15.19) 582 17 Planar Four-Bar Mechanism stationary value at \u03d5 = 0 : ( \u2212 r1) 2 + a2 = r22 , stationary value at \u03d5 = \u03c0 : ( + r1) 2 + a2 = r22 . } (17.41) In the vicinity of an angle \u03d5 for which 1/i has a stationary value the angle between the lines P12P30 and P31P32 is very sensitive to changes of \u03d5 . The desired angle \u03d5 can, therefore, be determined graphically rather precisely by checking the orthogonality. In order to determine for a given four-bar all positions with a stationary value of 1/i the four-bar and the center P12 must be drawn for a number of (monotonically increasing) angles \u03d5 over the entire possible range \u03c61 \u2264 \u03d5 \u2264 \u03c62 ",
            " In this case, the ratio L4/L1 is > 1 in every position, and it increases monotonically when the blades are closing. With shears of this kind reinforcement steel rods of 15 mm diameter can be cut by hand. Every point fixed in the plane of the coupler traces a coupler curve when the four-bar is moving through its entire range. It is the complexity of these curves to which the four-bar owes much of its importance in engineering (see Fig. 17.2). In the following sections properties of coupler curves are investigated. The curvature of coupler curves was the subject of Sect. 15.3.3 (see Fig. 15.19). Figure 17.15 is started by drawing the four-bar A0A1B1B0 and a point C fixed in the plane of the coupler A1B1 . This plane is represented by the coupler triangle (A1,B1,C). Subject of investigation is the coupler curve generated by C . To this basic figure lines A0A2C and B0A3C are added thus creating two parallelograms. In the next step, triangles similar to the coupler triangle are drawn as shown with bases A2C and A3C . This results in points B2 and B3 . Finally, another parallelogram defining the point C0 is drawn"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002975_tvt.2019.2943414-Figure17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002975_tvt.2019.2943414-Figure17-1.png",
        "caption": "Fig. 17. Schematic diagram of the test bench.",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. change of permeability is 0.22, while that for the proposed model without considering the change of permeability is 0.46 V. TEST BENCH The main components of the test bench are the high-power driving motor (350 kW), the electric control cabinet, the transmission, the cooling system, the data acquisition system, and the torque sensor installed between the PMR and the driving motor, as shown in Fig. 17 and 19. Fig. 18 shows the liquid-cooled PMR prototype. The cooling system includes a water pump, a cooling tank, and a water pipe. Two thermocouple sensors used for measuring water temperature were fixed on the water inlet and outlet, respectively. The materials of the magnet are sintered Nd-Fe-B(N38SH). To reduce the influence of the high temperature, the flow rate of water in the cooling water pipe is approximately 150 L/min, and the retarder must be completely cooled to the environment temperature prior to the next test"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure18.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure18.8-1.png",
        "caption": "Fig. 18.8 Spherical parallel robot",
        "texts": [
            " A = \u23a1 \u23a3\u2212S1c1 C3S4 + S3C4c4 C1S3s4 \u2212 S1s1(C3C4 \u2212 S3S4c4) \u2212S1s1 \u2212S3s4 C1(C3S4 + S3C4c4) + S1c1(C3C4 \u2212 S3S4c4) C1 C3C4 \u2212 S3S4c4 S1[s1(C3S4 + S3C4c4) + S3c1s4] \u23a4 \u23a6 . (18.54) For c4 and s4 the expressions (18.3) are substituted. The matrix A is then a function of \u03d51 . The matrix establishes the relation [n2 n3 n2 \u00d7 n3] = [ex ey ez]A(\u03d51) . (18.55) Substitution of (18.55) and (18.53) into (18.52) results in the desired parameter equations for the coupler curve: 658 18 Spherical Four-Bar Mechanism\u23a1 \u23a3x y z \u23a4 \u23a6 = 1 S2 2 A(\u03d51) \u23a1 \u23a3C5 \u2212 C2C6 C6 \u2212 C2C5 S2 sin \u03b6 \u23a4 \u23a6 . (18.56) The spherical linkage with center 0 shown in Fig. 18.8 is a parallel robot. The position of its triangular platform (A,B,C) is controlled by the angles of rotation \u03b1i about fixed (not necessarily orthogonal) axes. The kinematics has been investigated by Gosselin, Sefriou and Richard [3, 4]. The problem of direct kinematics is to determine all positions of the platform when the angles \u03b1i (i = 1, 2, 3) are given. The solution to this problem is found in Sects. 18.3.1 and 18.3.4 . When the angles are given, the points A0 , B0 and C0 are fixed. Imagine that in this position the connection C between the binary link C0C and the triangle (A,B,C) is opened"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001460_tmag.2013.2239271-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001460_tmag.2013.2239271-Figure9-1.png",
        "caption": "Fig. 9. Prototype.",
        "texts": [
            " It was observed that the phase current is approximately 2 A and the high-speed rotor keeps on rotating approximately at 1450 after the high-speed rotor slips. The target -axis current ( A) was given so that the high-speed rotor will not slip. The N-T curve with A is shown in Fig. 8. It was observed that the high-speed rotor does not slip. Therefore the current limiting can prevent the high-speed rotor from slipping. In order to verify the computed N-T curves, the N-T characteristics were measured using a prototype shown in Fig. 9. First, the maximum transmission torque was measured. As shown in Fig. 10, the maximum transmission torque is 0.53 Nm, which is lower than the computed torque. This is thought to be due to the assembly errors. The transmission torque at 22.5 deg is different from that at 0 deg. This is because the positional relationship between the low-speed rotor and stator in the measurement is different from that in the analysis. Next, the N-T curve was measured under a control period of 200 s. A load on the low-speed rotor was increased until the low-speed rotor stopped"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002994_j.mechmachtheory.2019.103679-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002994_j.mechmachtheory.2019.103679-Figure1-1.png",
        "caption": "Fig. 1. 5-DOF hybrid machine tool.",
        "texts": [
            " The dimension parameters of the scale model are obtained and the dynamic characteristics of the full-size system are predicted on the basis of the scaling factor of the fundamental scaling parameter. The remainder of this paper is organized as follows. Section 2 addresses the scaling laws related to dynamic characteristics. Section 3 derives the scaling factors of natural frequencies and mode shapes in a partial similitude condition. Section 4 predicts the dynamic characteristics of the full-size machine tool. In Section 5 , some conclusions are summarized. The 5-DOF hybrid machine tool considered in this study is shown in Fig. 1 . The machine tool consists of a 2-DOF planar parallel manipulator, a 2-DOF milling head, and a feed worktable. The milling head is serially fixed on the moving platform of the planar parallel mechanism while the feed worktable is fixed on the base beneath the milling head, carrying the workpiece along the horizontal direction. Thus, the machine tool is a combination of both parallel and serial mechanisms, which means it is a hybrid machine tool. The schematic of the 2-DOF planar parallel manipulator is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000221_s0006-3495(83)84406-3-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000221_s0006-3495(83)84406-3-Figure4-1.png",
        "caption": "FIGURE 4 Shape used for computation of moment of inertia of an outer doublet. For simplicity of computation, a doublet is drawn as two overlapping singlets with the dimensions shown. This slightly overestimates the moment of inertia in the overlap region, but this is more than compensated for by use of the average value of the radius of the annulus in the computation of the moment of inertia. Because the body coordinates are oriented as shown (with the x axis perpendicular to the paper), the off-diagonal elements of the moment of inertia matrix are zero by symmetry. XO (not shown) is a vector from the origin of the coordinate system to the center of either singlet microtubule.",
        "texts": [
            " It can be shown (Crandall and Dahl, 1959) for slender members that the twisting moment generated by Kz is given by Mz = -CIlZZKZ, (15) where Izz, is the moment of inertia around the Z axis. Similarly, the bending moment is given by Mi=-EIj1Kji=L, 2 (16) where Ij = fA xjxjdA. Electron microscopic studies show that typical dimensions for an outer doublet are -20 nm from the center of the B subfiber to the center of the A subfiber, and wall thickness is -5 nm. For convenience of computation, we replace the outer doublet by a pair of overlapping tubules, as shown in Fig. 4. The area of one of the annuli is 27r r'It. The moments of inertia are given by I. = 2 r2dA = 2 f (x. + r')2dA = 2 Area (X2 + r2), IXX = 2f (X. + r' cos )2rtdO = 2 Area(X + 2 and rP2 Iy,==2Area . (17) 2 Using a value of E = 4 * 107 pN/tUm2 (Hines and Blum, 1979) and choosing v = 1/3, one obtains the following approximate values for the bend resistances of an individual doublet: EXX = 3.6, Eyy = 1.2, Ezz = 5.4 pN,tm2. Recent measurements of the bending resistance of isolated dou- 'When an elastic material is stretched, it also becomes slightly thinner"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000133_med.2008.4602174-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000133_med.2008.4602174-Figure1-1.png",
        "caption": "Fig. 1. The quadrotor concept",
        "texts": [
            " \u2022 The UAV possesses all the means that are required to participate in an in-door positioning system, and to be able to acquire its position data. \u2022 The UAV is able to communicate with a ground station, at least in the respect of accepting commands and reporting data. According to future plans multiple UAVs are intended to build and control them in several cooperative schemes, hence the communication is worth to be realized in such a way that a network with suitable topology could be formed. The concept of the quadrotor helicopter is illustrated in Figure 1. The actuator system consists of four rotors placed in the four corners of a planar square, those ones placed oppositely rotate in the same direction, while the perpendicular ones rotate reversely. The attitude and the movement of the quadrotor can be controlled by suitable changing the revolution of the rotors that results in different thrust and torsion. The rotors are driven by electric motors; its revolution can efficiently be controlled by local electronic motor controllers. The rotor drive motor control has been realized as independent module that is implemented in four instances on every vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001058_s11432-013-4787-8-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001058_s11432-013-4787-8-Figure11-1.png",
        "caption": "Figure 11 The low altitude parachute extraction airdrop schematic view.",
        "texts": [
            " It can be seen that the SMDO/BS method presents excellent guidance command (Vc, \u03b3c, and \u03c7c) tracking capability. Virtual control variables for the flight path loop (\u03bc and \u03b1) and wind-axis angle loop (p, q, and r) can closely track their ideal commands. Meanwhile, the aerosurface deflections are within their magnitude and rate limitations. In this section, the proposed SMDO/BS flight control law is applied to the low-altitude parachute extraction airdrop operation, in which the aircraft suffers severe disturbance during the heavy cargo airdropping. The process of the airdrop is shown in Figure 11. The airdrop flight contains five stages: initial level flight, descending, flare, cargo drop, and climbing. The simulation scenario is as follows: 1) The aircraft descends at t = 5 s with a climb angle \u03b3 = \u22122.5\u25e6. 2) Flare at the height of 25 m. 3) Keep altitude when entering drop altitude (5 m). 4) Begin to drop the first cargo at t = 50 s. 5) Climb up at t = 70 s. The airdrop configuration is shown in Table 4. The aerodynamic parameters uncertainties are as follows: \u23a7\u23aa\u23aa\u23a8 \u23aa\u23a9 C\u2032 L = (0.8\u2212 0.5\u03b1)CL, C\u2032 D = (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002660_tia.2019.2920923-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002660_tia.2019.2920923-Figure2-1.png",
        "caption": "Fig. 2. Equivalent pulsating force and bending moment on one PM pole",
        "texts": [
            "5 p n ( N /m 2 ) Angle (Mech.degree) FEM Analytical 10 4 Fig. 1. Comparison result of electromagnetic exciting force density on one pole between the analytical method and FEM Since the PM pole of the motor can be assumed as a pure rigid body, the unevenly distributed electromagnetic forces acting on one PM pole can be equivalent to two parts [14]: one is the concentrated pulsating force acting on the center of the pole, and the other is the additional bending moment to twist the pole, which can be seen in Fig.2. The equivalent pulsating radial force can be obtained by parallel moving or integrating the radial force densities on one pole. For simplicity, only 1 among  k is considered hereinafter. So, the pulsating force are obtained as 2 1 2 1 0 1 0 ( ) 2 sin( ) 2 cos( ) 2 C np p nC p r p t l p Rd l R B jZ Z t Z p             (2) where pl is the length of pole, 2 ( 2 ) / (2 )C j p   , 1 ( 2 ) / (2 )C j p    , 1 2= /pb t is the number of slots under one pole shoe, pb is magnetic pole width, 2t is tooth pitch of the rotor, and R is the radius of the inner surface of the pole as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001525_j.mechmachtheory.2013.04.001-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001525_j.mechmachtheory.2013.04.001-Figure6-1.png",
        "caption": "Fig. 6. Machining principle of crown worm.",
        "texts": [
            " However, the obtained data illustrate that the high load-carrying capacity and good lubrication condition are in planar internal gear single-enveloping crown worm drive. The machining method of crown worm is different from that of any other toroidal worm, because that the cutter and its rotation center must be located on the both sides of the crown worm. To solve this problem, a new method, which can be named as virtual center distance machining principle, is proposed based on the theory of rigid body motion. As shown in Fig. 6, o is the rotation axis of the workbench, p is the random working point on the planar grinding wheel, ot and pt are the positions of o and p at some instant, respectively. B is the rotational motion of the crown worm and it rotates about axis z1 with the angular velocity vector \u03c9w. A is the rotational motion of the workbench and it rotates about axis o with the angular velocity vector \u03c9b. X and Y are the rectilinear motion of the workbench with the velocity vectors vX and vY, respectively. \u03c9p is the angular velocity vector of the planar grinding wheel",
            " Based on the theory of rigid body motion, the rotational motion of the planar grinding wheel that rotates about axis og can be decomposed into the rotational motion of the planar grinding wheel that rotates about axis o and the translational motion of the workbench along the arc oot . To keep the working plane always tangent to the main basic circle, the kinematics relation must be met as following: \u03c9g rogp \u00bc vo \u00fe\u03c9b rop: \u00f016\u00de Here, vo = vX + vY is the translational velocity vector of the workbench along the arcoot with the center og. And the following kinematics relation can be obtained: vX \u00fe vY \u00bc \u03c9g rogo \u03c9b \u00bc \u03c9g : \u00f017\u00de Based on the machining principle of the crown worm tooth surface (Fig. 6), a NC toroidal worm grinder is modified, as shown in Fig. 7. The headstockwas placed on a swash-blockwith the inclination angle of \u03b4, and theworkbenchwas placed on a pad. Themodified grinder has four numerically closed-loop controlled axes: the longitudinal rectilinearmotion X, the transversal rectilinearmotion Y, and the rotational motions A and B. According to the Eq. (17), the kinematics relation of four motion axes can be determined. A crownwormwith the major design parameters of example B, was grinded on the modified grinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000259_robot.2008.4543696-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000259_robot.2008.4543696-Figure1-1.png",
        "caption": "Fig. 1. In order to catch the red object, Humanoid Robot takes a hold with his left hand to keep its balance.",
        "texts": [
            " In Section IV, we detail robust posture computation by introducing wrench stability margin. Section V presents the first results of robust posture control. Finally, section VI summarizes the presented control and indicates some possible future research directions. We use a robotic approach and more precisely joint control to handle HR dynamics. Our HR is a set of articulated branches of rigid bodies, organized into a highly redundant arborescence (ndof: number of degrees of freedom). It consists of 32 joints (Fig. 1). The skeleton is modeled as a multibody system. The root body of the HR tree is the thorax. This root has 6root DoF and is not controlled. We decided to use human data for modeling our HR [13][9][7]. Unilateral contacts seen as Coulomb frictional contacts are ruled by a non linear model i.e.: | f t c| < \u00b5 f n c with f n c , f t c respectively the normal and tangent contact forces and \u00b5 , the dry-friction factor. As a linear formulation for our optimization problem is needed, we use a linearized Coulomb model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002506_j.jsv.2017.08.029-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002506_j.jsv.2017.08.029-Figure1-1.png",
        "caption": "Fig. 1. Bearing contact model.",
        "texts": [
            " The overall radiation noise is obtained through the superimposed calculation of the acoustic fields, and the result is analyzed and validated through experimental methods afterwards. In this paper, the outer ring is fixed to simulate the actual working condition, the inner ring rotates under stable rotation speed, the cage and the balls are guided by the inner ring. Assuming that the mass centers of the components coincidence with the geometrical centers, the dynamic model of the bearing can be described by the coordinate systems shown in Fig. 1. In Fig. 1, the inertial coordinate system{O;X,Y,Z} is fixed, X axis coincidences with rotation axis of the bearing, Y axis and Z axis show two different radial directions of the bearing respectively. Inner ring coordinate system {Oi;Xi,Yi,Zi}is used to describe the dynamic response of the inner ring, with Oi coincident with the geometric center of the inner ring, Xi coincident with the rotation axis of inner ring, Yi and Zi show two different radial directions of inner ring respectively. Similarly, cage coordinate system{Oc;Xc,Yc,Zc} correspond to the cage, with the origin of coordinate and axes represent the corresponding position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.6-1.png",
        "caption": "Figure 10.6. Moment of momentum about a moving point Q in a simple machine.",
        "texts": [
            " (IOAO) That is, the total moment ofmomentum ofa body about a point 0 in an inertial reference frame is equal to the moment about 0 of the momentum of the center ofmass plus the moment ofmomentum relative to the center ofmass. This is the same rule recorded in (8.27) for a system of particles. The foregoing concepts for the moment of momentum hQ about a point Q and the moment of momentum hr Q relative to Q applied to a simple rig id body in motion in an inertial reference frame are illustrated in an example. Example 10.3. A connecting rod QR ofa simple machine shown in Fig. 10.6 is modeled as a homogeneous thin rod of length e, uniform cross section, and mass a per unit length. The rod is hinged at Q at a distance ex from the center 0 of a flywheel that turns with a constant angular velocity n = Qk, as shown, in the inertial ground frame 0= {o; I, J, k} fixed at O. Determine (i) the moment of momentum of the rod relative to Q and (ii) its moment of momentum about Q. Solution of (i). The moment of momentum hrQ of the rod relative to Q is determined by (l0.37), in which the rigid body velocity of a rod particle P relative to Q in the ground frame 0= {O ; I ,J,k} is given by rep, t) = yep, t) - vQ = w x rep, t), (IOAla) Dynamics of a Rigid Body 425 where rep, t ) = ri , referred to the rod frame 2 = {Q;i, j , k}, and the total angular velocity of the rod frame 2 in the ground frame 0 is W == W 20 ",
            "49) dt st The same derivative rule applies to liQ in (10,43), and also to lic = lirc in either (10.44) or (10,48) . We shall return to this major rule later. We conclude with an illustration involving (10,42) , (10,46), and (10,48) applied to a rigid rod. Example 10.4. Use the results for Example 10.3, page 424, to determine (i) the total torque about the hinge Q, and (ii) the total torque about the center of mass C, required to sustain the motion of the thin rod. Solution of (i), The total torque about the moving point Q in Fig. 10.6 can be found from either (10,42) or (10,46) . Let us consider (10.46), note that f. maf .r*(YB, t) x maQ = --I X maQ2a = __Q2 sin dk, 2 2 Dynamics of a Rigid Body 429 (lO.SOc) (lO.SOd) and recall hrQ = (me2/3)(fJ+ Q)k from (1O.4ld) , which is a vector referred to the moving rod frame 2whose total angular velocity iswJ = (Q + fJ)k in (l0.41 b). Because wJ is parallel to hrQ , (l0.49) simplifies to \u2022 a> 8hrQ([13, t) me2 .\u2022 hrQ (;:7D, t) = = -,8k. (lO.SOb) Or 3 Hence , use of (lO.SOa) and (1O.S0b) in (l0",
            " In the principal basis only the body 's geometry and mass distribution determine I Q , and hence also the principal directions ebboth being independent of time in ({J .Hence forward, in application s where it is clear that a particular principal reference system is used , the hat notation and the supersc ript Qmay be discarded to simplify expressions like (10.62) . Example 10.5. Appl y the foregoing results to find the moment of momentum relative to Q for the connecting rod of the simple machine in Fig. 10.6, page 425. Dynamics of a Rigid Body 433 Solution. The rod frame 2 = {Q; i, j , k} in Fig. 10.6 is a principal reference frame for which ek == ik and whose total angular velocity referred to frame 2 is given in (10041 b). Hence, WI = W2 = 0, W3 = ~ +Q are the principal components Wk == Wk . The principal components of the moment of inertia about the rod's end point Q, bearing in mind the basis directions, may be read from (9A6d) or from Thus, (10.62) yield s hrQ = 13~w3i3' that is, (1O.63b) (10.64) This is the same as (10Ald) obtained earlier by direct integration. Let the reader show that the nontrivial principal moments of inertia about the center of mass are I~ = IfJ = me 2/ 12, and thus confirm that the moment of momentum relative to the center of mass is hrc = (me2/12) (~ + Q) k, as shown differently in (10",
            "99) and similarly (10.100), reduces to the simple principal component expression, (10.102) (10.103a) In particular, for a rotation about a fixed principal axis e3 , say, with c03 == wand /B == I, (10.102) yields the familiar elementary relation KrQ= 4/w2 for the kinetic energy relative to Q. Example 10.11. (i) Apply (10 .95) to determine the total kinetic energy of the connecting rod of the simple machine shown in Fig . 10.6, page 425. (ii) Repeat the calculation based on (10.94). Solution of (i). Since Q in Fig. 10.6 is a moving base point, the total kinetic energy of the rod is obtained from (10.95). With w = (~ +Q)k by (10A1b) and hrQ in (10A1d), (10.99) yields the kinetic energy of the rod relative to Q: 1 me2 . 2 KrQ([JJJ , t) = \"2W . hrQ = 6({3 + Q) . e . The same result also follows easily from (10.102). With r \" = w x r* = \"2({3 + Q)j and use of (lOA1e) and (10.103a), (10.95) yields the total kinetic energy of the connecting rod: Solution of (ii). The solution based on (10.94) is simpler to construct"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure4.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure4.16-1.png",
        "caption": "Fig. 4.16 Gear transmission example: spur gearing",
        "texts": [
            " A wide range of industrial rotational applications use a transmission device between load and electrical machine. Reasons for this may be due to physical load enclosure constraints, i.e., where the machine cannot be directly attached. In other instances, the mismatch between optimum load and machine speeds must be resolved by making use of a rotational to rotational transmission device. For this purpose gears or pulley\u2019s are used. Gears are wheels with teeth which mesh with each other, as shown in the example given in Fig. 4.16. The use of gears allows the transfer of forces without slippage, which is in contrast with pulley/belt systems, where this phenomenon can occur. The relationship that exists between the torque and force of the two gears shown in Fig. 4.16 may be considered by application of Newton\u2019s second and third laws. In this example, the electrical machine is arbitrarily connected to gear 1 with radius r1 and provides a shaft torque Te with rotational speed \u03c9m 1. The load is connected to gear 2 with radius r2 to which the load torque Tl is applied. The relationship between the rotational speeds \u03c9m 1 and \u03c9m 2 follows from the observation that the tangential speed of both gears must be equal (no slippage), which gives 112 4 Drive Principles \u03c9m 1r1 = \u03c9m 2r2. (4.24) The relationship between machine driving torque and load torque may be found by taking into account that the driving gear (gear 1 in this example) exerts a force Fa (as shown in Fig. 4.16) on the teeth of gear 2. According to Newton\u2019s third law an equal but opposite force Fr will be exerted on gear 1. If the gears are replaced by a set of pulleys, this force will be transferred via the belt. Observation of Fig. 4.16 and application of Newton\u2019s second law gives Te \u2212 r1Fr = J1 d\u03c9m 1 dt (4.25a) r2Fa \u2212 Tl = J2 d\u03c9m 2 dt (4.25b) where J1 and J2 represent the inertia of the electrical machine (with gear 1) and load (with gear 2), respectively Subsequent elimination of the force variables Fa and Fr from Eq. (4.25) and using Fa = Fr (Newton\u2019s third law), as well as Eq. (4.24) gives Te \u2212 ( r1 r2 ) Tl = \u239b \u239c\u239c\u239c\u239dJ1 + ( r1 r2 )2 J2 \ufe38 \ufe37\ufe37 \ufe38 Jeq \u239e \u239f\u239f\u239f\u23a0 d\u03c9m 1 dt . (4.26) Expression (4.26) represents Newton\u2019s second law expressed in terms of the machine variables Te, \u03c9m 1. The result shows that the load inertia J2 appears as an equivalent inertia Je on the drive side of the transmission, which is computed according to Jeq = ( r1 r2 )2 J2. (4.27) Hence, the inertia Jeq seen at the machine side of the transmission will be greater than the actual load inertia J2 in case r1 > r2, which is the case shown in Fig. 4.16. Note that Eq. (4.26) can be derived easily by considering the change of kinetic energy stored in the system. 4.3 Drive Dynamics 113 The process of transmitting power from the electrical machine to the load is considered in this subsection with the aid of Fig. 4.17. Shown in Fig. 4.17 are two rotating masses with inertia J1 and J2, which are assigned to the rotor of the electrical machine and load, respectively. A coupling of some type, which may simply be a shaft, is used to link the two masses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.65-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.65-1.png",
        "caption": "Fig. 2.65 Front-wheel-drive (FWD) powertrain physical model: 1 \u2013 internal combustion engine (ICE), 2 \u2013 flywheel plus M-M clutch, 3 \u2013 M-M transmission, 4 \u2013 M-M differential, 5 \u2013 axle M-M shaft, 6 \u2013 coupling, 7 \u2013 wheel-hub, 8 \u2013wheel-tyre [CAPITANI ET AL. 2000, 2001 \u2013 Left image].",
        "texts": [
            "2 Automotive Vehicle Driving Performance A conventional M-M powertrain is the part of an automotive vehicle connecting the ECE or ICE to the propeller or driven axles, may include drive shaft, M-M clutch, transmission, and differentials. Everything that is involved in the process of moving the vehicle forward is included in the definition of the classical M-M powertrain, namely, ECE or ICE, M-M clutch, transmission, shafts, differentials, and road-driven wheels. For instance, a vehicle\u2019s driveline consists of the parts of the powertrain excluding the ECE or ICE, M-M clutch and transmission. Figure 2.65 shows a physical model of a front-wheel drive (FWD) powertrain for DBW AWD propulsion mechatronic control including ICE, flywheel plus M-M clutch, transmission, differential, axle shaft, coupling, wheel-hub, and wheel-tyres [CAPITANI ET AL. 2000, 2001]. In Figure 2.66 is shown a physical model of a 2WD and/or 4WD powertrain for DBW AWD propulsion mechatronic control including: ICE, ICE, front axle M-M differential with or without viscous coupling (VC), permanent 4WD centre M-M differential with VC, part-time 4WD manual lock, viscous transmission (VT) and driveline, where the latter includes a driveshaft, a rear-axle M-M differential with VC, four axles, and four wheel-tyres [NEWTON ET AL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.78-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.78-1.png",
        "caption": "Fig. 2.78 Classical M-M transmission arrangement for the M-M DBW 4WD propulsion mechatronic control system [NEWTON ET AL., 1989].",
        "texts": [
            " From the power-splitting IA M-M differential, one shaft is taken forward to the front axle and the other rearwards to the rear axles. Both axles contain their own axle M-M differentials and final drive gears, but that at the front takes the flexible joints (FJ), universal joints (UJ), or constantvelocity joints (CVJ) at D its outer ends. Those are indispensable in permitting the front wheels to be steered. For DBW four-wheel driven (4WD) \u00d7 SBW four-wheel steered (4WS) automotive vehicles, all the axles contain FJs or UJs or CVJ at their ends that are indispensable to allow the front and rear wheels to be steered (see Fig. 2.78). The power-splitting IA M-M differential at C in the transfer box is the mechanism that shares the input value of torque from the \u2018propeller shaft\u2019 or \u2018Cardan shaft\u2019 uniformly between the two output drive shafts to the wheels, irrespective of the reality that they may be revolving at different values of wheel angular velocity, for instance on taking a corner. Thus, the power-splitting IA M-M differential at C is indispensable for sharing out the drive uniformly between the front, middle, and rear axles and to allow for the fact that, when the automotive vehicle is driven around, the mean values of the angular velocity of the front wheels are different from those of the middle and rear wheels and therefore the values of the angular velocity of all the propeller shafts must be at variance too"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure4-1.png",
        "caption": "Fig. 4. Graphic model o",
        "texts": [
            " According to reference [18], flexibility matrix of the straight circular flexible spherical joint is as follow: C \u00bc c1 0 0 0 0 0 0 c2 0 0 0 c3 0 0 c2 0 c3 0 0 0 0 c4 0 0 0 0 c3 0 c5 0 0 c3 0 0 0 c5 2 666666664 3 777777775 \u00f02\u00de where c1 c5 are expressed respectively as follows: c1 \u00bc 4I1 pE c2 \u00bc 64I3 pE \u00fe 2\u00f0j \u00fe v\u00deI1 pG c3 \u00bc 64rI2 pE c4 \u00bc 64 1\u00fe m\u00f0 \u00deI2 pE c5 \u00bc 64I2 pE \u00f03\u00de where k = 1 represents the average shear stress, m is the Poisson\u2019s ratio of the material, I1; I2; I3 are intermediate variables and expressed respectively as follows: I1 \u00bc 1 2r 1 n\u00f0n\u00fe2\u00de \u00fe 2 n\u00f0n\u00fe2\u00de\u00f0 \u00de\u00f03=2\u00de arctan ffiffiffiffiffiffi n\u00fe2 n q n o I2 \u00bc 8 pr3E n\u00f0n\u00fe2\u00de\u00f0 \u00de3 6n5\u00fe30n4\u00fe70n3\u00fe90n2\u00fe59n\u00fe15 6\u00f0n\u00fe1\u00de3 \u00fe 4n2\u00fe8n\u00fe5ffiffiffiffiffiffiffiffiffiffi n\u00f0n\u00fe2\u00de p arctan ffiffiffiffiffiffi n\u00fe2 n q I3 \u00bc 1 8r n\u00f0n\u00fe2\u00de\u00f0 \u00de3 8n4\u00fe32n3\u00fe57n2\u00fe50n\u00fe15 6\u00f0n\u00fe1\u00de2 \u00fe 5\u00f0n\u00fe1\u00de2ffiffiffiffiffiffiffiffiffiffi n\u00f0n\u00fe2\u00de p arctan ffiffiffiffiffiffi n\u00fe2 n q \u00f04\u00de The load-bearing branch can be considered as a beam model, whose stiffness matrix can be obtained from Eq. (1). The graphic model of the flexible series branch is shown in Fig. 4(a). In order to simplify the theoretical modeling analysis, the thin wedgeshaped beams at both ends are replaced with thin rectangular beams. The simplified model is as shown in Fig. 4(b). Flexible series branch structure and flexible unit coordinate system diagram are shown in Fig. 5 and the local coordinate system of each flexible basic unit is established at the distal center of each flexible unit. L, L1, L2, b, rs represent the total length of the flexible series branch, the length of the thin rectangular beam, the length of the long rectangular beam, the width of flexible serial branch and the radius of the flexible spherical joint, respectively. When the six-component external force F acts on the reference point at the end of the flexible series branch, each flexible unit has elastic deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001482_s10846-013-9927-2-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001482_s10846-013-9927-2-Figure6-1.png",
        "caption": "Fig. 6 Defined body frame and ship frame",
        "texts": [
            " Consequently, the guidance law treats the ship and the vehicle as point masses, not considering their sizes, volumes, and attitude. However, shipboard landing involves controling the aerial vehicles for landing on the moving platforms. The target of the guidance law is to make the vehicle land on a moving ship. Unless the heading angles are considered, the generated guidance commands could result in unintended results. Therefore, the guidance commands should be transformed, to consider the attitude of the helicopter and the ship. Figure 6 shows two different frames for the helicopter and the ship, and their respective Euler angles. The body frames, relative to the ship and the rotorcraft, are defined as \u201cship frame\u201d and \u201cbody frame\u201d, respectively. The Euler angles are defined by the three angles that describe a rotation in a certain sequence from one frame of reference relative to another. The designed guidance law utilizes the relative distance error to generate the velocity commands Uship, Vship, and Wship, relative to the the ship frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.8-1.png",
        "caption": "Fig. 3.8 Resultant of two rotations about skew axes",
        "texts": [
            " From this it follows that the position and the shape of the hexagon are determined by twelve independent parameters. For reasons explained later the hexagon is called spatial triangle or screw triangle (Yang [51], Roth [44]). In Sects. 3.11 and 3.12 analytical relationships are developed for the screw triangle. When in the given screw displacements 1 and 2 s1 and s2 are changed (all other parameters held fixed), then the lines g2 and g3 undergo lateral displacements. This has no effect on \u03d5res whereas all other parameters of the resultant screw displacement are effected. In Fig. 3.8 the special case s1 = s2 = 0 is shown, i.e., the resultant of two pure rotations about skew axes ( S1 , n1 , \u03d51 , S2 , n2 , \u03d52 and g1 are the same as in Fig. 3.7). The points A1 and A2 coalesce in a single point A , and B1 and B2 coalesce in a single point B . Remark: In 1848 Cayley [7],v.1 gave analytical solutions for the resultant of two successive screw displacements as well as for the inverse problem of decomposing a given screw displacement into two screw displacements with prescribed characteristics",
            " Thus, the same hexagon determines three screw displacements about g1 , g2 , g3 which carry the body from its initial position via two intermediate positions back into the initial position 3.8 Dual Numbers 97 rotations with prescribed characteristics. The decomposition is the subject of Cayley\u2019s Theorem 3.4. A given screw displacement can be represented as resultant of two subsequent pure rotations. The axis of one rotation may be prescribed arbitrarily (but not parallel to the axis of the resultant screw displacement). Then the axis of the other rotation as well as the two rotation angles are determined. The geometrical solution is explained in Fig. 3.8 . Let it be assumed that the resultant screw displacement and the axis S2 are prescribed as shown. The axes S2 and Sres determine the common perpendicular g2 and its endpoints B and C2 . Point C1 is determined by sres , and g3 is determined by \u03d5res . Point A is the point of intersection of g3 with the plane through B and perpendicular to S2 . The axis S1 of the first rotation is the common perpendicular of g3 and g1 = AB . Finally, \u03d51/2 and \u03d52/2 are the angles between g1 and g3 and between g1 and g2 , respectively",
            "112) reduce to \u03d5res = \u03d51 , nres = n1 , sres = s1 + s2 cos\u03b1 , u = \u22121 2 e3 + 1 2 s2 sin\u03b1 ( e1 sin \u03b1 2 + e2 cos \u03b1 2 + e3 cot \u03d51 2 ) = \u22121 2 e3 + 1 2 s2 sin\u03b1 ( e3 \u00d7 n1 + e3 cot \u03d51 2 ) . \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad (3.115) The leading term (\u2212 /2)e3 is the perpendicular vector from the arbitrarily chosen origin 0 onto the screw axis n\u03021 . If an arbitrary point on n\u03021 is chosen as origin 0 , u = 1 2 s2 sin\u03b1 ( e3 \u00d7 n1 + e3 cot \u03d51 2 ) . (3.116) The absolute value is |u| = \u2223\u2223\u2223 s2 2 sin \u03d51 2 sin\u03b1 \u2223\u2223\u2223 . (3.117) Special case s1 = s2 = 0 (resultant of pure rotations about nonintersecting axes; see Fig. 3.8): Equations (3.108) and (3.109) remain valid without change. Equations (3.110) and (3.112) reduce to sres sin \u03d5res 2 = \u22122 sin \u03d51 2 sin \u03d52 2 sin\u03b1 , (3.118) 116 3 Finite Screw Displacement u sin2 \u03d5res 2 = 4 { \u2212 e1 sin 3 \u03b1 2 [ sin\u03d52 \u2212 sin\u03d51 + sin(\u03d51 \u2212 \u03d52) ] + e2 cos 3 \u03b1 2 [ sin\u03d52 + sin\u03d51 \u2212 sin(\u03d51 + \u03d52) ] + e3(cos\u03d51 \u2212 cos\u03d52) } . (3.119) These equations govern the even more special case of the resultant of two 180\u25e6-rotations about skew axes. With \u03d51 = \u2212\u03c0 (equivalent to \u03d51 = \u03c0 ) and with \u03d52 = \u03c0 they yield \u03d5res = 2\u03b1 , sres = 2 , nres = e3 , u = 0 ",
            " Dual-Quaternion Formulation 117 u sin2 \u03d51 2 = \u2212e1 sin \u03d52 2 sin2 \u03b1 2 [ sres sin \u03d52 2 cos \u03b1 2 \u2212 sin \u03d5res 2 sin \u03d5res + \u03d52 2 sin \u03b1 2 ] + e2 sin \u03d52 2 cos2 \u03b1 2 [ sres sin \u03d52 2 sin \u03b1 2 \u2212 sin \u03d5res 2 sin \u03d5res \u2212 \u03d52 2 cos \u03b1 2 ] + 1 4 e3 [ sres sin\u03d52 sin\u03b1+ (cos\u03d5res \u2212 cos\u03d52) ] . (3.123) Equation (3.122) determines \u03d52 : tan \u03d52 2 = sres sres cot \u03d5res 2 cos\u03b1\u2212 2 sin\u03b1 . (3.124) With this angle \u03d52 (3.120) and (3.121) determine cos\u03d51/2 and n1 sin\u03d51/2 . The vector u determined by (3.123) is the perpendicular from the midpoint of g2 in Fig. 3.8 onto the first rotation axis. The equations fail in the case sin\u03b1 = 0 (axes S2 and Sres parallel). When instead of S2 the axis S1 is given, \u03d51 , \u03d52 and S2 are determined as follows. The unknown second rotation is the resultant of the inverse of the first rotation followed by the given screw displacement. In (3.108) \u2013 (3.112) the following changes are made. 1. The basis e1,2,3 is placed at the midpoint of the common perpendicular g3 of the given axes Sres and S1 . The quantities and \u03b1 specify the relative location of these axes"
        ],
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    },
    {
        "image_filename": "designv10_12_0000733_0022-2569(71)90002-4-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000733_0022-2569(71)90002-4-Figure8-1.png",
        "caption": "Figure 8. Transformation of coordinates.",
        "texts": [
            " The characterist ic function for the motion o f p is described by From this relation the support function o(~) of the second cam profile d can be derived by analogy to (1.7): thus we arrive at 3'7\" r = q J - ~ + - g = r + y , a = l sin qJ = l . sin (,9+T). (2.2) Developing the last expression and comparing it with (1.7) we find t7 -= u cos y + ~ sin -y, (2.3) which leads to the algebraic identity u \" + O\"-- 2ut~ cos y = l e sin=' y = const. (2.4) This means in geometrical interpretation that the end-points of the perpendiculars Op = u and Op = a have constant distance l \u2022 sin , / (see Fig. 8). If, as in Figs. 1 and 4, the first disk profile c has an axis of symmetry , x, containing the cam center O, it is easy to see that the second disk profile ~ has also an axis of symmetry , .?, forming in O the angle -,/with x. Double-disk cams as just described in Section 2 can be c o n s t r u c t e d - w i t h i n certain l i m i t s - f o r any motion law ~(~). An interesting geometr ic problem is raised by the question whether there exist cam mechanisms with two rigidly connected oscillating straight-line followers p ",
            "4), the relation u 2 + t~'-' - 2ua \u2022 cos y = sin 2 y (4.1) for the central distances u = u(r) and ~ = u ( r + y ) of two adjacent profile tangents p and p forming the prescribed view angle ~ p P p = ~ r - 3 , in the point P of the isoptic circle o of c. This relation expresses the e lementary fact that the segment joining the end-points of the distances u and t~ has constant length sin V; it represents a chord subtending the angle y at the circumference of an auxiliary circle with unit diameter O P (Fig. 8). As the relation (4.1) is valid for all values of the independent variable z it is an identity in r and a functional equation for the unknown function u(r ) . If we consider the quantities u and t~ as special coordinates of the point O, localizing it by its distances from the axes p and p for an observer in the sys tem E2, the relation (4.1) may be considered as the equation of that circle 6 with center P and radius l = 1 which is the path of O in the course of the relative motion El/E2 (Fig. 9). For simplification it seems advisable to introduce normal cartesian coordinates v,g by means of the linear t ransformations u = a v + ~ O .=cos(4-:) with (4.2) The new axes have common bisectors with p ,p and Fig. 8 shows the geometr ic meaning of v and-~. N o w the equation of the unit circle O reads simply v2+-v 2 = 1. (4.3) This condition is equivalent to (4.1) and might be verified by direct substitution. The function a u -- f l~ _ a u (r) -- f lu (r + 7) (4.4) U(T) = 0 ~ 2 _ _ ~ 2 - - sin), has the same period 23, as u(z). Calculating its value for r + y we find, with attention to 10 the periodici ty o f u ( r ) \" c ( r + 7 1 = c~u(r+y) - / 3 u ( r + 2 - / ) = c~a-~u= c. sin 5, c~-' - / 3 e (4,5) Knowing with (4"
        ],
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    },
    {
        "image_filename": "designv10_12_0001311_icuas.2013.6564711-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001311_icuas.2013.6564711-Figure4-1.png",
        "caption": "Fig. 4. Reference frames used in the development.",
        "texts": [
            " As can be inferred from Figure 3(b) the vehicle presents symmetry both around the x-z plane and the y-z plane. Hence, the development of the equations is the same for all four arms if the reference frame is adequately transformed. For this reason, here only the equations with respect to arm 3 will be developed and then, the equations regarding the remaining arms can be obtained by an appropriate frame change. arm 3 will be referred to, herein, as Standard arm or arm 3 indifferently. With the nomenclature stablished in Figure 4 the angular velocity of the of rotor in arm 3, expressed in terms of reference attached to the motor stator (frame 3), will be given by: 3\u03c9 = 3i1p+3 j1q +3 k1r\ufe38 \ufe37\ufe37 \ufe38 Vehicle Motion + 3j1\u03b7\u0307\ufe38\ufe37\ufe37\ufe38 servoblock + 3i2\u03b3\u0307\ufe38\ufe37\ufe37\ufe38 push pull + 3k3\u2126\ufe38\ufe37\ufe37\ufe38 Motor (2) where the vectors iij ijj ikj represent the unit vectors of reference frame j expressed in terms of the reference frame i, see Figure 4 where the reference frames are detailed. The angular acceleration is the derivative of the angular velocity, hence 3\u03b1 = d3\u03c9/dt. The inertia tensor of the rotor, Figure 3(a), is symmetric because of the use of 3-blade propellers. The reference frame 3 is coincident with the principal inertia axes of the rotor, and so the inertia tensor is constant around those axes and it is given by: 3I =  Ixx 0 0 0 Iyy 0 0 0 Izz  (3) Thus, the moments can be calculated with the Euler equation around the reference frame 3: 3M = 3I3\u03b1+ 3\u03c9 \u00d7 3I3\u03c9 (4) Introducing and simplifying all the expressions above, the moments that the spinning body applies onto the airframe in the reference frame of the vehicle, 1MGyro, are obtained as: 1MGyro = R3to1(\u22123M) =  1MGyroX 1MGyroY 1MGyroZ  (5) where,1MGyroX , 1MGyroY and 1MGyroZ are the scalar moments in each axis which are specified on the appendix. Now, taking advantage of the vehicle symmetry these equations can be transformed to express the action of any other of the vehicle arms by switching the axes and maintaining the sign criteria in Figure 4. This is done by adding up each individual arm: 1MGyroj = R3toj 1MGyro (6) where R3toj represents the transform matrix from arm 3 to the arm j, obviously, because the equations have been developed in arm 3, R3to3 is the identity. Thus, the total action exerted by the four different arms will be: MGyroTotal = 4\u2211 j=1 1MGyroj (7) The thrust generated by the propellers is modelled by means of constant thrust coefficient given by: T = \u03c1A(\u2126R)2CT and Q = \u03c1A(\u2126R)2RCQ (8) Experimentally the coefficients were found to be: CT = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.7-1.png",
        "caption": "Fig. 13.7 Unsymmetrical coupling of coplanar shafts 1 , 2 , 3 , 4 by three Hooke\u2019s joints resulting in \u03d5\u03074 \u2261 \u03d5\u03071",
        "texts": [
            "6a) is subjected to the following three-step operation: Step 1: In an arbitrary position shaft 2 is cut thus splitting the entire system into a left part 1 and a right part 2 Step 2: Part 2 including joint 2 and the bearing of shaft 3 is rotated as one single rigid body about the axis of shaft 2 through an arbitrary angle \u03c8 Step 3: In the new position \u03c8 the two parts of shaft 2 are rigidly joined together. In the special case \u03c8 = \u03c0 , the new position is the position shown in Fig. 13.6b . If \u03c8 = \u03c0 , the axes of shafts 1 and 3 are skew in the new position. Example n = 4 : Equation (13.37) shows that the condition a4 = 1 is satisfied in each of the following three cases. Case a: (\u03b22, \u03b23) = (\u03c02 , 0) and cos\u03b11 cos\u03b12 = cos\u03b13 Case b: (\u03b22, \u03b23) = (0 , 0) and cos\u03b12 cos\u03b13 = cos\u03b11 Case c: (\u03b22, \u03b23) = (0 , \u03c0 2 ) and cos\u03b13 cos\u03b11 = cos\u03b12 . In Fig. 13.7 case (c) is illustrated by a system of coplanar axes with \u03b13 = \u03b11 = 20\u25e6 and cos\u03b12 = cos2 20\u25e6 (\u03b12 \u2248 28\u25e6). This example shows that geometrical symmetry of the coupling of shafts 1 and 4 is not a necessary condition for the identity of input and output angular velocity. Example n = 5 : The condition a5 = 1 is satisfied by altogether seven different combinations (\u03b22, \u03b23, \u03b24) and by associated conditions on \u03b11 , . . . , \u03b14 . The details are left to the reader. See also Duditza [4, 7]. In Fig. 13.8 a simple example with five coplanar axes is shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.13-1.png",
        "caption": "Figure 7.13. Spherical pendulum motion.",
        "texts": [
            " Show that the loci of all points of maximum height is an ellipse x~ (Ym - b)2 a2 + b2 = I , (7.82g) where a = v5/2g and b = a12. 0 260 Chapter 7 Example 7.15. The spherical pendulum. One end of a thin, rigid rod oflength eand negligible mass is fastened to a bob P of mass m, and its other end is attached to a smooth ball joint at O. In view of the constraint, the bob moves on a spherical surface of radius e, so this device is called a spherical pendulum. The bob is given an arbitrary initial velocity Vo at a point A located in the horizontal plane at the distance h below 0 in Fig. 7.13. Find three equations that determine the velocity of P as a function of the vertical distance z below 0, and describe how the motion x(P , t) may be found from the results. Solution. To find viz), it proves convenient to introduce cylindrical coordinates (r, \u00a2, z)with origin at the ball joint 0 and basis directed as shown in Fig. 7.13, with e, downward. The velocity of P is given by (see (4.59) in Volume 1) (7.83a) We wish to determine i , r\u00a2, and 2 as functions of z. Three equations are needed. The first equation is obtained from the energy principle. The forces that act on P are its weight mg and the workless force T exerted by the rod. Therefore, the principle of conservation of energy (7.73), with Vo = 0 at 0, yields !mv2 - mgz = mEo; (7.83b) where Eo == E /m is the total energy per unit mass. The speed v of P is thus determined by (7",
            "83a), we see that only the component mr\u00a2 of the linear momentum mv has a moment about the line OQ, namely, r (mr\u00a2 )ez . Therefore, h o . e, = mr2\u00a2 = n, and with y == ry /m,we have 2'r \u00a2 = y . (7.83d) (7.83e) (7.83f) This provides another equation relating the unknown function s. The constant y is determined from the initial conditions. Let e\", denote e\", at A. Then mvo . e\", is the only component of the initial linear momentum having a moment about the line OQ, and hence y = rovo . e\",= rovocos(vo, e\",), wherein ro= (e2 - h2)1/2 in Fig. 7.13. The final equation is derived from the suspension constraint: e2 = r 2+ Z2. This gives r = (e2 - Z2) 1/2, and hence . zzr = - .Je2 - Z2 A few moments reflection reveals that i , r\u00a2 , and zare now known as functions of z. Indeed , upon substituting (7.83d) and (7.83e) into (7.83c) , we reach . 2 2g 2 2 Eo y 2z =-[(e - z )(z+-)--],e2 g 2g which determines z(z) . And with r (z) = (e - Z2)1/2, f ez) given by (7.83e), and r\u00a2 = y / r(z) from (7.83d), it is now a straightforward matter to write the velocity (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002614_iet-epa.2018.5242-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002614_iet-epa.2018.5242-Figure3-1.png",
        "caption": "Fig. 3 FEM model of machine \u03b1 (a) Geometrical structure of the modelled machine, (b) Exemplary solution of the magnetic flux density",
        "texts": [
            " The velocity presented using (6) is determined by the rotation equation of the solid [47] J\u03b2 + \u03bb\u03c9 = Tem + Tload (7) where J \u2013 moment of inertia; Tem \u2013 electromagnetic torque; Tload \u2013 external load torque; \u03c9 \u2013 angular speed of the rotor; \u03b2 \u2013 angular acceleration; \u03bb \u2013 damping factor (a coefficient dependent on mechanical losses). The moment of inertia of the motor coupled with a DC generator was determined experimentally using a coasting method. The system of equations of (6) and (7) describes the electromagnetic\u2013mechanical coupling. It should be noted that deformations and vibrations are not considered. Fig. 3a shows a geometrical structure of the modelled machine. Owing to the symmetry along the z-axis, a half-two-dimensional model was used to reduce the calculation time. The mesh consists of \u223c20,000 elements. The rotor core was divided into \u223c3400 elements and the stator core was divided into \u223c8800 elements. The maximum length of the element's edge in the rotor core is \u223c5 mm, and in the stator core, it is \u223c1.6 mm. To improve solution convergence, additional areas with a denser mesh have been introduced, e.g. in the air gap. After this operation, the air gap is not divided into two regions, but instead, it is divided into three regions. Computations were performed with a transient type solver. Simulation parameters were determined by convergence studies. An exemplary solution of the magnetic flux density is shown in Fig. 3b, and a spectrum of the supply current for a voltage containing a subharmonic of frequency fsh = 5 Hz and value ush = 2.5% U1 is presented in Fig. 4a. An analogical spectrum based on measurements is presented in Fig. 4b. The calculated and measured values of subharmonic current are equal to 34.3% Irat and 36.3% Irat, respectively. A much larger discrepancy is found for interharmonic components (Figs. 4a and b), but they have a negligible effect on machine heating. The FEM model is used among other purposes for calculations of machine currents and power losses distribution under various power quality disturbances, including voltage deviation and voltage unbalance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001610_s11071-017-3369-5-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001610_s11071-017-3369-5-Figure2-1.png",
        "caption": "Fig. 2 Two typical nonlinearities: a dead zone and b backlash",
        "texts": [
            " It requires neither information on input nonlinearities nor the state of the system. 2. It does not require the construction of an inverse model of a nonlinearity, yet yields a satisfactory compensatory effect. 3. The control system has a simple structure, which makes the method easy to apply to real-world problems. Throughout this paper, \u03bbmin(\u0393 ) and \u03bbmax(\u0393 ) are the minimumandmaximumeigenvalues of a squarematrix \u0393 , respectively; and [ \u039811 \u039812 \u039822 ] = [ \u039811 \u039812 \u0398T 12 \u039822 ] . We consider a nonlinear system (Fig. 1) with either a dead zoneor backlash (Fig. 2). The state-space equation of the system is{ x\u0307(t) = Ax(t) + B\u03a8 (u(t)), y(t) = Cx(t), (1) where x(t) \u2208 R n is the state; y(t) \u2208 R is the output; u(t) \u2208 R is the control input; A \u2208 R n\u00d7n , B \u2208 R n\u00d71, and C \u2208 R 1\u00d7n are constant matrices; and \u03a8 (\u00b7) is the input nonlinearity. An input dead zone is described by \u03a8 (u(t)) = \u23a7\u23a8 \u23a9 u(t) \u2212 br , u(t) > br , 0, bl \u2264 u(t) \u2264 br , u(t) \u2212 bl , u(t) < bl , (2) where br (> 0) and bl (< 0) are the breakpoints of the dead zone in the positive and negative directions, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003055_mcs.2020.2976384-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003055_mcs.2020.2976384-Figure3-1.png",
        "caption": "FIGURE 3 The definition of the thigh and shank angles ( thi and )shi and knee joint positions ( ).ki Note that shank angles are not required for estimations. However, as explained in the \u201cResults and Discussions\u201d section, during experiments with inertial measurement units, shank angles were used to indirectly calculate the knee angles.",
        "texts": [
            " This objective can be achieved through well-established controllers, such as impedance and PD controllers. In Figure 2, for the controller in (b) to be operative, the estimator in (a) is an absolute requirement. This study concentrates on Figure\u00a02(a). As seen in Figure 2, the inputs could be the thigh angular velocity thio or thigh angle .thi In addition, it is possible to make a combined input as [ , ].x th thi i= o The effect of each input type on the estimation quality will be investigated in detail in the \u201cResults and Discussions\u201d section. Figure 3 gives the definitions of thigh and knee angles ( thi and .)ki The definition of shank angle hsi i s also shown, since it will be used later. More details will be provided in the \u201cResults and Discussions\u201d section Authorized licensed use limited to: Auckland University of Technology. Downloaded on May 27,2020 at 22:40:12 UTC from IEEE Xplore. Restrictions apply. 54 IEEE CONTROL SYSTEMS \u00bb JUNE 2020 when IMU data are used to evaluate the estimation quality. It should be noted that the estimation algorithm does not require shank angles",
            "4, and 1.6 m/s on a treadmill. The subjects were different from the other 21, and the experiments were performed in another lab. The thigh angular velocity, thigh angle, and shank angle ( )shi were obtained during the experiments. Although the estimator needs only one thigh IMU, two IMUs were used so that we could calculate the corresponding knee joint positions ki indirectly from the measured thigh and shank angles after the experiments. The definition of the knee joint positions ki is illustrated in Figure 3 according to ( ).180k sh thi i i= - - As mentioned, we need to know the expected knee joint positions for comparison with the estimated knee positions. Based on the obtained data, the following investigations were performed. As before, the training and test inputs were [ , ].th thi io The training data were for walking at 0.5, 1, and 1.5 m/s (from motion-capture cameras), and the test inputs were for walking 0.6, 0.9, 1.2, 1.4, and 1.6 m/s (IMU data). The training group was composed of five randomly selected subjects from the Authorized licensed use limited to: Auckland University of Technology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002670_elps.201900270-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002670_elps.201900270-Figure1-1.png",
        "caption": "Figure 1. Steps for the fabrication of the electrochemical platform: (A) CAD design of the 3D printed mold used for prototyping of the PDMS devices. The internal relief structures were 20 mm length \u00d7 600 \u03bcm width \u00d7 1 mm height; (B) PDMS device obtained using the 3D printed mold; (C) PDMS miniaturized cell with the integrated working, pseudo-reference and counter electrodes; (D) geometric area of the electrodes delimited with adhesive tape, and (E) electrochemical platform connected to the potentiostat such as used during the measurements.",
        "texts": [
            "4 mm diameter brass extruder nozzle. Ten molds were printed at once. It was made using ABS filament, a layer height resolution of 200 \u00b5m, and a printing speed of 40 mm/s. The mold obtained has the internal dimensions of 30mm length\u00d7 20mm width \u00d7 7 mm height. Moreover, it contains 0.80 mm thickness walls around and three internal relief microstructures with the dimensions of 20 mm length \u00d7 600 \u00b5m width \u00d7 1 mm height, which were responsible for the molding of the microchannels in the PDMS device. Figure 1A shows the layout of the 3D printed mold. The PDMS structures used here were produced according to a well-established protocol described elsewhere [30\u201332]. Briefly, PDMS monomer and its curing agent were mixed at 9:1 ratio, degassed under vacuum, and then deposited over the 3D printed mold. The walls around the mold avoided PDMS leakage. The PDMS was then cured at 70\u00b0C for 3 h and peeled off from the mold after this time. Since ABS is stable until ca. 85\u00b0C, the 3D printed molds were not damaged during curing step. The PDMS devices obtained were 30 mm length \u00d7 20 mm width \u00d7 7 mm height. The three microchannels molded in the center of these devices were 20 mm length \u00d7 600 \u00b5m width \u00d7 1 mm depth with a separation of 2.9 mm among them. Figure 1B presents a picture of one of the PDMSmicrodevices produced through this protocol. The working, counter, and pseudo-reference electrodes employed here for electrochemical sensing consisted of 0.7 mm diameter pencil graphite leads (type 2B). The silver pseudoreference electrode was obtained by coating one pencil graphite leadwith homemade silver conductive glue prepared by mixing nail base coat and silver powder at 1:1 ratio w/w. These electrodes were then placed inside the microchannels in the PDMS device, such as shown in Fig. 1C. The geometric area of the electrodes was delimited using electrical adhesive tape. For this, a Silhouette Cameo 3 cutting plotter (Silhouette Brasil, Belo Horizonte, MG, Brazil) was utilized to cut 13 mm squares in the adhesive tape, which were pinned over the surface of the microdevice aiming to delimit the geometric area of the electrochemical sensors, as exhibited in Fig. 1D. This device was used as an electrochemical miniaturized cell with a maximum supported volume of ca. 300 \u00b5L. \u00a9 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com An Autolab potentiostat/galvanostat model PGSTAT 128N (Metrohm Autolab, Utrecht, The Netherlands) equipped with extreme low current module and connected to a computer running general purpose electrochemical system (GPES) 4.9 software was used for cyclic voltammetry (CV) and squarewave voltammetry (SWV) experiments. All the voltammetric experiments were performed using the developed device and the integrated three-electrode system composed by bare pencil graphite leads as working and counter electrodes, and the pencil graphite lead coated with silver conductive glue as pseudo-reference electrode. The electrical connections were attached directly in the pencil graphite leads as displayed in Fig. 1E. The human blood serum used as sample was provided by the AcademicalHospital of the Federal University ofMatoGrosso do Sul (HU-UFMS, Campo Grande, MS, Brazil). The human urine sample was collected from a healthy adult ca. 1 h before the analysis. Both samples were spiked with known amounts of DOPA and AC standards and directly diluted in the running buffer. No other pre-treatment step was performed. The surface of the pencil graphite leads was investigated through SEM. A JSM-6380LV instrument (Jeol, Tokyo, Japan) was used to obtain images at different magnifications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure3-1.png",
        "caption": "Fig. 3. (a) The planar four-bar platform (b) the spherical four-bar platform.",
        "texts": [
            " When all the orienta- tions of revolute joints in the closed-loop linkage intersect at a specified point, the 1-DOF spherical platform is devised. If every two adjoining revolute joints form two skew lines, the 1-DOF Bennett platform is acquired. Also, two groups of revo- lute joints of the platform are intersecting at two moving points. For these four-bar configurable platforms, two alternative revolute joints are connected by links. Meanwhile, the rest revolute joints are assembled on end-effectors. The schematic diagrams are depicted in Fig 3 . Since the task of the configurable platform spans extra space in general, the parallel mechanism with configurable plat- forms can be viewed as a kinematically redundant mechanism. The degree of redundancy of the mechanism can be deduced from the mobility of the configurable platform. In accordance with the size and shape of the object to be fetched, the ge- ometry of configurable platforms needs to be designed appropriately. For the symmetrical 1-DOF single-loop mechanism with n links, the joint screw of the mechanism behaves as an ( n - 1) dimensional twist system [28] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.117-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.117-1.png",
        "caption": "Fig. 2.117 Lancer Evolution Mitsubishi intelligent electric vehicle [Mitsubishi Corporation Press Release of August 24, 2005].",
        "texts": [
            "7 E-M DBW AWD Propulsion Mechatronic Control Systems 303 Should the rear SM&GWs lose traction, on the other hand, and therefore tend to rotate further than the front ones, the drive may be automatically transferred to the front SM&GWs, even if they are in the freewheeling mode. A conventional M-M DBW 4WD automotive vehicle has numerous disadvantages in comparison to a 2WD version: its fuel consumption is poorer, it is heavier, due to the presence of the drive shaft and other components, and it also requires a floor tunnel for the drive shaft to pass through. Accordingly, it may be decided to use E-M DBW 4WD to optimise (minimise) these disadvantages and to ensure adequate performance in actual driving, for instance, as the AEV shown in Figure 2.117 [MITSUBISHI 2005]. Also, the reduction of fuel consumption in DBW 4WD may be minimised by using DBW 4WD propulsion only when necessary and by recuperating braking and/or cornering mechanical energy using both the FWD and RWD. Automotive Mechatronics 304 CH-E/E-CH Storage Batteries - A CH-E/E-CH storage battery consists of two or more cells that may be linked in series (to provide multiples of cell voltage) and/or in parallel (to provide more capacity [Ah] from the resulting voltage). In Figure 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000134_iet-epa:20060212-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000134_iet-epa:20060212-Figure1-1.png",
        "caption": "Fig. 1 Voltage limit ellipse and current limit circle considering stator resistance",
        "texts": [
            " As has been mentioned, in case that the motor has relatively large stator resistance value, if current reference for maximum torque control is calculated without considering stator resistance, calculated reference will exceed output capability causing saturation of the current regulator. The specifications of the machine for the EPS system are listed in the Table, indicating that per unit resistance value is relatively larger per unit value of d and q axes inductance. Such saturation increases in strength in accordance with rotor speed increase, because the output of the motor is limited not only by current limit circle but also by voltage limit ellipse [11]. In Fig. 1, the relationship between current limit circle, voltage limit ellipses and torque hyperbolic curves is shown. All graphs are drawn in d\u2013q current plane. Voltage ellipse can have different shapes whether stator resistance is considered or not. If stator resistance is included, voltage ellipse rotates counterclockwise and the angle of rotation is decided by stator resistance and inductances. As a result, there are two crosspoints of voltage limit ellipse and torque hyperbolic curve for maximum torque per voltage (MTPV) control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000717_s12541-010-0076-2-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000717_s12541-010-0076-2-Figure5-1.png",
        "caption": "Fig. 5 Rotor profiles of one novel twin-screw kneader",
        "texts": [
            " On the contrary, the mounting errors can be calculated if the profile errors are known. In order to mix and malaxate high viscosity materials, the authors have presented a novel differential twin-screw kneader.8,9 The teeth of female rotor (right hand) and male rotor (left hand) are 4 and 1, respectively; both the outer diameters of the female rotor and the male rotor are 60 mm; the lead length of the rotors are 200 mm and 50 mm, respectively; the backlash between the female and male rotor is b \u03b4 \u2032 = 0.2 mm ( b b \u03b4 \u03b4 \u2032= /2). Figure 5 shows the end u A \u2206 u A z u z \u2211 \u2211\u2206 (a) mounting distance error u A\u2206 (b) mounting angle error \u2206\u03a3 Fig. 4 Error analysis of grinding for screw rotors section of the female and male rotors of the novel differential twinscrew kneader. The grinding efficiency of CBN tool depends, to a greater extent, on the grit size of tools. The term \"grit size\" here means the sizes of CBN crystals. CBN abrasive material spec DLII, grit size No. 150# was selected, with the nominal particle size range of 75~106 \u00b5m. The average of grit size is 1c \u03b4 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003592_j.oceaneng.2021.109186-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003592_j.oceaneng.2021.109186-Figure1-1.png",
        "caption": "Fig. 1. The ship position and parameters.",
        "texts": [
            " This paper is organized as follows: after this introduction, Section 2 presents the problem formulation and preliminaries. In Section 3, the kinematic virtual control is designed by the backstepping method. Section 4 builds the dynamic control including the SMC, ESO and input optimization. Then, Section 5 provides the global structure and stability analysis. Section 6 gives the simulation analysis. Finally, the conclusions are given in Section 7. The under-actuated ship position in the horizontal plane and the motion parameters are shown in Fig. 1.where, u is the surge velocity; v is the sway velocity; r is the yaw rate; \u03d5 is the heading angle; U=(u2+v2)1/2 is the ground velocity; \u03b2 = arctan (v/u) is the drift angle; \u03b4 is the rudder angle, |\u03b4|\u2264\u03b4max and |\u0394\u03b4|\u2264\u0394\u03b4max are the rudder amplitude and increment constraints; n is the propeller revolution, nmin \u2264 n \u2264 nmax and |\u0394n|\u2264\u0394 nmax are the propeller amplitude and increment constraints. In this paper, the ship motion system that used for the final simulation is replaced by the MMG model. The MMG model was proposed by Ship Manoeuvring Mathematical Model Group in 1970s, and could be expressed as (Zhang et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure1-1.png",
        "caption": "Fig. 1. A general redundantly actuated parallel manipulator.",
        "texts": [
            " A general n-DOF redundantly actuated parallel manipulator has m actuated joints, satisfying m>n. The unit screws of the twists of the actuated joints are denoted as Sj\u0302 i(i=1, 2,\u22ef, m). Here, overconstraints [33] of the redundantly actuated parallel manipulator are not taken into account. Thus, the number of the constraint wrenches imposed on the moving platform is 6\u2212n, and the number of the actuation wrenches imposed on the moving platform ism. The constraint and actuation wrenches are denoted as $r,j(j=1, 2,\u22ef, 6\u2212n) and $a,i(i=1, 2,\u22ef,m), respectively, just as shown in Fig. 1. For without loss of generality, not just as shown in Fig. 1, each limb can have more than two actuators or impose more than two constraint wrenches, and each limb can impose both the actuation and constraint wrench simultaneously. Dynamics of the redundantly actuated parallel manipulator includes forward dynamics and inverse dynamics. Forward dynamics is referred to that given the desired actuated forces/torques, what are the acceleration, velocity, and configuration of the manipulator's moving platform, while inverse dynamics is referred to that given the desired acceleration, velocity, and configuration of the manipulator's moving platform, what are the actuated forces/torques"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003718_s40430-021-02834-8-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003718_s40430-021-02834-8-Figure4-1.png",
        "caption": "Fig. 4 Force representation of crank-slider mechanism [27]",
        "texts": [
            "2 2 \u23a1 \u23a2\u23a2\u23a2\u23a3 \ud835\udf152xc Gi \ud835\udf15\ud835\udf032 2 \ud835\udf152yc Gi \ud835\udf15\ud835\udf032 2 \u23a4 \u23a5\u23a5\u23a5\u23a6 + 2?\u0307?2 3\ufffd j=2 ?\u0307?j \u23a1\u23a2\u23a2\u23a3 \ud835\udf152xc Gi \ud835\udf15\ud835\udf032\ud835\udf15\ud835\udefe2 \ud835\udf15yc Gi \ud835\udf15\ud835\udf032\ud835\udf15\ud835\udefe2 \u23a4\u23a5\u23a5\u23a6 + 3\ufffd j=2 ?\u0308?j \u23a1\u23a2\u23a2\u23a3 \ud835\udf15xc Gi \ud835\udf15\ud835\udefej \ud835\udf15yc Gi \ud835\udf15\ud835\udefej \u23a4\u23a5\u23a5\u23a6 + 3\ufffd j=2 ?\u0307?2 2 \u23a1 \u23a2\u23a2\u23a2\u23a3 \ud835\udf152xc Gi \ud835\udf15\ud835\udefe2 2 \ud835\udf152yc Gi \ud835\udf15\ud835\udefe2 2 \u23a4 \u23a5\u23a5\u23a5\u23a6 + 3\ufffd j=2 3\ufffd j=2 ?\u0307?j?\u0307?k \u23a1 \u23a2\u23a2\u23a2\u23a3 \ud835\udf152xc Gi \ud835\udf15\ud835\udefej\ud835\udf15\ud835\udefek \ud835\udf152yc Gi \ud835\udf15\ud835\udefej\ud835\udf15\ud835\udefek \u23a4 \u23a5\u23a5\u23a5\u23a6 (k \u2260 j) Journal of the Brazilian Society of Mechanical Sciences and Engineering (2021) 43:185 1 3 185 Page 6 of 18 superposition principle. The contact between the bearing and journal is also assumed to be permanent. Equations\u00a013\u201315 are written according to Fig.\u00a04, showing a free diagram of a slider-crank mechanism using Newton\u2019s second law and Euler equations: Fi(i+1)x and Fi(i+1)y represent the joint force applied to link (i + 1) of link i in two x and y directions. Moreover, shaking forces and moments that flow from the frame to the piston and the crank link are shown in Eqs.\u00a016\u201318. (13)Fi(i+1)x + F(i+2)(i+1)x + ( \u2212m(i+1)x\u0308Gi+1 ) = 0 (14)Fi(i+1)y + F(i+2)(i+1)y + ( \u2212m(i+1)y\u0308Gi+1 \u2212 m(i+1)g ) = 0 (15) \u2211 MG(i+1) \u2212 IG(i+1) ?\u0308?(i+1) = 0 (16) \u2211 Fshx = \u2211 F41x + \u2211 F21x \u2211 F41 and \u2211 F21 represent the forces resulting in the slider-frame and crank-frame joints; respectively. Also, j shows the number of joint clearances. Horizontal and vertical forces at the place of crank-frame joint resulting from input torque and inertia effect of the second, third and fourth links are obtained separately according to Eqs.\u00a019\u201326 by means of Fig.\u00a04 showing forces and torque applied to the mechanism as follows [24]: (17) \u2211 Fshy = \u2211 F41y + \u2211 F21y (18)Msh = xG4i\u2297 \u2211 F41y i (19)FI 21x = Tin cos 2 l2 sin ( 2 \u2212 2 ) (20)FI 21y = Tin sin 2 l2 sin ( 2 \u2212 2 ) (21)FII 21x = [ \u2212 ( m2x\u0308G2 ) K2L2 sin ( \ud835\udf032 + \ud835\udefc2 ) + K2L2 cos ( \ud835\udf032 + \ud835\udefc2 )[ m2y\u0308G2 + m2g ]] cos \ud835\udefe2 l2 sin ( \ud835\udf032 \u2212 \ud835\udefe2 ) \u2212 ( m2x\u0308G2 ) (22) FII 21y = [ \u2212 ( m2x\u0308G2 ) K2L2 sin ( \ud835\udf032 + \ud835\udefc2 ) + K2L2 cos ( \ud835\udf032 + \ud835\udefc2 )[ m2y\u0308G2 + m2g ] + ( IG2 ?\u0308?2 )] sin \ud835\udefe2 l2 sin ( \ud835\udf032 \u2212 \ud835\udefe2 ) \u2212 ( m2y\u0308G2 ) \u2212 ( m2g ) (23) FIII 21x = \u2212 ( m3x\u0308G3 )[ G3B sin ( \ud835\udf033 + \ud835\udefc3 + \u03a8 ) + ( r3 ) sin \ud835\udefe3 ] cos \ud835\udefe2 K3L3 sin(\ud835\udefe2 \u2212 \ud835\udf033 \u2212 \ud835\udefc3) + G3B sin ( \ud835\udf033 + \ud835\udefc3 + \u03a8 \u2212 \ud835\udefe2 ) + ( r3 ) sin(\ud835\udefe3 \u2212 \ud835\udefe2) + [ m3y\u0308G3 + m3g ][ G3B cos ( \ud835\udf033 + \ud835\udefc3 + \u03a8 ) + ( r3 ) cos \ud835\udefe3 ] cos \ud835\udefe2 K3L3 sin(\ud835\udefe2 \u2212 \ud835\udf033 \u2212 \ud835\udefc3) + G3B sin ( \ud835\udf033 + \ud835\udefc3 + \u03a8 \u2212 \ud835\udefe2 ) + ( r3 ) sin(\ud835\udefe3 \u2212 \ud835\udefe2) + ( IG3 ",
            "31 Table 5 Decreasing ratios the subcomponents of balancing function of mechanisms A and B (suggested by this work) relative to mechanisms C, D, E and F (suggested by [23]) Decreasing ratio (%) A to C A to D A to E A to F B to C B to D B to E B to F F 21x 78.04 84.62 76.51 72.72 77.12 83.98 75.53 71.57 F 21y 72.53 76.54 69.51 70.22 70.90 75.14 67.70 68.45 F 41y 83.95 85.61 80 83.18 83.27 85 79.16 82.47 Msh 78.85 80.66 75.09 77.94 77.84 79.73 73.90 76.89 1 3 result of optimization, shaking force and shaking moment of the selected optimal mechanisms of this study are much lower than that of the original mechanism and the mechanisms suggested by the optimization results of ref [23]. Figure\u00a04 gives the crank-frame and follower-frame joint forces which are the subcomponents of shaking force after the optimization. There is a certain decrease of the force values. The X component of the crank-frame joint force of point A decreased by 78.045, 84.62, 76.51 and 72.72 relative to points C, D, E and F, respectively. These ratios for point B are 77.125, 83.98, 75.53 and 71.57. The Y component of the crank-frame joint force of point A decreased by 72.53, 76.54, 69.51 and 70.22 relative to points C, D, E and F, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.16-1.png",
        "caption": "Fig. 15.16 Center of acceleration G and accelerations a1 , a2 of points Q1 , Q2",
        "texts": [
            " Multiplying this equation by a , (15.38) by aA and taking the difference results in rG = arA \u2212 aAr a\u2212 aA . (15.39) Solving this equation for a yields the expression a = aA r \u2212 rG rA \u2212 rG . (15.40) Equations (15.37) \u2013 (15.40) correspond to (15.33) \u2013 (15.36). In (15.38) the factor (i \u03d5\u0308 \u2212 \u03d5\u03072) is the same for all points of \u03a32 . This factor has the effect of stretch rotation of r \u2212 rG . Let \u03b1 be the angle of this stretch rotation. The angle is \u03c0/2 in the special case \u03d5\u0307 = 0 , and it is \u03c0 in the special case \u03d5\u0308 = 0 . Figure 15.16 shows the general case with the center of acceleration G and with the accelerations a1 and a2 of two points Q1 and Q2 , respectively. By attaching to Q1 not only a1 , but also a2 and the acceleration zero of G the triangle (P1,P \u2217 2,Q1) is obtained. From (15.38) it follows that the triangles (G,Q1,P1) and (G,Q2,P2) are similar, and from Theorem 15.5 it follows that the triangles (P1,P \u2217 2,Q1) and (Q1,Q2,G) are similar. These two similarities are the geometrical interpretations of (15.40) and (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.12-1.png",
        "caption": "Fig. 13.12 Single serial chain of a Unitru coupling",
        "texts": [
            " The same constraints that are exerted by the spherical joint S can be exerted by placing two additional five-d.o.f. chains parallel to the first one. For reasons of dynamic balancing and of simplicity of design three identical chains are placed at intervals of 120\u25e6. The so-called Clemens coupling shown schematically in Fig. 13.11 is derived from Fig. 4.11. The serial chain R1S2R2 of this coupling is placed three times in parallel. On each shaft the three revolute axes fixed on the shaft are placed 120\u25e6 apart. The three spherical joints are permanently in the bisecting plane \u03a3 . The shafts 1 and 2 in Fig. 13.12 are connected to the sides of the rigid isosceles triangle (01,C,02) of base length 2 and apex angle 2\u03b2 by two pairs of revolutes R1 , R2 and R3 , R4 . At 01 the axis of R1 intersects both shaft 1 and R2 orthogonally, and at 02 the axis of R4 intersects both shaft 2 and R3 orthogonally. In the figure the symmetrical position is shown in which the shafts intersect in the bisecting plane \u03a3 normal to 0102 and passing through C . When the shafts are held fixed in this position, rotation of the triangle about the line 0102 causes both shafts to rotate through identical angles \u03d5 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002069_1.4030242-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002069_1.4030242-Figure2-1.png",
        "caption": "Fig. 2 von Mises equivalent contact stress distribution along the characteristic contact points: (a) point A, (b) point C, and (c) point E",
        "texts": [
            " (4) The inner hub of the pinion was constrained in axial and tangential directions. (5) The left and right boundaries of the pinion were constrained in radial direction. The sample of meshed model of a spur gear at different contact positions along with the above boundary conditions are shown in Fig. 1. Validation of the FE Model. The FE calculation of the contact stress is done on the meshed model of the gear pairs. The von Mises equivalent stress distribution sample for the torque of 302 Nm is shown in Fig. 2. The theoretical results obtained from Eq. (2) along the path of contact were used for the validation of FE model. The calculation of values corresponding to every point along the contact line will be tedious and time consuming. Hence, the characteristic contact points were selected and their corresponding values were plotted. Figure 3 shows the comparison plot of the active contact stresses between the theoretical analysis and the FE analysis of the spur gear pair. Friction Factor Developed for the Gear Pairs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000200_iccas.2007.4406594-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000200_iccas.2007.4406594-Figure2-1.png",
        "caption": "Fig. 2 Tilt-Rotor Unmanned Aerial Vehicle (Smart UAV)",
        "texts": [
            " Our proposed algorithm in this paper can deal with various constrains that are gain margin, phase margin, rising time, maximum overshoot and requirements of handling qualities, etc. \u2211\u222b = +\u2212= n i ii t t outref cwdtyytWJ f 1 2 }))(({ 0 refy )(tW iw ic outy The tilt-rotor UAV has been developed by Korea Aerospace Research Institute (KARI) for a robust and intelligent tilt rotor UAV exhibiting high-speed cruise and vertical take-off and landing capabilities since 2002.[1] The tilt-rotor UAV shown in figure 2 will perform various civil missions including disaster detection and management, weather forecasting, and environmental monitoring, etc. For reference, the Smart UAV controls operate as shown in figure 3. In helicopter mode, pitch control is archived through longitudinal cyclic, roll control through both differential collective pitch and lateral cyclic, yaw through differential longitudinal cyclic and heave through collective pitch with rotor governing. In conversion mode, the rotor controls are gradually blended out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001092_1350650113506571-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001092_1350650113506571-Figure1-1.png",
        "caption": "Figure 1. Replacing helical gears with several thin spur gears.",
        "texts": [
            " Then, the problem would be to calculate the lubricant Elm thickness and friction coefficient as well as the contribution of asperities in carrying the load between two rollers with the known geometry and the loading condition. The performance parameters are predicted using the load-sharing concept of Johnson et al.16 and modified Moes\u2019 equation.22 Geometry analysis of helical gears In the helical gears, unlike spur gears, length of contact line during an engagement cycle of a pair of teeth is variable. The geometry analysis starts with dividing the helical gear (with width b) into n spur gears along its axis at equal differential distances (db) (as shown in Figure 1), where each of the gears is rotated a small angle relative to the previous gear. The contact of each pair of spur gears along the line of action is replaced with contact to two cylinders. The Hertzian contact area between a pair of cylinders is also illustrated in Figure 1. Non-uniform load distribution model of Pedrero et al.,20 which is used in this paper, is based on the elastic energy stored in the gear tooth. The energy of a gear tooth consists of three components, i.e. bending, compressive, and shear loading. The total elastic potential energy of a gear is calculated by considering all pairs of teeth in contact. The load distribution is calculated using an approximate equation for the inverse unitary potential energy and minimizing it. For determining the position of contact point (c) in the helical gear, two parameters must be introduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001615_s10846-017-0512-y-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001615_s10846-017-0512-y-Figure12-1.png",
        "caption": "Fig. 12 The UAV platform used in the flight test",
        "texts": [
            " IFLY-G2 provides two kinds of combined navigation modes, GPS/INS and AHRS/DR with output of real-time attitude angle, 3D position, 3D speed and other information. In the field experiment, A Novaltel DGPS module is combined with the IFLy-G2. Microhard IPn920 data transceivers are adopted as communication equipment. The autopilot and the ground control station applied in the HIL simulation are directly used to construct the flight test system. Figure 11 shows the constructed flight control system for the test bed. Figure 12 shows the UAV platform in the field experiment, which is also used in our previous work to track a moving ground target [26]. Basic parameters of the UAV are shown in Table 2. 5.2 Results of the Field Experiment Plenty of field experiments are conducted using the flight test system. The results show that the proposed control structure passed HIL simulation can be easily applied to the actual system. Some results of the field experiments are given from Figs. 13 to 18. Figure 13 shows the 3-D trajectory of the UAV in the field experiment",
            " But, slight overshot exists in this process. Consequently, the UAV touches down 31 m before the reference landing point. Figure 18 shows the pitch ngle of the UAV in this procedure. Throughout the decline phase, the pitch angle is minus. When the UAV declines to a height of 2 m, the UAV does a flare maneuver, and begins to track a pitch angle of 2\u25e6, until touchdown. The reason for the slight oscillation after touchdown is that the damped nose gear made by bending steel profiles is elastic, as shown in Fig. 12. As shown in the field experiment results, using the proposed control structure, each layer of the control problem is tackled well. The attitude controller performs well enough to track a desired attitude, such as the flare maneuver. The UAV tracks the reference glide path smoothly, though the initial height error is as large as 43 m. As a result, the UAV touches down on the runway at a safe attitude, and lands safely at last. The results of the field experiment not only demonstrate the effectiveness of the proposed hierarchical control structure, but also verify the developed test system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001806_tasc.2016.2524026-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001806_tasc.2016.2524026-Figure1-1.png",
        "caption": "Fig. 1. Topology of 12/10-pole BFSPM motor.",
        "texts": [
            " Based on the FSPM motor, a type of novel bearingless FSPM (BFSPM) motors with the single winding are proposed and investigated [9]. The purpose of this paper is to compare the configurations and electromagnetic performances of a 12-stator-slot/10-rotorpole BFSPM motor and a 12-stator-slot/14-rotor-pole BFSPM motor. In Section II, the configurations and operating principles of the two motors will be described. In Section III, the electromagnetic characteristics of both motors will be analyzed and compared using the finite element analysis (FEA). Finally, conclusion will be drawn in Section IV. Fig. 1 and Fig. 2 show the configurations of three-phase 12/10-pole and 12/14-pole BFSPM motors, respectively. In Fig. 2, the stator contains 12 segments of \u201cE\u201d-shape magnetic cores, between which 12 pieces of magnets are sandwiched. The magnets are magnetized circumferentially in alternative opposite directions. The concentrated armature coils are wound around the adjacent teeth and PM, and suspending coils are wound around the middle teeth. The key difference between the two motors is that the \u201cU\u201d-shaped magnetic cores are adopted in 12/10-pole motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003332_j.robot.2020.103425-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003332_j.robot.2020.103425-Figure1-1.png",
        "caption": "Figure 1: Components of the HKE and the actuator",
        "texts": [
            " Finally, parameter of the mathematical model has been estimated by solving the optimization problem using Genetic Algorithm (GA). The HKE has four DoF, which consists of two hip and knee joints in each leg. Its structure is assembled by seven different parts, i.e. waist, two pelvises, two femurs and two tibias. Waist is located on the top, and two legs are connected to it by two pelvises on the left and right side of the waist. Femurs are coupled to the pelvises by a revolute joint. Two tibia links are connected to the femurs as a child link. Figure 1 shows the actual structure of the HKE, in which hip and knee are active and ankle is fixed passive joints. In this structure, femur is from the hip joint to the knee joint, and tibia is from the knee joint to the underside of the foot. In addition, the HKE is divided to an immovable and movable component, in which waist and pelvis are locked to the body of the wearer, while femur and tibia are the movable parts. Moreover, each joint is 3 Jo ur na l P re -p ro of connected to a DC motor, and a quadrature encoder is placed at its output shaft to measure the angular trajectory of the joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000928_j.mechmachtheory.2012.10.007-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000928_j.mechmachtheory.2012.10.007-Figure13-1.png",
        "caption": "Fig. 13. a) Dimensions of PMC gear and bearings; b) loads on the PMC gear and bearings; c) loads and moments on the free body diagram.",
        "texts": [
            " Hence, the pericyclic motion causes a dynamic load at the center of gravity of the PMC gears. The rate of change of angular momentum of the PMC defines the dynamic load produced by the pericyclic motion. Firstly, the angular momentum of the PMC is calculated from H \u2192 GP \u00bc Ip \u22c5\u03a9 \u2192 PMC . Here the term [Ip] is the centroidal moment of inertia tensor of the PMC gear. The angular momentum of the PMC is calculated relative to the center of gravity (CG). The dimensional parameters used in the PMC dynamics analysis are shown in Fig. 13-a. In this paper, the PMC gears are assumed as rigid annular cylinders with the external diameter (Dext), gear bore diameter (Dbore) and the height (h). Hence, the PMC gear moment of inertia in xp\u2013yp\u2013zp coordinate frame is: where Ipxx \u00bc \u03c0\u03c1h 48 3 4 D4 ext\u2212D4 bore \u00fe h2 D2 ext\u2212D2 bore Ipyy \u00bc Ipxx Ipzz \u00bc \u03c0\u03c1h 32 D4 ext\u2212D4 bore Ipxy \u00bc Ipxz \u00bc Ipyz \u00bc 0 \u00f023\u00de \u03c1 is the density of the gear material. Acceleration magnitude in the kinematical design space for \u03c9out=1 rad/s at \u03b2=2\u00b0 and 5\u00b0; a) as a function of N1/N2; b) as a function of reduction ratio",
            " (4) and M \u2192 OT is rewritten for steady state condition as: MOT \u00bc Ipyy\u2212Ipzz \u22c5\u03c9in\u22c5 sin\u03b2\u22c5 \u03c9in\u22c5 cos\u03b2 \u00fe\u03c9p \u00f029\u00de The (Ipxx\u2212 Ipzz) term is non-zero for the annular cylinders. The increase in gear diameter and in gear height amplifies the magnitude of the overturning moment based on Eq. (23). The carrier speed (\u03c9in) contributes significantly to the overturning moment order of magnitude. Due to term sin(\u03b2) in Eq. (29), it is possible to reduce the overturning moment magnitude by selecting a small nutation angle. The direction of M \u2192 OT relative to the PMC coordinate frame is illustrated in Fig. 13-b. The overturning moments of twin PMC design have the samemagnitudes but opposite directions for each PMC gear which cancels the net external moment loads. PMC loads and moments vectors with their effective locations are illustrated in Fig. 13-b and c. The tooth loads (Fig. 7-b) were established in Eqs. (14), (15) and (16). Tangential (Ft), Radial (Fr) and Axial (Fa) mesh loads are parallel to xp\u2013yp\u2013zp coordinates, respectively. The coordinates the tooth mesh loads in xp\u2013yp\u2013zp frame are shown by L \u2192 c and L \u2192 d for left and right meshes, respectively, as shown in Fig. 13. The bearing reaction loads are presented as R \u2192 c and R \u2192 d in Fig. 13-b and c at their effective locations. The position vectors of the bearings C and D are presented by L \u2192 Rc and L \u2192 Rd, respectively. These coordinates are calculated based on the bearing type and bearing dimensions. The bearing C is selected to support the axial and the radial loads while the bearing D supports only radial loads. The bearing reaction loads at bearing C and D are R \u2192 c \u00bc Rcx Rcy Rcz T and R \u2192 d \u00bc Rdx Rdy 0 T , respectively (Fig. 13-b\u2013c). The input torque is shown in Fig. 13-bwith the symbol Tin and converted to the PMC body fixed coordinates using transformationmatrix shown in Eq. (1). The torque vector in PMC frame is: where T \u2192 p \u00bc 0 \u2212Tin sin\u03b2 Tin cos\u03b2f gT \u00f030\u00de The bearing reaction loads are the only unknown parameters in Fig. 13-c. There are 5 unknown bearing reaction loads with the known case of Rdz=0. To solve these 5 unknowns, the equilibrium of the forces (\u2211F \u2192 p \u00bc 0) and the equilibrium of the moments at the CG (\u2211M \u2192 G \u00bc 0) are considered. The unknown reaction loads (Rcx, Rcy, Rcz, Rdx, Rdy) are calculated from the simultaneous solution of \u2211F \u2192 p \u00bc 0 and \u2211M \u2192 G \u00bc 0. The equilibrium of the forces is: \u2211F \u2192 P \u00bc F \u2192 c \u00fe F \u2192 d \u00fe R \u2192 c \u00fe R \u2192 d \u00fem \u2192 PMC \u00bc 0 \u00f031\u00de , F \u2192 c and F \u2192 d are tooth load vectors of the PMC gears.m \u2192 PMC is the weight of the PMC gear resolved in xp\u2013yp\u2013zp coordinates",
            " In this example, 25:1 reduction ratio Pericyclic Transmission designs (Table 1) are investigated with 760 HP input power (Pin) and 270 rpm output speed (\u03c9out) at a constant gear height, h=50.8 mm (h=2inch), and with \u03b2=5\u00b0. Mmesh and MOT are presented by solid line and solid line with markers, respectively. The magnitude of MOT increases as a function of gear mean pitch diameter. Here, mean pitch diameter (Dmp) is assumed to be in the center of the face width (f). The PMC gear external diameter (Dext) and bore diameter (Dbore) are calculated as a function of Dmp and f, (Fig. 13). The increase in Dmp generates larger moment of inertias (Ipyy, Ipzz) and largerMOT. As shown in Fig. 14, gear diameter change is not effective on the magnitude ofMmesh, because mesh forces (F \u2192 c and F \u2192 d) are inverse proportional to Dmp. The reduction of tangential tooth load magnitude as the gear diameter increase was presented in Fig. 10. The total moment (Mtotal) is presented with dashed line in Fig. 14. The magnitude of Mtotal increases with the gear diameter increase. Moreover, the direction ofMtotal changes from negative to positive after the critical diameter which is 175",
            " bi is approximated for steel rollers as: bi \u00bc 3:35\u22c510\u22123 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q max= l\u22c5\u03c1r\u00f0 \u00de q \u00f036\u00de Here, \u03c1r is the equivalent radius of curvature of the outer race and the cylindrical roller and formulated as: where \u03c1r \u00bc dbi \u00fe dbo\u22122db 2\u22c5 dbi \u00fe dbo\u00f0 \u00de\u22c5db \u00f037\u00de , db, dbi and dbo are roller, bearing inner race, bearing outer race mean diameters, respectively. In this paper, the bearing where inner race diameter (dbi) equals to the gear outer diameter while the bearing outer race diameter is defined as (dbo=dbi+db). The effective location of the bearing reaction loads (LRc and LRb in Fig. 13) are calculated based on the bearing dimensions and cone angle by LR=0.5\u22c5(dbi+0.5\u22c5dbo)/sin \u03be. The effect of the gear diameter change on the PMC support bearing normal and axial reaction loads is illustrated in Fig. 15-a. The normal loads on both bearings show a similar trend and magnitude from smaller diameters to larger. The axial load is very small compared to the radial loads. This is caused by the opposite directions of the axial mesh loads. Because the axial mesh loads are approximately equal to each other and point in the opposite directions, the resultant axial reaction load at the bearing C is very small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003262_j.msea.2020.139999-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003262_j.msea.2020.139999-Figure2-1.png",
        "caption": "Fig. 2. Schematic of laser metal deposition.",
        "texts": [
            " The chemical compositions of the substrate and metal powder used in the experiment are shown in Table 1. Fig. 1. SEM image of 630 stainless steel powder. Table 1. Chemical composition of the materials used [wt.%] Material C Si Mn P S Cr Ni Mo Nb & Ta Cu N 630 stainlesssteel (powder) 0.05 0.6 0.72 0.013 0.05 15.8 4.63 0.1 0.25 4.66 0.1 630 stainless- steel (substrate) \u22640.07 \u22641 \u22641 \u22640.04 \u22640.03 15-17.5 3-5 - 0.15-0.45 3-5 - The laser melt deposition equipment employed in this study was an MX3 direct metal tool (DMT) developed by Insstek, and the process illustration thereof is shown in Fig. 2. A high-power laser beam was locally irradiated onto the substrate to form a melt pool on the substrate surface, to which powder was supplied through a nozzle. The melt pool, in which the substrate and powder are melted and mixed together, undergoes rapid solidification, resulting in the formation of a metal layer with a fine and dense structure. The 3D model was sliced to a uniform thickness, and the segmented sections were adjusted to the tool path (e.g., zigzag and spiral) for fabrication. Additionally, the nozzle scanning speed could be set to adjust the time required to form a single layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000480_j.ijnonlinmec.2010.12.010-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000480_j.ijnonlinmec.2010.12.010-Figure1-1.png",
        "caption": "Fig. 1. The Jeffrey\u2013Onishi problem [14]: a cylinder translating with complex speed U and rotating with angular velocity O near a no-slip wall and experiencing, in general, a non-zero net force and torque. The interior of the annulusro jzjo1 (shown right) is transplanted, under the mapping z\u00f0z\u00de given in (11), to the fluid region in the z-plane above the no-slip wall and outside the moving cylinder. Points labelled with the same letter correspond under the mapping (11).",
        "texts": [
            " Defining the stress tensor as sij \u00bc pdij\u00fe2meij \u00f09\u00de then, if ds denotes arclength along some curve with unit normal vector n, the complex form of the quantity sijnj ds (where ni are the components of n) can be shown to be 2mi dH ds ds, H\u00f0z\u00de f \u00f0z\u00de\u00fezf u\u00f0z\u00de\u00fegu\u00f0z\u00de: \u00f010\u00de This result is useful for the computation of the hydrodynamic force and torque on a body. Although the boundary value problems for Stokes flows of interest here are not conformally invariant there is still significant advantage in adopting a conformal mapping approach. Consider a circular cylinder of radius r centred at (0,d) above a wall along the real axis in a z-plane (Fig. 1). The fluid region above the wall and exterior to the circular swimmer is a doubly connected region and it is known [21] that there exists a conformal mapping to any such domain from a parametric annulus ro jzjo1. It is simply the Mo\u0308bius mapping z\u00f0z\u00de \u00bc iR z\u00fe1 z 1 , \u00f011\u00de where R is a real constant. jzj \u00bc 1 maps to the real axis, jzj \u00bc r maps to the cylinder and z\u00bc 1 maps to the point at infinity. A rotational degree of freedom in the Riemann mapping theorem has been used to suppose that z\u00bc 1 maps to the point at infinity; any other point could have been chosen but this choice is made for convenience"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001272_1.4024103-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001272_1.4024103-Figure5-1.png",
        "caption": "Fig. 5 Contact point displacement",
        "texts": [
            " In order to check the compatibility between the two different selection methods, the surface displacement is studied. The structural displacement at the contact point dp is the quantity that sums-up raceway displacements. Here, dp does not appear explicitly in the coupling, but it helps to understand how the new geometry affects the ball displacement, and its magnitude can be compared to the ball displacement due to contact. The contact point displacement dp is the contribution of the change of conformity df and the curvature center displacement dCc : dp!\u00bc df ! \u00fe dCc ! , as shown in Fig. 5. Then, for the inner ring df ! \u00bc \u00f0fnew fold\u00deD sin ac xi1 ! cos ac yb1 ! (1) dCc ! \u00bc da xi1 !\u00fe dr yb1 ! (2) where ac is the contact angle. equivalent punctual forces, and the Hertz pressure distribution Fig. 4 Geometry of the point selection area for the torus fitting Journal of Tribology JULY 2013, Vol. 135 / 031402-3 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 06/05/2014 Terms of Use: http://asme.org/terms The value of dp is compared for the two selection methods shown in Fig",
            " No major differences between the torus fitting (TF) and simplified torus fitting (TS) methods are observed. The full and simplified torus fittings only differ from the inclusion of the conformity change. The relative difference on the normal force does not exceed 5%; it indicates that the effect of the conformity change is less significant than the effect of the raceway curvature center displacement. The corresponding axial and radial displacements of the right inner ring curvature centers (as defined in Fig. 5) are given in Table 4 for two opposite balls at azimuth angles of h\u00bc 0 deg and h\u00bc 180 deg. It is interesting to note that, despite a few changes in the numerical values, it hardly affects the internal load distribution. The maximum change of conformity is observed for the inner right contact of the ball at h\u00bc 180 deg. When using the full torus fitting method, the conformity at this contact is 0.5214, which represents a relative difference of 0.4% compared to its initial value and a difference of 39 lm on the raceway radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.17-1.png",
        "caption": "Figure 5.17. Schema for evaluation of the center of gravity of a uniform cylinder in a variable. parallel gravitational field.",
        "texts": [
            " The location of the center of gravity will depend on the variable gravitational field strength g(P) and the orientation of the body, which also might be nonhomogeneous. So, if the body is moved to a different configuration at another place in a variable gravity field, the center of gravity generally is not at the same place in the body frame; and hence the center of gravity generally is not a unique point in the body frame . Example 5.8. A homogeneous cylinder ~ of height h and its base at the distance a from the Earth's center F in frame <I> = {F; Ik } is shown in Fig. 5.17. Show that the center of gravity in a variable gravity field is not an invariant point in the body reference frame. J The Foundation Principles of Classical Mechanics 49 (5.67a) (5.67b) (5.67c) Solution. The second equation in (5.59) gives the variable gravitational field strength g(P ) =MG/X2 at P due to the Earth. The Earth's mass is M =m(gjo) and X is the distance from F to a material parcel at P having weight dw(P) = g( P)dm(P) = (M G/ X 2)adX, where a = m] h is the mass per unit length of gj. Integration in accordance with (5.64) shows that the weight of the cylinder in the given configuration will vary with the distance a from the Earth: _ mMG r: dX _ mMG W(gj) - -h- 10 X2 - a(a + h) ' The location x(gj) = XI + YJ +ZK of the center of gravity from F is given by (5.66). With x(P) = XI+ YJ + ZK in Fig. 5.17 , we find by symmetry about the I-axis that Y= Z = 0 and rio - MmGr dX MmG (a +h)W(;'lu)X=-- -=--In -- . h 0 X h a Using (5.67a) and introducing i == X - a, we obtain the location i of the center of gravity in the body frame IfJ = {O; id in Fig . 5.17: i = a [I + h/a In (1 + ~) - 1] . h]a a This result shows that the center of gravity in the body frame varies with a, the vertical distance of 0 from the center of the Earth . If the body is moved vertically to another place, the location i of the center of gravity in the body frame will change"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.7-1.png",
        "caption": "Fig. 7.7 (a) A bistable compliant mechanism and (b) its pseudo-rigid-body model",
        "texts": [
            " The boundary conditions for the fixed-pinned beam described earlier are one end fixed (force and moment reactions), and the other end pinned (force reactions only). Other Segments Pseudo-rigid-body models have been developed for other types of segments, including fixed-guided segments, functionally binary pinned-pinned segments, beams loaded with a moment at the end, and beams with follower loads. Mechanisms. The real power of the pseudo-rigid-body model for individual segments is realized when they are applied to compliant mechanisms that contain such elements. For example, consider the compliant bistable mechanism illustrated in Fig. 7.7(a). Since the flexible segments have the geometry and boundary conditions of the fixed-pinned segment discussed earlier, they can be modeled using the pseudo-rigid-body model for that segment. The resulting pseudo-rigid-body model for the mechanism is shown in Fig. 7.7(b). This mechanism will be discussed in more detail as an example. Example model. Consider a brief example for the compliant, micro, bistable mechanism illustrated in Fig. 7.7(a) [29]. Its corresponding pseudo-rigid-body model is shown in Fig. 7.7(b). The torsional spring constants are calculated from the geometry and material properties. The potential energy, V , for the mechanism is V = 1 2 (K2\u03c82 + K3\u03c83), (7.7) where Ki is the spring constant for joint i, and \u03c82 = (\u03b82 \u2212 \u03b820) \u2212 (\u03b83 \u2212 \u03b830) and \u03c83 = (\u03b84 \u2212 \u03b840) \u2212 (\u03b83 \u2212 \u03b830) (7.8) and \u03b8i is the angle of link i, which can be found using traditional kinematic analysis. The input torque, M2, is M2 = dV d\u03b82 = K2\u03c82(1 \u2212 h32) + K3\u03c83(h42 \u2212 h32), (7.9) where h32 = r2 sin(\u03b84 \u2212 \u03b82) r3 sin(\u03b83 \u2212 \u03b84) and h42 = r2 sin(\u03b83 \u2212 \u03b82) r4 sin(\u03b84 \u2212 \u03b83) ",
            "12) h\u2032 42 = dh42 d\u03b82 = r2 r4 [ cos(\u03b83 \u2212 \u03b82) sin(\u03b83 \u2212 \u03b84) (h32 \u2212 1) \u2212 sin(\u03b83 \u2212 \u03b82) cos(\u03b83 \u2212 \u03b84) sin2(\u03b83 \u2212 \u03b84) (h32 \u2212 h42) ] . (7.13) The potential energy curve (equation (7.9)), the required crank torque (equation (7.11)), and the second derivative of potential energy (equation (7.13)) are particularly useful in defining the mechanism behavior. The input torque is zero at points of relative minimum (stable equilibrium position) or maximum (unstable equilibrium) potential energy. The global minimum of potential energy occurs when the mechanism is in its undeflected position. This position is shown in solid lines in Fig. 7.7(a). The second stable equilibrium position has some energy stored but is a local minimum of potential energy and therefore is a stable equilibrium position. The energy stored is evident in the deflected member shown in dashed lines in Fig. 7.7(a). There are many active research topics in compliant mechanisms and new areas continue to be discovered. A subset of topics is mentioned here and then three examples are discussed in more depth. Compliant mechanism design methods have been an important area of research. This includes optimization methods [10, 11, 23, 27, 43, 45, 48, 50, 56], design of precision flexures [6, 16, 17, 31, 46, 54], building blocks [30], and the pseudo-rigid-body model approach discussed previously. Classes of compliant mechanisms studied include multistable mechanisms [4, 5, 28, 33, 41], metamorphic mechanisms [8, 9, 52], contact-aided compliant mechanisms [3, 13, 34, 35], compliant joints [40, 49, 55], medical devices [7, 36], origami inspired mechanisms [12] and statically balanced mechanisms [14, 42]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.139-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.139-1.png",
        "caption": "Fig. 2.139 HEV driving circumstances during staring [DRIESEN 2006].",
        "texts": [
            " As a result, mechanical energy from the axle acts on the E-M motor, turning it in effect into a M-E generator such that the torque directly from the ICE to the axle is re-circulated, thereby lowering transmission energy conversion efficiency in that range. Changing the operating range of the ICE to high speed and low load for the equivalent power output enables recirculation to be avoided, but it also reduces the ICE\u2019s energy efficiency. An exemplary series/parallel HEV layout with an ICE and two electrical machines is shown in Figure 2.138 [DRIESEN 2006]. In Figure 2.139 is shown the HEV driving circumstances during starting when the ICE remains off to save liquid fuel and the E-M motor drives the series/parallel HEV. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 336 In Figure 2.140 HEV driving circumstances are shown during normal driving when the ICE starts and may drive the series/parallel HEV and produce electrical energy for the E-M motor or is charging the CH-E/E-CH storage battery. In Figure 2.141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003164_1.3662578-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003164_1.3662578-Figure8-1.png",
        "caption": "Fig. 8 Spinning moment versus normal load for several conflgurations1 >/rin. balls, MIL 7808 Oil",
        "texts": [
            " The ball is resisted in its motion by both spinning moments Ms and rolling moments MR. The rolling moments have been determined already from the flat-plate experiments. Moment equilibrium of the ball requires Transactions of the A S M E Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use FS = 4 (J\\IS COS ~2 + MR sin 0 (2) Using this relation, the spinning moment has been determined for a variety of situations and the results are plotted in Fig. 8. On this log-log plot, all the slopes are approximately Vs, agreeing quite well with the analysis of Poritsky, Hewlett, and Coleman [4], They integrated the friction force over the contact ellipse to obtain a spinning moment. A constant spin-friction coefficient Us and a normal stress distribution equal to the Hertz distribution were assumed. The result is Ma = | HgNaWk) where E{k) is the complete elliptic integral of the second kind, k = [1 - (6Va s)] , /\u00bb (3) a is the major semiaxis of the contact zone, and b is the minor semiaxis of the contact zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000993_med.2012.6265864-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000993_med.2012.6265864-Figure4-1.png",
        "caption": "Fig. 4. Hovering Operation Principles and Coordinate Frames",
        "texts": [
            " This connection enables the seamless data transfer between the GCS and the experimental platform and it is used for wireless telemetry and for updating various parameters of our system\u2019s controller in operation time. Finally, the control action signals computed by the main control process are output to the INT ERFACER process and consequently forwarded to the ARM-microcontroller which handles the low-level communication with the Actuator Control Subsystem. The UPAT\u2013TTR\u2019s hovering mode operation principles are illustrated in Figure 4. The total thrust is produced by the 3 rotors and it is used to control the hovering altitude. The rolling motion is controlled by the differential thrusting of the main 2 rotors, the pitching motion by the tail rotor\u2019s thrust and the yawing motion by rotating the tail rotor perpendicular to the body axis and thus producing a lateral thrust component. The main rotors are not actively controlled and will be used in the future to control the vehicle in forward flight and to achieve conversion from rotorcraft to fixed-wing aircraft flight mode. Let B = {Bx, By, Bz} be the coordinates Body-Fixed Frame (BFF) and E = {N, E, D} be the Earth North-East-Down (NED) Local Tangential Plane (LTP) as depicted in Figure 4. 978-1-4673-2531-8/12/$31.00 \u00a92012 IEEE 1581 Also let U = {u, v, w} be the BFF-based and aligned linear velocity vector, \u2126 = {p, q, r} the BFF-based angular rotation rate vector, X = {x, y, z} the LTP-based linear velocity vector and \u0398 = {\u03c6 , \u03b8 , \u03c8} the LTP-based angular rotation rate vector. The transformation of linear velocities and angular rates from the BFF to the LTP are provided by the skew-symmetric rotation matrix RB\u2192W and the TaitBryan angles transformation matrix JB\u2192W [6]. X\u0307 = RB\u2192IU , (1) \u0398\u0307 = JB\u2192I\u2126 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002789_tec.2019.2898640-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002789_tec.2019.2898640-Figure4-1.png",
        "caption": "Fig. 4. Prototypes. (a) Machine A and Machine C. (b) Machine B.",
        "texts": [
            " In addition to the distribution of the time-space harmonic MMFs, the amplitudes of the harmonic currents also affect the rotor harmonic eddy-current losses. The amplitudes of the harmonic currents depend on the electromagnetic parameters and the control mode of some specific prototypes. Therefore, three prototypes will be utilized for further investigation below. Table I lists the comparison of the parameters between the machine A, C with the conventional short-pitching distributed windings and the machine B with split-phase winding. Fig. 4 depicts the structures of these prototypes. All the prototypes are equipped with the same annular samarium cobalt magnet magnetized in parallel and the same titanium alloy sleeve. By increasing the number of conductors per slot and reducing the 0885-8969 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. > IEEE PES Transactions on Energy Conversion< 6 number of wires per conductor in machine B, the phase voltages of the three machines are close to each other, as well as the DC bus voltages",
            " In order to evaluate the influence of these un-eliminated harmonic fields, it is necessary to quantify the total harmonic eddy-current losses. In this subsection, the total harmonic eddy-current losses of the three machines calculated by FEM and analytical method W ) W ) 0885-8969 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. > IEEE PES Transactions on Energy Conversion< 7 are compared. According to the parameters of Table I and the winding arrangements of Fig. 4, the 2D finite element model is established. The time-varying phase currents shown in Fig. 5 are injected into the windings and the rotors are set to rotate synchronously with respect to the fundamental MMF in which k = 1 and v = 1. Meanwhile, the magnets are not magnetized. Therefore, the harmonic eddy-current losses can be calculated. Fig. 8 presents the distribution of the ohmic-loss densities of the machines at the time instants of t1, t2 and t3, respectively. At these time instants indicated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001645_1464419317727197-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001645_1464419317727197-Figure4-1.png",
        "caption": "Figure 4. Bearing test rig: (a) photo of test rig and (b) internal structure of bearing box.",
        "texts": [
            " Due to the interaction forces shown in Table 6, the average wear rate with different cage unbalance masses at the rotating speed of 6600 r/min are shown in Figure 3. It can be seen that the wear rate of the cage guiding surface obviously increases with the increase of cage unbalance mass; however, the wear rate of the cage pocket has no evident increase. The simulation of cage wear qualitatively agree with the following experimental observation. A test rig is specially developed to measure the cage motions of a ball bearing in three dimensions, and diverse prescribed unbalance masses are added on the cage. The bearing test rig is shown in Figure 4(a), which consists of motor, coupling, supporting, shaft, and bearing box. An angular contact ball bearing of 7013AC as the tested bearing is installed on the end of the cantilever shaft. At operating conditions, a constant radial force (along the z direction) and axial force (along the x direction) is applied on the bearing house and the corresponding values are measured by force transducers as shown in Figure 4(b). The eddy current probe is used to measure the cage motions in radial and axial directions. Two probes (yc, zc) are installed in the bearing house at 90 apart and another two probes (xc1, xc2) are fixed on a subpanel at 180 apart as shown in Figure 4(b). In addition, a data capture system is used to obtain the data and its sampling frequency is 4000 Hz. The cage is designed with four screwed holes symmetrically in circumference and the various cage unbalance conditions are realized by fixing different mass nuts on the screwed holes. The initial without additional mass and the cage unbalance masses of 1.6 g, 3.5 g, 6.8 g are shown in Figure 5. The experiments are performed on the above test rig at different operating conditions as listed in Table 3 and the external loads correspond to the simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.17-1.png",
        "caption": "Fig. 3.17 Quantities associated with screw displacements (n\u0302, \u03d5\u0302) carrying the line r\u03021 into the line r\u03022",
        "texts": [
            "126) become (with a Taylor series expansion for u ) \u03d5 = \u03d51 + \u03d52 = 0 , p = p1 + p2 , n = n1 = n2 , u = \u2212e3 2 \u03d51 \u2212 \u03d52 \u03d51 + \u03d52 . \u23ab\u23ac \u23ad (3.174) This means that the resultant screw axis intersects the e3-axis orthogonally at a point u which depends on the ratio \u03d52/\u03d51 . The points P1 , P2 and P3 in Fig. 3.14a are collinear. Special case \u03b1 = 0 (parallel screw axes) and \u03d52 = \u2212\u03d51 : According to (3.129) the resultant displacement is a pure translation s . With s1 = p1\u03d51 and s2 = p2\u03d52 = \u2212p2\u03d51 it is s = [(p1 \u2212 p2)e1 \u2212 e2]\u03d51 . (3.175) This displacement is normal to e3 . In Fig. 3.17 two skew lines are defined by their unit line vectors r\u03021 and r\u03022 . The line vector r\u03022 is produced from r\u03021 by the screw displacement (n\u03023, \u03b1\u0302) with the dual unit vector n\u03023 along the common perpendicular and with the dual screw angle \u03b1\u0302 = \u03b1+\u03b5 between the two lines. Without loss of generality, it is assumed that 0 < \u03b1 < \u03c0 whereas may be positive, zero or negative. The dual unit vector n\u03023 is one of the basis vectors n\u0302i (i = 1, 2, 3) of a dual basis which has its origin at the midpoint 0 of the common perpendicular",
            " Determine all rotations (n, \u03d5) about a fixed point 0 which carry a body-fixed line passing through 0 from a given position r1 into another given position r2 . The lines r1 and r2 and the angle \u03b1 between them are shown in Fig. 1.11a . Figure 1.11b explains cartesian basis vectors n1 , n2 , n3 . They are related to r1 and r2 through (1.220) and (1.221): n1 = r1 + r2 2 cos \u03b1 2 , n3 = r1 \u00d7 r2 sin\u03b1 , n2 = n3 \u00d7 n1 , (3.176) r1,2 = n1 cos \u03b1 2 \u2213 n2 sin \u03b1 2 . (3.177) 3.14 Screw Displacements Effecting a Prescribed Line Displacement 129 The notation in Fig. 3.17 is chosen such that in the case = 0 the dual angle \u03b1\u0302 is the angle \u03b1 of Fig. 1.11, and that the dual vectors r\u0302i (i = 1, 2) and n\u0302i (i = 1, 2, 3) are the vectors ri (i = 1, 2) and ni (i = 1, 2, 3), respectively. The solution to the rotation problem of Fig. 1.11 is a one-parametric manifold of rotations (n, \u03d5) . With a free parameter \u03c8 it is given in (1.222) and (1.228) in the form n = n1 cos\u03c8 \u2212 n3 sin\u03c8 , cot \u03d5 2 = \u2212 cot \u03b1 2 sin\u03c8 . (3.178) All vectors and angles are transferred into dual form by defining dual parts as follows: \u03b1\u0302 = \u03b1+ \u03b5 , \u03d5\u0302 = \u03d5+ \u03b5s , \u03c8\u0302 = \u03c8 + \u03b5u , (3",
            "178) are transferred into the dual forms n\u0302 = n1 cos \u03c8\u0302 \u2212 n3 sin \u03c8\u0302 , cot \u03d5\u0302 2 = \u2212 cot \u03b1\u0302 2 sin \u03c8\u0302 . (3.182) The dual part of the first equation yields w = \u2212u(n1 sin\u03c8 + n3 cos\u03c8) . (3.183) This together with the first Eq.(3.178) yields for the perpendicular n \u00d7 w from 0 onto the screw axis the expression n\u00d7w = un2 . (3.184) From this it follows, first, that all screw axes intersect the line n\u03022 at right angles and, second, that the free parameter u (positive, zero or negative) represents the length of the perpendicular from 0 onto the screw axis. This is shown in Fig. 3.17 . The line n\u03022 is called nodal line of the two lines r\u03021 and r\u03022 . 130 3 Finite Screw Displacement The dual part of the second Eq.(3.182) is an equation for s : \u2212s/2 sin2 \u03d5 2 = /2 sin2 \u03b1 2 sin\u03c8 \u2212 u cot \u03b1 2 cos\u03c8 . (3.185) For sin2 \u03d5/2 and for other functions of \u03d5 the following expressions in terms of \u03c8 are known from (1.227) and (1.226): sin2 \u03d5 2 = sin2 \u03b1 2 1\u2212 cos2 \u03b1 2 cos2 \u03c8 , sin \u03d5 2 cos \u03d5 2 = \u2212 sin \u03b1 2 cos \u03b1 2 sin\u03c8 1\u2212 cos2 \u03b1 2 cos2 \u03c8 , (3.186) 1\u2212 cos\u03d5 = 1\u2212 cos\u03b1 1\u2212 cos2 \u03b1 2 cos2 \u03c8 , sin\u03d5 = \u2212 sin\u03b1 sin\u03c8 1\u2212 cos2 \u03b1 2 cos2 \u03c8 . (3.187) With the first Eq.(3.186) s becomes a function of u and \u03c8 : s = u sin\u03b1 cos\u03c8 \u2212 sin\u03c8 1\u2212 cos2 \u03b1 2 cos2 \u03c8 . (3.188) With Eqs.(3.178) for n and \u03d5 and with the equations for w , n \u00d7 w and s the two-parametric manifold of screw displacements (n\u0302, \u03d5\u0302) solving Problem 1 is uniquely determined. The special screw displacements (n\u03023, \u03b1\u0302) and (n\u03021,\u00b1\u03c0) shown in Fig. 3.17 belong to this manifold. The associated parameter values are \u03c8 = \u2212\u03c0/2 , u = 0 for the first and \u03c8 = 0 , u = 0 for the second. Pure rotations satisfy the condition s = 0 , i.e., u = tan\u03c8 sin\u03b1 . (3.189) This condition defines the one-parametric submanifold of rotations in the two-parametric manifold of screw displacements. The special rotation with parameter values \u03c8 = 0 , u = 0 belongs to this submanifold. The manifold of all rotation axes defines a ruled surface. Let x , u , z be the coordinates of points of this ruled surface along n1 , n2 and n3 , respectively",
            "14 Screw Displacements Effecting a Prescribed Line Displacement 131 of displacement of point A is the quantity (rP \u2212 rB) \u00b7 r2 = (rP \u2212 rA) \u00b7 r2 . The analysis to follow shows that the essential measure of displacement is the quantity \u03c3 = (rP \u2212 rB) \u00b7 r2 cos\u03b1/2 . Further below \u03c3 is prescribed. However, before doing so, \u03c3 is determined for the screw displacements solving Problem 1 as function of \u03c8 and u . Let be the vector leading from the point of intersection of a screw axis n\u0302 with the nodal line n2 to point A . Figure 3.17 yields the expression = \u2212 ( un2 + 1 2 n3 ) . (3.190) The associated measure of displacement is \u03c3 = { (1\u2212 cos\u03d5)[(n \u00b7 )n\u2212 ] + sin\u03d5n\u00d7 + sn } \u00b7 r2 cos \u03b1 2 . (3.191) The term sn is due to translation, and the remaining terms are copied from (1.37). The scalar products are expressed in terms of \u03c8 and u with the help of (3.190), (3.177) and (3.178): n \u00b7 = 1 2 sin\u03c8 , n \u00b7 r2 = cos \u03b1 2 cos\u03c8 , \u00b7 r2 = \u2212u sin \u03b1 2 , n\u00d7 \u00b7 r2 = 1 2 sin \u03b1 2 cos\u03c8 \u2212 u cos \u03b1 2 sin\u03c8 . \u23ab\u23aa\u23ac \u23aa\u23ad (3.192) For s , for (1 \u2212 cos\u03d5) and for sin\u03d5 the expressions (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002948_s12206-019-0501-0-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002948_s12206-019-0501-0-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of bearing with surface defects.",
        "texts": [
            " Since the width of the defect is much smaller relative to the ball diameter, the additional displacement \u0394 is tiny when the ball is riding over the defect. It can be assumed that the depth d of the defect is greater than the additional displacement \u0394, then the influence of the depth of the defect is not taken into account. Here, the rectangular defect is assumed as an example, the defect with other shapes can be considered through the similar way; however, in present two degrees of free-dom for deep-groove ball bearing, the defect shapes have negligible effect as shown in Appendix A. Fig. 3 shows the schematic diagram of bearing with surface defects. As the outer ring is fixed, the azimuth angle of outer raceway defect always keeps unchanged as: ( 1)j j e e eW Dz a= + - , j = 1,2 (16) where \u03b1e is the azimuth angle of the outer race defect center. When multiple defects are distributed on the outer raceway, assuming the difference between the azimuth angle of nth defect and the azimuth angle of the first defect is \u03b8e n, then the azimuth angle range of nth defect is e e nj j n ez z q= + , j = 1,2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003332_j.robot.2020.103425-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003332_j.robot.2020.103425-Figure2-1.png",
        "caption": "Figure 2: Configuration of the actuator",
        "texts": [
            " In this structure, femur is from the hip joint to the knee joint, and tibia is from the knee joint to the underside of the foot. In addition, the HKE is divided to an immovable and movable component, in which waist and pelvis are locked to the body of the wearer, while femur and tibia are the movable parts. Moreover, each joint is 3 Jo ur na l P re -p ro of connected to a DC motor, and a quadrature encoder is placed at its output shaft to measure the angular trajectory of the joints. The actuators of the HKE consist of DC motors connected to the joints by gearboxes to provide trajectory and torque for each joint. Figure 2 illustrates the schematic configuration of the actuator, in which torque from DC motor (Tm) 4 J u is transferred to the gearbox to reduce the speed and increase the output torque (Tl). A shaft transfers the generated torque to the link, which are connected to patient leg to assist them in retrieving their walking ability. The gearbox of the actuator is a combination of a worm gear and a reduction gear as a driving and driven mechanism, respectively. The gearbox is coupled with rotary shaft to reduce the angular velocity and increase torque generated by the DC motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure15-1.png",
        "caption": "Fig. 15. Proposed IPM rotor for high-speed application [22].",
        "texts": [
            " In [22], an IPM rotor made from high mechanical strength and low core losses material is proposed. The feasibility of using Authorized licensed use limited to: Cornell University Library. Downloaded on May 23,2021 at 07:48:33 UTC from IEEE Xplore. Restrictions apply. 2605SA1 for the proposed rotor to improve the performance of the motors, such as higher power density and higher efficiency, is studied and confirmed. The structure of the IPM rotor and the parameters of a demonstrator motor are presented in Fig. 15 and Table II, respectively. To ensure that the rotors are safe at the maximum speed, the rotors\u2019 stresses are first analyzed. By using software Abaqus, the stresses at the maximum speed of the two rotors made from different core materials are simulated and compared in Fig. 16. It is clear that the maximum stresses locate at the flux bridges\u2019 inner contours of the rotor cores. Because of higher mass density of 10JNEX900, the maximum stress of HR is slightly higher than that of AR. The maximum stress of HR is 359 MPa, which is much lower than the tested yield strength (570 MPa) of the rotor core material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002846_s11249-019-1202-7-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002846_s11249-019-1202-7-Figure2-1.png",
        "caption": "Fig. 2 The schematic diagram of gear contact",
        "texts": [
            " The casehardening properties are represented by a hardness gradient mode. The contact fatigue behavior is described by the Dang Van multiaxial fatigue criterion. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for the calculation of stress field and surface deformation. In this study, it is assumed that the thermal effect and initial residual stress are negligible. Ggear meshing can be simulated by a three-dimensional line contact at each engaging position [26], as shown in Fig.\u00a02: a rigid roller contacts with a deformable half space. The interaction at the interface is divided into two parts\u2014the lubrication approach on the surface and solid mechanics approach under the surface\u2014which are incorporated by the film thickness equation under the isothermal assumption. The residual stress obtained from the elastoplastic approach is superimposed on to the load-induced elastic stress field during the iteration. The stress field thus determined is combined with the Dang Van multiaxial criterion to evaluate the fatigue performance",
            " Figure\u00a07b shows the von Mises stress of the EHL and PEHL solutions. The sub-surface stress is obviously impaired by the plastic strain. Compared with He\u2019s solution [22], in which the maximum pressure and von Mises of PEHL are 1871.39 and 1006.62 MPa, respectively, the calculated results are 1868.48 and 991.02\u00a0MPa, respectively. The proposed PEHL model shows good agreement with He\u2019s solution. The verified model was applied on a gear pair coming from the intermediate parallel stage of a 2\u00a0MW wind turbine gearbox, as shown in Fig.\u00a02. The parameters of gears and lubricant are given in Table\u00a03. To obtain the influence of case depth on contact performance, the computational domain is chosen as \u22122 \u2264 x\u2215b \u2264 2 , \u22120.5l \u2264 y\u2215b \u2264 0.5l, 0 \u2264 z\u2215b \u2264 4 , where b is the maximum Hertzian contact half-width and l is the length of contact zone. The domain is discretized to a grid of 128 \u00d7 128 \u00d7 64 to balance the computational accuracy and efficiency. To investigate the Tribology Letters (2019) 67:92 1 3 92 Page 8 of 15 fatigue property of the gear pair under harsh conditions, the input torque is selected as two times the rated torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000513_ical.2008.4636193-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000513_ical.2008.4636193-Figure2-1.png",
        "caption": "Fig. 2. The onboard computer system of BabyLion.",
        "texts": [
            " One set of experiments has been conducted to prove the effective payload (excluding the TREX 450\u2019s own weight) is up to 320 g, which is beyond the weight budget of our designed onboard computer system. As such, we could summarize that TREX 450 helicopter is well suited to our mini UAV helicopter design. The onboard computer system design is the most challenging part in the overall BabyLion\u2019s construction due to the extremely strict payload (320 g only). Furthermore it must be fully functional to be suitable for both indoor and outdoor flight tests. The finally designed onboard system, which is only 210 g and shown in Figure 2, has all of the necessary functions of HeLion/SheLion and consists of the following four components: 1) main processing board; 2) navigation sensor; 3) wireless module and 4) battery pack. The main processing board, named Stargate, is based on the ARM structure. Its processing unit belongs to Intel\u2019s X-scale with the working frequency of 400 MHz. One complete set of I/O ports, including 51-pin GPIO, serial port, PCMCIA slot and compact flash (CF) slot, is provided for data exchange, servo control and wireless communication"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001883_s00170-017-0363-5-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001883_s00170-017-0363-5-Figure2-1.png",
        "caption": "Fig. 2 Coordinate systems of the visual rack cutter",
        "texts": [
            " In order to obtain modified tooth surfaces with a predesigned fourth-order TE function, modifications of tooth surfaces are calculated in this study via generating motion of a visual rack cutter. The visual generating rack cutter is used to describe the corresponding transmission relationship between a gear drive with the predesigned fourth-order TE function. Based on the theory of gearing, tooth surfaces of a cylindrical gear can be generated by a rack cutter. Ease-off topography of a tooth surface represents a set of modification values at all grid points that describes modifications on the overall tooth surface. As shown in Fig. 2, if tooth surfaces of a cylindrical gear are not modified, the corresponding model of the visual rack cutter coincides with that of a theoretical rack, and the corresponding modification value at each grid point of easeoff topography of the theoretical rack cutter is zero. Generated tooth surfaces of the gear pair are fully conjugated and mesh with a theoretical constant transmission ratio and zero TE (0TE). In Fig. 2, the curved surface stands for a modified tooth surface of the generated gear. As shown in Fig. 2, coordinate systems Sa(Xa, Ya, Za) and Sb(Xb, Yb, Zb) are rigidly connected to the visual rack cutter; Sc(Xc, Yc, Zc) is a movable coordinate system, which horizontally moves with the visual rack cutter along the Ybaxis. The position vector and the unit normal vector of the visual rack cutter are represented as rc uc; lc\u00f0 \u00de \u00bc uccos\u03b1n \u00fe acuc2sin\u03b1n\u2212dpcos\u03b1n ucsin\u03b1n\u2212acuc2cos\u03b1n \u00fe am\u2212dpsin\u03b1n cos\u03b2 \u00fe lcsin\u03b2 \u2212ucsin\u03b1n \u00fe acuc2cos\u03b1n\u2212am \u00fe dpsin\u03b1n sin\u03b2 \u00fe lccos\u03b2 2 4 3 5 \u00f012\u00de nc uc\u00f0 \u00de \u00bc sin\u03b1n\u22122acuccos\u03b1n \u2212 cos\u03b1n \u00fe 2acucsin\u03b1n\u00f0 \u00decos\u03b2 cos\u03b1n \u00fe 2acucsin\u03b1n\u00f0 \u00desin\u03b2 2 4 3 5 \u00f013\u00de respectively, where uc and lc are surface coordinates of the generating rack cutter blade, \u03b2 is the spiral angle, \u03b1n is the pressure angle, am is half of the face width, dp is the position of the parabolic vertex, and ac is the parabolic modification coefficient in the visual generating rock cutter tooth profile direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002271_tie.2018.2809463-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002271_tie.2018.2809463-Figure12-1.png",
        "caption": "Fig. 12. Magnetic field distribution of 12-slot/10-pole dual three-phase machines with different PM shapes. (a) Sinusoidal field shaped rotor, (b) Sinusoidal with harmonics field shaped rotor.",
        "texts": [
            " This is due to the fact that the third harmonic back-EMF for both the machines with the sinusoidal field shaped rotor and sinusoidal with harmonics field shaped rotor is small, as given in Fig. 8 and Fig. 10. Electromagnetic torque of 12-slot/10-pole dual three-phase machines with different PM shapes Ipeak=15A. Fig. 11. Electromagnetic torque with third harmonic current injected under the same rms value constraint. The FE predicted open-circuit field distribution of the dualphase machines with sinusoidal field shaped rotor and sin+3rd field shaped rotor are shown in Fig. 12. It can be seen that with the injected harmonics in the airgap flux field, the flux density in teeth increases. However, it will not cause saturation issue. Meanwhile, the iron loss in stator is analyzed by FE methods, the iron loss of the machine with sinusoidal field shaped rotor is 1.21 W. With the third harmonic injected in the airgap flux density, the iron loss increased to 1.47 W. The power losses including copper loss, core loss and eddy current PM loss together with the efficiency of the dual threephase 12-slot/10-pole machine with and without third harmonic injection into the outer frame of the PM and current waveforms are investigated and summarized in TABLE V"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure6.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure6.4-1.png",
        "caption": "Fig. 6.4 Internal torques andmotionswhen the load torqueTy acts in the counterclockwise direction around axis oy",
        "texts": [
            " The analysis of the torques and motions acting on the gyroscope with one side support is conducted by the regulations described in Chap. 5. The mathematical model for the motions of the gyroscope considers the action of the load torque Ty around axis oy in a counterclockwise direction. The load torque T = Mgl is generated by the weightW of the gyroscope around axis ox. The action of the external load torque Ty generates the following system of inertial torques acting around axes of the gyroscope (Fig. 6.4): (a) The resistance torque Tr.y = Tct.y + Tcr.y generated by the centrifugal Tct.y and Coriolis forces Tcr.y around axis oy is acting in a clockwise direction (i.e. in the opposite direction of the action of load torque Ty). (b) The procession torque Tp.y = Tin.y + Tam.y generated by the common inertial forces Tin.y and the change in the angular momentum of the spinning rotor Tam.y originated on axis oy but acting around axis ox in a clockwise direction (i.e. in the opposite direction of the action of the gyroscope weight T )",
            "54) Jx d\u03c9x dt = \u22128 ( 4\u03c02 + 17 38\u03c02 + 161 )[ Ty + 9 ( 4\u03c02 + 17 2\u03c02 + 9 ) Mgl ] + ( 8 9 ) J\u03c9\u03c9x (6.55) where the torque of the gyroscope weight (Eq. 6.52) is removed because themodified precession torque Tp.y contains it, other components are as specified above. The gyroscope with one side support and horizontal location (\u03b3 = 0\u00b0) turns under the action of the two external torques Ty and T, which act around axes oy and ox, respectively. The value of the first torque Ty is half of the value of torque T (i.e. Ty=0.05 Wgl). The actions of the torques and motions are presented in Fig. 6.4. The technical data related to the gyroscope are presented in Table 6.1 and Fig. 6.2. The angular velocity of the sinning rotor is 10,000 rpm. All Eqs. (6.52)\u2013(6.55) are modified because \u03b3 = 0\u00b0. Equation (6.55) expresses the gyroscope motion around axis ox. Substituting the initial data of the gyroscope (Table 6.1) into Eq. (6.55) for horizontal location of the gyroscope yields the following equation: 3.38437 \u00d7 10\u22124 d\u03c9x dt = \u22128 ( 4\u03c02 + 17 38\u03c02 + 161 ) [ 0.05 + 9 \u00d7 ( 4\u03c02 + 17 2\u03c02 + 9 ) \u00d7 0.146 \u00d7 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003287_s00170-020-06104-0-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003287_s00170-020-06104-0-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of the layer-by-layer model",
        "texts": [
            " Nevertheless, the spot diameter of the laser beam is only a few hundred microns, indicating that tens of thousands or even millions of scanning tracks are required to produce the part. Besides, the part manufacturing time is up to dozens of hours. Current computational efficiency is therefore almost impossible to directly calculate the LPBF process which fully reflects the real working conditions. To solve the problem, some researchers developed a layerby-layer model to predict the deformation and residual stress of the large-sized parts [24, 25]. As depicted in Fig. 1, the part is divided into multiple equivalent powder layers along the deposition direction. The thickness of each equivalent layer is equal and consists of one or multiple powder layers. The laser irradiating powder bed is simplified into a process that an equivalent heat resource heats the equivalent layer, leading to a significant improvement of the simulation dimension. Also, several assumptions were applied in the model to simplify the simulation process [26]. The powder bed was considered to be a homogeneous, isotropic, and continuous media"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure3.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure3.1-1.png",
        "caption": "FIGURE 3.1. Reference Coordinates and Dimensions.",
        "texts": [
            " The presented mathematical procedure in this chapter is based on the work discussed by Armenakas et al. (1969), for the free vibration case. Their technique was refined by Hamidzadeh et al. (1981) to develop an analytical approach for studying the free, as well as, forced vibrations for these structures. The presented mathematical procedure implements the linear elasto-dynamic theory and formulates the displacements and stresses to satisfy the required boundary conditions for both cases of free and forced vibrations. Figure 3.1 describes the cylindrical coordinates and the required geometrical parameters. H.R. Hamidzadeh, R.N. Jazar, Vibrations of Thick Cylindrical Structures DOI 10.1007/978-0-387-75591-5_3, \u00a9 Springer Science+Business Media, LLC 2010 30 3. Vibration of Single-Layer Cylinder 3.1 Governing Equation The governing equation of motion for a cylinder in invariant form was developed and presented in equation (2.58) in the previous chapter, and for continuity is repeated here. \u03bc\u22072u+ (\u03bb+ \u03bc)\u2207 (\u2207 \u00b7 u) = \u03c1 \u22022u \u2202t2 (3",
            "1 Frequency Factor To simplify the presentation of results and comparison with other established results for specific cases, natural and resonant frequencies are normalized and introduced as the frequency factor, which is defined by the following equation: \u2126 = \u03c9 \u03c9s (4.1) where, \u03c9s = \u03c0v2 H . (4.2) \u03c9s is defined as the lowest simple thickness shear frequency of an infinite plate of thicknessH with the same elastic constants as those of the cylinder. The parameter \u03c9 is the excitation frequency, in units of rad/ s. For the purpose of comparing of results, the frequency factor is the same as the one defined by Armenakas et al. (1969). 4.2 Geometry of the Cylinder The definitions of the various geometric parameters are evident in figure 3.1. However, a more thorough description is given here. The variables a and b indicate the inner and outer radii of the cylinder, respectively. H is H.R. Hamidzadeh, R.N. Jazar, Vibrations of Thick Cylindrical Structures DOI 10.1007/978-0-387-75591-5_4, \u00a9 Springer Science+Business Media, LLC 2010 48 4. Modal Analysis of Cylindrical Structures defined as the thickness of the cylinder and R is the mean radius of the cylinder. In the numerical computation, a range of H/R = 0.0 to 2.0 was considered. The case of H/R = 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001264_we.1530-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001264_we.1530-Figure3-1.png",
        "caption": "Figure 3. Setup and load system of a four-contact-point slewing bearing.",
        "texts": [
            "1,2 These bearings are illustrated in Figure 1. Although small turning speed and range are required in both cases, it must be ensured that the bearings\u2019 friction moment remains as small as possible, in order to avoid unnecessarily large pitching or yawing forces; for this reason, ball bearings are generally used. Figure 2 shows angular four-contact-point bearings for yaw and pitch control. These bearings (yaw and blade bearings) are subjected to high static loads; moreover, continuous deformation of the bearing support is unavoidable.1 Figure 3 shows the topology of this type of bearing, together with the usual load system acting on it: axial and radial forces, as well as a tilting moment; in the most unfavourable load case, the radial force is perpendicular to the tilting moment. Bearings of WTGs must withstand both static (extreme) and fatigue loads; static loads can easily be estimated at early stages of the design process. Thus, a first selection of the bearings is commonly performed considering only the static load-carrying capacity; this initial selection is necessary in order to design other components of the WTG, such as the rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003254_s11431-020-1588-5-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003254_s11431-020-1588-5-Figure5-1.png",
        "caption": "Figure 5 (Color online) Stability margin illustration of the six-legged robot Hexa-XIII.",
        "texts": [
            " (13)G m B G y p r m m m B m3\u00d73 T The homogeneous vector of foot tips P( ) =G tip 4\u00d71 x y z( , , , 1)t t t T in GCS are calculated by eq. (14). P T T P= , (14)G B B H H tip G tip where TB H denotes the homogeneous transformation matrix from HCS to BCS. TG B denotes the homogeneous transfor- mation matrix from BCS to GCS. PH tip denotes the foot tip position vector in HCS calculating by leg kinematics. The touchdown status of each legs should be determined, all the projections of touchdown supporting points generate the supporting polygon (see Figure 5). The position vector of the supporting point is x z i nP( ) = ( , 0, ) , =1 to , (15)G i t t itip0 touchdown where ntouchedown is the amount of touchdown legs. When the six-legged robot walking on terrains, all the supporting legs always form a convex polygon. Therefore, we can calculate the distances from the projection of mass center to each edges of the supporting polygon. Vedge denotes the edge vector from projection point i to projection point i+1. Vedge is calculated by eq. (16). ( )( ) ( ) ( ) ( ) i n i n V P P P P ( ) = , if < , , if = "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001483_j.ijmecsci.2014.02.021-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001483_j.ijmecsci.2014.02.021-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a two gear system model.",
        "texts": [
            "com/locate/ijmecsci International Journal of Mechanical Sciences http://dx.doi.org/10.1016/j.ijmecsci.2014.02.021 0020-7403 & 2014 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail address: cyzhou@bit.edu.cn (C.Y. Zhou). approximations for primary and secondary resonances. Furthermore, by discussing the instability conditions, relations between physical parameters and instability regions can be explicitly established. 2. Two stage gear system model The two stage spur gear system composed by three shafts and two pairs of spur gears is illustrated by Fig. 1. Gear 1 is fixed on the input shaft; gears 2 and 3 are assembled to the intermediate shaft; and gear 4 is installed on the output shaft. Input and output moments T1 and T2 are exerted on the system as shown. The gears have base radii Ri, i\u00bc1,2,3,4. The moments of inertia of gears are Ii. The rotation angle of gear i is \u03b8i. The mesh stiffnesses vary periodically with gear tooth contact. A typical time dependent mesh stiffness variation is like a square wave. Denote ksi \u00f0i\u00bc 1;2;3\u00de as constant torsional stiffness of shaft; k1 and k2 as time-varying meshing stiffness which can be divided into two parts as ki \u00bc kgi \u00fekvi \u00f0t\u00de i\u00bc 1;2: \u00f01\u00de here kgi and kvi \u00f0t\u00de are average and time varying components of mesh stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001482_s10846-013-9927-2-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001482_s10846-013-9927-2-Figure5-1.png",
        "caption": "Fig. 5 Navy procedure 2: relative wind landing",
        "texts": [
            " If there is a possibility of a crash or a failure to touchdown, the vehicle immediately increases its altitude and moves sideways, to reinitiate the landing steps. If the cross wind is more than 5 m/s, and its direction is within the range of 0\u25e6 to 90\u25e6, the forward facing landing procedure is dangerous Distance Landing step Guidance command Fig. 3 Relative wind vector summation V H W A and not suitable. In this case, the \u201crelative wind landing procedure\u201d is a suitable approach for safe shipboard landing (Fig. 5). 1. The vehicle approaches the ship from the leeward side. In this situation, the aircraft faces into the relative wind. 2. Next, the vehicle continues to fly upward, to the hover position above the landing zone. 3. Finally, the altitude is decreased and the the vehicle accurately touches down on the landing zone. During this procedure, the nose of the helicopter is always into the relative wind. 4. If a precise landing is impossible, the helicopter attempts to recover altitude and escape the ship, while maintaining the same direction it came from"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003906_i560114a007-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003906_i560114a007-Figure2-1.png",
        "caption": "FIGURE 2. EFFECT OF TEMPERATURE ON TvAVE HEIGHT",
        "texts": [
            " Further, the removal of oxygen with inert gas is time-consuming; and the suggested (14) use of bisulfite was found in the course of the present work to affect the wave heights of aldehydes. Since preliminary work gave erratic results which were found to be due in part to changes in temperature, a small constant-temperature bath was arranged to hold the cell during analysis. The influence of temperatures and p H is well illustrated by the relative heights of the first acrolein waves (Figure 1, curves 1 and 3). Temperature-concentration curves were made (Figure 2). I n the case of both acrolein waves, temperature control is necessary for accurate results since 1' of temperature change causes an 0.8 per cent error. The effect of p H on the accuracy of acrolein determinations may be seen in Figure 3, which shows curves for concentrationwave heights a t p H 4.8 to 11 of the first acrolein wave. Curves for p H 4.8 and 11 are included, although the values are not reproducible, since when the analysis is repeated immediately on the same solution the wave height has become smaller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.8-1.png",
        "caption": "Fig. 13.8 Coupling of coplanar shafts 1 , 2 , 3 , 4 , 5 by four Hooke\u2019s joints resulting in \u03d5\u03075 \u2261 \u03d5\u03073 \u2261 \u03d5\u03071",
        "texts": [
            " In Fig. 13.7 case (c) is illustrated by a system of coplanar axes with \u03b13 = \u03b11 = 20\u25e6 and cos\u03b12 = cos2 20\u25e6 (\u03b12 \u2248 28\u25e6). This example shows that geometrical symmetry of the coupling of shafts 1 and 4 is not a necessary condition for the identity of input and output angular velocity. Example n = 5 : The condition a5 = 1 is satisfied by altogether seven different combinations (\u03b22, \u03b23, \u03b24) and by associated conditions on \u03b11 , . . . , \u03b14 . The details are left to the reader. See also Duditza [4, 7]. In Fig. 13.8 a simple example with five coplanar axes is shown. It is the combination of two systems of the type shown in Fig. 13.6b . The parameters are \u03b22 = \u03b23 = \u03b24 = 0 and \u03b11 = \u03b12 = \u03b13 = \u03b14 = \u03b1 . Shafts 1 , 3 and 5 have identical angular velocities \u03d5\u03075 \u2261 \u03d5\u03073 \u2261 \u03d5\u03071 . In every system with coplanar axes i = 1, . . . , n the property \u03d5\u0307n \u2261 \u03d5\u03071 is preserved if the three-step operation explained for the case n = 3 is applied analogously, i.e., by cutting an arbitrary intermediate shaft j = 2 , . . . , n \u2212 1 and by a rigid-body rotation of the part located beyond the cut shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureA.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureA.4-1.png",
        "caption": "Fig. A.4 Schematic of the propeller design with two (a), three (b), four (c) and six (d) blades mounted on a hub",
        "texts": [
            " 212 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects Tct = 8 81 {\u221a[( 4 9 R )2 + ( 98)2 ]3 \u2212 ( 98)3 }\u221a 2 3 R \u221a 9 16 + R2 + 9 16 ln [ 4 3 (\u221a 9 16 + R2 + R )] \u00d7 MR\u03c02\u03c9\u03c9x (A.3.20) where all parameters are as specified above. Themassmoment of paraboloid inertia is computed by the following solution. The change in the mass moment of inertia of the arbitrary micro-disc that perpendicular to axis of the paraboloid is presented by the following equation: dJ = 1 2 y2dm (A.3.21) where y is the arbitrary radius of the paraboloid external surface (Fig. A.4), dm = \u03c1dV,dV = \u03c0y2dz, where m is the mass, \u03c1 is the density, V is the volume of the paraboloid, respectively. Substituting defined parameters into Eq. (A.3.21) and transforming yield the following: dJ = 1 2 y2\u03c1\u03c0y2dz = 1 2 y4\u03c1\u03c0dz (A.3.22) Equation (A.3.22) is represented by the integral form and dz = 2ydy, y = \u221a z; transforming and solving yield the following result: J\u222b 0 dJ = L\u222b 0 1 2 y4\u03c1\u03c02ydy (A.3.23) giving rise to the following result: J = 1 6 \u03c1\u03c0y6 = 1 6 \u03c1\u03c0y2y2y2 = 1 6 (\u03c1\u03c0R2L)R2 = 1 6 MR2 (A",
            " The inertial forces acting on the propeller are generated by the centre mass of the hub and centre mass of the blades, whose locations and actions are different. The several blades mounted on a hub are considered as one holistic object spinning around the axel. The action of inertial forces generated by the blade\u2019s and the hubmasses is considered on a propeller running. The blade\u2019s mass m is located on the defined distance r on the propeller, and the mass centre of the propeller\u2019s hub is mh. The blades of the propellers of the different design numbered as I, II, III, IV, V and VI that presented in Fig. A.4. The design of the propeller is complex, and to define its mass moment of inertia around the centre of rotation is the special problem. For simplicity for the following analysis, the design of propeller is presented by the blades mounted on the cylindrical hub. The mass moments of inertia for propellers with several blades are represented by the common expression Jp = nJ + Jh, where J is the mass moments of inertia of the blade, n is the number of the blades, and Jh is the mass moments of inertia of the hub",
            "4) The following steps of solutions are the same as presented in sections above dTct dt = mr2\u03c92 1 2 (1 \u2212 cos 2\u03b1) d\u03b3 dt (A.4.5) t = \u03b1 \u03c9 , dt = d\u03b1 \u03c9 , \u03c9dTct d\u03b1 = mr2\u03c92\u03c9x 1 2 (1 \u2212 cos 2\u03b1) (A.4.6) dTct = mr2\u03c9\u03c9x 1 2 (1 \u2212 cos 2\u03b1)\u03b1d\u03b1. (A.4.7) Tct\u222b 0 dTct = \u03c0\u222b 0 mr2\u03c9\u03c9x 1 2 (1 \u2212 cos 2\u03b1)d\u03b1 (A.4.8) Tct \u2223\u2223\u2223Tct0 = mr2\u03c9\u03c9x 1 2 ( \u03b1 \u2212 sin 2\u03b1 2 )\u2223\u2223\u03c0 0 (A.4.9) Tct = 1 2 \u03c0mr2\u03c9\u03c9x (A.4.10) The blades of the propeller are located at upper and lower sides relatively axis ox. The centrifugal forces act on the upper and lower blades, and then the total resistance torque T ct for the propellers with several blades (Fig. A.4a\u2013d) is obtained when the result of Eq. (A.4.10) is increased according to the number of propeller\u2019s blades. The value of the resistance torque generated by the rotating blade is changed by sinus law and expressed by the following equation: Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 221 Tct = 1 2 mr2\u03c9\u03c9x\u03c0 sin \u03b1 = 1 2 \u03c0 J\u03c9\u03c9x sin \u03b1 (A.4.11) where J = mr2 is the conventional mass moment of inertia of the propeller\u2019s blade; other parameters are as specified above. The change in the value of the total resistance torque T ct for the propellers with several blades (Fig. A.4a\u2013d) can be presented by the diagrams demonstrated in Fig. A.5. These diagrams show the change and fluctuation of the resistance torque T ct generated by the centrifugal forces of the propeller with several blades. The equations for maximal and minimal values of the resistance torques for the propellers are represented in Table A.4. Analysis of Eq. (A.4.11) shows that the value of the resistance torque generated by the centrifugal forces of the rotating blades depends proportionally on the following components: \u2013 the vertical, horizontal or angular location of the blades relative axis, \u2013 the mass and the number of the blades, \u2013 the radius of the location of the blade mass, \u2013 the angular velocity of the propeller and \u2013 the angular velocity of the precession",
            " The mass moment of inertia of one blade is J = mR2 + mL2/12 (parallel-axis theorem). The hub mass is 10 kg and radius of 0.1 m, which the mass moment of inertia is Jh = mhR2/2. The propeller is spinning at 3000 rpm. An external torque acts on the propeller, which rotates with an angular velocity of precession 0.5 rpm. These data are used to determine themaximal value of the resistance and precession torques generated by the centrifugal, inertial and Coriolis forces, as well as the change in the angular momentum of the spinning propeller (Fig. A.4a). Solving this problem is based on Eqs. (A.4.31) and (A.4.30). Substituting the initial data into the aforementioned equations and transforming yield the following result: Tp = [ nJ (\u03c0 2 cos\u03b1 + 1 ) + ( 2 9 \u03c02 + 1 ) Jh ] \u03c9\u03c9x = [ 2 \u00d7 5 \u00d7 ( 0.52 + 0.82 12 ) \u00d7 (\u03c0 2 + 1 ) + ( 2 9 \u03c02 + 1 ) \u00d7 10 \u00d7 0.12 2 ] \u00d7 3000 \u00d7 2\u03c0 60 \u00d7 0.5 \u00d7 2\u03c0 60 = 130.899Nm Tr = [ 1 2 (\u03c0 sin \u03b1 + cos\u03b1)nJ + ( 2 9 \u03c02 + 1 ) Jh ] \u03c9\u03c9x 228 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects = [ 1 2 \u00d7 3.297 \u00d7 2 \u00d7 5 \u00d7 ( 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure2-1.png",
        "caption": "Fig. 2. Stress results of the wheel disc after the first process.",
        "texts": [
            " The material of the wheel disc is DP600 advanced high-strength steel with the initial thickness of 4 mm, and the other significant mechanical parameters affecting the forming results include density, elastic modulus, Poisson\u2019s ratio, yield stress, hardening coefficient and anisotropy parameters are shown in Table 1. The friction coefficient between the tool and wheel disc is 0.12 and the stamping speed is 40 mm/s. Hill48 anisotropic yield model of the steel material and Kinematic(Voce) law [7] are used in the finite element analysis of stamping process. The flow curve is shown in Fig. 1. The dynamic explicit algorithm is selected for the simulations of stamping process [8]. The stress distribution of the wheel disc after the first process is shown in Fig. 2, in which the residual stress of one circle is approximately invariant. The two principal stresses in radial and circumferential directions are shown in Fig. 3. Then, the simulation results in first process including thickness, strain, stress et al. are transferred into the second process for further forming analysis. Similarly, the second and the third processes are also simulated, and the corresponding results are also transferred into the next process. Figs. 4 and 5 show the distribution of two principal stresses of the residual stress after the second and third stamping processes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001797_j.wear.2016.01.021-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001797_j.wear.2016.01.021-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the FZG back-to-back gear test rig. #1 test gearbox, #2 load clutch, #3 slave gearbox, #4 torque and speed sensor and #5 motor.",
        "texts": [
            " This paper aims to answer the question, qualitatively as well as based on surface parameters, what are the characteristics of asperity wear during gear contact. Furthermore the paper will investigate the question how friction, as a complementary indicator, behaves during running-in. To analyze running-in, ten tests were performed in a FZG backto-back gear test rig. Both the evolution of the surface topography and the friction response were measured. A schematic of the FZG test rig is shown in Fig. 1. To evaluate the friction response, a speed and torque sensor (#4) measured the input torque (loss torque) to the power loop, from the motor (#5). It is important to note that new pairs of gears were used in each test, and hence the gear test rig had to be disassembled and reassembled after each test. The back-to-back test rig works by the recirculation of power inside the power loop. The only power added serves to keep the gears rotating, in other words the motor adds the power losses, which is used to measure the gear tooth friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002127_cjme.2015.0710.091-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002127_cjme.2015.0710.091-Figure6-1.png",
        "caption": "Fig. 6. Altmann No. 35 transmission gear",
        "texts": [
            " Note that for a complicated mechanism, it should be simplified firstly to break down the difficult problems into some easier ones, which is a common and nice choice. From this example it is found that although the linkage has three loops, there is no any motion couple among them and this property has been expressed in three-loop graph, as shown in Fig 5(b). Therefore, for kinematic analysis the loop graph should be considered and analyzed. For the example of Altmann No. 35[18], how to analyze the mobility of the strong coupling multi-loop spatial mechanism is shown hereby. The structure diagram and several parts of this mechanism are shown in Fig. 6(a). Fig. 6(b) is its kinematic diagram. Two cubic blocks c1 and c2 are installed on the input and output shafts b1 and b2 by two revolute pairs, respectively, Fig. 6(a) and Fig. 6(b), and meanwhile c1 connects with c2 by a planar kinematic pair. On the top and bottom of c1 and c2, another thin block e with cylindrical concave surface is installed, respectively. Thus there are total four thin blocks which connect with two tablets CE and JH, and on each tablet there are two half-cylindrical convex. Each tablet joins two thin blocks e by two cylindrical pairs, C, E or J, H, and it also joins with frame by top or lower two revolute pairs D or I. Here concave ei and block ci could be regarded as only one link since between them it is impossible to give rise to any relative motion. In addition, it can be seen that this transmission system keeps strictly symmetrical in geometry. According to the schematic diagram of the mechanism in Fig. 6(b), there are seven links and eleven kinematic pairs including four revolute pairs A, D, G and I, six cylindrical pairs B, C, E, F, H, and J, and a planar pair K which has three DOFs. Obviously, the result is wrong if the over-constraints are ignored: ( ) ( )6 1 6 7 11 1 19 0 11.iM n g f = - - + + = - - + + =-\u00e5 (23) Fig. 6(c) shows a schematic diagram with only revolute pairs, in which the four dotted lines AD, AI, GD and GI also denote the same frame. For this complex multi-loop mechanism, Euler\u2019s Theorem can be adopted to obtain the number of the independent loops of the mechanism as 1 11 7 1 5.l g n= - + = - + = (24) LU Wenjuan, et al: Over-Constraints and a Unified Mobility Method for General Spatial Mechanisms Part 2: Application of the Principle \u00b78\u00b7 That indicates there are five independent loops in this mechanism including the first loop ABKFGA, the second one ABCDA, the third DEFGD, the fourth GFHIG and the fifth ABJIA. The over-constraints of this mechanism may exist in each closed loop. Therefore, the constraints in each loop should be analyzed and recognized respectively and then the over-constraints of this mechanism can be obtained. So the following steps are taken to solve this difficult problem. 4.1 Sub-mechanism ABKFGA The coordinate system is shown in Fig. 6(b), in which X-axis is along the center axis, and Z-axis is perpendicular to the paper plane. Then, the screw system of the five kinematic pairs in loop ABKFGA can be expressed by the following nine screws: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 2 1 2 3 1 7 7 2 1 0 0; 0 0 0 , 1 0 0; 0 , 0 0 0; 1 0 0 , 0 0 0; 1 0 0 , 0 0 0; 0 1 0 , 0 0 1; 0 0 0 , 1 0 0; 0 , 0 0 0; 1 0 0 , 1 0 0; 0 0 0 . A B B K K K F F G e f e f = = = = = = = = = $ $ $ $ $ $ $ $ $ (25) The nine screws are linearly dependent and only five screws are independent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure6-1.png",
        "caption": "Fig. 6 Two panels connected by an elastic hinge. a The initial, b an intermediate and c the final configurations predicted by the 8-node solid-shell element model SC8R. The crease element A1A2A3A4 is defined using nodes on the side edges of the two panels",
        "texts": [
            " An elastic hinge is realized by having four nodes along A1A3 common to the two panels. The crease element A1A2A3A4 with initial fold angle ho = p, see Fig. 5a, provides the elastic effect to the hinge. A rest angle loading with hrest = 0 is applied to unfold the panels. An intermediate configuration at h & 2p/3 and the final configuration at h = 0 are shown in Fig. 5b, c, respectively. The animation video is given in Online Resource 1. In the second method of modelling, A2 and A4 that define the crease element are then changed to nodes on the side edges of the panels, See Fig. 6. In other words, the crease element is initially flat (ho = 0) and fully folded in the final configuration (hrest = p). The animation video is given in Online Resource 2. In the third method of modelling, the S4R shell element model in ABAQUS is employed, see Fig. 7. The element possesses 4-node on the mid-surface of the plate/shell and each node has 3 translational and 3 rotational dofs. The boundary conditions prescribed to Bis and Cis are the same as those in SC8R. To avoid coupling the rotational dofs of the elements modelling the two panels, the two panels are created separately"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000424_ests.2009.4906554-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000424_ests.2009.4906554-Figure2-1.png",
        "caption": "Figure 2. Assembly showing operation with (a) outer-rotor fixed and (b) stator segments fixed.",
        "texts": [
            " The advantages of using magnetic gears over traditional gearboxes include inherent overload protection. Gears which are pushed by torque transients over their torque rating will slip, instead of possibly breaking teeth. They also provide the advantage of lower acoustic noise due to the loss of mechanical contact between the teeth. Furthermore, with the loss of contact between teeth, lubrication is negated and thus maintenance due to oil changes [5]. 978-1-4244-3439-8/09/$25.00 \u00a92009 IEEE 477 II. SELECTION OF GEAR PARAMETERS In the concentric planetary gear shown in Fig. 2, there are two possibilities for operation. The different possibilities shown in Fig. 2 have different gearing ratios. In Fig. 2a, the outer permanent magnet ring is fixed, while the stator pieces and inner permanent magnet ring rotate concurrently. In Fig. 2b, the stator pieces are fixed while the two permanent magnet rings are counter-rotated. At the same time, the pole combination for the outer permanent magnet and inner permanent magnet rings should be considered. The combination of pole pairs can determine not only the gear ratio, but also the amount of ripple in the torque transmission. In certain applications a high amount of torque ripple may not be acceptable. However, there could be a trade-off to keep the gear ratio high in order to reduce the size of the electric machine. The gearing ratios derived in [4] cover both modes of operation, given by (1) and (2). A larger difference between pole pairs, p, or stator pieces, ns, in (1) and (2) will result in a higher gearing ratio. Equation (1) covers the mode of operation described in Fig. 2a, while (2) covers the mode of operation in Fig. 2b. The gearing ratios for chosen pole-pair ratio models are given in Table I. pnG s /= (1) p pnG s \u2212= (2) By picking thirteen different pole pair combinations in Table I, twenty six different gearing ratios can be simulated and studied for their torque ripple characteristics. The dimensions chosen for the simulation of the different gear models was based upon the notion that a future prototype would be built from one of these models. Thus dimensions are scaled down from a gear which would be implemented on a ship, to one which will be implemented in the lab"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002856_ab3c3a-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002856_ab3c3a-Figure13-1.png",
        "caption": "Fig. 13. Experimental setup and measurement method. (a) Experimental setup for the average velocity and output torque of the proposed robotic finger. (b) Measurement method of the average velocity and output torque.",
        "texts": [
            " (a) Experimental setup for 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an u c 14 measuring the trajectories of points P and Q. (b) Measured trajectories of points P and Q at 68.592 kHz and 20 Vpp. 4.2 Mechanical performances Due to the fact that average rotational velocity and output torque are important indicators for evaluating the proposed robotic finger prototype, the experimental investigation was carried out. The experimental system was set up, as shown in Fig. 13(a). This system is composed of a signal generator (AFG3022B, Tektronix, USA), two power amplifiers (HFVA-153, Nanjing Foneng, China), a direct current (DC) power supplier (YB1732A, Lvyang, China), four photoelectric sensors (E3F-20L/20C1, Yingbai, China), an oscilloscope (DPO2014, Tektronix, USA), and a computer. When laser light from the photoelectric sensor is blocked, its pulse signal can be used to record time. Four photoelectric sensors powered by DC power and one oscilloscope constituted a time acquisition system (Sample frequency: 31.3 kHz). Fig. 13(b) shows the measured method, in which the phalanges A and C dragging weights rotate around their corresponding shafts when the piezoelectric transducer in phalanx B is power on. When the phalanx A passes through the photoelectric sensor-1, it is time t1. As the phalanx A passes through the photoelectric sensor-2, it is time t2. Therefore, the average rotational velocity of the phalanx A driven by the phalanx B can be computed by Eq. (5), and the output torque of the phalanx A driven by the phalanx B can be computed by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure1.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure1.10-1.png",
        "caption": "Fig. 1.10 A bat moving at speed v will continue to move in a straight line at speed v unless there is a force on the bat. To rotate a bat so its CM rotates in an arc of radius R at speed vCM, there needs to be a centripetal force F D mv2 CM=R acting along the bat toward the axis of rotation. That force is generated by the batter pulling on the handle and is the largest single force on the bat, exceeding the weight of the batter by the end of the swing",
        "texts": [
            " Even if the tip rotated at constant speed there would be an acceleration of the tip due to its change in direction. That acceleration is always in a direction pointing to the center of the circle. It is called a centripetal acceleration, meaning that it points to the center. If the radius of the circle is R and the speed of the tip at any instant is v, then the centripetal acceleration is given by a D v2=R. For example, if v D 30 m s 1 and R D 1:0 m then a D 900 m s 2. If the tip is headed north at this time and is veering around to the west, then it is accelerating in the west direction at 900 m s 2 (Fig. 1.10). Suppose that you open a door by pushing with a force F on the door knob as shown in Fig. 1.11. If the distance from the knob to the door hinge is d then the quantity D F d is defined as the torque acting on the door. If you push at a point closer to the hinge then the door will be more difficult to open since the torque will be smaller, assuming you push with the same force F but at a smaller distance d . The difference between the two situations can be explained in terms of the work required 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002952_s12555-018-0400-7-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002952_s12555-018-0400-7-Figure1-1.png",
        "caption": "Fig. 1. General continuum robot driven by wire. It experiences twist deformation due to the low structural stiffness.",
        "texts": [
            " [16] proposed a shape reconstruction method with an electromagnetic sensor at the end effector to control the robot by using a third-order Bezier curve and Levenberg\u2013Marquardt algorithm based on the position information of the end effector. The methods in other studies are based on a dynamic model of the robot to improve control accuracy [17, 18]. However, these studies do not take into account twist deformation, which occurs when a continuum robot is used to handle target tissues from the body. Twist deformation is due to the low structural stiffness of the robot mechanism comprising multiple joints, as c\u20ddICROS, KIEE and Springer 2019 shown in Fig. 1. It is often observed in MIS robots that utilize continuum mechanisms to undergo a bending state during tissue handling, making it difficult to perform the operation [19]. In such robots, the arms must be bent for surgical tasks requiring triangulation positioning [20]. Although a continuum mechanism is also employed in endoscopes, twist deformation does not occur because the endoscope is not in direct contact with the tissues. The rotational motion around the longitudinal axis of the robot body is unconstrained because of the structural characteristics of wire-driven robots",
            " The remainder of this paper is organized as follows: Section 2 presents the static analysis of a continuum robot to predict the twist torque. In Section 3, the models proposed for twist deformation prediction are presented. In Section 4, several experiments conducted to verify the reliability of the proposed models are presented. Section 5 discusses the results obtained using the proposed models. Section 6 presents concluding remarks. 2. STATIC ANALYSIS OF TWIST TORQUE This section presents the static analysis of the twist torque of a continuum robot driven by four wires, as shown in Fig. 1. For an analysis of the twist torque that occurs when a load is applied at the end effector of a continuum robot, the model shown in Fig. 1 can be simplified by applying the following common static boundary conditions: 1) constant external force; 2) the components at all interfaces are rigid; and 3) the effect of friction on the structure is negligible. To satisfy the above conditions, we assume that the four wires are rigid and there is no clearance in any element constituting the continuum robot. In addition, the continuum robot can be assumed to be a single body because it is a hyper-redundant type robot in which multiple joints make one movement through a wire [18]. With these assumptions, the robot shown in Fig. 1 can be considered to be a curved beam with an arbitrary curvature, as shown in Fig. 2. It is also assumed that the robot body is made of the same material. The static analysis of this curved beam has been well established in a previous study [29]; however, the static analysis in this section is specifically carried out for a continuum mechanism. When an external force F is applied at the end of the robot along the z\u0302E direction, twist torque T and deformation \u03a8 are generated at the end of the robot, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure10-1.png",
        "caption": "Fig. 10. Three-dimensional model.",
        "texts": [
            " 9 (a), (d) and (e), as the medium gear basic circle radius increases, it can be discovered that the contact points move along the axial direction of the IHB gear tooth surface, the contact areas on the left and right tooth surface are moved toward the middle plane and decreased, the distribution of contact points is more concentrated, and the contact ellipse area is bigger. According to the above-derived tooth surface equations, the precise three-dimensional models of the novel hourglass worm drive are established and shown in Fig. 10 . And the finite element model is shown in Fig. 11 , there are 18,230 elements with 23,157 nodes in the finite element model. Compared with the gears and bevel gears, the finite element analysis boundary conditions of the hourglass worm gear drive require special considerations, and it is set as shown in Fig. 12 . It is assumed that the IHB gear is at rest relative to the fully constrained at the rigid surface I. The OPE hourglass worm has only one degree of freedom as rotational motion of its axis z 2 , while other degrees of freedom are constrained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.31-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.31-1.png",
        "caption": "Fig. 2.31 Principle layout of the adaptive cruise control (ACC) and preview distance control (DC) [T\u0150RNGREN 2002].",
        "texts": [
            " Other methods of ACC should include receiving a roadside signal that gives an optimum value of the vehicle velocity for the vehicle when travelling within certain traffic control areas. ACC, within the AEMC with the preview distance control (PDC), as well as the brake-by-wire (BBW) all-wheel-braked (AWB) conversion mechatronic control for co-operation with the DBW AWD propulsion mechatronic control, can also be integrated, with road-speed governing, and a manual ECE or ICE TMC is accessible for a power take-off (see Fig. 2.31) [T\u0150RNGREN 2002]. Consider a DC maintaining desired values of the vehicle velocity and distance from other vehicles, safety implies: Reliable operation, for example, achieving the desired distance; Ensuring, for example, that a fault somewhere does not cause an undesired ECE or ICE command. Compared also with a steer-by-wire (SBW) all-wheel-steered (AWS) conversion mechatronic control system, here reliability of the steering function is directly related to safety. Radar Cruise Control (RCC) (Low-velocity following mode included) - At values of vehicle velocity lower than 30 km/h, if the preceding vehicle stops, a warning through display and alarm is given to stimulate the driver to press on the brake, as well as in the incident where the driver is late in pressing the brakes, stops the automotive vehicle (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000016_bf00498035-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000016_bf00498035-Figure1-1.png",
        "caption": "Fig. 1. Main parts of the oxygen stabilized glucose electrode. 1, Oxygen electrode; 2, Electrode housing; 3, Fermenter lid; 4, Pt-gauze with immobilized enzymes; 5, Pt-coil (cathode); 6, Semipermeable membrane; 7, Electrolysis voltage source; 8, Reference voltage; 9, Differential amplifier; 10, PID-controller; 11, Electrolysis current controller; I, Electrolysis current",
        "texts": [
            " On the other hand, there is thus a maximum concentration of glucose that it can assay, limited by its intrinsic enzyme parameters, since dilution of the sample does not occur. One problem encountered with enzyme electrodes based on oxidase enzymes is the oxygen supply for the enzymic reaction. This problem is largely solved by the principle of oxygen stabilization, described by Enfors 1981. We report here on a new autoclavable, oxygen stabilized glucose electrode and on fed-batch cultivations of Escherichia coli using this electrode. Materials and Methods Electrodes. The oxygen stabilized glucose electrode was designed according to Fig. 1. Oxygen electrodes were galvanic and built after the principles of Johnson et al. 1964. The outer enzyme electrode housing was made from polycarbonate and had a close fit around the oxygen electrode. The electrode housing was fitted with a cellulose acetate membrane of porosity 25 A toward the broth. As the electrolytic anode, a 25-mesh Pt net of 8 mm diameter was used. The enzymes were immobilized directly upon the net. A 20 mm Pt wire 2 mm in diameter immersed in the broth served as cathode of the electrolytic circuit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000417_j.jsv.2008.04.008-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000417_j.jsv.2008.04.008-Figure1-1.png",
        "caption": "Fig. 1. Torsional gear model.",
        "texts": [
            " ARTICLE IN PRESS Nomenclature CM, CR torque on pinion, on gear I1, I2 pinion, gear polar moment of inertia Rb1, Rb2pinion, gear base radii u \u00bc \u00f0\u00f0 Rb1\u00de=Rb2\u00de speed ratio Z1, Z2 tooth number on pinion, on gear Greek symbols a relative amplitude variation of mesh stiffness bb base helix angle D mesh deflection e damping factor rk dimensionless amplitude of speed fluctuation (harmonic k) W \u00bc R t 0 O1\u00f0x\u00dedx time-dependent pinion angular variable y1, y2 torsional degrees of freedom on pinion, on gear o0 natural frequency of the system with averaged mesh stiffness O10 average (nominal) rigid-body angular velocity of pinion O1\u00f0t\u00de;O2\u00f0t\u00de \u00bc uO1\u00f0t\u00de rigid-body angular velocity of pinion, of gear G. Sika, P. Velex / Journal of Sound and Vibration 318 (2008) 166\u2013175 167 normal forces on the mating flanks. The mechanical model shown in Fig. 1 stems from the classic one degree-of-freedom system which has been widely used for the simulation of gear nonlinear dynamic behaviour since the late 1950s [4\u20137]. Introducing the mesh deflection D \u00bc cos bb\u00f0Rb1y1 \u00fe Rb2y2\u00de, the semi-definite equations of motion are transformed into the following differential equation (see Nomenclature): \u20acD\u00fe 2 o0 _D\u00fe o2 0\u00f01\u00fe af\u00f0t\u00de\u00deD \u00bc G\u00f0t\u00de, (1) where e is the damping factor; o0 \u00bc cos bb ffiffiffiffiffiffiffiffiffiffiffiffiffi km=M\u0304 p is the natural frequency associated with the averaged mesh stiffness km; M\u0304 \u00bc I1I2=\u00f0I1R2 b2 \u00fe I2R2 b1\u00de is the equivalent mass; G\u00f0t\u00de \u00bc \u00f0cos bb=M\u0304Rb2\u00de\u00f0CR \u00fe uI2 _O1\u00f0t\u00de\u00de represents the sum of the nominal resisting torque along with the inertial torque caused by acceleration; f(t) accounts for the time variations of the mesh stiffness function; y1, y2 are the small torsional angles superimposed on rigid-body rotations for the pinion and the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002503_sibcon.2017.7998581-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002503_sibcon.2017.7998581-Figure10-1.png",
        "caption": "Fig. 10. Pipe with footstep sequences marked on it; 1 \u2013 the pipe, 2 \u2013 the opening in the pipe 3 \u2013 markers that indicate originally generated footstep positions; 4 \u2013 markers that indicate footstep positions after the correction",
        "texts": [
            " Figure 9 illustrates the results of the algorithm\u2019s operation. The solution shown in fig. 9 was obtained for the following value of W :       = 2.00 01 W . (8) This choice of W gives the algorithm an incentive to shift the foot placement by changing its \u03d5 coordinate rather than s . We can observe that the sequence of footstep positions obtained after the correction procedure avoids the obstacle. After the correction is applied, the corrected sequence is mapped back onto the pipe, using formula (4). The result is shown in fig. 10. We can observe that the footstep sequence obtained after the correction closely follows the boundary of the opening in the pipe. The closeness with which the sequence follows the opening depends on the size of the bounding polyhedron. By choosing a polyhedron significantly larger than the obstacle it is bounding, we can generate a sequence that stays further from that obstacle. We should point out that the algorithm discussed here only provides the positions where points iK should come in contact with the inner surface of the pipe, but the robot also needs to know how to step from one position to the next"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.47-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.47-1.png",
        "caption": "Fig. 15.47 Phase 2 with center of rotation P and with P0 on the edge A\u2032B\u2032",
        "texts": [
            " At the final angle \u03d5 = \u03c0/2 the curve K and all curves E3(b) terminate on the line y = 1 . In particular, E3(0) terminates at the point Q0 with the coordinate x = cot\u03b1 , and K terminates at the point Q3 with the coordinate x = 2 cot\u03b1 . The curved section of G35 starts at the point S\u2217 (see Fig. 15.45 and (15.168)), and it terminates with \u03d5 = \u03c0/2 at the intersection of g2 and E3(0) . Reflection of G35 on g produces G31 . The domain \u03933 is the shaded area of the sector between g1 and g2 . Phase 2 : Figure 15.47 shows a rectangle and a point P0 in positions satisfying the conditions (a) and (b). For the center of rotation P the dashed auxiliary lines yield the x -coordinates xP = (sin\u03d5 + b cos\u03d5)/ sin\u03b1 , yP = (cos\u03d5\u2212 b sin\u03d5)/ sin\u03b1 . Elimination of \u03d5 yields x2 P + y2P = (1 + b2)/ sin2 \u03b1 . The normal n(\u03d5) intersects the line A\u2032B\u2032 between A\u2032 and B\u2032 only if xP \u2265 xA . With the angle \u03c8 shown in the figure this condition is \u03d5 \u2265 \u03c0/2 \u2212 \u03b1 \u2212 \u03c8 or sin\u03d5 \u2265 sin(\u03c0/2 \u2212 \u03b1 \u2212 \u03c8) . With sin\u03c8 = b/ \u221a 1 + b2 , cos\u03c8 = 1/ \u221a 1 + b2 the condition becomes sin\u03d5 \u2265 (cos\u03b1\u2212 b sin\u03b1)/ \u221a 1 + b2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000525_ichr.2010.5686851-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000525_ichr.2010.5686851-Figure1-1.png",
        "caption": "Fig. 1. Diagram of a planar bipedal robot. Absolute angles and torques.",
        "texts": [
            " Section III is devoted to the dynamic models and the resolution of the closed structure problems. The problem of trajectory optimization is presented in section IV. Numerical tests for the different bipeds are discussed in section V. Finally, section VI offers our conclusions and perspectives. To compare the performance of the planar bipedal robot in function of the knee joint, we use the same characteristics of length, mass and inertia for both bipeds. The bipedal robots are depicted in compass gait fig.1 with the two structures of the knee joint, see fig.2. Table (I) presents the physical data of the biped which are issued from the hydroid bipedal robot [18]. 978-1-4244-8690-8/10/$26.00 \u00a92010 IEEE 379 The dimensions of the four-bar structure are chosen with respect to the human characteristics measured by J. Bradley et al. by radiography in [19]. Figure 3 represents the cross four-bar knee structure. This parallel structure needs just one actuator on the drive angle \u03b11. Let us introduce \u0393m = [\u0393p1 ,\u0393p2 ,\u03931,\u03932,\u03933,\u03934] T 1 of the applied joint torques vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure3.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure3.6-1.png",
        "caption": "Fig. 3.6 Schematic of the spinning cylinder",
        "texts": [
            "025349538 Nm Tp = ( 2\u03c02 + 9 9 ) J\u03c9\u03c9x = ( 2\u03c02 + 9 9 ) \u00d7 1.0\u00d7 0.12 2 \u00d7 3000\u00d7 2\u03c0 60 \u00d7 0.05\u00d7 2\u03c0 60 = 0.026263390 Nm where J = MR2/2 is the moment of inertia of the disc [6]. The spinning cylinder is the typical component of the gyroscopic device. The actionof the inertial forces generated by the mass elements of the spinning cylinder definitely should be considered. The cylinder is spinning with a constant angular velocity \u03c9 around its horizontal axis oz in a counterclockwise direction when viewed from the tip of axis oz (Fig. 3.6). The system of coordinates oxyz locates at the centre of the cylinder\u2019s symmetry. The cylinder\u2019s mass elements m are located on the radius is (2/3)R and along the length L, creating the rotating cylinder around axes oz. An external torque is applied to the spinning cylinder and generated the centrifugal forces of the cylinder\u2019s mass elements that are resisted on the action of external torque. The analytical approach for themodelling of the action of the centrifugal forces f ct generated by the mass elements of the spinning cylinder is the similar as represented for the spinning disc in Sect. 3.1.1. It is considered the rotatingmass elements located on the cylindrical surface of a 2/3 radius for the left side of the spinning cylinder (Fig. 3.6). These mass elements generate the change in the vector\u2019s components f ct\u00b7z = f ct sin \u03b3 , whose directions are parallel to the axis oz. Other components of the centrifugal forces that located at upper and low sides and left and right sides of the spinning cylinder are similar. The integrated product of components for the vectors changes in centrifugal forces f ct\u00b7x, and their radius of location relative to axis ox generates the resistance torque T ct\u00b7x acting opposite to the external torque. Similar resistance torques are generated by the mass elements located on the planes of the cylinder that parallel to the plane xoy (Fig. 3.6). The analysis of the inertial torque generated by the centrifugal forces of the rotating cylinder is similar as described the inertial resistance torque produced by the centrifugal forces of the spinning disc as the reaction on the action of the external torque. The action of the external torque leads to the turning of the cylinder\u2019s plane xoy onto the small angle \u03b3 around axis ox and to changing its location represented by the plane y*ox (Fig. 3.2). The resistance torque produced by the centrifugal force of themass element is expressed by the following equation: Tct = fct\u00b7z ym (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000663_iros.2009.5354646-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000663_iros.2009.5354646-Figure5-1.png",
        "caption": "Figure 5 shows the result of the zero cross-track angle control. The helicopters within the graphs are not true to scale.",
        "texts": [],
        "surrounding_texts": [
            "If \u00b7 \u00a0 \u00a0 \u00a0 0\n- calculation of integral part Only in close range of the destination the integral part of the controller is used to eliminate a steady state deviation from the desired position. But in contrast to a classic I-controller the parameter is not constant. It varies regarding the moving direction.\n\u00a0 , \u00b7 \u00a0 0 , and \u00a0 , \u00b7 \u00a0 0 ,\nWith cos \u00b7 \u00a0 and sin \u00b7 and \u00a0 \u00a0 \u00a0 .\nAs the angles \u03b8d and \u03c6d the integrals have to be limited, either with respect to the direction by\n\u00a0 \u00b7 \u00a0\nif \u00a0 \u00a0, and with , analogously.\nDue to the reason, that the integral part is not adapted while cruising on a transition flight, it may happen the target position cannot be reached under changing weather conditions. Thus the following term was added to the controller and is calculated with the frequency of 120Hz.\n\u00a0 \u00b7 0.99\nif \u00a0 and \u00b7 \u00a0 \u00a0 .\nC. Damping The damping is the most important term to stabilize the UAV on a position, because a 4-rotor-helicopter is an underactuated system with almost no internal damping characteristics. Hence, three different kinds of damping are added to the controller: The along-track velocity-damping ATSD, the cross-track velocity-damping and the acceleration-damping AD. Where ATSD is variable and CTSD and AD are constant. That means and are adapted by: \u00a0 \u00a0 sin \u00b7 cos \u00b7\nsin \u00b7 \u00a0cos \u00b7 \u00a0 cos \u00b7 sin \u00b7\ncos \u00b7 \u00a0 sin \u00b7 and must be limited again with respect to the direction by\n\u00a0 \u00b7 \u00a0 / , if \u00a0 , \u00a0analogously.\n- Velocity damping It must be distinguished between ATSD and CTSD due to the reason that a damping towards the target is not desirable while being on transition flight. However, close to the destination the full damping should be available in any direction.\nHence, the parameter kATSD is dynamic with respect to d with:\n0, , \u00a0\n\u00b7 ,\nwith , with\u00a0 and \u00a0 \u00b7 . The damping-terms can now be determined by:\n\u00a0 \u00b7 cos \u00b7 \u00a0 \u00b7 sin \u00b7\nwith 2 , and \u00a0 . and as control parameters.\n- Acceleration damping The damping is applied to antagonize abrupt disturbances. But the AD shall only impact the UAV during acceleration and not during deceleration. Thus AD is calculated as follows:\n\u00b7 , 0 0 \u00a0 0 0 0,\nanalogously. is the control parameter.\nVI. SIMULATIONS Firstly, several simulations on Matlab/Simulink have been performed. This chapter presents some results. The flight dynamics of the 4-rotor-helicopter, i.e. the coupled system of six differential equations, have been implemented using Matlab/Simulink [3], [4]. The C-code of the implemented control system was embedded by means of a s-function into the simulation environment. Hence, successful validation can be performed by porting the code to the flight demonstrator.\nA. Track Flight\nThe UAV was programmed to fly 320 m directly southbound and back to the starting point with a constant wind from north with a wind-speed of 2-3 m/s. As expected the wind leads to an increased velocity while flying southwards. Hence, the UAV overshoots the destination in the south.",
            "B. Zero Cross Track Angle Control\nThe simulated flight was manually started at waypoint (wp) 1. The UAV was maneuvered along an arc with a velocity of 10 m/s to wp 2. As soon as the UAV reached this point, the position controller was switched on and wp 1 was set as its destination. It can be seen that the UAV tries to get back on track. The farther it is away from the destination, the stronger the UAV heads towards the track.\nC. Simulcast Position and Altitude control\nThe first waypoint (wp 1) is located in a height of 30 m and is considered as starting position. After having reached the starting position, a simulcast position and altitude change has been sent. As can be seen in figure 6, the UAV first starts to compensate the altitude difference of 20 m. After that it is heading into the new position located 100 m north. This is the effect of the term of the position controller. The next waypoint 3 is located in the same height but 90 m east. Towards waypoint 4 again a simulcast position and altitude change was executed, but in this case the new height lay 10 m below the previous waypoint. This time the position and altitude difference is compensated simultaneously, because only takes effect if the desired height is higher than the actual. The last procedure of the\nsimulation is similar to the stage before. From waypoint 4 back to the start position the desired height is again 10m lower.\nVII. EXPERIMENTS This chapter provides the results of the experiment. The already in Matlab/Simulink implemented controller was ported to an ARM7 controller on the UAV. Then, the same test scenarios were flown as shown in the previous chapter. However the actual wind conditions were measured on ground and estimated for wind conditions in higher altitudes.\nA. Track Flight In figure 7 the real progress of the same 320 m track flight\nas previously described is shown.\nfigure 7: experiment \u2013 320 m track flight\nThe chronological sequence of the experiment in comparison to the simulation is almost the same. One difference can be found in the fluctuating velocity while flying from one waypoint to the other. This is due to wind gusts. Hence, there are some modifications of the bearing as effect of the \u201czero cross-track angle control\u201d.\nB. Simulcast Position and Altitude control In figure 8 the result of the experiment can be seen. The trajectories of the experiment and the simulations are similar. The differences base on the presence of wind (up to 5m/s measured on the ground) and additional gusts in the outdoor experiment. Thus, the integral part of the controller is built.\nFor example during flight from waypoint 1 to waypoint 2 the trajectory is different in the first section. During the height compensation phase, the UAV is pushed away by the wind because of the absence of the proportional part of the controller. Additionally, due to the integral effect of the controller, the UAV is moving away if increasing the thrust to gain height, i.e. the thrust vector is not straightly directed upwards while holding position",
            "figure 8: experiment - rectangle\nFurther, it can be seen that the UAV tries to stay on track while moving from one waypoint to the other \u2013 as reaction on the wind conditions. Especially between waypoint 4 and 1 the UAV is blown away from its track and heads back towards it.\nVIII. CONCLUSION In this paper a control algorithm able to cover all requirements necessary for autonomously operating a VTOL UAV has been introduced. The developed controller was simulated and tested successfully in outdoor experiments. With this controller a 4 rotor helicopter is able to deal with constant wind up to 10m/s as well as with gusts. Furthermore, this controller can be applied to fly in urban scenarios due to its ability to fly along predefined tracks. Finally, with the novel control system the UAV is able to fly with the maximum possible speed without the risk of losing height during track flight.\nThe experiments were executed on basis of the GPS-data. Nevertheless this algorithm is sensor-independent.\nIX. OUTLOOK During the simulation and experiments one became aware of some improvements. The first problem occurred at heavy wind conditions, if the maximum allowed thrust and the maximum allowed attitude angles are not sufficient. Simply increasing the maximum allowed angle does not solve the problem adequately. The maximum allowed thrust has to be increased otherwise the UAV will not be able to maintain the actual altitude. Hence, a solution has to be found, so that the position errors do not increase. It has to consider maximum allowed thrust and angles with respect to the danger that there are not enough reserves for the attitude controller.\nAnother improvement would be the extension of the cross-track proportional part with an integral part to antagonize crosswinds better and to avoid permanent track errors.\nACKNOWLEDGMENT This research activity was performed in cooperation with Rheinmetall Defence Electronics GmbH, Bremen and partialy sponsored by CART (competitive aerial robot technologies) research cluster in Bremen, Germany.\nWe would like to thank Hannes Winkelmann and S\u00f6nke Eilers for their continuous support and help. They greatly contributed to the simulation environment.\nREFERENCES [1] S.Bouabdallah, P.Murrieri and R.Siegwart, Design and Control of Indoor Micro Quadrotor, IEEE-International Conference on Robotics and Automation 2004, New Orleans, USA, pp. 4393 \u2013 4398.\n[2] M. Kemper, M. Merkel and S. Fatikow: \"A Rotorcraft Micro Air Vehicle for Indoor Applications\", Proc. of 11th Int. IEEE Conf. on Advanced Robotics, Coimbra, Portugal, June 30 - July 3, 2003, pp. 1215- 1220.\n[3] M.Kemper, S.Fatikow: Impact of Center of Gravity in Quadrotor Helicopter Controller Design, in: Proc. of Mechatronics 2006, 4th IFAC Symposium on Mechatronic Systems, Heidelberg, Germany, September 12th - 14th 2006, pp. 157-162.\n[4] M.Kemper, Development of an Indoor Attitude Control and Indoor Navigation System for 4-Rotor-Micro-Helicopter, Dissertation, University of Oldenburg, Germany, 02. Feb 2007.\n[5] M.Mahn, M.Kemper: A Behaviour-Based Navigation System for an Autonomous Indoor Blimp, in: Proc. of Mechatronics 2006, 4th IFAC Symposium on Mechatronic Systems, Heidelberg, Germany, September 12th - 14th 2006, pp. 837-842\n[6] Jan Wendel, Integrierte Navigationssysteme, Oldenbourg Wissenschaftsverlag GmbH, March 2007\n[7] U-blox AG, Essentials of Satellite Navigation, Compendium Doc ID: GPS-X-02007-C, April 2007 Available: http://www.u-blox.com/customersupport/docs/GPS_Compendiu m(GPS-X-02007).pdf\n[8] R.Brockhaus, Flugregelung, Springer Verlag, Berlin, 2. Auflage, neubearb. A. (Juli 2001)\n[9] W.R\u00fcther-Kindel, Flugmechanik \u2013 Grundlagen und station\u00e4re Flugzust\u00e4nde, script ws 2006/2007, Available: http://www.tfhwildau.de/ll05/3.Semester/Flugmechanik/\n[10] G.M.Hoffmann, H.Huang, S.L.Waslander and C.J.Tomlin, Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment, AIAA Guidance, Navigation and Control Conference and Exhibit, 20-23 August 2007, Hilton Head, South Carolina, AIAA 2007- 6461\n[11] G.P.Tournier, M.Valenti and J.P.How, Estimation and Control of a Quadrotor Vehicle Using Monocular Vision and Moir\u00e9 Patterns, AIAA Guidance, Navigation and Control Conference and Exhibit,21-24 August 2006, Keystone, Colorado, AIAA 2006-6711\n[12] R.He, S.Prentice and N.Roy, Planning in Information Space for a Quadrotor Helicopter in a GPS-denied Environment, IEEE International Conference on Robotics and Automation (ICRA 2008), 19-23 May 2008, Pasadena Conference Center, Pasadena, CA, USA\n[13] O.Meister, R.M\u00f6nikes, J.Wendel, N.Frietsch, C.Schlaile and G.F.Trommer, Development of a GPS/INS/MAG navigation system and waypoint navigator for a VTOL UAV, SPIE Unmanned Systems Technology IX, Volume 6561, pp. 65611D, 9-12.April 2007, Orlando, FL, USA\n[14] B.Hofmann-Wellenhof, M.Wieser and K.Legat, Navigation: Principles of Positioning and Guidance, Springer Verlag, Wien, 1.Auflage, Oktober 2003\n[15] T.Puls, H.Winkelmann, S.Eilers, M.Brucke and A.Hein, Interaction of Altitude Control and Waypoint Navigation of a 4 Rotor Helicopter, German Workshop on Robotics (GWR 2009), 09-10 June 2009, Braunschweig, Germany, accepted"
        ]
    },
    {
        "image_filename": "designv10_12_0001796_s12541-015-0346-0-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001796_s12541-015-0346-0-Figure4-1.png",
        "caption": "Fig. 4 Roller-inner race contact geometry",
        "texts": [
            " Qi,e and Mi,e denote the contact forces and moments, respectively, between the roller and the inner and outer races. Fig. 3 shows cross sections in the yz plane of the inner and outer races with out-of-roundness errors. The inner and outer race errors ei and eo shown in Fig. 3 are defined as negative values in this study, though these errors may be positive or negative. Because of the out-ofroundness errors of the bearing races, the contact forces between the roller and races must be modified. Fig. 4 shows the contact geometry between a roller and the inner race. The roller-inner race contact force and moment can be calculated using the well-known slicing technique,17,24 as (1) , (2) where c is the contact constant; ns is the total number of slices; and \u0394lk and \u03b4k are the slice length and the contact compression, respectively, of slice k. \u03b4k is defined as , (3) where \u03b40 and \u03b2 \u00d7 lk are the contact compressions due to the translation motion and relative angular misalignment \u03b2 between the roller and inner race, respectively, and hk and drk are the crown drops due to the modified roller profile and the out-of-roundness of the inner race, respectively. drk can be easily determined from Fig. 4 with the radius difference defined as , (4) where R and r are the nominal and instantaneous inner raceway radii, respectively, at an arbitrary position along the contact line. . (5) The time-varying angle \u03d5(t) depends on the instantaneous orbital position angles \u03d5r(t) and \u03d5s(t) of the roller and the rotating race, as demonstrated in Fig. 5. These angles are defined as (6) (7) , (8) where \u03a9 and \u03a9m are the angular speed of the inner race and the orbital speed of roller, respectively. The contact force and moment between the roller and nonrotating outer race can be calculated in a manner similar to the inner race with the quantity \u03d5s(t) omitted from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.18-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.18-1.png",
        "caption": "Figure 7.18. Geometry of a conic section.",
        "texts": [
            "96e) yields the path equation d r(\u00a2) = 1+ A, 'e coe q: in which, by definition, (7.96g) 2E y 2 e= 1+--2 \u2022 mJL (7.96h) Thus, the plane motion of P for all time is given by d x(P , t) = r(\u00a2)er(\u00a2) = er (\u00a2 ).1+ ecos\u00a2 7.12.2. Geometry of the Orbit and Kepler's First Law (7.96i) The total energy E in the second relation of (7.96h) may be positive, negative, or zero. Thus, in particular, when E = -mJL /2d < 0, e = \u00b0and, by (7.96g), the orbit is a circle of radius r = d. Otherwise, (7.96g) describes the polar equation of a conic section in Fig. 7.18-defined as the locus of a point P that moves in a plane in such a way that the ratio of its distance I0 P I from a fixed point 0 in the plane to its distance IDP I from a fixed line is constant. The fixed point is called the focus. The fixed line is known as the directrix, and the constant ratio 280 Chapter 7 (7.97a) of the two distances is called the eccentricity . With the focus at the origin 0 of frame <t> = {o; I, j} in Fig. 7.18, the directrix is a straight line BD parallel to j at a distance \u00a3 from 0 along i. The eccentricity is defined by lopl r e = -=- = > o.IDPI \u00a3 - r cos\u00a2 Solving this relation for r(\u00a2), we obtain the general equation (7.96g) in which d == t e. (7.97b) Equation (7.96g) shows that r(-\u00a2) = r (\u00a2), so the path is symmetric about the line \u00a2 = 0, the i-axis. The chord along the j-axis (parallel to the directrix) through the focus 0 is called the latus rectum.When \u00a2 = Jr / 2, (7.96g) shows that r(Jr/ 2) = d, and hence 2d is the length of the latus rectum "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001542_imccc.2013.326-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001542_imccc.2013.326-Figure2-1.png",
        "caption": "Figure 2. Force and torque diagram of the quadrotor UAV",
        "texts": [
            " Due to the complexity of the flight dynamics of the quadrotor UAV, it is difficult to build an accurate model. To simplify the model process and facilitate the flight control design, the flight dynamics model is deduced under the following assumptions The quadrotor UAV is a rigid-body and the aircraft structure and elastic deformation are ignored. The center of gravity coincides with the origin of the body coordinate system. The airframe structure is tough symmetry and the asymmetry airflow and the air compressibility are ignored. The quadrotor UAV under consideration is given in Fig. 2. Rotor 1 and rotor 3 contra rotate. Rotor 2 and rotor 4 rotate clockwise. Force and torque diagram of the quadrotor UAV are analyzed in Fig. 2 Let , ,B x y z be the frame attached to the vehicle and , ,E x y z denote the inertial frame as shown in Fig. 2 the origin of the inertial frame is set to the take-off point. The rotation matrix :R B E depends on the three Euler angles ( , , )T representing, respectively, the yaw, the pitch and the roll. c c s s c c s s s c s c ( , , ) c s s s s c c s c c s s s s c c c R (1) Where, cx for cos x and sx for sin x . The thrust generated by rotor i is given by 2 i if b (2) Where 0b is a parameter depending on the density of the air, the radius of the propeller, thel chord length and the number of blades[7]. The total thrust in , ,B x y z is 4 4 2 1 1 i i i i T f b (3) The total torques caused by the rotor drag in , ,B x y z are 2 2 2 2 2 1 4 2 3 2 2 2 2 1 1 2 3 4 4 1 2 1 ( ) ( ) ( 1)i i i b l b l (4) Where 1l and 2l denote the longitudinal and horizontal distance between the rotor and the center of gravity respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003709_tec.2021.3052365-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003709_tec.2021.3052365-Figure7-1.png",
        "caption": "Fig. 7. Stator surface.",
        "texts": [
            " The pole pitches of NRT\u00b1pf pole pair space harmonics are: ( )fRT g pN pN r fRT \u00b1 =\u00b1 2 2\u03c0 \u03c4 (29) The magnetizing MMF amplitudes Fe NRT\u00b1pf induced by the current layers corresponding to NRT\u00b1pf pole pair space harmonics are: fRT fRT fffRT pN pN spp e pN JCF \u00b1 \u00b1 \u00b1 = \u03c0 \u03c4 \u03bb\u03b4,, (30) Then, the equivalent current density amplitudes corresponding to the NRT\u00b1pf pole pair space harmonics are: ( ) spp sum rppsumw pN t pN ffff fRT fRT CCCkNIJ ,,,, /23 +\u22c5 \u22c5 = \u00b1 + \u03c4 (31) ( ) spp dif rppdifw pN t pN ffff fRT fRT CCCkNIJ ,,,,- /23 +\u22c5 \u22c5 = \u00b1\u03c4 (32) The iron losses generated by the NRT\u00b1pf pole pair space harmonics in the stator can be determined by the post-processing using the 2D FEA model. 3) NST\u00b1pf space harmonic The NST\u00b1pf pole pair space harmonics\u2019 main contribution to the stray load loss is to generate iron losses and rotor cage losses, and the calculation domain is in the rotor. In the corresponding 2D FEA model, the rotor is slotted and the stator surface is smooth shown in Fig. 7, and the ferromagnetic material fills the stator component. Based on (17) and (18)\uff0c the amplitudes of the magnetizing MMFs corresponding to the NST\u00b1pf pole pair space harmonics in the airgap obtained by the GAFMT are: sum sppw t pN fffST CkNIF ,, 23 \u22c5 \u22c5 =+ \u03c0 \u03bb\u03b4 (33) dif sppw t pN fffST CkNIF ,,- 23 \u22c5 \u22c5 = \u03c0 \u03bb\u03b4 (34) In the corresponding 2D FEA models, the thin equivalent current layers are added, and the current densities j NST\u00b1pf sre:         = \u00b1 \u00b1\u00b1 xtJj fST fSTfST pN pNpN \u03c4 \u03c0 \u03c9 cos (35) where J NST\u00b1pf and \u03c4 NST\u00b1pf are the current density amplitudes and the pole pitches corresponding to the NST\u00b1pf pole pair space harmonics in the airgap, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.6-1.png",
        "caption": "Fig. 13.6 The two possible couplings of coplanar shafts 1 , 2 , 3 by two Hooke\u2019s joints resulting in \u03d5\u03073 \u2261 \u03d5\u03071",
        "texts": [
            " , \u03b1n\u22121 and on the shaft parameters \u03b22 , . . . , \u03b2n\u22121 . Example n = 3 : Equation (13.35) shows that a3 = 1 requires \u03b22 = 0 and, in addition, cos\u03b11/ cos\u03b12 = 1 , i.e., |\u03b11| = |\u03b12| . This result was to be expected. In Figs. 13.6a and b the two possible arrangements with coplanar shafts 1 , 2 and 3 are shown. 13.3 Series-Connected Hooke\u2019s Joints 399 At this point the condition of coplanarity of the three shafts is abandoned. Obviously, the property \u03d5\u03073 \u2261 \u03d5\u03071 is preserved if the planar system (for example, the one in Fig. 13.6a) is subjected to the following three-step operation: Step 1: In an arbitrary position shaft 2 is cut thus splitting the entire system into a left part 1 and a right part 2 Step 2: Part 2 including joint 2 and the bearing of shaft 3 is rotated as one single rigid body about the axis of shaft 2 through an arbitrary angle \u03c8 Step 3: In the new position \u03c8 the two parts of shaft 2 are rigidly joined together. In the special case \u03c8 = \u03c0 , the new position is the position shown in Fig. 13.6b . If \u03c8 = \u03c0 , the axes of shafts 1 and 3 are skew in the new position. Example n = 4 : Equation (13.37) shows that the condition a4 = 1 is satisfied in each of the following three cases. Case a: (\u03b22, \u03b23) = (\u03c02 , 0) and cos\u03b11 cos\u03b12 = cos\u03b13 Case b: (\u03b22, \u03b23) = (0 , 0) and cos\u03b12 cos\u03b13 = cos\u03b11 Case c: (\u03b22, \u03b23) = (0 , \u03c0 2 ) and cos\u03b13 cos\u03b11 = cos\u03b12 . In Fig. 13.7 case (c) is illustrated by a system of coplanar axes with \u03b13 = \u03b11 = 20\u25e6 and cos\u03b12 = cos2 20\u25e6 (\u03b12 \u2248 28\u25e6). This example shows that geometrical symmetry of the coupling of shafts 1 and 4 is not a necessary condition for the identity of input and output angular velocity. Example n = 5 : The condition a5 = 1 is satisfied by altogether seven different combinations (\u03b22, \u03b23, \u03b24) and by associated conditions on \u03b11 , . . . , \u03b14 . The details are left to the reader. See also Duditza [4, 7]. In Fig. 13.8 a simple example with five coplanar axes is shown. It is the combination of two systems of the type shown in Fig. 13.6b . The parameters are \u03b22 = \u03b23 = \u03b24 = 0 and \u03b11 = \u03b12 = \u03b13 = \u03b14 = \u03b1 . Shafts 1 , 3 and 5 have identical angular velocities \u03d5\u03075 \u2261 \u03d5\u03073 \u2261 \u03d5\u03071 . In every system with coplanar axes i = 1, . . . , n the property \u03d5\u0307n \u2261 \u03d5\u03071 is preserved if the three-step operation explained for the case n = 3 is applied analogously, i.e., by cutting an arbitrary intermediate shaft j = 2 , . . . , n \u2212 1 and by a rigid-body rotation of the part located beyond the cut shaft. This operation may even be performed repeatedly with different intermediate shafts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.88-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.88-1.png",
        "caption": "Fig. 2.88 Subaru has constantly triumphed without changing its basic mechanism; it draws upon the benefits of both its horizontally-opposed piston ICE and its longitudinally configured drivetrain [FUJI 2004].",
        "texts": [
            "4m in 2009; Growth driven by vehicle safety and stability coupled with VSC and brake intervention systems; Reduction of fuel consumption from tank to wheel; Important market for automotive technology. Another technology that the automotive scientists and engineers have developed through these original layout concepts is a symmetrical M-M DBW 4WD propulsion mechatronic control system. This unique element of the automotive technology combines a horizontally-opposed piston-type ICE or ECE with a longitudinally configured drivetrain or powertrain (see Fig. 2.88) [FUJI 2004]. Automotive Mechatronics 256 With its low centre of gravity (CoG), the horizontally-opposed piston ICE or ECE delivers lower rolling forces to the automotive vehicle in cornering and stable surface traction. At the same time, the longitudinally configured drivetrain delivers superior manoeuvrability by placing the heavy transmission between the wheelbases, thereby making the yaw moment of inertia smaller. Although M-M DBW AWD propulsion is becoming a standard vehicle powertrain configuration, this trend will in no way detract from the technological advantages held by vehicle manufacturers which they have built up in the ultimate development arena of the World Rally Championships (WRC)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000768_j.1475-1305.2008.00558.x-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000768_j.1475-1305.2008.00558.x-Figure2-1.png",
        "caption": "Figure 2: Schematic and actual experimental caustics layout",
        "texts": [
            " \u00fel (1) The half-width l of the contact area is liked to the applied load through the relation [22]: l \u00bc ffiffiffiffiffiffiffiffiffiffiffi 2kRP p r (2) where k \u00bc (1 ) m2)/pE, assuming the same Young\u2019s modulus and Poisson\u2019s ratio for the bodies in contact, R \u00bc R1R2/(R1 + R2) is the equivalent radius of curvature and P \u00bc Z l l p\u00f0s\u00deds is the applied load per unit width. The experimental set-up for obtaining caustics from a transparent test specimen with contact stress singularities is illustrated in Figure 2. The light beam of a laser passes through a special filter and two convergent lenses, to become a convergent beam. In front of and behind the specimen, screens are placed at distances zo parallel to the mid-plane of the specimen. From the reflected and transmitted (in case of transparent specimen) light rays from the specimen interference fringes (caustics) are formed on the screens. Because of the divergent light beam, the produced caustics are magnified by a specific factor km, given by the relation [19]: km \u00bc zo \u00fe zi zi (3) where zo is the distance between the mid-plane of the specimen and the screen and zi is the distance between the focal point and the mid-plane of the specimen",
            " The governing set of equations is the following (expressed in terms of the meshing angle x): e230 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd j Strain (2011) 47, e227\u2013e233 doi: 10.1111/j.1475-1305.2008.00558.x LSF\u00f0x\u00de \u00bc 1 3 \u00fe 1 3 tan x tan hLPSTC for 0 x < hLPSTC (11) LSF\u00f0x\u00de \u00bc 1 for hLPSTC x hHPSTC (12) LSF\u00f0x\u00de \u00bc 1 3 \u00fe 1 3 tan h tan x tan h tan hHPSTC for hHPSTC < x h (13) The light source for the caustics experimental set-up was a He\u2013Ne laser, equipped with a system of optical filters and lenses to produce the required convergent beam. The specimens (Figure 2) were segments from standard 20 involute gears with module m \u00bc 20 mm and z \u00bc 18 teeth, consisting of four teeth each. These were cut on a CNC machining centre from a t \u00bc 5 mm thick poly-methyl-methacrylate [(PMMA) Plexiglas; Huifeng Organic Plastic Co., Ltd, Wenzhou, China] sheet, selected for its high elastic modulus and its optically isotropic properties. The specimens were placed on a specially designed fixture allowing fine adjustment of the meshing angle, while at the same time allowing loading up to 2000 N to be exerted using calibrated weights"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000728_j.triboint.2008.12.010-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000728_j.triboint.2008.12.010-Figure1-1.png",
        "caption": "Fig. 1. Layout of dent-generating test rig.",
        "texts": [
            " Therefore, in order to conduct testing that most closely resembled actual service conditions, we altered the surface roughness of the rolling elements by adding dents using foreign matter. No material processing was used to alter the surface roughness. The test was conducted using three sets of bearings; A, B, and C. The bearings from set A had rolling elements with dents. The bearings from set B also had rolling elements with dents, but these were different from the dents in the rolling elements of set A. The bearings from set C had new (standard) rolling elements that were free of any dents. Fig. 1 shows the test rig used to generate the dents in the bearings. The design of the cantilever test rig is such that a radial load is applied directly to the test bearing. Table 1 lists the test conditions used to generate dents on the rolling elements and raceways of each bearing. Dents were generated by operating the bearings, for one hour, using a lubricant that was contaminated with foreign matter. The hardness of foreign matter used for generating dents was HV 870 for the rolling elements of the bearings from set A, and HV 520 for the rolling elements of the bearing from set B",
            "53 (mm) Rz \u00bc 0.28 (mm) Rz \u00bc 0.11 (mm) Raceway Dents were generated with foreign matter of HV 520 Ra \u00bc 0.039 (mm) Rz \u00bc 0.61 (mm) L of life test 2.0 2.7 3.0 Symbol in Fig. 2 m \u2019 J elements and the raceways were thoroughly cleaned. Life testing was conducted under clean lubrication conditions, a radial load of 6.2 kN, a rotating speed of 3900 min 1, and forced-circulation oil lubrication (ISO-VG68). Although the test rig used for this clean life test was basically the same as that for generating dents (see Fig. 1), a different lubricating method was used. Oil-bath lubrication was used when generating dents, and forced-circulation oil lubrication with 10 and 3mm filtering was used during clean life testing. Fig. 2 shows the results of the life test in the form of a Weibull plot. In this figure, the single-line arrow denotes a bearing without flaking, and the double-line arrow denotes a bearing with flaking on the rolling element. Among the bearings with flaking, only one of the bearings from set C had flaking on the rolling elements; all the others had flaking on the raceways",
            " Therefore, one solution to enhance the service life of a ball-bearing operating under conditions of contaminated lubricant would be to improve the dent resistance of the rolling elements. Accordingly, we assembled some test bearings using rolling elements made from nitride precipitated material, in which dent resistance was improved. Life testing was then conducted using these bearings under the conditions of contaminated lubricant. The test rig used for this life test was of the same design as the rig illustrated in Fig. 1. Test conditions were the same as those listed in Table 1 for bearings from set A. Test conditions included a 6206 bearing; a radial load of Fr \u00bc 6.2 kN; a rotating speed of n \u00bc 3000 min 1; and oil-bath lubrication (ISO-VG68 lubricant). Foreign matter used for contamination included: a hardness of HV 870; particle sizes ranging from 74 to 147mm; and a quantity of 0.05 g per 1.2 l of lubrication oil. The raceway material was standard, through-hardened, tempered SAE52100 steel and the rolling elements were nitride-precipitated material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002750_0142331216650022-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002750_0142331216650022-Figure6-1.png",
        "caption": "Figure 6. Schematic view of the inertia wheel inverted pendulum.",
        "texts": [
            "comDownloaded from controllers have robust behaviours and the outputs asymptotically track the sinusoidal input references. Also, Figure 4 shows the time responses of the saturated control signals for each axis. The curves drawn by the XY-table are illustrated in Figure 5 where point A is the initial point for drawing. This figure also shows the robust performance of the saturated ISM-GCNF controllers. Example 2: Inertia wheel inverted pendulum In this example, an under-actuated inertia wheel inverted pendulum (Figure 6) is considered. This system consists of an inverted pendulum equipped with a rotating wheel. The dynamical equations of this system are as follows (Andary et al., 2009): X P : _x1(t) _x2(t) = x2(t) 15:4472 sin x1(t) + 0 32:8731 |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} B sat(u(t))+ d(x, t)\u00f0 \u00de h(t)= 1 0\u00bd |ffl{zffl} C x(t) 8>>>< >>: \u00f048\u00de where x1(t)= u(t) is the angular position, x2(t)= _u(t) is the angular velocity and u is the torque applied by the actuator, which is saturated by umax = (0:1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.7-1.png",
        "caption": "Fig. 14.7 Generation of z\u2032 from z by two successive reflections in lines g1 (first reflection) and g2 and the resulting rotation about the pole P",
        "texts": [
            " Theorem 14.2. The resultant displacement z\u2032 \u2212 z caused by two successive reflections in parallel lines with normal vectors r01 = r01m (first reflection) and r02 = r02m is the translation 2(r02 \u2212 r01) by twice the distance of the two lines in the direction normal to the lines. The translation changes sign when the order of reflections is changed. 14.3 Resultant Displacements. Commutativity Conditions 419 The two successive reflections and the rotation about P referred to in Theorem 14.1 are shown in Fig. 14.7 . According to the last sentence in this theorem two successive reflections are commutative if and only if the reflecting lines g1 and g2 are orthogonal. The resultants TS and ST : Let e be the unit vector in the direction of the reflecting line (sense of direction arbitrary). The translation is t = mm \u00b7 t+ ee \u00b7 t (m \u00b7m = e \u00b7 e = 1 , m \u00b7 e = 0 ) . (14.31) For the two resultant displacements the relationships between the final position z\u2032 and the initial position z are according to (14.29) TS : z\u2032 = (I\u2212 2mm) \u00b7 z+ 2r0 + t , ST : z\u2032 = (I\u2212 2mm) \u00b7 (z+ t) + 2r0 ",
            "5 on three rotations about non-coplanar axes intersecting at a single point (see the spherical triangle in Fig. 1.7). If the intersection point moves to infinity, the spherical triangle degenerates to the planar pole triangle. Let Q be an arbitrary point fixed in \u03a3 and let Q1 , Q2 and Q3 be the points in the reference plane \u03a30 where Q is located in the positions 1 , 2 and 3 of \u03a3 . These points are called homologous points of Q . At every pole the two sides of the triangle and the enclosed semi-rotation angle create the situation shown in Fig. 14.7 . Every two of the points Q1 , Q2 and Q3 are carried into each other by a sequence of two reflections in sides of the triangle. The altogether six reflections are sharing one and the same reflection point Q\u2032 . In Fig. 14.11 this reflection point is shown in the triangle (Q1,Q2,Q3). The circumcircle of this triangle and its center Q0 are shown as well. The homologous points Q1 , Q2 , Q3 are now simply called circle points. In what follows, relationships between circle points, poles and the points Q\u2032 and Q0 426 14 Displacements in a Plane are developed, first by geometrical and then by analytical methods",
            " The reason is that the resulting equations express the fact that the numbers e\u2212i\u03d5ij/2(Q0 \u2212 Pij) and (Qi \u2212 Pij) have equal directions. The solution is not unique if Qi is located in a pole. This is the special case (b) explained above. Two positions of a plane determine a pole and a rotation angle, and three positions determine a pole triangle. Hence four positions determine altogether six poles and four pole triangles. In Fig. 14.18 the four positions are defined by the points Ai , Bi (i = 1, 2, 3, 4). The poles are constructed according to the rules of Fig. 14.7 . In what follows, it is assumed that no pole is at infinity and that no two poles coincide. All relative positions are known if the positions 2 , 3 and 4 relative to position 1 are known. These three relative positions are determined by altogether nine parameters. These are two coordinates for each of the three poles P1k and the rotation angles \u03d51k (k = 2, 3, 4). Between the poles and the semi-rotation angles of every pole triangle exist the relationships shown in Fig. 14.11 and in (14.45). Every pole is pole in two triangles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001463_j.jfranklin.2014.10.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001463_j.jfranklin.2014.10.003-Figure1-1.png",
        "caption": "Fig. 1. The schematic of the quadrotor.",
        "texts": [
            " The rotorcrafts possess six degrees of freedom (6DOF) and have the ability to move in a three-dimensional space. Therefore, compared to wheeled vehicles, the aerial vehicles have advantages on mapping, indoor exploration, surveillance, inspection, etc. The unmanned rotorcraft discussed in this paper rg/10.1016/j.jfranklin.2014.10.003 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. ding author. Tel./fax: \u00fe86 29 84744111. dresses: liuhao13@buaa.edu.cn (H. Liu), xijx07@mails.tsinghua.edu.cn (J. Xi), .tsinghua.edu.cn (Y. Zhong). is a quadrotor aerial vehicle as shown in Fig. 1. This kind of rotorcraft has some advantages over the regular rotorcraft due to its four independent rotors. By varying the angular speeds of the rotors, the quadrotor can change its aerodynamic forces and moments without the need of a swashplate to control the blade pitch angles. Besides, the need for a tail rotor is eliminated because the rotors are paired to rotate in opposite directions and thereby the resultant moment in the conventional rotorcraft is canceled [5]. In fact, quadrotors have become ideal experimental platforms for the aerial vehicle control research worldwide (see, e",
            " Furthermore, the proposed robust control method can also be extended to the closed-loop control system design for uncertain high-order systems. The remaining parts of this paper are organized as follows: the nonlinear mathematical model of the quadrotor is described in Section 2; the design procedure of the robust motion controller is presented in Section 3; Section 4 analyzes the robust tracking properties of the closed-loop system; Experimental results are shown in Section 5; Section 6 draws the concluding remarks. As depicted in Fig. 1, the quadrotor has four control inputs: the rotational speeds of the four rotors, and has 6DOF: the pitch, roll, and yaw angles, the longitudinal and latitudinal positions, and the height. The longitudinal (front and back) rotors rotate clockwise whereas the latitudinal (left and right) rotors spin in the opposite direction. The rotorcraft will pitch and hence move longitudinally if the angular speed of the front rotor is increased and that of the back rotor is decreased. A roll and a latitudinal motion of the quadrotor results from changing the rotational velocities of the left and right rotors in the opposite directions. Increasing (reducing) the angular speeds of the longitudinal rotors while reducing (increasing) those of the latitudinal rotors causes the yaw movement. The sum of thrusts produced from each rotor results in the up-down (height) motion of the rotorcraft. Let \u03b1\u00bc Ex Ey Ez denote an earth-fixed inertial frame and \u03b2\u00bc Ebx Eby Ebz a frame attached to the quadrotor with origin in the center of mass of the vehicle as shown in Fig. 1. The vector \u03be\u00bc \u03bex \u03bey \u03bez T indicates the position of the origin of the body-fixed frame \u03b2 with respect to the inertial frame \u03b1. \u03bex denotes the longitudinal position of the vehicle, \u03bey the latitudinal position, and \u03bez the height. Moreover, let \u03b7\u00bc \u03b8 \u03d5 \u03c8\u00bd T indicate the three Euler angles, the pitch angle \u03b8, the roll angle \u03d5, and the yaw angle \u03c8, which determine the rotation matrix R from the inertial frame \u03b1 to the body-fixed frame \u03b2: R\u00bc C\u03b8C\u03c8 C\u03c8S\u03d5S\u03b8 C\u03d5S\u03c8 S\u03d5S\u03c8 \u00fe C\u03d5C\u03c8S\u03b8 C\u03b8S\u03c8 C\u03d5C\u03c8 \u00fe S\u03d5S\u03b8S\u03c8 C\u03d5S\u03b8S\u03c8 C\u03c8S\u03d5 S\u03b8 C\u03b8S\u03d5 C\u03d5C\u03b8 2 64 3 75; where Ci \u00bc cos \u00f0i\u00de and Si \u00bc sin \u00f0i\u00de"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002786_s12206-018-1216-3-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002786_s12206-018-1216-3-Figure20-1.png",
        "caption": "Fig. 20. (a) QPZZ test platform; (b) bearing with inner and outer ring fault; (c) acceleration sensor location.",
        "texts": [
            " As seen, the REFF fe and its frequency doubling 2fe are identified productively. In this case, the FERgram method can efficiently separate the fault information and accurately determine that the rolling bearing is under compound fault composed by inner ring and rolling element defective, while the EEMD-ICA method, WPT-SK method, E-Kurtogram method and TEERgram method cannot realize such functionality. The experimental signal of the rolling bearing under inner and outer ring fault is obtained from QPZZ test platform. Fig. 20(a) displays the QPZZ test platform. The experiment bearing is SKF6205 deep grove ball bearing and its basic parameters are shown in Table 5. Fig. 20(b) displays the groove (1.5 mm in diameter and 0.2 mm thick) is machined on the bearing inner and outer ring respectively through wire-cutting technology. Fig. 20(c) describes that the bearing vibration signals are obtained from an acceleration sensor fixed on the pedestal of the defective bearing. The driver motor rotary speed n = 1466 r/min, and the sampling frequency Fs = 12800 Hz. The bearing parameters shown in Table 5 are introduced into the Eq. (11), where the IRFF fi = 132.2 Hz, and the ORFF fo = 87.7 Hz can be obtained. Figs. 21(a) and (b) present the experiment signal waveform and its ES, respectively. As seen, the ORFF fo and its frequency doubling 2fo - 5fo are extracted effectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002130_s12206-015-1233-4-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002130_s12206-015-1233-4-Figure10-1.png",
        "caption": "Fig. 10. Bearing axial displacement test bench.",
        "texts": [
            " Therefore, the contact angle is almost constant in the working condition with large pretightening force. Comparing the curves at 20\u00b0C and 80\u00b0C, bearing contact angle increases with the rise of temperature at high speed. When the axial force is 6000 N and the temperature rises by 60\u00b0C, the bearing contact angles of NSK 7206AW and NSK 7206BW increase 4\u00b0 and 5\u00b0, respectively. Comprehensively analyzing Figs. 8 and 9, temperature is the main factor affecting the bearing contact angle in the working condition. Test bearing axial displacement on the designed test bench. Fig. 10 shows the test bench, which comprises the mechanical part, the temperature measurement part, the axial displacement measuring device and the control-display part. The servo motor drives bearing rotation, whose speed can be controlled by computer. Apply the axial force of bearing with two axial force applying devices symmetrically placed, which ensures the axial force applied evenly. And the value of axial force can be read from the display device. The bearing temperature is measured by infrared temperature instrument and resistance temperature sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003707_j.mechmachtheory.2021.104284-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003707_j.mechmachtheory.2021.104284-Figure7-1.png",
        "caption": "Fig. 7. Structure of parallel manipulator 6 P US + UPU.",
        "texts": [
            " \u03c9 o jk = \u03b7 \u00b7 e \u00b7 {[ ( J z j G )T \u00b7 n z j ] + ( J r j G )T } \u00b7 e j \u00b7 \u03d5 o \u2032 j ( \u03c5o j ) \u00b7 y h k (61) Based on the error backward propagation, adjustment algorithm of weight coefficient for hidden layer node is as follows. \u03c9 h ki = \u2212\u03b7 \u2202\u03b5 \u2202\u03c9 h ki = \u03b7 \u00b7 \u03b4h k \u00b7 x i (62) Here local gradient of hidden layer node is as follows. \u03b4h k = \u03d5 h \u2032 k ( \u03c5h k ) \u00b7 2 \u2211 \u03b4o j \u00b7 w o jk (63) j=1 Manipulator 6 P US + UPU is taken as prototype in this section to operate simulation and to verify the effectiveness of proposed neural network synchronous control for redundantly actuated parallel manipulator. The structure of manipulator 6 P US + UPU is shown in Fig. 7 . It contains six actuated branches in type P US, one constraint branch in type UPU, one moving platform and one frame. It takes 5 degrees of freedom and 6 degrees of actuation. Then it is a redundantly actuated parallel manipulator, and its degree of redundancy is 1. Prismatic joints in the branches with type P US are taken as actuated joints. Five of those joints are defined as non-redundant actuated joints and corresponding branches as non-redundant branch, while the rest as redundant. Relevant geometrical and inertial parameters about the prototype are as shown in Tables 1 and 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003491_j.jsv.2020.115919-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003491_j.jsv.2020.115919-Figure14-1.png",
        "caption": "Fig. 14. DDS platform.",
        "texts": [
            " This section mainly give the simulation study to demonstrate the descriptive capabilities and asymmetry reason of the spectrum. The experimental studies will be conducted in the following sections. The experimental studies operated on a planetary gearbox from a Drivetrain Dynamics Simulator (DDS) platform at the University of Electronic Science and Technology of China (UESTC), Equipment Reliability and Prognostic, and Health Management Laboratory (ERPHM). The configuration of the test rig is given as in Fig. 14 : Fig. 14 shows that the DDS consists of a 2.24kW three-phase electronic drive motor controlling the input speed, connecting one stage of the planetary gearbox as a reducer, then linking a parallel shaft gearbox and a brake at the end to supply loading. Two accelerometers (Sensitivity:100mv/g) were mounted vertically and horizontally on the planetary gearbox to collect vibration data. Assemble parameters of the planetary gearbox are listed in Table 7 . The rotational frequency of the shaft is set as 30Hz and 50 Hz, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure19-1.png",
        "caption": "Fig. 19. Stress results of wheel 1 under the load applied at 0-deg.",
        "texts": [
            " In this section, two types of wheels with the same materials but different structures and sizes (as shown in Table 1) are selected to verify the feasibility of the method. For convenience, the parameter m1 and m2 obtained in 5.1 and 5.2 are recognized to be suitable to predict the fatigue life of the two wheels. The simulation processes of the stamping and the cornering fatigue test of the two wheels are similar with above. The model of wheel 1 is 16 6 J with five bolt holes, and the stress distributions of wheel 1 is shown in Fig. 19 under the load applied at 0-deg. The dangerous area locates at the connecting position between the bolt hole and the strengthening rib, as shown in Fig. 18. One typical point in this area (Point B in Fig. 20) is selected to calculate the operating stress, and this point suffers an approximate cosine form of alternating stress in one cycle (Fig. 21). A comparison of the operating stress in one cycle before and after the superposition of the residual stress is shown in Fig. 21. The corresponding fatigue life is estimated by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001084_j.ejcon.2013.08.001-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001084_j.ejcon.2013.08.001-Figure3-1.png",
        "caption": "Fig. 3. Inverted pendulum on a cart.",
        "texts": [
            " The phase portrait for this unstable open-loop \u00f0uk \u00bc 0\u00de system with initial conditions x0 \u00bc \u00bd2 2 T is displayed in Fig. 1. Fig. 2 presents the time evolution of xk for this system with initial conditions x0 \u00bc \u00bd2 2 T under the action of the proposed control law. This figure also includes the applied inverse optimal control law, which achieves stability. The proposed robust inverse optimal control presented in Section 3 is illustrated by stabilizing the inverted pendulum on a cart at the upright position [24] (see Fig. 3), which is difficult to control due to the fact that it is an underactuated system, F ! being the only control input. The continuous-time dynamics of the inverted pendulum is given as [24] _x \u00bc vx _vx \u00bc ml\u03c92 sin \u03b8 mg sin \u03b8 cos \u03b8\u00fe F ! M\u00fem sin 2 \u03b8 _\u03b8 \u00bc\u03c9 _\u03c9 \u00bc ml\u03c92 sin \u03b8 cos \u03b8\u00fe\u00f0M\u00fem\u00deg sin \u03b8 Ml\u00feml sin 2 \u03b8 F ! cos \u03b8 Ml\u00feml sin 2 \u03b8 \u00f039\u00de where x is the car position, vx is the car velocity, \u03b8 is the pendulum angle, \u03c9 is the angular velocity, M is the mass of the car, m is the point mass attached at the end of the pendulum, l is the length of the pendulum, g is the gravity constant and F "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000877_j.jmatprotec.2012.06.011-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000877_j.jmatprotec.2012.06.011-Figure2-1.png",
        "caption": "Fig. 2. Clad measurements for the calculation of dilution.",
        "texts": [
            " combination of the following process parameters: axial motion speed, mass flow and power modulation. Catchment efficiency represents the fraction of added material that was effectively attached to the surface. It can be calculated by the measurement of the mass difference of the sample, before and after the process, divided by the total amount of powder supplied in the process. The dilution was calculated by the ratio of the height of the clad under the substrate surface (h1) and the total clad thickness (h2 and h1), as shown in Fig. 2. The increase of dilution value implies into more material characteristics changes, generating, e.g. brittle phases which can cause crack formation by thermal stress during the process. With the average used laser power the dilution seemed to increase along the coating due to an overheating of the workpiece. The analyses were made with the inspections of the cross sections at the beginning of the coatings where the coating seemed to be more homogeneous. The laser power was an average between the peak power and the bottom power used in a power modulated laser process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure3.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure3.2-1.png",
        "caption": "Fig. 3.2 Schematic of acting centrifugal forces, torques and motions of the spinning disc",
        "texts": [
            " Usubamatov, Theory of Gyroscopic Effects for Rotating Objects, https://doi.org/10.1007/978-981-15-6475-8_3 33 The direction of the vector of tangential velocity changes continuously, i.e. the mass elements move with acceleration. The rotation of mass elements with acceleration generates the plane of centrifugal forces, which disposes of perpendicular to the axis of the spinning disc [6\u20139]. If an external torque is applied to the spinning disc, the plane of the rotating centrifugal forces inclines and resists to the action of the external torque (Fig. 3.2). The turning of the plane of the rotating centrifugal forces around axis ox that passes along the diameter line leads to the change in the directions and locations of centrifugal force vectors f ct generated by the mass elements. Vectors f ct, whose directions coincide with the line of axis ox (i.e. located on 0\u00b0 and 180\u00b0 from the line of axis ox), remain on the plane xoy. Other centrifugal force vectors f ct are located on the inclined plane xoy* and exhibit a non-identical change in their directions. The maximal declination of vectors f*ct from the line of axis oy shows vectors that are located at 90\u00b0 and 270\u00b0 from the line of axis ox (Fig. 3.2). These variable directions of centrifugal force vectors generate a change in vector components f ct\u00b7z that are parallel to rotating disc axle oz. The integrated product of the components\u2019 vector changes in centrifugal forces f ct\u00b7z, and their variable radius of location relative to axis ox generates the torque T ct that acts opposite to the action of the external torque T. The following analytical approach formulates the resistance torque produced by the change in the location of centrifugal forces generated by the rotating mass elements of the disc due to the action of the external torque being applied to the rotating disc",
            " At this stage, for the mathematical modelling, the weight of the rotor axle and the action of frictional forces are disregarded. The rotating centrifugal forces of the disc are in balance, and their directions are at right angles to axis oz. The action of external torque turns the plane xoy of rotating centrifugal forces to angle \u03b3 around axis ox with a new disposition of the plane xoy*. The change in the plane of the centrifugal forces generates the integrated resistance torque produced by the centrifugal force of the mass element (Fig. 3.2) and is expressed as follows: Tct = \u2212 fct\u00b7z ym = \u2212maz ym (3.1) where T ct is the torque generated by the centrifugal force of the mass element, f ct\u00b7z is the change in the centrifugal force and ym is the distance of the disposal of the mass element along axis oy. The sign (\u2212) of the resistance torque T ct means the action in the clockwise direction. The change in centrifugal force of themass element is expressed by the following equation: fct\u00b7z = fct sin \u03b1 sin \u03b3 = mr\u03c92 sin \u03b1 sin \u03b3 = [ M(2/3)R\u03c92 2\u03c0 \u03b4 ] sin \u03b1 sin \u03b3 = MR\u03c92 3\u03c0 \u03b4 \u03b3 sin \u03b1 (3",
            "2) where fct = mr\u03c92 = [ M(2/3)R\u03c92 2\u03c0 \u03b4 ] = MR\u03c92 3\u03c0 \u03b4 is the centrifugal force of the mass element m; m = M 2\u03c0[(2/3)R] \u03b4 2 3 R = M 2\u03c0 \u03b4 in which M is the mass of the disc; r = (2/3)R is the radius of the mass elements location; R is the external radius of the disc; \u03b4 is the sector\u2019s angle of the mass element\u2019s location; \u03c9 is the constant angular velocity of the disc; \u03b1 is the angle of the mass element\u2019s location; \u03b3 is the angle of turn for the disc\u2019s plane (sin \u03b3 = \u03b3 for the small values of the angle). Substituting the defined parameters into Eq. (3.1) yields the equation of the resistance torque produced by the centrifugal forces of the mass element. Tct = \u2212MR\u03c92 3\u03c0 \u00d7 \u03b4 \u00d7 \u03b3 \u00d7 sin \u03b1 \u00d7 ym (3.3) where ym = (2/3)Rsin\u03b1 is the distance of the mass element\u2019s location on the disc\u2019s plane relative to axis ox (Fig. 3.2) and the other components are as specified above. Equation (3.3) allows for the definition of the integrated torque produced by a change in the centrifugal forces generated by the disc\u2019s mass elements, wherein all components should be presented in a form appropriate for integration. Moreover, Eq. (3.3) contains variable parameters whose incremental components are independent and represented by different symbols. The change in centrifugal forces represents the distributed load applied along the length of the circle and angle \u03b1 where the disc\u2019s mass elements are located. Figure 3.2 depicts the locations of the change in centrifugal forces f ct\u00b7z of the disc. A distributed load can be equated with a concentrated load applied at a specific point along axis oy, which is the centroid at the semicircle. The location of the resultant force is the centroid (point A, Fig. 3.2) of the area under the curve, which is calculated by the known integrated equation. yA = \u222b \u03c0 \u03b1=0 fct\u00b7z ymd\u03b1\u222b \u03c0 \u03b1=0 fct\u00b7zd\u03b1 (3.4) where fct = MR\u03c92 3\u03c0 \u03b4 \u03b3 sin \u03b1. Substituting Eq. (3.2) and other components into Eq. (3.4) and transformation yields the following expression. yA = \u222b \u03c0 \u03b1=0 fct\u00b7z ymd\u03b1\u222b \u03c0 \u03b1=0 fct\u00b7zd\u03b1 = \u222b \u03c0 \u03b1=0 MR\u03c92 3\u03c0 \u03b4 \u00d7 \u03b3 \u00d7 2 3 R sin \u03b1 sin \u03b1d\u03b1\u222b \u03c0 \u03b1=0 MR\u03c92 3\u03c0 \u03b4 \u00d7 \u03b3 sin \u03b1d\u03b1 = MR\u03c92 3\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 2 3 R sin2 \u03b1d\u03b1 MR\u03c92 3\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 = R 3 \u222b \u03c0 0 (1\u2212 cos 2\u03b1)d\u03b1\u222b \u03c0 0 sin \u03b1d\u03b1 (3.5) where the expression MR\u03c92 3\u03c0 \u03b4 \u03b3 is accepted as constant for the Eq",
            " The direction of the resistance torque\u2019s action is in the clockwise direction which expressed by the sign (\u2212) and opposite to the action of the external torque and the direction of the angular velocity around axis ox. This resistance torque is restraining torque and acting only in case of gyroscope motion around axis ox under the action of the external torque. The value of the resistance torque is always less than the value of the external torque. External torque applied to a gyroscope causes the plane of the spinning rotor to turn around axis ox, as shown in Fig. 3.2. This turn leads to a change in the direction of the mass elements\u2019 tangential velocity. The change in tangential velocity is expressed in the acceleration of rotating mass elements and their inertial forces. This change varies along the circumference where mass elements are disposed of. The directions of the variable change in tangential velocity vectors Vz are parallel to the spinning rotor\u2019s axle oz (Fig. 3.3). The maximal changes in direction have the velocity vectors V* of the mass element located on the line of axis ox",
            " Similar resistance torques are generated by the mass elements located on the planes of the cylinder that parallel to the plane xoy (Fig. 3.6). The analysis of the inertial torque generated by the centrifugal forces of the rotating cylinder is similar as described the inertial resistance torque produced by the centrifugal forces of the spinning disc as the reaction on the action of the external torque. The action of the external torque leads to the turning of the cylinder\u2019s plane xoy onto the small angle \u03b3 around axis ox and to changing its location represented by the plane y*ox (Fig. 3.2). The resistance torque produced by the centrifugal force of themass element is expressed by the following equation: Tct = fct\u00b7z ym (3.33) where T ct is the torque generated by the centrifugal force of the spinning cylinder\u2019s mass element; f ct\u00b7z is the axial component of the centrifugal force. The following expression represents the equation for the component of the mass element\u2019s centrifugal force for the arbitrarily chosen plane that is perpendicular to axis of the cylinder (Fig. 3.2): fct\u00b7z = fct sin \u03b3 = m\u03c92 2R 3 sin \u03b1 sin \u03b3 (3.34) where fct = m\u03c92(2/3)R sin \u03b1 is the centrifugal force of the mass element m (Fig. 3.2); m = [(M/2)/2\u03c0l] \u03b4 l; M/2 is the mass of the half cylinder; l = L/2 is the line that forms the left side of the cylinder surface of the mass element\u2019s location; R is the external radius of the cylinder; \u03b1 is the angle of the mass element\u2019s location; \u03b4 is the sector\u2019s angle of the mass element\u2019s location on the plane that parallel to plane xoy; l is the element of the cylinder\u2019s length; \u03c9 is the constant angular velocity of the cylinder; \u03b3 is the angle of turn of the cylinder\u2019s plane around axis ox (sin \u03b3 = \u03b3 for the small values of the angle)",
            " Substituting the defined parameters into Eq. (3.34) yields the following equation: fct\u00b7z = M\u03c922R sin \u03b1 2\u00d7 2\u03c0(L/2) \u00d7 3 l \u03b4 \u03b3 = M\u03c92R 3\u03c0L \u03b4 \u03b3 l sin \u03b1 (3.35) where all components are as specified above. Substituting Eq. (3.35) into Eq. (3.33) brings the equation of the resistance torque produced by the centrifugal forces of the mass element. Tct = MR\u03c92 3\u03c0L \u00d7 \u03b4 \u00d7 \u03b3 \u00d7 l \u00d7 sin \u03b1 \u00d7 ym (3.36) where ym = (2/3)R sin \u03b1 is the distance of the mass element\u2019s location on the disc\u2019s plane relative to axis ox (Fig. 3.2) and other components are as specified above. Equation (3.36) contains variable parameters whose incremental components are independent and represented by different symbols. Additionally, Eq. (3.36) allows for defining the integrated torque generated by the action of the centrifugal forces\u2019 axial components of the spinning cylinder\u2019s mass elements, wherein all components should be presented in a form appropriate for integration. The action of the centrifugal forces\u2019 axial components represents the distributed load applied across the length of the line forming the cylinder. Figure 3.2 depicts locations of the axial components of centrifugal forces f ct\u00b7z generated by the mass elements m of the arbitrary plane of the spinning cylinder. The distributed loads are equated with a concentrated load applied at a specific point along axis oy, which is the centroid at the semicircle of the cylinder. The location of the resultant force is the centroid (point A, Fig. 3.2) of the area under the curve of each plane of the mass element along axis oz. The distance of the location of point A is defined by the expression ym that is represented by the following equation: yA = \u222b \u03c0 \u03b1=0 \u222b L/2 l=0 fct\u00b7z ymd\u03b1dl\u222b \u03c0 \u03b1=0 \u222b L/2 l=0 fct\u00b7zd\u03b1dl = \u222b \u03c0 \u03b1=0 M\u03c92R 3\u03c0L \u03b3 \u03b4 \u00d7 2 3 R sin \u03b1 sin \u03b1d\u03b1 \u222b L/2 0 dl\u222b \u03c0 \u03b1=0 M\u03c92R 3\u03c0L \u03b3 \u03b4 sin \u03b1d\u03b1 \u222b L/2 l=0 dl = M\u03c92R 3\u03c0L \u03b3 \u03b4 2 3 R \u222b \u03c0 \u03b1=0 sin 2 \u03b1d\u03b1 \u222b L/2 0 dl M\u03c92R 3\u03c0L \u03b3 \u03b4 \u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 \u222b L/2 0 dl = R \u222b \u03c0 0 (1\u2212 cos 2\u03b1)d\u03b1 3 \u222b \u03c0 0 sin \u03b1d\u03b1 (3.37) where the expression M\u03c92R 3\u03c0L \u03b4 \u03b3 is accepted at this stage of computing as constant for the Eq",
            " The action of an external torque on the spinning ring inclines the plane of the rotating centrifugal forces that resist the action of the external torque. The following analysis of acting forces and motion of the spinning ring is similar as for rotation disc represented in Sect. 3.1, this chapter. There is a minor difference in the presentation of location of the mass elements of the ring R. The variable directions of centrifugal force vectors generate a change in vector components f ct\u00b7z that are parallel to rotating ring axis oz (Fig. 3.2, this chapter). The change in the plane of the centrifugal force generates the resistance torque T ct of the mass element and is expressed as follows: Tct = \u2212 fct\u00b7z ym = \u2212maz ym (3.51) where f ct\u00b7z is the change in the centrifugal force and ym is the distance of the disposal of the mass element along axis oy. The change in the centrifugal force of the mass element is expressed by the following equation: fct\u00b7z = fct sin \u03b1 sin \u03b3 = ( MR\u03c92 2\u03c0 ) \u03b4 sin \u03b1 sin \u03b3 = MR\u03c92 2\u03c0 \u03b4 \u03b3 sin \u03b1 (3.52) where fct = MR\u03c92 2\u03c0 \u03b4 is the centrifugal force of themass elementm;m = M 2\u03c0R \u03b4R = M 2\u03c0 \u03b4 inwhichM is themass of the ring;R is the radius of themass elements location; \u03b4 is the sector\u2019s angle of the mass element\u2019s location; \u03c9 is the constant angular velocity of the ring; \u03b1 is the angle of the mass element\u2019s location; \u03b3 is the angle of turn for the ring\u2019s plane (sin \u03b3 = \u03b3 for the small values of the angle) around axis ox. Substituting the defined parameters into Eq. (3.51) yields the equation of the resistance torque produced by the centrifugal forces of the mass element. Tct = \u2212MR\u03c92 2\u03c0 \u00d7 \u03b4 \u00d7 \u03b3 \u00d7 sin \u03b1 \u00d7 ym (3.53) where ym = R sin \u03b1 is the distance of the mass element\u2019s location on the ring\u2019s relative to axis ox and the other components are as specified above. The location of the resultant force is the centroid (point A, Fig. 3.2, this chapter), which is calculated by the known integrated equation. yA = \u222b \u03c0 \u03b1=0 fct\u00b7z ymd\u03b1\u222b \u03c0 \u03b1=0 fct\u00b7zd\u03b1 (3.54) Substituting Eq. (3.52) and other components into Eq. (3.54) and transformation yields the following expression. yA = \u222b \u03c0 \u03b1=0 fct\u00b7z ymd\u03b1\u222b \u03c0 \u03b1=0 fct\u00b7zd\u03b1 = \u03c0\u222b \u03b1=0 MR\u03c92 2\u03c0 \u03b4 \u00d7 \u03b3 \u00d7 R sin \u03b1 sin \u03b1d\u03b1 \u222b \u03c0 \u03b1=0 MR\u03c92 2\u03c0 \u03b4 \u00d7 \u03b3 sin \u03b1d\u03b1 = MR\u03c92 2\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 R sin2 \u03b1d\u03b1 MR\u03c92 2\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 = R 2 \u222b \u03c0 0 (1\u2212 cos 2\u03b1)d\u03b1\u222b \u03c0 0 sin \u03b1d\u03b1 (3.55) The following solutions are the same as presented in Sect",
            " The analytical approach for the modelling of the action of the centrifugal forces of the spinning sphere is similar to the spinning disc represented in Chap. 3. The rotating mass elements of the spinning sphere are located on the surface of the 2/3 sphere radius. The analysis of the acting inertial forces generated by themass element of the sphere is considered on the arbitrary planes that parallel to the plane of the maximal diameter of the sphere (Fig. A.1) that is the same as the plane of the thin disc represented in Fig. 3.2 of Chap. 3. The plane of the mass elements generates the change in the vector\u2019s components f ct.z, whose directions are parallel to the spinning sphere axle oz. The integrated product of components for the vector\u2019s change in the centrifugal forces f ct.z and their variable radius of location relative to axis ox generate the resistance torque T ct acting opposite to the external torque. The resistance torque T ct produced by the centrifugal force of the mass element of the sphere is expressed by the following equation: Tct = \u2212 fct",
            "2) where fct = mr sin \u03b1 sin \u03b2\u03c92 = [ M(2/3)R\u03c92 sin \u03b1 sin \u03b2 4\u03c0 \u03b4 ] is the centrifugal force of the mass element m; m = M 4\u03c0[(2/3)R]2 \u03b4[(2/3)R]2 = M 4\u03c0 \u03b4, M is the mass of the sphere; 4\u03c0 is the spherical angle; \u03b4 is the spherical angle of the mass element\u2019s location; r = (2/3)Rsin\u03b1sin\u03b2 is the radius of the mass elements location; R is the external radius of the sphere; \u03c9 is the constant angular velocity of the sphere; \u03b1 is the angle of the mass element\u2019s location on the plane that parallel to plane xoz; \u03b2 is the angle of the mass element\u2019s location on the plane pass axis oz; \u03b3 is the angle of turn for the sphere\u2019s plane around axis ox (sin \u03b3 = \u03b3 for the small values of the angle) (Fig. 3.2, Chap. 3). Substituting the defined parameters into Eq. (A.1.1) yields the following equation: Tct = \u2212MR\u03c92 6\u03c0 \u03b4 \u03b3 sin \u03b1 sin \u03b2 \u00d7 ym = \u2212MR\u03c92 6\u03c0 \u03b4 \u03b3 sin \u03b1 sin \u03b2 \u00d7 2 3 R sin \u03b1 sin \u03b2 = \u2212MR2\u03c92 9\u03c0 \u03b4 \u03b3 sin2 \u03b1 sin2 \u03b2 (A.1.3) where ym = (2/3)R sin \u03b1 sin \u03b2 (Fig. A.1) is the distance of the mass element\u2019s location on the sphere\u2019s plane relative to axis ox, other components are as specified above. The action of the centrifugal forces\u2019 f ct.z axial components represents the distributed load where the sphere\u2019s mass elements are located (Fig. 3.2, Chap. 3). The resultant torque is the product of the resultant centrifugal forces and the centroid at the semicircle. The location of the resultant force of the one plane is the centroid (point A, Fig. 3.2, Chap. 3) that is defined by the expression ym. For the hemisphere, the centroid is defined by the following expression: yA = \u222b \u03c0 \u03b1=0 \u222b \u03c0 \u03b2=0 fct.z ymd\u03b1d\u03b2\u222b \u03c0 \u03b1=0 \u222b \u03c0 \u03b2=0 fct.zd\u03b1d\u03b2 = \u222b \u03c0 \u03b1=0 MR\u03c92 6\u03c0 \u03b4 \u03b3 2 3 R sin2 \u03b1d\u03b1 \u222b \u03c0 0 sin \u03b22d\u03b2\u222b \u03c0 \u03b1=0 MR\u03c92 6\u03c0 \u03b4 \u03b3 sin \u03b1d\u03b1 \u222b \u03c0 0 sin \u03b2d\u03b2 = MR\u03c92 6\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 2 3 R sin2 \u03b1d\u03b1 \u222b \u03c0 0 sin \u03b22d\u03b2 MR\u03c92 6\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 \u222b \u03c0 0 sin \u03b2d\u03b2 194 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects = R \u222b \u03c0 0 (1 \u2212 cos 2\u03b1)d\u03b1 \u222b \u03c0 0 (1 \u2212 cos 2\u03b2)d\u03b2 6 \u222b \u03c0 0 sin \u03b1d\u03b1 \u222b \u03c0 0 sin \u03b2d\u03b2 (A",
            " The analytical approach for the modelling of the action of the centrifugal forces generated by themass elements of the spinning cone is the same as represented for the spinning disc in Sect. 3.1, Chap. 3. The rotating mass elements of the spinning cone are located on the cone surface which maximal radius is the 2/3 radius of the base of the cone. The analysis of the acting inertial forces generated by the mass element of the cone is considered on the arbitrary planes that parallel to the plane of the base of 200 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects the cone (Fig. A.2) that is the same as the plane of the thin disc represented in Fig. 3.2 of Chap. 3. Similar resistance torques are generated by the mass elements located on the planes of the cone that parallel to the plane xoy. The resistance torque T ct produced by the centrifugal force of the mass element is expressed by the following equation: Tct = fct.z ym (A.2.1) where is f ct.z is the axial component of the centrifugal force; ym = (2/3)(2/3)R sin\u03b1 = (4/9)R sin\u03b1 is the distance of the location of the cone\u2019s plane of the centre mass and mass element along axis oz and relatively to axis ox",
            " The focus of the parabola locates at the point o of the system coordinate oxyz. The rotating mass elements of the spinning paraboloid are located on the paraboloid surface which maximal radius is the 2/3 radius of the base of the paraboloid. The analysis of the acting inertial forces generated by the mass element of the paraboloid is considered on the arbitrary planes that parallel to the plane of the base of the paraboloid (Fig. A.3) that is the same as the plane of the thin disc represented in Fig. 3.2 of Chap. 3. The rotating centrifugal Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 207 forces of the paraboloid\u2019s mass elements is declined and resisted opposite to the action of external torque. The analytical approach for the modelling of the acting centrifugal forces generated by the mass elements of the spinning paraboloid is the same as represented for the spinning cone in Sect. A.2.4. Similar resistance torques are generated by the mass elements located on the planes of the paraboloid that parallel to the plane xoy (Fig",
            "1 Centrifugal Forces Acting on Blades of a Spinning Gas Turbine The rotation of the blade mass elements generates the plane of centrifugal forces, which disposes of perpendicular to the axis of the spinning shaft. If an external torque T is applied to the shaft, the plane of the rotating centrifugal forces inclines and resists to the action of the external torque. The change in the plane of the centrifugal force generates the resistance torque T ct produced by the centrifugal force f ct.z of the blade mass (Fig. 3.2, Chap. 3) and is expressed as follows: Tct = \u2212 fct.z ym = \u2212maz ym (A.5.1) where ym is the distance of the disposal of the mass element along axis oy,; other components are as specified at previous sections. The change in the centrifugal force of the mass element is expressed by the following equation: fct.z = fct sin \u03b1 sin \u03b3 = mr\u03c92 sin \u03b1 sin \u03b3 = Mr\u03c92 n \u03b3 sin \u03b1 (A.5.2) 230 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects where fct = mr\u03c92 = Mr\u03c92 n nis the centrifugal force of the blade m; m = M nr nr = M n n in whichM is the mass of the blades; n is the number of blades; n is the one blade; other components are as specified at previous sections. Substituting the defined parameters into Eq. (A.5.1) yields the equation of the resistance torque generated by the centrifugal forces of the mass element. Tct = \u2212Mr\u03c92 n \u00d7 n \u00d7 \u03b3 \u00d7 sin \u03b1 \u00d7 ym (A.5.3) where ym = r sin\u03b1 is the distance of the mass of a blade location relative to axis ox (Fig. 6), and the other components are as specified above. The location of the resultant force is the centroid (pointA, Fig. 3.2, Chap. 3) which is calculated by the known integrated equation. yA = \u222b \u03c0 \u03b1=0 fct.z ymd\u03b1\u222b \u03c0 \u03b1=0 fct.zd\u03b1 (A.5.4) Substituting Eq. (A.5.2) and other components into Eq. (A.5.4) and transforming yields the following expression. yA = \u222b \u03c0 \u03b1=0 fct.z ymd\u03b1\u222b \u03c0 \u03b1=0 fct.zd\u03b1 = \u222b \u03c0 \u03b1=0 Mr\u03c92 n \u00d7 n \u00d7 \u03b3 \u00d7 r sin \u03b1 sin \u03b1d\u03b1\u222b \u03c0 \u03b1=0 Mr\u03c92 n \u00d7 n \u00d7 \u03b3 sin \u03b1d\u03b1 = Mr\u03c92 n n \u03b3 \u222b \u03c0 \u03b1=0 r sin 2 \u03b1d\u03b1 Mr\u03c92 n n \u03b3 \u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 = r \u222b \u03c0 0 (1 \u2212 cos 2\u03b1)d\u03b1 2 \u222b \u03c0 0 sin \u03b1d\u03b1 (A.5.5) where the expression Mr\u03c92 n n \u03b3 is accepted as constant for Eq"
        ],
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        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure18.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure18.2-1.png",
        "caption": "Fig. 18.2 Spherical four-bar in limit positions of the input link",
        "texts": [],
        "surrounding_texts": [
            "Grashof\u2019s conditions for the planar four-bar were deduced from Figs. 17.1a,b,c which show limit positions of the input link. These positions are characterized by collinearity of coupler and output link. In the case of the spherical four-bar, the equivalence to collinearity of coupler and output link is the coincidence of the great circles of coupler and output link. If, for convenience, great-circle arcs are drawn as straight lines, the Figs. 18.2a,b,c are equivalent to Figs. 17.1a,b,c . The triangles are spherical triangles. The angles \u03c61 and \u03c62 are limit values of the input angle \u03d51 . The cosine law for spherical triangles yields the equations cos(\u03b13 \u00b1 \u03b12) = cos\u03b11 cos\u03b14 + sin\u03b11 sin\u03b14 cos(\u03c61,2 \u2212 \u03c0) . (18.5) Hence cos\u03c61,2 = cos\u03b11 cos\u03b14 \u2212 cos(\u03b13 \u00b1 \u03b12) sin\u03b11 sin\u03b14 . (18.6) The same expressions are obtained from the condition that in (18.3) A2 + B2\u2212R2 = 0 . Equations (18.2) yield (with the abbreviations c1 = cos\u03d51 and s1 = sin\u03d51 ) A2 +B2 \u2212R2 = S2 1 [c 2 1(S 2 3C 2 4 \u2212 S2 4C 2 3 ) + s21S 2 3 ] + 2c1S1S4(C1C4 \u2212 C2C3) +C2 1 (S 2 3S 2 4 \u2212 C2 3C 2 4 ) + C2(2C1C3C4 \u2212 C2) . (18.7) Substituting S2 3 = 1\u2212 C2 3 , S2 4 = 1\u2212 C2 4 and s21 = 1\u2212 c21 this is rewritten in the form 642 18 Spherical Four-Bar Mechanism S2 1 [(1\u2212 C2 3 )\u2212 c21(1\u2212 C2 4 )] + 2c1S1S4(C1C4 \u2212 C2C3) + C2 1 [(1\u2212 C2 3 )\u2212 C2 4 ] +C2(2C1C3C4 \u2212 C2) = \u2212S2 1S 2 4c 2 1 + 2c1S1S4(C1C4 \u2212 C2C3) + S2 3 \u2212 C2 1C 2 4 + C2(2C1C3C4 \u2212 C2) = \u2212[S1S4c1 \u2212 (C1C4 \u2212 C2C3)] 2 +(C1C4 \u2212 C2C3) 2 + S2 3 \u2212 C2 1C 2 4 + C2(2C1C3C4 \u2212 C2) = \u2212[S1S4c1 \u2212 (C1C4 \u2212 C2C3)] 2 + S2 2S 2 3 = \u2212[(C2C3 + S2S3)\u2212 (C1C4 \u2212 S1S4c1)] \u00d7[(C2C3 \u2212 S2S3)\u2212 (C1C4 \u2212 S1S4c1)] . (18.8) The roots c1 of this expression are, indeed, the quantities in (18.6). The input link is fully rotating relative to the base if Eqs.(18.5) yield cos(\u03c61 \u2212 \u03c0) \u2265 +1 as well as cos(\u03c62 \u2212 \u03c0) \u2264 \u22121 . These are the conditions cos(\u03b14 + \u03b11) \u2265 cos(\u03b13 + \u03b12) , cos(\u03b13 \u2212 \u03b12) \u2265 cos(\u03b14 \u2212 \u03b11) . (18.9) The special case of four identical link lengths \u03b11 = \u03b12 = \u03b13 = \u03b14 is treated first. Equations (18.5) yield \u03c61 \u2212 \u03c0 = 0 , \u03c62 \u2212 \u03c0 = \u03c0 . This means that the input link can rotate full circle relative to the base. In what follows, it is assumed that at least two link lengths are different. Let \u03b1min and \u03b1max = \u03b1min be the smallest and the largest link length, respectively, and let \u03b1\u2032 and \u03b1\u2032\u2032 be the other link lengths so that \u03b1min \u2264 \u03b1\u2032 , \u03b1\u2032\u2032 \u2264 \u03b1max . Because of the assumption 0 < \u03b1i \u2264 \u03c0 (i = 1, 2, 3, 4) the second condition (18.9) is equivalent to |\u03b13 \u2212 \u03b12| \u2264 |\u03b14 \u2212 \u03b11| . (18.10) The first condition is satisfied if either \u03b14 + \u03b11 \u2264 \u03b13 + \u03b12 \u2264 2\u03c0 \u2212 (\u03b14 + \u03b11) or 2\u03c0 \u2212 (\u03b14 + \u03b11) \u2264 \u03b13 + \u03b12 \u2264 \u03b14 + \u03b11 . } (18.11) Condition (18.10) and the first condition (18.11) are satisfied if and only if \u03b11 + \u03b14 \u2264 \u03c0 , \u03b11 + \u03b12 + \u03b13 + \u03b14 \u2264 2\u03c0 , \u03b11 = \u03b1min or \u03b14 = \u03b1min , \u03b1min + \u03b1max \u2264 \u03b1\u2032 + \u03b1\u2032\u2032 . } (18.12) Condition (18.10) and the second condition (18.11) are satisfied if and only if \u03b11 + \u03b14 \u2265 \u03c0 , \u03b11 + \u03b12 + \u03b13 + \u03b14 \u2265 2\u03c0 , \u03b11 = \u03b1max or \u03b14 = \u03b1max , \u03b1min + \u03b1max \u2265 \u03b1\u2032 + \u03b1\u2032\u2032 . } (18.13) In conclusion, link 1 is a fully rotating crank if either the set of conditions (18.12) or the set of conditions (18.13) is satisfied. The last two of the con- 18.3 Coupler Curves 643 ditions (18.12) are formally identical with Grashof\u2019s condition for the planar four-bar. Conditions (18.13) are different. Examples: Conditions (18.12) are satisfied by the set of parameters \u03b11 = 50\u25e6 , \u03b12 = 100\u25e6 , \u03b13 = 120\u25e6 , \u03b14 = 80\u25e6 , and conditions (18.13) are satisfied by the set of parameters \u03b11 = 120\u25e6 , \u03b12 = 70\u25e6 , \u03b13 = 100\u25e6 , \u03b14 = 160\u25e6 . The above results apply also to the mechanism RCCC . Like planar four-bars also spherical four-bars fall into the categories of crank-rockers, double-cranks, double-rockers and foldable four-bars. A spherical four-bar is foldable if \u03b1min + \u03b1max = \u03b1\u2032 + \u03b1\u2032\u2032 ."
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.3-1.png",
        "caption": "Figure 5.3. Geometry for determination of the center of mass of a tube.",
        "texts": [
            " It is clear, for example, that the center of mass of a homogeneous, circular cylindrica l tube is at the geometrical center on its axis- plainly a place that is not occupied by a particle of the tube. On the other hand, the center of mass of a similar solid cylinder has the same location. These assertions are evident from symmetry considerations. Nevertheless, it is instructive to review integration methods typically involved in the use of (5.12) or (5.14), because similar techniques are used for both homogeneous and nonhomogeneous bodies for which symmetry may not be so evident. Example 5.2. (i) Compute the location of the center of mass of the homogeneous, cylindrical tube described in Fig. 5.3. (ii) Find the center of mass when the density varies linearly from the constant value Po at z = 0 to 2po at z = e. Solution of (i). The circular tube shown in Fig. 5.3 has an inner radius r., outer radius ro , and length e.Because the material is homogeneous, the center of mass is at the centroid determined by (5. 14) in which (5.15a) The Foundation Principles of Classical Mechanics 13 is the material volume of the tube. It is natural to introduce cylindric al coordinates in the imbedded frame tp = {o ; ik } , whose origin is at the base of the tube.Then the position vector x (P, t ) == x (P) of a particle P of 93 and the elemental volume at P in Fig. 5.3 may be expressed as x (P) = r (cos \u00a2i + sin \u00a2j)+ zk and dV (P ) = r drdodz:Hence, with (5.14), the center of mass location x*( 93, t) == x*(93) in rp is given by V (93)x *(93) = t\" t1ro (r cos \u00a2i+ r sin \u00a2j + zk) rdr d zd\u00a2 . (5.l 5b)10 10 r, The first two integrals in the angle \u00a2 vanish. Therefore, as anticipated from the symmetry, the center of mass lies on the axis of the tube. Integration of the remaining term in (5. l5b) and use of (5. l5a) yields x*(93) = ij2k, that is, the center of mass is at the center of the void",
            " 14 ChapterS Solution of (ii). We are given that the mass density of the tube varies linearly from Po at z = 0 to 2po at z = i, and hence p = Po (l + zli). Because p varies only along the tube 's length, the simultaneous geometrical and mass distribution symmetries about the tube's axis imply that the center of mass is on the axis. Therefore, x * = y* = 0 and only the z* component need be found. Hence , (5.12) yields m( gj)z* = 1zdm . (5.15c) qj The method of slices shows that for the annular ring in Fig. 5.3 the volume element dV = Adz , where A = n (r; - r?) is the constant area of the ring. The mass is then found by (5.10) : m( gj) = PoA it(I +~) d : = ~APoi , and the right-hand side of (5.15c) becomes Lzdm = PoA itz (I +~) d z = ~PoAi2. Therefore, by (5.15c), the center of mass is on the axis of the tube at z* = 5lj9 from its base at o. Clearly, the center of mass is not the centroid , which is located at z* = i l2 in accordance with (5.14) . 0 5.2.3.3. Momentum ofthe Center ofMass ofa Rigid Body We shall now derive an important result relating the momentum of a rigid body to the momentum of its center of mass",
            " Let a = '1W denote the mass per unit length of the homogeneous body, so that m = o t: Now, neglect terms of order w2 in (9.27) to obtain the moment of inertia tensor for a thin rod: I m\u00a32 ('* .* )e = 12 122 + 133 ' where the rod axis is the ir -axis in cp = {C; iZ l. 9.5.2. Moment of Inertia of a Circular Cylindrical Body (9.28) The inertia tensor for a homogeneous, circular cylindrical tube of inside radius r., outside radius r0 ' and length \u00a3 is derived relative to a center of mass body frame cp = {C; in situated at \u00a3/2 from 0 in Fig. 5.3, page 13, with i3= k. The result is then applied to find the inertia tensor for a solid cylinder, an annular lamina, a thin circular disk, and a thin rod. We begin with the cylindrical tube. The moment of inertia about the z-axis is obtained from the last equation in (9.14). Introducing cylindrical coordinates with x 2+ l = r2 and noting that dm = p2nr\u00a3dr, we have 133 = 1.r2dm = 2np\u00a3 fror3dr = ::'p\u00a3(r: - ri)\u00b7 >ii3 r i 2 With m = pA\u00a3 and the cross sectional area A = n(r; - r;), we obtain m (2 2)133 = 2\" ro + ri \u2022 (9",
            " The Moment of Inertia Tensor 369 Solution, The center of mass of the homogeneous drilled block !?l3 = !?l3s \\ fl is at the center of the hole. Here !?l3s denotes the solid rectangular block and fl identifies a homogeneous circular cylinder of the same material which we imagine fills the hole. Thus, with respect to ip, (9.36) yields (9.37a) Recalling (9.26) for a homogeneous solid parallelepiped with w =hand (9.31) for a homogeneous solid cylinder of radius R, bearing in mind the arrangement of the coordinate axes in Fig. 9.5 and in Fig. 5.3, page 13, for the cylinder, we obtain from (9.37a), referred to the body frame cp = {C; it}, f7l) msh 2 , . ms 2 2 ' . ' .IcCJOJ) = -6-111+12(h +e )(122+133) [ meR 2 ,. me ( 2 e 2 ) ' . ,.]- -2-111 + 4 R +\"3 (122 + 133) , (9.37b) wherein the mass m s of the solid block and me of the cavity body are given by (9.37c) Hence, by (9.4) , the mass of the drilled block is m(!?l3) = m s - me = pe(h2 - 7TR2). (9.37d) Use of (9.37c) and (9.37d) in (9.37b) yields the moment of inertia tensor components for the homogeneous, drilled parallelepiped referred to the center of mass frame ip: 1 m("
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure2.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure2.1-1.png",
        "caption": "Fig. 2.1 Velocity vectors polygon of the rotating point",
        "texts": [
            " Users of these equations calculate the acceleration that gives highmagnitude andmechanisms designed for high loads and stresses than have fewer values. This circumstance is the reason that devices do not have failures. However, the sufficient magnitude of the acceleration of machine elements leads to an increase in the sizes, weight and cost of machines that decrease their quality. The factors mentioned above impose a need to derive correct equations of the radial and absolute accelerations of a rotating object about a fixed axis. rate of change of its angular velocity. Figure 2.1 shows the link op with the radius r in a pure rotation, pivoted at point o on the xoy plane. A solution to the acceleration problem of a rotating object graphically requests only three equations: V = \u03c9r is a linear velocity, \u03b1t is a tangential acceleration, and \u03b1r is a radial acceleration of a rotating object. The corrected analytic approach considers acceleration analysis of the rotating object, which is subjected to a variable angular velocity. Figure 2.1 demonstrates two positions of the point p that are separated by an angle \u03b1. The velocity vector of the point p will change along the curvature of motion and due to a rotation with a variable speed. The magnitudes of linear velocities of initial V in and final V fn of the point p are different. Hence, the velocity polygon of the rotating point p is vectorially solved for these changes in the velocity, V c. Vc = Vin + Vfn (2.5) The vector, V c, is the change in the linear velocity that can be presented by two vectors that are radial velocity V r and tangential one V t",
            "6) The radial velocity vector V r to this curvature is directed towards the centre o of rotation and crosses the vector velocity V fn at the point f. The expression of the variable linear velocity of a point is given by the following equation: Vfn = r\u03c9in + \u03b5r t (2.7) where Vin = r\u03c9in, \u03c9in\u2014an initial angular velocity of a rotating point, and \u03b5rt is an extra velocity of a moving point due to an acceleration one, other parameters of equation are as specified above. For the following analysis, the radial velocity vector V r is represented as the sum of two vectors V r\u00b7bf and V r\u00b7fd, of segments bf and fd, respectively (Fig. 2.1). Vr = Vr\u00b7bf + Vr\u00b7fd (2.8) The small angle \u03b1 is presented by the following expression \u03b1 = \u03c9int + \u03b5t2 2 that is the sector with the accelerated angular velocity of the rotating point p (Fig. 2.1). This sector is represented by the following components: \u03b1 = \u03b4 + \u03b3 , where \u03b4 = \u03c9int is the sector with initial angular velocity and \u03b3 = \u03b1 \u2212 \u03b4 = \u03b5t2 2 is the sector with accelerated angular velocity. The two components of Eq. (2.8) are expressed by the following equations: Vr\u00b7bf = Vin sin \u03b4/2 (2.9) Vr\u00b7fd = Vfn sin(\u03b4/2 + \u03b3 ) (2.10) where the vector V r\u00b7fd is presented by the segment fd= ec. Substituting Eqs. (2.9) and (2.10) into Eq. (2.8) yields the following equation of the radial velocity for the rotating point p",
            " The new acceleration analysis of a rotating object should be used in the educational process of kinematics and dynamics of machinery. In addition, engineers and researchers for analysis of a machine work at transient conditions can use the new equations of accelerations of a rotating object about the fixed axis. Computing the inertial forces generated by the rotating mass elements of spinning objects that manifest gyroscopic effects should be conducted by the derived equations of the acceleration presented above. The rotating object shown in Fig. 2.1 has the initial angular velocity of 10 rad/s, accelerates at the rate of 5 rad/s2 and has the radius of rotation of 0.1m. It is necessary to determine the magnitudes of the tangential component and the radial component of accelerations and absolute one of the point p after 5 s of rotation. The radial acceleration is defined by Eq. (2.15) and the component of Eq. (2.4), which the results are shown as \u2022 Solution by Eq. (2.15) ar = r [ \u03c92 in + 3 4 \u03b5t\u03c9in + ( \u03b5t 2 )2 ] = 0.1 \u00d7 [ 102 + (3/4) \u00d7 5 \u00d7 5 \u00d7 10 + (5 \u00d7 5/2)2 ] = 44"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002569_j.procs.2018.07.094-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002569_j.procs.2018.07.094-Figure7-1.png",
        "caption": "Fig. 7. Manipulator configurations while traversing point to point motion in Cartesian space.",
        "texts": [
            "/ Procedia Computer Science 00 (2018) 000\u2013000 4.2. Trajectory Planning for Point to Point Motion In this case, Trajectory planning of 3-DOF manipulator for point to point motion has been simulated with and without obstacles in the workspace. The optimal trajectories has been evaluated by posing it as a non-linear constrained optimization problem with an objective shown in Eq. 6. The constraints of an optimization problem is the end-conditions of the manipulator such as starting point, goal point, start velocities and end velocities. Fig. 7 shows the path traced by end-effector by minimizing the objective while satisfying the constraints. In this case, collision avoidance is also considered, for which collision detection is required. Collision detection is carried out by finding the intersecting points of links and obstacles and then by increasing the joint displacements such that the V. V. M. J. Satish Chembuly et al. / Procedia Computer Science 133 (2018) 627\u2013634 633 V. V. M. J. Satish Chembuly et al./ Procedia Computer Science 00 (2018) 000\u2013000 7 configurations leading to collision move away from obstacle, which was explained in sec"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003164_1.3662578-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003164_1.3662578-Figure4-1.png",
        "caption": "Fig. 4 Manner of defining rolling friction coefficient and rolling moment",
        "texts": [
            " This was accomplished using a 3-in-thick piece of soft rubber between plates at the top of the apparatus to absorb any lack of parallelism between the testing-machine surfaces, or wedging effect due to the motion of the center plate. There was little difficulty in repeating measurements from setup to setup. The testing machine indicated the same total load at any position of the middle plate. The variables studied were lubricant, temperature, groove angle, conformity at the contact, and stress level. Flai-Svrface Tests. The first tests used l'/i-in. balls on flat surfaces and confirmed the results of Drutowski [3], Defining a rolling-friction coefficient fiR as in Fig. 4, most values of nR were in the range 10~4 \u2014\u2022 10~5. A rolling friction of this small value may be accounted for entirely by internal hysteresis or damping of the metal. Rolling friction is perhaps more realistically measured in terms of a rolling moment MR defined as in Fig. 4. A similar total moment may be calculated for balls in V-grooves if the ball diameter is replaced by the distance S as shown in Fig. 7. Fig. 5 shows a typical curve for flat-plate tests on a log-log plot. Two regions are noted: An apparently elastic region below 150-lb load and a plastic region above 150-lb load. The dividing line between the two regions occurs at a stress of about 190,000 psi for this steel. These results are not reported or analyzed in detail as they do not differ from Drutowski's work"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002830_s00170-019-04001-9-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002830_s00170-019-04001-9-Figure14-1.png",
        "caption": "Fig. 14 Schematic illustration showing the effect of hatch spacing on the deposition of AlSi10Mg alloys. a 2.0 mm. b 2.4 mm. c 2.8 mm",
        "texts": [
            " Figure 13 shows the density of AlSi10Mg alloy samples produced at the laser power of 3000 W, scanning velocity of 600 mm/min, and hatch spacing of 1.2\u20132.8 mm. It can be seen that the density of the AlSi10Mg alloys firstly increases and then decreases with the increase of the hatch spacing when the laser power and scanning velocity are constant. When the hatch spacing is 2.0 mm, the surface defect of the alloy is the least, and the density is as high as 95.9%. For this group of processing parameters, the laser power of 3000W, scanning velocity of 600 mm/min, and hatch spacing of 2 mm are the optimum parameters. Figure 14 shows the schematic diagram of the deposit of AlSi10Mg alloys layer by layer. It can be seen that the overlap area of the single-track AlSi10Mg alloy decreases in each layer with the larger hatch spacing, causing pores between the layers. These pores gradually accumulate to eventually form defects, reducing the quality of the formed alloy and leading to a lower density of the alloy. Figure 15 shows the Vickers microhardness of the AlSi10Mg alloys prepared by LAM under different processing parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003784_s11012-021-01372-w-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003784_s11012-021-01372-w-Figure8-1.png",
        "caption": "Fig. 8 FS tooth profile generated by offsetting curve B",
        "texts": [
            " The equation of the translation curve B is obtained as follows: x0 \u00bc rc d\u00f0 \u00decosU 3\u00f0 \u00de X3cosU 3\u00f0 \u00de Y3sinU 3\u00f0 \u00de \u00fe rm y0 \u00bc rc d\u00f0 \u00desinU 3\u00f0 \u00de \u00fe X3sinU 3\u00f0 \u00de Y3cosU 3\u00f0 \u00de : 8< : \u00f038\u00de The derivative of Eq. (38) with respect to u K-1 is obtained: _x0 \u00bc rc d\u00f0 \u00de _U 3\u00f0 \u00de sinU 3\u00f0 \u00de _X3 cosU 3\u00f0 \u00de \u00fe X3 _U 3\u00f0 \u00de sinU 3\u00f0 \u00de _Y3 sinU 3\u00f0 \u00de Y3 _U 3\u00f0 \u00de cosU 3\u00f0 \u00de _y0 \u00bc rc d\u00f0 \u00de _U 3\u00f0 \u00de cosU 3\u00f0 \u00de \u00fe _X3 sinU 3\u00f0 \u00de \u00fe X3 _U 3\u00f0 \u00de cosU 3\u00f0 \u00de _Y3 cosU 3\u00f0 \u00de \u00fe Y3 _U 3\u00f0 \u00de sinU 3\u00f0 \u00de 8>>>< >>>: \u00f039\u00de Based on Eq. (39), the tilt angle of the tangent T of the translation curve B is obtained as follows: h1 \u00bc arctan _y0 _x0 : \u00f040\u00de The second step is to derive the FS tooth profile, as shown in Fig. 8. The curve D is generated by offsetting the curve B, which is the FS tooth profile. Therefore, based on Eqs. (38) and (40), the equation of the FS tooth profile is obtained as follows: xF \u00bc x0 \u00fe R sin\u00f0h1\u00de yF \u00bc y0 R cos\u00f0h1\u00de h1 p 2 ; or xF \u00bc x0 R sin\u00f0h1\u00de yF \u00bc y0 \u00fe R cos\u00f0h1\u00de h1\\ p 2 ; \u00f041\u00de where R is the offset distance. The third step is to design the CS tooth profile. It can be seen from the first two steps that the FS tooth profile is generated by first translating the trajectory of a point on the CS original circle and subsequently offsetting it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.9-1.png",
        "caption": "Figure 10.9. Rotation about an asymmetric body axis fixed in space.",
        "texts": [
            "79d) Dynamicsof a RigidBody 445 This result shows that a moment about the k-axis perpendicular to the plane of the plate is required to sustain the motion even when the angular velocity is constant. This torque rotates with the k-axis normal to plate and produces alternating reactions at the support bearings. A square plate (\u00a3 = w), however, can spin at a constant angular speed without application of any torque whatsoever. 0 Exercise 10.5. Apply (10.65) to confirm (10.79d). o Solution of (ii). To relate Me to the plate frame cp' = {C; i~} for which J is the axis of rotation and k' =k in Fig. 10.9, we use (10.79a) and the vector transformation law (3.l07a): M~ = AMe, where A = [Ajkl = [cos(( , ik ) ], to obtain (10.7ge) (10.79f) in which M, are the components in (10.79d). Thus, referred to cp', the total torque exerted on the plate is mw\u00a3(\u00a32 - w2) , , wmw2\u00a32 ,M ( . , 2k) . e = 12(\u00a32 + w2) -WI +W + 6(\u00a32 + w2)J . The torque about the bearing axle j' is related to the applied drive torque T, and the remaining components, which arise from the asymmetrical distribution of mass about the plate diagonal , are restraining torques supplied by the bearings at A and B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001420_s11431-013-5433-9-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001420_s11431-013-5433-9-Figure8-1.png",
        "caption": "Figure 8 Wrench system of LFC chain.",
        "texts": [
            " General screw S is defined as o \u03bb        s S s s , (1) where s is a unit vector in the direction of screw axis; o  s r s is the moment of the screw axis about the origin of a reference coordinate system; r is the position vector of an arbitrary point on the screw axis; \u03bb denotes the pitch of the screw. A revolute joint is represented by a unit screw with zero pitch as o         s S s . (2) A prismatic joint is represented by a screw with infinite pitch as         0 S s . (3) Next, FCL chain structures are enumerated, attaching a reference coordinate system o-xyz to the chain, shown in Figure 8. The wrench system of the chain is given as       1 2 = 0 0 0; , = 0 0 1; 0 0 0 ,     r r r i j kS S S (4) where 1 rS denotes a constraint couple in direction [i j k]T and 2 rS denotes a constraint force coincident with axis z. 2 2 2 1i j k   , i, j, and k are arbitrary constants that cannot be simultaneously equal to zero. With two such constraints, all feasible twists of the chain form a four-system  gS . Four basic twists are obtained as           1 2 3 4 = 0 ; 0 0 0 , = 0; 0 0 0 , = 0 0 0; 0 1 0 , = 0 0 0; 1 0 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.9-1.png",
        "caption": "Fig. 15.9 The body-fixed \u03b7-axis is constrained to pass through the frame-fixed point A , and the body-fixed point B is constrained to move along the frame-fixed y-axis. Fixed centrode kf , moving centrode km and trajectory of body-fixed point Q",
        "texts": [
            "14) is satisfied by the coordinates x = y = 0 of A independent of R , whereas the polarcoordinate equation r(\u03d5) = cos\u03d5+ R shows that r = 0 is possible if and only if R \u2264 . 15.1 Instantaneous Center of Rotation. Centrodes 461 The generation of ellipses and of limac\u0327ons of Pascal by means of an elliptic trammel is made use of in many engineering apparatuses (examples see in Wunderlich [30]). Example 3 : Body with one line passing through a fixed point and with one point moving along a fixed line In Fig. 15.9 the x, y-system is the fixed frame \u03a31 , and the \u03be, \u03b7-system is the moving body \u03a32 . The body-fixed \u03b7-axis is constrained to pass through point A fixed in the frame at x = a , and point B fixed on the body at \u03be = b is constrained to move along the frame-fixed y-axis. To be determined are the equations of the fixed centrode kf in the x, y-system and of the moving centrode km in the \u03be, \u03b7-system. In addition, equations are to be formulated for the trajectory of the body-fixed point Q with coordinates \u03be = v , \u03b7 = u (arbitrary)",
            " Fixed centrode kf : The instantaneous center P is the intersection of the normal to the \u03b7-axis at A and the normal to the y-axis at B . The x, ycoordinates of P are expressed in terms of the angle \u03d5 : x = a+y tan\u03d5 , y = a tan\u03d5+ b cos\u03d5 = a tan\u03d5+ b \u221a 1 + tan2 \u03d5 . (15.16) Elimination of tan\u03d5 results in the equation y2 \u2212 a(x\u2212 a) = b \u221a y2 + (x\u2212 a)2 . (15.17) In the special case b = 0 , this is the parabola y2 = a(x\u2212 a) . In the special case b = a , it is the parabola y2 = a(2x \u2212 a) . In this case, Fig. 15.9 is symmetric. The pole P is equidistant from the fixed point A and from the 462 15 Plane Motion fixed y-axis. Hence A is the focus, and the y-axis is the directrix of the parabola. The moving centrode is the congruent parabola \u03b72 = a(2\u03be \u2212 a) with focus B and with the \u03b7-axis as directrix. In the general case b = 0 , a , squaring of (15.17) produces a quadratic equation for x\u2212 a with the solutions x\u2212 a = y a2 \u2212 b2 ( ya\u00b1 b \u221a y2 + a2 \u2212 b2 ) . (15.18) This equation is satisfied by the coordinates x = a , y = 0 of A ",
            " From this it follows that the parabolas are located symmetrically with respect to the altitude h of the triangle, and that this altitude is the common tangent at P . The motions shown in Figs. 15.10a and b can be interpreted in a different way as follows. The body-fixed line \u03b7 = \u22121 is moving through the fixed point 0 , and the body-fixed point A is moving along a fixed line y =const ( y = 0 in Fig. 15.10a and y = \u22121 in Fig. 15.10b ). With this interpretation both motions turn out to be special cases of Fig. 15.9. The notation is different, however. Figure 15.10a is the special case b = 0 , and Fig. 15.10b is the special case a = b = 1 . From (15.17) it was deduced that in the former case one of the centrodes is a parabola, and that in the latter case both centrodes are congruent parabolas. Example 5 : Centrodes of couplers in four-bar mechanisms The quadrilateral A0ABB0 shown in Fig. 15.11 is a foldable four-bar mecha- 15.1 Instantaneous Center of Rotation. Centrodes 465 nism in antiparallelogram configuration",
            " In what follows, n homologous points on a circle are called circle points, and the center of the circle is called center point. The slider-crank mechanism in Fig. 17.29a is a degenerate four-bar in that one center point Q0 is at infinity. The circle is a straight line. The elliptic trammel in Fig. 15.4 has two sliders. In the inverted slider-crank mechanism in Fig. 17.29b and in the inverted elliptic trammel the sliders are pivoted at center points Q0 fixed in \u03a30 . The associated circle points Q1, . . . ,Qn are at infinity. In the mechanism shown in Fig.15.9 one slider is pivoted in the frame \u03a30 and the other in the coupler \u03a3 . This mechanism equals its inverse. Three prescribed positions can be generated by four-bars of all types including the previously listed degenerate forms. Three prescribed positions determine a pole triangle (P12 ,P23 ,P31 ). Since three points are always located on a circle, one out of three circle points Q1 , Q2 , Q3 can be chosen arbitrarily. The other two circle points are then found as is shown in Fig. 14.11 by 17.14 Four-Bars Producing Prescribed Positions of the CouplerPlane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.6-1.png",
        "caption": "Figure 6.6. Schemaof the IBMinkjet printingprocess.Copyright 1977byInternationalBusinessMachines Corporation; reprinted by permission,",
        "texts": [
            " So long as the tower is within the gun's range, the result is independent of the muzzle speed and of the masses of the objects involved; it depends only on the initial coordinates of B and the angle of elevation of the gun. Explain why Arnold Aardvark, living in a world where this solution is meaningful, was wise not to have used the umbrella as a parachute. 0 116 Chapter 6 The same projectile ideas together with the basic law (6.15) for the electric force on a charged particle have a fascinating application in ink jet printing technology. An inkjet printer, illustrated schematically in Fig. 6.6, produces an image from tiny, charged spherical droplets of electrically conductive ink fired from a drop generating nozzle, approximately 1/1000 in. diameter, at the rate of 117,000 drops per second. The conductive droplets pass between charging electrodes where they are selectively charged electrostatically by command from programmed electronic control circuits that describe the image characters in terms of charge-no charge language. Moving at roughly 40 mph initially, the charged droplet s pass through a constant electric field that directs them onto the paper",
            " In this way, the ink jet printer quietly composes characters of high quality at a rate of about 80 characters per second , a full line of type across a standard page in about 1 sec. Of course, these operating rates will vary with printer design and evolving technology. To understand its fundamental working principle, we shall determine the relative motion of a droplet P of mass m and charge q having an initial velocity Vo relative to the printer carriage . Since the carriage has a uniform velocity Ve, as indicated in Fig. 6.6, the reference frame cp = {o ; id fixed in the charger at o is an inertial frame in which Newton's law may be applied . For simplicity, aerodynamic drag and wake effects, and the influence of electric repulsive forces between the charged droplets are neglected . Then, as shown in the free body Dynamics of a Particle 117 diagram in Fig. 6.6a, the total force F(P, t) = Fe+W acting on a drop P is due to its weight W = -mgj and the constant applied electric force Fe= qE = qEj. Hence, F( P, t) = (qE - mg)j is a constant force. From (6.1) and the initial condition Vo = voi, we obtain the velocity of the drop relative to the printer carriage whose constant velocity is vc = Vck : v(P , t) = voi + (cE - g )tj with c == q[m, (6.28a) (6.28c) (6.28b) With Xo = 0 initially, integration of (6.28a) yields the motion of a droplet relative to the printer carriage: I x(P , t) = voti + 2(cE - g)t2j . Hence , the path of the droplet relative to the carriage is a parabola 1 y(x ) = -2(cE - g)x 2. 2vo Let us imagine for simplicity that the deflection plates of length d extend from the origin at the charger to the paper surface, as suggested in Fig. 6.6. Then (6.28c) holds for 0 S x S d. (See Problem 6.22.) Therefore, at x = d, the droplet deflection or scan height h == y(d) at the paper surface is determined by d2 h = 2v2 (cE - g) . (6.28d) o The result (6.28d) shows that when an electrostatically charged drop enters the uniform electric field, the electric force alters its free fall trajectory and deflects it vertically by an amount proportional to its charge. An uncharged drop is collected in a gutter that returns the unused ink to its reservoir as shown in Fig. 6.6. A charged drop impacts the paper. Alphabetic or any other characters, shown schematically in Fig. 6.6, are formed by directing the ink dots onto the paper in patterns determined by the printer electronics. The decision to charge or not to charge is made automatically 117,000 times each second . The formula (6.28d) shows that the character height is inversely proportional to the square of the stream speed Vo which is controlled by the pump pressure . The printer controls the character height automatically by its pump control circuit. In this way, the ink jet printer is able to rapidly generate various characters of high quality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.10-1.png",
        "caption": "Fig. 13.10 Bicardanic homokinetic coupling",
        "texts": [
            " Each revolute axis intersects one shaft axis orthogonally. Rotations in these revolutes keep plane E normal to plane \u03a3 independent of the angular position \u03d5 of the shafts. In the figure plane E is shown in the positions \u03d5 = 0, \u03c0 and \u03d5 = \u00b1\u03c0/2 . The Tracta coupling is widely used in the automotive field because of the following properties: Inclination angles up to 50\u25e6 ; compact form; simple assembly; no loss of lubrication; large wear-resistant contact surfaces. 402 13 Shaft Couplings In the homokinetic coupling shown in Fig. 13.10 two revolutes on either side of plane \u03a3 constitute the central cross of a Hooke\u2019s joint each connecting one shaft to the intermediate body 3 . For this reason the coupling is referred to as bicardanic coupling. Body 3 is a cylinder with the axis 01-02 inside of which centrally placed rings 4 provide a planar joint in plane \u03a3 for the smaller circular disc 5 . Normal to this disc another hollow cylinder 6 is rigidly connected. This cylinder is guide for two spherical bodies fixed at the ends of shafts 1 and 2 at equal distances from 01 and from 02 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure12-1.png",
        "caption": "Fig. 12. Stress results of the wheel under the load applied at 0-deg.",
        "texts": [
            " The modal analysis of this finite element model shows that the first natural frequency of the steel wheel is about 275 Hz, and the corresponding rotational speed is 16,500 rpm. But in the cornering fatigue test, the steel wheel is fixed while the load rotates with the speed of 1200 rpm (far below the rotational speed corresponding to the first natural frequency), thus the dynamic rotational loading process can be converted into a static problem. To simulate the cornering fatigue test, the load is respectively applied on the end of the moment arm at every 22.5 deg. The stress distribution of the wheel under the load applied at 0-deg position is shown in Fig. 12. There are large operating stresses around the area (dangerous position) between the bolt hole and the bump ring (shown in Fig. 14). Each point of the wheel is in different deformation conditions, which can be determined by the third invariant of the stress deviator [14], as shown in Fig. 13. One dangerous point is selected and defined as point A in Fig. 14 to research its stress state in the following investigation. Fig. 15 is a stress curve from the data of the cornering stress of point A (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003040_taes.2020.2988170-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003040_taes.2020.2988170-Figure2-1.png",
        "caption": "Fig. 2: Diagram of the feature point on disabled satellite",
        "texts": [
            " To hover and track the feature point on the target, re should be nullified, and the axis xbc in Fbc should be aligned towards the feature point S on the target. In Fig. 1, pt, p\u2217t and st are projected to Fbt, satisfying pt = p\u2217t + st. As a result, pt can be obtained if p\u2217t is given. In order to align the tracking sensor of the chaser to the feature point S on the target, the axis xbc should be controlled to point to the feature point. Define pd = Cbc btp \u2217 t + re as the position vector of the feature point in Fbc, where Cbc bt represents the frame transformation matrix from Fbt to Fbc. Thus, as shown in Fig. 2, the right ascension and declination of pd are obtained as \u03b1 and \u03b3. The axis xbc is aligned to S if both \u03b1 and \u03b3 are zero. The frame transformation matrix from Fbc to Fd, Cd bc, is expressed as Cd bc = ybc (\u2212\u03b3) zbc (\u03b1) =  cos \u03b3 cos\u03b1 sin\u03b1 cos \u03b3 sin \u03b3 \u2212 sin\u03b1 cos\u03b1 0 \u2212 cos\u03b1 sin \u03b3 \u2212 sin\u03b1 sin \u03b3 cos \u03b3  (4) where Cd bc can be converted to the corresponding quaternion qe = [q1, q2, q3, q4] T, representing the difference between the current attitude to the desired attitude. Define q\u03c1 = [q2, q3, q4], thus, qe = [q1, q\u03c1] T",
            " Yushan Zhao majored general mechanics for his bachelor degree in Northwestern Polytechnical University between February, 1978 and January, 1982, and then got his master degree in 1985 and Ph.D degree in 1995. During 1998 and 1999, he engaged in advanced studies in Samara University of Aeronautics and Astronautics in Russia. He taught in Northwestern Polytechnical University from February, 1982 to June, 2002, and then worked in Beihang University since 2002, where he was awarded the excellent teacher of Beihang University. Figure Captions: Fig. 1: Diagram of relative position between chaser and target Fig. 2: Diagram of the feature point on disabled satellite Fig. 3: Diagram of the relative positions of satellite P and satellite E Fig. 4: Schematic diagram of learning logic in x-channel Fig. 5: The critic fuzzy inference system in x-channel Fig. 6: The expected hovering position to the feature point on the target Fig. 7: Membership functions Fig. 8: Time histories of the relative states by using the PSTC Fig. 9: Contrast of control acceleration under adaptive controller and PSTC(a) Fig. 10: Contrast of control acceleration under adaptive controller and PSTC(b) Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001883_s00170-017-0363-5-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001883_s00170-017-0363-5-Figure6-1.png",
        "caption": "Fig. 6 Coordinate systems of the form-grinding wheel and the workpiece",
        "texts": [
            " (34), (35), and (43) form a system of six equations that is solved for six unknowns \u2202\u03b5g1 \u2202\u03c3 , \u2202\u03b5g2 \u2202\u03c3 , \u2202\u03b5p1 \u2202\u03c3 , \u2202\u03b5p2 \u2202\u03c3 , \u2202\u03c6g \u2202\u03c3 , and \u2202\u03c6p \u2202\u03c3 for given misalignments. Profile calculation of a form-grinding wheel in the formgrinding process is a key step. The form-grinding wheel profile is formed by rotation of a contact line, which is between the form-grinding wheel surface \u03a3w and the workpiece surface, around a grinding wheel axis. A coordinate system Sw(Xw, Yw, Zw) is established to describe the relative position relationship between the form-grinding wheel and a workpiece, as shown in Fig. 6. In this section, one first takes the gear as the workpiece. In Fig. 6, coordinate systems Sw(Xw, Yw, Zw) and Sg(Xg, Yg, Zg) are rigidly attached to the form-grinding wheel and the gear, respectively, the Zg-axis is the rotation axis of the gear, the Zw-axis is the rotation axis of the form-grinding wheel, a is the distance between centers of the grinding wheel and the gear, and \u03c8w is the angle between the Zg-axis and the Zw-axis. The transformation relationship between Sg and Sw can be written as Xw \u00bc a\u2212X g Yw \u00bc \u2212Ygcos\u03c8w\u2212Zgsin\u03c8w Zw \u00bc \u2212Ygcos\u03c8w \u00fe Zgsin\u03c8w 8< : \u00f044\u00de Based on the theory of gearing, a necessary constraint between the normal vector ng(uc, \u03c6g) and the relative velocity vgw is ng uc;\u03c6g \u22c5vgw \u00bc 0 \u00f045\u00de where ng uc;\u03c6g \u00bc nxg nyg nzg 2 4 3 5 \u00bc Lpc \u03c6g sin\u03b1n\u22122acuccos\u03b1n \u2212 cos\u03b1n \u00fe 2acucsin\u03b1n\u00f0 \u00decos\u03b2 cos\u03b1n \u00fe 2acucsin\u03b1n\u00f0 \u00desin\u03b2 2 4 3 5 \u00f046\u00de In the coordinate system Sw, the angular velocity \u03c9 can be written as \u03c9 \u00bc 0 \u2212\u03c9sin\u03c8w \u03c9cos\u03c8w\u00f0 \u00deT \u00f047\u00de The use of Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001293_0954406214543490-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001293_0954406214543490-Figure1-1.png",
        "caption": "Figure 1. The carrier and the planets.",
        "texts": [
            " This paper consists of five parts: the first is a review on the research modeling of the misalignment error on the gear pairs and load sharing of planetary gear set with machining errors. Then, the transmission error of gear pair on every transverse cross section, mesh stiffness of external and internal gear pairs and dynamic and static model of planetary gear set are given in the second section. A numerical method solving contact problem is presented in the third section. The numerical solution is obtained and the analysis on the characteristic of misalignment error of carrier is presented in the fourth section. Conclusions are given in the final section. Figure 1 shows the scheme of the carrier and the planets and a three-dimensional coordinate system wherein the shaft axis of the carrier coincides with the Z-axis. The parameter definitions of misalignment are shown in Figure 2 where OG is the shaft axis of carrier with misalignment. The axis of the carrier is tilting around the point O where O is in the end face of the carrier. Here, it needs to be noted that the point O stays stationary. The deviation of point O is not discussed as it will give rise to change of relative position of sun\u2013planet and ring\u2013planet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.8-1.png",
        "caption": "Fig. 14.8 Geometric construction of pole P and rotation angle \u03d5 from the positions of two points before and after a rotation. P lies on the midnormals of A1A\u2032 1 and of A2A\u2032 2 . Fig. a: The midnormals do not coincide. Fig. b: The midnormals coincide. P lies on the lines A1A2 and A\u2032 1A \u2032 2 . Fig. c: Special case \u03d5 = \u03c0 : P is midpoint of A1A\u2032 1 and of A2A\u2032 2",
        "texts": [
            "25) applied to both points yields two equations for the unknowns p and w : z\u20321 = p+ w(z1 \u2212 p) , z\u20322 = p+ w(z2 \u2212 p) . (14.34) The solutions are w = z\u20322 \u2212 z\u20321 z2 \u2212 z1 , p = 1 1\u2212 w z\u2032i \u2212 w 1\u2212 w zi (i = 1, 2) . (14.35) The rigid-body property |z\u20322 \u2212 z\u20321| = |z2 \u2212 z1| = has the consequence that |w| = 1 . Therefore and with (14.27) the solutions determine the angle \u03d5 14.3 Resultant Displacements. Commutativity Conditions 421 and the pole: w = ei\u03d5 = z\u20322 \u2212 z\u20321 z2 \u2212 z1 , p = 1 2 [ (z\u2032i + zi) + i (z\u2032i \u2212 zi) cot \u03d5 2 ] (i = 1, 2) . (14.36) In Fig. 14.8a these results are interpreted geometrically. The expression for w determines uniquely (except for 2\u03c0) the angle \u03d5 between the dashed lines A1A2 and A\u2032 1A \u2032 2 . The formulas for p express the fact that the pole P is the intersection point of the midnormals of A1A \u2032 1 and A2A \u2032 2 . The angle \u03d5 is the angle at P in the isosceles triangles (A1,P,A \u2032 1) and (A2,P,A \u2032 2) . The triangle (P,A1,A2) fixed in \u03a3 is rotated about P into the position (P,A\u2032 1,A \u2032 2) . In Fig. 14.8b A1A \u2032 1 and A2A \u2032 2 are parallel. In this case, P is the intersection of the lines A1A2 and A\u2032 1A \u2032 2 . In Fig. 14.8c all four points A1 , A\u2032 1 , A2 , A\u2032 2 are collinear. In this case, \u03d5 = \u03c0 , and the pole P is midpoint between A1 and A\u2032 1 and also midpoint between A2 and A\u2032 2 . End of proof. The resultants SC and CS : Both resultants are glide reflections. For both resultants the line of reflection and the translation along this line are constructed geometrically by displacing an isosceles triangle from an initial position 1 via an intermediate position 2 into the final position 3 . This geometrical approach is simpler than the analytical approach by means of complex numbers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000029_s00170-006-0851-5-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000029_s00170-006-0851-5-Figure1-1.png",
        "caption": "Fig. 1 Spatial 3-RPS parallel manipulator",
        "texts": [
            " Unlike serial manipulators, not all the kinematic pairs of a PM are actuated and therefore the presence of passive kinematic pairs is a typical characteristic of these mechanisms. On the other hand, due to a compact topology, PMs are more precise and stiff than their serial counterparts, however suffer from a limited workspace, poor dexterity, and a recurrent problem of the so-called local singularities. These drawbacks have a direct connection with the nominal degrees of freedom assigned to the moving platform, the number of limbs, and the dimensions of the mechanism. A 3-RPS parallel manipulator, see Fig. 1, is a mechanism where the moving platform is connected to the fixed platform by means of three limbs. Each limb is composed by a lower body and an upper body connected each other by means of a prismatic joint. The moving platform is connected at the upper bodies via three distinct spherical joints while the lower bodies are connected to the fixed platform by means of three distinct revolute joints. The prismatic joints are actuated independently providing three degrees of freedom over the moving platform",
            " Furthermore, clearly the limb lengths are restricted to Pi Bi\u00f0 \u00de Pi Bi\u00f0 \u00de \u00bc q2i i 2 1; 2; 3f g: \u00f02\u00de Finally, three compatibility constraints can be obtained as follows P2 P3\u00f0 \u00de P2 P3\u00f0 \u00de \u00bc a223; \u00f03\u00de P1 P3\u00f0 \u00de P1 P3\u00f0 \u00de \u00bc a213; \u00f04\u00de and P1 P2\u00f0 \u00de P1 P2\u00f0 \u00de \u00bc a212: \u00f05\u00de Expressions (1\u20135); form a system of nine equations in nine unknowns given by {X1, Y1, Z1, X2, Y2, Z2, X3, Y3, Z3}. It is worth mentioning that expressions (1) were not considered, in the form derived here, by Tsai [13], and therefore the analysis reported in that contribution requires a particular arrangement of the positions of the revolute joints over the fixed platform accordingly to the reference frame XYZ. Furthermore, clearly expressions (1) are applicable not only to tangential 3-RPS parallel manipulators, like the mechanism of Fig. 1, but also to the socalled concurrent 3-RPS parallel manipulators. 2.2 Analytical form solution In this subsection expressions (1)\u2013(5) are systematically reduced into a non linear system of three equations in three unknowns. Afterwards, a 16th-order polynomial in one unknown is derived using the Sylvester dialytic elimination method. Expressions (1) yields three linear equations given by Xi \u00bc f Zi\u00f0 \u00de i 2 1; 2; 3f g: \u00f06\u00deFig. 2 The geometric scheme of a generic 3-RS structure Afterwards, the substitution of (6) into expressions (2) leads to Y 2 1 \u00bc Pi i 2 1; 2; 3f g; \u00f07\u00de where pi are second-degree polynomials in Zi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002051_tmag.2015.2436913-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002051_tmag.2015.2436913-Figure2-1.png",
        "caption": "Fig. 2. (a) Linear propelling motion of the spiral microrobot controlled by magnetic gradient. (b) Drilling motion of the spiral microrobot controlled by rotating uniform magnetic field.",
        "texts": [
            " In this paper, a navigating and drilling spiral microrobot actuated by a gradient and rotating uniform magnetic field is proposed to navigate through complex human blood vessels and unclog blocked human vessels. The proposed spiral microrobot, as shown in Fig. 1, consists of a cylindrical body that contains a cylindrical magnet and two spiral drilling blades on the shaft. The cylindrical magnet can rotate freely inside the magnet slot of the body and align in any direction by the application of an external uniform magnetic field. Then, several experiments are performed to demonstrate and verify the selective navigating and drilling motions of the prototyped spiral microrobot. Fig. 2(a) shows a linear motion of the spiral microrobot propelled by a magnetic gradient. To move along the x-direction, the magnetization direction of the magnet inside the microrobot has to align along the x-direction by 0018-9464 \u00a9 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. the application of a uniform magnetic field in the x-direction. Then, applying the magnetic gradient generated from MNS causes the spiral microrobot to move in the aligned direction of the magnet. The propulsive magnetic force is proportional to the magnetic moment of the magnet m and the magnetic gradient B as follows: F = \u2212\u2207(m \u00b7 B) (1) where the magnetic gradient is externally applied by the MNS. To perform the drilling motion, the freely rotatable cylindrical magnet of the spiral microrobot has to rotate by the application of a uniform magnetic field along the y-axis, as shown in Fig. 2(b). Then, the uniform magnetic field rotating with respect to the x-axis will generate magnetic torque T, allowing the microrobot to perform drilling motions, as shown in Fig. 2(b). The torque is the product of the magnetic moment of the magnet and the rotating magnetic field as follows: T = m \u00d7 B. (2) From (2), the magnet tends to align in the direction of the applied uniform magnetic field. Fig. 3(a) shows the rotating uniform magnetic field, which can be defined in the following equation [8]: B = B0(cos \u03c9tU + sin \u03c9tN \u00d7 U) (3) where B0, \u03c9, N, and U are the magnitude and angular velocity of the rotating uniform magnetic field, a unit vector of the rotating axis, and a unit vector normal to N, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000448_j.jsv.2008.09.050-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000448_j.jsv.2008.09.050-Figure1-1.png",
        "caption": "Fig. 1. A photograph of the experimental rig showing the drive shaft on the left-hand side and the driven shaft on the right-hand side.",
        "texts": [
            " Then in Section 3 we develop a mathematical model for the relative gear motion which incorporates eccentricity, and which is developed further in Section 4 under simplifying assumptions of high stiffness and high damping which match the experimental set-up. Sections 5 and 6 develop contour plots which relate the disconnection amplitude to the phase and amplitude of the input forcing for theory and experiment, respectively. Fair agreement is found, and Section 7 discusses how modelling the surface finish of the gears could explain the discrepancies. Finally Section 8 presents conclusions and discusses practical consequences for the research. The experimental rig, shown in Fig. 1 (previously described in Ref. [24]), has been designed to capture relative gear trajectories. It consists of a 5.5Nm servomotor, which rotates a 1:1 meshing gear pair. The gears are module 6, 108mm pitch circle diameter, steel spur gears. The centre distance of the gears has been increased by 3.5mm over the standard separation distance to increase the backlash size to 3 10 2 rad, allowing improved sensor resolution. The gears used in this experiment were precision ground to satisfy BS436 Grade 6 (equivalent to ISO 1328-2) standard"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.1-1.png",
        "caption": "Figure 8.1. Momentum and impulse reaction in firing a gun.",
        "texts": [
            " Therefore, in this case,for a system ofparticles subject tofinite externalforces, the instantaneous momentum of the center of mass is constant during the internal impulsive interval. This is shown differently in (7.12) for a system of two particles on which the mutual instantaneous impulsive forces are equal , oppositely directed internal forces . Example 8.1. A gun of mass M fires a shell S of mass m with a muzzle velocity vSG = Vo relative to the gun barrel G, at an elevation angle ex in the ground frame <I> = {F;Ik } in Fig. 8.1. The gun carriage C is mounted on a greased horizontal track. (a) Find the instantaneous recoil velocity VGF of the gun (i.e. the center of mass of the gun assembly ). (b) Compare the magnitude v of the instantaneous, absolute muzzle velocity VSF of the shell in <I> with its relative value Vo . (c) What is the instantaneous impulsive reaction exerted by the track on the gun carriage? 0 306 ChapterS Solution of (a). The gun and shell are modeled as center of mass objects-\"a system of two particles "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure6.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure6.14-1.png",
        "caption": "Fig. 6.14 Hyperbolic mechanism for the generation of a plane",
        "texts": [
            " The hyperbolic paraboloid, too, is a 1-d.o.f. mechanism when all generators are interconnected by spherical joints at every point of intersection. By the same line of arguments it is proved that in every position the mechanism is a hyperbolic paraboloid with the equation depending on the free parameter \u03bb : 2\u2211 i=1 x2 i ai \u2212 \u03bb = x3 (a2 , a3 = const , a2 \u2264 \u03bb \u2264 a3 ) . (6.106) Hyperbolic Mechanism for the Generation of a Plane The minimal system of rods constituting a hyperbolic mechanism consists of five rods (see Fig. 6.14). Two skew rods g and g1 representing generators of regulus 1 are interconnected by three rods of constant lengths (generators of regulus 2). The spherical joints on g and g1 may be placed arbitrarily subject only to the inequality condition P1P2 : P1P3 = Q1Q2 : Q1Q3 (in the case of equality the five lines would be generators of a hyperbolic paraboloid). Every generator of regulus 2 intersects all generators of regulus 1 and exactly one of them at infinity. Hence there exist a single generator of regulus 2 parallel 240 6 Overconstrained Mechanisms to g and a uniquely defined intersection point of this generator with g1 . Let Q be this point. When the 1-d.o.f.-mechanism is moving, each joint Qi is moving on a sphere around Pi (i = 1, 2, 3). Point Q , in particular, is moving on a sphere of infinite radius, i.e., in a plane E normal to g . Let 0 be the point where g intersects E . When E and g are held fixed as is shown in Fig. 6.14, the mechanism has the additional degree of freedom of rotation about g . Hence Q is free to move (in a certain ring-shaped region) in the fixed plane E . This generation of a plane by a mechanism having only spherical joints represents a spatial analog to the generation of a straight line by a Peaucellier inversor (see Sect. 17.13). De la Hire is the author of Theorem 6.2. Mutually orthogonal tangents to an ellipse with semi axes a and b (arbitrary) intersect on the circle of radius \u221a a2 + b2 about the center of the ellipse"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001128_9781118562857.ch1-Figure1.36-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001128_9781118562857.ch1-Figure1.36-1.png",
        "caption": "Figure 1.36. Measurement of track geometry by the triangulation method",
        "texts": [
            " To overcome this limitation, dual-wavelength-based pyrometers are used to measure the melt-pool temperature [HUA 08, SON 11a]. Figure 1.35a shows the schematic arrangement of a temperature measurement setup as the laser beam reaches point a (i.e. at the beginning of the pulse) on the substrate and then reaches point b and c respectively, as shown in Figure 1.35a. When the laser beam passes these points, the average energy deposited at the unit width surface along the scan direction on the substrate increases resulting in an increase in the temperature (see Figure 1.36b). The temperature reaches a maximum when the laser beam is at the shortest distance from point d, i.e. point b. As the laser moved further ahead, the temperature falls due to heat loss due to conduction and convection. In LRM, the melt-pool temperature depends upon laser power, beam size, scan speed and powder feed rate as controllable processing parameters. It also depends on uncontrollable parameters, i.e. surface roughness, the incident angle of the laser beam, etc. [HUA 08]. The effect of these parameters is presented in Table 1.8. 1.8.2.Measurement of track geometry Precise control in track geometry governs the overall shape and size of the laser rapid manufactured component, as the track is an elementary block of the fabrication. Triangulation and image processing based techniques have been tried to estimate the dimension of track geometry. The triangulation technique uses an external line laser source and camera, as presented in Figure 1.36. In this scheme, an external laser is scanned over the molten/solidified track near the molten pool and a reflected laser is collected at the camera. Then, the triangulation algorithm is employed to measure the track geometry. Due to its high temperature, the molten pool is an immense heat source emitting light in the broader range of wavelengths from ultraviolet to infrared. The CCD/CMOS based cameras with neutral density filter (10\u201320% transmission) are generally employed to capture the image of the melt-pool [HER 10, SON 11b, MEH 07, CRA 11]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003214_j.measurement.2020.107897-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003214_j.measurement.2020.107897-Figure7-1.png",
        "caption": "Fig. 7. Schematic of a re",
        "texts": [
            " So far, with the consideration of the planet gears are treated differently, the rotational expressions of the sun gear and the planet carrier to be a tidal period are provided. The motion period under the scenario of identically treated will be introduced in the next. When researchers focus on the signal modeling of the faulty sun gear, planet gears are usually treated identically to highlight the fault symptoms of the sun gear [20,33]. In this regard, suppose that the equipped N planet gears are identical, again take the closet fault-meshing position as the initial position. The schematic illustration of this period is shown in Fig. 7. In Fig. 7, all the assembled planet gears are annotated in the same color to highlight their identities. This motion period of the sun gear\u2019s fault-meshing positions is defined as the time duration or the number of rotations that take for the sun gear\u2019s faulty tooth and an arbitrary planet gear returning to the initial position simultaneously. We name this period as a \u2018relaxed-tidal\u2019 period and will derive the generalized expression in terms of rotation angles aswell. For equally spaced N planet gears, each time that the planet carrier rotates 2p N radians (1N cycles), a planet gear will reach to the initial position exhibited in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003296_j.jsv.2020.115712-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003296_j.jsv.2020.115712-Figure10-1.png",
        "caption": "Fig. 10. Considered different planet gear health scenarios. (a) Healthy; (b) Crack; (c) Tooth broken; (d) Tooth missing.",
        "texts": [],
        "surrounding_texts": [
            "The sideband indicators, namely SER, ISER, SI, LSA, and SLF are calculated based on their expressions and experimental data. The diagnosis accuracies for sun gear and planet gear health scenarios of these indicators are acquired based on the validation scheme in Fig. 7 . The set hyperparameters of SVM, DNN, and XGboost are listed in Table 5 . According to Table 5 , the training and testing accuracy of the indicators via different classification algorithms and experimental data are shown in Figs. 19\u201330 . After applying 10 fold CV of the testing results, the results of three intelligent classification algorithms are shown in Figs. 31 and 32 . In Figs. 31 and 32 , each horizontal line represents the results acquired by SVM, XGBoost, and DNN, respectively; each vertical line represents the results of SER, ISER, SI, LSA, and SLF, respectively; the values in the figure represent diagnosis accuracies. From the above observations, the diagnosis accuracy of the ISER through three classification algorithms are highest than others, which are highlighted with rectangle boxes in Figs. 31 and 32 . The experimental studies are witnessed the ISER outperforms than other sideband related indicators in both sun gear and planet gear fault diagnosis."
        ]
    },
    {
        "image_filename": "designv10_12_0002179_rnc.3608-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002179_rnc.3608-Figure3-1.png",
        "caption": "Figure 3. Experimental two-degree-of-freedom helicopter model [29].",
        "texts": [
            " In the sense of fast compensation for the uncertainties, the new algorithm exhibits the ability of estimating the perturbations with limited information. In other words, it equips the ability of SMC with perturbation estimation without need for further information of very-high-order state. The latter was a fundamental requirement in [11]. In brief, compared with the existing ASMC design (e.g., [9\u201315]), the new design (18) greatly improves the system robustness and maintains a lower overall gain while the sliding mode is built. To validate the effectiveness of the proposed schemes, we consider a 2-DOF helicopter simulator model (Figure 3) actuated with two propellers [29]. The front propeller controls the elevation of the helicopter nose about the pitch axis, and the back propeller controls the side to side motions of the helicopter about the yaw axis [29]. We define Copyright \u00a9 2016 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control (2016) DOI: 10.1002/rnc Jp Cml 2 R D KppVp CKpyVy Bp P mgl cos ml2 sin cos P 2 (37) Jy Cml 2 cos2 R D KypVp CKyyVy By P C 2ml 2 sin cos P P (38) where Vp and Vy are the applied forces, the pitch angle position, the yaw angle position, P and P the pitch and yaw angular velocities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure7-1.png",
        "caption": "Fig. 7.Meshing of pinion and gear.",
        "texts": [
            " 6(c) is larger somewhat than the target value. Therefore, the validity of the formalization of the deviations was confirmed. The tooth surface form of the pinion member that has good performance mating with the existing gear member is considered based on tooth contact analysis. In this case, the tooth surface form of the pinion member is designed and the appropriate amounts of profile modification and crowning are calculated. The pinion and gear members are assembled in a coordinate system Oh-xhyhzh as shown in Fig. 7 in order to analyze the tooth contact pattern and transmission errors of the pinion and gear members. Suppose that \u03d5p and \u03d5g are the rotation angles of the pinion and gear, respectively. The position vectors of the pinion and gear tooth surfaces must coincide and the direction of two unit normals at this position must be also coincide in order to contact the two surfaces. Therefore, the following equations yield [25]: B \u03d5p xp up;\u03c8p \u00bc C \u03d5g xg ug ;\u03c8g B \u03d5p np up;\u03c8p \u00bc C \u03d5g ng ug ;\u03c8g \u00f017\u00de where B and C are the coordinate transformation matrices for the rotation about yh and zh axes, respectively: B \u03d5p \u00bc cos\u03d5p 0 sin\u03d5p 0 1 0 \u2010 sin\u03d5p 0 cos\u03d5p 2 4 3 5 C \u03d5g \u00bc cos\u03d5g \u2010 sin\u03d5g 0 sin\u03d5g cos\u03d5g 0 0 0 1 2 4 3 5: \u00f018\u00de Since |np| = |ng| = 1, Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure2-1.png",
        "caption": "Figure 2 An overhang sliced by the equidistant surface of the original surface",
        "texts": [
            " The conventional path filling strategies are applicable when these slices are flattened onto planes. To realize the five-axis manufacturing, a five-axis algorithm is deduced, making it possible to adjust the orientation of the built piece dynamically.What is more, a curvature-speed-width (CSW) model is introduced to control the width of the bead by coupling the curve curvature with proper travel speed. To fabricate an overhang built on a curved surface by AM, equidistant surfaces of the original surface are generated to slice the overhang (Figure 2). The cylindrical or conical surfaces a can be described with quadric equations, making the calculation of slicing and path planning easier. With these equations, we can deduce the spatial mapping functions. In this section, firstly, we introduce the intersection between the triangle-meshed 3Dmodel and a cylindrical or conical surface; secondly, the path planning method on cylindrical or conical surfaces is presented. To simplify the calculation of slicing, we propose a unit equation for cylindrical and conical surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003464_j.addma.2020.101657-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003464_j.addma.2020.101657-Figure2-1.png",
        "caption": "Fig. 2. (a) ASTM E8 tensile specimen\u2019s geometry and dimensions. (b) ASTM E399-17 CT specimen\u2019s geometry and dimensions.",
        "texts": [
            " 1 along with an illustration of the tensile and compacttension fracture specimens overlaid on the pre-forms. Following the SLM process pre-forms were carefully machined out of the substrate plate and AM material. The pre-forms from the three groups (i.e. hybrid, AM and wrought) were heat-treated following two commonly used stress-release procedures for AM Ti-6Al-4V, namely: 650 \u25e6C for 3 h or 800 \u25e6C for 4 h. Both heat treatments were held and cooled in vacuumed furnace. Finally, the pre-forms were machined into tensile specimens (Fig. 2a, in accordance with ASTM E8) and compacttension (CT) specimen (Fig. 2b, following ASTM E399-17). The tensile specimen\u2019s geometry was selected to comply with the geometrical limitations induced by the plate thickness. Special care was taken while machining the specimens to ensure that the AM-wrought interface is located at: i. The center of the gauge for the tensile specimens. ii. Bellow the notch tip and parallel to the CT specimen\u2019s symmetry plane (designated as \u201cTop\u201d) iii. Directly ahead of the notch tip and along the CT specimen\u2019s symmetry plane (designates \u201cSymmetric\u201d)",
            " Both SEM and computed X-ray tomography of the failed hybrid specimen did not reveal an increased level of porosity at the AM side of the specimen, in line with the strain measurements and the relatively large distance between the necking region and AMwrought interface. The fracture toughness samples were prepared and tested in accordance with the International Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials ASTM E399-17. The choice of sample geometry (Fig. 2b) was somewhat limited due to the geometric restrictions imposed by the wrought plate dimensions and CT25 specimens were extracted from the In-plane direction of the plate. Similar to the testing plan in Section 3.2, the wrought and AM materials were tested for both heat treatments, as to set a baseline for the measurements of the hybrid material. The test groups and number of specimens within each are summarized in Table 3. While the tensile properties of the wrought material were found to be only weakly sensitive to the choice of heat treatment, the fracture toughness was observed to vary by close to 10% between the two heat treatments, making the 650 \u25e6C/3 h favorable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003254_s11431-020-1588-5-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003254_s11431-020-1588-5-Figure2-1.png",
        "caption": "Figure 2 (Color online) Leg structure (a) and hip coordinate system definitions (b).",
        "texts": [
            " Therefore, we design the waist mechanism to realize the robot turn. The waist mechanism consists of the waist motor and screw (see Figure 1), which connects the upper body and lower body of the robot. The legs 1, 3, 5 are fixed on the upper body, and legs 2, 4, 6 are fixed on the lower body. When changing the lengths of screw, the angle between the upper and lower body is changed. So that the Hexa-XIII robot can change locomotion direction and realize turning. The leg structure and coordinate system are illustrated in Figure 2. Two motors are fixed on the hip. Therefore, the inertia of moving parts of the leg is reduced. The leg components are illustrated in Figure 2(a). Figure 2(b) shows the kinematic definitions of the leg kinematics. The HCS is located at the center of the hip motor axis and knee motor axis. lAB denotes the length of the upper linkage and lBE denotes the length of the lower linkage. The hip motor drives the rotation of the thigh, corresponding rotation angle named \u03b8t, and \u03b8s denotes the rotation angle of the shin. x y zP =( , , )H f T is the toe vector in HCS, and ( )q = , t s denotes the vector of the input joint\u2019s angle. The expressions of leg kinematics are derived as follows: In the plane xoy of HCS, the angle \u03c8 of the vector lAE is derived by eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001196_j.triboint.2013.06.016-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001196_j.triboint.2013.06.016-Figure2-1.png",
        "caption": "Fig. 2. Bearing house with heaters.",
        "texts": [
            " When assembled in the modified Four-Ball machine the rolling bearing assembly is submitted to a continuous air flow, forced by two 38 mm diameter fans running at 2000 rpm, cooling the chamber surrounding the bearing house. The rolling bearing is lubricated by an oil volume of 14 ml. This volume was selected so that the oil level reaches the centre of the roller, such as advised by the manufacturer. The rotational speeds were chosen considering the available range of our machine and also the rotational speeds usually used in the wind turbines. For example, the low speed planetary shaft is about 1 m/s and the high speed shaft is about 6.5 m/s. The heater (Fig. 2) is used to increase and maintain a constant operating temperature at a desired value (80 1C for the study case). The thermocouple (III) is used to control the oil operating temperature, because the heater control system is a PID with feedback. A detailed presentation of the test procedure can be found in [25]. The machine was started at the desirable speed and ran until it reached a constant operating temperature (80 1C), induced by the heaters. Under these conditions, four friction torque measurements were performed: three values are stored and the most dispersed one was disregarded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002831_ec-08-2018-0364-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002831_ec-08-2018-0364-Figure5-1.png",
        "caption": "Figure 5. Finite element methodmodel of the harmonic drive",
        "texts": [
            ", 2011). The contact pair of FS and outer ring is also set as frictional type to simulate the effect ofWG on FS. In the internal of WG, there is a slide between balls and outer ring, so their contact pairs are set as frictional type, while the other contact pairs are set as bonded, which have no effect on the analysis of FS. And they are just used to ensure the positions of the balls and to avoid rigid body displacement. The geometric models are meshed to generate elements and nodes as shown in Figure 5. The FS is divided into cylinder and gear rim. The cylinder is meshed in the style of sweep, and refined mesh is used on the gear teeth as shown in Figure 5(c). The inner and outer rings of the bearing are meshed by sweep. The balls are meshed by freedom. These elements are chosen as first-order-type brick elements SOLID185. The CS is considered as rigid, and it is modeled with a mass element MASS21 in ANSYS. The contact elements CONTA174 and TARGE170 are placed on the surfaces which are set on the contact pairs. As shown in Figure 5(b), the contact elements of CS are generated by Mapped Face Meshing, so that the element size is the same as the tooth surface of FS. There are totally 431,689 elements and 493,882 nodes in the FEMmodel of the HD. In the structural analysis of the HD, boundary conditions are defined as Figure 6. Fixed Support is set on the face of input hole of cam. Remote Displacement is set on the outer surface of CS, and all six degrees of freedom (DOF) are set as zero to constrain the displacements of CS. The load of the harmonic reducer is torque, which is applied in the form of moment on the output hole surface of FS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002991_s0263574719001620-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002991_s0263574719001620-Figure3-1.png",
        "caption": "Fig. 3. Representation of submechanism m2.",
        "texts": [],
        "surrounding_texts": [
            "Moreover, fuzzy SMC has used the dubious neuron and neural network for solving the optimization problems. Thus the proposed model has attained the optimal point that converges fast with the adopted control strategy.\nIn 2015, Fang et al.5 controlled the single-phase active power filter (APF) using the model reference adaptive sliding mode (MRASMC) based on neural network and radial basis function (RBF). The symphonic current in APF system was removed by combing the adaptive control technique with the neural network. This model has attained the asymptotic stability of the system by tuning the weight of the neural network online. Finally, the proposed model has provided better performance by enhancing the performance of DC side voltage in the case of tracking.\nWith the best performance in the thermal regulation of the quick thermal processing (RTP) system, the SMC can control the uncertainties of the system. In 2016, Xiao et al.6 used the assertive modes to design the RTP system by SMC. Here, the parabolic partial differential equation was used to formulate the temperature dynamics of the system. Further, the dominant modes of the system were extracted by the eigenfunctions, which in turn have determined the assertive dynamics of the system. Subsequently, Galerkin\u2019s method was adopted to frame the diminished model of the dominant modes. Later, the compensation of the nonlinear uncertainty of SMC was achieved by the nonlinear finitedimensional reduced model.\nIn 2016, Zhang et al.7 used the mismatched and matched disturbances to search the disturbance rejection control problem for Markovian jump linear systems (MJLSs). Concurrently, current state and the disturbances were authorized by the continuous and discontinuous extended SMC. Hence the existing disturbances were effectively denied by the design of composite controllers.\n1.1.2. Review. The methods such as composite controllers and probabilistic models fall off in computational efficiency and capricious problem domains. Thus, methods based on intelligent schemes include fuzzy sets and neural networks, that provide good performance for SMC on the robotic system,1 process control millng head reference,37 etc. is attained by the neural network, on comparing diverse, intelligent controllers. In fact, the primary benefit of the neural network is learning with the lack of prior knowledge, integrity and achievable for real-time systems. However, it suffers from some issues such as reduced probability of adapting precise weight functions, regularization problem, and model gap between the problem space and characteristics of the system. Moreover, those problems are highly proportional to each other. The learning knowledge of the network is enhanced by adapting the weight functions. Since the accessible updating model in ref. [1] was a function of derivation, it cannot be improved substantially. As a result, it generates the incremented margin among the actual data of the system and function of the sliding mode, the third problem as described earlier. Therefore, the margin can be reduced by the weight functions and leads to accurate prediction. However, the problem of overfitting requires a suitable regularization function. Thus the improvement is mainly needed for contributions to the conventional neural networks for facilitating the sliding mode function and tuning of design variables.1 However, the reported literature does not show the contributions on precise selection of such design variables. In addition, the neural network-based SMC still needs additional improvements in terms of current system models, though it outperforms the SMC.\nThe locomotion pattern of inchworm robot is constructed per Fig. 1, to derive the dynamic relations. This pattern comprises a sequence of connected joints that take the forward locomotion. According to the locomotion of the robot, the distance crossed by the robot per complete cycle can be determined using Eq. (1), where \u03c8 indicates the gait angle of the robot and L indicates the length of the arm. The architecture model is illustrated in Fig. 4.\nD = 2L (1 \u2212 cos\u03c8) (1)\nSubsequently, the categorized submechanisms associated with the motion pattern are denoted as m1,m2,m3, and m4, where the representations of m1 and m2 are shown in Figs. 2 and 3, respectively. One or more links remain static in the submechanism (which are marked in blue color in Fig. 1)\nhttps://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574719001620 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 18 Nov 2019 at 20:24:57, subject to the Cambridge Core terms of use, available at",
            "due to sufficient friction acting on the links. The remaining submechanisms such as m3 and m4 are defined based on contrary trajectory orientation. A local coordinate system is used to map the angles associated with these models. As the entire submechanisms are solved, the angles are transformed into a global coordinate system.\nEq. (2) depicts the geometries\u2019 constraint of the system, where \u03d5m represents the angle of the mth link due to the positive direction of the horizontal axes \u03c6m = \u03c6m\u22121 + \u03b8m, n refers to the number of joints and \u03b8m indicates the joint angles, respectively.\nn\u2211 m=1 sin \u03d5m = 0 (2)\nhttps://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574719001620 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 18 Nov 2019 at 20:24:57, subject to the Cambridge Core terms of use, available at",
            "This section obtains the dynamic equation of the submechanism m1. The manipulator is considered to act in the vertical plane x \u2212 y as shown in Figs. 2 and 3. The velocity and position of the origin of the mth link are denoted as Vi and Pi. According to ref. [1], the velocity centroid of the ith link is represented in Eq. (3), and its square is represented in Eq. (4), where, \u03c6\u0307i denotes the derivative form of \u03c6i and Lm indicates the length of the mth link; definitions of Cmn and Smn are given in Eq. (5a) and (b).\nV\u0302i = Vi + Li 2 \u03c6\u0307i (\u2212 sin \u03c6im\u0302 + cos \u03c6in\u0302 ) (3)\nV\u03022 i = L2 p\n4 \u03c6\u03072\ni + i\u2211\nm=1 i\u22121\u2211 n=1 LmLn\u03c6\u0307m\u03c6\u0307nCmn (4)\nCmn = cos (\u03c6m \u2212 \u03c6n) (5a)\nSmn = sin (\u03c6m \u2212 \u03c6n) (5b)\nMoreover, Eq. (6) depicts the height of the ith link.\nH\u0302i = Pi+1.n\u0302 \u2212 1\n2 Li sin \u03c6i = i\u2211 n=1 (Ln sin \u03c6n)\u2212 Li 2 sin \u03c6i (6)\nThe total kinetic energy is expressed in Eq. (7) followed by Eq. (8), where Ii specifies the moment of inertia and mi indicates the mass of the ith link, respectively.\nKe = 1\n2 3\u2211 i=1 ( miV\u0302 2 i + Ii\u03c6 2 i ) (7)\nKe = 1\n24 mL2\n( 28\u03c6\u03072\n1 + 16\u03c6\u03072 2 + 4\u03c6\u03072 3 + 36\u03c6\u03071\u03c6\u03072c12 + 12\u03c6\u03072\u03c6\u03073c23 + 12\u03c6\u03073\u03c6\u03071c31 )\n(8)\nIn addition, Eq. (9) provides the total gravitational potential energy.\nGe = 3\u2211\ni=1\nmigH\u0302i (9)\nGe = 1\n2 mgL (5 sin \u03c61 + 3 sin \u03c62 + sin \u03c61) (10)\nAs per the model of Coulomb friction, Eq. (13) defines the virtual works associated with the applications of entire non-consecutive forces in the system. Here, \u03c4\u0307 indicates the joint torques applied to the link, Ri indicates the non-consecutive forces, and Ff specifies the frictional forces exerted on the edge of the link. Moreover, \u03c7i = Li ( cos \u03c6i + \u03bc\u0302 sin \u03c6i ) , \u03bc\u0302=\u03bcsgn (et.\u03bdt), and \u03c1 denotes the Kronecker delta factor.\n\u2202w = \u03c4\u0307 .\u2202\u03b8 + ( Ff m\u0302 + Mn\u0302 ) .\u2202Pi+1 (11)\n\u2202w = 3\u2211\ni=1\n\u03c4\u0307i\u03c1 (\u03c6i \u2212 \u03c6i\u22121)+ M ( \u03bc\u0302\n3\u2211 i=1 Li sin \u03c6i\u03c1\u03c6i + 3\u2211 i=1 Li cos \u03c6i\u03c1\u03c6i\n) (12)\n\u2202w = 3\u2211\ni=1\n(\u03c4\u0307i \u2212 \u03c4\u0307i\u22121 + \u03c7iM) \u03c1\u03c6i = 3\u2211\ni=1\nRi\u03c1\u03c6i (13)\nThe relationship of the Euler and Lagrange contributes the equation of motion that is represented in Eq. (14).\nRj = d\ndt\n( \u2202Ke\n\u2202\u03c6\u0307j\n) \u2212 \u2202Ke\n\u2202\u03c6j + \u2202Ge \u2202\u03c6\u0307j (14)\nhttps://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574719001620 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 18 Nov 2019 at 20:24:57, subject to the Cambridge Core terms of use, available at"
        ]
    },
    {
        "image_filename": "designv10_12_0002714_s1560354715030016-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002714_s1560354715030016-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " With this choice of variables, Eqs. (3.1) take the following form: x\u03071 = x1(Ax1 + Bx2), x\u03072 = x1(Cx1 + Dx2). (3.7) Rescaling time as d\u03c4 = x1dt reduces the system to a linear system. The trajectories of the linear system x \u2032 1 = Ax1 + Bx2, x \u2032 2 = Cx1 + Dx2, (3.8) obviously consist of the trajectories of the original system. It is only that the direction of motion in the original system depends also on the sign of the variable x1. As an example, consider the linear system (3.8) with the equilibrium in the form of a stable node (Fig. 1a). Figure 1b shows a phase portrait of the original nonlinear system (3.7). In contrast to the linear system, the trivial equilibrium of the nonlinear system is unstable. It is worth emphasizing that the change of stability does not always occur during the transition from a linear to a nonlinear system. REGULAR AND CHAOTIC DYNAMICS Vol. 20 No. 3 2015 Theorem 5. Let p = 2 and suppose that the system (3.1) admits a first integral F in nondegenerate quadratic form. Then the system has an entire straight line of equilibrium points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001307_iet-epa.2012.0342-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001307_iet-epa.2012.0342-Figure2-1.png",
        "caption": "Fig. 2 Auxiliary models needed for air-gap function identification",
        "texts": [
            " For this purpose, a very simple FEM has been used but the plot can also be obtained using conformal mapping, curvilinear squares and a number of other approaches. In this paper, a three-phase four-pole salient-pole synchronous machine, the parameters of which are given in the Appendix, will be used for study of the proposed method. This machine has 36 stator slots with 3 slots per pole per phase. To separate the effect of stator slot openings, the numerical gap function for this machine can be obtained in two steps. Step 1: As shown in Fig. 2a, the stator slots are neglected and a one turn coil carrying 1 A is assumed as an excitation current on the rotor. For this configuration, the MMF in the air gap can be obtained from winding function approach. Also from FEA, the flux lines in the air gap can be obtained and is shown in Fig. 2a. Now, using (19), the effective gap function can be determined for this configuration. Fig. 3 shows the resulted air gap function for one pole of machine under study. Step 2: To find the stator slot opening effect on the gap function, in this step, as shown in Fig. 2b, rotor saliency is 393 & The Institution of Engineering and Technology 2013 a Model for step 1 b Model for step 2 neglected and a round rotor is considered instead of a salient case. A one turn coil carrying 1 A is assumed as an excitation source on the stator. The MMF in the air gap can be obtained from the winding function approach for this configuration. From FEA, the flux lines in the air gap can be determined. Now, using (19), the numerical gap function can be determined for this configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure13-1.png",
        "caption": "Fig. 13. Elliptical contact on a ring.",
        "texts": [
            " The electrical conductance between two contact surfaces Si and Sj (contact surfaces at contact points i and j respectively) located on the surface of a homogeneous spherical particle k is given by: Ck i j \u00bc 1 Rk i j \u00bc \u03b3SiS j 2Vb 1\u2212cos\u03b8\u00f0 \u00de \u00f020\u00de where \u03b3 is the electrical conductivity of steel (\u03b3=5.8 \u00d7 107S.m\u22121), Vb is the volume of a rolling component, \u03b8 is the angle formed by the points i and j. \u03b8 is equal to \u03c0 for a radial ball bearing. The coupling between the mechanical and electrical computation is calculated by Hertz's theory. The components of the cage are insulating, therefore only the rolling components are involved in current transfer. In the ball bearing context, the ball\u2013race contact surface is elliptical as shown in Fig. 13. The exact solution for the ellipsoid radii is quite complex. Hamrock and Brewe [29] suggested an approximate solution, based on elliptical integrals. Each elliptical contact area is characterized by its semi-major axis a and its semi minor axis b. The ellipticity parameter k \u00bc b a is given by the following approximation: k\u2248 \u03b12=\u03c0 \u00f021\u00de \u03b1= \u03b1inn or \u03b1out according to the ball/ring contact type, given in Section 2. A dimensionless variable \u03c7\u2248 1\u00fe q \u03b1, with q \u00bc \u03c0 2\u22121 is used to approximate the solution of the ellipsoid radii"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.22-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.22-1.png",
        "caption": "Fig. 15.22 Four-bar of Fig. 15.19 with inflection circle, cubic of stationary curvature, directrix, asymptote, focus \u03a6 , cardinal point H and Ball\u2019s point U of the coupler",
        "texts": [
            "107) From these equations it follows that P1 lies halfway between the asymptote and the line parallel to the asymptote and passing through \u03a6 . Example: The coupler of the four-bar mechanism shown in Fig. 15.19 is considered again. The points Q1 and Q2 are both vertices because every point of a circular trajectory is a vertex. Hence the x, y-coordinates of these points determine the parameters \u03bb and \u03bc , the cubic of stationary curvature, its asymptote, the normal pole P3 , the radii of curvature of the centrodes and the points H and \u03a6 of the coupler in the instantaneous position shown. In Fig. 15.22 the cubic of stationary curvature, its asymptote and the points H and \u03a6 are shown together with various other lines and points which are explained later. End of example. Directrix of the Cubic of Stationary Curvature In Fig. 15.23 the x, y-system with origin P1 is the same as in previous figures. Let Q\u0302 be an arbitrary point (not yet confined to the straight line referred to as directrix). The diagonal in the rectangle defined by the axes and by the lines parallel to the axes and the perpendicular from the origin onto this diagonal define the point Q ",
            " From Eqs.(15.107) for the coordinates of H and \u03a6 it follows that the line P1H is parallel to the directrix and that, furthermore, \u03a6 is the midpoint of the perpendicular from the origin P1 onto the directrix. Equations (15.109) map H and \u03a6 into points H\u0302 and \u03a6\u0302 , respectively, on the directrix. These points have the coordinates x\u0302H = \u2212\u03bc \u03bb2 \u2212 \u03bc2 , y\u0302H = \u03bb \u03bb2 \u2212 \u03bc2 , x\u0302\u03a6 = 1 2\u03bc , y\u0302\u03a6 = 1 2\u03bb . (15.112) Point \u03a6\u0302 is the midpoint between the points of intersection of the directrix with the x- and y-axes. In Fig. 15.22 \u03a6\u0302 and lines for the construction of Q\u03021 and Q\u03022 from Q1 and Q2 , respectively, according to Fig. 15.23 are shown. 492 15 Plane Motion The cubic of stationary curvature intersects the inflection circle at the pole P1 and at one more point. This point is called Ball\u2019s point, denoted U . The trajectory of the point of \u03a32 coinciding with U has at this point not only zero curvature, but also zero rate of change of curvature. It is, therefore, a good straight-line approximation of its tangent UP2 . The coordinates of U are determined as follows",
            "104) the coordinates are expressed in terms of y2 , \u03bb and \u03bc : xU = y2 \u03bcy2(1\u2212 \u03bby2) (1\u2212 \u03bby2)2 + \u03bc2y22 , yU = y2 (1\u2212 \u03bby2) 2 (1\u2212 \u03bby2)2 + \u03bc2y22 . (15.115) With the expressions (15.114) Eqs.(15.109) determine the coordinates of the associated point U\u0302 on the directrix. It turns out that y\u0302U = y2 . This means that U\u0302 is the point of intersection of the directrix with the tangent to the inflection circle at the pole P2 . From this point U\u0302 Ball\u2019s point U can be constructed following the rules of Fig. 15.23. In Fig. 15.22 U\u0302 and U and the geometrical construction are shown. Remark: That the asymptote intersects the x-axis at the point x = xU\u0302 is a peculiarity of this example. Normally, this is not the case. At the beginning it was said that the trajectory of the point of \u03a32 coinciding with Ball\u2019s point U is a good straight-line approximation of its tangent UP2 . In engineering, straight-line approximations are required for many purposes. So-called level-luffing jib cranes, for example, are large-size four-bars maneuvering the load-lifting hook"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002392_0954406215616835-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002392_0954406215616835-Figure2-1.png",
        "caption": "Figure 2. Blades and generating cones for gear generating tool: (a) generating tool cones for concave side and (b) gen-",
        "texts": [
            " As shown in Figure 1, the cutting edge of headcutter blade is divided into four sections as the edge, toprem, profile, and flankrem. The cutting surfaces of at UNIV OF VIRGINIA on June 5, 2016pic.sagepub.comDownloaded from the head-cutter are generated by rotation of the blade about the Zt-axis, the rotation angle is g. Most of the generating of gear tooth surface is done by the profile section that is a straight line with the profile angle g. The fillet of the gear tooth surface is generated by the edge section with corner radius w. As shown in Figure 2, an arbitrary point Mb on the cutting surface of blade is determined by ug and g. The generating surface t about the profile section of the head-cutter blade is represented by vector function rt(ug, g) as rt\u00f0ug, g\u00de \u00bc \u00f0rG ug sin g\u00de cos g \u00f0rG ug sin g\u00de sin g ug cos g 2 64 3 75 \u00f01\u00de where rG is the head-cutter point radius, g is the blade angle, and ug and g are tooth surface parameters. The upper signs in equation (1) correspond to generation of concave side of the gear tooth surface, while the lower signs correspond to convex side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003024_s00202-020-00955-2-Figure24-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003024_s00202-020-00955-2-Figure24-1.png",
        "caption": "Fig. 24 Flux density in LSPMSM with maximum CPQI",
        "texts": [
            " The mechanical loss of the motor is 44 W which is identified from the reduced voltage test. Figure 23 illustrates the magnetic flux density in stator teeth of LSPMSM under pure sine waveform. The flux density in the motor should not exceed the prescribed limit; else saturation would occur in the core, so that it can reduce efficiency, power factor and overload capacity of the motor. It is observed that flux density in teeth without CPQI is around 1.35 Tesla. And for the maximum CPQI, flux density is increased to 1.4 Tesla in middle of the teeth. Figure 24 shows there is a slight saturation in the tip around 1.8 Tesla under the maximum CPQI. The saturation would also produce current harmonics that can increase voltage harmonics in the power system. So, the consideration of CPQI for magnetic circuit design is essential to avoid saturation in the teeth of the motor. LSPMSM and SCIM are designed to operate with pure sinusoidal supply voltage in industry. In practice, the input supply is distorted and fluctuating in industry due to sophisticated power electronic circuit and dynamic load variations in the power system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001353_j.neucom.2014.04.023-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001353_j.neucom.2014.04.023-Figure4-1.png",
        "caption": "Fig. 4. A schematic diagram of a symmetric gyroscope.",
        "texts": [
            " Finally, the proposed RABC fully tuned with adaptation laws is employed to control this system, and the simulated results are shown in Fig. 7. The tracking errors e1\u00f0t\u00deand e2\u00f0t\u00de for the three control methods are depicted in Fig. 8(a) and (b), respectively. As can be seen, the tracking errors of the proposed RABC fully tuned with adaptation laws are smaller than those of the RABC partially tuned with adaptation laws and the control results obtained using the WARC control method. 5.2. Gyros synchronization control system The mathematical model of a chaotic gyro system is obtained from [29], and is shown in Fig. 4. The dynamic Eq. (56) can be written Please cite this article as: C.-M. Lin, et al., Robust adaptive backstepping control for a class of nonlinear systems using recurrent wavelet neural network, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.04.023i as \u20acxd\u00f0t\u00de \u00bc \u03b1d\u00f0xd\u00f0t\u00de\u00de, also known as the master gyro system, where \u20ac\u03b8d\u00f0t\u00de\u00fe\u03b32d \u00f01 cos \u03b8d\u00f0t\u00de\u00de2 sin 3\u03b8d\u00f0t\u00de \u03b2d sin \u03b8d\u00f0t\u00de\u00fec1 _\u03b8d\u00f0t\u00de\u00fec2 _\u03b8 3 d\u00f0t\u00de \u00bc f sin \u03d6t sin \u03b8d\u00f0t\u00de \u00f056\u00de where f sin \u03d6t represents a parametric excitation, \u03b32d\u00f01 cos \u03b8d\u00f0t\u00de\u00de2= sin 3\u03b8d\u00f0t\u00de \u03b2d sin \u03b8d\u00f0t\u00de denotes a nonlinear resilience force, c1 _\u03b8d\u00f0t\u00de and c2 _\u03b8 3 d\u00f0t\u00deare linear and nonlinear damping terms, respectively [28]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001136_1.4005462-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001136_1.4005462-Figure3-1.png",
        "caption": "Fig. 3 Inverted pendulum parameters. A body with mass and inertia is held up by a massless rigid leg and disc-shaped foot. The ring is always touching the ground. Note that ~F is caused by contact and frictional forces while ~sR and ~sF are due to rolling resistance and spin friction, respectively.",
        "texts": [
            " \u20acb \u00bc _a cam\u00f0J1 \u00fe J2\u00de _b\u00fe amJ2\u00f0c cos\u00f0a\u00de a sin\u00f0a\u00de\u00de _h J1J2 \u00fe m\u00f0J2a2 \u00fe J1c2\u00de \u00fe Lb (1) \u20aca \u00bc _h2 cam\u00f01 cos2 a\u00de \u00fe \u00f0mc2 \u00fe 2J2\u00de sin a cos a\u00f0 \u00de m\u00f0a2 \u00fe c2\u00de \u00fe J2 \u00fe _h _b \u00f0ma2 \u00fe J1 \u00fe J2\u00de sin a\u00fe cam cos a m\u00f0a2 \u00fe c2\u00de \u00fe J2 \u00fe mg\u00f0c sin a a cos a\u00de m\u00f0a2 \u00fe c2\u00de \u00fe J2 \u00fe La (2) \u20ach \u00bc _a _h \u00f03J1J2 \u00fe 3J2ma2 \u00fe 2c2mJ1\u00de cos a\u00fe cmaJ1 sin a\u00f0 \u00de J1J2 \u00fe J2ma2 \u00fe c2mJ1\u00f0 \u00de sin a _a _b J1J2 \u00fe ma2\u00f0J1 \u00fe J2\u00de \u00fe J2 1 J1J2 \u00fe J2ma2 \u00fe c2mJ1\u00f0 \u00de sin a \u00fe Lh (3) Parameters c and a are the height of the pendulum and radius of the contact ring, respectively (Fig. 3). The pendulum has mass m and a diagonal inertia matrix with scalar entries J1 and J2 (Fig. 3). This simplified inertia matrix has been chosen to keep the size of the equations small enough to print, though the analysis that follows has been tested on a generic symbolic inertia matrix. Rolling resistance and spin friction terms are expressed in Eqs. (1), (2), and (3) as Lb, La, and Lh for brevity. The equations of motion of the 2D model of Wight et al. is embedded in the Euler pendulum equations presented above. The model equations of Wight et al. can be found by projecting the above model onto the X\u0302 Z\u0302 plane",
            " d2~rq dt2 \u00bc a\u20aca\u00fe \u00f0a _b\u00fe c _h sin a\u00de _h sin a\u00fe _a2c a\u20acb\u00fe c\u20ach sin a\u00fe 2c _h _a cos a\u00fe a _a _h sin a \u20acac\u00fe a _a2 \u00f0a _b\u00fe c _h sin a\u00de\u00f0 _h cos a\u00de 8< : 9= ; (A13) Expressions for the translational (of the COM, located at point q) and angular acceleration of the Euler pendulum in the 1\u0302 2\u0302 3\u0302 frame can be calculated by taking time derivatives of angular momentum (~Lq about the COM point q) and combining it with Eq. (A13). ~Lq \u00bc J\u00bd ~x (A14) d~Lq dt \u00bc J\u00bd _~x\u00fe ~x123 ~Lq (A15) The size of the expression for d~Lq=dt can be greatly reduced if [J] is allowed to be symmetrical about the 1\u0302 axis. For the purposes of this analysis, it is assumed that the inertia matrix has an axis of symmetry about the 1\u0302 axis (as Fig. 3 suggests). The equations of motion can now be found by examining the dynamics of the Euler pendulum. The only forces and torques acting on the inverted pendulum are due to gravity mg z\u0302, contact forces ~F, rolling resistance torque~sR, and spin friction torque~sF. m d2~rq dt2 \u00bc ~F mgz\u0302 (A16) The angular momentum equations are also quite similar to those of an Euler disk [27] with the addition of sR, a rolling resistance term, and sF, a spinning friction term, d~Lq dt \u00bc c1\u0302\u00fe a3\u0302 ~F\u00fe sRx\u0302T \u00fe sFx\u0302N (A17) The unknown contact force ~F can be eliminated using Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001795_1.a33288-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001795_1.a33288-Figure2-1.png",
        "caption": "Fig. 2 Coordinate frames.",
        "texts": [
            " Lemma1:Consider the scheme in Fig. 1, and assumeZ2 is a strictly passive system; if Z1 and Z3 are passive blocks, then r \u2208 L2. Lemma 2: The inequality 0 \u2264 jxj \u2212 x tanh \u03bbx \u2264 \u03f5\u2215\u03bb holds for any \u03bb > 0 and x \u2208 R, where \u03f5 is a constant that satisfies \u03f5 e\u2212 \u03f5 1 (i.e., \u03f5 0.2785). In this section, the relevant coordinate frames are first defined, then a 6-DOF relative translational and relative rotational mechanical model between target and pursuer is formulated. Four coordinate systems are defined as shown in Fig. 2 to describe the dynamics equations of spacecraft orbit and attitude motions. This frame, denotedF i, has its origin iO located in the center of the Earth. Its iz axis is directed along the rotation axis of the Earth toward the celestial North Pole, the ix axis is directed toward the vernal D ow nl oa de d by U N IV O F C A L IF O R N IA S A N D IE G O o n D ec em be r 28 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .A 33 28 8 equinox, and finally the direction of the iy axis completes a righthanded orthogonal frame",
            " (13), the initial tracking errors are e 0 _e 0 0 from Eq. (15), thus z 0 0 from Eq. (17). This means v 0 0 according to Eq. (26). From Eq. (28), we can conclude that v t \u2261 0. This implies that z t \u2261 0. From the definition of z t in Eq. (17) and z t \u2261 0, we know _e \u2261 \u2212\u039be, and the solution is e t \u2261 e\u2212\u039bte 0 . In view of e 0 0, we have e t \u2261 0 and _e t \u2261 0. Remark 3: Every term in Eqs. (18) and (24) has its accurate means; the PD feedback control term Kz is used to guarantee the strict passivity of Z2 in Fig. 2. Actually, following definition 4, except for the PD controller, any other controller that renders the transform function between z and e is strictly proper and exponential stable is also appropriate. uR is an adaptive variable structure term to suppress the influence of parametric uncertainties and unexpected disturbances. Remark 4: It is worthwhile to mention that the transient response performance of the relative motion tracking is mainly determined by desired trajectory qd in Eq. (13), and the steady-state performance and control effort are mainly determined by the feedback gain matrices K and \u039b in the proposed controller [Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001654_s00170-017-1048-9-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001654_s00170-017-1048-9-Figure9-1.png",
        "caption": "Fig. 9 Interaction of feed rate and tool path on average roughness (a, b) and mean roughness depth (c, d) using ANN and Poisson statistical analyses",
        "texts": [
            "With regards to the high brittle nature of SLM for as-built parts and low elastic modulus of Ti, cutter marks were observed in samples with higher feed rate and surface quality reduces [39, 41]. In other words, by increasing the feed rate, both static deflection and dynamic displacement increase and consequently surface roughness increases. This is confirmed by ANN and Poisson regression models. According to Figs. 9, 10, 11, 12, 13 and 14, the best surfaces were obtained on the lower feed rate in agreement with the literature [21, 26, 42]. Figure 9 shows how surface roughness changes with feed and tool path. A single colour in this plot corresponds to surface roughness value, and we used this representation in all subsequent figures. When using the helical tool path, the cutting edge is in position 1 (Fig. 10a, d) and machining in this cutting area has the highest efficiency because of sharp edges and the existence of the radial rake angle. Also, at point 1, the lag angle has the highest value and the immersion angle is very small, so the numerator and the second term of Eq",
            " In this position, the radial rake angle is zero and the wedge angle increases and chips are cut by non-sharp edges. Also, the lag angle is close to zero and the immersion angle has the highest value so the dynamic of the metal cutting process is similar to turning (single point/continues cutting), and based on Eqs. 16 and 29, an increase in cutting force is observed. By taking into account the low elastic modulus for titanium and high springback effect, the values of vibration and surface roughness increase. Figure 9a\u2013d shows that rougher surfaces were obtained when using the helical tool path [39, 41, 43\u201345]. Figure 10 also shows that using the linear tool path results in better surface quality associated with the movement of a cutting point on the cutter. Figure 11 shows that the surface roughness decreases by increasing the spindle speed, and this trend is proved by using both ANN and Poisson regression methods. In the machining of titanium, thermal softening initiation occurs in the range of 300\u2013500 \u00b0C. Also, titanium has high tendency to react with most of the cutting tools and this phenomenon leads to losing sharp edges, and the cutting area is moved toward the second position (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.79-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.79-1.png",
        "caption": "Fig. 2.79 Classical M-M transmission arrangement with the power-splitting inter-axle (IA) M-M differential for the M-M DBW 4WD propulsion mechatronic control system [Star - Truck Factory Starachowice, PL; FIJALKOWSKI 1985B].",
        "texts": [
            " As soon as the driver continues to drive the vehicle on solid ground, on the other hand, the driver must remember to unlock the hubs. Should the rear wheels lose traction, on the other hand, and therefore have a tendency to turn further than the front ones, the drive may automatically be transmitted to the front wheels, even if they are in the freewheeling \u2018modus operandi\u2019. A similar, classical M-M transmission arrangement with a power-splitting IA M-M differential for the M-M DBW 4WD propulsion mechatronic control system is shown in Figure 2.79 [FIJALKOWSKI 1985B]. Automotive Mechatronics 236 Along with the high-tech found in modern automotive vehicles comes a sophisticated three-mode M-M DBW 4WD propulsion mechatronic control system, as shown in Figure 2.80 [NISSAN 2002B]. This system has been developed to allow secure and relaxed driving under virtually all circumstances, with automotive mechatronics ensuring that optimum drive is instantaneously delivered to each wheel [NISSAN 2002B]. [Nissan \u2018s- X-Trial; NISSAN 2002B]. Where automatic 4WD is used, this is often applied by means of allmechanically based systems that require one pair of wheels to slip in order to bring in the other pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000877_j.jmatprotec.2012.06.011-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000877_j.jmatprotec.2012.06.011-Figure1-1.png",
        "caption": "Fig. 1. Coaxial (left) and off",
        "texts": [
            " The one step process aims on transporting the cladding material by a carrier gas. Among one step processes two possibilities of cladding are available based on the nozzle configuration. As shown by Seefeld et al. (2008) off-axis has the powder nozzle positioned at a defined angle, showing also with that nozzle configuration the possibility of laser cladding of steel with Stellite 21 at high speed laser cladding and the other is the coaxial where the powder nozzle is integrated around the optical system, described by Walz and N\u00e4geler (2008), as shown in Fig. 1. The configuration of the nozzle for the off-axis and coaxial nozzle, as nozzle characteristics like stand-off distance, nozzles exit angle and nozzle angle position to the substrate, have been so far separately studied. Yang (2009) studied the influence of the coaxial nozzle exit angle and the stand-off distance on the powder stream distribution, showing that a higher amount of powder can be obtained at the focus position through the reduction of the nozzle exit width. Cheikh et al. (2012) has also showed, through horizontal and vertical image analysis of the powder stream, at which stand-off distance the powder stream has a higher concentration of powder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001749_s12239-014-0053-3-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001749_s12239-014-0053-3-Figure2-1.png",
        "caption": "Figure 2. Tire\u2019s Radial Stifness: (a) Experiment scene and (b) Result comparison between experiment and simulation.",
        "texts": [
            " Besides, wheel is represented by rigid constrain and road is meshed by rigid element type, R3D4. For al material data of rubbers and cords and the arangement information of cords, please refer to appendix A2. For beter convergency in the simulation of transient roling, localy refined mesh is required on tread, which is discussed in the section 3. Please note that model verification and the simulation are implemented based on the refined model. 2.2. Model Verification Tire\u2019s radial stifness test and mode test are conducted to verify the model. Figure 2 (a) shows the test bed of radial stifness test. Tire is fixed with a steel axis. Load is applied by serving exciter. Force and displacement of tire are measured by relative sensors. The stifness of the test bed is large enough to avoid any large deformation and guarantee the reliability and accuracy. In the process of test, inner air pressure is maintained at 280 kPa. Force is loaded gradualy with the increment of 500 N. The maximum load is 5,000 N. Smal deviation occurs in the comparison between the load-displacement curve of experiment and simulation, depicted as Figure 2 (b). The deviation during the whole process is less than 3%. The model\u2019s radial stifness is verified. Figure 3 shows the equipment of modal test. The tire and its wheel are supported by a rigid steel cylinder. The natural frequencies of the supporting cylinder are far higher than those of the tire. In the process of test, inner air pressure is maintained at 140 kPa. According to the tire structure, deformation wil take place in three dimensions. Thus, three directions of response should be obtained at each single measuring point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002503_sibcon.2017.7998581-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002503_sibcon.2017.7998581-Figure4-1.png",
        "caption": "Fig. 4. Pipe 1 and its height map 2",
        "texts": [
            " The concept of height map is used in bipedal robotics to describe the supporting surface as a scalar function of two variables (see [18]). Here we define the height map as follows: )(),( sdsh \u2212=\u03d5 . (3) The height map function ),( \u03d5sh is a function of two scalar variables which can be thought of as local coordinates on the pipe\u2019s surface. Here the function ),( \u03d5sh does not depend on \u03d5 because the pipe has circular cross sections. For pipes with a more complex geometry ),( \u03d5sh might depend on \u03d5 . The procedure of constructing the height map for a given pipe can be thought of as \u201cunwrapping\u201d the pipe. Figure 4 shows a pipe and its height map. Figure 4 illustrates how the height map simplifies the geometry of the pipe. This motivates the use of the height map to plan the sequence of steps for the robot. Then the planned sequence is mapped back to the original pipe with another transformation, which can be thought of as \u201cwrapping\u201d the pipe. To make the wrapping unique we need to assign coordinate systems to each point on the centerline. Let )(1 se , )(2 se and )(3 se be the orthogonal unit vectors that form a coordinate system for a given point on the centerline (defined by the value of s )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002257_j.mechmachtheory.2017.12.007-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002257_j.mechmachtheory.2017.12.007-Figure1-1.png",
        "caption": "Fig. 1. Dual vectors in 3D space.",
        "texts": [
            " (5), (6) now reads: f ( x ) = f ( a 0 ) + \u03b5 1 a 1 f \u2032 ( a 0 ) + \u03b5 \u2217 ( a 2 f \u2032 ( a 0 ) + \u03b5 1 ( a 3 f \u2032 ( a 0 ) + a 1 a 2 f \u2032\u2032 ( a 0 ) )) (7) When applying the above results in trigonometric functions with the hyper-dual angle [25] \u03b8 = ( a 0 + \u03b5 a 1 ) + \u03b5 \u2217( a 2 + \u03b5 a 3 ) , one obtains the following representations for sine and cosine functions of a hyper-dual angle: sin ( \u03b8 ) = sin ( a 0 ) + \u03b5 1 a 1 cos ( a 0 ) + \u03b5 \u2217( a 2 cos ( a 0 ) + \u03b5 1 ( a 3 cos ( a 0 ) \u2212 a 1 a 2 sin ( a 0 ) ) ) cos ( \u03b8 ) = cos ( a 0 ) \u2212 \u03b5 1 a 1 sin ( a 0 ) \u2212 \u03b5 \u2217( a 2 sin ( a 0 ) + \u03b5 1 ( a 3 sin ( a 0 ) + a 1 a 2 cos ( a 0 ) ) ) (8) Table 1 summarizes the definitions of basic algebraic functions for dual numbers of orders DN 0 , DN 1 and DN 2 . It can be shown that basic trigonometric identities also pertain to DN 2 , for example: sin 2 ( \u03b8 ) + cos 2 ( \u03b8 ) = 1 , sin ( \u03b81 + \u03b82 ) = sin ( \u03b81 ) cos ( \u03b82 ) + sin ( \u03b82 ) cos ( \u03b81 ) , etc. 2.2. Scalar and vector products of DN 2 vectors Scalar and vector products of dual vectors of order 2, DN 2 , are derived next, using the notion of dual numbers [5,18] . With reference to Fig. 1 , let two dual vectors \u02c6 X 1 = a + \u03b5( \u03c1 1 \u00d7 a ) and \u02c6 X 2 = b + \u03b5( \u03c1 2 \u00d7 b ) represent two distinct line vectors and let n be the direction vector of the common perpendicular between these two lines, directed from a to b. When using the dual angle \u02c6 \u03b8 = \u03b8 + \u03b5 1 s to encompass the angle and the distance between these lines, and applying the vector triple product, the scalar product is [5] : \u02c6 X 1 \u00b7 \u02c6 X 2 = a \u00b7 b + \u03b5 ( a \u00b7 ( \u03c1 2 \u00d7 b ) + b \u00b7 ( \u03c1 1 \u00d7 a ) ) = a \u00b7 b + \u03b5 ( ( \u03c1 1 \u2212 \u03c1 2 ) \u00b7 ( a \u00d7 b ) ) = | a | | b | cos ( \u03b8 ) \u2212 \u03b5 ( s n \u00b7 | a | | b | s sin ( \u03b8 ) ) = | a | | b | ( cos ( \u03b8 ) \u2212 \u03b5s sin ( \u03b8 ) ) = | a | | b | cos ( \u0302 \u03b8 ) (9) and the vector product is: (10) We next extend each vector to be a dual vector of order 2, DN 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000084_j.triboint.2005.12.005-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000084_j.triboint.2005.12.005-Figure6-1.png",
        "caption": "Fig. 6. Finite element model of a general type of single row deep-groove ball bearing: (a) complete model; (b) cross section of side view; (c) enlarging illustration of local region in contact and (d) boundary conditions.",
        "texts": [
            "07 109N/m is assigned for these five types bearings. For external force ranging from 250 to 2500N the results from finite element model are shown in Fig. 5. According to the determinations of Eq. (11), exponent b is 1.3 for all typical bearings, and the factors K 0 for ball contacted by inner ring and outer ring are listed, in Table 3. These curvefitting parameters are applicable for bearing types mentioned above provided external force below 2500N. The finite element model of whole ball bearings as shown in Fig. 6 is also constructed and analyzed, and is used to verify and compare the determination results of MJHM and conventional JHM. Its boundary conditions include (a) G1: the displacements of all lines between the contact points of the inner ring, and the center of each ball, outer ring and the center of each ball, are constrained in the tangent and axial directions, respectively, (b) G2: all nodal d.o.f on the outer edge of the outer ring are constrained in all directions, (c) G3: all nodal d.o.f on the inner edge of the inner ring are coupled in the direction of loading and constrained in the perpendicular directions of radial load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure1-1.png",
        "caption": "Fig. 1. Tooth surface form of imaginary crown gear.",
        "texts": [
            " In this section, the tooth surface forms of skew bevel gears are modeled mathematically and simply in order to obtain threedimensional coordinates and unit normals on the tooth surface considering the machining using a CNC machining center. In general, the geometry of the skew bevel gears is achieved by considering an imaginary crown gear as the theoretical generating tool. Therefore, first the tooth surface form of the imaginary crown gear is considered. The number of teeth of the imaginary crown gear is represented by zi \u00bc zp sin\u03bbp0 \u00bc zg sin\u03bbg0 \u00f01\u00de where zp and zg are the number of teeth of pinion and gear, respectively, and \u03bbp0 and \u03bbg0 are the pitch cone angles of the pinion and gear, respectively. Fig. 1 shows the tooth surface form of the imaginary crown gear assuming to be straight bevel gears with depthwise tooth taper. O-xyz is the coordinate systemfixed to the crown gear and z axis is the crown gear axis of rotation. Point P is a reference point atwhich tooth surfaces meshwith each other and is defined in the center of tooth surface. Rm is themean cone distance. b is the facewidth.Mn is the normal module. \u03b1 is the pressure angle. The circular arcs with large radii of curvatures are defined both in xz and xy planes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003693_tie.2021.3051547-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003693_tie.2021.3051547-Figure23-1.png",
        "caption": "Fig. 23 Major components of SRM prototype.",
        "texts": [
            " 22(a) shows the instantaneous torque waveforms with the current amplitude of 24A whilst the average torques with various current amplitudes are shown in Fig. 22(b). (a) Torque waveform with saturations V. EXPERIMENTAL VALIDATION In order to verify the previous AM results, experimental validation based on a three-phase 12-stator-slot/8-rotor-pole SRM prototype machine is presented. The key design parameters of the prototype machine are listed in Table I and the major components including the punched laminations, assembled rotor and stator, are shown in Fig. 23. Based on the typical square-wave current profile described in Fig. 4, the static torques of the prototype SRM are tested. The rotor of the machine is locked at each rotor position and the corresponding currents are applied into the three-phase windings, with which the torque output at this rotor position can be measured [38], [39]. Therefore, by rotating the machine step by step and injecting the corresponding currents, the torque waveform during one electric period can be measured. With the fixed current angle (\u03b1=60\u00ba) and different current amplitudes (Imax) including 16A, 24A and 32A, the test static torque waveforms during one electric period are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure19-1.png",
        "caption": "Fig. 19. Simulated magnetic flux density distributions of the motors with different rotors when the amplitude of phase current is 50 A. (a) 2605SA1. (b) 10JNEX900.",
        "texts": [
            " This is because the saturation flux density of 10JNEX900 is higher than that of 2605SA1. Furthermore, the magnetic flux density of the shaft of HR is much lower than that of AR. Because the flux leakage of HR is higher than that of AR, the air-gap PM excitation magnetic flux density of the former is lower than that of the latter as can be seen in Fig. 18. When the amplitude of phase current is 50 A, the torque of the two motors is around 1.2 N m. In this case, the magnetic flux density distributions of the two motors are compared in Fig. 19. The air-gap magnetic flux densities are compared in Fig. 20. It is found that HM has higher maximum flux density. Hence, it is believed that the HM has better overload ability. Authorized licensed use limited to: Cornell University Library. Downloaded on May 23,2021 at 07:48:33 UTC from IEEE Xplore. Restrictions apply. Because IPM motor not only generates magnetic torque, but also provides reluctance torque, it is necessary to use fluxweakening control to maximize the torque. When the phase rms currents are 20 A and 40 A, respectively, the torque as a function of current leading angle of the two motors is compared in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000108_1.2172182-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000108_1.2172182-Figure1-1.png",
        "caption": "FIG. 1. Schematics of DSPM and FSPM machines, and open-circuit field distributions.",
        "texts": [
            " This paper investigates the influence of the end effect on the flux-linkage and back-emf wave forms of FSPM and DSPM machines, in which leakage fields external to the stator core and in the end regions are more significant than in conventional PM brushless machines as a result of the doubly-salient structure and the magnets being mounted on the stator. Performance predictions from two-dimensional 2D and three-dimensional 3D magnetostatic finite element FE analyses are compared with the measurements. Figure 1 shows typical cross sections and open-circuit field distributions of representative three-phase DSPM and FSPM machines. Although the machines have similar topologies, in the DSPM machine a concentrated coil is wound on every stator tooth and the magnets are located in the stator core back, so that when the rotor rotates one rotor pole pitch the polarity of the flux linkage with a stator coil does not change. Thus, the coil flux-linkage and phase flux-linkage wave forms are unipolar. In the FSPM machine, a concentrated coil is wound around a pair of teeth, between each of which a permanent magnet is located, so that when the rotor rotates one rotor pole pitch the coil fluxlinkage and phase flux-linkage wave forms are bipolar. Consequently, a FSPM machine can exhibit a higher torque density. Although both machines have a salient structure, which is similar to that of a switched reluctance SR machine, the electromagnetic torque of both DSPM and FSPM machines results predominantly from the permanent magnet excitation torque, i.e., the reluctance torque component is relatively small. III. INFLUENCE OF END EFFECT A three-phase FSPM machine, Fig. 1 b , having 12- stator teeth and 10-rotor teeth dc link voltage=36 V, speed=400 rpm, outside diameter=90 mm, axial length =25 mm, air gap=0.5 mm, number of turns/phase=72, and NdFeB magnets with a remanence=1.2 T and a three-phase DSPM machine, Fig. 1 a , having 12-stator teeth and 8-rotor teeth dc link voltage=440 V, speed=1500 rpm, outer diameter=142 mm, axial length=75 mm, air gap=0.45 mm, number of turns/phase=260, and NdFeB magnets with a remanence=1.02 T are considered. Figures 2 and 3 show the air a Author to whom correspondence should be addressed; FAX: 44-114- 2225196; electronic mail: z.q.zhu@sheffield.ac.uk b FAX: 44-114-2225196; electronic mail: elp01yp@sheffield.ac.uk c FAX: 44-114-2225196 and 86-25-83791696; electronic mail: w.hua@sheffield"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure8-1.png",
        "caption": "Fig. 8. New parallel manipulators with telescopic legs: (a) HALF*; (b) HANA*.",
        "texts": [
            " They have the same mobility as that of the manipulator shown in Fig. 6. It is not difficult to find out that, compared with the HANA manipulators, the HANA* parallel manipulators introduced here also have the advantages in kinematics, architecture, manufacturing, energy cost, accuracy, and assembling for the similar reasons described in Section 2.1. Since there is no planar parallelogram in each manipulator of the new family, every leg can be designed as a telescopic link. For example, the HALF* and HANA* parallel manipulators with such links are shown in Fig. 8(a) and (b), respectively. Although, compared with the HALF and HANA parallel manipulators, the new manipulators have some advantages, they still have their own disadvantages. For example, the adoption of C joint may cause operational failure since it is a passive joint. To avoid this problem, we can apply the passive DOF to the manipulators. For example, in the HALF* manipulators, the joints connected to the moving platform in the first and second legs can be spherical joints, in each of which there is one passive DOF"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003449_tmag.2020.3022844-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003449_tmag.2020.3022844-Figure4-1.png",
        "caption": "Fig. 4. Selection of the stator variable of the conventional model",
        "texts": [
            " Coefficients according to the weight of each model were calculated, and the model with the highest harmonic coefficient among the models satisfying the target specifications was selected as the proposed model. III. VERIFICATION OF ELECTROMAGNETIC VIBRATION BASED In order to the analysis, a 10-pole 12-slot model, which is applied to an electric compressor, was selected as the conventional model. The cross-section of the full conventional model is shown in Fig. 3, and the specifications are shown in Table 1. Fig. 3. Cross-section of the conventional model To confirm the influence of the slot harmonic according to the airgap length g, the variables for the inner diameter of the stator are shown in Fig. 4. Each variable represents the radial distance of the points forming the inner diameter of the stator. Five variables were selected for half of the tooth, and the shape was symmetrical based on the center of the tooth. The length of Shoe1 of the conventional model was 1.8 mm, and for each variable, 0 mm, 0.9 mm, and 1.8 mm based on 0%, 50%, and 100% of the Shoe1 length were set as variable values. Then, 243 models were conducted through the FEA. Fig. 5 shows the analysis of the 0fe spatial harmonic of the conventional model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure9-1.png",
        "caption": "Figure 9 Three transforming steps of the rotation",
        "texts": [
            " If the rotation is performed via two of these three vectors vx(1,0,0), vy(0,1,0) and vz(0,0,1), the question can be described as: Known P1 \u00f0XP1 ; YP1 ; ZP1\u00de, v1s Xv1s ; Yv1s ; Zv1s\u00f0 \u00de and v1t Xv1t ; Yv1t ; Zv1t\u00f0 \u00de, calculate P 0 1 XP 0 1 ; YP 0 1 ; ZP 0 1 and the rotating angles around two vectors of vx(1,0,0), vy(0,1,0) and vz(0,0,1). After the transformation, we have P 0 1 \u00bc Mst P1, whereMst is the transformation matrix. In the following, two solutions are given. Solution 1 takes no consideration of the usable axes of the five-axis platform. Solution 2 takes it into consideration. Rotating v1s to v1t around C, includes three steps: translating from v1sC to O, then rotating v1s to v1t around O, and translating v1s from O to C, shown in Figure 9, corresponding to three transformation matrixes Mco, Msot and Moc respectively, written as Mst = Mco * Msot * Moc. The translation matrixes Mco and Moc can be represented as Mco \u00bc 1 0 0 1 0 XC 0 YC 0 0 0 0 1 ZC 0 1 2 664 3 775Moc \u00bc 1 0 0 1 0 XC 0 YC 0 0 0 0 1 ZC 0 1 2 664 3 775, while rotatingmatrixMsot is equal to the result of rotating around vectors vz, vy and vx by angles c, b and a, respectively, represented as Msot \u00bc 1 0 0 cosa 0 0 sina 0 0 sina 0 0 cosa 0 0 1 2 664 3 775 cosb 0 0 1 sinb 0 0 0 sinb 0 0 0 cosb 0 0 1 2 664 3 775 cosc sinc sinc cosc 0 0 0 0 0 0 0 0 1 0 0 1 2 664 3 775 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.2-1.png",
        "caption": "Fig. 17.2 Combination of four-bar and crank mechanism in a pump",
        "texts": [
            " It is this complexity in combination with simplicity of design which makes the planar four-bar the most important linkage in engineering. Literature on four-bars and on other linkages: Erdman (Ed.) [11], Artobolevski [1], Geronimus [16], Dijksman [10]. 567 J. Wittenburg, Kinematics, DOI 10.1007/978-3-662-48487-6_ 17 \u00a9 Springer-Verlag Berlin Heidelberg 2016 568 17 Planar Four-Bar Mechanism In many machines a certain desired property is achieved by combining a four-bar with additional elements. A typical example is shown in Fig. 17.2 . Without the motor-driven crank mechanism MDB drawn with dashed lines the mechanism is a four-bar A0ABB0 with base A0B0. None of its links is able to rotate full cycle relative to the base. When this four-bar is moving through its entire range, the coupler-fixed point C traces the dotted coupler curve. A section of this curve is a very good straight-line approximation. The combination of the four-bar A0ABB0 with the crank mechanism MDB results in a machine in which C is moving periodically back and forth the straight section when the crank is rotating",
            " The dimensions should be chosen such that in this position the instantaneous centers P13 , P10 and P20 are almost collinear as shown. In this case, the ratio L4/L1 is > 1 in every position, and it increases monotonically when the blades are closing. With shears of this kind reinforcement steel rods of 15 mm diameter can be cut by hand. Every point fixed in the plane of the coupler traces a coupler curve when the four-bar is moving through its entire range. It is the complexity of these curves to which the four-bar owes much of its importance in engineering (see Fig. 17.2). In the following sections properties of coupler curves are investigated. The curvature of coupler curves was the subject of Sect. 15.3.3 (see Fig. 15.19). Figure 17.15 is started by drawing the four-bar A0A1B1B0 and a point C fixed in the plane of the coupler A1B1 . This plane is represented by the coupler triangle (A1,B1,C). Subject of investigation is the coupler curve generated by C . To this basic figure lines A0A2C and B0A3C are added thus creating two parallelograms. In the next step, triangles similar to the coupler triangle are drawn as shown with bases A2C and A3C ",
            " It has real roots \u03b3 for angles \u03b2 satisfying the condition cos\u03b2 \u2265 2\u2212\u221a 5 (\u03b2 < 104\u25e6 approximately). Additional material on coupler curves is found in Mayer [27] and Mu\u0308ller [28, 30, 31]. Coupler curves which are symmetrical with respect to the base line A0B0 have an Eq.(17.84) in which y appears in terms of even orders only. For this it is necessary that sin\u03b2 = 0 . This means that the generating coupler point C lies on the coupler line AB (not necessarily between the points A and B ). The coupler curve in Fig. 17.2 is an example. According to the Roberts-Tschebychev theorem every such coupler curve is generated by two more four-bars. Also in these four-bars the coupler point lies on the coupler line. In Eq.(17.84) for symmetrical coupler curves with sin\u03b2 = 0 the parameters are b1 = \u03b7 and b2 = \u03b7\u2212a where \u03b7 is the parameter used in Fig. 17.19 . Of particular interest are intersection points of the coupler curve with the axis of symmetry. With y = 0 the following equation is obtained for these points which is of third order in x and in \u03b7 : 604 17 Planar Four-Bar Mechanism (\u03b7 \u2212 a)(x\u2212 )(x2 + \u03b72 \u2212 r21)\u2212 \u03b7x[(x\u2212 )2 + (\u03b7 \u2212 a)2 \u2212 r22] = 0 ",
            " The number m of points that can be prescribed is smaller than nine if the additional requirement exists that the angle \u03d5k\u2212\u03d51 of rotation of the input crank associated with the passage from point P1 to point Pk is prescribed for k = 2, . . . ,m . The only free angle is \u03d51 . This means that altogether ten free parameters exist while the number of equations to be satisfied is 2m as before. From the equality 2m = 10 it follows that at most five points can be prescribed. Methods for solving this problem see in Freudenstein [15] and Dijksman [8]. 17.12 Coupler Curves with Prescribed Properties 617 Coupler curves with approximately straight-line segments have important engineering applications (see Fig. 17.2). The earliest straight-line approximation was invented by Watt8 for the purpose of guiding the piston in his steam engine. His four-bar is a symmetrical double-rocker of second kind with link lengths , r1 , a , r2 satisfying the conditions r1 = r2 = r and = 2 \u221a r2 + (a/2)2 . The ratio a/r is a free parameter. In Fig. 17.34a the four-bar with link lengths r = 35 , a = 24 and = 74 is shown in four positions. The figure-eight-shaped coupler curve generated by the midpoint C of the coupler is symmetric to both the base line A0B0 and the midnormal of this base line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.1-1.png",
        "caption": "Figure 10.1. Schema for quantities appearing in Euler 's laws.",
        "texts": [
            " These moments are the total contact torque and the total body torque acting on the body about Q. Concentrated forces and their moments about Q are included as pointwise distributions. If all torque s are moments of forces about any fixed point in an inertial frame <1> = {F;ed and, as usual, mass is conserved, the second law (10.3) may be derived from the first law applied to an incremental distribution of force dF(P , t)= yep , t)dm(P) , the increment being a continuous function of P and t acting on the material parcel of mass dm(P) at P. First, recall the notation in Fig. 10.1. Then with respect to any fixed point 0 in <1>, by (10.10), Mo(!1J, t) =1.. Xo(P, t) x yep, t) dm ,0') d1 dho ($ , t)= - xo(P , t) x yep , t) dm = , dt Y!l dt wherein v =X=*== *0, because 0 is fixed in <1> . This is Euler's second law (10.3). Note , however, that in order to move the time derivative outside the integral, it is necessary to use a fixed referential configuration of the body, which may be deformable and changing with time. Without getting into these details, it suffices to know that this is always possible, and it is certainly true for any rigid body $ , our princ ipal concern here"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002094_j.conengprac.2014.08.012-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002094_j.conengprac.2014.08.012-Figure1-1.png",
        "caption": "Fig. 1. Definition of the earth-fixed and body-fixed frames.",
        "texts": [
            " Under assumption of small motions and considering the ship as a slender body with port/starboard symmetry, its horizontal and vertical motions may be decoupled from each other so that only the surge, sway and yaw motions\u2014those to be controlled by the DPS\u2014are considered in the mathematical model (Lewis, 1989; Sorensen & Strand, 2000). The vessel responses to the environmental and actuator loads are then calculated through a set of equations of motions derived in two different coordinate systems, as shown in Fig. 1. The first, OXYZ, is an Earth-fixed frame that can be considered as inertial for the present problem. The other frame (GXGYGZG) is a body-fixed one, whose axes coincide with the ship's principal axes of inertia. Both systems are assumed to be parallel to the water surface, and the direction of current, wind and waves are defined according to their orientation related to the OX-axis. As a DPS is exclusively intended to control low-frequency motions, only those loads due to current and the slowly varying components of wind and waves are to be considered in the models for both the controller and the observer, together with those induced by the actuators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001372_icra.2014.6907352-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001372_icra.2014.6907352-Figure5-1.png",
        "caption": "Fig. 5. Establishment of Variables Left figure: Variables for statics analysis of a pushed object Right figure: Variables for kinematic analysis of a tilted object",
        "texts": [
            " \u2016SPO(\u03b8O,\u03b8E)\u2212 v\u0303i\u2016 < \u03b5th (9) In the following three subsections, we introduce the example of the implementation and the integration of general SPOs available by the dual-arm robot. 1) Statics Analysis of the Pushed Object: Pushing (\u03c3push) is one of the most basic operation. In the following, we analyze the statics of the pushed object on the floor. The object shape is assumed to be rectangular in this case, but many objects are approximated in this assumption. Setting variables as shown in left of Fig.5, equilibrium equations of forces and moments are as follows: fhx = f (10) fhz + n = mg (11) cmg = lfhz + hfhx + pn (12) The object starts to move in the following two conditions: eq.(13) is the condition of tilt and eq.(14) is that of slide. p \u2264 0 \u21d0\u21d2 fhx \u2265 cmg \u2212 lfhz h (13) f > \u03bcn \u21d0\u21d2 fhx > \u03bc(mg \u2212 fhz) (14) Therefore, the movement of the pushed object (\u03c3push(\u03a9\u0398)) is classified into \u201dtilt\u201d, \u201dslide\u201d, and \u201dstill\u201d (Fig.6 left). 2) Strategy and Key Motion: We set the strategy Si and key motion v\u0303i as Table",
            "(16), and determine as 5) in the procedure. x\u0307h \u2248 x\u0307, \u03b8\u0307h \u2248 \u03b2\u0307 (16) The visual recognition of the large object is difficult because the object is close to the robot and covers the field of view. Therefore, we used the kinematic information of the hands in this case. 4) Calculation of Tilt / Slide Detection Threshold: The threshold xh,th, \u03b8h,th should be changed depending on the height of the grasping point h because the assumed relation between xh and \u03b8h changes during object tilting. As shown in right of Fig.5, d and \u03b1 are defined by d = \u221a l2 + h2, \u03b1 = arctan h l (17) Supposing that \u03b8h is small enough, xh is given by xh = d cos\u03b1\u2212 d cos(\u03b1+ \u03b8h) = d(cos\u03b1\u2212 cos\u03b1 cos \u03b8h + sin\u03b1 sin \u03b8h) = d \u03b8h sin\u03b1 = \u03b8h h (18) Using the constant margins xh,mrg(> 0) and \u03b8h,mrg(> 0), the threshold is defined as follows. xh,th = xh \u2212 xh,mrg, \u03b8h,th = \u03b8h \u2212 \u03b8h,mrg (19) When \u03b8h,th is set to be constant, xh,th is derived as follows from eq.(18) (Fig.6 right). xh,th = (\u03b8h,th + \u03b8h,mrg)h\u2212 xh,mrg (20) In this subsection, we propose another SPO"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003040_taes.2020.2988170-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003040_taes.2020.2988170-Figure1-1.png",
        "caption": "Fig. 1: Diagram of relative position between chaser and target",
        "texts": [
            " The arrow, pt, represents the position vector of point P in Fbt and p\u2217t represents the vector from Authorized licensed use limited to: University of Exeter. Downloaded on June 15,2020 at 12:55:34 UTC from IEEE Xplore. Restrictions apply. 0018-9251 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. point S to point P in Fbt. The vector rpt is defined as rpt = rt + pt as shown in Fig. 1. Define [w] \u00d7 \u2208 R3\u00d73, which satisfies the matrix as [w] \u00d7 =  0 \u2212w3 w2 w3 0 \u2212w1 \u2212w2 w1 0  (1) In Fbc, define qc = [qc1, qc2, qc3, qc4] T to represent the quaternion of the chaser with respect to Fi, then the kinematics and the dynamics of the chaser are expressed as r\u0307c = vc \u2212 [\u03c9c] \u00d7 rc v\u0307c = \u2212[\u03c9c] \u00d7 vc + 1 m (f + df ) q\u0307c = 1 2 qc \u25e6 \u03c9c \u03c9\u0307c = \u2212J\u22121c [\u03c9c] \u00d7 Jc\u03c9c + J\u22121c (\u03c4 + d\u03c4 ) (2) where rc, vc and \u03c9c represent the position, velocity, and angular velocity of mass point C in Fbc; f and df represent the control force and disturbance force on C in Fbc; \u03c4 and d\u03c4 represent the control torque and disturbance torque on C in Fbc; m and Jc represent the mass and inertia of the chaser",
            " In Fbt, with ignoring the external forces and torques, the mass point T of the target satisfies the following equations r\u0307t = vt \u2212 [\u03c9t] \u00d7 rt v\u0307t = \u2212[\u03c9t] \u00d7 vt q\u0307t = 1 2 qt \u25e6 \u03c9t \u03c9\u0307t = \u2212J\u22121t [\u03c9t] \u00d7 Jt\u03c9t (3) where qt = [qt1, qt2, qt3, qt4] T represents the attitude quaternion of the target with respect to Fi; rt, vt and \u03c9t represent the position, velocity, and angular velocity of mass point T in Fbt; Jt represents the inertia of the target. To hover and track the feature point on the target, re should be nullified, and the axis xbc in Fbc should be aligned towards the feature point S on the target. In Fig. 1, pt, p\u2217t and st are projected to Fbt, satisfying pt = p\u2217t + st. As a result, pt can be obtained if p\u2217t is given. In order to align the tracking sensor of the chaser to the feature point S on the target, the axis xbc should be controlled to point to the feature point. Define pd = Cbc btp \u2217 t + re as the position vector of the feature point in Fbc, where Cbc bt represents the frame transformation matrix from Fbt to Fbc. Thus, as shown in Fig. 2, the right ascension and declination of pd are obtained as \u03b1 and \u03b3",
            " Yushan Zhao majored general mechanics for his bachelor degree in Northwestern Polytechnical University between February, 1978 and January, 1982, and then got his master degree in 1985 and Ph.D degree in 1995. During 1998 and 1999, he engaged in advanced studies in Samara University of Aeronautics and Astronautics in Russia. He taught in Northwestern Polytechnical University from February, 1982 to June, 2002, and then worked in Beihang University since 2002, where he was awarded the excellent teacher of Beihang University. Figure Captions: Fig. 1: Diagram of relative position between chaser and target Fig. 2: Diagram of the feature point on disabled satellite Fig. 3: Diagram of the relative positions of satellite P and satellite E Fig. 4: Schematic diagram of learning logic in x-channel Fig. 5: The critic fuzzy inference system in x-channel Fig. 6: The expected hovering position to the feature point on the target Fig. 7: Membership functions Fig. 8: Time histories of the relative states by using the PSTC Fig. 9: Contrast of control acceleration under adaptive controller and PSTC(a) Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003510_s11665-021-06037-z-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003510_s11665-021-06037-z-Figure15-1.png",
        "caption": "Fig. 15 Two-way flow in abrasive flow machining. Source: (Ref 14)",
        "texts": [
            " The constraints associated with AFB include: \u2022 Microfatigue Microcracks are found due to repeated rubbing of abrasives on the surface \u2022 Nonuniform polishing Different levels of polishing are ex- Journal of Materials Engineering and Performance pected, because the speed of a point moving on the surface depends on the distance from its location to the rotating axis, and a SLM part has different surface finishes relative to the building direction \u2022 Sharp features Sharp points and edges are rounded off in this process, masking while tedious is required to protect these features \u2022 Recycling Further study is needed to determine the useful life of the abrasives Abrasive flow machining (AFM) is a postprocessing technique that can polish internal and external features of AM metal parts. The erosion mechanism stems from the interaction of a workpiece surface and the abrasive medium flow at different attack angles. In general, higher pressure and relative velocity of the medium results in a higher material removal rate, and the finer the abrasive size, the smoother the resulting surface. A viscoelastic fluid containing appropriate abrasive medium can be engineered to flow across a part surface in one direction or both directions in a reciprocating action (Fig. 15). By controlling the viscosity of the media (abrasive fluid containing abrasives), the system can either be more effective to round off sharp corners (low viscosity) or to polish uniform surfaces (high viscosity). Common abrasives and corresponding hardness for AFM are listed in Table 5. The AFM process is used to polish the surface of Maraging 300 steel (Fe-18Ni-9Co-5Mo) fabricated by selective laser melting. Material hardness varies for as-printed samples without heat treatment (35.5 HRC) and heat-treated samples (55"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003164_1.3662578-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003164_1.3662578-Figure6-1.png",
        "caption": "Fig. 6 Rolling moment versus normal load for several configurations\u2014 1 'A - in. balls, MIL 7808 Oil",
        "texts": [
            " It might be noted that in the usual range of viscosity, widely different types of oil or no oil at all gave the same force readings when used on flat plates. V-Groove Tests. The next group of tests replaced two of the flat surfaces with V-grooves of various conformities. Common practice defines conformity/as: f - ' f CD where rB is the radius of the race and D is the ball diameter. Using this definition, a flat plate has \u00b0\u00b0 conformity while a typical ball bearing has 52 \u2014\u00bb\u2022 54 per cent conformity. Fig. 6 shows data for various configurations. All the data have been reduced to a common basis of one ball with two contact points. The rolling moment on a flat plate is almost negligible when compared to balls rolling in various types of V-grooves. This difference is attributed to the spinning action that the ball has as it rolls in the groove. A free-body diagram of a ball rolling in a V-groove may be drawn as in Fig. 7. The ball is resisted in its motion by both spinning moments Ms and rolling moments MR",
            " For a circular contact zone (b/a = 1), this reduces to: 37T M s = ( 4 ) l b If the contact zone is elliptical with a/6 > 7, less than a 2 per Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use cent error results if E(k) is taken equal to unity. For intermediate values, E(k) must be taken from tables. As the radius of the contact zone varies as N1 / ' , it follows that M s varies as N'^' as confirmed by the experimental results. Equation (3) has been used to evaluate the friction coefficient for the data shown in Fig. 6, using the appropriate normal loads and conformity. The result is shown in Fig. 9 where friction coefficient has been plotted versus mean compressive stress in the contact zone. A value of fxs = 0.07 describes most of the data quite well. There seems to be a trend toward higher values of at low stresses. However, this should be taken as tentative, since the data become relatively less accurate as the loads are decreased. Examination of an actual force trace for the V-groove, Fig. 10(a), shows a predominating square wave, as expected, plus higher frequency variations which seem to repeat almost exactly from cycle to cycle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure5.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure5.1-1.png",
        "caption": "FIGURE 5.1. Cross Section of a Three Layered Cylinder.",
        "texts": [
            " It should be noted that: ur is the displacement in the r direction, u\u03b8 is the displacement in the \u03b8 direction, uz is the displacement in the z direction, \u03c3rr is the normal radial stress in the r direction, \u03c4r\u03b8 is the shear stress in the \u03b8 direction and normal to r, \u03c4rz is the shear stress in the z direction and normal to r, and X is the constant vector given previously in equation (3.83) Then equation (5.1) can be presented as: {d}n = [D]n {X}n (5.2) where, the vector {d}n is: {d}n = n ur h1 u\u03b8 h2 uz h3 \u03c3rr h1 \u03c3r\u03b8 h2 \u03c3rz h3 oT n (5.3) and [D]n previously appeared in equation (3.107), and n is the circumferential wave number. 5. Vibration of Multi-Layer thick cylinders 83 5.5 Propagator Matrix for a Three Layer Cylinder The layered cylinder is assumed to be formed by three different visco-elastic layers bounded by inner and outer interfaces (see Figure 5.1). The third layer has a thickness of H3 = r3 \u2212 r2 and is bounded by inner and outer interfaces located at radii of r2 and r3, respectively. Each of the viscoelastic cylinders is characterized by a complex compressional wave velocity v1, complex shear wave velocity v2, density \u03c1, Poisson\u2019s ratio \u03bd, and a material loss-factor \u03b7. The mathematical formulation is used to develop a relation between displacements and stresses at the boundaries of each layer and consequently obtains a propagator matrix relating displacements and stresses of the inner boundaries to the outer ones",
            " Therefore, points (2) and (3), and (4) and (5), have the same displacements and stresses. As presented in equation (5.2), the displacements and stresses vector for any point on the cylinder can be given as follows: {d}np = [D]np {X}np (5.4) 84 5. Vibration of Multi-Layer thick cylinders where, n is the circumferential wave number and p is the point number. Using the general equation of (5.1), the following equations can be written for each point in the medium. Writing the displacements and stresses vector for the six points presented in Figure 5.1 and dropping subscript n for simplification one can write the following equations for points (1) through (6). point (1): {d}1 = [D]1 {X}1 (5.5) point (2): {d}2 = [D]2 {X}2 (5.6) point (3): {d}3 = [D]3 {X}3 (5.7) point (4): {d}4 = [D]4 {X}4 (5.8) point (5): {d}5 = [D]5 {X}5 (5.9) point (6): {d}6 = [D]6 {X}6 (5.10) Points (1) and (2) are on the same layer, therefore: {X}1 = {X}2 (5.11) Therefore, using these equalities and equations (5.5) and (5.6) yield: {d}2 = [D]2 [D] \u22121 1 {d}1 (5.12) Points (3) and (4), and (5) and (6), are on layers two and three respectively, this implies that points (3) and (4), and (5) and (6), have the same unknown constants, therefore: {X}3 = {X}4 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001139_j.mechmachtheory.2011.12.011-Figure4-1.png",
        "caption": "Fig. 4. The change of the actuated forces versus t and ka,2.",
        "texts": [
            " Then, the components Fx, Fz and My of the external force $F can be expressed in the frame A as Fx \u00bc \u22121 106 cos\u03b8\u00fe 2:5 106 sin\u03b8 Fz \u00bc \u22121 106 sin\u03b8\u22122:5 106 cos\u03b8 My \u00bc 2:5 106 8>< >: \u00f054\u00de Assume that the moving platform rotates with a constant velocity _\u03b8 \u00bc \u2212\u03c0=360rad=s, i.e., \u03b8=(\u2212\u03c0/360)t, and the time t is varied from 0 to 60s. To illustrate the change of the actuated forces and internal forces with respect to the stiffness of the actuationwrenches, let ka,2 range from 0.8\u00d7109N/m to 1.2\u00d7109N/m. Then from expressions (52) and (53), the change of the actuated forces and internal forces with respect to t and ka,2 can be obtained using the Matlab 7.8 software, just as shown in Fig. 4 and Fig. 5. From Figs. 4 and 5, we can get that the internal forces are equal to zero and the actuated force \u03c41 is equal to \u03c42, when ka,2=ka,1=1.0\u00d7109N/m. The graphs also show that the actuated force \u03c42 is smaller than \u03c41 when ka,2bka,1=1.0\u00d7109N/m, and the actuated force \u03c42 is larger than \u03c41 when ka,2>ka,1=1.0\u00d7109N/m. The internal forces exist within the solution to inverse dynamics of the redundantly actuated forging manipulator 2SPS+R when ka,2\u2260ka,1=1.0\u00d7109N/m, which are utilized to coordinate the elastic deformation of the forging manipulator 2SPS+R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.35-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.35-1.png",
        "caption": "Fig. 15.35 Cycloid z1 enveloped by the diameter of a rolling wheel and evolute z2",
        "texts": [
            " The motion of cycloid z1 inside z2 is creating n chambers of periodically changing volumes. This phenomenon has found engineering applications. If the crank is driven by a motor, the chambers can be used for pumping fluid. By controlling the pressure inside the chambers by means of a rotating distribution valve z1 , the crank can be driven (the crank rotating n times as fast as z1). The 504 15 Plane Motion systems shown in Figs. 15.34a and b are special cases of cycloidal gearings. For additional material on this subject see Sec. 16.1.2. Consider the cycloid z1 in Fig. 15.35. It is the trajectory of the point C fixed on wheel 1 rolling on wheel 0 . This generating system is referred to as system r0, r1 . As straight-line position with angles \u03d51 = \u03d52 = 0 the position is chosen when C is located at the vertex C0 of z1 . Then the parameters are r0 < 0 and r1 > 0 . The circle on which C0 is located is called circle of vertices. Its radius is 2r1 \u2212 r0 . The line P10C is the normal n to z1 at C . The tangent t passes through the point P\u2217 12 common to wheel 1 and to the circle of vertices (wheel 1 is Thales\u2019 circle in the right-angled triangle (P10,C,P \u2217 12))",
            "130) shows that this is the rotation angle of a wheel with radius 2r1 instead of r1 rolling on the same sunwheel 0 . In the figure this wheel is shown in the position \u03b1 as dashed line. The tangent t is a diameter fixed on this wheel. These results are summarized in 15.5 Trochoids 505 Theorem 15.8. A cycloid generated as point trajectory in a system r0, r1 is enveloped by a diameter fixed on the planetary wheel in the system r0, 2r1 Consider the special case r0 = \u22122r1 shown in Fig. 15.36. The circle of vertices has the radius R = 2|r0| . The epicycloid has two cusps. From Fig. 15.35 the general formula \u03b2 = (P10P \u2217 12C)= 1 2\u03c0\u2212 1 2 (\u03d51\u2212\u03d52) is known. In the special case under consideration, this becomes \u03b2 = 1 2\u03c0\u2212\u03d52 . In Fig. 15.36 it is seen that \u03b2 is also the angle between the line P20P \u2217 12 and the perpendicular s to the line P20C0 . A light beam having the direction of s is reflected on the circle of vertices in the direction of the tangent to the cycloid. This explains a phenomenon which can be observed in a cup of coffee in early-morning sunshine. Parallel sun rays are reflected on the inner wall of the cup (circle of vertices of radius R )",
            " The first generating system is the system r0, 1 3r0 . According to the theorem the cycloid is enveloped by a diameter fixed on the planetary wheel in the system r0, 2 3r0 . This system is also the second generating system of the same cycloid. In other words: The endpoints of the enveloping diameter of the planetary wheel in the second generation are tracing the cycloid. This property is known already from Fig. 15.34b . Steiner\u2019s hypocycloid is the only hypocycloid having this property. Next, the evolute of the cycloid z1 in Fig. 15.35 is determined. Let it be called z2 . By definition, z2 is the curve which is enveloped by the normal n of z1 . The following facts are obvious: 1. n is tangent to z2 ; n is passing through P10 which is located on the circle with radius r0 2. t is tangent to z1 ; t is passing through P\u2217 12 which is located on the circle with radius 2r1 \u2212 r0 506 15 Plane Motion 3. P20P10 is collinear with P20P \u2217 12 ; both n and t are rotating with \u03b1\u0307 ; n is orthogonal to t . A direct consequence of these facts is Theorem 15.9. (Bernoulli, de la Hire)7 The evolute of a cycloid z1 in the system r0, r1 is another similar cycloid z2 , which is the trajectory of a point in the new system pr0, pr1 with p = r0/(2r1 \u2212 r0) . The circle of vertices in the new system is identical with the circle of the sunwheel in the initial system. The vertices of the evolute z2 coalesce with the cusps of z1 . Figure 15.35 shows the evolute z2 and in dashed lines the wheels of the new system. Further properties of cycloids and of trochoids in general are found in Wunderlich [30] and Strubecker [28]. Higher-order trochoids were investigated by Wunderlich [29]. An ordinary cycloid8 is the trajectory of an arbitrary point (not just a circumferential point) fixed on a circular wheel which is rolling along a straight line. This is the situation when in Fig. 15.26 r0 is infinite. In what follows, the notation shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001326_s00170-014-5763-1-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001326_s00170-014-5763-1-Figure5-1.png",
        "caption": "Fig. 5 FE mesh used in the simulation",
        "texts": [
            " While, for the solid laser spot with a topflat intensity distribution, the scanning energy intensity was higher at the center than at the boundary. For the hollow laser beam, the hollow ratio \u03b7 was varied with the defocused distance and consequently affected the thermal field in the clad. Li [20] found that the hollow ratio \u03b7 in the cladding region IV was in the range of 0.15~0.75. 3.3 Numerical implementation of thermal analysis A nonlinear transient thermal model was developed using ANSYS. A nonuniform mesh was adapted to the zones of high thermal gradients, as shown in Fig. 5. The finest element size used in the clad zone was set at 0.2 mm, and a coarse mesh with element edge size up to 2 mm was used in the substrate far from the clad zone. Symmetry was considered at the middle plane along the direction of X. Hence, only half of the geometry was modeled. There were a total of 28,700 elements with 8-node brick SOLID70 in the thermal analysis [21]. The element \u201cbirth and death\u201d option was used to simulate the additive nature of the process. In this method, the elements of the cladding layer were defined at the beginning of the process but \u201ckilled\u201d by multiplying their stiffness (or conductivity, or other analogous quantity) by a severe reduction factor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000450_s11249-010-9592-6-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000450_s11249-010-9592-6-Figure2-1.png",
        "caption": "Fig. 2 Photograph of apparatus",
        "texts": [],
        "surrounding_texts": [
            "and therefore can potentially allow measurement of film thickness between rough surfaces. Third, modern visible light photon detection equipment is extremely sensitive, so that very low levels of fluorescence emission down to as little as that emitted from one molecule can be measured. Despite these strengths, fluorescence has been used only sparingly to study lubricant behaviour.\nFluorescence was first applied to tribology in the 1970s, where Ford and co-workers studied free lubricant films on roller and raceway surfaces in rolling element bearings [12]. Their method relied on natural fluorescence in the oil, which emitted in the visible range when excited by a UV mercury lamp. The technique was subsequently improved by replacing the mercury lamp with a He\u2013Cd laser, which had associated benefits of simplified optics and increased working distance [15]. Films down to 1 lm thickness were measured.\nSince Ford\u2019s study, there have been a number of other studies based on fluorescence. Most of these have used the technique of laser-induced fluorescence (LIF), where a fluorescent species is excited by a laser at one frequency and the intensity of emission at a different frequency is detected to indicate the fluoresce concentration and thus the lubricant film thickness. Shaw et al. [16, 17] and Richardson and Borman [18] applied LIF to monitor film thickness between piston and liner. The emitted light was transmitted from the contact through the cylinder liner by means of a fibre optic cable. One of the strength of this approach is that there is effectively no upper bound on measured film thickness, it is robust regarding temperature variation, and it can measure both the film thickness in the piston/liner contact and also the lubricant on the out-ofcontact cylinder surface. Tanimoto et al. have used laserinduced fluorescence to map the migration of free surface films from the wear scars on hard disks [19].\nFluorescence has been used extensively to measure film thickness in sealing applications, because it is either important to know the volume of lubricant present (rather than the separation of surfaces), or large film thickness mean optical interferometry is not possible [20\u201324]. A notable example of this is research by Poll and co-workers [20], where an actual rotary seal was run against a glass shaft. Here, film thicknesses as low as 0.35 lm were measured. Work carried out at Lulea\u030a University measuring film thickness in hydraulic cylinder seals, is summarised in reference [22], which demonstrates the ability of laserinduced fluorescence to study soft contacts, whose optical properties preclude the use of optical interferometry. An interesting technique that uses two fluorescent dyes has been developed for rotary seals by Hidrovo and co-workers [24]. One dye absorbs incident laser light, and subsequently fluoresces providing the excitation for a second dye. In this way, film thickness is obtained independently\nof background noise. This technique is currently limited in its application, since it requires a thick fluorescent film to operate.\nThere has been very little application of fluorescence to concentrated EHL contacts, probably because optical interferometry already provides a powerful means of analysing such small contact areas. To the author\u2019s knowledge, the only example of fluorescence applied to a concentrated contact has been studied by Sugimura et al. [25, 26]. They reported problems of interference and sensitivity. The former they were able to model, but sensitivity issues were more problematic. However, in this study, photon detection equipment, as well as fluorescent dye technology has advanced significantly. Further details of the problem of interfering of light emitted by the fluorescently dyed lubricant can be found in the following reference [27].\nAn extremely insightful application of fluorescence to study lubricant behaviour has been carried out by Pit et al. to study liquid slip at solid surfaces [7]. Pit used a process known as fluorescence recovery after photo-bleaching (FRAP). FRAP was first demonstrated by Axlerod [28], and is achieved as follows. A relatively unstable fluorescent dye is added to the fluid. Initially a tightly focussed, high power laser is used to illuminate the fluid; this has the effect of destroying the dye molecules inside the small illuminated region. Then, the sample is illuminated using a much lower power laser, causing the non-bleached molecules present to fluoresce. Subsequent diffusion and flow of the surrounding fluorescent fluid sample into the bleached area can then be monitoring. Pit used this rate of replenishment to prove that lubricant slip at the wall occurred between two sliding flat plates. The ultimate aim of this study is to apply FRAP to an EHL contact to investigate shearing and slip. In this article, however, only a simpler method of dye introduction, which mimics a FRAP experiment, is presented.\n2 Experimental Technique\n2.1 Fluorescence Apparatus\nA lubricated contact is produced using a conventional optical interferometric, ball on disc test rig (PCS Instruments Ltd., Acton, UK), where a steel ball is loaded against a glass disc, as shown in Fig. 1. Both ball and disc can be rotated independently to give a range of slide-roll-ratios, however, only pure rolling conditions were used in this study. The lubricant is held in a temperature-controlled bath (\u00b10.5 C) and the ball is half-immersed in lubricant to ensure fully flooded conditions.\nIn this study, the contact was located beneath a fluorescence microscope (Axovaria manufactured by Zeiss,",
            "Jena, Germany), with a 920 Olympus Neofluor objective. Excitation was provided using a solid-state, diode-pumped pulsed laser, which produced a beam of wavelength 532 nm (Laser2000 Ltd., Northants, UK). It has a repetition rate of 0.2\u201320 kHz and average maximum power output of 40 mW at 3 kHz, which is sufficiently low to ensure no bleaching of the dyed lubricant over the duration of the test.\nA high speed camera with a built-in image intensifier (Focusscope SV200-i, manufactured by Photron Ltd., West Wycombe, UK) was mounted above the beam splitter, so that it received the emitted fluorescence from the contact. The intensifier was required as a relatively small amount of light was emitted from the contact during the required 4 ls exposure. Each light pulse emitted from the laser was synchronised to fall within the exposure of the high speed camera, so that no erroneous fluctuations in measured intensity (beating) occurred.\nAs described in Sect. 3.2, the fluorescent light emitted from the contact is of longer wavelength than the excitation of the laser. This allows the separation of the two light beams by a dichroic beam splitter located between the objective and camera as shown in Figs. 1 and 2. The\ncharacteristics of the beam splitter as well as the laser and dye wavelengths are shown in Fig. 3.\nStop 1 was opened fully for all tests. Stop 2 was opened sufficient to illuminate/view the circular contact area. Other optical components Lens 1, Filter 1 (used to allow only 532 nm light through), the beam expander and tilting mirrors used for laser beam alignment were mounted onto a common rail with the laser source.\n2.2 Lubricant\u2013Dye Combinations\nGlycerol was used as the lubricant for the majority of testing, since its polar nature allows it to dissolve a range of commercially available dyes. For this study, the dye Eosin was dissolved at a concentration of 0.04% by mass. Eosin was chosen since its absorption peak coincided with the excitation wavelength of the available laser (532 nm) and its quantum yield was sufficiently high to result in bright, well-defined images of the contact. The absorption and emission spectra for Eosin are shown in Fig. 3, alongside the characteristics of the dichroic beam splitter used to separate excitation and emitted light.\nDue to the difficulty in identifying reasonable cost, hydrocarbon-soluble dyes which fluoresced at the",
            "wavelength of the laser excitation, the option of using the natural fluorescence of un-dyed lubricant was considered (as used by Smart et al. [12]). This approach was not implemented, however, since the high intensity afforded by a commercially available dye was required to capture images of the thin lubricant films being studied. An additional advantage of using a dye is that the intensity of the emitted fluorescence can be precisely controlled by varying the concentration of dye used.\n2.3 Dye Entrainment Method\nIn order to observe how lubricant flows though a contact, the following procedure was implemented. Initially, a clean disc was loaded against the steel ball, and the lubricant bath filled with pure (un-dyed) glycerol; whilst a single drop of fluorescer-containing glycerol was carefully placed on the lower surface of the otherwise clean disc, upstream of the contact. Then, as the disc was subsequently rotated, the dyed portion of lubricant moves towards the contact before reaching the meniscus, and being entrained. Images of the entrained fluorescence were then recorded to show the path of the lubricant through the contact. This was possible as differences in physical properties between the fluorescerfree and fluorescer-containing lubricant are negligible at the fluorescer concentration used.\nA source of error in this approach is the diffusion of dye due to random molecular motion. It is accepted that diffusion occurs in the period of time between the dyed lubricant reaching the meniscus and inlet of the contact; what is critical however is the extent that random diffusion occurs as the dye passes through the contact, since this effect will mask the observed mixing due to fluid flow. The extent of random diffusion can be calculated by solving Ficks\u2019 second law, giving the variation in concentration with time and distance from the point of contact between dyed and un-dyed lubricant proportions (at the meniscus). For the entrainment speed of 0.075 ms-1 that was used, the time taken for the fluid to flow through the contact is of the order of 5 ms, which gives a calculated change in dye concentration due to diffusion of\\1%. This is because the time taken for the dye to pass through the contact is very small compared to the time for the dye to pass through the meniscus. The solution of Ficks\u2019 second law used here, has been omitted for brevity; however, it can be found in most textbooks on diffusion, for instance [30, pp. 28\u201331].\nThe diffusion coefficient used in the above calculation is that for glycerol, which at atmospheric pressure has a value of 0.06 m2 s [31]. However, it has been shown [31] that diffusion coefficients for glycerol are nearly inversely proportional to liquid viscosity. Therefore, diffusion of the dye will be further reduced due to the elevated viscosities present within the contact.\nFigure 4 shows a fluorescence intensity map obtained from a contact fully flooded with Eosin-doped glycerol in steady-state conditions. If film thickness measurement was the objective of these tests, this intensity map could be converted to a map of film thickness by applying a calibration. Such a calibration would be achieved by plotting the known film thickness versus fluorescent intensity from a fluorescence image of the ball loaded statically against the disc as was done by Sugimura [26]. From Fig. 4, the typical horseshoe shape is clearly visible. The dark region at the outlet of the contact is due to cavitation; around which streamers can be seen. Since the presence of lubricant in this region is reduced, it appears darker. This highlights a further possible area of study using fluorescence, i.e. study of the separation of lubricant between ball and disc, once it leaves the rear of the contact.\nFigure 5 shows the profile of intensity taken along the dashed line in Fig. 4, where the typical film shape and constriction can be seen at the outlet. Also plotted in Fig. 5 is the optical interference measurement of film thickness for the contact lubricated under the same conditions. Although, the fluorescent intensity is not calibrated to film thickness, there is clearly a good match between the two measurements. It should be noted that fluorescent intensity gives a measure of the amount of lubricant present, rather than the gap thickness. Therefore, within the cavitated region fluorescence and optically measured thickness cannot be compared, and have not been plotted in Fig. 5.\nFigure 6 shows the fluorescent maps obtained when the fluorescent dye entrainment technique described in Sect. 2.3 was carried out. The lubricant progression through the contact is evident, from time = 0, when no dye is present in the contact, to 5.5 ms later when the contact is flooded"
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.17-1.png",
        "caption": "Figure 6.17. Relative motion of a slider block on a rotating table.",
        "texts": [
            " The first concerns the free sliding motion of the block due to inertial forces induced by the table's rotation. The second problem is similar, but more interesting. An additional controlling spring is introduced, and depending on the nature of two physical parameters, one due to the rotation and the other due to the spring, the governing equation of motion may have a solution of either trigonometric or hyperbolic type, or neither. 6.9.1. Uncontrolled Motion of a Slider Block A block S of mass m shown in Fig. 6.17 is constrained initially by a cord fastened at the end point A of a smooth slot milled in a table that turns in the horizontal plane with a constant angular speed co.When the string is cut suddenly, the block slides freely in the slot. We wish to determine the motion xeS, t) of the slider block relative to the spinning table, and the behavior of the force that acts on the block as a function of its position in the slot and as a function of time. The free body diagram of the sliding block is shown in Fig. 6.17a. Of course , the string force Fs = 0, and the weight of the block is W = - Wk. Because the slot is smooth, it exerts on S only the normal contact forces N = -Nj in the plane of the table and R = Rk perpendicular to it. The total force acting on S is F =N+R +W, and hence the equation of motion for S in the inertial frame <I> = {F;Ik } fixed in the laboratory is given by F = -Nj + (R - W)k = mas . (6.76a) The absolute acceleration as of S in <I> may be obtained from (4.48) . With ao = 0, W f = wk, Wf = 0, and xeS, t) = xi +aj in the reference frame cp = {0 ; ik } fixed in the table, as shown in Fig. 6.17, the total acceleration of S referred 144 Chapter 6 to ep is (6.76b) Substitution of (6.76b) into (6.76a) yields the scalar equations N = m(aw2 - 2wx) , R=W. (6.76c) The first of these equations determines the motion x(t) of S relative to the table, and the next one determines the normal contact force N either as a function of x or of t. The last relation confirms that since there is no motion of S normal to the table, the slot reaction force R balances the weight W, so that R +W = 0 in (6.76a). Therefore, in future problems where the motion is constrained to a smooth horizontal plane, for simplicity, the trivial normal equilibrated forces may be ignored. The first equation in (6.76c) has the same form as the homogeneous equation (6.58) whose solution is given by (6.59) . Therefore, the slider' s motion is given by x(t) = A sinh cot+ B cosh cot. (6.76d) The slider is initially at rest at x(O) = a in frame tp, as shown in Fig. 6.17, and hence x(O) = O. Thus , with x (t ) = Aw cosh on + Bw sinhwt , it follows that Dynamics of a Particle A = 0, B = a; hence 145 x(t) = a cosh cot, x(t) = awsinhwt. (6.76e) Therefore, the motion of S relative to the table frame may be written as x(S , t) = a(coshwti + j) . (6.76f) Use of (6.76e) in the second equation in (6.76c) gives the slot reaction force N = - NJ as a function of time; N = N(t) = -maw2(l - 2sinhwt)j. (6.76g) Alternatively, use of the identity (6.63) yields the slot reaction force as a function of the slider's position along the slot: (6",
            "fi em, and the previous formulas show that N vanishes, and then reverses its sense of application, after t* ~ 0.023 sec when S has moved a distance d\" = x* - a ~ 2.086 em from its initial position . When the string was cut, the motion of the block along the slot was no longer controlled, and the inertial effect of the table's rotation drove the slider increasingly farther from its rest state toward the end of the slot. The controlling effect of an additional spring force is illustrated next. 6.9.2. Controlled Motion and Instability of a Slider Block Suppose that the string shown in Fig. 6.17 is replaced by a linear spring of stiffness k fastened at A and to the block S, initially at rest at the natural state of the spring at x = a but otherwise free to slide in the smooth slot. We wish to investigate the motion x(S, t) of the block relative to the rotating table. The free body diagram of the sliding block is shown in Fig. 6.17a in the table frame tp, The forces are the same as before with the addition of the spring force Fs = -k(x - a)i. Since there is no motion normal to the horizontal plane, R +W = 0, as noted before . Therefore, the equation of motion for S in the inertial 146 frame <1> , but referred to the table frame rp, is given by F = N +Fs = -Nj - k(x - a)i = mas. Here we recall (6.76b) to obtain the scalar equations x+ p2(l - 1J2)x = ap\" , N =m(aw 2 - 2wi) , wherein, by definition, Chapter 6 (6.77a) (6.77b) (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001562_j.conengprac.2013.12.004-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001562_j.conengprac.2013.12.004-Figure3-1.png",
        "caption": "Fig. 3. Blade-fixed frame of the main rotor.",
        "texts": [
            " In addition, the stabilizer bar, which receives only the cyclic inputs required for it to act as a lagged-rate feedback system that aids flying, should be considered because explicitly modeling the stabilizer bar can provide important information about the helicopter, such as a precise identification of the physical parameters of the stabilizer and rotor (see Mettler, 2003). In this section, we derive the dynamics of the main rotor. Flapping motion is one part of the rotation motion of the blade. We can establish the blade-fixed reference frame by considering the axes fixed in the blade (which is parallel to the principal axes), origin at the hinge (with the i-axis along the blade span), the j-axis perpendicular to the span and parallel to the plane of rotation, and the k-axis completing the right-hand set (Fig. 3). Then, the rotation matrix from the body-fixed frame to the blade-fixed frame can be expressed as Rr b \u00bc cos \u03b2 cos \u03a8 cos \u03b2 sin \u03a8 sin \u03b2 sin \u03a8 cos \u03a8 0 sin \u03b2 cos \u03a8 sin \u03b2 sin \u03a8 cos \u03b2 2 64 3 75 \u00f05\u00de where \u03b2 is the flapping angle and \u03a8 is the azimuth of the blade. The blade rotates mainly from the rotation of the fuselage, the rotation of the rotor hub, and flapping motion. The angular velocity components of the blade represented in the blade-fixed reference frame are \u03c9i \u03c9j \u03c9k 2 64 3 75\u00bc cos \u03b2 cos \u03a8p cos \u03b2 sin \u03a8q sin \u03b2r \u03a9 sin \u03b2 sin \u03a8p\u00fe cos \u03a8q _\u03b2 sin \u03b2 cos \u03a8p\u00fe sin \u03b2 sin \u03a8q cos \u03b2r \u03a9 2 64 3 75 \u00f06\u00de where \u03a9 is the rotation speed of the main rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.6-1.png",
        "caption": "Figure 2.6. Balanced 6-dof mechanism with springs",
        "texts": [
            ",,2,2211 igrmgrmgrmdhk l l iiiiililililil il iu 6 1 6 1 1117 1 i i ililil il liullp dhk l lmglglmD 6 1 22111 1 i iiiiilil il l rmrmrm l gl 6 2 1 18 i ililil il i pp dhk l a axgmD 6 2 22111 1 i iiiiilil il iui rmrmrm l mag 6 2 1 19 i ililil il i pp dhk l b bygmD 6 2 22111 1 i iiiiilil il iui rmrmrm l mbg 6 2 1 110 i ililil il i pp dhk l c czgmD 6 2 22111 1 i iiiiilil il iui rmrmrm l mcg and where a1i = a1 \u2013 ai, b1i = b1 \u2013 bi, c1i = c1 \u2013 ci. Similarly to the previous cases, when the coefficients of the configuration variables in Equation (2.36), i.e. Di (i = 1, \u2026, 10) vanish, the total potential energy will be constant. Thereby, sufficient conditions for the static balancing for this type of mechanism are 10...,,1,0 iDi (2.37) An example of balanced mechanism is represented schematically in Figure 2.6. Dynamic balancing involves two conditions, namely, force balancing and the condition on the angular momentum given in Equation (2.8). It should be clearly understood that dynamic balancing is a property of the moving masses and that it is not related to actuation. A dynamically balanced mechanism will be reactionless for any location of the actuators, provided that the inertia of the actuators is included in the conditions. Similarly to what was presented for static balancing, the dynamic balancing of the simple planar four-bar linkage is first presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.13-1.png",
        "caption": "Figure 6.13. An ideal spring-mass system.",
        "texts": [
            " When m is displaced a distance 8 from the natural , unstretched spring configuration, it exerts on the spring a uniaxial force FH given by (6.64). In response, the spring exerts an equal but oppositely directed restoring force Fs = - FH = -k8, called the springforce, that acts always to return the mass toward the natural state of the spring . Hence, if released, the mass will vibrate under the alternating extension and compression reactions of the spring itself. Let us first study the oscillations of the mass on a smooth horizontal surface, as shown in Fig. 6.13. To characterize the horizontal oscillatory motion of the mass , we suppose that m is given an initial uniaxial velocity Vo = voi from its natural equilibrium configuration in et> = {F ;i,j} shown in Fig. 6.13. The free body diagram of m is shown in Fig . 6.I3a. The weight W is balanced by the normal reaction N of the smooth surface, so the only force that affects the horizontal, uniaxial motion of m is the spring force Fs = -kxi, in which x =8 denotes the displacement of m, the change of length of the spring from its natural state . Therefore, the equation 134 Chapter 6 of motion of m, namely, Fs = mii, becomes with p =I\"f. (6.65a) This equation has the form (6.50) whose general solution is given by (6",
            " The motion of a particle P initially at rest at the origin is governed by the equation x - q2x = e\" , Find the motion of P. 6.33. Themotionsof twoparticles P and Q aregovernedby thefollowingscalarequationsof motion: x(P , t) + p2x(P, t) = g and x(Q, t) - p2X(Q, t) = g , in which p and g are constants. Initially. each particle is started separatelyat theplacex(O) = Xowitha speed vo.Find themotions of P and Q and discuss their physical nature. Determine their common motion when p = O. 6.34. A linearspring-masssystemshownin its naturalstate in Fig.6.13,page 134,is givenan instantaneous initial speed Vo= 3ft/sec on a smoothhorizontal surface.Themassm = 8 Ibm and the spring stiffnessk = 3 Ib/in. Suppose that g = 32 ft/sec\".What is themaximumdisplacement of m? Caution: See Chapter 5 remarks on measure units, page 86. 6.35. A linear spring of stiffness k supports weights Wand nW connected by a cord, as shown. Initially, the system is at rest. (a) Determine the accelerationof the load nW immediately Problem 6.35. 208 Chapter 6 after the cord supporting the load W is cut",
            " The exact solution for z(t ) may be obtained from (7.83f) in terms of Jacobian elliptic function s introduced later; however, we shall not pursue this problem further . (See Synge and Griffith.) 0 Exercise 7.13. Apply the Newton-Euler law to formulate the spherical pendulum problem. Hint: Show that zr = -4rdf2/dz. 0 Example 7.16. Constant energy curve s in the phase plan e. Use the energy principle to derive the differential equation for the smooth, horizontal motion of the linear spring-mass system in Fig. 6.13. page 134. Show that\"the phase plane trajectories, the curves in the x v-plane , are curves of constant total energy. 262 Chapter 7 Solution. The free body diagram is shown in Fig. 6.13a. The weight of the oscillato r and the normal surface reaction do no work in any rectilinear motion along the smooth horizontal surface . The elastic potential energy of the linear spring force acting on m is given by (7.65) : Vex ) = !kx2, wherein V(O) = 0 in the natural state x = O. The system is conserva tive with kinetic energy K = ! mi2, so the energy principle (7.73) yields !mi2 + ! kx2 = E, (7.84a) The equation of motion is obtained by differentiati on of (7.84a) with respect to the path variable x or with respect to time; we find mx + kx = O",
            " The results for all values of flo ::: 60\u00b0 must be discussed, but it is anticipated that questions concerning the effects of variations in the period and the potential influence of larger amplitudes may arise . Provide your supervisor with a brief preliminary report that will convey clearly all of the desired information. 7.59. (a) The small amplitude period of a simple pendulum is 2 sec. What is its period for an amplitude ex = \u00b1If / 2 rad? (b) Suppose the same pendulum has just adequate initial velocity to complete a full revolution . Find the time required for the bob to advance 90\u00b0 from its lowest position. 7.60. A spring-mass system similar to that in Fig. 6.13, page 134, consists of a mass m attached to two concentric springs . The inner spring has linear response with stiffness k[. The other is a nonlinear conical spring with stiffness k2 , whose spring force is proportional to the cube of its extension x from the natural state. The mass is given an initial displacement Xo from the natural state and released to oscillate on the smooth horizontal surface . (a) Derive the equation of motion for m, and solve it to obtain an integral for the travel time t = t(x)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001144_20110828-6-it-1002.03266-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001144_20110828-6-it-1002.03266-Figure1-1.png",
        "caption": "Fig. 1. Prototype of Dual-fan VTOL air vehicle having lateral and longitudinal tilting rotors.",
        "texts": [
            " A complete dynamic model of this type of UAVs is provided in details in this paper. This entirely new system, which uses only the dual lift-fans themselves for control, has been developed recently Gress (2007). It utilizes the inherent gyroscopic properties and driving torques of the fans for vehicle pitch control, and it eliminates the need for external control elements or lift devices. The system enables agile and compact VTOL air vehicles by generating pure and extensive moments rather than just forces. Fig. 1 shows the prototype of the VTOL UAV used to do simulations of predicted pitch, yaw and roll motions by considering the propellers\u2019 tilt angles as inputs to the complete model of this type of vehicle that is presented in this paper. This prototype is called eVader. The remainder of this paper is organized as follows: In Section II a lift-fan OAT mechanism and its capability of providing the three required moments (pitch, roll and yaw) are described. The proposed model is derived in Section 978-3-902661-93-7/11/$20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003341_s12206-020-0129-0-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003341_s12206-020-0129-0-Figure2-1.png",
        "caption": "Fig. 2. The force vector diagrams of ball: (a) Without the gyroscopic moment of ball; (b) with the gyroscopic moment of ball.",
        "texts": [
            " According to the Hertz theory of point contact, ik\u03b4 and ok\u03b4 can be expressed as: 2 3 2 3 \u00ec \u00e6 \u00f6 \u00ef = \u00e7 \u00f7 \u00ef \u00e8 \u00f8 \u00ed \u00e6 \u00f6\u00ef = \u00e7 \u00f7\u00ef \u00e8 \u00f8\u00ee ik ik ik ok ok ok Q\u03b4 K Q\u03b4 K (5) where Qik and Qok denote the contact loads of ball-inner raceway and ball-outer raceway, respectively, and the Kik and Kok are the load-deformation coefficients of ball-inner raceway and ball-outer raceway, respectively. In order to obtain the explicit expressions of contact loads Qik and Qok, the vector diagram method is applied in the force analysis of ball instead of the orthogonal decomposition method. For comparison, the mechanical state of ball without considering the gyroscopic moment is given first. As shown in Fig. 2(a), the vector equilibrium equation of ball can be written as: 0+ + = uuur uuur uuur ck ik okF Q Q (6) where uuur ckF is the vector of ball centrifugal force, according to the sine theorem of plane triangle, one can obtain: ( )sin sin sin = = - ik ok ck ok ik ik ok Q Q F \u03b1 \u03b1 \u03b1 \u03b1 (7) ( ) ( ) sin sin sin sin \u00ec =\u00ef -\u00ef \u00ed \u00ef = \u00ef -\u00ee ok ik ck ik ok ik ok ck ik ok \u03b1Q F \u03b1 \u03b1 \u03b1Q F \u03b1 \u03b1 (8) When the gyroscopic moment of ball is taken into account, as shown in Fig. 2(b), the vector equilibrium equation of ball can be rewritten as: 0+ + + + = uuur uuur uur uuur uur ck ik ik ok okF Q T Q T (9) where uur ikT and uur okT are the friction forces in ball-inner raceway and ball-outer raceway contacts, respectively. Since the friction forces are used to offset the action of ball gyroscopic moment, the follow expressions can be obtained: 2 2 \u00ec =\u00ef\u00ef \u00ed \u00ef =\u00ef\u00ee gk ik ik gk ok ok M T \u03bb D M T \u03bb D (10) where Mgk is the gyroscopic moment of ball. 1+ =ik ok\u03bb \u03bb (11) In order to further determine the sizes of Tik and Tok, several different allocation schemes of the frictions were given in previous literatures, and the most representative allocation methods are given by Jones based on the Raceway Control Hypothesis: Inner Raceway Control Hypothesis: =ik\u03bb 0",
            " To overcome this defect, an improve allocation scheme of the frictions in ball-raceway contacts was given based on the equal friction coefficient assumption [8]. 21 = = = + gkik ok ik ok ik ok MT T\u03bc Q Q Q Q D (12) 2 2 \u00ec =\u00ef +\u00ef \u00ed \u00ef =\u00ef +\u00ee gkik ik ik ok gkok ok ik ok MQT Q Q D MQT Q Q D (13) thus \u00ec =\u00ef +\u00ef \u00ed \u00ef = \u00ef +\u00ee ik ik ik ok ok ok ik ok Q\u03bb Q Q Q\u03bb Q Q (14) Based on the above analysis, the vector equilibrium equation of ball can be further simplified as: 0+ + = uuur uur uuur ck ik okF F F (15) \u00ec = +\u00ef \u00ed = +\u00ef\u00ee uur uuur uur uuur uuur uurik ik ik ok ok ok F Q T F Q T (16) As shown in Fig. 2(b), according to the sine theorem of plane triangle: ( )sin sin sin = = - ik ok ck ok ik ik ok F F F \u03b8 \u03b8 \u03b8 \u03b8 (17) \u0394 \u0394 = -\u00ec \u00ed = -\u00ee ik ik ik ok ok ok \u03b8 \u03b1 \u03b1 \u03b8 \u03b1 \u03b1 (18) According to Eqs. (12) and (13), one can obtain: 21\u0394 \u0394 \u0394 arctan \u00e6 \u00f6 = = = \u00e7 \u00f7 +\u00e8 \u00f8 gk ik ok ik ok M \u03b1 \u03b1 \u03b1 Q Q D (19) - = -ik ok ik ok\u03b8 \u03b8 \u03b1 \u03b1 (20) therefore ( ) ( ) ( ) ( ) sin \u0394 sin sin \u0394 sin \u00ec - =\u00ef -\u00ef \u00ed -\u00ef =\u00ef -\u00ee ok ik ck ik ok ik ok ck ik ok \u03b1 \u03b1 F F \u03b1 \u03b1 \u03b1 \u03b1 F F \u03b1 \u03b1 (21) In addition, the ball-raceway contact loads Qik and Qok can be written as: cos\u0394 cos\u0394 =\u00ec \u00ed =\u00ee ik ik ok ok Q F \u03b1 Q F \u03b1 (22) Besides, the centrifugal force and gyroscopic moment of ball can be expressed: 20"
        ],
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    },
    {
        "image_filename": "designv10_12_0001090_isie.2011.5984510-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001090_isie.2011.5984510-Figure1-1.png",
        "caption": "Figure 1. Quadrotor configuration frame system",
        "texts": [
            " In Section II the nonlinear quadrotor dynamics and the linearization based on multiple PWAs, are presented, followed by the mathematical formulation of the physical constraints. In Section III the development of the full MPC scheme, for the translational and the rotational movements of the quadrotor, are presented. Finally in Section IV extended simulation results that depict the efficiency of the proposed control scheme are depicted followed by the conclusions in the last Section V. In this article, the model of the UAV is corresponding to a small\u2013sized unmanned quadrotor, as the one depicted in Figure 1. The quadrotor\u2019s motion is governed by the lift forces produced by the rotating blades, while the translational and rotational motions are achieved by means of difference in the counter rotating blades. Specifically the forward motion is achieved by the difference in the lift force, produced from the front and the rear rotors velocity, the sidewards motion by the difference in the lift force from the two lateral rotors, while the yaw motion, is produced by the difference in the counter\u2013 torque between the two pairs of rotors front\u2013right and back\u2013 left",
            " 978-1-4244-9312-8/11/$26.00 \u00a92011 IEEE 2243 For deriving the model of the quadrotor, the following assumptions should be made: a) the structure is rigid and symmetrical, b) the center of gravity and the body fixed frame origin coincide, c) the propellers are rigid, and d) the thrust and drag forces are proportional to the square of propeller\u2019s speed. Two coordinate systems have been utilized, i.e. the Body\u2013fixed frame B= [B1,B2,B3] T and the Earth\u2013fixed frame E = [Ex,Ey,Ez] T . The quadrotor in Figure 1, as it has been appeared in [8], can be described as: X\u0307 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03c6\u0307 \u03c6\u0308 \u03b8\u0307 \u03b8\u0308 \u03c8\u0307 \u03c8\u0308 z\u0307 z\u0308 x\u0307 x\u0308 y\u0307 y\u0308 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03c6\u0307 \u03b8\u0307 \u03c8\u0307a1 + \u03b8\u0307a2\u03a9r +b1U2 \u03b8\u0307 \u03c6\u0307 \u03c8\u0307a3 \u2212 \u03d5\u0307a4\u03a9r +b2U3 \u03c8\u0307 \u03b8\u0307 \u03d5\u0307a5 +b3U4 z\u0307 g\u2212 (cos\u03c6 cos\u03b8)U1/m x\u0307 (cos\u03c6 sin\u03b8 cos\u03c8 + sin\u03d5 sin\u03c8)U1/m y\u0307 (cos\u03c6 sin\u03b8 sin\u03c8 \u2212 sin\u03d5 cos\u03c8)U1/m \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (1) U = \u23a1 \u23a2\u23a2\u23a2\u23a3 U1 U2 U3 U4 \u03a9r \u23a4 \u23a5\u23a5\u23a5\u23a6= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 b(\u03a92 1 +\u03a92 2 +\u03a92 3 +\u03a92 4) b(\u2212\u03a92 2 +\u03a92 4) b(\u03a92 1 \u2212\u03a92 3) d(\u2212\u03a92 1 +\u03a92 2 \u2212\u03a92 3 +\u03a92 4)\u2212\u03a91 +\u03a92 \u2212\u03a93 +\u03a94 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 (2) a1 = (Iyy \u2212 Izz)/Ixx a2 = Jr/Ixx a3 = (Izz \u2212 Ixx)/Iyy a4 = Jr/Iyy a5 = (Ixx \u2212 Iyy)/Izz b1 = la/Ixx b2 = la/Iyy b3 = 1/Izz (3) where the state vector X \u2208 \u211c12, contains the translational components \u03be = [x, y, z]T , \u03be\u0307 = [x\u0307, y\u0307, z\u0307]T and the rotational components of the quadrotor, with respect to the ground, defined by the vectors \u03b7 = [\u03c6 , \u03b8 , \u03c8]T , \u03b7\u0307 = [\u03c6\u0307 , \u03b8\u0307 , \u03c8\u0307]T "
        ],
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    },
    {
        "image_filename": "designv10_12_0003352_asjc.2318-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003352_asjc.2318-Figure1-1.png",
        "caption": "FIGURE 1 Quadrotor configuration",
        "texts": [
            " Various configuration errors and nonlinear disturbance observer design have been presented in Section 3. Section 3 also explains the development of the geometric controller while compensating for the external disturbances along with the proofs. Simulation results and Experimental results on a hardware setup have been presented in Section 4 and Section 5 respectively. The dynamic model of a quadrotor is obtained by considering two frames of reference. The inertial frame of reference is denoted by {OI ,XI ,YI ,ZI}with the origin as OI as shown in Figure 1. The body fixed frame of reference is denoted by {OB,XB,YB,ZB}with the origin as OB. To define the configuration of a rigid body with respect to an inertial frame, we need to specify both the position and orientation of the rigid body with respect to the inertial frame. Let us define some symbols before writing the dynamic equation of motion. x \u2208 R3: position of origin of body fixed frame with respect to earth fixed frame, R \u2208 SO(3): rotation matrix to specify the orientation of body fixed frame with respect to earth fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure14-1.png",
        "caption": "Fig. 14 The initial configurations of a the Miura-ori and b the kirigami in which b = 90",
        "texts": [
            " The Miura-ori has 90 minor and major folds whilst this number decreases to 26 for the kirigami. Thus, Uc for the Miura-ori: Uc for the kirigami = 90: 26. The numerical predictions are in good agreement with this ratio, see Fig. 13a. The same ratio also holds for the magnitude of the reaction force which is shown in Fig. 13b. The animation videoes for Miura-ori and the derived kirigami are given in Online Resources 9 and 10, respectively. 5.5 Pinching the Miura-ori and the derived Kirigami This example considers the Miura-ori and its derived kirigami pinched at nodes A and B, see Fig. 14a, b. Node B is fixed whilst node A is prescribed with U = W = 0 andV = - 0.03. Node C is restrained from moving along the X-direction to avoid the rigid body rotation about the Y-axis. The crease stiffness per unit length is k = 1 and b equals 90 in the initial configuration. The other settings are the same as the previous example except that the initial time step for the kirigami resumes to 1. Figure 15a shows the final configuration for the Miura-ori which resembles a saddle and is in agreement with the experiment (Schenk and Guest 2011). To quantify the curved surface, a polynomial surface of degree 2 in both X and Y is constructed by least-square fit using the marked nodes in Fig. 14a, b. The curvatures jx and jy at node C are evaluated (Liu and Paulino 2017). The histories of the curvatures and reaction force (Y-component) are plotted against the displacement-VA in Fig. 15b. The results for the kirigami are shown in Fig. 15c, d. For both structures, jx and jy vary almost linearly with the displacement. Due to the removed facets, the reaction force of the kirigami is much lower than that of the Miura-ori. Moreover, the final configuration of kirigami is shallower than that of the Miura-ori, see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001818_978-3-319-19740-1_15-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001818_978-3-319-19740-1_15-Figure7-1.png",
        "caption": "Fig. 7 Coordinate systems associated with the contact model in Fig. 6",
        "texts": [
            " The geometry of the tooth surfaces of a pair of mating pinion and gear can be generally represented by the position vector, unit normal and unit tangent in the coordinate systems S1 and S2 that are rigidly connected to the pinion and the gear, respectively, as follows, Pinion : r1 \u00bc r1\u00f0u1; h1;u1\u00de n1 \u00bc n1\u00f0u1; h1;u1\u00de t1 \u00bc t1\u00f0u1; h1;u1\u00de f1\u00f0u1; h1;u1\u00de \u00bc 0 8>>< >: ; \u00f013\u00de Generated gear : r2 \u00bc r2\u00f0u2; h2;u2\u00de n2 \u00bc n2\u00f0u2; h2;u2\u00de t2 \u00bc t2\u00f0u2; h2;u2\u00de f2\u00f0u2; h2;u2\u00de \u00bc 0 ; 8>< >: \u00f014\u00de Formate gear : r2 \u00bc r2\u00f0u2; h2\u00de n2 \u00bc n2\u00f0u2; h2\u00de t2 \u00bc t2\u00f0u2; h2\u00de 8< : : \u00f015\u00de Step 3: Assembly of the pinion and gear members in their running position, as shown in Fig. 6, and representing the tooth surfaces of both members in a global coordinate system Sf that is fixed to the frame, including the assembling parameters, nominal offset and displacement E0 \u00fe DE, gear axial displacement \u0394G, pinion axial displacement \u0394P, and nominal shaft angle and displacement R0 +\u0394 R, as shown in Fig. 7. Given the initial contact position on the gear flank, the assembling displacements are determined using the improved algorithm described in [4]. Default displacement values of DE, \u0394G, \u0394P, and \u0394 R are zero. Using the concept of potential contact lines, an advanced version of TCA has been developed for modeling and simulation of meshing for both face-milled and face-hobbed spiral bevel and hypoid gear drives. The algorithm of TCA is based on the identification of the tooth surface gaps along the potential contact lines and is determined by Eq",
            " The angular displacements of the pinion and the gear, /1 and /2 are explicitly represented in terms of functions of the surface normals as, /1 \u00bc sin 1 cos d1\u00bde2f e1f \u00f0e1f n1f \u00de e2f n2f \u00f0e1f n1f \u00dee2f d1; \u00f017\u00de /2 \u00bc sin 1 cos d2\u00bde1f e2f \u00f0e2f n2f \u00de e1f n1f \u00f0e2f n2f \u00dee1f d2: \u00f018\u00de Here, d1 \u00bc tan 1 \u00bd\u00f0n1f e1f \u00de e1f e2f \u00f0n1f e1f \u00de e2f ; d2 \u00bc tan 1 \u00bd\u00f0n2f e2f e2f e1f \u00f0n2f e2f \u00de e1f where n1f and n2f are unit normals of the pinion and gear tooth surface, which are calculated under /1 \u00bc 0 and /2 \u00bc 0; and e1f and e2f are unit vectors on the axes of the pinion and gear shown in Fig. 7. Equations 16 and 17 are derived based on the contact condition that, at the contact point, the surface normals are co-linear. Step 4: Determination of the effective contact boundary, the overlapped area of mating tooth surfaces. The contact boundary on the gear member is determined using the conjugate image of the pinion tooth surface and vice versa. Step 5: Calculation of the potential contact lines on both members using Eqs. 1\u20135 under the given displacement values of DE, \u0394G, \u0394P and \u0394R, and the ease-off value D at each point of potential contact lines within the effective boundary of contact shown in Fig"
        ],
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    },
    {
        "image_filename": "designv10_12_0000995_j.jfranklin.2013.09.008-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000995_j.jfranklin.2013.09.008-Figure2-1.png",
        "caption": "Fig. 2. The helicopter flight control platform.",
        "texts": [
            " Noticing the fact that [28] STsgn\u00f0S\u00de \u00bc \u2211 m i \u00bc 1 jSijZ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u2211 m i \u00bc 1 jSij2 s \u00bc \u2016S\u2016 \u00f030\u00de So ST\u0393\u03c6 sgn\u00f0ST\u0393\u03c6\u00de \u00bc \u2016ST\u0393\u03c6\u2016 \u00f031\u00de ST\u039bPx sgn\u00f0ST\u039bPx\u00de \u00bc \u2016ST\u039bPx\u2016 \u00f032\u00de Considering 0oAr I sr IrB, the following expressions can be obtained: \u00f0I s A\u00deA 1\u2016ST\u039bQF\u00f0x\u00de\u2016o0 \u00f033\u00de Because A Bo0; I s AoB A and \u00f0I s\u00deA 14I, A 1\u00f0I s\u00de\u00f0B A\u00deA 140 \u00f034\u00de A 1\u00f0I s A\u00de40 \u00f035\u00de A 1\u00f0I s A\u00deoA 1\u00f0I s\u00de\u00f0B A\u00deA 1 \u00f036\u00de A 1\u00bd\u00f0I s\u00de\u00f0A B\u00de\u2016ST\u0393\u03c6\u2016 \u00f0I s A\u00deST\u0393\u03c6 o0 \u00f037\u00de A 1\u00bd\u00f0I s\u00de\u00f0A B\u00de\u2016ST\u039bPx\u2016 ST \u00f0I s A\u00de\u039bPx o0 \u00f038\u00de ST\u039bQF\u00f0x\u00der\u2016ST\u039bQF\u00f0x\u00de\u2016 \u00f039\u00de Considering Eqs. (33)\u2013(39), the conclusion of _Vo0 can be obtained. So the theory is proved. 4. Simulation verification Here only the nonlinear MIMO system for self-repairing control is simulated as that the SISO system is the special case of the MIMO system. The helicopter flight control platform is shown in Fig. 2 [29]. To simplify, only the vertical flight model is investigated in this paper. The vertical dynamic model of helicopter has been developed in the paper [29]. The state is assigned x1 \u00bc h, x2 \u00bc _h, x3 \u00bc\u03c9, x4 \u00bc \u03b8c and x5 \u00bc _\u03b8c, then the fault dynamic model can be re-written as follows _x\u00bc x2 0:25CT \u00f0x4\u00dex23 0:1x2 0:1x22 17:66 0:7x3 0:0028x23 0:005x2:3 sin x4 13:92 x5 800x4 65x5 0:1x23 sin x4 \u00fe 434:88 2 6666664 3 7777775 \u00fe 0 0 0 0 0:1088 0 0 0 0 0:254 2 6666664 3 7777775 uth u\u03b8c \" # \u00f040\u00de where CT \u00f0x4\u00de \u00bc 0:032592\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:001062238\u00fe 0:06145x4 p 2 , h is the helicopter altitude above the ground and \u03b8\u03b8c is the collective angle of blade; \u03c9 is the rotational speed of the rotor blade; the input of the throttle is uth and the input of the collective servomechanism is u\u03b8c "
        ],
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        "image_filename": "designv10_12_0001128_9781118562857.ch1-Figure1.32-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001128_9781118562857.ch1-Figure1.32-1.png",
        "caption": "Figure 1.32. Effect of: (a) scan speed; and (b) powder feed rate on track geometry",
        "texts": [
            " As the Eulerian method of description is used, the laser-material interaction time at the observation plane will be limited to interaction time (\u03c4). Therefore, the interaction time is divided into finite time steps (\u0394t) to simulate the temporal temperature distribution and track geometry. Figure 1.31 presents the temporal track geometry and melt-pool at three discrete time steps \u0394t= \u03c4 /10, \u0394t= \u03c4 /2 and \u0394t= \u03c4. The effect of the laser beam, in mixed mode at various laser scanning speeds, on track geometry was numerically simulated. Figure 1.32a presents the simulated results of the effect of the scan speed on the predicted track, i.e. scan speeds of 300, 600, 1,000 and 3,000 mm/min with a fixed laser power (Pl) of 800 W and powder feed rate (mp) of 8 g/min. A decrease in the track height was observed with the increase in scan speed, due to the reduced powder feed per unit length when sufficient laser energy per unit length is available. Also, the track width decreased with the increase in the scan speed; this is primarily due to a reduced interaction time. The effect of the laser beam in mixed mode at various powder feed rates on track geometry was also numerically simulated. Figure 1.32b presents the simulation results of the effect of the powder feed rate on track geometry, i.e. rates of 3, 5, 8 and 12 g/min with a fixed laser power (Pl) of 800W and scan speed (u) of 300 mm/min. It was also observed that at a constant laser power, the track height increases to a certain value with the increase in the powder feed rate and thereafter saturates. This is because a minimum laser energy per unit length is required to melt the incoming powder per unit length. A number of track geometries were simulated using the developed model with different sets of processing parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.6-1.png",
        "caption": "Fig. 15.6 Mutually perpendicular lines g1 and g2 guided through fixed points A and B (a) and exploded view of Oldham coupling (b)",
        "texts": [
            " In the assembled state the ring transmits the rotational motion of shaft 1 to shaft 2 . Relative to each pair 2 Stanislo Fenyi, Forschungszentrum Karlsruhe 394 13 Shaft Couplings of trunnions the ring executes a screw motion. It is assumed that shaft 1 is in pure rotation relative to the frame (angle of rotation \u03d51 ). In order to function properly the bearings of shaft 2 must allow shaft 2 to execute a screw motion composed of a rotation \u03d52 and a translation z . In the special case \u03b1 = 0 , the joint is the Oldham coupling shown in Fig. 15.6 . In the special case = 0 , the joint is Hooke\u2019s joint shown in Fig. 13.1 , and all screw displacements are pure rotations. The following kinematics investigation is based on the principle of transference. The rotational part of the problem is identical with that of a Hooke\u2019s joint with parameter \u03b1 . The principle of transference is applied to Eq.(13.4): tan\u03d52 tan\u03d51 = \u2212 cos\u03b1 . (13.22) The angle \u03b1 is replaced by \u03b1\u0302 = \u03b1 + \u03b5 , and the angle \u03d52 is replaced by \u03d5\u03022 = \u03d52+\u03b5z . The angle \u03d51 is not effected because shaft 1 is, by assumption, in pure rotation",
            " Darboux [7] showed that this special motion is the only nonplanar motion (planar in the narrower sense defined following (15.1)) having the property that every body-fixed point is moving in a plane (see also Bottema/Roth [4]). After this digression the plane motion shown in Fig. 15.4a is considered again. In what follows, the inverse motion is investigated. This means that the small circle k2 is stationary. The large circle k1 is rolling on k2 . Every diameter of k1 is sliding through a fixed point on k2 . This is shown in Fig. 15.6a . The two mutually perpendicular diameters of k1 which up to now were fixed guides for moving points A and B are now moving lines g1 and g2 which are guided through fixed points A and B , respectively. An engineering realization is the Oldham coupling of which an exploded view is shown in Fig. 15.6b . The fixed points A and B are located on the axes of two parallel shafts with discs 1 and 2 . Grooves on these discs are guides for the lines g1 and g2 which are materialized as rails on the central disc 3 . The Oldham coupling transmits the angular velocity of one shaft to the other. 15.1 Instantaneous Center of Rotation. Centrodes 459 Figure 15.7a shows the circle k1 rolling on the fixed circle k2 . As in Fig. 15.4a the radii are denoted for k1 and /2 for k2 . Also the notations P and M for the instantaneous center of rotation and for the center of k1 are the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.3-1.png",
        "caption": "Figure 2.3 Part design, CAD data slicing, and building up the part layer by layer in PBF processes [6]. Courtesy: EOS North America, Adam J. Penna.",
        "texts": [
            " A particular component can sometimes be built in various orientations, but an optimal manufacturing strategy utilizes the most efficient build orientation for the shortest build time, least material consumption, and best build quality. Based on the build strategy the component design is modified and support structures are added and/or extra material added for some surfaces that may need machining, etc. The next steps involve slicing the model into multiple layers and CAM toolpathing for each layer. Powder bed fusion (PBF) technologies slice the solid model in horizontal 2D layers (Fig. 2.3) [6], directed energy deposition (DED) technologies can use horizontal 2D layers as well as 3D layers following 3D surfaces. This becomes particularly important while adding metal to existing parts or components for remanufacturing and/or surface-coating applications or hybrid manufacturing. 14 Science, Technology and Applications of Metals in Additive Manufacturing Fig. 2.4 shows a typical deposition toolpath simulated on a CAD model for a five-axis deposition process using DMDCAM software [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000007_978-1-4613-2811-7_7-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000007_978-1-4613-2811-7_7-Figure1-1.png",
        "caption": "Figure 1. Point sets relevant to analysis ofthe milling process.",
        "texts": [
            " AUTOMATIC N/C CODE GENERATION The problem that was studied is as folIows: \"Given complete geometrical descriptions of apart to be produced, the stock from which it is to be machined, and the available tooling and fixtures, design appropriate algorithms and representations wh ich will automatically yield an acceptable strategy (setups and toolpaths) to produce the part on a milling machine.\" In the area of aids to N/C code generation there have been two parallel activi ties, one working with sculptured surfaces [Tan 1979] and the other on unsculp tured components. Each has used an N/C vertical milling machine for the manufacture of the test pieces. The unsculptured work reported here has con centrated on prismatic parts describable by the PADL-l system [Voelcker and Requicha 1977]. here and shown in Figure 1 [Armstrong 1982]. Related work on N/C code veri fication has been carried out at the University ofRochester [Hunt and Voelcker 1982]. Figure 1 illustrates a typical milling operation setup. Material removal is con cerned with the transformation of the initial workpiece Wo to the final compo ne nt P by using tooling T and fixtures F as necessary. In analysing the milling process there are two main classes of tooling objects to be considered: \u2022 S, which is any part of the cutter, chuck and machine tool to be considered in collision detection but which must not be used to attempt to remove ma terial, and \u2022 C, which is the part of the cutter which is designed to remove material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002764_2971763.2971778-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002764_2971763.2971778-Figure2-1.png",
        "caption": "Figure 2. Racket surface is subdivided into 48 measuring points pm(x, y) on a 20 mm grid. The coordinate origin is fixed at the racket throat. The sensors A, B, and C are highlighted by circles at the outer edge of the racket. The longitudinal axis (along the wooden fibres) is represented by the y-axis, the transverse axis (perpendicular to the fibres) by the x-axis, respectively.",
        "texts": [
            " We used the TSP Buran CCF (weight 91 g) as a racket type with harder wood material and the Imperial Allround ST (weight 85 g) as a racket type with softer wood material. Both rackets were combined with multiple rubbers of different degrees of hardness. This hardness is classified by the Shore hardness test [19] for polymers and varies increasingly from very soft to very hard. All combinations are shown in Table 1. We subdivided the racket surface into 48 measuring points pm(x, y) on a 20 mm grid with the coordinate origin at the throat (Figure 2). All columns (transverse axis) were between x = [\u221260, 60] mm, all rows (longitudinal axis) laid between y = [5, 145] mm. Sensor A was located at PA = (\u221267, 25) mm, sensor B at PB = (67, 25) mm and sensor C at PC = (0, 145) mm. The sensitive impact area of the rubbers were within a range of x = [\u221275, 75] mm and y = [0, 160] mm. For data collection, all racket combinations were horizontally mounted on a Manfrotto Magic Arm and table tennis balls (diameter 40 mm) were thrown perpendicular from variable heights within 1 m resulting in different speeds, forces and spins at least ten times on every single measuring point pm(x, y)",
            " \u2206tAB = (\u03c4A \u2212 \u03c4B) \u00b7 T (4) \u2206tAC = (\u03c4A \u2212 \u03c4C) \u00b7 T (5) \u2206tBC = (\u03c4B \u2212 \u03c4C) \u00b7 T (6) In Figure (5), the normalized data and the subset data for the threshold calculation are shown. The horizontal lines represent the thresholds \u03beu,j and \u03bel,j and the vertical lines indicate the corresponding threshold crossings of the signals S\u0303j(xi). Since the propagation speeds in wood and the appropriate running times were expected to be non-linear, we developed a time difference distribution model (TDDM) based on \u2206tAB , \u2206tAC and \u2206tBC with the training data sets for every racket combination. All recorded time differences \u2206tj for all 48 measuring points pm(x, y) (shown in Figure 2) were averaged after an outlier rejection based on mean \u00b5\u2206tj and standard deviation \u03c3\u2206tj with a rejection distance of q = 3 (7). \u2206tj,m = 1 N \u00b7 N\u2211 i=1 \u2206tj,m \u2223\u2223\u2223\u2223 |\u2206tj,m |< (\u00b5\u2206tj,m + q\u00b7\u03c3\u2206tj,m ) (7) N = number of non-rejected values 0 \u2264 m < 48 j = {AB,AC,BC} Subsequently, the averaged time differences \u2206tj,m were arranged over the x-y-coordinate plane of the racket. The gaps in between the measuring points pm(x, y) were interpolated within a 1 mm grid over the whole racket dimensions [2]. The resulting TDDM is shown using colored maps in Figure 6 for racket rubber combination (No"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002490_j.electacta.2017.06.166-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002490_j.electacta.2017.06.166-Figure1-1.png",
        "caption": "Fig 1. Schematic diagram of the three-electrodes cell used in the electrochemical measurements: (A) Working FTO electrode, (B) Auxiliary electrode, (C) Reference electrode, (D) Acrylic plate with the solution reservoir, (E) Acrylic plate and (F) polymer film gasket with a 3 mm diameter aperture defining the electrode area (0.07 cm2), (G) Acrylic plate with undercut to fit a FTO working electrode, (H) Acrylic plate for structural reinforcement, (I) bolts and (J) nuts to assemble the cell.",
        "texts": [
            " Cyclic voltammetry and electrochemical impedance spectroscopy (EIS) measurements were carried out using an EcoChemie Autolab PGSTAT30 potentiostat/galvanostat and a conventional three electrodes cell constituted by an Ag/AgCl(3.0 mol\u00b7L-1 KCl) reference, a platinum plate counter and a modified FTO working electrode. Electrochemical impedance spectra were recorded from 0.01 to 100,000 Hz, modulating the frequency of a sinusoidal potential wave (amplitude = 10 mV) superimposed to a DC potential. Chronoamperometry measurements were carried out using an Autolab PGSTAT 302N potentiostat/galvanostat and a three-electrodes cell (Fig. 1) made of four acrylic plates assembled with nuts and bolts, as shown in Fig. 1. The top plate (D) has a cylindrical tube used as solution reservoir connected to the modified FTO working electrode (A) through 3 mm coaxial holes in plate (E) and the polymeric film (F), used to avoid solution leakage and to define the electrode area (0.0707 cm2). Plate (H) was used just to enhance the robustness of the cell. The Ag/AgCl (3.0 mol\u00b7L-1 KCl) reference (C) and a platinum wire counter electrodes (B) were placed in the solution reservoir in order to assemble the three electrodes system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002506_j.jsv.2017.08.029-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002506_j.jsv.2017.08.029-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of forces acting on the inner ring.",
        "texts": [
            " The friction noise is generated by the friction vibration between the balls and inner/outer rings, and the impact noise is generated by the impact vibration between the balls and the cage. As the outer ring is regarded as a fixed component, the vibration is transferred to other components, and radiates in the form of noise. Therefore, the bearing noise can be seen as the superimposed result of the friction and impact noise, and the bearing can be decomposed into several sub-sources. The contact between the balls and inner ring leads to the friction vibration, the forces acting on the inner ring is shown in Fig. 2. Where FRhij, FRxij are the frictional forces between the jth ball and raceway in plane XbjOZbj and YbjOZbj, respectively. FRhij is produced by the gyroscopic motion of the balls, and can be expressed as. FRhij \u00bc 2Jj uhj . u 2 sin aij Dw (1) where Jj is the rotational inertia of the jth ball, uhj is the angular velocity of the gyroscopic motion in plane XbjOZbj, u is the working revolution, aij is the contact angle of the jth ball and inner ring, Dw is the ball diameter. FRxij compose of the rolling friction and sliding friction force, and can be expressed as FRxij \u00bc Jj _uxj "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001879_icrom.2016.7886760-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001879_icrom.2016.7886760-Figure1-1.png",
        "caption": "Fig. 1: Coordinate frame of the quadrotor",
        "texts": [
            " In this paper, due to the nonlinear model of quadrotor helicopter, the constraints on states and inputs and also power sources limitations, SDRE and \u03b8 \u2212 D methods are utilized for attitude and altitude control of a quadcopter and results are compared with LQR approach. The rest of the paper is organized as follows. The dynamical model of quadcopter is proposed in the section II. Section III presents the SDRE method and approximate solution of HJB equation which is known as \u03b8 \u2212D. In the the section IV, a numerical example is presented and simulation results are illustrated. Section V contains the conclusion. The equations of motion can be derived using two coordinate frames as shown in Fig. 1. Model derivation is based on the following assumptions: \u2022 Quadcopter has a symmetrical structure. \u2022 Quadcopter is a rigid body. \u2022 The center of gravity and the body frame origin are coincided. \u2022 Variation of thrust and drag are proportional to the square of propellers speed. Attitude of quadrotor helicopter is introduced by three Euler angles. The \u03c6, \u03b8 \u03c8 are roll, pitch and yaw respectively. rT = [x y z] is position of quadrotor in inertial frame. The dynamical equations of quadrotor helicopter can be written in following form [17]: x\u0308 = (cos\u03c6 sin \u03b8 cos\u03c8 + sin\u03c6 sin\u03c8)u1 m y\u0308 = (cos\u03c6 sin \u03b8 sin\u03c8 \u2212 sin\u03c6 cos\u03c8)u1 m z\u0308 = \u2212g + cos\u03c6 cos \u03b8 u1 m \u03c6\u0308 = \u03b8\u0307\u03c8\u0307 Iyy\u2212IzzIxx \u2212 Jr Ixx \u03b8\u0307\u2126r + u2 Ixx \u03b8\u0308 = \u03c8\u0307\u03c6\u0307 Izz\u2212Ixx Iyy + Jr Iyy \u03c6\u0307\u2126r + u3 Iyy \u03c8\u0308 = \u03c6\u0307\u03b8\u0307 Ixx\u2212Iyy Izz + u4 Izz (1) where m is the total mass of quadrotor, g denotes acceleration due to gravity, Ixx, Iyy and Izz are inertias of the quadrotor and Jr denotes the inertia of propeller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000412_156855309x420039-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000412_156855309x420039-Figure15-1.png",
        "caption": "Figure 15. 4.1\u25e6 (walk gait).",
        "texts": [
            " In the simulations, quadrupedal passive dynamic walking was observed and some types of gait could be observed in the simulation similar to the experiments. The details are described as follows. Referring to Figs 15, 17, 21 and 23, the simulation results piloted stable limit cycles. Thus, these walking results mean it could walk stably. K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 493 Figure 14 is the simulation result with piloted hip joint angles at 30\u201340 s with a slope angle of 4.1\u25e6. This graph shows that the robot walked stably with a walking gait. Figure 15 shows the limit cycles of this simulation result. In this graph, the motion of the front leg was different from that of the hind leg. Thus, it can be said that the front leg and hind leg have different functions. Figure 16 is the simulation result with piloted hip joint angles at 30\u201340 s with a slope angle of 4.53\u25e6. Motions of the diagonal foot were more synchronized and this can be considered as a trot gait. Figure 17 clearly shows the difference between the walk gait and trot gait. As shown in Fig. 15, there is a remarkable difference in hind leg motion. 494 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 495 496 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 497 498 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 K. Nakatani et al. / Advanced Robotics 23 (2009) 483\u2013501 499 In the simulation, the slope angle was changed gradually from 4.1\u25e6 to 4.5\u25e6. Limit cycles in Fig. 19 are not clear and we cannot see what kind of gait was used. In the time interval from 10 to 20 s, limit cycles in Fig. 21 are similar to those in Fig. 15. In the time interval from 30 to 40 s, limit cycles in Fig. 23 are similar to those in Fig. 17. Figure 21 is the simulation data for a slope angle of 4.1\u25e6. Figure 23 is the simulation data for a slope angle of 4.5\u25e6. Thus, it can be said that Quartet 4 with the invariable body can change its walk gait to trot continuously when the slope angle was gradually changed from 4.1\u25e6 to 4.5\u25e6. In this way, gait transition could be considered as the transition of limit cycles. In biped passive dynamic walking, when the slope angle was gradually changed, the biped passive dynamic walker changed its gait from one-period to two-period"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.7-1.png",
        "caption": "Figure 8.7. Forces actingon a rigid system of threeparticles.",
        "texts": [
            "53), respectively; and the total mechanical power expended , the rate of working of the external forces only, may be similarly decomposed. Exercise 8.6. Show that (8.66) follows from (8.62). D Example 8.6. A pipeline valvehandle consists of three equally spaced handle grips of equal mass m attached to the valve body of mass M by thin rigid torque bars of equal length eand negligible mass. The handle, initially at rest, is turned by forces f( and f2 of equal constant magnitude F applied at two grips in the plane of, and perpendicular to the torque bars, as shown in Fig. 8.7. The handle turns freely without friction. (a) Apply the work-energy principle to find as a function of time the angular speed w(t) of the handle. (b) Derive the same result by use of the moment of momentum principle. Solution of (a). We model the handle as a rigid system of three particles of equal mass m attached by massless rigid rods to the valve body, which is a particle of mass M at C, the center of mass of the system. Since the handle turns freely without friction at C, the reaction force of the valve body is equipollent to a single force R at C that does no work in the motion; and, of course, the normal gravitational force also is workless. The work done by the remaining applied external forces , relative to the center of mass, is determined by the first equation in (8.66), and hence, with reference to Fig. 8.7, fl/rc = 1f( . dp, +1f2 \u00b7 dP2 = r Fe2' U\u00a2e2 + r Fn2 ' ed\u00a2n2 . 6', 6'2 Jo Jo Dynamics of a System of Particles Hence, 1I/rc = 2Fe\u00a2. 323 (8.67a) (8.67b) Notice that since C is fixed in <1> , 11/* =0 in (8.55); hence, by (8.63), 11/= 1I/rc also is the total work done on the rigid system. Since each of the three handle particles has the same speed !PII = f\u00a2 relative to C, and because the system is at rest initially, the change in kinetic energy (8.52) relative to the center of mass is 3 2 ' 2 !:::.Krc = \"2mf \u00a2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure5.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure5.6-1.png",
        "caption": "Fig. 5.6 Forces acting on the gyroscope with one side free support",
        "texts": [
            "3 and enable for calculating the value of torques by the equations represented in Table 3.1. The action of inertial torques is displayed on the motion of the gyroscope suspended from the flexible cord. The equation of gyroscope motion around axis ox at the horizontal location (\u03b3 = 0) is represented by Eq. (5.29) of Sect. 5.3. Theweight of the gyroscope and inertial torques are acting on the one side free support of the flexible cord. The picture of the resulting reactions of all forces on the support is demonstrated in Fig. 5.6. The resulting torques acting around axes ox and oy (Eqs. (5.47) and (5.48), Sect. 5.3), enable to defining the angular accelerations \u03b5x and \u03b5y around axes ox and oy of the gyroscope, respectively, by the following equation: Ti = Ji\u03b5i (5.50) where Jx = 1.9974649 \u00d7 10\u22124 kgm2 is the mass moment of the gyroscope inertia around axis ox and oy (Table 5.2), other components are as specified above. Substituting defined parameters into Eq. (5.50) and transformation yields the following result: 5.3 The Practical Test of Gyroscope Motions 101 \u03b5x = Tx Jx = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001547_iros.2013.6696825-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001547_iros.2013.6696825-Figure20-1.png",
        "caption": "Figure 20. Image after the head section has climbed over the step.",
        "texts": [
            " Thus, the proposed approach leads to reduced friction and steps of the robot, and is thus effective in enabling the robot to smoothly pass through an elbow. In this section we explain the requirement for the head section to guide the robot when the robot is passing through an elbow. Figure 19 shows an image of the head section climbing over a step that is between an elbow and a straight pipe. First, to climb over the step, the ABS part needs to proceed in the direction of travel, therefore the tip of the head section needs to be flexible. Figure 20 shows an image after the head section has climbed over the step. If the head section is flexible, the base of the head section buckles, therefore the head unit collides with the elbow. Thus, the base of the head section needs a pulling force that pulls it backward because the head unit needs to proceed in the direction of traveling. Figure 21 shows an image of the new head section we developed, and Table 3 shows the specifications. The new head section climbs over the step using the flexibility of a compression spring, and pulls itself backward by using the pulling force of the extension spring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001470_0016-0032(65)90310-8-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001470_0016-0032(65)90310-8-Figure8-1.png",
        "caption": "FIG. 8. Misalignment of accelerometer sensitive axis. Fro. 9. Displacement of sampling axis.",
        "texts": [],
        "surrounding_texts": [
            "ruined from a knowledge of the accelerations of the points L~. By making small angle approximations for 50~, the following vector equations can be written for ~ /and i~:\n~Il~ ___= o~/~l,~ + lij~v~'~JAO~ cos ~ b ~ j + likL.k + oJyA0i sin \u00a2i~k} ( i j k ) = (123), (231), (312). (14)\nIn Eq. 14 li~, l,.j and lik are given as\n1, = AOi(llk sin ~bi + lij cos ~b.i) l~i = l~ cos ~olt l lk= l~ sin o~:t.\nFrom the knowledge of the velocities and accelerations of the points L~ relative to the vehicular axes V~, the accelerations of the points L~ with respect to the inertial axes expressed as projections along the vehicular axes can be written under the stated assumption 9 q- ~2 ~ <~ wfl2,\n= ~ d-A~-t- 2wf (ao jl~j - ~.kl~k) q- AO~0f 2 (l~k sin \u00a2~ q- l~j cos ~ ) ] + e , i [ - A ~ - \u00a2 o / 2 1 i j - - 2o~flt~/~ + hO~2~fl~ (l~ cos ~ - - l~ sin ~b~) + ~k~A ~ -- o~pl~ -- 2o~fl2~1~ -- A0~2o~flt, \u00a2 (l~ cos ~b~-- l~ sin ~b~)\n( i j k ) = (123), (231), (312). (15) Equation 15 can be expressed as\n(-4)~t~.L~ = A~'~ q- A / ~ q- A J ~ .\nThe accelerometers will read\nA ~ = A~' + A / c o s (o~ft + \u00a2/~)A0~ + AJ sin (~yt + ~k~)A0~. (16)\nSubstituting Eq. 15 into Eq. 16 and neglecting second degree terms in AO~, the indicated accelerations of the accelerometers are\nA~,,, = A~ + AO~o~f~(l~, sin ~b~ + l~j cos ~b~) + cos \u00a2~(Av~ - - , , f~l~ - 2 o ~ v ~ l ~ ) + sin ~k~(AVk - o~y~l~ - 2o~y~2v~l~)-] (17) where A~ is given by Eq. 6.\nBy obtaining the samples for Eq. 17 at the times indicated by Eq. 7 and by suitably adding and subtracting these samples we obtain the following:\n1(,,1i~ + A ~ , , ) = a~ - - AO~(2o~f~2v~l~ cos ~b~ + ~ l~ cos ~k~) ~ A ( ~1,,, - A~,, ,) = %~ + AO~(Av~ cos ~k~ + Av~ sin ~k~ + o~:l~ cos ~k~) (18) 1 f A , = - ~ a ,~ + A~, ,~) a~' AO~(2co:f~il~ cos ~k~ q- o~:~l~ sin ~b~) \u00bd(A~,,~ - A ~ , , , ) = ~ ' q- AO~(--A,~ sin ~k\u00a2 -b A** cos ~k~ q- ~ l~ sin ~k~).\nThe errors in the components of linear accelerations and angular velocities are given by the A0~ terms of Eq. 18, the dominant error being contributed by the terms \u00a20~I~ cos ~b~A0~.\nVol. 280, No. 4, October 1965 313",
            "Sensi t ive Axes of the Acce lerometers Misa l igned w i t h the R o t a t i o n Axes\nThe sensitive axes of the accelerometers make a small angle AO/ with axes V / a n d the projections of these sensitive axes on the ViVk plane make an angle of ~ / w i t h the vehicular axes Vs. These angles are indicated in Fig. 5 for the one dimensional case. The analysis is similar to the previous section. The final equations corresponding to Eq. 18 are\n\u00bd(A/1,, + A,2m) = a/ - AO/(2~/P,,///cos ~ / + ~/2l/cos ~I,/) \u00bd ( A / a m - - A/2m) = ~ 7 i -~- AO/(A~/cos ~ i + Ark sin'Iz/)\n\u00bd(All,,, + A~2,,,) = am' - hO/(2~/9v~/~ cos ~I,/+ ~f21~ cos ~/)\n\u00bd(A~l,m - A/2,m) = W/' + AO~(--A~. sin ~z/ + A,k cos ~/) (ijk) = (~23), (231), (312). (19)\nThe errors given by the AOi terms are similar to the errors obtained in the previous section.\nS a m p l i n g Errors\nA uniform error of At in the sampling times of Eq. 7 will produce a corresponding small angular error of A ~ in the vectors i/. A one dimensional version of this error is indicated in Fig. 9. Due to this small angular error A~/in i~ the corresponding error equations in the computat ion linear acceleration and angular velocities are\n314 j o u ~ . , of The Franklin Institute",
            "i (A,~. , + A,2.,) = a , ~ ]\n' A a , , | (ijk) = (123) , (231) , (312) . (20)\nA uniform error in time At creates corresponding errors only in angular velocities while the linear accelerations are unchanged.\nS u m m a r y\nThe effects of the errors in l inear acce le ra t ion a nd a ngu l a r veloci ty due to m i s a l i g n m e n t are given in T a b l e I.\n(1) Victor B. Corey, \"Measuring Angular Accelerations with Linear Accelerometers,\" Control Engineering, Mar. 1962. (2) V. A. Bodner, and V. P. Seleznev, \"On the Theory of Inertial Systems Without a Gyrostabilized Platform,\" Izvestia Akad. Nauk, Otdel Tekh. Nauk, Energetikai Avtomatika, Jam-Feb., 1960. (3) H. Goldstein, \"Classical Mechanics,\" Chap. IV, Reading, Mass., Addison Wesley Publishing Co., 1950.\nVol. 2,o, No. 4, O:to~,, 1965 3 1 5"
        ]
    },
    {
        "image_filename": "designv10_12_0002381_j.measurement.2015.12.006-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002381_j.measurement.2015.12.006-Figure8-1.png",
        "caption": "Fig. 8. The measurement data shown in Solidworks.",
        "texts": [
            " Matrix M0 represents the coordinate transformation from the work pieces\u2019 coordinates to the workbench coordinate, which includes a rotating transformation represents as Matrix M1 and a shifting transformation represents as Matrix M2. M1 \u00bc cos d sin d 0 0 sin d cos d 0 0 0 0 1 0 0 0 0 1 2 666664 3 777775 \u00f013\u00de M2 \u00bc 1 0 0 0 0 1 0 0 0 0 1 z 0 0 0 1 2 666664 3 777775 \u00f014\u00de M0 \u00bc M1 M2 \u00bc cos d sin d 0 0 sin d cos d 0 0 0 0 1 z 0 0 0 1 2 666664 3 777775 \u00f015\u00de Transform the measurement coordinate data which got from the measurement experiments according to the above method. Afterwards, import the results into the three-dimensional design software Solidworks as shown below (see Fig. 8). 5.2. Pitch deviation calculation and analysis The pitch of the curve-face gear pair is defined as the arc length of the pitch curve between two adjacent corresponding flanks in this paper. Therefore, it can be expressed as follows p1i \u00bc Z u12 u11 \u00bdr2\u00f0u1\u00de \u00fe r02\u00f0u1\u00de 1=2 du1 \u00f016\u00de p2i \u00bc Z u22 u21 \u00bdv2\u00f0u2\u00de \u00fe w2\u00f0u2\u00de \u00fex2\u00f0u2\u00de 1=2 du2 \u00f017\u00de The nominal pitch of the non-circular gear and the curve-face gear pair are the same. pt1 \u00bc pt2m \u00bc L1 z1 \u00bc pm \u00bc 12:5664 mm \u00f018\u00de The individual pitch deviation Df pt \u00bc p0 t pt \u00f019\u00de The pitch accumulative error DFp \u00bc Xn 1 Df pt \u00f020\u00de In accordance with the definition of pitch, the measured coordinates which are corresponding with the theoretical can be confirmed as the intersections of the pitch curves and the curves made up of the measurement coordinate data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003749_s00170-021-07105-3-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003749_s00170-021-07105-3-Figure1-1.png",
        "caption": "Fig. 1 a Design and dimension of cylinder sample (units in mm) and b arrangement of the single tracks inside the cylinder sample",
        "texts": [
            " Again, microCT is used to characterize the pores, and metallography is performed to reveal the melt pool boundary. Moreover, the normalized enthalpy is utilized to characterize the transition of the melt pool from the conduction mode to the keyhole mode. Further, the powder scale numerical model is used to investigate the heat transfer and melt flow behavior at different power and speed combinations from the same LED. A small-scale model is developed to understand the underlying physics behind the change of melting mode from conduction to keyhole. Figure 1 presents the hollow cylinder sample design used to contain the single tracks. During the X-ray imaging, it is necessary to ensure adequate X-ray transmission (130 kV source) through the sample. As the density of IN625 (8440 kg/m3) is high, the diameter of 3 mm is used in this study to allow proper transmission. Figure 1 b shows the arrangement of 12 mm long single tracks, which are formed between the notches. The notches work as a reference and is used to locate the tracks during the CT scanning. The tracks are formed with a 0.7 mm gap as Matthews et al. [17] showed that there is a significant powder depletion around the single tracks in the SLM process. EOSM270 is used to fabricate the samples with 40 \u03bcm layer thickness in this study. The tracks are formed with the user parameters, while the hollow cylinder is fabricated using EOS M270 GP1 parameters (195 W laser power, 750mm/s scan speed, and 120 \u03bcmhatch spacing). The sample is fabricated in the positive Z-direction, as shown in Fig. 1b. The hollow region is filled with IN625 powder particles due to the nature of the process, which remains contained inside the cylinder after fabrication. Linear energy density (LED) is the ratio of laser power and scan speed, LED J mm \u00bc P W\u00f0 \u00de v mm s : \u00f01\u00de The laser power, scan speed, and the corresponding LEDs used in this study are listed in Table 1. In this study, the scan speeds from 200 to 1200 mm/s are used for a constant power of 195 W, while the constant speed of 200 mm/s is used for power ranging from 105 to 195 W"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000103_intmag.2006.375771-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000103_intmag.2006.375771-Figure2-1.png",
        "caption": "Fig. 2. Open-circuit field distributions at different rotor rotation positions, 2400rpm",
        "texts": [
            " The stator core comprises laminated \u201cU\u201d-shaped modules, between which are placed circumferentially magnetised permanent magnets, the polarity of the magnetization being reversed from one magnet to the next. Thus, each pole, which carries a concentrated coil, is formed from two adjacent laminated modules and a permanent magnet [2][3]. Since the permanent magnets are on the stator, thermal management is easier than in conventional PM brushless machines. However, as with DSPM motors, significant leakage flux exists at the outer surface of the stator, as will be evident from Fig. 2. Since the leakage flux varies as the rotor rotates, and also changes with the load, it may induce an unacceptable eddy current loss in the frame. However, this has never been addressed in literature. In the paper, the leakage flux and resultant eddy current loss in the frame are investigated by 2-D time-domain finite element analysis and validated experimentally on an FSPM motor whose rated output power and maximum speed are 100W and 2400rpm, respectively. The variation of the opencircuit leakage flux density at various radial distances from the outer edge of a magnet is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001946_j.matdes.2018.05.032-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001946_j.matdes.2018.05.032-Figure1-1.png",
        "caption": "Fig. 1. Sketch map of laser melting deposition showing the three directions: growth direction (OZ), laser scanning direction (OY) and transverse direction (OX).",
        "texts": [
            " This was used to fabricate plate-like specimens. In order to prevent the melt pool from oxidation, the experiments were conducted inside an argon-purged processing chamber with oxygen content b100ppm. The lasermelting deposition additivemanufacturing processing parameters were as follows: laser power was 5000W, beam scale was 6 mm, laser scanning speed was 800\u20131500 mm/min, and powder feed rate was 15\u201325 g/min. The dimensions of the plate-like specimen were approximately 300 mm \u00d7 300 mm \u00d7 35 mm, as shown in Fig. 1. Metallographic specimens were prepared by conventional mechanical polishingmethod. Amixture of 1mlHF, 6ml HNO3 and 100mlH2O was used as the etching agent. The microstructures of specimens were characterized by OM and SEM. And OM was carried out using a LECICA-DM 4000 M, SEM was done on a JEOL-6010. Sheet specimens were ion polished and examined using the FEI NANO SEM 430 for EBSD. The scan gap used for as-deposited specimens was 0.1 mm. The three dimensional (3D) structure of \u03b1 lath had been investigated as follow: the center ofmicrohardness indentationwas used to locate \u03b1 phase, and the indentation size was used to calculate the polishing depth, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001020_j.msec.2012.08.043-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001020_j.msec.2012.08.043-Figure1-1.png",
        "caption": "Fig. 1. Schema of principle of biosensor for glucose detection.",
        "texts": [
            " The PAH-coated gold nanoparticles and PAH-coated magnetic nanoparticles were dispersed in 20 mM phosphate buffer (pH 7.3) containing 6% of BSA, 4% of GOD and 10% of glycerol, as optimized in our previous work [50]. After 1 h of mixing, these solutions were centrifuged (for gold nanoparticles) or decanted under magnetic field (formagnetic nanoparticles) in the same conditions as described before and redispersed in 20 mM phosphate buffer. 0.2 \u03bcL of these solutions was deposited onto the sensitive area of the working sensor (Fig. 1). For preparation of the reference sensor, PAH-coated gold nanoparticles and PAH-coated magnetic nanoparticles were dispersed in 20 mM phosphate buffer (pH 7.3) containing 10% of BSA and 10% of glycerol. After separation and redispersion in 20 mM phosphate buffer, 0.2 \u03bcl of these solutionswas deposited onto the sensitive area of the reference sensor. The sensors were then placed in saturated GA vapor for 30 min. After exposure, the biosensors were dried at room temperature for 15\u201330 min and stored at 4 \u00b0C before the experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003568_j.mechatronics.2021.102540-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003568_j.mechatronics.2021.102540-Figure6-1.png",
        "caption": "Fig. 6. Illustration of the 3D kinematics model. The end-effector velocity is aligned with the path tangent.",
        "texts": [
            " The proposed kinematic model describes a space velocity vector of constant speed \ud835\udc63\ud835\udc51 expressed in the base frame: when the translational speed of the end-effector is constrained to be a constant, a set of spherical coordinates can fully describe a given 3D Cartesian velocity vector. The parameters \ud835\udf03 and \ud835\udf13 continuously modify the orientation of the robot end-effector frame. Denote the component of the current robot end-effector velocity vector \ud835\udc63\ud835\udc51 in the base frame as \ud835\udc63\ud835\udc51 = [\ud835\udc63\ud835\udc51\ud835\udc65, \ud835\udc63\ud835\udc51\ud835\udc66, \ud835\udc63\ud835\udc51\ud835\udc67]\ud835\udc47 . The orientation \ud835\udf03 and \ud835\udf13 can be calculated according to: \ud835\udf03 = atan2(\ud835\udc63\ud835\udc51\ud835\udc66, \ud835\udc63\ud835\udc51\ud835\udc65), \ud835\udf13 = atan2( \u221a \ud835\udc632\ud835\udc51\ud835\udc65 + \ud835\udc63 2 \ud835\udc51\ud835\udc66, \ud835\udc63\ud835\udc51\ud835\udc67). (25) The variables associated with this 3D kinematic model for the endeffector frame are defined through the base and end-effector frames as shown in Fig. 6. Without loss of generality, we assumed the direction of the velocity vector \ud835\udc63\ud835\udc51 to be aligned with the \ud835\udc4c -axis of the end-effector frame. As shown in Fig. 6, the objective of the control laws for \ud835\udc621 and \ud835\udc622 is to align the velocity orientation, shown by the red arrow, with that of the converging path tangent, shown by the green arrow. The objective of the motion control in the end-effector frame is to orient the velocity vector based on the path tangent provided by the converging path planner. To transform the local tangent ?\u20d7? on the converging path into the orientation variables defined in (24), we have: \ud835\udf03 = atan2(\ud835\udc61 , \ud835\udc61 ), \ud835\udf13 = atan2(\ud835\udc51 , \ud835\udc61 ). (26) \ud835\udc51 \ud835\udc66 \ud835\udc65 \ud835\udc51 \ud835\udc65\ud835\udc66 \ud835\udc67 where \ud835\udc51\ud835\udc65\ud835\udc66 = \u221a \ud835\udc612\ud835\udc65 + \ud835\udc612\ud835\udc66"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000900_s12283-011-0062-7-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000900_s12283-011-0062-7-Figure4-1.png",
        "caption": "Fig. 4 A diagrammatic explanation of how the impact angle is calculated",
        "texts": [
            " Goodwill and Haake [16] and Knudson [17] have investigated spin, citing the playing or impact angle as a factor affecting its generation. The impact angle is easy to measure and control in a laboratory setting where the racket is often held stationary. Although more complex, the impact angle was calculated using the ball/racket velocities and the local z axes (perpendicular to the racket face). The impact angle is calculated for the instant of impact. The calculation of the playing angle consists of three distinct steps as shown in Fig. 4. To summarise, the characteristics obtained using this methodology include: \u2022 Ball and racket velocity in three directions, \u2022 Racket angular velocity around three axes, \u2022 Racket/ball impact position, \u2022 Ball spin. The calibration and manual marker tracking accuracy was assessed by tracking the distances between tape markers and comparing these distances to those measured directly from the racket. This was compared with the distance between the re-projected co-ordinates. It was found individual marker position could be reconstructed to within \u00b12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure5.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure5.2-1.png",
        "caption": "Fig. 5.2 Schematic of acting torques on the gyroscope with one side free support",
        "texts": [
            " The system of the inertial forces, which are centrifugal, common inertial, Coriolis forces, and the change in the angular momentum of the spinning rotor (Chap. 3) are used for formulating the analytic models for the torques and motions of the gyroscope with one side free support. Except these torques are considered the action of centrifugal and Coriolis forces generated by centre mass of the gyroscope [9]. The action of external and inertial torques is considered on the example of the gyroscope suspended from the flexible cord that represented in Fig. 5.2. The one side free support of gyroscope enables avoiding the action of the frictional forces on gimbals and simplifies mathematical models for motions and practical implementation. The mathematical model of motions for gyroscope with one side free support is formulated for the common case of the gyroscope with the inclined axis on the angle \u03b3 . Analysis of the acting forces and motions on the gyroscope is conducted on the base of several rules and regulations. The equations of the gyroscope\u2019s motions have accepted the motions in the counterclockwise direction that is positive and in the clockwise direction that is negative. At the starting condition, the action of the gyroscope\u2019s weight represents the load torque T with the point of rotation around the support o at the system of coordinates oxyz (Fig. 5.2). Analysis of the torques acting on the gyroscope demonstrates the following peculiarities. The external load \u00a9 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 R. Usubamatov, Theory of Gyroscopic Effects for Rotating Objects, https://doi.org/10.1007/978-981-15-6475-8_5 81 torque T that is produced by the gyroscope weight W generates the system inertial torques acting around axes ox and oy (Fig. 5.2). These torques are represented by the following interrelated components: (a) The action of the weight W of the gyroscope produces the system of inertial torques generated by rotating mass of the spinning rotor namely the centrifugal T ct\u00b7i common inertial T in\u00b7i and Coriolis forces T cr\u00b7i and the change in the angular momentum T am\u00b7i that are components of the resistance T r\u00b7i and procession torques T p\u00b7i acting around axis i; (b) The resistance torque T r\u00b7x generated by the centrifugal T ct\u00b7x and Coriolis forces T cr\u00b7x acting around axis ox (T r\u00b7x = T ct\u00b7x + T cr\u00b7x); (c) The procession torques T p\u00b7x generated by the inertial forces T in\u00b7x and the change in the angular momentum T am\u00b7x originated on axis ox but acting around axis oy (T p\u00b7x= T in\u00b7x+ T am\u00b7x); d) The precession torque T p\u00b7x, in turn, generates the resistance torque T r\u00b7y of centrifugal forces T ct\u00b7y and of Coriolis forces T cr\u00b7y acting around axis oy (T r\u00b7y = T ct\u00b7y + T cr\u00b7y) that dependant on the procession torque Tp\u00b7x; (e) The precession T p\u00b7x and resistance T r\u00b7y torques formulating the resulting inertial torques acting around axis oy (T rst\u00b7y = T p\u00b7x \u2212 T r\u00b7y); (f) The resulting torqueT rst\u00b7y, in turn, generates the precession torqueT p\u00b7y originated on axis oy but acting around axis ox (T p\u00b7y= T in\u00b7y+ T am\u00b7y) where the T in\u00b7y is compensated by T ct\u00b7y (d), which justification presented in Chap",
            " Rotation around axes ox and oy of the centre mass of the gyroscope generates the following torques: (a) The torque generated by the centrifugal force of the rotating gyroscope centre mass around axis oy and acting around axis ox (b) The torque generated by Coriolis force of the gyroscope centre mass rotating around axes ox and oy and acting around axis oy. The inertial forces generated by the centre mass can be removed from equations of the gyroscope motions when these torques have small values of a high order. The mathematical model is represented by the differential equations in Euler\u2019s forms based on all acting torques summed around two axes ox and oy (Fig. 5.2). Jx d\u03c9x dt = T cos \u03b3 + Tct\u00b7my \u2212 Tct\u00b7x \u2212 Tcr\u00b7x \u2212 Tam\u00b7y (5.1) Jy d\u03c9y dt = Tin\u00b7x cos \u03b3 + Tam\u00b7x cos \u03b3 \u2212 Tcr\u00b7y cos \u03b3 \u2212 Tcr\u00b7my (5.2) where Jx = Jy is the mass moment of gyroscope inertia about axis ox and oy, respectively, that calculated by the parallel axis theorem; \u03c9x and\u03c9y are the angular velocity of precession around axis ox and oy, respectively; T = Wl = Mgl is the torque generated by the gyroscope weight W around axis ox; M is the mass; g is the gravity acceleration; l is overhang distance of the gyroscope centre mass to the free support; T ct,my is the torque generated by the centrifugal forces of the rotating gyroscope centre mass around axis oy",
            " This conventional radius Rc should replace the external radius R of the simple disc-type rotor in equations of Table 5.1. Equations (5.5) and (5.6) represent acting torques and motions of the spinning rotor around axes ox and oy, respectively. The location of the gyroscope with one side free support is distinguished from the locationwith fixed support. The gyroscope with one side support suspended from the flexible cord about the point o represents the movable system of free motion at the horizontal plane xoz (Fig. 5.2). Analysis of the forces acting on the gyroscope demonstrates the following properties. At the starting condition, the action of the gyroscope weight and the precession torque leads to its turns around axis ox and oy. At the same time, the resistance torques of the centrifugal and Coriolis forces are counteraction torques around axis ox and oy. In turn, the gyroscope motion around axis oy activates the precession torque of the inertial forces and the rate of change in the angular momentum around axis ox",
            " The value of the product\u03c9\u03c9x is constant for the given data of the gyroscope. The increase in the angular velocity of \u03c9 of the spinning disc leads to the decrease of the angular velocity \u03c9x of the gyroscope and vice versa. The increase in the torque produced by the gyroscope weight does not change in the resulting inertial torque but changes in the location of the gyroscope. This condition is the result of the interrelated action of the inertial torques and angular velocities around axes (Eq. 4.9, Chap. 4). The surplice of the load torque T around axis ox (Fig. 5.2) excesses the value of the resulting resistance inertial torque T r\u00b7x that leads to the fast turn down of the gyroscope. The new location of the gyroscope gives the same value of the torque produced by the gyroscope weight that corresponds to the value of the resulting inertial torque. This circumstance is predetermined by the law of mechanical energy conservation. The equation of the potential and kinetic energies of the gyroscope and the work of the inertial torques is represented by the following analysis. For the given example (Fig. 5.2), the location of the gyroscope at the system of coordinate oxyz expresses its gravitational potential energy that is a conservative force. The motion of the gyroscope mass expresses its kinetic energy. The action of the inertial resistance expresses the negative work. The datum of energies has accepted the line that below on h of the horizontal location of the gyroscope. The total energies of the gyroscope at any points of the location are remained constant and expressed by the following equation: PM1 + K1\u00b7M \u2212 A1\u00b7Ti = PM2 + K2\u00b7M \u2212 A2\u00b7Ti (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003000_j.conengprac.2019.104272-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003000_j.conengprac.2019.104272-Figure1-1.png",
        "caption": "Fig. 1. Sketch and test rig of hydraulic differential cylinder system at the Chair of Dynamics and Control (UDuE), (1) proportional directional control valve, (2) oil supply in chamber A, (3) oil supply in chamber B, (4) moving mass, and (5) load cylinder.",
        "texts": [
            " The input-output exact feedback linearization approach is applied to linearize the nonlinear system model to be used for PIO design and SMC approach. Furthermore, the sliding mode control law is defined based on the estimation results and the stability of the whole system (SMC controller together with PIO) is shown using Lyapunov theory. Investigation of the closed-loop robustness against modeling errors and external disturbances is experimentally validated using a hydraulic differential cylinder test rig (Fig. 1). Consequently the contributions of this paper can be summarized as: \u2022 Designing a PIO for the uncertain nonlinear dynamical model of a hydraulic cylinder using exact feedback linearization approach \u2022 Developing a novel PIO-based SMC scheme by combining the PIO and SMC approaches for a hydraulic differential cylinder system to enhance the disturbance attenuation and robustness performance \u2022 Establishing a stability proof considering the convergence of controller tracking error and unknown input observation error simultaneously \u2022 Investigation of closed-loop robustness against modeling errors and external disturbances by using an improved implementation environment and newly introduced robustness criteria The paper is organized as follows: the model of the hydraulic cylinder used for experimental results is introduced in Section 2",
            " The PIO design is briefly reviewed in Section 3.1 which is in combination with SMC the core of this contribution. Subsequently, the proposed method for position control of the hydraulic differential cylinder as well as the stability proof are detailed in Sections 3.3 and 4. Finally in Section 5 the experimental results using a hydraulic differential cylinder test rig are given to evaluate the proposed method for robust motion control purpose. A model of a hydraulic differential cylinder with a proportional control valve as shown in Fig. 1 (Jelali & Kroll, 2012) is given by ?\u0307?(\ud835\udc61) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc652 1 \ud835\udc5a(\ud835\udc651) [ (\ud835\udc653 \u2212 \ud835\udc654 \ud835\udf11 )\ud835\udc34\ud835\udc34 ] \ud835\udc38\ud835\udc5c\ud835\udc56\ud835\udc59(\ud835\udc653) \ud835\udc49\ud835\udc34(\ud835\udc651) ( \u2212\ud835\udc34\ud835\udc34\ud835\udc652 ) \ud835\udc38\ud835\udc5c\ud835\udc56\ud835\udc59(\ud835\udc654) \ud835\udc49\ud835\udc35(\ud835\udc651) ( \ud835\udc34\ud835\udc34 \ud835\udf11 \ud835\udc652 ) \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 + \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0 0 \ud835\udc38\ud835\udc5c\ud835\udc56\ud835\udc59(\ud835\udc653) \ud835\udc49\ud835\udc34(\ud835\udc651) \ud835\udc44\ud835\udc34(\ud835\udc653) \ud835\udc38\ud835\udc5c\ud835\udc56\ud835\udc59(\ud835\udc654) \ud835\udc49\ud835\udc35(\ud835\udc651) \ud835\udc44\ud835\udc35(\ud835\udc654) \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \ud835\udc62(\ud835\udc61) + \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0 \ud835\udc51(\ud835\udc61) 0 0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 , = \ud835\udc87 (\ud835\udc99) + \ud835\udc88(\ud835\udc99)\ud835\udc62(\ud835\udc61) + \ud835\udc85(\ud835\udc61), \ud835\udc66(\ud835\udc61) = \u210e(\ud835\udc99) = \ud835\udc651(\ud835\udc61), (1) with the variant mass \ud835\udc5a(\ud835\udc651) = \ud835\udc5a\ud835\udc4f\ud835\udc4e\ud835\udc60\ud835\udc56\ud835\udc50 + \ud835\udf0c\ud835\udc53\ud835\udc59(\ud835\udc49\ud835\udc34(\ud835\udc651) + \ud835\udc49\ud835\udc35(\ud835\udc651)), (2) the volumes \ud835\udc49\ud835\udc34, \ud835\udc49\ud835\udc35 in chambers \ud835\udc34 and \ud835\udc35 as \ud835\udc49\ud835\udc34(\ud835\udc651(\ud835\udc61)) = \ud835\udc49\ud835\udc50\ud835\udc34 + \ud835\udc651(\ud835\udc61)\ud835\udc34\ud835\udc34, \ud835\udc49\ud835\udc35(\ud835\udc651(\ud835\udc61)) = \ud835\udc49\ud835\udc50\ud835\udc35 + (\ud835\udc3b \u2212 \ud835\udc651(\ud835\udc61))\ud835\udc34\ud835\udc35 , 0 \u2264 \ud835\udc651(\ud835\udc61) \u2264 \ud835\udc3b, the disturbance \ud835\udc51(\ud835\udc61) as \ud835\udc51(\ud835\udc61) = \ud835\udc53\ud835\udc47 \ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59(\ud835\udc61) \ud835\udc5a(\ud835\udc651) , (3) the hydraulic flows \ud835\udc44\ud835\udc34(\ud835\udc653(\ud835\udc61)) = { \ud835\udc35\ud835\udf08\ud835\udc60\ud835\udc54\ud835\udc5b(\ud835\udc5d0 \u2212 \ud835\udc653(\ud835\udc61)) \u221a \u2223 \ud835\udc5d0 \u2212 \ud835\udc653(\ud835\udc61) \u2223, \ud835\udc62 \u2265 0 \ud835\udc35\ud835\udf08\ud835\udc60\ud835\udc54\ud835\udc5b(\ud835\udc653(\ud835\udc61) \u2212 \ud835\udc5d\ud835\udc61) \u221a \u2223 \ud835\udc653(\ud835\udc61) \u2212 \ud835\udc5d\ud835\udc61 \u2223, \ud835\udc62 < 0, \ud835\udc44\ud835\udc35(\ud835\udc654(\ud835\udc61)) = { \u2212\ud835\udc35\ud835\udf08\ud835\udc60\ud835\udc54\ud835\udc5b(\ud835\udc654(\ud835\udc61) \u2212 \ud835\udc5d\ud835\udc61) \u221a \u2223 \ud835\udc654(\ud835\udc61) \u2212 \ud835\udc5d\ud835\udc61 \u2223, \ud835\udc62 \u2265 0 \u2212\ud835\udc35\ud835\udf08\ud835\udc60\ud835\udc54\ud835\udc5b(\ud835\udc5d0 \u2212 \ud835\udc654(\ud835\udc61)) \u221a \u2223 \ud835\udc5d0 \u2212 \ud835\udc654(\ud835\udc61) \u2223, \ud835\udc62 < 0, with \ud835\udc35\ud835\udf08 = \ud835\udc44\ud835\udc41 \u221a 0",
            " (31) Under the conditions that the polynomial \ud835\udc602 + \ud835\udc502\ud835\udc60 + \ud835\udc501 and the matrix [ \ud835\udc68 \u2212\ud835\udc731\ud835\udc6a \ud835\udc75 \u2212\ud835\udc732\ud835\udc6a 0 ] are Hurwitz (assuming the sliding surface design condition, Lemmas 1 and 2), the matrix \ud835\udc68\ud835\udf09 in (31) is also Hurwitz so the system ?\u0307? = \ud835\udc68\ud835\udf09\ud835\udf43 is exponentially stable. Therefore, according to Lemma 5.5 in Khalil (1996) system (31) is ISS. Consequently, it can be derived from Lemma 3 and design condition of sliding surface that the states of system (31) satisfy lim\ud835\udc61\u2192\u221e\ud835\udf43(\ud835\udc61) = 0. Subsequently the steady state reference tracking error together with the observer estimation errors converge to zero under the proposed observer-based control law. The proposed observer-based robust control approach is validated using the test rig (Fig. 1) and related system model (1). In this work robustness of the closed loop system has been investigated in the presence of external disturbances (e.g. friction force), internal disturbances (e.g modeling errors and other nonlinearities), and additive measurement noise. The external disturbances are considered as the friction force \ud835\udc53\ud835\udc53\ud835\udc5f\ud835\udc56\ud835\udc50 (\ud835\udc99, \ud835\udc61) between the mass and its bearing surface and the disturbance force \ud835\udc53\ud835\udc50\ud835\udc66\ud835\udc59\ud835\udc56\ud835\udc5b\ud835\udc51\ud835\udc52\ud835\udc5f(\ud835\udc99, \ud835\udc61) generated from a 2nd hydraulic cylinder (with passive dynamics acting oppositely, see Fig. 1). An uncertainty of the moved mass \ud835\udee5\ud835\udc5a can be considered additionally. Leakages between the cylinder chambers and external oil leakages are neglected in this consideration; their influence on the cylinder dynamics is negligible. The experiments of the robust control design are carried out using regular working conditions. For evaluating the robustness performance, additional noise of different levels is added to related measurements. To implement the different control methods in real time, a compact system is designed as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000984_asjc.543-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000984_asjc.543-Figure1-1.png",
        "caption": "Fig. 1. 2DTORA system configuration.",
        "texts": [
            " The rest of paper is organized as follows. In Section II, the dynamics of the 2DTORA is developed based on Lagrange equations. Next, the controllability analysis is performed in Section III. Then the energy-based controller is derived in Section IV. Based on the controller, a state feedback controller without measuring the angular velocity is proposed in Section V. Finally, simulations are presented for the proposed controller before implications for simulation results are discussed. The system shown in Fig. 1 represents a 2DTORA system, that includes two perpendicular oscillation carts and an eccentric rotational proof mass. The outer oscillation cart of mass My is connected to a fixed wall by a linear spring of stiffness ky; the inner cart of mass Mx is connected onto a wall of the outer cart by a linear spring of stiffness kx. Note that, for a given 2DTORA system as in Fig. 1, we have My > Mx. The outer cart and inner cart are constrained to have onedimensional translational motion with y and x denoting the travel distance, respectively, and the two dimensional translational motions of the carts are perpendicular to each other. The proof mass actuator attached to the inner cart has mass m and moment of inertia I about its center of mass, which is located at a distance r from the point about which the proof mass rotates. The motion occurs in a horizontal plane; therefore, no gravitational forces need to be considered. In Fig. 1, t denotes the control torque applied to the proof mass, while Fx and Fy are the translational disturbance forces applied to the moving carts. Let x, x and y, y denote the translational position and velocity of the inner cart and outer cart, respectively, and let q and \u03b8 denote the angular position and velocity of the rotational proof mass. The total energy of the system is a sum of the kinetic energy K and the potential energy P. The total kinetic energy K is the sum of kinetic energy Kx, corresponding to the equivalent mass of Mx, kinetic energy Ky, corresponding the equivalent mass of My, and kinetic energy of the proof mass Km"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002284_j.advengsoft.2018.05.005-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002284_j.advengsoft.2018.05.005-Figure3-1.png",
        "caption": "Fig. 3. (a) TRB test bench: comparator pencil, strain gauge and load cell assembly. (b) FE model's relative displacement and experimental data at various values of P. (c) Detail of the relative displacement. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)",
        "texts": [
            " According to these selected criteria, the elements that meet this requirement are those that have a mesh size of 0.2 mm (MAPE and a lower computational cost than the threshold considered for all studied P preloads). The relative displacement of the inner and outer raceways was considered in validating the FE model once the mesh size had been adjusted. The relative displacement of the inner and outer raceways is used mainly to verify that there is an appropriate definition of the mesh size of the FE model, the coefficients of friction and the elastic properties (E and \u03bd). Two Red Crown comparator pencils, Fig. 3(a), are used to measure relative displacement experimentally. In the FE model, it is measured between two nodes that belong to the plane of symmetry of the model itself (Fig. 2(a)). As in the mesh size adjustment process, the P values of the loads were 300, 400, 500 and 600 N and the Fr value was 2000 N. Fr was applied to the TRB by a load cell (HBM U3 that had 5KN of capacity). The P was applied by a screw drove a steel sleeve along on the inner raceway. P loads were measured by a strain gauge affixed to a steel sleeve that pushed the inner raceway as the screw turned. Fig. 3(b) shows the differences between the relative displacements obtained from test bench and those from the FE models for various values of P and Fr. The dashed line indicates the experimentally produced relative displacement, whereas the solid line indicates that produced by the FE models. These pairs of curves show that there has been a reduction in the difference between the relative displacements obtained. Also, Fig. 3(b) shows that the greater relative displacement occurred when the lowest P was applied, and the minimum relative displacement was obtained when the highest P was applied to both FE models and experimental data. Fig. 3(b) also shows as the preload rises, the raceway roller contact stiffness rises and the TRB deformation declines. Fig. 3(c) shows in detail the different relative displacement reached values experimentally and through the FE models. This stiffness variation agrees well with the load\u2013deflection relationship that Harris and Kotzalas [1] and Kania [23] reported previously, which indicates that the higher value of preload in a TRB, the greater its rigidity is. From Fig. 3(b), it can be deduced that the relative displacements with the FE models, if the mesh size valid, were in agreement with the experimental data and the FE model's preset parameters (Ebearing=200 GPa, Ehub=208 GPa, \u03bd=0.29 and coefficients of friction=0.001 and 0.2). Although the loads used in the optimization process were higher (see Table 4) than those loads used in the adjustment process, the preset parameters as well as the mesh size described in Section 2.2.1 were set for all FE simulations of the optimization process [24]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.17-1.png",
        "caption": "Fig. 3.17 Conventional FMB system [AMESIM\u00ae 2004].",
        "texts": [
            " AMESIM\u00ae [2004] focuses on an overview of the hybrid BBW AWB mechatronic control system and then briefly describes the theoretical development of a predictive YSC algorithm for the proposed BBW AWB dispulsion. Simulation results and some experimental results are presented. Besides, sample in-vehicle test results are presented for an ABS control algorithm similar to the predictive YSC. An EFMB or EPMB or EMB BBW AWB dispulsion mechatronic control system, a next-generation braking system, may stop automotive vehicles 3.4 BBW AWB Dispulsion Mechatronic Control Systems 461 by electrical signal rather than by the FMB systems shown in Figure 3.17, as used on most conventional brake systems today [AMESIM\u00ae 2004]. The BBW AWB technology is expected to offer increased safety and vehicle stability to consumers and it may provide benefits to manufacturers who may be able to combine vehicle components into modular assemblies using cost-effective manufacturing processes [AMESIM\u00ae 2004]. Summing up, the EMB BBW AWB dispulsion mechatronic control systems represent the following advantages [AMESIM\u00ae 2004]: Eliminates fluidic lines and substitutes with E-M actuators; Environmentally friendly due to lack of brake fluid or air; Lower servicing requirements; no necessity to exchange/bleed brake fluid or air; Much easier integration of different mechatronic control systems: ABS, ESP system, traffic management systems, and so on; Braking conceivably the most unmistakable safety-critical system, there- fore safety standards must be high"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002700_j.jmapro.2019.12.016-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002700_j.jmapro.2019.12.016-Figure1-1.png",
        "caption": "Fig. 1. A model of the roller enveloping hourglass worm gear set.",
        "texts": [
            " In this paper, a tooth profile equation for the single roller enveloping hourglass worm under error conditions was derived first based on the general principle pertaining to the formation of the worm tooth surface and the engagement mechanism of the single roller enveloping worm gear set. Simulation analysis was conducted on the generated worm tooth surface using numerical methods. Prototypes of the presented worm gear set were then fabricated and contact areas of the head of the grinding rod were analyzed using a metallurgical microscope. An optimal grinding method to machine the worm tooth surface was then proposed based on a substantial body of experimental analysis and theoretical research. Fig. 1 displace the complex tooth surface of the roller enveloping hourglass worm. In order to achieve high precision transmission, the complex worm tooth surface has to be perfectly engaged within the spaces between the rollers of the worm wheel. Authors proposed a new grinding process in fabricating the worm tooth surface and its principle completely matches the practical machining situation. As illustrated in Fig. 2, while rotating about its own axis, the worm being fabricated also rotate around a fixed axis k1 together with the roller worm wheel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure14-1.png",
        "caption": "Figure 14. Stress distribution for piston considering lattice structure as half of",
        "texts": [
            " For the next approach, the void has been modelled as a separated bonded piece assuming a 50% material density (aluminum) to the rest of the piston. However the cooling gallery would mean the crown, undercrown and ring grooves would run significantly cooler and thus have a higher fatigue limit what was taken into account for this analysis. Under this assumption, piston mass was reduced in a 9% and same loaded case setup and boundary conditions presented on previous section have been repeated. Equivalent von-Misses stress has been studied in detail for the three piston numbered regions as it is shown in Figure 14. material density As it is observed in Table 8, stress is reduced at region 2 and 3 under the assumption of considering the lattice structured region as same material than the rest of the piston, but assuming half of its density. As it is observed peak stress at the top of the piston remains more-orless unaltered whatever assumption was done. Meanwhile the peak stresses at the pin bore (region 3) are within the safety material limit. In order to complete the light-weighting analysis on the piston work it has been planned to repeat the heat transfer and FEA stress analysis with the same piston model but introducing a real lattice structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.13-1.png",
        "caption": "Figure 5.13. Geometry for the gravitational interaction between a wire ring and a particle.",
        "texts": [
            " The gravitational interaction between a wire ring and a particle, and between a wire ring and a thin rod are studied. It is confirmed that when a material object is sufficiently far from the field source, the gravitational interaction reduces to the fundamental law (5.46) for two particles. The gravitational torque exerted on a rod by a semicircular wire is then described in an exercise. We begin with the gravitational interaction between a solid body and a particle . Example 5.6. Interaction between a wire ring and a particle. A homogeneous, thin circular wire !::k3o of radius R and mass m., is shown in Fig. 5.13. The Foundation Principles of Classical Mechanics 39 (5.54a) (5.54b) Determine the gravitational field strength of the wire ring at a point P on the normal axis through its center o. Show that the resultant gravitational force exerted by f!l3o on a particle of mass m placed at P reduces to the gravitational force (5.46) between two particles when P is far enough from 0 such that IXI \u00bb R. Solution. The resultant field strength of the circular wire f!l3o at the place X = Zk is determined by (5.50) in which the relative position vector reX) of the point P from the parcel of mass dm; of f!l3o is given by r'(X) =re = X - R = Zk - Re, in terms of the cylindrical reference variables shown in Fig. 5.13. With r2 = Z2+ R2, the integrand in (5.50) may be written as e Zk-Rer Introducing a = mo/2n R, the mass per unit length of the homogeneous wire, and ds = Rdo, its elemental length, we have dm ; = o ds = 2~ mod\u00a2. Then, with (5.54a) in (5.50), noting that both Z and R are fixed quantities, and setting the limits of integration over f!l3o , we obtain the resultant field strength of the circular wire at X: g(X) = _ Gmo 3 (Zk [2Jr d\u00a2 _ R [2Jr erd\u00a2) , 2n(Z2 + R2)'i 10 10 in which er = cos \u00a2i +sin \u00a2j ",
            "c13) o-; (bo-ao)g(:7u)=--=-- -- k. m(.c13) a.b; .\u20ac o The reader will find it informative to work through the following exercises. These review the previous examples in the solution of a similar problem for a semicircular wire. In addition , the gravitational torque effect is illustrated. Exercise 5.3. Interaction betweena semicircular wire and a thin rod. Suppose that the ring in the previous example is replaced by a semicircular wire of radius R in the upper half plane so that \u00a2 E [- I' I] (see Fig. 5.13), while the rod retains the configuration shown in Fig. 5.14. Recall the sequence of equations (5.54a) through (5.54d) . Show that the semicircular wire produces on the normal axis through 0 at X = Zk a resultant gravitational field strength given by Gmog(X) = , (2Ri -:rrZk) ; (5.56a) n (Z2 + R2)'i and hence the resultant gravitational force exerted by the wire on the rod is F(.c13) = Gmom [~(bao - abo)i -:rr (bo - ao)k] ,:rr.\u20acaobo R where a., and b; are defined in (5.55c). (5.56b) o Exercise 5",
            "0 I kg is fastened by a string of length I = 16 cm to a hinge pin at r =4 ern from the center of a smooth horizontal table on which the bob rests . The table turns with a constant angular speed to , as shown in the figure. Relative to an observer in the table reference frame, the pendulum executes oscillations of small amplitude f30 and period r = 0.5 sec. Find the angular speed of the table and compute the string tension T when f3 = f3o . Problem 6.47. 6.48. Gravitational attraction by a fixed, homogeneous, thin ring of radius R and mass M induces a particle P of mass m to move along its normal central axis , as shown in Fig. 5.13 . (See Example 5.6, page 38.) (a) Derive the differential equation of motion for P. (b) Show that for sufficiently small displacements X(P, t) from the center 0, the motion of P is simple harmonic. What is the frequency of its small oscillations? 6.49. A smooth , rigid rod of length 2b is attached to a table that turns in the horizontal plane with a constant angular velocity w , as shown . A slider block S of mass m is released from rest relative to the rod at a distance a from its midpoint O . (a) Determine the horizontal force R exerted by the rod on the slider as a function of its distance x from O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure19.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure19.1-1.png",
        "caption": "Fig. 19.1 Vectors ri and locating the body i center of mass and a mass element dm",
        "texts": [
            " It may also be a finite force applied to dm . Constraint forces caused by ideal kinematical constraints in joints do not contribute to virtual power because for every pair of constraint forces F1 = +F and F2 = \u2212F (actio = reactio) the term \u03b4r\u03071 \u00b7F1+\u03b4r\u03072 \u00b7F2 is equal to zero. First, the contribution of a single rigid body i to the sum in (19.3) is formulated. Let ri be the radius vector of the body center of mass Ci in e and let, furthermore, be the body-fixed vector from Ci to the mass element dm (see Fig. 19.1). These definitions establish the three kinematics equations below. The last equation expresses the fact that Ci is the body 666 19 Dynamics of Mechanisms center of mass. r = ri + , \u03b4r\u0307 = \u03b4r\u0307i + \u03b4\u03c9i \u00d7 , r\u0308 = r\u0308i + \u0308 , \u222b mi dm = 0 . (19.4) With these equations a single integral in (19.3) is\u222b mi \u03b4r\u0307 \u00b7 (r\u0308 dm\u2212 dF) = \u222b mi (\u03b4r\u0307i + \u03b4\u03c9i \u00d7 ) \u00b7 [(r\u0308i + \u0308) dm\u2212 dF] = \u03b4r\u0307i \u00b7 (r\u0308imi \u2212 Fi) + \u03b4\u03c9i \u00b7 (\u222b mi \u00d7 \u0308 dm\u2212 \u222b mi \u00d7 dF ) . (19.5) The force Fi is the resultant applied force on body i . Its line of action passes through the body center of mass Ci "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure10-1.png",
        "caption": "Fig. 10. The tooth profile with k2 = 0.4.",
        "texts": [],
        "surrounding_texts": [
            "The contact ratio can be defined as the average number of teeth of each gear in contact. It can also be defined as the ratio of the angle rotated by the gear between starting and end points of contact to the angle between two adjacent teeth which (the latter angle) is equal to 2\u03c0 divided by the number of teeth [19]. As illustrated in Fig. 13, B presents the intersection point between the line of action and the addendum circle of the driven gear and C is the intersection point between the line of action and the addendum circle of the driving gear. Assuming that the driving gear rotates in a clockwise direction, two gears would firstly engage at B, and finally separate at C. The contact ratio of the gear drive can be expressed as where \u03b5 \u00bc \u03a8 2\u03c0=z1 \u00f055\u00de \u03a8 denotes the angle between O1B and O1C . The parameters are set with the same values as those in examples 1 and 2. According to Eq. (55), the corresponding contact ratio of the gears with different parameters of k1 and k2 are listed in Table 1. Under the same parameters, the contact ratio of an involute gear drive is also listed in Table 1. From the obtained numerical results, the following conclusions can be made. (i) From Figs. 2 and 3, it can be seen that the greater k1 and k2, the closer the parabola to the x0-axis. From Figs. 9 and 10, the closer the parabola to x0-axis, the greater the corresponding angle \u03c8 will be. Thus, according to Eq. (55) the values of the contact ratio will increase with increased parameters k1 and k2. This has been confirmed by the results shown in Table 1. (ii) The contact ratio of the proposed gear drive varies from 1.3738 to 1.5694 in the example. The lowest value is nearly 10% less than that of the involute gear drive. Such gear drives can be applied in gear pumps since less contact ratio is advantageous to ease the trapping phenomenon [20,21]. However, low contact ratio will decrease the combined gear bending strength when more than one simultaneous contact points are considered."
        ]
    },
    {
        "image_filename": "designv10_12_0002572_j.solener.2018.07.069-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002572_j.solener.2018.07.069-Figure13-1.png",
        "caption": "Fig. 13. Schematic of the surfaces and directions followed in the hardness test.",
        "texts": [
            " Microstructure of the samples was observed at PSA's Materials Lab using Leica DMI 5000 digital microscope. Measurement of microhardness of the samples was also performed at PSA's Materials Lab using Struers Duramin HMV-2 microhardness tester at the load of 300 kgf for 15 s (HV0.3). Because of the anisotropic build process, two cross-sections are considered. One is a cross section view parallel to the build direction, and the other is a top view, perpendicular to the build direction. For each specimen an average of 10 measurements were carried out both on cross section and top view (Fig. 13). Before and after heat treatment each specimen was also weighed using Mettler Toledo Classic balance with an accuracy of\u00b1 0.0001 g. Fig. 3(a) and (b) respectively shows the microstructure in cross section and top view of as-fabricated Ti6Al4V manufactured by SLM. The cross section and top view of non-heat treated indicate a fully acicular \u03b1\u2032 martensite. Cross section view reveals long, parallel columnar shape original \u03b2 grains, which are oriented in the building direction (z-direction) as was also reported previously in (Thijs et al",
            " Effects of the heat treatment atmosphere contamination were manifested in some specimens by colouring their upper surface and the graphite depositions (adsorption) from the graphite crucible. Because the purpose of this paper is to present the feasibility of using the CSE in the heat treatment of SLM Ti6Al4V in solar furnaces, the detailed studies of these issues will be in the further works. Vickers hardness both for as-fabricated and heat treated SLM Ti6Al4V specimens was measured. Untreated and heat treated samples were evaluated in different points using an indentation time of 15 s. Fig. 13 illustrates the cut (a) and the surfaces where the hardness was measured (b). Specimens were evaluated from top to bottom edge, in cross section (Fig. 13(b)) and from the edge of cross section to the contour edge in the direction indicated by arrows in (Fig. 13(b)). The Vickers hardness values for as-fabricated and heat treated SLM Ti6Al4V specimens evaluated in cross section and horizontal plan (top view) are shown in Table 3 and plotted in Figs. 14\u201316. As seen in Fig. 3, and accordingly to other investigations(Vrancken et al., 2012; Yadroitsev et al., 2014; Facchini et al., 2010; Simonelli et al., 2012), cooling rate after SLM process is high enough to result in formation of the \u03b1\u2032 martensitic microstructure in the as-fabricated specimens. For the as-fabricated material, the graph shows the hardness increases with the distance to the edge, reaching the highest values at the centre of the specimens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001098_2013-01-2292-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001098_2013-01-2292-Figure3-1.png",
        "caption": "Figure 3. Deformation due to a force",
        "texts": [],
        "surrounding_texts": [
            "The following outlines a method of compensation which accounts for geometric offsets and counteracts deformation from the weight of the robot and weight of the payload. In practice this method has been able to position a large serial link robotic arm with \u223c200kg end effector within 0.15mm (3-sigma error) over a volume of 2m \u00d7 3m \u00d7 3m. Error associated with a rigid link Every link of a robot manipulator can be described by 6 parameters that define a transformation between the two connection points of the link: Each of these terms has nominal value and an offset error: In a rigid link there is exactly one free parameter, \u03b8, allowing motion. In all cases examined here \u03b8 is a pure rotation, though in general a translational component is also possible. In the simplest case the measurement of theta is exactly the motion of the link offset, however in the general case the offset is \u0398(\u03b8). Thus the equation for the final transformation is: As an example, in the specific case of rotation about \u03b3 the parameters are defined as: Additional error associated with a flexible link One of the added challenges of a serial link robotic manipulator over a conventional linear machine is the links of a robotic manipulator are both flexible and experience a large range of forces and torques dependent on position: These forces and torques cause an additional deflection d(F). In the generalized link geometry, for small deformations there is a linear relationship between each element of force or torque and each element of positional or rotational offsets. Defining Jd as the Jacobian of d(F) with respect to F: While this error depends on force, it is otherwise independent of the robot position. Adding this error, the equation for the transformation of a non-rigid link becomes: F for any link and robot position can be computed as the sum of weights and torques applied from the other links, F(X1, X2, X3, \u2026), however since the deformations are small the equations can be written in closed form as Fapprox(\u03b81, \u03b82, \u03b83, \u2026). Thus the full transformation for the link is:"
        ]
    },
    {
        "image_filename": "designv10_12_0002046_jbm.b.33215-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002046_jbm.b.33215-Figure1-1.png",
        "caption": "FIGURE 1. Chemical structures of (a) PES, (b) PVP, and (c) genistein.",
        "texts": [
            "20,21 The improved trend of antioxidant, anti-inflammatory and antiplatelet adhesion properties of the genistein modified PES/PVP blends is discussed in relation to the genistein concentration. PES (Ultrason E 6020P), an amorphous polymer having a weight average molecular weight (Mw5 46,000), was provided by BASF Corporation (Wyandotte, MI), whereas PVP (Mw5 40,000) was purchased from Sigma-Aldrich (St. Louis, MO). Genistein (>98% purity) was bought from MDidea Exporting division (Yin Chuan, Ningxia, China). Figure 1 shows the chemical structures of PES, PVP, and genistein. Blood was donated by the first author and healthy volunteers. Venous blood was collected in lithium heparin Vacutainer tubes (Becton Dickinson, Rutherford, NJ) and used immediately after collection. The amount of blood collected from any single individual met the criteria for exemption from institutional review board oversight. The pure PES and PVP polymer pellets were vacuum-dried at 100 C for 24 h and dissolved in DMSO separately. Genistein solution was also prepared using DMSO as the solvent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002407_1.4033387-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002407_1.4033387-Figure10-1.png",
        "caption": "Fig. 10 The simulation environment established in VERICUT",
        "texts": [
            " Then, the NC code which is suitable for the SIEMENS 840D SYSTEM should be made according to the tool path of the worm in the process of generating the face-gear. What is more, the 3D model of the worm built in the environment of CATIA should be imported in 071013-6 / Vol. 138, JULY 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935094/ on 02/08/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use the environment of VERICUT as a tool. Finally, the preparation work for the simulation is finished, as shown in Fig. 10(a). The detailed coordinate transformation mapping of the VERICUT model is shown in Fig. 10(b). The movable coordinate systems OA;OB;OC are rigidly connected to the worm, the face-gear, and the machine model, respectively, and rotate around their axes, respectively. At the same time, the coordinate systems OA0; OB0; OC0 are fixed in the relative part of the machine model. MB;A is the coordinate transformation matrix from OA to OB. M2;w is the coordinate transformation matrix from Ow to O2 (Fig. 7). The motion relationship of each axis in the VERICUT model can be obtained due to MB;A \u00bcM2;w"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002212_jeb.155416-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002212_jeb.155416-Figure1-1.png",
        "caption": "Fig. 1. Marker position, global coordinate system and torque directions. 3D skeletal model of Kassina maculata (from CT scans) in oblique (A), dorsal (B) and anterior (C) views. Global coordinate systems shown; in B and C, the Z and Y axes (respectively) are coming out of the page. Black dots mark the positions of the tarsometatarsal (TMT) (1), ankle (2), knee (3), hip (4), vent (5), head (6) and sacral (7) kinematic markers in A. In B and C, dark red arrows show the approximate orientation of the ground reaction force midway through a jump; curved black arrows show the directions of the external torques (generated by ground reaction force) on the ankle, knee and hip joints; curved pink arrows show the directions of the opposing muscle torques required to balance external torques.",
        "texts": [
            " Frogs were fed crickets, waxworms and bloodworms three times per week; once a week, crickets were dusted with mineral powder. All husbandry and experimental procedures were in accordance with UK Home Office regulations (Licence 70/8242) and Royal Veterinary College Ethics and Welfare Committee. External skin markers were made by cutting white plastic circles using a screw punch (Nonaka Mfg. Co. Ltd., Japan) with a 5 mm hollow point drill bit; these circles were painted on one side with a black marker. Seven markers were applied to anatomical landmarks on the body and the left hind limb using cyanoacrylate adhesive (Fig. 1A). Forces exerted during jumping were recorded using a Nano17 force/torque transducer (ATI Industrial Automation, Apex, NC, USA) mounted in a purpose-built trackway. To record single-foot forces, a small stiff aluminium plate (flush with the trackway surface) was rigidly fixed to the load cell providing sufficient area for foot contact. Force data during jumping were acquired at 2000 Hz with acquisition to PC (NI-6289) controlled by a custom-written LabVIEW (National Instruments, Austin, TX, USA) script",
            " Frogs were simultaneously filmed at 250 frames s-1 at a 1/1500s shutter speed using two high-speed Photron FASTCAM Jo ur na l o f E xp er im en ta l B io lo gy \u2022 A dv an ce a rt ic le cameras (Photron Ltd, San Diego, USA) positioned dorsal and lateral to the force plate; an angled mirror placed opposite the lateral camera at 60\u00b0 from the horizontal was used to obtain a third view. A custom-built 49 point calibration object was used to calibrate the three views. Video data were acquired using the Photron FASTCAM Viewer and synchronized with force data using a post-trigger. Both the cameras and force transducer used a right-handed global reference frame in which the X-axis (mediolateral) pointed right, the Y-axis (fore-aft) pointed forward and the Z-axis (dorsoventral) pointed up (Fig. 1A). Frogs were positioned with the marked left hind leg resting on the force plate (to obtain single-foot forces) and facing the lateral camera, and were encouraged to jump forwards (positive Y) to a dark box by sudden movements or gentle tapping of the unmarked hind foot. A range of jump angles were elicited by varying the height of the box. Trials were conducted at 22.5 \u00b0C. After experiments animals were weighed and measured, and markers were gently removed. Kinematic data from the three views were calibrated and markers digitized to XYZ coordinates using open source script (Hedrick, 2008) in MATLAB (MathWorks, Natick, USA)",
            " The norms of the XY and XZ components give torque magnitudes about the Z and Y Jo ur na l o f E xp er im en ta l B io lo gy \u2022 A dv an ce a rt ic le axes, respectively, permitting us to evaluate contributions to limb protraction/retraction (i.e., anterior/posterior rotation) versus abduction/adduction (i.e., dorsal/ventral rotation) (Fig. 5, Table 3 and supplementary material Table S2). Positive (counterclockwise) XY torques indicate that the GRF acts to retract the limb segment; positive XZ torques indicate the GRF acts to abduct the limb segment (Fig. 1B, C). Internal torques generated by the frog\u2019s muscles in either plane must counteract external torques. Therefore, to facilitate further discussion, we will refer to joint torques from the muscles\u2019 point-of-view: negative XY torques retract limb segments whereas positive XZ torques adduct segments (Fig. 1B, C). In addition to being analysed in absolute time, data were normalized by percent of jump contact time for comparison and statistical analyses (Figs. 2-5 and supplementary material Figs. S4 and S5). The end of each jump (in which the last toe left ground) was defined as take-off. Jump start was defined as the onset of velocity at the hip marker (closest to the COM, see Richards et al. submitted). Within this interval (i.e., jump start to take-off), data was resampled to 100 points using interpolation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000952_iros.2011.6094775-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000952_iros.2011.6094775-Figure2-1.png",
        "caption": "Fig. 2. Coordinate system and control inputs of the two-dimensional quadrocopter model.",
        "texts": [
            " Section VI presents experimental results 978-1-61284-456-5/11/$26.00 \u00a92011 IEEE 5179 demonstrating the validity of the calculated trajectories, and Section VII provides a conclusion. In this section, a two-dimensional model of the quadrocopter is presented and a non-dimensionalizing coordinate transformation is applied, which allows to describe the quadrocopter using only two parameters. The two-dimensional quadrocopter model has three degrees of freedom: the horizontal position x, the vertical position z, and the pitch angle \u03b8, as shown in Fig. 2. We assume that the angular velocity \u03b8\u0307 can be set directly without dynamics and delay. This is motivated by the very high angular accelerations that quadrocopters can reach (typically on the order of several hundred rad/s2), while the angular velocity is usually limited by the gyroscopic sensors used for feedback control on the vehicle [3]. As demonstrated by experimental results shown in Section VI, the model mismatch caused by this assumption is small, and it leads to tractable derivations in the following chapters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002834_j.ijrmhm.2019.104998-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002834_j.ijrmhm.2019.104998-Figure9-1.png",
        "caption": "Fig. 9. LPBF Collimator with the resultant ultra-fine pinhole (a) and typical vertical surface roughness of an as built LPBF tungsten part (b).",
        "texts": [
            "5 mm steps and the 0.5mm LPBF collimator moved in 0.5mm step sizes. This pencil beam was raster scanned across the detector surface via the automated scanning table. The detector signals induced by the charge collection process were then digitised, recorded and processed using digital electronics. The results were characterized using count rate. The tungsten collimator was fabricated without any visible defects or delamination during the melting process and a relatively smooth surface was produced. Fig. 9 (a) shows a photograph of the LPBF collimator with the resultant ultra-fine pinhole. Also shown, in Fig. 9 (b), is an SEM micrograph of the as built and typical vertical surface roughness of a LPBF tungsten part. The volume of unmelted adherent particles on the SEM in Fig. 9 (b) contributed to the dimensional variations and production accuracy of the pinhole, leading to the final pinhole diameter of ~0.5 mm. These results were also compared to the measurements carried out using the long plug pin gauges and it was observed that the 0.5mm gauge could fit tightly through the pinhole. On the other hand, a pin gauge of 0.6 mm diameter was not able to pass through the pinhole of the collimator. The impact of such deviation is dependent on the size of the feature and in this case, the relatively small dimension of the pinhole meant that the mean deviation was ~16%"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002572_j.solener.2018.07.069-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002572_j.solener.2018.07.069-Figure1-1.png",
        "caption": "Fig. 1. Island laser scanning strategy.",
        "texts": [
            "02\u20134.10%, Fe: 0.16\u20130.18%, C: 0.013\u20130.010%, O: 0.091\u20130.092, N: 0.008\u20130.010%, H: 0.005\u20130.004%, Ti: rest. All SLM specimens were fabricated in a single batch with layer thickness of 25 \u00b5m, laser power of 200W in the skin surface and 370W in the core surface, hatch space of 0.095mm, and laser scanning speed range of 1200\u20131500mm/s. The SLM process took place in Ar atmosphere and as scanning strategy was used a continuous on skin surfaces and alternate islands of 5\u00d7 5 mm (so-called island strategy) (Fig. 1) on core surfaces. The building axes of specimens were parallel to the Z direction according to the ISO/ASTM52921-13 (ISO, 2013). Heat treatments of SLM Ti6Al4V were carried out in the horizontal (SF40) and vertical (SF5) furnace on Solar Platform in Almer\u00eda using Concentrated solar energy (CSE), as energy source. SF40 are 40 kW power and 7000 kW/m2 peak flux solar in a focus of 12 cm in diameter. Its optical axis is horizontal, and it is of the on-axis type, the heliostat, parabolic concentrator and focus are aligned on the optical axis of the parabola"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.5-1.png",
        "caption": "Fig. 12.5 Piercing mill",
        "texts": [
            "31) The result u = 0 tells that the screw axis intersects the common perpendicular of the two shafts orthogonally at the midpoint 0 , and the result for \u03c9n tells that the screw axis n lies along e2 . The two raccording hyperboloids are congruent. They are in external contact along the resultant screw axis. Seamless steel tubes are hot-rolled in a so-called piercing mill by a process known as rotary piercing of tubes over plug (patent Mannesmann; see VDIZeitschrift Heft 25 (1890) and Fro\u0308hlich [4]). The principle is explained in Fig. 12.5. Two identical rollers 1 and 2 of radius R are rotating with equal angular velocities \u03a9 about skew axes. The common perpendicular of the axes is the z-axis normal to the plane of the drawing. The projected angle \u03b1 between the axes is bisected by the x-axis. A cylinder 3 of radius r with its axis along the x-axis is in contact with each roller at a single point on the z-axis (at z = r with the top roller 1 and at z = \u2212r with the bottom roller 2 ). At these points the rollers have circumferential velocities v1 and v2 of equal magnitude \u03a9R and directions as shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000717_s12541-010-0076-2-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000717_s12541-010-0076-2-Figure3-1.png",
        "caption": "Fig. 3 Modified axial section with surface equidistance method",
        "texts": [
            " (13): ' 2 ' 1 cos cos u u u u R R Z Z \u03b4 \u03b5 \u03b4 \u03b5  = + \u2212  = + (13) The angle \u03b5 between the normal vector u n and the rotation vector u k of the grinding wheel can be obtained from Eq. (14): cos u u u k n n \u03b5 \u22c5 = (14) The direction of the normal vector u n and the normal vector n in the trajectory between the grinding wheel and the screw rotor is same. In coordinate system ,\u03c3 u n can be expressed as: u x y z n n i n j n k= + + (15) From the transformation between u \u03c3 and \u03c3 : sin cos u k j k= \u2212 \u03a3 + \u03a3 (16) Substituting Eq. (17) and Eq. (18) into Eq. (16), \u03b5 can be given by Eq. (19): 2 2 2 cos sin cos z y x y z n n n n n \u03b5 \u03a3 \u2212 \u03a3 = + + (17) Figure 3 shows the calculation of modified axial section with surface equidistance method. In Figure 3, the tangent angle \u03b8 at each point at the theoretical axial section should satisfy the following: If 0 / 2,\u03b5 \u03c0\u2264 \u2264 the tangent angle \u03b8 at each point is an obtuse angle. Then the relationship between \u03b5 and tangent angle \u03b8 is given by: / 2 ;\u03b8 \u03c0 \u03b5= + when / 2 ,\u03c0 \u03b5 \u03c0< \u2264 the tangent angle \u03b8 at each point is an acute angle, then the relationship between \u03b5 and tangent angle \u03b8 is given by: .\u03b8 \u03c0 \u03b5= \u2212 As a complex system, error compensation is an effective method to improve the machining precision of the workpiece",
            " In order to evaluate the machining error, the influences of tooth profile errors affected by mounting angle error and mounting distance error as well as the wear of CBN wheel are analyzed as followings. The tooth profile error of in rotor surface increased with the increasing of mounting angle error .\u2206\u03a3 However, for the male rotor mentioned above, the tooth profile errors of the rotor first decreased then increased from bottom to top of screw groove when given same mounting distance error u A\u2206 (see Figure 7(b)). The influence curves of profile errors f n with mounting angle error are shown in Figure 3. In Figure 7, the profile error of female rotor is negative error, while the profile error of male rotor is positive. It is the different mounting angle lead to such difference, that is: the screw direction of female rotor and the mounting angle \u2211 is a positive value, while screw direction of male rotor is left and the mounting angle \u2211 is a negative value. Generally, the profile errors in rotor surface increased with the increasing of mounting distance error . u A\u2206 According to the calculation, the influence trendency of the tooth profile error affected by mounting distance error u A\u2206 will be changed with different rotor surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003066_tec.2020.3004227-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003066_tec.2020.3004227-Figure1-1.png",
        "caption": "Fig. 1. Half of the geometry of a fractional-slot SAVPM machine",
        "texts": [
            " Laplace's and Poisson's equations of magnetic vector potential in Fourier coefficients are established under the given permeability, and are solved by separation technique of variables. In the iterative procedure, soft-magnetic material permeability is updated according to flux density until error meets requirement. NA solves the magnetic field and performances of a SAVPM machine. Frozen permeability method (FPM) is used to determine PM flux linkage and d-axis inductance under load. Results from the NA model have been compared with those from FEA and experiments. II. SUBDOMAIN MODEL Half of the geometry of a fractional-slot (8-stator-pole/ 18-slot) SAVPM machine is shown in Fig. 1, which adopts two-tangential-layer windings and external-rotor structure. The cross-section of tooth body cores and PMs are rectangular. The part of PMs near air-gap has two openings with the first larger than the second for minor flux leakage. Spoke array PMs and rotor poles are fastened by an aluminum case. Width of tooth body cores is w and current density of two layers in slot i are and respectively. Height of PMs in magnetized direction is and \u2206 is rotor angular position (\u2206= 0 when center lines of a PM and a slot align)",
            " Angles of tooth shoes, rotor pole shoes near and far from air-gap are , and respectively. Soft-magnetic material permeability is . The whole model is divided into seven subdomains, i.e., tooth body cores and slots (subdomain I), tooth shoes and slot openings (subdomain II), air-gap (subdomain III), rotor pole shoes near air-gap and second PM openings (subdomain IV), rotor pole shoes far from air-gap and first PM openings (subdomain V), rotor pole body cores and PMs (subdomain VI), aluminum case (subdomain VII) shown in Fig. 1. Corresponding geometric radii at a certain rotor angular position are shown in the right side of subdivision of tooth cores and rotor pole cores in Fig. 2, i.e., inner and outer radii of slots and respectively, inner and outer radii of air-gap and respectively, inner and outer radii of first PM opening and respectively, inner and outer radii of aluminum case and respectively. Tooth body cores, tooth shoes, rotor pole shoes near and far from air-gap and rotor pole body cores are subdivided into , , , and tangential pieces",
            " The averaged magnetic vector potential of winding x ( = 1 or 2) in slot i in layer l is written into as following = 1 ( , )( ) / ( ) / (46) where = \u2212 /4 . Development of (46) is written into as following = 1 \u2212 ( ) (47) where is the n-th Fourier coefficient of the averaged magnetic vector potential column vector of winding x in slot i in layer l written into as following = ( ) \u22ef \u22ef = + 2 \u2212 \u2212 \u2212 2 \u2212 + \u22124 (48) The flux linkages of 3-phase of winding x in layer l are written into as following = \u22ef \u22ef ( / ) (49) where = , t is the number of unit machines, and is the number of turns in series per coil. Winding distribution shown in Fig. 1 determines matrix written into as following = 100 010 \u2212100 001 100 00\u22121 010 001 0\u221210 (50) = 100 00\u22121 \u2212100 001 0\u221210 00\u22121 010 \u2212100 0\u221210 (51) The flux linkages of 3-phase are written into as following = \u2211 (52) where = . A self inductance, e.g. phase a, is written into as following = ,( ) \u2212 , (53) where is the current of phase a. ,( ) and , are the flux linkages of phase a excited by PMs and , and only PMs respectively. The EMFs of 3-phase are calculated by the law of electromagnetic induction written into as following = \u2212 = \u2212\u03a9 \u0394 (54) where = , and \u2126 is mechanical angular speed in radians/second"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure5-1.png",
        "caption": "Fig. 5. Tooth contact of hourglass worm drive.",
        "texts": [
            " The OPE hourglass worm surface equation of the right flank can be derived and described in coordinate system \u03c3 2 as follows: R 1 ( v , t , \u03d5 1 ) = ( M 12 [ r g R (v , t) 1 ]T )T R ( v , t , \u03d5 1 ) = 0 (11) Where \u03d5 2 = i 12 \u03d5 1 . M 12 = \u23a1 \u23a2 \u23a2 \u23a3 \u2212 cos \u03d5 1 cos \u03d5 2 cos \u03d5 1 sin \u03d5 2 sin \u03d5 1 a cos \u03d5 1 sin \u03d5 1 cos \u03d5 2 \u2212 sin \u03d5 1 sin \u03d5 2 \u2212 cos \u03d5 1 \u2212a sin \u03d5 1 \u2212 sin \u03d5 2 \u2212 cos \u03d5 2 0 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 In the same way, the OPE hourglass worm surface equation of the left flank can be described in coordinate system \u03c3 2 as follows: r L 1 ( v , t , \u03d5 1 ) = ( M 12 [ r g L (v , t) 1 ]T )T L ( v , t , \u03d5 1 ) = 0 (12) As shown in Fig. 5 (a) and (b), the contact line L I between the IHB gear and the medium gear, and the contact line L II between the OPE hourglass worm and the medium gear are simultaneously present on the medium gear tooth surface. These contact lines do not coincide but intersect each other. Therefore, after the medium gear is removed, the meshing between the OPE hourglass worm and the IHB gear is in-point contact, as shown in Fig. 5 (c). The contact line between the IHB gear and the medium gear in coordinate system \u03c3 1 is shown in Fig. 6 (a). The IHB gear tooth surface and contact line L I are projected onto the plane x 1 o 1 y 1 , as shown in Fig. 6 (b). The cross section tooth profile of IHB gear is an involute curve, and the cross section tooth profile of medium gear is a beeline, as well as the geometry relationship of cross section tooth profile is illustrated in Fig. 6 (b). In coordinate system \u03c3 1 , the unit normal vector of the IHB gear surface 1 is given as follows: n R 1 ( u , \u03b8 ) = [ \u2212 sin ( \u03b4\u2212\u03b8\u2212u ) \u221a 1+ cos 2 \u03b1tan 2 \u03b2R \u2212 cos ( \u03b4\u2212\u03b8\u2212u ) \u221a 1+ cos 2 \u03b1tan 2 \u03b2R cos \u03b1 tan \u03b2R \u221a 1+ cos 2 \u03b1tan 2 \u03b2R ] T (13) In coordinate system \u03c3 1 , the unit normal vector of the medium gear surface g is given as follows: n R 1g = M R 1g M R ga n R a (14) Where M R 1 g = [ cos (\u03b4 \u2212 \u03b8 \u2212 u ) sin (\u03b4 \u2212 \u03b8 \u2212 u ) 0 \u2212 sin (\u03b4 \u2212 \u03b8 \u2212 u ) cos (\u03b4 \u2212 \u03b8 \u2212 u ) 0 0 0 1 ] , M R ga = [ 1 0 0 0 sin \u03b2bR \u2212 cos \u03b2bR 0 cos \u03b2bR sin \u03b2bR ] Using Eqs",
            " (4) and (9) , the contact lines on the right flank of medium gear tooth surface g can be determined and described as: r g R (v , t) R ( v , t , \u03d5 1 ) = 0 (18) Similarly, the contact lines L II on the left flank is described as: r g L (v , t) L ( v , t , \u03d5 1 ) = 0 (19) Here, the rotation angle \u03d51 is an input value, and its value is fixed when the instantaneous contact line is considered. By all appearance, the meshing between the OPE hourglass worm and the medium gear is in-line contact at different positions in different moments. As shown in Fig. 5 , the intersection of the contact line L I and the contact line L II is the contact point of the IHB gear and the OPE hourglass worm. Using Eqs. (16) and (18) , the contact point of the hourglass worm drive on the right flank is derived through solving the following equations: r 1 R ( m R ) = r g R (v , t ) R ( v , t , \u03d5 1 ) = 0 (20) Similarly, the contact point of the hourglass worm drive on the left flank is represented through solving the following equations: r 1 L ( m L ) = r g L (v , t ) L ( v , t , \u03d5 1 ) = 0 (21) Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000972_978-3-642-22164-4_2-Figure2.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000972_978-3-642-22164-4_2-Figure2.3-1.png",
        "caption": "Fig. 2.3 Kinematic car model",
        "texts": [
            " Only the main points of the presented results are demonstrated. Practical application of HOSM control is presented in a lot of papers, only to mention here [1, 6, 15, 19, 26, 44, 46, 53, 51]. Consider a simple kinematic model of car control x\u0307 = V cos\u03c6 , y\u0307 = V sin\u03c6 , \u03c6\u0307 = V \u0394 tan\u03b8 , \u03b8\u0307 = v, where x and y are Cartesian coordinates of the rear-axle middle point, \u03c6 is the orientation angle, V is the longitudinal velocity, \u0394 is the length between the two axles and \u03b8 is the steering angle (i.e. the real input) (Fig. 2.3), \u03b5 is the disturbance parameter, v is the system input (control). The task is to steer the car from a given initial position to the trajectory y = g(x), where g(x) and y are assumed to be available in real time. Define \u03c3 = y\u2212 g(x). Let V = const = 10m/s,\u0394 = 5m,x = y = \u03c6 = \u03b8 = 0 at t = 0,g(x) = 10sin(0.05x)+ 5. The relative degree of the system is 3 and the quasi-continuous 3-sliding controller (Section 2.5.2) solves the problem. It was taken \u03b1 = 2,L = 400. The resulting output-feedback controller (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure16.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure16.9-1.png",
        "caption": "Fig. 16.9 Internal pin gearing with ten pins on the larger wheel 1 and with nine teeth on wheel 2 . Epitrochoid e traced by the center of the pin and parallel tooth flank f2",
        "texts": [
            " The tip B of the tooth shown in the large figure is the point of intersection of f2 with the line \u03b7 = \u03c0 8 \u03be . It is associated with u \u2248 103.5\u25e6 . In conclusion: The arc A\u2013B of f2 has contact with f1 in the narrow interval 93.2\u25e6 < u < 103.5\u25e6 of f1 . To the right of A the tooth flank must be given a form avoiding contact with the pin. The arc A\u2013C of f2 interferes with the pin. This problem of interference does not occur when the centers of the pins are placed on a circle of radius < r1 , for then the cycloid z and the parallel curve f2 do not have cusps. End of example. Example: In Fig. 16.9 a case of internal gearing is shown. The outer wheel 1 has n1 = 10 pins, and the inner wheel 2 has n2 = 9 teeth, so that r2/r1 = n2/n1 = 9/10 . The centers of the pins of radius \u03c1 are placed on a circle of radius \u03bbr1 with \u03bb > 1 . With the angle u shown in the figure the flank f1 of the pin having its center on the x-axis is given by the equations x(u) = \u03bbr1 \u2212 \u03c1 cosu , y(u) = \u2212\u03c1 sinu . (16.36) Equation (16.23) is sin(u+ \u03d51) = \u03bb sinu . (16.37) The solution for u as function of \u03d51 is u(\u03d51) = tan\u22121 sin\u03d51 \u03bb\u2212 cos\u03d51 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure3.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure3.3-1.png",
        "caption": "Fig. 3.3 Schematic of acting forces, torques and motions of the spinning disc",
        "texts": [
            " External torque applied to a gyroscope causes the plane of the spinning rotor to turn around axis ox, as shown in Fig. 3.2. This turn leads to a change in the direction of the mass elements\u2019 tangential velocity. The change in tangential velocity is expressed in the acceleration of rotating mass elements and their inertial forces. This change varies along the circumference where mass elements are disposed of. The directions of the variable change in tangential velocity vectors Vz are parallel to the spinning rotor\u2019s axle oz (Fig. 3.3). The maximal changes in direction have the velocity vectors V* of the mass element located on the line of axis ox. The two vectors V located 90\u00b0 and 270\u00b0 from the line of axis ox and whose directions are parallel to the line of axis ox do not exhibit any changes. A change in the velocity vectors refers to the accelerated motions az of the rotor\u2019s mass elements m that generate inertial forces f in. The integrated product of the components of the inertial forces f in of the mass elements and their variable radius of disposition relative to axis oy represent inertial torque T in acting on axis oy",
            "17) allows for the definition of the integrated torque produced by a change in the inertial forces generated by the disc\u2019s mass elements, wherein all components should be presented in a form appropriate for integration. Expression of Eq. (3.16) is the same as Eq. (3.3), and the following solution is the same that yields the equation for precession torque. The change in inertial forces represents the distributed load applied along the length of the circle and angle \u03b1 where the disc\u2019s mass elements are located. Figure 3.3 depicts the locations of the change in inertial forces f in\u00b7z of the disc. A distributed load can be equated with a concentrated load applied at a specific point along axis ox, which is the centroid at the semicircle. The location of the resultant force is the centroid (point B, Fig. 3.3) of the area under the curve, which is calculated by the known integrated equation. yB = \u222b \u03c0 \u03b1=0 fin\u00b7z xmd\u03b1\u222b \u03c0 \u03b1=0 fin\u00b7zd\u03b1 (3.17) where fin = MR\u03c92 3\u03c0 \u03b4 \u03b3 sin \u03b1 Substituting Eq. (3.2) and other components into Eq. (3.17) and transformation yields the following expression. yB = \u222b \u03c0 \u03b1=0 fin\u00b7z xmd\u03b1\u222b \u03c0 \u03b1=0 fin\u00b7zd\u03b1 = \u222b \u03c0 \u03b1=0 MR\u03c92 3\u03c0 \u03b4 \u00d7 \u03b3 \u00d7 2 3 R cos\u03b1 sin \u03b1d\u03b1\u222b \u03c0 \u03b1=0 MR\u03c92 3\u03c0 \u03b4 \u00d7 \u03b3 sin \u03b1d\u03b1 = MR\u03c92 3\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 2 3 R cos\u03b1 sin \u03b1d\u03b1 MR\u03c92 3\u03c0 \u03b4 \u03b3 \u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 = 2R 3\u00d72 \u222b \u03c0 0 sin \u03b1d sin \u03b1\u222b \u03c0 0 sin \u03b1d\u03b1 (3.18) where the expression MR\u03c92 3\u03c0 \u03b4 \u03b3 is accepted as constant for the Eq",
            "61): Tin = 5 72 \u03c03 J\u03c9\u03c9x (3.62) where all components are represented in Sect. 3.3.1. The resistance torque T cr generated by the Coriolis force of the rotating mass element is expressed by Tcr = \u2212 fcrym = \u2212maz ym (3.63) where all components are as specified above. The following solution is the same as presented in this chapter, Sect. 3.3, in which comments are omitted \u03b1z = dVz dt = d(\u2212V cos\u03b1 sin \u03b3 ) dt = V cos\u03b1 d\u03b3 dt = R\u03c9\u03c9x cos\u03b1 (3.64) Tcr = \u2212M \u03b4 2\u03c0 \u00d7 R\u03c9\u03c9x cos\u03b1 \u00d7 yC = \u2212MR\u03c9\u03c9x \u03b4 2\u03c0 cos\u03b1 \u00d7 yC (3.65) The centroid (point C, Fig. 3.3, this chapter) is expressed by the following equation. yC = \u222b \u03c0 \u03b1=0 fct\u00b7z ymd\u03b1\u222b \u03c0 \u03b1=0 fct\u00b7zd\u03b1 = \u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 2\u03c0 cos\u03b1 \u00d7 R sin \u03b1d\u03b1\u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 2\u03c0 cos\u03b1d\u03b1 = \u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 2\u03c0 cos\u03b1 \u00d7 R sin \u03b1d\u03b1\u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 2\u03c0 cos\u03b1d\u03b1 = MR2\u03c9\u03c9x \u03b4 2\u03c0 \u222b \u03c0/2 0 cos\u03b1 sin \u03b1d\u03b1 MR2\u03c9\u03c9x \u03b4 2\u03c0 \u222b \u03c0/2 0 cos\u03b1d\u03b1 = \u222b \u03c0/2 0 1 2 sin 2\u03b1d\u03b1\u222b \u03c0/2 0 cos\u03b1d\u03b1 (3.66) Tcr\u222b 0 dTcr = MR2\u03c9\u03c9x 2\u03c0 \u00d7 \u03c0\u222b 0 d\u03b4 \u00d7 \u03c0\u222b 0 \u2212 sin \u03b1d\u03b1\u00d7 1 2 \u222b \u03c0 0 sin 2\u03b1d\u03b1\u222b \u03c0 0 cos\u03b1d\u03b1 (3.67) Tcr \u2223\u2223\u2223Tcr0 = MR2\u03c9\u03c9x 2\u03c0 \u00d7 ( \u03b4 \u2223\u2223\u03c0 0 ) \u00d7 ( cos\u03b1 \u2223\u2223\u03c0 0 ) \u00d7 \u2212 1 2\u00d72 cos 2\u03b1 \u2223\u2223\u2223\u03c0/2 0 sin \u03b1 \u2223\u2223\u2223\u03c0/2 0 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.60-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.60-1.png",
        "caption": "Fig. 2.60 Double-track, full vehicle physical model fixed on the vehicle and single-track, half vehicle (bicycle) physical model fixed on the road [MAKATO 1995].",
        "texts": [
            " Automotive vehicle motion is usually described by the velocities (forward -- U = vx, lateral \u2013 V = vy, vertical \u2013 W = vz, roll -- \u03c6& = p, pitch -- \u03b8& = q and yaw -- \u03c8& = r) with respect to the automotive vehicle fixed coordinate system. Automotive vehicle attitude and trajectory through the course of a manoeuvre are defined with respect to a left-hand orthogonal axis system fixed on the on/off-road surface. It is normally selected to coincide with the vehicle\u2019s fixed coordinate system at the point where the manoeuvre is started. Automotive Mechatronics 212 The coordinates (see Fig. 2.60) are as follows: X \u2013 forward travel; Y \u2013 travel to the left; Z \u2013 vertical travel (positive upward); \u03a8 \u2013 heading angle (angle between x and X in the ground plane); \u03bd \u2013 course angle (angle between the vehicle\u2019s velocity vector and X axis); \u03b2 \u2013 sideslip angle (angle between x axis and the vehicle\u2019s velocity vector). The fundamental law from where most automotive vehicle dynamics analyses begin is the second law formulated by Sir Isaac Newton (1642--1727). The law applies to both translational and rotational systems [DEN HARTOG 1948; GILLESPIE 1992]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002866_s11012-019-01053-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002866_s11012-019-01053-9-Figure2-1.png",
        "caption": "Fig. 2 Model of a normal gear tooth (healthy gear)",
        "texts": [
            " Therefore, the calculation of mesh stiffness for cracked spur gears is considered as follows: First, calculate the mesh stiffness of the normal tooth (equivalent to healthy gear). Second, calculate the mesh stiffness of the cracked tooth. And then calculate the mesh stiffness for the normal tooth with the effect of tooth crack. Finally, the total mesh stiffness during one rotation period could be obtained by considering the contact ratio. 2.2 Mesh stiffness model of a normal gear tooth As showed in Fig. 2, the gear is considered as a variable cross-section cantilever with a fixed boundary from the center of the base circle. The center of the base circle is used as the coordinate origin to create the xoy coordinate system. According to the Timoshenko beam theory [29], the total potential energy accumulated in a tooth should consist of four parts: bending energy Ub, shear energy Us, axial compressive energy Ua, and Hertzian energy Uh. They can be expressed as following Ub \u00bc F2 2kb \u00bc Z xB 0 \u00bdFb\u00f0xF x1\u00de FayF 2 2EIx1 dx1 \u00fe Z xF xB \u00bdFb\u00f0xF x2\u00de FayF 2 2EIx2 dx2 \u00f01\u00de Us \u00bc F2 2ks \u00bc Z xB 0 1:2F2 b 2GAx1 dx1\u00fe Z xF xB 1:2F2 b 2GAx2 dx2 \u00f02\u00de Ua \u00bc F2 2ka \u00bc Z xB 0 F2 a 2EAx1 dx1\u00fe Z xF xB F2 a 2EAx2 dx2 \u00f03\u00de where kb, ks and ka are the bending, shear and axial compressive stiffness, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002493_s00170-017-0668-4-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002493_s00170-017-0668-4-Figure5-1.png",
        "caption": "Fig. 5 Schematic of surface grinding process",
        "texts": [
            " This model maps the envelop motion trajectory of the abrasive grains on the workpiece surface to yield the grinding workpiece surface. The input data include wheel speed, platform feed rate, depth of cut, and grinding wheel surface data, while the output of the model is the 3D data of the workpiece surface. In the previous section, discrete data points are used to represent the grinding wheel surface. Therefore, the envelope of the discrete data points means the establishment of the grinding trajectory of the grinding wheel. As shown in Fig. 5, the model uses two coordinate systems to describe the grinding motion: one is the local coordinate system {o} which is fixed in the center of the one side of the grinding wheel, and the other is fixed on the workpiece surface {g}. These coordinate systems are initially separated by distances of 0, 0, and (R-d) along the x, y and z axes, respectively. Figure 5a shows that most of the data points have a certain initial angle \u03b80 before rotation. Figure 5b indicates the position of the grinding wheel at the t1 time after \u0394t where \u03b81 = \u03b80 \u2212 w \u00b7\u0394t (w is the grinding wheel speed with a value of 2\u03c0N). With the protrusion height, initial rotation angle, and other conditions of the data points, the envelop of the abrasive grains in the local coordinate system {o} is obtained. The envelope of the grinding trajectory at any time under the local coordinate system {o} can be transformed to the coordinate system {g} (the sign is negative when the process is up-grinding)",
            " In order to simplify the complexity of the analysis, the following conditions are assumed in the modeling process: 1. The calculated cutting depth is the actual cutting depth in the grinding process. 2. The plow, crush, and built-up edge phenomena are not considered in the grinding process. 3. The workpiece material in contact with the cutting edge of the abrasive grains is completely removed when the grinding wheel is feeding. Referring to the literature of Zhou Xi [13], the workpiece surface generation method is shown below. As shown in Fig. 5a, the workpiece surface is divided into rectangular grids with a definite resolution, and matrix gij represents the height of the rectangular grid where the horizontal and vertical grid numbers are i and j, respectively. The heights of the rectangular grids can be set to a uniform value, and the measured grinding wheel surface data can also be the initial input of matrix gij for the simulation of the multi-pass grinding. The envelope trajectory of the grinding wheel in the {g} coordinate system has been deduced, but not all the envelope points will influence the surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000521_epc.2008.4763350-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000521_epc.2008.4763350-Figure3-1.png",
        "caption": "Fig. 3. Cross-section of a BLDC machine with misplaced Hall sensors.",
        "texts": [
            " Therefore, the stator flux linkages and electromagnetic torque equations have to be modified as follows ( )( ) ( ) ( ) \u2211 \u221e = \u2212 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u239f \u23a0 \u239e \u239c \u239d \u239b +\u2212 \u239f \u23a0 \u239e \u239c \u239d \u239b \u239f \u23a0 \u239e \u239c \u239d \u239b \u2212\u2212 \u2212 += 1 12 3 2 3 2 12sin 12sin 12sin ' n r r r nmabcs n n n K\u03bb \u03c0 \u03c0 \u03b8 \u03b8 \u03b8 iL\u03bb sabcs (3) ( )( ) ( ) ( ) \u2211 \u221e = \u2212 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u239f \u23a0 \u239e \u239c \u239d \u239b +\u2212 \u239f \u23a0 \u239e \u239c \u239d \u239b \u239f \u23a0 \u239e \u239c \u239d \u239b \u2212\u2212 \u2212 \u22c5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 = 1 12 3 2 3 2 12cos 12cos 12cos ' 2 n r r rT cs bs as nme n n n i i i K\u03bbPT \u03c0 \u03c0 \u03b8 \u03b8 \u03b8 (4) where the inductance matrix is \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 +\u2212\u2212 \u2212+\u2212 \u2212\u2212+ = mlsmm mmlsm mmmls s LLLL LLLL LLLL 5.05.0 5.05.0 5.05.0 L . (5) In (3) and (4), m\u03bb\u2032 is the magnitude of the fundamental component of the permanent magnet rotor flux linkage. The coefficients nK denote the normalized magnitudes of the thn flux harmonic relative to the fundamental component. Also in (5), lsL is the stator leakage inductance and mL is the stator magnetizing inductance. A cross-sectional view of an equivalent two-pole PMSM with misplaced Hall Effect sensors is depicted in Fig. 3. Here, the H1\u2019, H2\u2019, and H3\u2019 represent the ideally placed Hall sensors, while H1, H2, and H3 denote the actual non-ideal sensors. The quantities A\u03c6 , B\u03c6 and C\u03c6 denote the misplacement angles for H1, H2 and H3 respectively. Here v\u03c6 is the advance firing angle [1]. In normal motor operation 6\u03c0\u03c6 =v . Output state of each Hall sensor as a function of rotor position is defined in Table 1. Note that these signals also depend on the advance firing angle v\u03c6 as well as the positioning errors in electrical degrees A\u03c6 , B\u03c6 and C\u03c6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002503_sibcon.2017.7998581-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002503_sibcon.2017.7998581-Figure2-1.png",
        "caption": "Fig. 2. Diagram of the walking in-pipe robot",
        "texts": [
            " Figure 1 shows a concept design of the robot. It should be noted that the algorithms described in this paper are not exclusive for six-legged in-pipe robots and would work with a wide range of mechanical designs. The algorithms can be easily extended to handle different number of legs. It would also work for legs with a different structure compared to the one presented in fig. 1. The links that are supposed to come in contact with the inner surface of the pipe have contact pads mounted on their tips. In fig. 2 we use the following notation: iK are contact pads represented as a single point ( 6,1=i ), iC and iD are actuated rotational joints, C is the center of mass of the body link of the robot and i\u03c8 and i\u03b8 are angles that describe the relative orientation of the links that form robot\u2019s legs. III. GEOMETRIC DESCRIPTION OF THE PIPELINE The algorithms presented in this paper rely on a certain geometric description of the pipeline where the motion takes place. We consider pipes without branches and a circular cross section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.3-1.png",
        "caption": "Figure 8.3. Schema for the moment of momentum about a moving reference point.",
        "texts": [
            "33) holds only for an arbitrary fixed point o in an inertial frame <I>; but use of a moving reference point often is essential and more practicable. Therefore, we seek those circumstances for which the moment of momentum principle in the form (8.33) may hold for a moving reference point. First, consider the moment about a moving point Q of all forces that act on the system, and recall from (8.31) that the torque of the mutual internal forces about 312 Chapter 8 (8.35) any point in <t> vanishes. Then using notation introduced in Fig. 8.3, we have n n n M Q =L rk x Fk =L rk x fk =L rk x Pk. k=! k=1 k=1 whereint Fk = bk +fk = Pk and rk is the vector of Pk from Q. The moment about point Q of the momenta Pk =mkxk in <t> of all particles of the system is given by n hQ(!l , t) = L rk x Pk, k=l and hence n n hQ = L rk x Pk+ L rk x Pk . k=l k=l Since rk = Xk - rand r = vQ in Fig. 8.3, the first product term yields (8.36) (8.37) n nL rk x Pk = -vQ x L Pk = -vQ X p\" . k=1 k=! Thus, with this relation in (8.37) and recalling (8.35), we obtain the first form of the moment ofmomentum principle for a moving reference point Q: dhQ(!l, t) * MQ(!l, t) = + vQ x P . dt (8.38) Consequently,there existmovingpoints Qwith respect to whichMQ(!l, t) = hQ(!l, t) has the sameform as (8.33)for a fixedpoint 0, if andonly if v., x p* = O. t Note that Xk = Xk +R is the vector of Pk in <t> and R, not shown here, is the constant vector of the fixed point 0 from the origin F in Fig. 8.3. Hence, Xk = Xk, Xk = Xk throughout these results. See also Fig. 8.2. Dynamics of a Systemof Particles 313 Thi s hold s when (i) triviall y, eith er Q or the center of mass C is at rest in <1>, or (ii) when the velocity of Q is parallel to the velocity of the center of mass. In particular, this is so when Q is the center of mass. Theref ore, the moment about the center ofmass of the external fo rces acting on a system ofparticles is equal to the time rate ofchange of the moment ofmomentum about the center ofmass, which may be either at rest or moving arbitra rily in <1>: McCfJ, t ) = dh cCfJ , t ) . dt Thi s is the first center of mass f orm of the moment ofmomentum principle. (8.39) (8.40) 8.6.2. Second Form of the Moment of Momentum Principle for a Moving Point Another formulation for the torque about a moving point Q, suggested by (8.22) and other results sketched in the previous section, is to express (8.38) in terms of the moment ofmomentum relative to Q, namely, n hrQ(fJ, t ) = L rk x mkrb k= 1 in accordance with (8.23). Here rk is the position vector of Pk from Q in Fig. 8.3 . To relate (8.36) and (8.40), we recall (8.24) in which 0 is replaced by Q to obtain hQ(fJ , t ) = hrQ(fJ, t ) +m(fJ)r* x vQ, (8.41) wherein r* = xQis the position of the center of mass from Q. Differentiation of (8.4 1) with respect to time in <I> gives hQ = hrQ+m(fJ)i\"* x vQ +m(f3 )r* x aQ' in which aQ = vQ is the acceleration of Q in <1> . With m(fJ)i\"* = p* - m(f3)vQ from Fig. 8.3, the last equation may be written as (8.42) (8.43) Therefore, in place of (8.38) , we find the secondform ofthe moment ofmomentum principle for a moving reference point Q: dh rQ * MQ(fJ , t) = dt + r x m(fJ)aQ. Consequently, there exist points Q with respect to which MQ(fJ, t) = hrQ(fJ, t ) has the same basic form (8.33) for a fixed point, if and only if r* x m(f3)aQ = O. Thi s occurs when (i) triviall y, Q is either at rest or in uniform motion in <I> so that aQ = 0, in which case Qmay be cho sen as the origin of an inertial frame, (ii) the acceleration of Q is along a line passing through the center of mass so that r* and aQ are parallel vectors, or (iii) Q is the center of mass so that r* = 0, this being the most general of these situations for a moving reference point",
            " 0 The kineti c energy K({3 , t) of a system of particles {3 = {Pkl in frame cp = {o ; id of Fig . 8.3 is defined as the sum of the kinetic energies Kk(t) == K(Pb t) of particles Pi: n n 1 K({3, t) ==L Kk(t) = L \"2mkvk . Vb (8.50) k=] k= 1 where Vk = Xk . With m({3) defined by (5.3), the kinetic energy K*({3 , t) of the center ofmass is defined by 1 K*({3 , t) == -m({3)v* . v\", (8.51) 2 wherein v*({3, t) = x*({3, t) is the velocity of the center ofmass of the system in tp, To relate (8.50) and (8.51), with reference to Fig. 8.3, substitute the relation Vk = v* + iJk in (8.50) and expand the result to obtain 1 n n I K({3 , t) = -m({3)v*\u00b7 v* + v* \u00b7 L mk!'1k+ L -mk!'Jk . iJk\u00b7 2 k= ] k=1 2 Then, by (5.8), the second term vanishes and the last term is the kinetic energy of the system relative to the center ofmass C, defined by n I Krd{3, t) ==L -mk!'Jk . Pk' k=] 2 318 Hence, with (8.51), we obtain K({J , t ) = K*({J , t) + K,d{J , t ). Chapter 8 (8.53) That is, the kinetic energy ofa system ofparticles is equal to the kinetic energy of the center ofmass plus the kinetic energyofthe system relative to the centermass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001423_physrevlett.109.128105-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001423_physrevlett.109.128105-Figure5-1.png",
        "caption": "FIG. 5 (color online). (a) Three-dimensional shapes of optimal swimmers for r\u0302min \u00bc 0:1, 0.2, 0.5, and 0.7. (b) Some ciliated protozoa: Litonotus cygnus, Amphileptus pleurosigma (drawn after Ref. [24]) and Paramecium caudatum.",
        "texts": [
            " We have shown that with a moderate curvature a surface-propelled swimmer can increase its swimming efficiency by about 20% relative to a sphere. Ciliated microorganisms make wide use of it, as the majority of them has a strongly elongated shape. But it is much more surprising that the efficiency can be further increased by growing two protrusions along the symmetry axis. Although there are certainly other limitations on the body shape, there are still a number of microorganisms that have at least one such ciliated protrusion. Remarkable examples include, e.g., Litonotus and Amphileptus [24,25], which are shown in Fig. 5. We therefore conclude that not only do the cilia beat in a way that is very close to the theoretical optimum [3], but the body shape of many microorganisms also assumes a form that enables efficient propulsion. I thank Natan Osterman for comments on the manuscript and Rok Kostanjs\u030cek for discussions on protozoa. This work was supported by the Slovenian Research Agency (Grants No. P1-0099 and No. J1-2209). *Andrej.Vilfan@ijs.si [1] M. J. Lighthill, Commun. Pure Appl. Math. 5, 109 (1952). [2] J. Blake, J"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003094_j.addma.2020.101550-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003094_j.addma.2020.101550-Figure10-1.png",
        "caption": "Fig. 10. Bulk samples fabricated by SLM with large working distance, a) square sample, b) circular sample.",
        "texts": [
            " The optimal processing parameters were determined based on these values. Results showed that 316 L parts with relative density up to 99 % can be obtained. Finally, the parameters with laser power of 300 W, scanning velocity of 600 mm/s and hatch spacing of 0.05 mm were selected to fabricate bulk 316 L samples. The achieved relative density, top surface roughness and side surface roughness were (98.92 \u00b1 0.15)%, Ra (9.27 \u00b1 2.03) \u03bcm and Ra (15.05 \u00b1 1.73) \u03bcm respectively. The fabricated bulk samples are shown in Fig. 10. Table 3 Chemical compositions of stainless steel 316 L powder. Element Cr Mn Mo Ni P Si C S O Fe Composition (wt%) 17.06 1.49 2.69 11.3 0.011 0.7 0.016 0.005 0.069 Bal. Fig. 8. morphologies of single track. a) partial melting, b) serious balling, c) continuous but uneven track, d) continuous and even track. C. Liu et al. Additive Manufacturing 36 (2020) 101550 After the determination of processing parameters for solely SLM, hybrid SLM/CNC milling experiments were performed to validate its effectiveness in improving dimensional accuracy and surface quality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000905_02640414.2011.553963-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000905_02640414.2011.553963-Figure3-1.png",
        "caption": "Figure 3. The centre of the ball was defined as the origin of the local coordinate system of the ball; when y\u00bc 0 and j\u00bc0, the x, y, and z axes are parallel to the respective axes of the global reference frame.",
        "texts": [
            "125 cm), radius of the FT marker (0.3 cm), and finger thickness (1.2+ 0.1 cm). The angular velocity vector of the ball spin immediately after ball release was calculated from the four reflective markers attached to the pitched baseball using the methods described by Jinji and Sakurai (2006). The spin axis was derived from the positional changes of the reflective markers attached to the baseball and the equation of a sphere. The centre of the ball was defined as the origin (RB) of the local reference frame of the ball (Figure 3). The direction of the angular velocity vector was expressed in the global reference frame; it was defined by the azimuth y (the angle between XG and the projection of the spin axis in the horizontal plane) and the elevation j (the angle between the spin axis and horizontal plane). When y is positive, the direction of the angular velocity vector is towards the home plate. When j is positive, the direction of the angular velocity vector is upward. Pearson\u2019s product\u2013moment correlation coefficients were calculated to determine the relationship between the direction of the spin axis and the parameters representing the angles of the hand direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure6-1.png",
        "caption": "Fig. 6. Serial limbs and two-drive hybrid limbs: (a) R 2 R 2 P a R 2 (b) PR 2 P a R 2 (c) R 2 R M P a R 2 (d) R 2 R N P a R 2 (e) PR N P a R 2 .",
        "texts": [
            " To avoid the influence on the workspace, which is caused by the added linkages, an additional revolute joint or translational joint is arranged to form the five-bar mechanisms. Then the R 2 R M P a R 2 hybrid limb is derived. When the active joints are prismatic joints, the slider-crank linkage is utilized to actuate the passive joints. Employing the PRRR slider-crank linkage (indicated as R N ) to actuate the second revolute joints in the R 2 R 2 P a R 2 chain, the R 2 R N P a R 2 hybrid limb is obtained. Then the serial limbs R 2 R 2 P a R 2 can be transformed into R 2 R M P a R 2 and R 2 R N P a R 2 two-drive hybrid limbs, as shown in Fig. 6 . Similarly, the serial limb R 2 R 2 R 2 can also be converted into three-drive hybrid limbs. When the five-bar mechanism actuates the second passive joint, the third revolute joint can also be driven by another planar mechanism. Therefore, the R 2 R M R M , R 2 R N R M and R 2 R N R N hybrid limbs can be derived. Because the corresponding kinematic joints of the serial limbs are located on one plane, the PR 2 P a R 2 limb and the PR 2 R 2 limb can also be transformed into the PR N P a R 2 limb and the PR N R N limb, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002094_j.conengprac.2014.08.012-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002094_j.conengprac.2014.08.012-Figure2-1.png",
        "caption": "Fig. 2. Maneuvres for simulations.",
        "texts": [
            " Smooth variation of the references for position, velocity and acceleration is required by the controller. These signals are generated by applying a step change to the following fourth-order transfer function: H\u00f0s\u00de \u00bc 1 \u00f025s\u00fe1\u00de2 0:022 \u00f0s2\u00fe0:0404s\u00fe0:022\u00de \u00f078\u00de The transfer function of Eq. (78) is employed for each degree of freedom of the vessel, and the amplitude of the step function corresponds to the vessel's final desired position. The simulation begins with the initial setpoint vector \u00bd0 m;0 m;01 constant for 100 s, and then the ship is demanded to move to \u00bd20 m; 10 m;151 , as indicated in Fig. 2. Notice that these maneuvres check the performance of the observer and the controller simultaneously for set point changes and for the alteration in the relative environmental loads due to the change in the vessel heading. The combination of the vessel's parameters indicated in Appendix C with heading angle \u03c8 \u00bc 0 results in the order of magnitude of some elements of \u0398\u00fe 4 1011. Also, numerical analyses have shown that z1 10 1, z2 10 1 and z3 10 2, leading to f P 107 kN, which is not compatible with the actuators capacity as indicated in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure1.55-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure1.55-1.png",
        "caption": "Fig. 1.55 Elementary wiring connections for hybrid-electric full-time DBW 4WD propulsion and BBW 4WB dispulsion mechatronic control systems with the torque-proportioning FWD and RWD as well as CWD E-M differentials [FIJALKOWSKI 1997].",
        "texts": [
            " Differences in theoretical values of the wheel velocity (wheel velocity when no slip or skid occurs) and the concept of cooperation between the front and rear SM&GWs generally affect the gross tractive effort and slip distribution. Analysis and experiments indicate that the development of new-concept axleless FWD and RWD as well as CWD E-M differentials which can provide the optimum distribution of gross tractive effort and slip between front and rear SM&GWs, is of practical importance. Typically, in FWD and RWD as well as CWD E-M differential layout, Figure 1.55, a series electrical connection (cabling) is interposed between the electrical power source, that is the FE and/or CH-E/E-CH storage battery power-outputs, as well as FWD and RWD units [FIJALKOWSKI 1997]. The function of a series electrical connection is to transfer the drive electrical energy from the electrical energy source to both the front and/or rear SM&GWs. Automotive Mechatronics 106 The CWD E-M differential in the series electrical connection is also necessary to distribute the drive equally between the front and rear SM&GWs and to allow for the fact that, when the intelligent vehicle is driven in a circle, the mean values of the wheel velocity of the front SM&GWs is different from that of the rear SM&GWs and therefore the values of the wheel velocity of the two FWD and RWD units must differ too",
            "14 Purpose of RBW 107 driving, is generally provided for use if the intelligent vehicle is required to operate on metalled roads. As is well-known from the principle of Ackerman\u2019s 2WS SBW conversion mechatronic control system, the front SM&GWs always tend to roll further than the fixed-geometry rear SM&GWs, because their radius of turn is always larger, a parallel electrical connection (cabling) can be interposed between the electrical energy source (EES) as well as FWD and RWD units and the CWD E-M differential may be omitted from the drive E-M powertrain line (see Figure 1.55). In practice, this usually takes the form of the two separate FWD and RWD units, single on each front or rear SM&GWs, on which there are rotary controls which can be locked by the H&TD, but they has to stop and get out to do so. As soon as the H&TD again drives his intelligent vehicle on firm ground, however, s/he must remember to unlock the FWD and RWD units. Should the rear SM&GWs lose traction, on the other hand, and therefore tend to rotate further than the front ones, the drive may automatically be transferred to the front SM&GWs, even if they are in the freewheeling mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.105-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.105-1.png",
        "caption": "Fig. 2.105 HF transmission arrangement for the F-M DBW 2WD propulsion mechatronic control system of a heavy-duty truck [FPDA 2004].",
        "texts": [
            " The characteristic of the powertrain (ECE or ICE and H-F transmission) may be determined through different programs. In addition to these functions, the E-TM+C ECU can manipulate the torque on each wheel to improve the driving stability of the HFV. The inclusion of the mechatronic control for the active suspension results in a fully active DBW AWD propulsion mechatronic control. A typical HF transmission arrangement for the HF DBW 2WD propulsion mechatronic control system of a heavy-duty truck, the so termed hydrostatic drive, with brake energy recovery, is shown in Figure 2.105 [FPDA 2004]. An interesting concept of the HF transmission arrangement for the HF DBW 2WD propulsion mechatronic control system of a heavy-duty tractor for transportation of containers on or off \u2018Ro-Ro\u2019 type vessels is shown in Figure 2.106. Owing to the inertial mechanical energy store (IMES), that is, the engined and/or pumped flywheel (E&PF) application in a heavy-duty tractor (see Fig. 2.106), can not only produce great fossil fuel savings but also low pollutant emissions. It is especially valid in loading compartments of \u2018Ro-Ro\u2019 type vessels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure4.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure4.1-1.png",
        "caption": "Fig. 4.1 External and inertial torques acting around axes on the spinning disc",
        "texts": [
            " The action of the interrelated torques is manifested by the big difference in the angular velocities around axes of the spinning disc. The ratio of their angular velocities around axes is maintained and can be changed by the action of complex interdependency of the external and inertial torques on the spinning disc. The interrelated action of all torques on the spinning disc is described by the studies presented below. The action of the external and inertial torques around axes on the rotating disc is demonstrated in Fig. 4.1 where the disc locates symmetrically relatively of its supports at the system of coordinate oxyz. The interrelated action of the inertial torques is considered for the common case when the axis of the spinning disc turns in counterclockwise direction around axis ox. For the starting condition is considered, the horizontal location of the spinning disc axis \u03b3 = 0. The following steps consider the action of the external torque T on the spinning disc that generates the sequential simultaneous activation of the inertial torques around two axes",
            " The kinetic energies of the inertial torques acting around axes originated and distributed equally along axes ox and oy due to their interrelations. \u2022 The value of the inertial torques, angular velocities and their interrelations around axes of the spinning disc is maintained by the principle of the mechanical energy conservation law. \u2022 The external load torque generates the resistance and precession inertial torques acting around two axes. The precession torques represent the internal load that can be expressed by the external torque. The statement of equality of kinetic energies along axes for the spinning disc (Fig. 4.1) is proofed by the following confinement. The inertial torques originated along each axis indirectly express the potential and kinetic energies of the spinning disc. The sum of these inertial torques of one axis in the absolute value should be equal to the sum of the inertial torques in the absolute value of another axis. This statement presents the principle of the conservation of mechanical energy. The inertial torques that originated along axis ox have presented the torques generated by the action of centrifugal, Coriolis and common inertial forces and the change in the angular momentum",
            " It means the value of the inertial torques acting around one axis does not coincide with the value of inertial torques around another axis. If the value of the inertial torque is big, then the value of the angular velocity should be small for one axis and vice versa. This is the principle of the conservation of mechanical energy for the rotating objects. The equality of the kinetic energies of the spinning disc motions around two axes ox and oy enables for expressing the equation of the equality of the inertial torques acting around the same axes. This analytical expression is represented by the following equation (Fig. 4.1): \u2212Tct\u00b7x \u2212 Tcr\u00b7x \u2212 Tin\u00b7y \u2212 Tam\u00b7y = Tin\u00b7x + Tam\u00b7x \u2212 Tct\u00b7y \u2212 Tcr\u00b7y (4.4) Substituting expressions of the torques (Table 3.1, Chap. 3) into Eq. (4.4) and transformation yields the following equation: 68 4 Properties and Specifies of Gyroscopic Torques \u22122\u03c02 9 J\u03c9\u03c9x \u2212 8 9 J\u03c9\u03c9x \u2212 2\u03c02 9 J\u03c9\u03c9y \u2212 J\u03c9\u03c9y = 2\u03c02 9 J\u03c9\u03c9x + J\u03c9\u03c9x \u2212 2\u03c02 9 J\u03c9\u03c9y \u2212 8 9 J\u03c9\u03c9y (4.5) where the sign (\u2212) and (+) means the clockwise and counterclockwise directions of the action of the inertial torques around two axes, respectively. Simplification of Eq. (4.5) yields the following result: \u03c9y = \u2212(4\u03c02 + 17)\u03c9x (4.6) where the sign (\u2212) means the direction of the action of the inertial torque that can be omitted from the following analytical considerations. Equation (4.6) demonstrates the actual ratio of the angular velocities of the spinning disc around two axes for the given example of consideration (Fig. 4.1). Analysis of Eqs. (4.5) and (4.6) shows the following peculiarity. The expression of the resistance torque Tct\u00b7y = 2\u03c02 9 J\u03c9\u03c9y generated by the centrifugal forces acting around axis oy is the same as the expression of the precession torque T in\u00b7y generated by the inertial forces acting around axis ox Tin\u00b7y = 2\u03c02 9 J\u03c9\u03c9y . These expressions have the same sign, value, condition of origination and can be compensated in Eq. (4.5) by the algebraic rule:\u2212 2 9\u03c0 2 J\u03c9\u03c9y = \u2212 2 9\u03c0 2 J\u03c9\u03c9y . In the equations of the spinning disc motions around two axes, the initial resistance torque of one axis is compensated by the initial precession torque of another axis, which actions are around different axes do not coincide",
            " This statement enables the combination of the mechanical energies of the rotating disc around two axes to be described. The change in the value of external torque leads to a change in the value of the kinetic energy of the spinning disc that expresses in the inertial torques acting around two axes. The values of inertial torques are always less than the value of the external torque that generates the kinetic energies of inertial torques acting around axes of a gyroscope. For the spinning disc with inclined axis on the angle \u03b3 of the common location and with the load torque acting around axes ox and oy (Fig. 4.1), the equality of the kinetic energies of the spinning disc is represented by the modified Eq. (4.4): \u2212Tct\u00b7x \u2212 Tcr\u00b7x \u2212 Tin\u00b7y \u2212 Tam\u00b7y = Tin\u00b7x cos \u03b3 + Tam\u00b7x cos \u03b3 \u2212 Tct\u00b7y cos \u03b3 \u2212 Tcr\u00b7y cos \u03b3 (4.7) Substituting expressions of the torques (Table 3.1, Chap. 3) into Eq. (4.7) and transformation yields the following equation: \u2212 2\u03c02 9 J\u03c9\u03c9x \u2212 8 9 J\u03c9\u03c9x \u2212 2\u03c02 9 J\u03c9\u03c9y \u2212 J\u03c9\u03c9\u03b3 = 2\u03c02 9 J\u03c9\u03c9x cos \u03b3 + J\u03c9\u03c9x cos \u03b3 \u2212 2\u03c02 9 J\u03c9\u03c9y cos \u03b3 \u2212 8 9 J\u03c9\u03c9y cos \u03b3 (4.8) Simplification of Eq. (4.8) yields the following result: \u03c9y = \u2212 [ 2\u03c02 + 8 + (2\u03c02 + 9) cos \u03b3 2\u03c02 + 9 \u2212 (2\u03c02 + 8) cos \u03b3 ] \u03c9x (4",
            " Newmathematicalmodels for the inertial torques acting on the rotating disc and motions describe the gyroscopic properties and can be useful for modelling the behaviour for the gyroscopic devices that is routing work for practitioners. Analysis and practical observation of the acting gyroscopic devices with external load torque demonstrate the following properties: \u2022 The permanent external torque and the angular velocity of the spinning disc generate the eight inertial torques acting around axes of gyroscope rotation. The inertial torques indirectly express the mechanical energies of the gyroscope motions that depend on the angular velocity of the spinning disc\u03c9 and the angular velocity of precession \u03c9x around axis ox (Fig. 4.1). The product of these two angular velocities is always constant, \u03c9\u03c9x = const. Increasing or decreasing the angular velocity\u03c9 of the spinningdisc leads to decreasingor increasing the angular velocity \u03c9x of precession, respectively. This statement expresses the principle of conservation of mechanical energy. \u2022 The value of the inertial torques and hence the angular velocity of precession \u03c9x depends on the value of the external torque, the disc\u2019s mass moment of inertia J and its angular velocity \u03c9",
            " The method of deriving mathematical models for the inertial torques acting on the spinning disc and ring represents a basis for developing the equations of the inertial torques for any spinning objects in engineering. Applications of the fundamental principles of the gyroscope theory for the typical design of the spinning objects in engineering are presented in Appendixes A and B. New fundamental principles and new mathematical models for the torques acting on the spinning disc enable the formulating of the analytic models for motions of the gyroscope gimbals. The action of external and inertial torques is considered on the example of the spinning disc represented in Fig. 4.1. The mathematical model of motions for gyroscope around axes of gimbals is formulated for the case of the action of the load torque around axis ox and frictional torques of the gimbal supports around axes ox and oy. The frictional torques of supports acting around axes ox and oy represent the external load torques that change the value of inertial torques of the spinning disc. The frictional torque of supports of the spinning disc acting around axis oz does not effect on the gimbalmotions. It leads to a decrease in only the angular velocity of the spinning disc. The equations of the gyroscope gimbals motions have formulated by the rules of the interrelations of the inertial torques generated by the spinning disc acting on the gimbals that represented above. The location of the axis of the spinning disc is accepted as horizontal. The mathematical model for the spinning disc of common motions around the gimbal axes is represented by the differential equations in Euler\u2019s forms based on all acting torques summed around two axes ox and oy (Fig. 4.1). The secondary inertial torques (T ct\u00b7y and T in\u00b7y) generated by the common inertial and centrifugal forces acting around axes are removed from the following equations by the processing presented in Eq. (4.5). Jx d\u03c9x dt = T \u2212 Tf\u00b7x \u2212 Tct\u00b7x \u2212 Tcr\u00b7x \u2212 Tam\u00b7y\u03b7 (4.14) Jy d\u03c9y dt = (Tin\u00b7x + Tam\u00b7x \u2212 Tcr\u00b7y) cos \u03b3 \u2212 Tf\u00b7y (4.15) where \u03c9x and \u03c9y are the angular velocity of the gyroscope gimbals around axes ox and oy, respectively; T ct\u00b7x, T cr\u00b7x, T cr\u00b7y, T in\u00b7x, T am\u00b7x and T am\u00b7y are inertial torques generated by the centrifugal, Coriolis, inertial forces and the change in the angular momentum acting around axes ox and oy, respectively (Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.6-1.png",
        "caption": "Fig. B.6 Torques acting on the free rolling disc on a flat surface",
        "texts": [
            " This motion of the inclined thin discmanifests the gyroscopic effects as the action of the centrifugal, common inertial and Coriolis forces and the change in the angular momentum. The action of these forces enables the rolling disc to be brought back to a vertical position. The study of the action of the inertial forces and motion of a rolling thin disc on a flat surface assumes that the disc rolls with the constant angular velocity. A rolling disc is slightly tilted in its path on a flat surface (Fig. B.6). This tilt causes its variable travel on a curved path. The rolling disc produces the torque generated by its gyroscopic weight. In turn, this torque results in the following inertial torques (Table 3.1, Chap. 3): \u2022 The resistance torques based on the action of the centrifugal T ctx and Coriolis forces T crx acting around axis ox. \u2022 The precession torques based on the action of the change in the angularmomentum T amx of the rolling disc and the common inertial forces T inx acting around axis oy",
            " \u2022 The curvilinear motion of the disc generates the centrifugal force in the disc centre mass which acts horizontally and creates the torque T ct.m about the contact point of the disc with the surface. This torque acts in the same direction as the combined resistance torques around axis ox that altogether bring the disc to a vertical position. \u2022 The frictional force generated by the disc weight at the contact point with the surface produces the frictional torque T f.y that acts around axis oy in the clockwise direction. Appendix B: Applications of Gyroscopic Effects in Engineering 251 Figure B.6 demonstrates the action of the external and inertial torques on the rolling disc that moves on the flat surface. The mathematical models for the motions of the rolling disc are based on the action of torques mentioned above around axes ox and oy and represented by the following equations in Euler\u2019s form: Jx d\u03c9x dt = T \u2212 Tct.m \u2212 Tct.x \u2212 Tcr.x \u2212 Tam.y (B.6.1) Jy d\u03c9y dt = Tin.x cos \u03b3 + Tam.x cos \u03b3 \u2212 Tcr.y cos \u03b3 (B.6.2) where Jx = Jy = MR2/4 + MR2 is the mass moment of the disc inertia around axis ox and oy, respectively, that calculated by the parallel axis theorem; \u03c9x and \u03c9y is the angular velocity of precession around axis ox and oy, respectively; T = Mg R sin\u03b3 is the torque generated by the disc weight W around axis ox; T ct,my is the torque generated by the centrifugal forces of the centre mass of the rolling disc around axis oy",
            " For the high value of the angular velocity \u03c9, the right side of Eq. (B.6.10) is always bigger than its left side. This is the reason that free rolling disc on the flat surface does not fall to the side until its angular velocity reached the minimal value. B.6.1 Working Example The mathematical model for the motion of the rolling disc on the flat surface is considered for the example whose data is presented in Table B.1. The action of the external and internal torques on the disc is represented in Fig. B.6. The rolling disc initially possesses an inclined axle. It is necessary to find the values of the internal torques exerted on the rolling disc and its precessions. 254 Appendix B: Applications of Gyroscopic Effects in Engineering Separating variables, transforming and representing in the integral form give the following: \u03c9x\u222b 0 d\u03c9x \u03c92 x \u2212 0.675359339\u03c9x + 0.074961015 = \u221219.367467413 \u03c9x t\u222b 0 dt (B.6.12) The left integral is represented by the following form: \u03c9x\u222b 0 d\u03c9x (\u03c9x \u2212 0.53533225)(\u03c9x \u2212 0.1400270844) = \u221213"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure8.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure8.3-1.png",
        "caption": "Fig. 8.3 Forces and torques acting on the gyroscope with the counterweight",
        "texts": [
            " The analytical and practical results of the tests are represented by the gyroscope timemotions and the value of the precessed torque converted to the force acting on the digital scale. The mathematical model for the gyroscope motion around axis ox is similar to the model for the gyroscope suspended from a flexible cord [14]. The difference of the equation for the gyroscope motion is the absence of the action of the precession torques originated around axis oy and acting around axis ox (Figs. 8.1 and 8.2). Figure 8.3 represents the action of the external and inertial torques on the gyroscope stand. These technical data enable for formulating of the hypothetical mathematical model for the motion of the gyroscope under the action of the external and inertial torques by the following Euler\u2019s differential equation: Jx d\u03c9x dt = T \u2212 Tfx \u2212 Tct\u00b7x \u2212 Tcr\u00b7x (8.1) where \u03c9x is the angular velocity of the gyroscope around axes ox; T is the resulting torque generated by the weight of the gyroscope components; T ct\u00b7x, T cr\u00b7x, are inertial torques generated by the centrifugal and Coriolis forces acting around axis ox (Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002866_s11012-019-01053-9-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002866_s11012-019-01053-9-Figure4-1.png",
        "caption": "Fig. 4 Model of a normal gear tooth with the effect of tooth crack",
        "texts": [
            " (1) and (2), the bending stiffness and shear stiffness of the cracked tooth can be obtained according to different cases: Case 1 When yD [ yA& a1\\ac 1 kb \u00bc Z rb cos ab lc cos h 0 3\u00bdrb x1 cos a1 2 2EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2in min\u00f0x21; r2in\u00de ph i3dx1 \u00fe Z rb cos ab rb cos ab lc cos h 12\u00bdrb x1 cos a1 2 EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p \u00ferb sin ab lc sin h h i3dx1 \u00fe Z ac ab 12\u00bd1 cos a1\u00f0\u00f0a\u00feab\u00de sin a\u00fe cos a\u00de 2\u00f0a\u00feab\u00de cos a EL\u00bdsin a\u00fe \u00f0ab a\u00de cos a\u00fe sin ab \u00f0lc=rb\u00de sin h 3 da \u00fe Z a1 ac 3\u00bd1 cos a1\u00f0a\u00feab\u00de\u00f0sin a\u00fe cos a\u00de 2\u00f0a\u00feab\u00de cos a 2EL\u00bdsin a\u00fe \u00f0ab a\u00de cos a 3 da \u00f025\u00de 1 ks \u00bc Z rb cos ab lc cos h 0 1:2\u00f01\u00fe m\u00de cos a21 EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2in min\u00f0x21; r2in\u00de p dx1 \u00fe Z rb cos ab rb cos ab lc cos h 2:4\u00f01\u00fe m\u00de cos a21 EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p \u00ferb sin ab lc sin h dx1 \u00fe Z ac ab 2:4\u00f01\u00fe m\u00de cos a21\u00f0a\u00feab\u00de cos a EL\u00bdsin a\u00fe \u00f0ab a\u00de cos a\u00fe sin ab \u00f0lc=rb\u00de sin h da \u00fe Z a1 ac 1:2\u00f01\u00fe m\u00de cos a21\u00f0a\u00feab\u00de cos a EL\u00bdsin a\u00fe \u00f0ab a\u00de cos a da \u00f026\u00de Case 2 When yD yA or yD [ yA& a1 ac 1 kb \u00bc Z rb cos ab lc cos h 0 3\u00bdrb x1 cos a1 2 2EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2in min\u00f0x21; r2in\u00de ph i3dx1 \u00fe Z rb cos ab rb cos ab lc cos h 12\u00bdrb x1 cos a1 2 EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p \u00ferb sin ab lc sin h h i3dx1 \u00fe Z a1 ab 12\u00bd1 cos a1\u00f0\u00f0a\u00feab\u00de sin a\u00fe cos a\u00de 2\u00f0a\u00feab\u00de cos a EL\u00bdsin a\u00fe \u00f0ab a\u00de cos a\u00fe sin ab \u00f0lc=rb\u00de sin h 3 da \u00f027\u00de 1 ks \u00bc Z rb cos ab lc cos h 0 1:2\u00f01\u00fe m\u00de cos a21 EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2in min\u00f0x21; r2in\u00de p dx1 \u00fe Z rb cos ab rb cos ab lc cos h 2:4\u00f01\u00fe m\u00de cos a21 EL ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p \u00ferb sin ab lc sin h dx1 \u00fe Z a1 ab 2:4\u00f01\u00fe m\u00de cos a21\u00f0a\u00feab\u00de cos a EL\u00bdsin a\u00fe \u00f0ab a\u00de cos a\u00fe sin ab \u00f0lc=rb\u00de sin h da \u00f028\u00de where yA represents the y-coordinate of the point A, which is half of the tooth thickness at the addendum circle. 2.4 Mesh stiffness model of a normal tooth involved the effect of tooth crack As the gear mesh passed the cracked tooth, the adjacent gear tooth gets into engagement (see Fig. 4). Although the crack does not affect the mesh tooth directly, it can affect the deflection of the gear body. Therefore, as the same in Sect. 2.2, the tooth crack does not contribute to Hertz contact stiffness and axial compression stiffness, but it will change the bending and shear stiffness. As can be seen from Fig. 4, with the crack taken into consideration, the area moment of inertia Ix2 and area Ax2 of the section is the same as the heathly gear tooth, while the area moment of inertia Ix1 and area Ax1 of the section of the gear body will be changed. They can be obtained by Ix1 \u00bc 2L 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2in min\u00f0x21; r2in\u00de q 3 0 x\\xD0 L 12 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 q \u00feyB0 lc sin\u00f0h\u00fe ui\u00de 3 xD0 x\\xG 2L 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 q 3 xG x\\xB 8>>>>< >>>>: \u00f029\u00de Ax1 \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2in min\u00f0x21; r2in\u00de ph i L 0 x\\xD0ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 p \u00feyB0 lc sin\u00f0h\u00fe ui\u00de h i L xD0 x\\xG 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b x21 ph i L xG x\\xB 8>>< >>: \u00f030\u00de where ui represents the angle between the central line of the cracked tooth to the central line of the mesh tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001621_1.4981168-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001621_1.4981168-Figure1-1.png",
        "caption": "FIGURE 1. A schematic diagram of the AM powder bed technique machine",
        "texts": [
            " The fabrication process replications continue from bottom to top until the product is completed [1]\u2013[4]. With the development of SLM over the past decade, the demand of the complex and new customize products on the market can be complied and simultaneously reduced the production time and manufacturing costs. Furthermore, SLM techniques are categorized green manufacturing by recycling the powder material that leads to zero wastage within the processes. In the AM powder bed technique as illustrated in Fig. 1. The piston raised the powder dispenser platform within the range of the thickness layer that been specified and then the re-coater arm distributed a layer of powder on top of the powder bed. A laser beam then melts and fuse the layer of powder metal, referring to the generated slice. After fabricating a layer was completed, the build piston will lower down the build platform and the following layer of powder is spread. The fabrication process repetitions continue from bottom to top until the part is completed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003287_s00170-020-06104-0-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003287_s00170-020-06104-0-Figure9-1.png",
        "caption": "Fig. 9 The schematic diagram of the compensation design: a original design, b as-built shape, c compensation design, and d target dimension",
        "texts": [
            "When the part thickness is small, the thermal accumulation effect between tracks is obvious due to short scanning track and low thermal conductivity of the material. High temperature occurs during the heating process, leading to an increase of the material contraction. Therefore, a high part deformation is found with a small thickness. However, as the part thickness increases, the thermal accumulation effect between tracks decreases while the contact area between part and substrate increases, causing a decrease of part deformation. To obtain a high precision part, the deformation control in LPBF is very necessary. Therefore, as shown in Fig. 9, a method of compensation design is proposed in the present paper. As depicted in Fig. 9a and b, the as-built thin-walled part has an inward contraction along the deposition direction. The parts are then designed to be outward expansion during CAD design, as shown in Fig. 9c. The value of outward expansion is \u0394L at any height, which has been obtained in Sections 4.1 and 4.2. Hence, the part with the target dimension can be fabricated, as shown in Fig. 9d. As depicted in Fig. 10, the X-direction deformations with original design and compensation design are compared in detail through the simulation with different part heights. It can be found that \u0394L of the compensated design part is significantly less than that of the original design part. As the part height ranges from 20 to 105 mm,\u0394L at any height of the part with the compensation design is less than \u00b120 \u03bcm. Since the effect of the thin-walled part dimension on the deformation is mainly studied and the scanning strategy is the same for all thin-walled parts, the value of mL is determined through the experimental data at different part thicknesses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure1.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure1.7-1.png",
        "caption": "Fig. 1.7 Example of an electrical vehicle propulsion unit which utilizes a liquid cooled AC\u2013DC converter and 55 kW switched reluctance machine [6, 8]",
        "texts": [
            " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Fig. 1.5 Example of commercial converter unit and integrated semiconductor module which can be used to build an inverter [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Fig. 1.6 Example of modern inverter technology with standard communication interfaces [25] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Fig. 1.7 Example of an electrical vehicle propulsion unit which utilizes a liquid cooled AC\u2013DC converter and 55 kW switched reluctance machine [6, 8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Fig. 1.8 (a) Example of a DSP control board architecture, which demonstrate the flexibility available in terms of interfacing to other peripherals [1], (b) a Texas Instruments LAUNCHPAD board of the C2000 family DSP [19] . . . . . . . . . . . . . . 10 Fig. 1.9 Typical design methodology used for electrical drives [3, 7, 18, 22] ",
            " The primary design constraint on the volumetric power density of the converter is thermal, i.e., the need to limit operating temperatures and guarantee sufficient thermal cycles of the semiconductor devices and corresponding packages. This implies that the volumetric power density is to a large extend governed by the specific losses of the devices in use, method of cooling, and drive operating conditions. In electric and hybrid vehicles high power density values for machine and converter are essential. An example of such as drive, as shown in Fig. 1.7, utilizes a liquid cooled DC to AC converter with a volumetric power density of 6000 kVA/m3 and a 55 kW switched reluctance machine with a power density of approximately 1.2 kW/kg. 8 1 Modern Electrical Drives: An Overview The controller and modulator (if used), as shown in Fig. 1.1, are part of an embedded system which is interfaced with the switching device drivers, and sensors (voltage and/or current and position/speed measurements). In addition, these specialized computer systems in the form of digital signal processors or micro-controllers are specifically tailored for electrical drive applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure7-1.png",
        "caption": "Fig. 7. (a) Contact lines on worm wheel tooth flank in Example A. (b) Contact lines in (o1; jo1, ko1) in Example A.",
        "texts": [
            " Consequently, the local meshing quality of the former contact zone is equivalent to be improved. In essence, it is considerably helpful to avoid the early failure of a DTT worm gear tooth surface. The value of K(2) in \u03a32B is calculated at every calculable point among the selected engagement points for each example. Because of space limitation, the corresponding calculation result is provided only for Example A as given in Table 2. When the worm is single-threaded just as Example A, K(2) is negative in the most of \u03a32B but is positive at a tiny area near line A\u2032B\u2032 (see Fig. 7, Table 2). This means that the new contact zone is composed at least of hyperbolic and elliptical points in this case. When the number of worm threads is three or greater, K(2) is negative within the whole of \u03a32B. That is to say, the new contact zone is composed only of hyperbolic points in this case. The basic difference between Examples A and B as listed in Table 1 is that the value of \u03c1 in Example B is bigger. The calculated results of ks and kL regarding these two examples indicate that the variation of \u03c1within a certain range has a little influence on the crown thickness of the edge-tooth for a DTT worm and its double-line working length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002814_j.mechmachtheory.2019.03.022-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002814_j.mechmachtheory.2019.03.022-Figure6-1.png",
        "caption": "Fig. 6. Sphere\u2019s free body diagram.",
        "texts": [
            " The motion occurs in the y i z i plane and the nut groove is considered fixed because the nuts does not rotate and because the coordinate system y b , used to determine the displacement of the sphere, is fixed with the nut. In both contact point there can be either sliding or rolling depending on the operating conditions. As for the dynamics in the z i axis, the rolling motion is governed by the screw\u2019s rotation. The displacement of the contact point B along y i , considered integral with the screw groove, is known from Eq. (1) and can be expressed as: y up = p 2 \u03c0 sin ( \u03b1\u2032 ) (13) Neglecting gyroscopic effects, sim ple dynamic equation can be easily derived from Fig. 6 for both the translational and rotational motion in the x i y i plane. The forces H A and H B are tangential contact forces which arise during rolling. They act both on the sphere and on the grooves, therefore they contribute to the reaction and friction forces and torques on the nuts and the screw. H A and H B are obtained adopting the continuous differentiable formulation proposed by Makkar et al. [70] which links the friction coefficient with the contact slip speed. The equivalent effect of rolling friction on the considered sphere has been moved as a tangential force on the screw, F rf , parallel to y i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003918_ji-1.1944.0119-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003918_ji-1.1944.0119-Figure1-1.png",
        "caption": "Fig. 1.\u2014Three-phase system with Petersen-coil earthed neutral and with an earth fault on one phase.",
        "texts": [
            " Loads on conductors in this country may be due to wind or ice or both, and while it may be possible to state what maximum wind velocity may occur, the formation of ice is quite unpredictable. In fact, ice does sometimes build up to an extent which for reasons of cost cannot be used as a design basis. It must therefore follow that on the rare occasions when such extreme conditions occur breakdowns are inevitable, and in this respect the design of overhead lines differs from that of other engineering structures. With the possibility of these breakdowns in mind, Fig. 1 has been prepared on lines similar to those followed by other investigators. This Figure shows the radial thicknesses of ice which copper conductors strung in conformity with the present Regulations will carry simultaneously with a wind pressure of 8 lb/sq ft when stressed, first, to threequarters of their breaking tensions and secondly to their full breaking tensions. All the curves indicate that the ice thickness varies a great deal with span length, thus leading to the conclusion that the general application of a factor of safety of 2 is misleading, and that any conductor strung in accordance with present practice has a greater margin of strength on short spans than on long spans",
            " 2 has been prepared, showing the variation with 2-4 2-2 2-0 V ic e , in c 5 \u00abg 1-4 E a a 0-8 0 6 0-4 0-2 - 0 - - 0 <?0s \u202215 s qin q in 0-10sq in 0-20 sq in 015 sq in 0-05 sq in ij in N? 8 S.W.G. 0*05 sq in N?8 S.W.G. \\ \\ \\ \\ \\ \\ \\ \\ V\\ \\ \\ \\s\" \\\\ V \\ \\ \\ \\ s \\ V \"-. \\ \\ \\ \\ \\ \\ \\ \\ \\\\ s \\ \\ s, \u2014\u2022 \u2014 - s. \u2014\u2014 Radial ice thickness to raise (a) %. breaking load shown (b) breaking load shown - \u2014 \u2022 - ^ ^ = \u2014 = \u2014 \u2014 - - - . ^ \u2014 - ~ \u2014 \u2014 ^ ^ - - - \u2022 ^ tension to \u2014 - \u2022 - . = \u2022 = - . \u2022 \u2014. \u2014 . . I \u2022\u2014r \u2014 \u2022 \u2014 i \u2014 \u2022* 1 0 100 200 300 400 500 600 700 800 900 1000 1100 Span, feet Fig. 1.\u2014Copper conductors strung in accordance with Electricity Commissioners' Regulations for h.v. lines. Ice thicknesses which, with a wind load of 8 lb/sq ft, will stress conductors to three-quarters breaking load and breaking load respectively. [ 4 6 4 ] conductor diameter of the radial thickness of ice necessary to stress to three-quarters of their breaking loads, twelve typical conductors of various sizes and materials strung in accordance with present practice. The variation in load-carrying capacity with span length has been indicated by plotting a vertical line for each conductor covering its normal range of span lengths",
            "f (ABSTRACT of a Measurements Section paper which was published in October, 1944, in Part II of the Journal) Although sensitive indicating wattmeter-type relays have been in use on the Continent since 1930 in Petersen-coil protected systems, they have not always given entirely satisfactory results, and the authors were led to look more carefully into the principles governing their operation when designing an equipment for a 66-kV overhead-line system. The normal schematic arrangement of the connections is given in Fig. \\{a). This diagram therefore IC\\ + Ici + -fe + h = h (added vectorially). The phase of IP is shown in Fig. 1(6), lagging behind EP, the voltage on the coil, by less than 90\u00b0. In a system consisting of two equal parallel feeders A and B with a fault on phase 3 of feeder B [Fig. 2(a)], there will be no earth-capacitance current in phase 3 of feeder A; hence the current (a) Schematic, including connections of an earth-fault relay. (b) Currents under earth-fault conditions. shows the relay connected to a single feeder with a fault on phase 3; the current coil is energized # from parallel-connected current transformers, and the voltage circuit from a secondary winding on the Petersen coil"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.113-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.113-1.png",
        "caption": "Fig. 2.113 Principle layouts of the planetary-gearless mechatronically-controlled steered, motorised and/or generatorised wheels (SM&GW) with brushless AC-AC or AC-DC-AC or AC-DC/AC-DC macrocommutator reluctance and/or IPM magnetoelectrically-excited in-wheel-hub motors/generators [FIJALKOWSKI 1985A, 1990, 1997C, FIJALKOWSKI AND KROSNICKI 1994].",
        "texts": [
            " The rotating housing may be made in the form of wheel hubs, designed to fit standard rim sizes. The mechatronically-controlled in-wheel-hub E-M/M-E motor/generator APVT may allow complete freedom in the design of smart AEVs. The in-wheel-hub E-M/M-E motor/generator may require minimum space and may be installed directly into the rim of the SM&GW because of its compact design. The result may be substantially increased ground clearance and the space between the direct-driven SM&GWs may be used to locate implements, for example. Figure 2.113 shows the principle layouts of the planetary-gearless SM&GWs with brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator reluctance and magneto-electrically excited [unwound mild-soft-iron (MSI) outer rotor and wound and IPM inner stator] in-wheel-hub motors/generators. The wheel-hub is designed so as to realise high stiffness with fewer materials by using \u2018modal (resonance frequency) analysis\u2019 and, together with the use of specially sealed, double row angular contact ball bearings, lubricated-for-life, and having pre-adjusted internal clearance, an excellent torque/mass ratio [Nm/kg] is realised, which is no comparison with the other in-wheel-hub motors/generators, and even with the conventional brushed DC-AC/AC-DC mechanocommutator in- 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001546_c3sm50672j-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001546_c3sm50672j-Figure2-1.png",
        "caption": "Fig. 2 (a) One and a half pitch lengths of a contacting helical filament pair, i and j. Thehelical radius andhelical angle forfilament jarerjand qj(r) respectively. (b)Aview of a region of contact, showing the filament parameters defined in eqn (2) and (3).",
        "texts": [
            " Notably, this allows for a generic expansion of the shape of the contacting lament around the point of contact, in terms of the local geometry of j and distance along j from this point, dsj \u00bc sj s*j (si), Xj sj \u00bc Xj s*j \u00fe dsjTj \u00fe dsj 2 kj 2 Nj \u00feO h dsj 3i ; (2) where Tj, Nj and kj, are the tangent, normal and curvature of lament j at s*j (si).23 From this expression we nd the interlament distance, D h Xj(sj) Xi(si), from |D(dsj)| 2 \u00bc |Dij| 2 + (dsj) 2(1 + kjDij$Nj) + O[(dsj) 3], (3) where Dij \u00bc Xj(s * j ) Xi(si) is the distance of closest contact from si to lament j, such that Dij$Tj \u00bc 0. These parameters are shown schematically in Fig. 2. Assuming that V(r) is sufficiently short-ranged compared to lament length and curvature, we may use eqn (3) to derive the cohesive energy contribution of the length element at si, dEij \u00bc dsi \u00f0\u00feN N d dsj V D dsj \u00bc g Dij ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe kjDij$Nj p dsi; (4) where g Dij \u00bc \u00f0\u00feN N duV ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dij 2 \u00fe u2 q ; (5) Soft Matter, 2013, 9, 8327\u20138345 | 8329 Pu bl is he d on 2 0 Ju ne 2 01 3. D ow nl oa de d by U ni ve rs ity o f W yo m in g on 1 5/ 09 /2 01 3 13 :4 0: 27 ",
            " We consider bundles whose packing is homogeneous along their length, such that cross-sectional packing in a plane perpendicular to z\u0302 differs only by the rigid rotation about the z\u0302 axis. Dening the position of lament i at a common plane z\u00bc 0 (arc-position si\u00bc 0), by the polar coordinates (ri, fi), the shape of the lament backbone follows the helical curve, Xi(zi) \u00bc ricos(fi + Uzi)x\u0302 + risin(fi + Uzi)y\u0302 + ziz\u0302, (7) where it is convenient to express position in terms of vertical height zi \u00bc sicos q(ri), where q(r) \u00bc arctan(Ur) is the helical angle of lament i with respect to z\u0302, shown in Fig. 2a.\u2020 The unit normal and curvature are easily calculated from the secondderivative of Xj with respect to arc-length, kj \u00bc U2rj 1\u00fe Urj 2 (8) Nj \u00bc cos(fj + Uzj)x\u0302 sin(fj + Uzj)y\u0302. (9) For a pair of laments, i and j, it is convenient to express the separation between curves in terms of a vertical offset, zij\u00bc zi zj, and the angular separation in the plane, fij \u00bc fi fj, \u2020 Note, that q(r) refers to the local tilt angle of laments at a radius r in the bundle, where as, in our notation, when tilt angle appears without an explicit radius, as q, it refers to helical angle at the outer radius of the bundle, which we call the twist angle of the bundle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.22-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.22-1.png",
        "caption": "Figure 6.22. Graph of four typical motions of a heavily damped system.",
        "texts": [
            " Since q < v, the damping factor e: \" is dominant ; so, whatever initial conditions may be assigned, once the particle passes through its relative equilibrium position, if at all, it will never do so again . The unique null solution of (6.861) is obtained in the time log(-B IA) to = .2q (6.86m) The viscosity in a heavily damped system is so great that the load cannot vibrate about its relative equilibrium position ; rather, it must creep slowly back to it as t -+ 00. Some typical cases are shown in Fig. 6.22. Curve 1 occurs for the initial conditions z(O) =0, z(O) = vo, from which - BIA = 1 and hence (6.86m) has only the trivial solution to = O. This motion begins with a push away from the equilibrium position and the mass can never cross it again; for, z -+ 0 again only as t -+ 00. Curve 2 in Fig. 6.22 illustrates the case z(O) = zo, z(O) = O. For the general case z(O) = zo, z(O) = vo, the motion may resemble either curve 2, 3, or 4. In the last instance, the load passes through its equilibrium position only once and then creeps gradually back to it from below. See Problem 6.62. Case(iii): Critically dampedmotion.ii t; = vt\u00bb = 1, the general solution of (6.86b) for which r2 = 0 is u = A + Bt;where A and B are integration constants. Dynamics of a Particle 157 Thus, by (6.86a), the general solution of (6.83) for the critically damped motion is z(t) = (A + tuw :\" . (6.86n) As t -+ 00, the motion z(t) -+ O. The critically damped motion, therefore, is similar to that for the heavily damped model illustrated in Fig. 6.22. Discussion of the motion graphs is left for the reader in Problem 6.63. From (6.85), the damping coefficient for this case has the value c* = 2mp = 2J;;k, (6.860) which is named the critical damping coefficient. This is the value of the damping coefficient at which the motion loses its oscillatory, lightly damped character in transition to a nonvibratory, heavily damped decaying motion. In view of (6.860), the damping ratio (6.85) in the general case is the ratio of the damping coefficient to its critical value: c v ~ = - = - ",
            " The crank has radius r and turns with a constant angular speed ai, as illustrated. (a) Derive the differential equation of motion for the bob m. (b) This equation has no known exact solution . Show, however, that for a small angular motion e(t) the differential equation reduces to the equation of motion for the forced vibration of an undamped, harmonic oscillator. Find its solution when the pendulum is released at a small angle eo with 0(0) = O. I9 Problem 6.61. 6.62. Discuss the free vibrational motion (6.861)of the heavily damped oscillator in relation to Fig. 6.22, page 156. Show that if the mass is released from rest, it can only creep back to its equilibrium position at z = 0 as t --+ 00 (similar to Curve 2). However, if released with initial velocity vo, it is possible that the load may cross its equilibrium position at one and only one instant to, as suggested in Fig. 6.22. Find to' 6.63. Repeat the details of the last problem for the critically damped, free vibrat ional motion described in (6.86n). 6.64. The pointer of a vibration instrument has mass m and is supported vertically by a spring of stiffness k. The base is subjected to a vertical motion u = AsinQt. (a) Derive the u ~ A sin n l Problem 6.64. Dynamics of a Particle 217 equation for the steady-state motion x(t) of the pointer relative to the instrument and determine its amplitude. (b) Let k = 5 Nlmm, m = 2 kg, and suppose that the pointer moves between the 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000283_j.triboint.2009.06.007-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000283_j.triboint.2009.06.007-Figure1-1.png",
        "caption": "Fig. 1. Instant gear tooth contact and its approximation to equivalent cylinders.",
        "texts": [
            " This leads to variations in the gear frictional properties and to failures such as pitting and scuffing that take place at different positions along the tooth flank. Information on instant contact behavior is therefore very useful in gaining a deeper understanding of these phenomena. This provides the basic information for estimation of gear train power losses and their lifetime. Very often spur gear profiles are approximated by cylinders with the same radius of curvature as the gear teeth at the instant contact point, as shown in Fig. 1. This provides the basis of the twin-disc test devices, which typically represents only a single point along the line of action in real gears at constant load and speed conditions. In addition, Ho\u0308hn et al. [1] list three main differences when gear and twin-disc contact is compared: (1) they have different kinds of surface topography and orientation, (2) film formation is continuous in discs but on gears a new oil film has to build up with every new engagement and (3) dynamic effects on discs are significantly smaller than in gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure18.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure18.9-1.png",
        "caption": "Fig. 18.9 Special spherical parallel robot",
        "texts": [
            " The binary link is then free to lead its point C on a circle about C0 , and the spherical four-bar A0ABB0 is free to lead its coupler-fixed point C along a coupler curve. Hence C is a point of intersection of this circle and this coupler curve. The maximum number of real points of intersection was shown to be eight. The calculation of these points is based either on Eqs.(18.26) and (18.27) or on Eq.(18.42). Gosselin and Gagne [5] investigated the special case when all angular system parameters equal \u03c0/2 . In what follows, their analysis is presented in a modified form. In Fig. 18.9 the mutually orthogonal rotation axes e11 , e12 , e13 are directed along the edges of the fixed cube 1 . The platform-fixed axes 0A , 0B , 0C are the axes e21 , e22 , e23 along the edges of another cube 2 representing the platform. Each pair of binary links connects an axis on cube 18.4 Spherical Parallel Robot 659 1 to an axis on cube 2 . The labeling of axes and of pairs of binary links is as follows. The pair connected to the axis e1i which is operated by the angle \u03b1i is referred to as pair i ",
            "59) With these coordinates and with the direction cosine matrix A defined by the equation e1 = A e2 the orthogonality conditions (18.58) have the forms \u2212S3a11+C3a21 = 0 , \u2212S1a22+C1a32 = 0 , C2a13\u2212S2a33 = 0 . (18.60) The problem of direct kinematics is to solve these equations for the direction cosines when the angles \u03b1i (i = 1, 2, 3) are given. It is known that with three angular position variables critical cases occur. Here, a critical case occurs when a single angle equals \u03c0/2 or \u2212\u03c0/2 . Example: From Fig. 18.9 it is seen that \u03b11 = \u03c0/2 is possible only in combination with \u03b13 = 0 and with n1 = e12 = e23 . In this position the platform is free to rotate about n1 , and \u03b12 is arbitrary independent of this rotation. Hence the platform position is 660 18 Spherical Four-Bar Mechanism not controllable if \u03b11 = \u03c0/2 . With a cyclic change of indices the same is true for \u03b12 = \u03c0/2 and for \u03b13 = \u03c0/2 . In order to avoid critical positions the robot must be operated in the range \u2212\u03c0/2 < \u03b1i < \u03c0/2 (i = 1, 2, 3). Solving Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001851_gt2016-56084-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001851_gt2016-56084-Figure2-1.png",
        "caption": "Figure 2. (a) The temperature field of originally designed blade and (b) a blade with PCS.",
        "texts": [
            " The originally designed blade (blade # I) and the blade (# II) with PCS are in the operation condition of non-stationary heating and centrifugal and gas loading. A comparative finite element numerical investigation of the thermal and strength states was carried out for both blades. According to the calculations, the blade with PCS has many advantages, such as a reduced mass flow rate of cooling air, weight, and increased lifespan (despite the fact that values of maximum temperatures for both blades are close to each other). Figure 2 shows the temperature distribution of the whole blade and at three cross-sections for the two blade designs. The design of the blade # II makes it very difficult to produce by casting (mass production requires special technology solutions); however, such a blade was produced by SLM. Figure 3 shows the stereolithography model of this blade, as well as some cross sections of blade produced by SLM using Ni-base superalloy powder. 2 Copyright \u00a9 2016 by ASME Downloaded From: http://proceedings.asmedigitalcollection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001662_j.ijleo.2017.11.053-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001662_j.ijleo.2017.11.053-Figure4-1.png",
        "caption": "Fig. 4. Membership functions of input variables si and output ufsi for i = , \u03d5.",
        "texts": [
            " 3; for each subsystem it contains an equivalent control part and single input single utput fuzzy logic control to estimate the hitting control. The equivalent ueqi,i = , \u03d5 control is calculated in such a way as to have s\u0307i = 0, i = , \u03d5 and the discontinuous control is omputed by: ufsi = FLC (si) i = , \u03d5 (37) here ufsi, i = , \u03d5 is the outputs of the FLC, which is obtained by the sliding surfaces variables si, i = , \u03d5. The fuzzy membership functions of the input variables si, i = , \u03d5 and output discontinuous control ufsi,i = , \u03d5 sets are resented by Fig. 4. All the membership functions of the fuzzy input variable are chosen to be triangular. The used labels of the fuzzy variable urfaces si are: {negative (N), zero (Z) and positive (P)}. The fuzzy labels of the hitting control variables ufsi are a singletons membership functions decomposed into three levels epresented by a set of linguistic variables: {negative (N), zero (Z) and positive (P)}. Table 2 presents the rules base which ontains 3 rules: In Fig. 3 the control law is computed by: ui = ueqi \u2212 ufsi = ueq \u2212 FLC (si) i = , \u03d5 (38) A time varying surface si,i = , \u03d5 is defined by si = ( d dt + i) n\u22121 ei(t) i = , \u03d5 (39) ere i is a strict positive constant, as our problem formulation is a third order differential equation then n = 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002346_s00773-015-0347-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002346_s00773-015-0347-9-Figure2-1.png",
        "caption": "Fig. 2 Structure of the RBFNN",
        "texts": [
            " Section 2 introduces the NN model and the description of dynamics of a vessel. In Sect. 3, the adaptive NN controller is presented in detail. The simulation and some performance studies are shown in Sect. 4, which is followed by discussions in Sect. 5. Conclusions and future work are given finally. Radial basis function neural network (RBFNN) is a type of feedforward approximator and is usually used to approximate continuous nonlinear functions [21]. It contains three layers: input layer, hidden layer and output layer, as shown in Fig. 2. In this paper, we take measurements from sensors as inputs and use the RBFNN to generate forces for fine manoeuvring. Assume the number of nodes in the three layers of the RBFNN are m, n, and p, respectively. Let X \u00bc \u00bdx1; x2; :::; xm T be the input vector and H \u00bc \u00bdh1; h2; :::; hn T be the hidden vector. The mapping from the input layer to the hidden layer is nonlinear. Here we use Gaussian function, the most commonly used radial basis function to approximate a nonlinear function: hi \u00bc exp\u00f0 jjX lijj2=2r2i \u00de; i \u00bc 1; 2; :::; n \u00f01\u00de where li \u00bc \u00bdli1; li2:::; lim T is the center of the ith Gaussian function and ri is the width of the ith Gaussian function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002839_3dp.2019.0017-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002839_3dp.2019.0017-Figure1-1.png",
        "caption": "FIG. 1. (a) Different build orientations. (b) Different hatch spacings.",
        "texts": [
            "012 Ti Balance D ow nl oa de d by S Y R A C U SE U N IV E R SI T Y f ro m w w w .li eb er tp ub .c om a t 1 0/ 21 /1 9. F or p er so na l u se o nl y. In this study, 12 \u00b7 12 \u00b7 6 mm prismatic samples were produced by SLM method from Ti6Al4V alloy powder material. The chemical composition of Ti6Al4V alloy is given in Table 1. Wear test samples were produced with the Concept Laser M LabR SLM device, with the manufacturing process parameters given in Table 2. In the study, three different build orientations and three different hatch spacings were used with SLM (Fig. 1). Casting Ti alloy was supplied from the market. Stress relief annealing was applied to the samples manufactured by SLM and casting method. The experiments were carried out in an argon gas atmosphere to reduce the oxidizing effect of the environment. The heat treatment processes were carried out in such a way that the samples were heated to 840 C for 4 h, kept at this temperature for 2 h, and then cooled in the furnace. Wear tests of the samples were carried out by a BrukerUMT tribometer testing machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.3-1.png",
        "caption": "Fig. 12.3 Relative velocity screw of two rotating bodies",
        "texts": [
            "1) have opposite signs, there are two screws of zero pitch on the cylindroid (see (3.169)). Proposition: All bodyfixed points P on the axes of these screws have the desired property. Proof: Zero pitch means that for an appropriate ratio \u03c91/\u03c92 such a point P has the resultant velocity v = v1 + v2 = 0 . This implies that v1 and v2 are collinear. Since the directions of v1 and v2 are independent of \u03c91 and \u03c92 also the direction of v is independent. End of proof. 362 12 Screw Systems The bodies shown in Fig. 12.3 are rotating about skew axes. The length of the common perpendicular is , and the projected angle is \u03b1 . Unit vectors n1 and n2 having the directions of the axes are attached to the midpoint 0 of the common perpendicular. This point 0 is the origin of a frame-fixed basis e . The basis vector e1 is directed along the bisector of the angle \u03b1 between n1 and n2 , and e3 is directed along the common perpendicular. The velocity screws of the bodies relative to the frame are \u03c91(n1 , a1 \u00d7 n1) , \u03c92(n2 , a2 \u00d7 n2) , a1,2 = \u2213 2 e3 ",
            " All reciprocal screws of given pitch p1 = \u2212p (arbitrary) passing through a given point P (arbitrary) are in the null plane associated with the null point P of the linear complex with axis (n,w) and with pitch p+ p1 . If a fifth-order screw system is given by five linearly independent screws (ni,wi + pini) (i = 1, . . . , 5), the single screw (n,w+ pn) reciprocal to all five is determined from (12.55). Example: In Sect. 12.2 the relative motion of two wheels rotating with constant angular velocity ratio \u03bc = \u03c92/\u03c91 = const about skew axes was shown to be a velocity screw \u03c9(n,n\u00d7r+pn) (see Fig. 12.3). The direction of 374 12 Screw Systems the axis is determined by the parallelogram rule \u03c9 = \u03c92 \u2212\u03c91 (Eq.(12.13)). The pitch p(\u03bc) is given in the first Eq.(12.18). The second equation for u(\u03bc) determines the point where the screw axis intersects orthogonally the common perpendicular of the two wheel axes. Imagine the two wheels to be a pair of gears with any kind of teeth appropriate for keeping the relative velocity screw constant. Let P be an arbitrary point at which, in the course of meshing, two tooth flanks are in tangential contact, and let n1 be the common unit normal vector at P "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure7.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure7.4-1.png",
        "caption": "Fig. 7.4 Torques acting on a spinning top with eccentricity of mass",
        "texts": [
            " Here, the function y = esin\u03b1 denotes the displacement of the eccentric mass that represents the excitation input, where e is the eccentricity of mass location. The frequency of this sine wave is also the frequency at which nutation occurs. The analysis of gyroscope motions and nutation is conducted using the example of a tilted top on the angle \u03b3 to the horizontal that is not well-balanced. The analysis of the top motions is conducted for its rotation around the support point O in the counterclockwise direction. The top\u2019s leg has the sharpened tip, in which, frictional torque acting on the leg is neglected (Fig. 7.4). If the axis of a top is released, then the force of gravity should tilt its axis in the direction of the action of this force. As a result, the top axis will begin to precess at about the vertical and horizontal. The motions of the top are accompanied by a visually undetectable nutational process, which decays rapidly according to the action of the inertial torques. Because of the inertial resistance torques, the proper rotation of the top gradually slows down, while the precession velocities correspondingly increase",
            "2 The Top Nutation 143 The motions of a not well-balanced spinning top are complex. The equation of nutation is formulated by the action of the system of inertial torques on the top generated by the action of external and internal forces. These forces represent the top weight, the centrifugal forces of eccentric mass and centre mass, and the centrifugal, common inertial forces and Coriolis forces generated by the rotating mass elements, and the change in the angular momentum. These forces are demonstrated in Fig. 7.4 and formulated by the equations represented in Table 3.1, Chap. 3. The centrifugal force of the eccentric mass generates the variable torque represented by the following equation. Tex = Fl = Me\u03c92l sin \u03b1 by axis ox (7.21) Tey = Fl = Me\u03c92l cos \u03b3 cos\u03b1 by axis oy (7.22) where F =Me\u03c92 is the centrifugal force generated by the rotating eccentric massM, l is the length of the top toy\u2019s leg, \u03b3 is the tilt angle of the top axis, \u03b1 is the angle that is used for calculating the maximum magnitude, while Tex and Tey are the torques acting around axes ox and oy, respectively",
            " The data defined above allow for the formulation 144 7 Mathematical Models for the Top Motions and Gyroscope Nutation of a mathematical model for a top motion around axes ox and oy in Euler\u2019s form. The torques acting on the top with eccentric mass are similar to the torques acting on the top represented in Sect. 7.1. Both models consider the top with one-sided support to be equal except for the added torque generated by the centrifugal force of the eccentric rotating mass. For simplicity, the motion of the top with eccentric mass does not consider the spiralled motion of its leg\u2019s tip. The torques acting on the not well-balanced top are presented in Fig. 7.4. As such, the mathematical model for a top motion around axes ox and oy is represented by the following system of equations: Jx d\u03c9x dt = T + Tct.my \u00b1 Tex \u2212 Tctx \u2212 Tcrx \u2212 Tamy (7.23) Jy d\u03c9y dt = (\u00b1Tey + Tinx + Tamx \u2212 Tcry) cos \u03b3 (7.24) where Ji = (MR2/4) + Ml2 is the top mass moment of inertia around axis i, while the sign (\u00b1) denotes (+) and (\u2212) as the positive and negative directions of the action, respectively, for the torque generated by the eccentric mass. The torques generated by the centrifugal forces of the rotating centre mass around axis oy is defined by the following equation: Tct,my = Fct",
            " Substituting the expression\u03c9y fromEq. (7.5) into Eq. (7.26) and transformation yield the following equation: Jx d\u03c9x dt = Mgl cos \u03b3 + Ml2 tan \u03b3 \u00d7 [ 2\u03c02 + 8 + (2\u03c02 + 9) cos \u03b3 2\u03c02 + 9 \u2212 (2\u03c02 + 8) cos \u03b3 ]2 \u00d7 \u03c92 x \u00b1 Me\u03c92l sin \u03b1 \u2212 { 2\u03c02 + 8 9 + [ 2\u03c02 + 8 + (2\u03c02 + 9) cos \u03b3 2\u03c02 + 9 \u2212 (2\u03c02 + 8) cos \u03b3 ]} J\u03c9\u03c9x (7.29) where all parameters are as specified above. The example considers the nutation process of a disc-type top whose data are represented in Table 7.2. The centre mass of the top is located at the plane of the disc (Fig. 7.4). The top initially possesses a displaced mass, while spinning around a vertical axis is conducted with nutation. The top moves around axis oy without the action of the frictional force on the support. The torque generated by the top weight W is as follows: 146 7 Mathematical Models for the Top Motions and Gyroscope Nutation T = Mgl cos\u03b3 = 0.02 \u00d7 9.81 \u00d7 0.02 \u00d7 cos75.0\u25e6 = 1.015605932 \u00d7 10\u22123 Nm (7.30) The torque generated by the centrifugal force of the top centre mass rotation around axis oy is as follows: Tct"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003339_tnsre.2020.2970207-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003339_tnsre.2020.2970207-Figure4-1.png",
        "caption": "FIGURE 4. Top view of Concave Sensor Module.",
        "texts": [
            " Further signal processing and computing are done in the application in the smart phone for saving hardware. The result can also be displayed by the smart phone and the data can be stored inside the smart phone. As a result of using minimal hardware for the device and the use of a flexible software solution for handling the sensor data, the cost of device will be very low. In this paper, we focus on the description of the wrist concave sensor and the signal processing module. As shown in Fig. 3 and Fig. 4, the concave oximeter sensor consists of a concave support structure, one red LED and one infrared LED and two photo-transistors. The soft concave support structure matches with the convexity of the human wrist, with the two LEDs inside the pinhole. The two photo-transistors are placed on the other end of the structure at a suitable distance from the LEDs. The separation distance has been verified after many experiments. The peak wavelengths of the red LED and infrared LED are 630nm and 880nm respectively, which are sensitive to the changes in oxygen saturation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure1.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure1.2-1.png",
        "caption": "Fig. 1.2 Bryan angles. Definition (a) and application in a two-gimbal suspension (b)",
        "texts": [
            "4 Bryan Angles 9 cos \u03b8 = a1233 , sin \u03b8 = \u03c3 \u221a 1\u2212 cos2 \u03b8 (\u03c3 = +1 or \u2212 1) , cos\u03c8 = \u2212a1223/ sin \u03b8 , sin\u03c8 = a1213/ sin \u03b8 , cos\u03c6 = a1232/ sin \u03b8 , sin\u03c6 = a1231/ sin \u03b8 . \u23ab\u23aa\u23ac \u23aa\u23ad (1.29) Let (\u03c8 , \u03b8 , \u03c6) be the angles associated with \u03c3 = +1 . The angles associated with \u03c3 = \u22121 are (\u03c0 + \u03c8 , \u2212\u03b8 , \u03c0 + \u03c6) . Both triples produce one and the same final position of the basis e2 . Numerical difficulties arise when \u03b8 is close to one of the critical values n\u03c0 (n = 0, 1, . . .). These angles are also referred to as Cardan angles. As before, the final position e2 of the body-fixed basis is the result of three successive rotations (Fig. 1.2a ). In the initial position prior to the first rotation the body-fixed basis coincides with e1 . The first rotation is carried out through an angle \u03c61 about the axis e11 . It carries the body-fixed basis into an intermediate position e2 \u2032\u2032 . The second rotation is carried out through an angle \u03c62 about the axis e2 \u2032\u2032 2 . It carries the body-fixed basis into a new intermediate position e2 \u2032 . The third rotation is carried out through an angle \u03c63 about the axis e2 \u2032 3 . It carries the body-fixed basis into the final position e2 . A characteristic feature of Bryan angles is the sequence (1,2,3) of rotation axes2. The desired expression for the matrix A12 is, again, the product of three matrices describing the individual rotations. Figure 1.2a shows that 2 In contrast to Euler angles each of the three body-fixed basis vectors is axis of one of the three rotations. Other possible sequences of rotation axes for Bryan angles are (3,2,1) and the cyclic permutations (2,3,1), (3,1,2), (2,1,3) and (1,3,2). In Sect. 18.4 the sequence (3,2,1) is used 10 1 Rotation about a Fixed Point. Reflection in a Plane e1 = A1e 2\u2032\u2032 , e2 \u2032\u2032 = A2e 2\u2032 , e2 \u2032 = A3e 2 , (1.30) A1 = \u23a1 \u23a2\u23a3 1 0 0 0 cos\u03c61 \u2212 sin\u03c61 0 sin\u03c61 cos\u03c61 \u23a4 \u23a5\u23a6 , A2 = \u23a1 \u23a2\u23a3 cos\u03c62 0 sin\u03c62 0 1 0 \u2212 sin\u03c62 0 cos\u03c62 \u23a4 \u23a5\u23a6 , A3 = \u23a1 \u23a2\u23a3 cos\u03c63 \u2212 sin\u03c63 0 sin\u03c63 cos\u03c63 0 0 0 1 \u23a4 \u23a5\u23a6 . (1.31) The desired matrix is A12 = A1A2A3 . When this is multiplied out and use is made of the abbreviations ci = cos\u03c6i , si = sin\u03c6i (i = 1, 2, 3), the matrix has the form A12 = \u23a1 \u23a2\u23a3 c2c3 \u2212c2s3 s2 c1s3 + s1s2c3 c1c3 \u2212 s1s2s3 \u2212s1c2 s1s3 \u2212 c1s2c3 s1c3 + c1s2s3 c1c2 \u23a4 \u23a5\u23a6 . (1.32) Bryan angles, too, can be illustrated by means of a rigid body in a twogimbal suspension system. The arrangement is shown in Fig. 1.2b . The bases e1 and e2 are attached to the material base and to the suspended body, respectively. The angles \u03c61 , \u03c62 and \u03c63 are, in this order, the rotation angle of the outer gimbal relative to the material base, of the inner gimbal relative to the outer gimbal and of the body relative to the inner gimbal. The three angles can be adjusted independently since the intermediate bases e2 \u2032\u2032 and e2 \u2032 are materially realized by the gimbals. For \u03c62 = 0 the three rotation axes are mutually orthogonal. As with Euler angles there exists a critical case in which the axes of the first and of the third rotation coincide",
            " aii = (nj \u00d7 nk) 2 = 1\u2212 a2i , aij = (ni \u00d7 nk) \u00b7 (nk \u00d7 nj) = aiaj \u2212 ak , a = n1 \u00b7 n2 \u00d7 n3 , a2 = 1\u2212 a21 \u2212 a22 \u2212 a23 + 2a1a2a3 = aiiajj \u2212 a2ij \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (i, j, k = 1, 2, 3 different) . (1.240) The parameters b1 , b2 , b3 represent the covariant coordinates of n . The contravariant coordinates c1 , c2 , c3 are defined through the equation n = c1n1 + c2n2 + c3n3 . They satisfy the equations 52 1 Rotation about a Fixed Point. Reflection in a Plane aci = n \u00b7 nj \u00d7 nk , a2c2i = (1\u2212 b2j )(1\u2212 b2k)\u2212 (bjbk \u2212 ai) 2 } (i, j, k = 1, 2, 3 cyclic) . (1.241) Solution: Comparison of Fig. 1.12 with Fig. 1.2b shows: If n3 , n2 , n1 form a right-hand cartesian basis e11 , e 1 2 , e 1 3 , the angles \u03d53 , \u03d52 , \u03d51 represent, in this order, the Bryan angles \u03c61 , \u03c62 , \u03c63, respectively. This particular case is characterized by the parameters ai = 0 , a = \u22121 and bi = ci (i = 1, 2, 3). The solutions \u03d51 = \u03c63 , \u03d52 = \u03c62 and \u03d53 = \u03c61 are calculated from (1.35) with the matrix elements of (1.49) with bi instead of ni (i = 1, 2, 3). In the general case, the solution is found from (1.238) as follows. Two scalar multiplications, one from the left by R(\u2212n3, \u03d53) and the other from the right by R(\u2212n1, \u03d51) , produce the equation (see the identities (1",
            "10 Principle of Transference 109 A\u0302 12 = \u23a1 \u23a2\u23a3 c\u03c8c\u03c6 \u2212 s\u03c8c\u03b8s\u03c6 \u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 s\u03c8s\u03b8 s\u03c8c\u03c6 + c\u03c8c\u03b8s\u03c6 \u2212s\u03c8s\u03c6 + c\u03c8c\u03b8c\u03c6 \u2212c\u03c8s\u03b8 s\u03b8s\u03c6 s\u03b8c\u03c6 c\u03b8 \u23a4 \u23a5\u23a6 +\u03b5 \u239b \u239du\u03c8 \u23a1 \u23a3\u2212s\u03c8c\u03c6 \u2212 c\u03c8c\u03b8s\u03c6 s\u03c8s\u03c6 \u2212 c\u03c8c\u03b8c\u03c6 c\u03c8s\u03b8 c\u03c8c\u03c6 \u2212 s\u03c8c\u03b8s\u03c6 \u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 s\u03c8s\u03b8 0 0 0 \u23a4 \u23a6 +u\u03b8 \u23a1 \u23a3 s\u03c8s\u03b8s\u03c6 s\u03c8s\u03b8c\u03c6 s\u03c8c\u03b8 \u2212c\u03c8s\u03b8s\u03c6 \u2212c\u03c8s\u03b8c\u03c6 \u2212c\u03c8c\u03b8 c\u03b8s\u03c6 c\u03b8c\u03c6 \u2212s\u03b8 \u23a4 \u23a6 +u\u03c6 \u23a1 \u23a3\u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 \u2212c\u03c8c\u03c6 + s\u03c8c\u03b8s\u03c6 0 \u2212s\u03c8s\u03c6 + c\u03c8c\u03b8c\u03c6 \u2212s\u03c8c\u03c6 \u2212 c\u03c8c\u03b8s\u03c6 0 s\u03b8c\u03c6 \u2212s\u03b8s\u03c6 0 \u23a4 \u23a6 \u239e \u23a0 . (3.84) The primary part is the matrix A12 of Eq.(1.28). Dual differentiation of the element (1,3), i.e., of the product s\u03c8s\u03b8 , yields the expression u\u03c8c\u03c8s\u03b8 + u\u03b8 s\u03c8c\u03b8 . These two terms are the elements (1,3) of the matrices associated with u\u03c8 and u\u03b8 . The same procedure is applied to the direction cosine matrix expressed as function of Bryan angles \u03c61 , \u03c62 and \u03c63 (see Fig. 1.2a and Eq.(1.32)). Each of the three subsequent rotations about the axes e11 , e2 \u2032\u2032 2 and e2 \u2032 3 = e23 is replaced by a screw displacement about the respective axis. The dual screw angles are denoted \u03c6\u0302i = \u03c6i + \u03b5ui (i = 1, 2, 3). They are dual Bryan angles. The associated dual direction cosine matrix is A\u0302 12 = \u23a1 \u23a3 c2c3 \u2212c2s3 s2 c1s3 + s1s2c3 c1c3 \u2212 s1s2s3 \u2212s1c2 s1s3 \u2212 c1s2c3 s1c3 + c1s2s3 c1c2 \u23a4 \u23a6 +\u03b5 \u239b \u239du1 \u23a1 \u23a3 0 0 0 \u2212s1s3 + c1s2c3 \u2212s1c3 \u2212 c1s2s3 \u2212c1c2 c1s3 + s1s2c3 c1c3 \u2212 s1s2s3 \u2212s1c2 \u23a4 \u23a6 +u2 \u23a1 \u23a3\u2212s2c3 s2s3 c2 s1c2c3 \u2212s1c2s3 \u2212s1s2 \u2212c1c2c3 \u2212c1c2s3 c1s2 \u23a4 \u23a6 +u3 \u23a1 \u23a3\u2212c2s3 \u2212c2c3 0 c1c3 \u2212 s1s2s3 \u2212c1s3 \u2212 s1s2c3 \u2212 c1s3 0 s1c3 + c1s2s3 \u2212s1s3 + c1s2c3 0 \u23a4 \u23a6 \u239e \u23a0 ",
            "22) The vectors are decomposed in basis e2 . With the help of (1.26) this results in the coordinate equations\u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 = \u23a1 \u23a3 sin \u03b8 sin\u03c6 cos\u03c6 0 sin \u03b8 cos\u03c6 \u2212 sin\u03c6 0 cos \u03b8 0 1 \u23a4 \u23a6 \u23a1 \u23a3 \u03c8\u0307 \u03b8\u0307 \u03c6\u0307 \u23a4 \u23a6 . (10.23) Inversion yields the desired differential equations:\u23a1 \u23a3 \u03c8\u0307 \u03b8\u0307 \u03c6\u0307 \u23a4 \u23a6 = \u23a1 \u23a3 sin\u03c6/ sin \u03b8 cos\u03c6/ sin \u03b8 0 cos\u03c6 \u2212 sin\u03c6 0 \u2212 sin\u03c6 cot \u03b8 \u2212 cos\u03c6 cot \u03b8 1 \u23a4 \u23a6 \u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 . (10.24) These equations are nonlinear. Numerical problems arise when \u03b8 gets close to one of the critical values n\u03c0 (n = 0,\u00b11, . . .) . Figure 1.2a yields for the angular velocity vector \u03c9 the expression \u03c9 = \u03c6\u03071e 1 1 + \u03c6\u03072e 2\u2032 2 + \u03c6\u03073e 2 3 . (10.25) The vectors are decomposed in basis e2 . With the help of (1.30) this results in the coordinate equations\u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 = \u23a1 \u23a3 cos\u03c62 cos\u03c63 sin\u03c63 0 \u2212 cos\u03c62 sin\u03c63 cos\u03c63 0 sin\u03c62 0 1 \u23a4 \u23a6 \u23a1 \u23a3 \u03c6\u03071 \u03c6\u03072 \u03c6\u03073 \u23a4 \u23a6 . (10.26) 334 10 Kinematic Differential Equations Inversion yields the desired differential equations:\u23a1 \u23a3 \u03c6\u03071 \u03c6\u03072 \u03c6\u03073 \u23a4 \u23a6 = \u23a1 \u23a3 cos\u03c63/ cos\u03c62 \u2212 sin\u03c63/ cos\u03c62 0 sin\u03c63 cos\u03c63 0 \u2212 cos\u03c63 tan\u03c62 sin\u03c63 tan\u03c62 1 \u23a4 \u23a6 \u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 "
        ],
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    },
    {
        "image_filename": "designv10_12_0003593_iemdc47953.2021.9449566-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003593_iemdc47953.2021.9449566-Figure2-1.png",
        "caption": "Fig. 2. Sectional view of the CAD model.",
        "texts": [],
        "surrounding_texts": [
            "As shown in Figs. 2 and 3, hollows are implemented into the classical shaft region. This leads to decreased rotor mass and inertia. Furthermore, the transition region between the active part and the bearings is conical-shaped in order to conduct the forces properly and to reduce mechanical stress concentration on the path from the rotor surface to the coupling. The closed pipe profile is particularly suitable for absorbing bending and torsional loads."
        ]
    },
    {
        "image_filename": "designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure4-1.png",
        "caption": "Fig. 4. The 8/4-4 type ring structure sensor with isometric legs.",
        "texts": [
            " ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rs cos \u03b32\u2212r cos\u03b12\u00f0 \u00de2 \u00fe Rs sin \u03b32\u2212r sin \u03b12\u00f0 \u00de2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rw cos \u03b22\u2212r cos\u03b12\u00f0 \u00de2 \u00fe Rw sin \u03b22\u2212r sin \u03b12\u00f0 \u00de2 q \u00bc Hs H \u00bc l l \u00f011\u00de Then, the size changes between the two structures can be expressed as Hs \u00bc H R2 s\u22122Rsr cos \u03b32\u2212\u03b12\u00f0 \u00de \u00bc R2 w\u22122Rwr cos \u03b22\u2212\u03b12\u00f0 \u00de : \u00f012\u00de In order to measure the six-axis force acted on shaft and hole parts, ring structure is introduced into the design of parallel sensors. Combining the characteristics of a platform structure, Yao et al. [25] proposed the 8/4-4 type ring structure sensor with isometric legs. The drawing is shown in Fig. 4. The inner and outer cylindrical surfaces are coaxial with the eight measuring limbs being placed equally between them. All the inner spherical joint centers are placed on the same circle belonging to the middle section of the inner cylindrical surface. The outer spherical joint centers are divided into two sets, each of which includes four joints. The two sets are placed on the upper and lower circles belonging to the outer cylindrical surface, respectively. The configuration is determined by the following parameters: R, r, H, \u03b11, \u03b12, \u03b21 and \u03b22",
            " The 4/8/4 type platform structure possesses the middle one used for pre-stress and the upper and lower platforms used for measurement and fixation, respectively. The 8/4-4 type ring structure possesses inner circle used for bearing load and outer circle used for fixation. Moreover, if we set Rs = Rw = R and \u03b32 = \u03b22 in Eq. (12), the 8/4-4 type ring structure will be obtained in the basis of the 4/8/4 type platform structure. The 4-4/4-4 type ring structure sensor with isometric legs [25] is proposed according to the 8/4-4 type ring structure redundant parallel six-axis force sensor with isometric legs which is shown in Fig. 4. The drawing of the 4-4/4-4 type ring structure sensor with isometric legs is shown in Fig. 5. The difference between this structure and the 8/4-4 type ring structure is that the inner spherical joints are divided into two sets which are placed on the upper and lower circles of the inner cylindrical surface, respectively. The configuration is determined by the following parameters: R, r,H, \u03b11,\u03b12, \u03b21 and \u03b22 which have the same meanings as those in Fig. 4. For the 4-4/4-4 type ring structure sensor, the force Jacobian matrix Eq. (3) can be got: GIV \u00bc A1\u2212B1 A1\u2212B1j j A2\u2212B2 A2\u2212B2j j A3\u2212B3 A3\u2212B3j j \u2026 A8\u2212B8 A8\u2212B8j j B1 A1 A1\u2212B1j j B2 A2 A2\u2212B2j j B3 A3 A3\u2212B3j j \u2026 B8 A8 A8\u2212B8j j 2 664 3 775 \u00f017\u00de where Ai\u2212Bi \u00bc r cos \u03b1i\u2212R cos \u03b2i r sin \u03b1i\u2212R sin \u03b2i 2H\u00bd T i \u00bc 1;2;3;4\u00f0 \u00de; A j\u2212B j \u00bc r cos \u03b1 j\u2212R cos \u03b2 j r sin \u03b1 j\u2212R sin \u03b2 j \u22122H T j \u00bc 5;6;7;8\u00f0 \u00de; Ai\u2212Bij j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00fe r2\u22122Rr cos \u03b1i\u2212\u03b2i\u00f0 \u00de \u00fe 4H2 q i \u00bc 1;2;3;4\u00f0 \u00de; A j\u2212B j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00fe r2\u22122Rr cos \u03b1 j\u2212\u03b2 j \u00fe 4H2 r j \u00bc 5;6;7;8\u00f0 \u00de; Bi Ai \u00bc rH sin \u03b1i \u2212rH cos\u03b1i Rr sin \u03b1i\u2212\u03b2i\u00f0 \u00de\u00bd T i \u00bc 1;2;3;4\u00f0 \u00de; B j A j \u00bc \u2212rH sin \u03b1 j rH cos\u03b1 j Rr sin \u03b1 j\u2212\u03b2 j h iT j \u00bc 5;6;7;8\u00f0 \u00de; \u03b1 \u00bc \u03b11 \u03b12 \u03b13 \u03b14 \u03b15 \u03b16 \u03b17 \u03b18\u00bd \u00bc \u03b11 \u03b11 \u00fe \u03c0 2 \u03b11 \u00fe \u03c0 \u03b11 \u00fe 3\u03c0 2 \u03b12 \u03b12 \u00fe \u03c0 2 \u03b12 \u00fe \u03c0 \u03b12 \u00fe 3\u03c0 2 and \u03b2 \u00bc \u03b21 \u03b22 \u03b23 \u03b24 \u03b25 \u03b26 \u03b27 \u03b28\u00bd \u00bc \u03b21 \u03b21 \u00fe \u03c0 2 \u03b21 \u00fe \u03c0 \u03b21 \u00fe 3\u03c0 2 \u03b22 \u03b22 \u00fe \u03c0 2 \u03b22 \u00fe \u03c0 \u03b22 \u00fe 3\u03c0 2 : The lengths of two sets of the limbs are shown in Eqs"
        ],
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    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-FigureD.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-FigureD.8-1.png",
        "caption": "Figure D.8. Th in circular rod.",
        "texts": [
            "3 to determine the mass of the casing and its moment of inertia about the z-axis, referred to the body frame rp = (o ; ik ) . i 3 .~. Problem 9.12. I, 398 Chapter 9 9.13. The figure shows an arbitrary diametral cross section of a homogeneous flywheel made of a grade of stee l of density P = 15 slug/ ft\", Determin e its moment of inertia about the z-axis, What is the radiu s of gyration about the z-axis? z\u2022~----- 20' --- - --+; 1/2' y Problem 9.13. 9.14. The moment of inertia tensor for a sector of a homogeneous circular rod is given in Fig. D.8. Derive its inertia tensor in a parallel frame tp = {C ; it} at its center of mass. What is the inertia tensor for a semici rcular wire referred to cp? 9.15. Derive by integration the inertia tensor for the thin rod in Fig . D.7, referred to frame rP = {O; ik } at its end point O. Confirm the result by use of the parallel axis theorem applied to the tensor Ie given there. 9.16. A nonhomogeneous thin rigid rod of length I has a mass density p(x ) that varies with the distance x from one end 0 such that dp (x )/dx = PI, a con stant, and p(O)= Po"
        ],
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    },
    {
        "image_filename": "designv10_12_0000085_j.cma.2005.05.055-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000085_j.cma.2005.05.055-Figure10-1.png",
        "caption": "Fig. 10. Function of transmission errors of Example 3 with error Dc = 3 0 for: (a) unloaded gear drive; (b) loaded gear drive with torque 250 N m.",
        "texts": [
            " 8 show the formation of the bearing contact at points of surface tangency that correspond to points 1, 2, 3 of function D/2,t(/1) (Fig. 7(b)). Drawings of Fig. 8 confirm existence of edge contact and zones of severe contact stresses. Results of stress analysis are represented in Fig. 9. (iii) Example 3: A misaligned gear drive with error of crossing angle Dc = 3 0 is considered. The pinion is generated by a grinding worm and double-crowning is provided by modified roll. As a result, a predesigned parabolic function of transmission errors is provided for the unloaded gear drive shown in Fig. 10(a) as D/2(/1). Transmission errors caused by Dc are absorbed. Fig. 10(b) shows the function of transmission errors D/2,t(/1) for a loaded gear drive. The gear of the drive is loaded by a torque of 250 N m. Due to elastic deformation of teeth, the magnitude A1 of maximal transmission errors is reduced to A2. The formation of the bearing contact for the loaded gear drive is shown in Fig. 11. The drawings of Fig. 11 confirm that the edge contact is eliminated. Contact and bending stresses are shown in Fig. 12. Reduction of stresses is confirmed (Fig. 12). (iv) Example 4: A standard misaligned helical gear drive is considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000288_s11071-009-9473-4-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000288_s11071-009-9473-4-Figure1-1.png",
        "caption": "Fig. 1 Geometry and forces exerted on link Tk",
        "texts": [
            " To describe the geometry of links, starting from the base link T0 we number the movable links sequentially from T1 to Tn and the joints from O1 to ON . Thus, except for the base link, every link has two joints; the link Tk has the joint Ok at its proximal end and the joint Ok+1 at the distal end. We now introduce several frames. First, the fixed frame O0 \u2212 x0y0z0 is attached to the base T0 at a convenient location. Consider the set of moving bodies Tk (k = 1,2, . . . , n) attached to the moving frames Ok \u2212 xkykzk . Along the zk-axis, an arbitrary Tk body has a relative helical motion with respect to Tk\u22121 (see Fig. 1). A combination of translation along and rotation about the same axis is called screw displacement (Tsai [1]). In what follows we apply the concept of successive screw displacements to geometrical analysis of closedloop chains and we note that a joint variable is the displacement required to move a link from initial location to actual position. But, a variable associated to an active joint is denoted as input variable of active joint. The geometric parameters describing the relative position of Tk with respect to adjacent link Tk\u22121 shall be uniquely determined: the translation displacement O \u2032 k\u22121Ok = \u03bbk,k\u22121 of the origin Ok and the joint angle \u03d5k,k\u22121 of rotation about the positive zk-axis according to the right-hand rule",
            " In the first case, the rigid body T\u03c4 moves in relative translation along the z\u03c4 -axis under the action of the force f\u03c4,\u03c4\u22121 = f\u03c4,\u03c4\u22121 u3 that is applied by a hydraulic or pneumatic system located in the neighboring frame T\u03c4\u22121. In the second case, it rotates by an electric motor developing a torque of moment m\u03c4,\u03c4\u22121 = m\u03c4,\u03c4\u22121 u3, pointed about the positive z\u03c4 -axis. We note that for a parallel robot, a single actuator that exerts a force or a torque between two adjacent links, drives each limb. Applying the free-body diagram procedure, Fig. 1 depicts the forces and moments acting on a typical link T\u03c4 that is connected to link T\u03c4\u22121 by joint O\u03c4 and to other link T\u03c4+1 by joint O\u03c4+1. The forces acting on link T\u03c4 by T\u03c4\u22121 can be reduced about O\u03c4 to a force f \u2032 \u03c4,\u03c4\u22121 and a moment m\u2032 \u03c4,\u03c4\u22121. Similarly, the forces acting on link T\u03c4 by T\u03c4+1 are reduced about O\u03c4+1 to a resultant force (\u2212aT \u03c4+1,\u03c4 f \u2032 \u03c4+1,\u03c4 ) and a resultant mo- ment (\u2212aT \u03c4+1,\u03c4 m\u2032 \u03c4+1,\u03c4 ), both converted into T\u03c4 frame. Note that the vectors fn,n\u22121 and mn,n\u22121 represent the force and the moment exerted on the platform Tn by the link Tn\u22121, for \u03c4 = n"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003384_s12555-019-0904-9-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003384_s12555-019-0904-9-Figure3-1.png",
        "caption": "Fig. 3. Sketch of the PVA.",
        "texts": [
            " Motivated by the above stable control strategies of two kinds of two-link systems, we divide the planar APA system into two parts to control by analyzing its mechanical structure. When the angle and the angular velocity of the third link of the planar APA system are controlled to zero, that is, q3 = 0 and q\u03073 = 0, the last two links can be regarded as a virtual passive link. In this case, the planar APA system is treated as a PVP. The PVP is shown as Fig. 2, where we mainly implement the control objective of the FAL. When the angle of the first link of the planar APA system is kept at a constant, the planar APA system is treated as a PVA. The PVA is shown as Fig. 3, where we mainly realize the control objectives of the SUL and TAL. 3. CONTROLLER DESIGN FOR PVP We achieve the control objective of FAL for the PVP in this section, and make the system be reduced to a PVA with all links stopping rotating. 3.1. Target angle solution of the FAL This subsection uses a geometry method to get the FAL\u2019s target angle corresponding to the target value of end-point. For Fig. 4, we firstly draw a circle C1, where the center of the circle is target position, and radius r1 is a sum of the length of the SUL and TAL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003214_j.measurement.2020.107897-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003214_j.measurement.2020.107897-Figure10-1.png",
        "caption": "Fig. 10. Planetary gearbox test rig.",
        "texts": [
            " In this section, the analysis of the motion periods to a revised signal model, and the completeness of the fault induced information has been studied. The experimental studies will be provided to demonstrate the above theoretical analysis. of the two models. In this section, experimental studies from a planetary gearbox will be provided. The experimental data are acquired from a planetary gearbox test rig at the University of Electronic Science and Technology of China (UESTC), Equipment Reliability and Prognostic and Health Management Laboratory (ERPHM). The configuration of the test rig is shown in Fig. 10. More detailed information can be found in Ref. [4]. The Geometry parameters of the planetary gearbox are listed in Table 2. The experiments operated on the planetary gearbox and the rotational frequency was set up with 30 Hz, data length of 13.8 s, and the sampling frequency is set to be 7680 Hz. Once the value of rotational frequency is known, the values of some characteristic frequency can be calculated [4], we list them in Table 3. Four sun gear health scenarios will be studied, as is shown in Fig",
            " Furthermore, the sidebands induced by the relaxed tidal period are highlighted and indicated by arrows, namely f m f rt ; f m f sun f rt and f m f shaft f rt . All the scenarios in Fig. 12 demonstrate the amplitude modulation effect caused by the motion period of the fault meshing positions. These exisiting sidebands are properly explained by the revised signal mdoel. Additionally, Some trends of these exisiting sidebands may indicate different fault symptoms and should become a meaningful future research directions. The experimental studies also conducted on the planetary gearbox of DDS platform (shown in Fig. 10). According to the assembled parameters listed in Table 2, the sun gear\u2019s rotations to be a tidal and relaxed-tidal period can be calculated based on expressions of ns t and ns rt , as are given in Table 4. Table 4 tells that ns t is 4 times of ns rt for the studied planetary gearbox. 28 groups of the four sun gear scenarios (Fig. 11) were collected under the rotational frequencies of 30 Hz and 50 Hz, respectively. All the data was captured with the time duration of 13.8s and the sampling frequency of 7680 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002160_icra.2016.7487629-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002160_icra.2016.7487629-Figure2-1.png",
        "caption": "Figure 2. TriCal\u2019s measuring device, installed on the IRB 120 robot, with the triangular platform installed on the table.",
        "texts": [
            " The tool\u2019s orientation is not included because our device only gives us information about its position. To model the elasticity in each gearbox, five nonkinematic errors were considered for joints 2\u20136. The elasticity in each gearbox is modeled as a linear torsional spring, as in [18]. Because the joint 1 axis is parallel to the direction of gravity, no torque is applied when the robot is stationary. Thus, no non-kinematic error parameter is associated with this joint. The experimental setup consists of three main components, as shown in Fig. 2: the ABB IRB 120 robot, a triangular platform, and the new measuring device. A. Triangular platform The robot is fixed to steel table, and so is a triangular platform, via an articulating base that allows us to change the platform\u2019s orientation. In our experiment, the platform is installed parallel to the robot\u2019s base. Each of the three 0.5-inch precision balls is installed on a magnetic mount. The mounts are placed at the three corners of the triangular platform. We chose to space them 300 mm apart, for two reasons: we wanted to be able to measure this distance accurately with our QC20-W Renishaw telescoping ballbar, and we wanted to enable collision-free measurements for any end-effector pose on the three precision balls (spheres)",
            " Thus, the simulated position errors after calibration do not include the impact of unmodeled parameters and leaves out other sources of errors, such as backlash in the gears, temperature, and the measurement uncertainty of the laser tracker. The actual experiment was divided into two main steps, which this section will describe in detail. First, we used the TriCal to measure the robot joint values needed for the identification process. After identifying the parameters of the robot, we then validated the performance of the calibration by using a laser tracker to measure positions inside the target workspace and in the whole workspace. A. Identification of the parameters The setup shown in Fig. 2 was used to obtain the meas- urements for the identification process. The 0.5-inch precision balls on the triangular platform have a diameter tolerance of \u00b10.0025 mm. The distances dij between the centers of each pair of balls were measured with a Renishaw telescopic ballbar, which has an uncertainty of \u00b10.001 mm. The room temperature was controlled to 22\u00b10.3\u00b0C. A pool of 300 configurations was generated using the algorithm from Section V. Of these, 45 configurations were selected randomly for identification",
            " The maximum error allowed in the measuring procedure, \u03b5, was set at 0.010 mm. After collecting the necessary measurements, the robot\u2019s parameters were identified using the linear least squares method. Table VI gives the parameter errors. We note that the compliance value of axis 6 is significantly higher than the other axes. This is explained by the fact that the torque applied on axis 6 is significantly lower than the other axes. B. Validation The experimental validation used the same setup as that shown in Fig. 2, except that the configurations were measured with a FARO ION laser tracker, and not by constraining the indicators of the TriCal. The laser tracker has a measurement uncertainty of 0.049 mm, and it was placed approximately 3 m in front of the robot. The three 0.5-inch precision balls were replaced by three SMRs in order to measure {W} with the laser tracker. After the three SMRs were measured, the triangular platform was removed from the robot workspace. The calibrator was attached to the measuring device with a rubber band, and the center sphere was replaced by a 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.37-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.37-1.png",
        "caption": "Fig. 15.37 Ordinary cycloid",
        "texts": [
            "35 shows the evolute z2 and in dashed lines the wheels of the new system. Further properties of cycloids and of trochoids in general are found in Wunderlich [30] and Strubecker [28]. Higher-order trochoids were investigated by Wunderlich [29]. An ordinary cycloid8 is the trajectory of an arbitrary point (not just a circumferential point) fixed on a circular wheel which is rolling along a straight line. This is the situation when in Fig. 15.26 r0 is infinite. In what follows, the notation shown in Fig. 15.37 is used. The radii of the circle and of point C are denoted r and b respectively ( r, b > 0 ). The angle of roll of the circle is \u03d5 (positive clockwise). The position \u03d5 = 0 is defined to be the position when the center as well as point C is on the imaginary axis with C being below the center of the circle. In this position these two points have the complex numbers i r and z = i (r \u2212 b) , respectively. In the position \u03d5 (arbitrary) the numbers are r\u03d5+ i r and 7 J. Bernoulli 1692, de la Hire 1694 8 Leibniz [23] quotes Cardinal de Susa (1454) to be the first to mention this curve 15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002832_j.msea.2019.138057-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002832_j.msea.2019.138057-Figure2-1.png",
        "caption": "Fig. 2. (a) The geometry and the locations where tensile test sample are cut of the 3D printed low carbon steel wall from the Gas Metal Arc Welding (GMAW) Metal Big Area Additive Manufacturing (MBAAM) Machine with the dimension in inches, (b) the tensile sample geometry with the dimension in mm.",
        "texts": [
            " In the current work, a rectangular thin wall consisting of 124 layers (see Fig. 1b) was built on a fully clamped build bar. Each layer consisted of two parallel and continuous longitudinal beads that started at alternating ends to achieve consecutive layers. After the wall was printed, it was cut from the base plate. Tensile samples were prepared for further examinations, primarily the in-situ high energy X-ray diffraction tensile test. 10 samples were prepared from the location and geometry as shown in Fig. 2a and Fig. 2b respectively. The samples labeled as B1\u2013B3 were samples cut out from the bottom of the wall close to the base plate. The samples T1-T3 were samples cut from the top of the wall, and L1-L2 and R1-R2 were the samples from the left and right side of the wall, respectively. The in-situ HEXRD tensile tests were performed at beamline 11-ID-C at the Advanced Photon Source (APS). Fig. 3 is a schematic illustration of the in-situ synchrotron-based HEXRD tensile test setup at beam line 11-ID-C of APS. The synchrotron beam energy and wavelength (l) were 106",
            " The incident beam was nearly square, (500mm by 500mm) and diffracted as it penetrated through the crystal aggregates of the entire thickness according to Bragg's law: =d \u03b8 \u03bb2 sinhkl hkl where hkl denote the Miller indices of the lattice planes, and dhkl and \u03b8hkl are the spacing and diffraction angle for the (hkl) planes, respectively. The diffracted X-ray beam from the lattice planes of a randomly textured polycrystalline material formed a series of cones each of which were associated with a specific lattice plane. A two-dimensional PerkinElmer \u03b1Si flat panel detector was located at a distance D behind the sample and captured the diffracted beams as circular Debye rings for different lattice planes. Fig. 2b illustrates the tensile sample geometry, with 18mm gage length. The custom-designed tensile load frame had a 13 kN capacity. The distance D was 1.896m and was calibrated via diffraction of a standard CeO2 sample. The tensile test was conducted in displacementcontrolled mode at a constant cross-head speed of 30mm/s. After each displacement increment of 40mm, the image on the area detector was recorded by a digital camera with ten 1-s exposures. The sample was positioned such that one of the planar surfaces (LD x TD) was normal to the incident beam during the in-situ tensile test",
            " Thus, the simulation can capture temperature variations during heating and cooling associated with wire cutting and interlayer transition. The validity of the modeling procedure was established by comparing the predicted and measured temperature histories at the base plate and the build plate distortion in the earlier publication by the authors [24]. The key features and equations used for the simulation can be found in the [24\u201326]. Six samples were tensile tested under the HEXRD beam, which included L1, L2, R1, R2 and B2 and T2 as shown in Fig. 2. The observations of the fracture surfaces show ductile fracture for all the samples. The true stress-strain curves and engineering stress-strain curves are shown in Fig. 4. From these curves, it can be seen that the yield and work hardening behaviors of the 4 samples on the side of the wall (L1, L2, R1, R2) are almost identical, except Sample L1 which has considerably smaller elongation. The stress-strain curves at the top and bottom of the wall (T2 and B2), on the other hand, have higher stresses, with sample B2 having the highest among the six samples",
            " 8c and 8d show the microstructure of the bottom of the build, close to the interface. The microstructure here consists of small grain boundary allotriomorphic ferrite grains with acicular ferrite (indicated with the blue arrows) within prior austenite grains. The smaller ferrite grains are due to the repeated thermal cycling unlike the top specimen which did not go through any thermal cycling. The laths in the acicular ferrite here are smaller in size than the sample from the top. Fig. 9 shows the predicted temperature profiles at four locations (B2, T2, L1, L2) as shown in Fig. 2, while Fig. 10 shows the close-up temperature profiles in the first 2000 s for the four locations (after the arc reached the respective points). The peak temperature recorded from the simulation at the three locations is slightly more than 2200 \u00b0C, which is well above the melting temperature expected for arc melting. It needs to be noted that the temperature profiles at R1 and R2 are similar to those of L1 and L2, respectively, and are not plotted in Fig. 10. The temperature history at the B2 and L1, L2 locations show repeated heating and cooling cycles due to the layer by layer deposition sequence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure1.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure1.12-1.png",
        "caption": "Fig. 1.12 Gimbal suspension system with nonorthogonal axes",
        "texts": [
            "230). Angeles [3] proposes a combination of both methods by formulating (1.230) not in terms of the coordinates of n1 , n2 and n1 \u00d7 n2 , but in terms of the coordinates of m1 , m2 and m1 \u00d7 m2 calculated from measured matrices Ai ,Bi (i = 1, 2) . 1.15 Illustrative Problems 51 The material of this section and of the next section was published in Wittenburg/Lilov [32]. Earlier contributions to the subject were made by Davenport [6] and Wohlhart [33]. In the nonorthogonal gimbal suspension system of Fig. 1.12 the inner axis has the direction n1 , and the outer axis has the direction n3 . If three rotations (n1, \u03d51) , (n2, \u03d52) , (n3, \u03d53) are carried out in this order, all three rotation axes n1 , n2 , n3 are given in the outer (base-fixed) reference frame. Let (n, \u03d5) be the resultant of this sequence of rotations. Its tensor R(n, \u03d5) is the product of the tensors of the three individual rotations (see (1.45)): R(n, \u03d5) = R(n3, \u03d53) \u00b7 R(n2, \u03d52) \u00b7 R(n1, \u03d51) . (1.238) The problem to be solved is the following",
            " aii = (nj \u00d7 nk) 2 = 1\u2212 a2i , aij = (ni \u00d7 nk) \u00b7 (nk \u00d7 nj) = aiaj \u2212 ak , a = n1 \u00b7 n2 \u00d7 n3 , a2 = 1\u2212 a21 \u2212 a22 \u2212 a23 + 2a1a2a3 = aiiajj \u2212 a2ij \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (i, j, k = 1, 2, 3 different) . (1.240) The parameters b1 , b2 , b3 represent the covariant coordinates of n . The contravariant coordinates c1 , c2 , c3 are defined through the equation n = c1n1 + c2n2 + c3n3 . They satisfy the equations 52 1 Rotation about a Fixed Point. Reflection in a Plane aci = n \u00b7 nj \u00d7 nk , a2c2i = (1\u2212 b2j )(1\u2212 b2k)\u2212 (bjbk \u2212 ai) 2 } (i, j, k = 1, 2, 3 cyclic) . (1.241) Solution: Comparison of Fig. 1.12 with Fig. 1.2b shows: If n3 , n2 , n1 form a right-hand cartesian basis e11 , e 1 2 , e 1 3 , the angles \u03d53 , \u03d52 , \u03d51 represent, in this order, the Bryan angles \u03c61 , \u03c62 , \u03c63, respectively. This particular case is characterized by the parameters ai = 0 , a = \u22121 and bi = ci (i = 1, 2, 3). The solutions \u03d51 = \u03c63 , \u03d52 = \u03c62 and \u03d53 = \u03c61 are calculated from (1.35) with the matrix elements of (1.49) with bi instead of ni (i = 1, 2, 3). In the general case, the solution is found from (1.238) as follows. Two scalar multiplications, one from the left by R(\u2212n3, \u03d53) and the other from the right by R(\u2212n1, \u03d51) , produce the equation (see the identities (1",
            "241) r1,2 = \u2223\u2223\u2223b1b3 \u2212 a1a3 \u00b1 \u221a (1\u2212 a21)(1\u2212 a23) \u2223\u2223\u2223\u221a (1\u2212 b21)(1\u2212 b23) . (1.257) \u0393 is the complete unit circle if and only if r1,2 \u2265 1 . In the case a1 = a3 = 0 , these conditions are satisfied for arbitrary quantities b1 , b3 . In the case b1 = b3 = 0 , they are satisfied if and only if a1 = a3 = 0 . Because of (1.239) this means: The solutions (1.250) for \u03d52 are real for arbitrary resultant rotations (n, \u03d5) if and only if n2 is orthogonal to both n1 and n3 . This is an important result. It means that the gimbal suspension system of Fig. 1.12 is capable of producing arbitrary angular orientations of the suspended body if and only if the axis between inner and outer gimbal is orthogonal to both the fixed outer gimbal axis and the axis between body and inner gimbal. Commonly used gimbal suspension systems have this property. Indeterminacy conditions: From Euler angles as well as from Bryan angles the phenomenon of gimbal lock is known. The angles are not fully determinate 1.15 Illustrative Problems 55 if the prescribed angular orientation of the body is characterized by gimbal lock. In the case of Euler angles, only \u03b8 and either \u03c8 + \u03c6 or \u03c8 \u2212 \u03c6 are determinate. In the case of Bryan angles, only \u03c62 and either \u03c61 + \u03c63 or \u03c61 \u2212 \u03c63 are determinate. The same phenomenon occurs here. Under certain conditions for the given quantities n , \u03d5 , n1 , n2 and n3 the gimbals in Fig. 1.12 are locked. In this case, only \u03d52 and either \u03d51 + \u03d53 or \u03d51 \u2212 \u03d53 are determinate. The derivation of these conditions is found in Wittenburg/Lilov [32]. The results can be summarized as follows. Indeterminacy occurs if the given data satisfy the conditions a3 = \u03c3a1 , b3 = \u03c3b1 , cos\u03d5 = \u03c3a2 \u2212 b21 a2 \u2212 b21 , sin\u03d5 = ac2 a2 \u2212 b21 (1.258) (\u03c3 = +1 or \u22121) . Equations (1.239) show that the leading two conditions are the orthogonality conditions n2 \u00b7 (n1 \u2212 \u03c3n3) = 0 and n \u00b7 (n1 \u2212 \u03c3n3) = 0 , respectively. The vectors n1\u2212n3 and n1+n3 are the mutually orthogonal bisectors of the angles between n1 and n3 . If the conditions (1.258) are satisfied, the angle \u03d52 and the angles \u03d51 + \u03c3\u03d53 are determined from the equations cos\u03d52 = \u03c3a2 \u2212 a21 1\u2212 a21 , cos(\u03d51 + \u03c3\u03d53) = 1\u2212 2a2c21 (1\u2212 a21)(1\u2212 b21) , sin\u03d52 = \u2212\u03c3a 1\u2212 a21 , sin(\u03d51 + \u03c3\u03d53) = 2ac1(a1b1 \u2212 \u03c3b2) (1\u2212 a21)(1\u2212 b21) . \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (1.259) If the axes of the gimbal suspension system in Fig. 1.12 are mutually orthogonal, the conditions (1.258) are identical with (1.197). In this section the problem posed in the previous section is solved by means of quaternions. Let D be the quaternion of the given resultant rotation (n, \u03d5) , and let D1 , D2 , D3 be the quaternions of the three rotations (n1, \u03d51) , (n2, \u03d52) and (n3, \u03d53) , respectively. According to Theorem 1.4 (Eq.(1.116)) these quaternions satisfy the equation D3D2D1 = D . (1.260) According to (1.107) D = ( cos \u03d5 2 , n sin \u03d5 2 ) . (1.261) 56 1 Rotation about a Fixed Point"
        ],
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    },
    {
        "image_filename": "designv10_12_0002596_s00170-018-2850-8-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002596_s00170-018-2850-8-Figure5-1.png",
        "caption": "Fig. 5 Grinding test platform",
        "texts": [
            " The wheel employed in the experiment is a resin-bonded corundum wheel (grit size 50/60) with a diameter of 400 mm and a width of 40 mm. Two Inconel 718 specimens are prepared by SLM and casting, respectively, both with a dimension of 150 mm in length, 15 mm in width, and 65 mm in height. During the grinding process, water-based cutting fluid is employed at a flow rate of 200 L/min and a pressure of 12 bar through a 100.0 mm\u00d7 1.0 mm rectangular nozzle to reduce the grinding temperature and clean the wheel surface. The grinding test platform is shown in Fig. 5. More detailed parameters for dressing and grinding are shown in Tables 2 and 3, respectively. During the grinding process, the wheel topography and the surface quality of the workpiece have always been in dynamic changes and it is impossible tomeasure them directly online in real-time. For the sake of investigating the dynamic changes of the grindability in the whole grinding process, a stepped (c)(b) Grinding Wheel Grinding Round #1 \u03c9 20\u03bcm\u00d7100 Grinding Wheel Grinding Round #2 \u03c9 20\u03bcm\u00d7100 SLM/Casting Inconel 718 Grinding Wheel Grinding Round #3 \u03c9 20\u03bcm\u00d7100 Grinding Wheel Grinding Round #4 \u03c9 20\u03bcm\u00d7100 SLM/Casting Inconel 718 SLM/Casting Inconel 718 SLM/Casting Inconel 718 Grinding Wheel SLM/Casting Inconel 718 1234 Ground Surface 1,2,3,4 Unprocessed Surface Worn Surface 1,2,3,41234 Initial Surface Radial Wear 3mm width each surface 2mm depth each step (a)Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000057_s0263574706003031-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000057_s0263574706003031-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the internal and external synergies. (a) Undisturbed motion. (b) Effect of the appearance of an unpowered DOF.",
        "texts": [
            " Finally, one may define ZMP: ZMP is the point on the support area (excluding the edge) for which Mx = 0 and My = 0, or more precisely: M inertial (without foot) x + M gravitational (without foot) x + Mx gravitational (of immobile foot) + Mexterenal x = 0 (1) M inertial (without foot) y + M gravitational (without foot) y + M gravitational (of immobile foot) y + Mexterenal y = 0. 7 It should be noted that in the early papers from this area it was still implicitly pointed out that the ground reaction force is formed as a sum of pressure forces of the ground on the foot. (See, for example ref. 8 (Fig. 3, p. 501) or ref. 5 (Fig. 1.2, p. 19)). 8 It is possible6,10 to prescribe also the motion at n \u2212 3 joints. Then, the rotational motion of the trunk about its vertical axis ensures that under the humanoid foot (in addtion to Mx = 0 and My = 0), the condition Mz = 0 is also fulfilled. The conditions Mx = 0 and My = 0 define the dynamic balance of the humanoid, whereas Mz = 0 prevents its deflection from the motion course in the case of insufficient friction between the foot and the ground. whereby the external moments result from all the external forces (wind, push, etc",
            " Note that in the situation when the arms are not engaged in any functional activity, they usually move so as to assist the waist in reducing the friction torque under the foot (feet). In this way, all n = nl + na + nn +nw joint motions (comprising reference motion) can be determined. It is quite clear that humanoid motion is realized by changing joints angles in the manner that will yield the desired relative position of the humanoid in its environment. To the periodic laws of change of joint angles \u03d5i(t), correspond the periodic laws of change \u03b2 i(t) (Fig. 1(a)), where \u03b2 i denotes the angular positions of the links with respect to the absolute coordinate frame. We call the laws of change \u03d5i(t) as internal synergy and \u03b2 i(t) as external synergy.(12)4,2. In order to control humanoid motion, the realization of internal synergy has to influence the external synergy in a unique way. As is known, one of the basic characteristics of a humanoid system is that this unique relationship can be lost because of potential rotation of the system about the foot edge and its overturning. To clarify the difference between the internal and external synergies, let us consider a highly simplified model in which reference motion is performed with the pelvis being constantly parallel to the horizontal plane and the legs moving in the planes that are always perpendicular to the ground. A sketch of this model (front view) is given in Fig. 1. If the system rotates about the foot edge (and falls), this 12 The term synergy, in the sense of a concerted and simultaneous action of the joints involved, was introduced into the terminology of locomotion biodynamics by Bernsteins.20 means that the coordinate (Fig. 1(b)) has arisen, which is \u2018uncontollable\u2019 because the corresponding DOF has no actuator. Under ideal conditions, the realization of the reference internal synergy \u03d50 i (t) means simultaneous realization of the reference external synergy \u03b20 i (t), whereby the ZMP is also in the reference position. However, perturbations are always present. Compensation for the perturbation is possible only by changing the action of the actuators of powered coordinates (\u03d5i, i = 1, . . . , n), whereby the overall system dynamics is changed. Besides, in order to ensure that the external synergy depend only on the internal synergy, the reference relationship between the humanoid and its environment has to be preserved ( = 0), i.e. there must exist a contact area (not degenerating to a line or point) between the foot and ground, as presented in Fig. 1(a). This requirement means that the condition of dynamic balance is fulfilled, which will be true if the ZMP is within the support area.(13) In the cases of disturbance under which = 0 still holds, this condition is fulfilled, so that the compensational action at the mechanism joints can directly influence the humanoid motion to return to the reference external synergy. In the case of larger disturbances, even if exact internal synergy is realized, the external synergy can be disturbed. For example, as a result of the influence of external disturbances, the locomotion mechanism may come to the position shown in Fig. 1(b), in which the support and contact with the ground are realized only at the edge of the supporting leg foot. In 13 To ensure dynamic balance, the ZMP should be within the support area (the edge excluded), and only if the ZMP is in the reference position (i.e. in the motion synthesis), such dynamic balance is termed reference balance. such case, even if desired internal synergy \u03d50 i (t) is performed perfectly, external synergy \u03b20 i (t) will deviate from desired one (the angles \u03b2i(t) will differ from the \u03b20 i (t) i.e. reference ones) due to the rotation of the complete locomotion system about foot edge. In the absence of disturbances, the external synergy \u03b2 depends only on the internal synergy angles \u03d5. To illustrate this, let us cosider, for example, only one coordinate. In Fig. 1, the trunk angle corresponding to the instantaneous external synergy is denoted as \u03b2TRUNK, and the one corresponding to the internal synergy as \u03d5TRUNK. In the absence of disturabnces, for the humanoid trunk from Fig. 1(a), we can write \u03b2TRUNK = \u03c0 2 \u2212 \u03d5TRUNK. If the disturbance is acting (Fig 1(b)), the angle \u03b2TRUNK for the upper part is not determined only by the angle \u03d5TRUNK, but also by the angle , so that the previous expression becomes \u03b2TRUNK = \u03c0 2 \u2212 (\u03d5TRUNK + ). This (very simplified) example well illustrates how the external synergy can be upset even if the internal synergy has been exactly realized. If, for any reason, the fulfillment of internal synergy is disturbed, this will reflect on the external synergy too. On the other hand, the external and not internal synergy, determines the conditions of gait repeatability with respect to the absolute coordinate frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.4-1.png",
        "caption": "Fig. 7.4 The cantilever of an atomic force microscope (AFM) is an example of compliance employed in high precision instruments",
        "texts": [
            " No Need for Lubrication Another consequence of eliminating friction is that lubricants are not needed for the motion. This is particularly important in biomedical implants, space applications, and at small scales where lubrication can be problematic. High Precision Flexures have long been used in high precision instruments because of the repeatability of their motion. Some reasons for compliant mechanisms precision are the backlash-free motion inherent in compliant mechanisms and the wear-free and friction-free motion described above. The cantilever associated with an atomic force microscope (Fig. 7.4) is an example application. Integrated Functions Like similar systems in nature, compliant mechanisms have the ability to integrate multiple functions into few components. For example, compliant mechanisms often provide both the motion function and a return-spring function. Thermal actuators are another example of integration of functions, as described later. High Reliability The combination of highly constrained motion of compliant mechanisms and wear-free motion result in high reliability of compliant mechanisms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.47-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.47-1.png",
        "caption": "Fig. 2.47 The positioning of a traction control system\u2019s sensors [MEMMER 2001].",
        "texts": [
            " Automotive Mechatronics 190 The yaw rate is a measure of an automotive vehicle's behaviour to do with the wheel\u2019s movement on its vertical z axis, in other words, tilting. It is important to measure the yaw rate for calculating the wheels\u2019 actual values of angular velocity, because when cornering, if the tilting of the wheels is not monitored, the angular velocity (speed) sensors may report incorrect data that could lead to a change in traction by the actuator when it is already satisfactory. Overall, an ATC system relies on three different sorts of sensors: angular velocity (speed) sensors, steering angle sensors, and yaw rate sensors (see Figure 2.47). When used together, they are quite effective in delivering the information required by the controller for effective ATC. Figure 2.48 exemplifies the system dynamics of a M-M drive shaft, differential, and drive wheels on on/off road surfaces affording differing levels of traction with adhesion coefficients \u03bcH and \u03bcL (high wheel and low wheel) [CZINCZEL 1995]. 2.1 Introduction 191 The torque activating from the driveshaft is disseminated equally between the wheels. The low wheel acts in response to imperfect adhesion potential by spinning during concise wheel acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003264_tvt.2020.3013342-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003264_tvt.2020.3013342-Figure1-1.png",
        "caption": "Fig. 1. The structure of the ECB.",
        "texts": [
            " In this paper, an improved ECB is taken as the research object, and the transient coupling model is studied to predict the process of the electromagnetic performance derating caused by heat accumulation. The previous water-cooled ECB with double salient poles has a water jacket integrated in the stator for heat dissipation [15]. The improved internal liquid cooling ECB, ECB for short, directly cools the stator inner ring where has the highest heat generation rate, which can keep the stator at low temperature. Rated performances and key parameters of this ECB are listed in Table I. The ECB consists of a rotor, a stator and a set of coils, as shown in Fig 1. The ECB is mounted in the sealed gearbox, and the rotor rotates with the drive shaft. The coils wound in the circumferential direction are surrounded by the rotor and stator, and are fixed on the stator. When the coils are energized, a toroidal magnetic field (B0) is generated around the coils. The salient poles are distributed on the outer ring of the rotor for magnetism gathering, and the magnetic induction on the inner surface of the stator is alternately distributed in the circumferential direction with a strong and weak order"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000776_tia.2011.2161855-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000776_tia.2011.2161855-Figure6-1.png",
        "caption": "Fig. 6. Stator flux vector and initial stator and rotor flux vectors.",
        "texts": [
            " According to the analysis in [14], the rate of change of torque at the instant in which a voltage vector is applied is given by dTe dt = C\u03a8r [V sin(\u03b8i \u2212 \u03b8r,0) \u2212 \u03c9\u03a8s,0cos(\u03b8s,0 \u2212 \u03b8r,0)] (10) where C is some constant which depends on the machine parameters and V is the magnitude of the applied voltage. \u03b8i, \u03b8r,0, and \u03b8s,0 are the stator voltage vector angle, initial rotor flux angle, and initial stator flux angle, respectively. \u03a8r and \u03a8s,0 are the rotor flux magnitude and initial stator flux magnitude, respectively (these parameters are shown in Fig. 6). The second term in (10) is independent of the applied voltage vector. Thus, the maximum rate of change of torque is determined by the first term of (10) which can be written as[ dTe dt ] max = max i {sin(\u03b8i \u2212 \u03b8r,0)} . (11) The rotor flux angle in (11) can be assumed equivalent to the stator flux angle since the slip angular velocity, in practice, is too small. Equation (11) indicates that the fastest torque response is achieved when the voltage angle is 90\u25e6 with respect to the stator flux angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000370_j.jmatprotec.2009.07.017-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000370_j.jmatprotec.2009.07.017-Figure9-1.png",
        "caption": "Fig. 9. Enlargement of irradiation spot.",
        "texts": [
            " The adhesion force was evaluated by measuring the cutting force when the consolidated structure was cut by a flat end mill. A milling machine f 70% chromium molybdenum steel powder, 20% copper alloy owder and 10% nickel powder. The mean diameter of the powder ixture was p = 25 m. Since the powder layer was loaded under ravity action only, its bulk density was 4190 kg/m3. The absorpion ratio of laser beam with a wavelength of = 1070 nm was 25% Furumoto et al., 2007). .2. Line consolidation The schematic enlargement of the laser irradiation area is shown n Fig. 9. The metal powder was deposited on the plate at a thickess of 50 m. The chalcogenide glass fiber was set at a distance of .2 mm from the laser irradiation area and at an angle of 45\u25e6 to the owdered surface. The center of the laser irradiation area always assed on the center axis of the fiber. Hence, the fiber could receive he infrared rays radiated from the laser irradiation area when the aser beam passed through the target area of the fiber. The accepance angle of the fiber used was 24\u25e6. Therefore, the passing length hrough the target area was 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003593_iemdc47953.2021.9449566-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003593_iemdc47953.2021.9449566-Figure3-1.png",
        "caption": "Fig. 3. Functional model after production.",
        "texts": [],
        "surrounding_texts": [
            "As shown in Figs. 2 and 3, hollows are implemented into the classical shaft region. This leads to decreased rotor mass and inertia. Furthermore, the transition region between the active part and the bearings is conical-shaped in order to conduct the forces properly and to reduce mechanical stress concentration on the path from the rotor surface to the coupling. The closed pipe profile is particularly suitable for absorbing bending and torsional loads."
        ]
    },
    {
        "image_filename": "designv10_12_0002083_j.mechmachtheory.2014.08.009-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002083_j.mechmachtheory.2014.08.009-Figure1-1.png",
        "caption": "Fig. 1. A cylindrical worm pair.",
        "texts": [
            " Generally speaking, as for an enclosed cylindrical worm gearing, the contact fatigue reliability is usually, more or less, higher than the bending fatigue reliability. In addition increasing the center distance and the module is beneficial to improve the reliability. Meanwhile the greater variance of the design parameters may lead to lower reliability as to a worm gear pair. \u00a9 2014 Elsevier Ltd. All rights reserved. Keywords: Reliability Sensitivity to reliability Worm drive Moment Edgeworth series 1. Introduction The cylindrical worm drive, as shown in Fig. 1, is an important and fundamental machine element, which is widely used in almost every industrial sector. The failure ofwormpairs often leads to a poor performance of the related parent systems, and sometimes even incurs serious accidents and subsequently great economic losses. Therefore, the reliability design of a worm gearing should have important implications but the relevant study has rarely been reported in the mainstream journals for a long time. In principle, it is not easy to calculate the reliability of a worm pair accurately"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.26-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.26-1.png",
        "caption": "Fig. 15.26 Wheels touching each other from the outside. For the straight-line position shown the parameters are r0 = \u22123 , r1 = 2 , b = 4",
        "texts": [
            " In this case, P(0) is tracing twice per period the oval formed by the three elliptic segments (see the arrows). From this it follows that the two areas denoted A2 and A3 are identical and that, furthermore, A(0) = \u22122A1 = A(1) \u2212 \u03c0 2 . With the side length L of the triangle A(1) = L2 \u221a 3/4 and = L \u221a 3/4 . Hence the area of the oval is A1 = 1 32L 2(3\u03c0 \u2212 4 \u221a 3) . Trochoids are trajectories of points C fixed on a planetary wheel 1 which is rolling on a stationary sunwheel 0 . In Figs. 15.26 and 15.27 all possible arrangements of wheels are shown. In Fig. 15.26 the wheels are touching each 496 15 Plane Motion other from the outside, and in Fig. 15.27 one wheel is inside the other. The one inside may be either wheel 1 or wheel 0 (see the small figure). The point C fixed on wheel 1 is located at a radius which is either smaller than or equal to or larger than the radius of wheel 1 . Depending on the arrangement of the wheels and on the location of C on wheel 1 trochoids come in many different shapes. This makes them interesting for engineering applications",
            " Wheel 0 is 500 15 Plane Motion touched by wheel 1 either in both mechanisms from the outside (Fig. 15.29) or in both mechanisms from the inside (Fig. 15.30). Trochoids generated by mechanisms of the former type are called epitrochoids, and trochoids generated by mechanisms of the latter type are called hypotrochoids. Epitrochoids and hypotrochoids alike are divided into three families: 1. Trochoids have double points if in the first generation the generating point C is outside the circle of wheel 1 , i.e., if |b/r1| > 1 . Such trochoids are called curtate trochoids (Fig. 15.26 and the limac\u0327on of Pascal in Fig. 15.8a ). 2. Trochoids have cusps on the circumference of wheel 1 if the generating point C is located on the circumference of wheel 1 (in both generations; |b/r1| = 1 ). Such trochoids are called cycloids (either epicycloids or hypocycloids). 3. Trochoids have neither double points nor cusps if in the first generation point C is inside of wheel 1 , i.e., if |b/r1| < 1 . Such trochoids are called prolate trochoids (Fig. 15.28 and the limac\u0327ons of Pascal in Figs",
            " The vertices of the evolute z2 coalesce with the cusps of z1 . Figure 15.35 shows the evolute z2 and in dashed lines the wheels of the new system. Further properties of cycloids and of trochoids in general are found in Wunderlich [30] and Strubecker [28]. Higher-order trochoids were investigated by Wunderlich [29]. An ordinary cycloid8 is the trajectory of an arbitrary point (not just a circumferential point) fixed on a circular wheel which is rolling along a straight line. This is the situation when in Fig. 15.26 r0 is infinite. In what follows, the notation shown in Fig. 15.37 is used. The radii of the circle and of point C are denoted r and b respectively ( r, b > 0 ). The angle of roll of the circle is \u03d5 (positive clockwise). The position \u03d5 = 0 is defined to be the position when the center as well as point C is on the imaginary axis with C being below the center of the circle. In this position these two points have the complex numbers i r and z = i (r \u2212 b) , respectively. In the position \u03d5 (arbitrary) the numbers are r\u03d5+ i r and 7 J",
            " The indiscriminate name ordinary cycloid is much older than this convention. The cusped ordinary cycloid has in the cusps the acceleration coordinates x\u0308 = 0 , y\u0308 = r\u03d5\u03072 . (15.134) Another property was shown in the example illustrating Fig. 15.21: In every position \u03d5 the point of rolling P is midpoint between the generating point C and the center of curvature M . The inverse motion of a circle rolling along a straight line is the rolling of a straight line g on a fixed circle k of radius r0 . This is the situation when in Fig. 15.26 r1 is infinite. In Fig. 15.39 the line g is tangent to k at point A . To be investigated are the trajectories traced by the point B fixed on g and by the point P rigidly attached to g at the distance h on the perpendicular 508 15 Plane Motion through B . In the case h < 0 , P is located on the other side of g , i.e., on the side toward the circle k . First, the trajectory of B . It is an epicycloid. Point A is the instantaneous center of rotation of g and, therefore, the center of curvature of the trajectory of B "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001144_20110828-6-it-1002.03266-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001144_20110828-6-it-1002.03266-Figure2-1.png",
        "caption": "Fig. 2. Fans tilted longitudinally 90\u25e6 for high speed forward flight.",
        "texts": [
            " OAT composes a differential or opposed lateral tilting element for generating gyroscopic and fan-torque pitching moments, and the collective longitudinal tilting component for producing them from thrust vectors, as well as for controlling horizontal motion. This mechanism can contribute more than just stability and control in the conventional sense. Using the dual-axis version makes it possible to have an independent control of all six axes Gress (2003). High Speed Flight: Transition to high speed flight or airplane mode is achieved by tilting the fans longitudinally 90 degrees Fig. 2, during which longitudinal stability is maintained by lateral tilting and by the horizontal stabilizer at the rear of the aircraft. Because VTOL air vehicles do not require runways, their lifting surface-areas do not need be as large as those of a conventional airplane. There would be no need for conventional control surfaces (except the horizontal stabilizer) and associated dual control system, thereby reducing weight, complexity, and cost. And, because the entire wing-halves (fan shrouds) tilt, and differential longitudinal tilting of the fans generates a gyroscopic rolling moment (whether in hover or airplane mode), roll rates of the vehicle will be substantially higher than those using a conventional wing with ailerons"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000421_cec.2007.4424647-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000421_cec.2007.4424647-Figure4-1.png",
        "caption": "Fig. 4. The microrobot \u2019Jasmine III plus\u2019.",
        "texts": [
            " Robots, when aggregating into an organism, can do it in different ways and so emerge different functionality. In Fig. 3 we demonstrate two different shapes (octopus-like and snake-like) which have different locomotion strategies. The question is how to control the building of shapes and so emergent functionality of the organism ? Evidently, that in this stage we have more questions than answers. We expect to clear these questions in a further research. Jasmine III plus. For performing the swarm-experiments and testing the embodiment concept we used the microrobots Jasmine, see Fig. 4. It is a public open-hardware development at www.swarmrobot.org, having a goal of creating a simple and cost-effective microrobotic platform and knowledge exchange in the swarm robotics community. The micro-robot is 26\u00d726\u00d720mm, uses the two Atmel AVR Mega microcontrollers: Atmel Mega88 (motor control, odometry, touch, color and internal energy sensing) and Mega168 (communication, sensing, perception, remote control and user defined tasks). Both micro-controllers communicate through highspeed two-wired TWI (I2C) interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000709_978-3-642-00629-6_14-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000709_978-3-642-00629-6_14-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the ship hull",
        "texts": [
            " They demonstrate the capability of the nonlinear six degree-of-freedom model in predicting the ship response in a turning-circle maneuver. Moreover, they illustrate the controlled response of the ship, which is generated by implementing the proposed controller on the reduced-order model. The results exhibit a robust performance of the controller in the presence of significant modeling uncertainties and environmental disturbances. Finally, the work is summarized and the main conclusions are drawn. The ship is treated as a rigid body having six degrees of freedom, namely, surge, sway, heave, roll, pitch and yaw (see Fig. 1). Two coordinate systems have been used. The first one is an inertial frame { }, ,X Y Z whose origin is located at an arbitrary point on the calm sea surface. The second coordinate system, { }, ,o o ox y z , is a non-inertial, body-fixed coordinate system attached to the ship at point o, which coincides with the center of floatation of the ship. The ( ),o ox z \u2212 plane is chosen to coincide with the vertical plane of symmetry of the ship hull. The ox \u2212 and oy \u2212 axes are directed towards the bow and the starboard of the ship"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000920_s11740-011-0349-3-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000920_s11740-011-0349-3-Figure1-1.png",
        "caption": "Fig. 1 Modeling of a linear guide with CoFEM",
        "texts": [
            " Fortunately some researchers recognized the potential and are developing the method in most cases for MBS, [1]. In this work the concept is being developed for FEM under the name \u2018\u2018Component Oriented Finite Element Modeling\u2019\u2019 or A. Dadalau (&) K. Groh M. Reu\u00df A. Verl Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), Stuttgart, Germany e-mail: alexandru.dadalau@isw.uni-stuttgart.de URL: http://www.isw.uni-stuttgart.de/ shortly CoFEM, [2]. For the considered linear guide system the modeling process with CoFEM is depicted in Fig. 1. The assembly of subcomponents is done automatically with the help of implemented algorithms and graphical user interface in the FEM software ANSYS. The assembled model is complex due to the 114 contacting surfaces (e.g. contact between balls and rails, runner block and rail, screws and linear guide). Nevertheless due to the modular modeling concept repeating components such as balls need to be modeled only once, whereat the multiple assembling of the same component at different positions and with different orientations is done automatically by the implemented algorithms. The aim of this work is to find more efficient ways of simulating the linear guide system shown in Fig. 1. As for this purpose many tests are required, simulating the full model in Fig. 1 would be very inefficient. A slice model of the full model is used instead. Then mesh convergence testing is performed in order to provide an accuracy of computed displacement below 1%. The converged mesh, boundary conditions and applied load are depicted in Fig. 2. From the mesh convergence testing on the slice model it can be concluded that already 1% accuracy requires a large number of DOF for the full model. The highest amount of DOF is consumed by the rolling elements, in this case by the balls. A single ball model would require 235,000 DOF. Simulating a quarter of the linear bearing in Fig. 1 would require 12 balls, thus leading to 2.82 millions DOF just for the balls. Therefore new methods for reducing the amount of DOF needed for the balls are proposed and presented here. Some of the presented methods preserve the capability of modeling rolling contact of the full model. As it will be shown this capability plays an important role for the overall stiffness of the considered linear guide system. In Fig. 2 the slice model of the linear guide system with within 1% converged mesh is depicted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003174_s11012-019-01115-y-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003174_s11012-019-01115-y-Figure2-1.png",
        "caption": "Fig. 2 Healthy external gear tooth when the tooth number is greater than 41: a approach process and b recess process",
        "texts": [
            " [5, 36], Hertzian stiffness of the ith pair of gear teeth can be written as follows: 1 khi \u00bc 1:275 L0:8F0:1 i E0:9 ;Fi \u00bc F LSRi \u00f09\u00de Fillet-foundation stiffness is an important part of the TVMS and can be calculated as follows: 1 kf \u00bc cos2am EL L uf Sf 2 \u00feM uf Sf \u00fe P \u00f01\u00fe Qtan2am\u00de ( ) \u00f010\u00de The parameters can be found in Ref. [37]. When the tooth number is greater than 41, the tooth profile of the external gear tooth is involute curves which go straight to the root circle (curvesMI and NJ), as shown in Fig. 2. Compared to Case 1, the expressions of the effective length d and section width hx in Case 2 can be modified as follows [9]: d \u00bc Rb\u00bd\u00f0a1 \u00fe a2\u00de sin a1 \u00fe cos a1 Rr cos a4 hx \u00bc Rb\u00bd\u00f0a2 a\u00de cos a\u00fe sin a \u00f011\u00de Using the derivation procedures similar to those in Case 1, the TVMS of the external gear tooth in Case 2 can be derived for approach process and recess process. Meanwhile, Hertzian stiffness and filletfoundation stiffness remain unchanged. Approach process: 1 kb \u00bc Z a5 a1 3 1\u00fe h1 \u00fe h2 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2EL a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3 da 1 ks \u00bc Z a5 a1 1:2 1\u00fe m\u00f0 \u00deh22 a2 a\u00f0 \u00de cos a EL a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd da 1 ka \u00bc Z a5 a1 h23 a2 a\u00f0 \u00de cos a 2EL a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd da \u00f012\u00de Recess process: 1 kb \u00bc Z a5 a1 3 1 h1 \u00fe h4 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2EL a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3 da 1 ks \u00bc Z a5 a1 1:2 1\u00fe m\u00f0 \u00deh24 a2 a\u00f0 \u00de cos a EL a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd da 1 ka \u00bc Z a5 a1 h25 a2 a\u00f0 \u00de cos a 2EL a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd da \u00f013\u00de 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003050_j.jmatprotec.2020.116745-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003050_j.jmatprotec.2020.116745-Figure5-1.png",
        "caption": "Fig. 5. the schematic (a) and experimental set-up (b) of the high-speed imaging system.",
        "texts": [
            " 4(a), the wire tip was placed at the rear region of the molten pool, meaning most of the laser beam was overlapped with the wire. (2) \u2212d/2<w<0, as shown in Fig. 4(a), the wire tip was placed at the leading region of the molten pool, meaning the wire was only partially overlapped with laser beam. A high-speed imaging system was established to observe the wire melting behaviors during the deposition with typical operating parameters and different correlations between wire and laser beam. The schematic and experimental set-up of the high-speed imaging system was shown in Fig. 5(a) and (b). The camera (Photron Fastcam mini UX 100 at a frame rate of 4000 f/s) and illuminator (MDL-N-808 with a wavelength of 808 nm) were located on the two sides of the laser head, which were perpendicular to the scanning direction and had an angle of 70\u00b0(\u03b2)and 60\u00b0(\u03b3) with respect to the horizontal surface. The typical processing parameters for investigating the wire melting characteristics were illustrated in Table 2. After the observation of the wire melting behaviors during laser deposition, the experimental results showed that different wire transfer modes were obtained under different distances between wire tip and laser beam, the details were discussed in part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002553_j.cirp.2018.04.087-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002553_j.cirp.2018.04.087-Figure2-1.png",
        "caption": "Fig. 2. Workpiece produced in this study.",
        "texts": [],
        "surrounding_texts": [
            "the L in\nthe for ner the the y of\nED ser\nthe ugh . By ing ring\nCIRP Annals - Manufacturing Technology xxx (2018) xxx\u2013xxx\nAn This The d to D is pact\nIRP.\nEffects of cladding path on workpiece geometry and impact toughness in Directed Energy Deposition of 316L stainless steel\nDaisuke Kono a,*, Akihiro Maruhashi a, Iwao Yamaji a, Yohei Oda b, Masahiko Mori (1)b\naDepartment of Micro-Engineering, Graduate School of Engineering, Kyoto University, Kyotodaigaku Katsura, Nishikyo-ku, Kyoto 615-8540, Japan bDMG MORI CO., LTD., 2-35-16 Meieki, Nakamura-ku, Nagoya, Aichi 450-0002, Japan\n1. Introduction\nAdditive manufacturing (AM) using the laser beam is expected to be an effective production method for high value products having a complex geometry in various industries. One of the latest CIRP keynotes summarizes AM technologies and related research trends [1]. Selective Laser Melting (SLM) is the most popular AM method. However, Directed Energy Deposition (DED) has many advantages such as repair and feature addition to an existing workpiece, large build capacity, and compatibility with laser heat treatment.\nFor industrial application of AM, the product quality includes the geometric accuracy and mechanical properties. The cladding path (trajectory) is an important factor because it influences the workpiece quality. In DED, it is widely known that the workpiece geometry is affected by the cladding path. In particular, an inappropriate cladding path easily deteriorates the geometric accuracy at the workpiece corner. Fundamental studies have been conducted to model the geometry of a single deposition line in DED [2,3]. However, the interaction between the adjacent lines should be taken into account to clarify the geometry deformation of practical thick workpieces consisting of several lines. In SLM, the geometric accuracy of the workpiece is evaluated using a bench mark test to investigate the optimal deposition condition [4]. The mechanism of the accuracy deterioration has not been discussed much.\nThe mechanical properties of 316L stainless steel produced by AM are a popular research topic. The studies on SLM cover a variety of criteria, such as the tensile strength [5\u20137], hardness [6,7], and\nthe impact toughness is another important factor when product is employed to vital parts, the impact toughness of 316 DED has not been reported.\nThis study investigates the influence of the cladding path on workpiece quality of 316L stainless steel. The corner geometries different cladding paths are compared. The cause of cor deformation is discussed on the cross section image of workpiece. Charpy impact tests are conducted to investigate impact toughness of the workpiece. The orientation dependenc the toughness is also discussed.\n2. Deposition with different cladding paths\n2.1. Method\nIn this study, 316L stainless steel powder was deposited by D method. The schematic of DED is illustrated in Fig. 1. The la beam is irradiated from the laser head onto the workpiece, and irradiated area locally melts. 316L steel powder is supplied thro the coaxial nozzle with an Argon carrier gas to the melt pool feeding the laser head, a metal line is deposited along the cladd path. Argon is used as the shielding gas to avoid oxidization du\nA R T I C L E I N F O\nKeywords: Additive manufacturing Laser Stainless steel\nA B S T R A C T\nThe cladding path in Directed Energy Deposition (DED) influences the workpiece quality. inappropriate cladding path easily deteriorates the geometric accuracy at the workpiece corner. study investigated the influence of the cladding path on the workpiece quality of 316L stainless steel. corner geometries for different cladding paths were compared. Charpy impact tests were conducte investigate the impact toughness of the workpiece. The impact toughness of 316L manufactured by DE comparable to the conventional material. The simple one directional path decreased the im toughness by approximately 20% compared to the toughness for bidirectional paths.\n\u00a9 2018 Published by Elsevier Ltd on behalf of C\nContents lists available at ScienceDirect\nCIRP Annals - Manufacturing Technology\njournal homepage: http: / /ees.elsevier.com/cirp/default .asp\nimpact toughness [5\u20137]. In DED, the tensile strength and hardness have been evaluated [8,9]. The tensile strength for a DED product is comparable to the cast and annealed wrought materials. Although\n* Corresponding author.\nE-mail address: kono@prec.kyoto-u.ac.jp (D. Kono).\nPlease cite this article in press as: Kono D, et al. Effects of cladding path on workpiece geometry and impact toughness in Directed Energy Deposition of 316L stainless steel. CIRP Annals - Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.087\nhttps://doi.org/10.1016/j.cirp.2018.04.087 0007-8506/\u00a9 2018 Published by Elsevier Ltd on behalf of CIRP.",
            "depo is us\nF geom Sect show scan dire over was at th wer was\n2.2.\nT\nPatt\nPatt\nPatt\nD. Kono et al. / CIRP Annals - Manufacturing Technology xxx (2018) xxx\u2013xxx2\nPle En\nsition process. A diode laser with a maximum power of 2 kW ed. The laser spot diameter is 3 mm. ig. 2 shows the workpiece geometry produced in this study. The etry was decided for producing Charpy test pieces described in ion 3. The workpiece was produced using eight cladding paths n in Fig. 3. The cladding paths were determined from two ning patterns in XY-plane and four layering patterns in Zction. The pitch of four lines in the same layer was 3 mm. The lap of lines was nominally 0% because the deposited line width approximately 3 mmat20 C.The depositionwasstoppedfor 3 s e start/end of each line for cooling. The laser power and feed rate e 2 kW and 1000 mm/min, respectively. The powder federate\n13.1 g/min. The height of the layer was 0.46 mm.\nGeometry of deposited workpiece\nhe results are classified into the following 3 patterns.\nern 1 No severe distortion : O2, R2.\nern 2 Deterioration at side AB or CD : O1, O3, R1, R3.\nern 3 Distortion at corner A or C : O4, R4.\nXY-plane in this experiment. The pictures of produced workieces are shown in Fig. 4. The deterioration at corners A or C occurs for O4 and R4 paths only in the higher layers. On the lower side of the workpiece, the corner geometry is comparable to that for O2 and R2 paths which have no severe distortion.\nThe result shows that the layering patterns in the Z-direction have a larger influence than the scanning patterns. The reason of the corner geometry deterioration is discussed in the following sections.\n2.3. Deterioration at side AB or CD\nThe deterioration in Pattern 2 is caused by the accumulation of the single line geometry. Fig. 5 shows the profile of a single deposition line. The start of the line is 0.1 mm higher than the nominal height because the feed motion was instantaneously stopped at the start of the laser irradiation.\nThe end of the line is concave and approximately 0.2 mm lower than the nominal height because the tail of the melt pool does not pass through the end. Fig. 6 shows the schematic of the deposition. The melt pool has the tail in the back of the laser spot. The increment of the workpiece height is achieved after the tail passes. The decrease of the layer height is accumulated in cladding paths resulting in Pattern 2. The scanning direction in adjacent layer should be opposite so as to cancel this effect.\n2.4. Distortion at corner A or C\nThe cross section of the workpiece is observed to investigate the start of the distortion. Fig. 7 shows the cross section near corner A. The test piece was mirror polished and etched for 1 min using aqua regia solution. In the 25th layer, the deposition line still has a certain thickness. However, in the 31st layer, the deposition line is showing distorted features. Thus, the distortion started from the 25th to 30th layer.\nThe reason of this distortion is assumed to be the deposition on an inclined surface resulting from the convex shape of the workpiece as shown in Fig. 8. Although the line overlap is set to 0% in this experiment, the overlap occurs and increases because the\nase cite this article in press as: Kono D, et al. Effects of claddin ergy Deposition of 316L stainless steel. CIRP Annals - Manufactu\nmelt pool becomes larger due to the increase in the fundamental workpiece temperature during the deposition. In an additional experiment, the line width increased linearly with the fundamental workpiece temperature to approximately 3.5 mm at 900 C.\nIn addition to the effect of the inclined surface, the large melt pool resulting from the high temperature at the corner accelerates the distortion. The cladding paths O4 and R4 have a reciprocation motion at the corners A and C, respectively. The workpiece temperature at these corners increases because the cooling time is short.\ng path on workpiece geometry and impact toughness in Directed ring Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.087",
            "d is ard cm2 and ere The and y of cm2 lose\ny is 20\u2013 y of ows\nfor for red ith\nper an rea rger\nure ross . In are ary. y is sily the ack ne.\nD. Kono et al. / CIRP Annals - Manufacturing Technology xxx (2018) xxx\u2013xxx 3\nIn this study, an undistorted workpiece is obtained using cladding paths O2 and R2. However, these paths also have a possibility of workpiece distortion due to the unavoidable convex shape of the workpiece which is resulting from an increased line overlap. A fundamental solution is to avoid the convex shape of the workpiece. The control of the layer height or width by the control of the laser power density and powder flow rate, considering the effect of the fundamental workpiece temperature on the deposited line geometry, is effective to avoid the distortion.\n3. Charpy impact test\n3.1. Experimental method\nCharpy impact tests were conducted to investigate the influence of cladding paths on the impact toughness of the workpiece. The orientation dependency of the toughness was also investigated. Three cladding paths, which are R2, O1 and O4, were selected for producing the Charpy test pieces. These paths correspond to the workpiece geometry patterns described in Section 2. Fig. 9 shows how the test piece was produced from the deposited workpiece. Charpy U-notch test pieces according to ISO 148-1 were used in this test. The dimensions of the test piece are 10 10 55 mm3. For the horizontal test piece, two test pieces were produced from upper and lower parts of the same workpiece to investigate the influence of the temperature history. They were called test piece H (High) and test piece L (Low), respectively. The vertical test piece was produced only by R2. The notch was fabricated in rough by wire electrical discharge machining and finished by machining. Charpy impact tester with a maximum energy of 300 J was used. Three test pieces were produced for each condition.\n3.2. Experimental result\nThe energy absorbed by the test piece was measured an shown in Fig. 10. The errorbar represents twice the stand deviation. The average value of the absorbed energy was 112 J/ for R2 path. The absorbed energies of typical 316L steel equivalent cast (ASTM CF-3M) without a heat treatment w reported as 169 J/cm2 and 62\u201365 J/cm2, respectively [10]. impact toughness for R2 path is 70% larger than that of the cast 34% smaller than the typical 316L steel. The absorbed energ 316L steel manufactured by SLM was reported to be 112\u2013140 J/ for machined notches [7]. The impact toughness for R2 path is c to that of the SLM material.\nThe effect of test piece orientation on the absorbed energ less than 10% for R2 path while this effect has been reported as 200% in SLM [5,6]. The difference between the absorbed energ test pieces L and H is less than 10% which is small. This result sh the uniform toughness of the produced workpiece.\nTheabsorbedenergy forO1claddingpathissmaller thanthose R2 and O4 paths by approximately 20%. To understand the reason this, a fractured surface was observed. Fig. 11 shows the fractu surface. Three workpieces were selected from the workpieces w small value of toughness and 90 J/cm2 or less absorption energy unit area and workpieces with high toughness value having absorption energy per unit area of 120 J/cm2 or more. The larger a of the gloss fractured surface shown in Fig. 11(b) shows the la percentage of the brittle fracture.\nThe cross section images of the ductile and brittle fract surfaces in the XY-plane are shown in Fig. 12. In Fig. 12(a), the c section of dimples, indicating the ductile fracture, are observed Fig. 12(b), columnar sub-grains and their cross sections observed. The brittle fracture was observed at the grain bound The columnar grain has an anisotropic ductility. The ductilit lower in the transverse direction because the crack ea propagates in the longitudinal grain boundary. Therefore, smaller toughness for O1 path could be explained by the cr propagation in the boundary of grains oriented in the XZ-pla\nPlease cite this article in press as: Kono D, et al. Effects of cladding path on workpiece geometry and impact toughness in Directed Energy Deposition of 316L stainless steel. CIRP Annals - Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.087"
        ]
    },
    {
        "image_filename": "designv10_12_0000982_rnc.1820-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000982_rnc.1820-Figure1-1.png",
        "caption": "Figure 1. Kinematic car model.",
        "texts": [
            " Remark 2 From the Proof, it is concluded that adaptive approach can also reduce the chattering effect if the parameter takes a small value. Remark 3 The implementation of the proposed controller requires real time estimation of the higher order total output derivatives The problem is solved by arbitrary-order robust exact finite time convergent differentiators. The r-order sliding controller combined with the .r 1/-order differentiator produces an output feedback universal controller for SISO processes with permanent relative degree [9, 18]. This part displays the control of a car (Figure 1). It has been used to verify the control strategy of HOSMC in [18, 22]. Here, the effectiveness of the proposed controller is proved by using the car control. The mathematical model of the car is formulated as Px1 D v cos.x3/ Px2 D v sin.x3/ Px3 D v=L tan.x4/ Px4 D u , (45) with x1 and x2 being the Cartesian coordinates of the rear-axle middle point, x3 the orientation angle, x4 the steering angle, v the longitudinal velocity, L the length between the two axles (LD 5 m), and u the control input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003174_s11012-019-01115-y-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003174_s11012-019-01115-y-Figure6-1.png",
        "caption": "Fig. 6 Spalled external gear tooth when the tooth number is less than 41: a approach process and b recess process",
        "texts": [
            "1 Spalling defect is on the external gear When the spalling defect appears on the external gear, two cases will be discussed in detail. The first case is that the tooth number is less than 41. The second case is that the tooth number is greater than 41. To model the spalling defect, a rectangular spall with dimensions ls\u00f0length\u00de ws\u00f0width\u00de hs (depth) is illustrated in Fig. 5. In the spalling area, the length of contact Ls, area of the cross section As and area moment of inertia Is can be modified as follows: Ls \u00bc L ls As \u00bc 2hxL hsls Is \u00bc 2 3 hx 3L 1 12 hs 3ls \u00f024\u00de When the tooth number is less than 41, as shown in Fig. 6, the spalling defect has modified the expressions of Ls, As and Is, as demonstrated in Eq. (24). Substituting these equations into Eq. (4), the TVMS of the external gear tooth with the spalling defect under sliding friction can be derived for approach process and recess process. Approach process: 1 kb \u00bc 1\u00fe h1 h2 Rr=Rb\u00f0 \u00de cos a3\u00bd 3 1\u00fe h1 h2 cos a2\u00bd 3 2ELh2sin 3a2 \u00fe Z a2 a1 3 1\u00fe h1 \u00fe h2 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3L hs= 2Rb\u00f0 \u00de\u00bd 3ls n oda 1 ks \u00bc 1:2 1\u00fe m\u00f0 \u00deh22 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd EL sin a2 \u00fe Z a2 a1 1:2 1\u00fe m\u00f0 \u00deh22 a2 a\u00f0 \u00de cos a E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda 1 ka \u00bc h23 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd 2EL sin a2 \u00fe Z a2 a1 h23 a2 a\u00f0 \u00de cos a 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda \u00f025\u00de Recess process: 1 kb \u00bc 1 h1 h4 Rr=Rb\u00f0 \u00de cos a3\u00bd 3 1 h1 h4 cos a2\u00bd 3 2ELh4sin 3a2 \u00fe Z a2 a1 3 1 h1 h4 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3L hs= 2Rb\u00f0 \u00de\u00bd 3ls n oda 1 ks \u00bc 1:2 1\u00fe m\u00f0 \u00deh24 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd EL sin a2 \u00fe Z a2 a1 1:2 1\u00fe m\u00f0 \u00deh24 a2 a\u00f0 \u00de cos a E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda 1 ka \u00bc h25 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd 2EL sin a2 \u00fe Z a2 a1 h25 a2 a\u00f0 \u00de cos a 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda \u00f026\u00de Hertzian stiffness depends on the length of contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000281_978-3-540-88464-4_2-Figure2.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000281_978-3-540-88464-4_2-Figure2.2-1.png",
        "caption": "Fig. 2.2. a) Schematic plot of insect leg morphology and approximate position of some mechanoreceptors, front view. b) joint between thorax and coxa, front view. c), d) two close ups showing the dorsal hair plate situated at the dorsal basis of the coxa (view from anterior). Forward movement of the coxa would move the hairs further below the membrane of the thoracic-coxal joint.",
        "texts": [
            " Most important for the investigation of the walking system of insects is the fact that each hemiganglion contains all necessary neurons for processing sensory information from the adjacent leg and all inter- and motoneurons for the production of a cyclic motor output to the muscles of the adjacent leg. Each abdominal segment also contains its own ganglion, except for the first few which might be fused with the metathoracic ganglion and the terminal ganglion which is again a fused ganglion from several segments. The main morphological characteristic of arthropods, specifically insects, is their exoskeleton. Therefore the muscles are arranged inside the tube-like skeleton (for details on muscular properties see Section 2.8: Actuators). The geometry of the leg is shown in Fig. 2.2. It usually contains five segments, coxa, trochanter, femur, tibia and tarsus. In the stick insect, as in many other insects, trochanter and femur form one rigid segment whereas, e.g., in the cockroach this joint is moveable to some extent. The coxa-trochanter (\u03b2 -) and femur-tibia (\u03b3-) joints are simple hinge joints with one degree of freedom corresponding to elevation and extension of the tarsus, respectively. The thorax-coxa (\u03b1-) joint, which connects the leg to the body, is more complex, but most of its movement is in a rostrocaudal direction around a fixed axis described by the Euler angles \u03c6 and \u03c8 ",
            " Morphologically, joint position and movement sensors come in different forms. The most obvious ones are the hair plates, groups of sensory hairs that are situated at joints in such a way that during movement of the joint the individual sensory hairs are bent by the soft joint membrane. The farther the joint is moved, the more each individual hair is bent and the larger is the number of hairs being bent. Such hair plates can be found at the thoracic-coxal (\u03b1-) joint and at the coxa-trochanter (\u03b2 -) joint (Fig. 2.2). Another important type of position sensors is the chordotonal organ. This is formed by sensory cells situated within partly elastic, partly rigid structures that span the joint. Movement of the joint leads to elongation or relaxation of the elastic part and of the sensitive structures of the sensory cells. An intensively investigated example is the femoral chordotonal organ [14] that monitors the femur-tibia (\u03b3-) joint. Chordotonal organs can also be found at the thorax-coxa (\u03b1-) joint with in part complex mechanical structures [121]",
            " Strong coupling leads to fixed phase relations, termed absolute coordination by v. Holst, whereas weak coupling still shows a preferred phase value, but other phases values might also occur (\u201crelative coordination\u201d). How are these legs coupled? The underlying control system has been studied in detail for insects, crayfish and cat. There are different local rules that are active between directly neighboring legs. Three such rules have been describe for the crayfish, five similar, but different in detail, for the stick insect (see Fig. 2.2; [47]. For the cat, four mechanisms have been described [60]). Fig. 2.14 shows the effect of a brief interruption of stance movement of one leg in the crayfish. The leg resumes normal coordination by shortening or prolonging the swing movement and/or the stance movements of some of the neighbouring legs. To illustrate the evaluation procedure, two responses to disturbances of legs 3 and 4 are shown. The situations in which prolongation of a swing occurs are presented in Fig. 2.16 in a form similar to a phase-response curve",
            "13, but as two antagonistic channels that drive the two antagonistic muscles of one joint. Furthermore, both parallel antagonistic channels are connected via high-pass filtered mutual inhibition (for details see [48]). This circuit is assumed to exist for each joint (for possible connections between joints of one leg, see Fig. 2.13). What are the properties of such an antagonistic structure? As an example, in Fig. 2.24 b retractor and protractor muscles move the thoracic-coxal joint (\u03b1-joint in Fig. 2.2). After central activation is switched on (Fig. 2.24 b, arrow), sensory input drives rhythmic motor output like that for swing-net and stance-net in Fig. 2.13. In the simulation, clear transitions between activations of agonist and antagonist are found even when the input values are very small (Fig. 2.24 b, third stance period or sixth swing period) or when the input shows soft transitions as in the case of a sinusoidal wave (not shown). These sharp transitions result from the inhibitory connections that form a kind of winner-take-all system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.60-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.60-1.png",
        "caption": "Fig. 3.60 Cross-section diagram of electro-mechanical brake (EMB) [L\u0170DEMANN 2002].",
        "texts": [],
        "surrounding_texts": [
            "Figure 3.58 shows the layout of a friction (a) disc EMB with the conven- tional rotary brushed DC-AC mechanocommutator brake-force-actuator motor [BALZ ET AL. 1996], designed by ITT Automotive, as well as (b) disc EMB and (c) ring EMB with the short-stroke linear tubular brushless DC-AC macrocommutator IPM magnetoelectrically-excited brake-force-actuator motor [FIJALKOWSKI AND KROSNICKI 1994]. 3.9 Electro-Mechanical Friction Disc, Ring and Drum Brakes 533 In these types of EMB, force is applied equally to both sides of the disc or ring rotor and braking action is achieved through the frictional action of inboard and outboard brake friction pads against the disc or ring rotor. The pads are contained within a calliper, shown in Figure 3.57, as is the wheel brake actuator. Although not a high-gain type of friction EMBs, disc or ring EMBs have the advantage of providing relatively linear braking with lower susceptibility to fading than friction drum EMBs. The E-M actuator is a disk EMB working on the calliper-principle. The E-M actuator\u2019s housing is connected firmly to the vehicle\u2019s steering knuckle. Both brake pads are fixed to the fist with one degree of freedom towards the active line of the clamping force. Figure 3.59 shows an example of a prototype of an EMB and its mounting in the vehicle [PETERSEN 2003]. Figures 3.58a and 3.60 show a cross-section diagram of an example of a prototype of the EMB actuator E-M motor. The E-M actuator is a conventional rotary brushless DC-AC mechanocommutator brake-force-actuator motor. The rotor gear forms the sun wheel of the planetary gear at the pad-sided end. The planet wheels of the planetary gear are in mesh with the internal-geared wheel, bolted in the brake cabinet, and power the planet carrier. Automotive Mechatronics 534 A planetary roller gear transforms the rotary motion into a translatory motion. The gear's spindle is hollow and contains a force measurement device as well as a pressure pin for the decoupling of rotary movements acting on the spindle. When activating the brake, the drive end brakepad may be moved through the pad support, whereas the pressure pin and the force sensor may be shifted towards the brake disc, caused by the spindle\u2019s motion [L\u0170DEMANN 2002]. The physical model of the EMB consists of a model of an E-M motor and a gearbox that transforms the rotary movement into a translatory movement. A non-linear characteristic for the conversion of the movement into a force, as well a linear friction physical model, is taken into account. Figure 3.61 shows the structure of the physical model of the EMB where the symbols have the following meanings: Air_Gap : Air gap between brake disc and brake pads; dges : Overall viscous friction; fi(I,\u03c9) : Feedback of the E-M motor on the current; fx(xS) : Transfer function between spindle position and clamping force; f\u03c9(\u03c9,Te) : Transfer function between angular velocity and friction torque; F : Clamping force; I : E-M motor armature current; J : Overall inertia; Te : Available torque; Tf : Friction torque; TL : Available load torque; TL = Te + Tf ; Tm : Electromagnetic torque; Tel : Electric time constant of the E-M motor; xS : Spindle position; Vges Transmission factor; \u03a6 : Rotation angle; \u03a8m : Magnetic flux; \u2126 : Angular velocity. 3.9 Electro-Mechanical Friction Disc, Ring and Drum Brakes 535 The EMB is servo-controlled by a cascade PID controller that consists of a current controller, an angular velocity controller, and a force controller, as shown in Figure 3.62. The index m denotes the measured values of the clamping force Fm, \u03c9 denotes the angular velocity, and I the current. Index b indicates the reference signal. From the brake-pedal measurements (brake-wish) the BBW AWB conversion mechatronic control system computes the desired clamping force (Fd) for each brake E-M actuator. After Fd has passed through an anti-windup routine, the slip-controller output Fb is passed to the EMB servo controller. Thus, the control output Fb cannot become larger than the desired clamping force Fd. Fb is the reference clamping force signal provided to the brake servo controllers of each wheel [SCHWARZ 1999; L\u00dcDEMANN 2002]. The static brake torque T can be calculated using the following equation: T = k i E R (3.30) where k - constant coefficient, depending on a construction of the short- stroke linear tubular brushless DC-AC macrocommutator IPM brake-force-actuator motor; i - brake application armature current of the short-stroke linear tubular brushless DC-AC macrocommutator IPM magneto-electrically-excited brake-force-actuator motor; E - effectiveness factor (ratio of the disc or ring rubbing surface to the input force on the shoes); R - brake radius. Brake force applied to the disc rotor by the pads is a function of the brake application armature current in the BBW dispulsion sphere and the constant coefficient of the wheel brake-force-actuator E-M motor. The static brake force Fcan is calculated with the following relationship: F = T/r, where r is the wheel-tyre rolling radius. Automotive Mechatronics 536"
        ]
    },
    {
        "image_filename": "designv10_12_0003778_j.mechmachtheory.2021.104407-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003778_j.mechmachtheory.2021.104407-Figure8-1.png",
        "caption": "Fig. 8. Comparison of the calculated results to the ANSYS simulation results under vertical load of 20 kN.",
        "texts": [
            " The iteration computation is not performed when the increment vector { q } meets the convergence criterion ( { q } < \u03b5). Then, calculate the updated displacement vector { u } new , block displacement { q } new , and equivalent contact load of all rollers N ij . Step 5: After the iteration ends, carry out an ANSYS simulation to validate the calculation results of the proposed ap- proach. Via this process, the accurate values of the block displacement { q } and the displacement vector { u } while considering flexibility can be obtained in response to a certain external load { P } . Fig. 8 presents the comparison of the calculated results from the proposed approach and ANSYS model from Ref. [10] . The calculated results of the proposed approach are in good agreement with the general trend of the ANSYS simulation results. A maximum error of 3.62% is found from comparison results, which validates the effectiveness of the proposed approach. In this study, the energy changes during the loading process are considered to analyze the stiffness behavior of the RLMG. For a rolling contact bearing [25] , the force that acts at the rolling center is inertial force, which must be considered when pure rolling occurs between the rolling element and the raceway"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002100_s026357471400071x-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002100_s026357471400071x-Figure8-1.png",
        "caption": "Fig. 8. The measuring object and the coordinate frames.",
        "texts": [
            " The experimental system for the kinematic calibration consists of the digitalized stereotactic apparatus and the INFINITE 2.0 portable CMMs with ScanWorks laser scanner (with an accuracy of 0.04 mm), shown in Fig. 6. It can be seen from Fig. 7, the digitalized stereotactic apparatus is in its reference configuration and kinematic parameters are given in Table V. 4.2.2. Experiment procedure and result. The three scanning planes, which are relatively stationary to link 5, are used to create the measurement coordinate frame {M}, as shown in Fig. 8. To establish the tool frame {H}, the origin of {M} should be translated to the probe so that the origin of {M} coincides with the centroid of the probe. Suppose the base frame {S} coincides with the tool frame {H} when the P O E -based calibration for serialrobotusing position m easurem ents 11 http://journals.cambridge.org Downloaded: 06 Apr 2014 IP address: 68.181.176.15 12 POE-based calibration for serial robot using position measurements http://journals.cambridge.org Downloaded: 06 Apr 2014 IP address: 68"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001818_978-3-319-19740-1_15-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001818_978-3-319-19740-1_15-Figure1-1.png",
        "caption": "Fig. 1 Face milling and face hobbing",
        "texts": [
            " This paper analytically defines and describes a generalized theory of ease-off and its application in the development of an advanced TCA program for both face-milled and face-hobbed spiral bevel and hypoid gears with multiple features of tooth surface modifications. In the gear industry, there are two categories of manufacturing processes for spiral bevel and hypoid gears, namely face milling and face hobbing. The major differences between face milling and face hobbing are: (1) in face hobbing, a timed continuous indexing is provided, while in face milling, the indexing is intermittently provided after cutting each tooth side or slot, which is also called single indexing. As shown in Fig. 1, in face milling, the inside and outside blades cut into the same slot at one time, while in face hobbing, the inside and outside blades cut into neighboring slots continuously; (2) the lengthwise tooth curve of face milled bevel gears is a circular arc with a curvature radius equal to the cutter radius, while the lengthwise tooth curve of face hobbed gears is a kinematic curve called the extended epicycloid, which is generated by the continuous indexing, a relative rolling motion between the cutter and the generating gear; (3) face hobbing gear designs use the uniform tooth depth system, while most face milling gear designs use tapered tooth systems; (4) due to the continuous indexing, the grinding process cannot be applied to face hobbing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003225_tec.2020.2995433-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003225_tec.2020.2995433-Figure8-1.png",
        "caption": "Fig. 8. Experimental setup for the 6PIM equipped with proposed pseudo-CW: (a) configuration and connections, (b) components and proposed pseudo-CW.",
        "texts": [
            "4). In the full-load condition, the nominal values of the stator current, shaft speed, and torque are 1.78 A rms, 2820 rpm and 0.151 N.m respectively. It should be noted that the 2D simulation results acceptably match with the analytical results. To validate both analytical calculations and the FEM simulation results, a test setup is prepared for evaluating the 6PIM performance experimentally. First, the baseline sixphase induction motor is equipped with the proposed pseudoconcentrated winding (Fig. 8). Then, an induction motor is coupled to the 6PIM shaft as the mechanical load, which its torque and speed are fully controlled using a drive system. For supplying the 6PIM, an autotransformer and two isolated transformers are placed between the network and the motor terminals. One auto-transformer tunes the motor input voltage and the two isolated transformers convert the three-phase network configuration to the symmetrical six-phase supply system required for the 6PIM, exerting 180 o phase shift between their secondary winding voltages. Fig. 8 presents the structure of the experimental setup. The rotor shaft is not loaded with any load torque and the results of the no-load test are obtained to study the starting condition, the inrush current, and the no-load steady state operation. Motor starts without any unexpected phenomena and the rotor speed increases until reaching the nominal noload speed of 2985 rpm (Fig. 6 (b)). The high inrush current of the stator winding decays as the rotor speed enhances (Fig. 5 (b)) until reaching the nominal no-load current of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureA.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureA.6-1.png",
        "caption": "Fig. A.6 Schematic of the spinning gas turbine",
        "texts": [
            " Such an analytical approach does not violet the scheme for computing inertial forces acting on a gas turbine. The same mathematical models give different values of the inertial forces acting on a gas turbine due to different geometry of its sections. A resulting value of inertial forces is presented their sum of forces acting on the whole construction of the gas turbine. The action of inertial forces generated by the blade\u2019s and the shaft masses is considered for one section of a gas turbine (Fig. A.6). The blade\u2019s mass m is located on the defined distance r on the section, and the mass centre of the turbine shaft is Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 229 ms. The blade mass m are disposed on the circle of radius r and rotated around axis oz with a constant tangential velocity. A.5.1 Centrifugal Forces Acting on Blades of a Spinning Gas Turbine The rotation of the blade mass elements generates the plane of centrifugal forces, which disposes of perpendicular to the axis of the spinning shaft",
            "0 kg; the number of the radial blades is 12, the number of the serial blades is 4; the radius location of the blades is 0.1 m at about the spin axis and spinning at 3000 rpm. External torque acts on the gas Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 235 turbine, which rotates with an angular velocity of 0.05 rpm. It is determined by the value of the resistance and precession torques generated by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum of the blades of the gas turbine (Fig. A.6). Solving this problem is based on the equations in Table A.6. Substituting the initial data into the aforementioned equations and transforming yield the following result: Tp = Tr = Tct + Tcr = ( \u03c02 2 + 1 ) J\u03c9\u03c9x = ( \u03c02 2 + 1 ) Mr2k lg n \u03c9\u03c9x = ( \u03c02 2 + 1 ) \u00d7 3.0 \u00d7 0.12 \u00d7 4 \u00d7 ln 12 \u00d7 3000 \u00d7 2\u03c0 60 \u00d7 0.05 \u00d7 2\u03c0 60 = 2.9110258927Nm where T r and T p are, respectively, the initial resistance and precession torques generated by the blades of the spinning gas turbine. 1. Cordeiro, F.J.B.: The Gyroscope. Createspace, NV, US (2015) 2",
            " The blocking of the turn of the airplane around axis oz deactivates the resistance inertial torquesT ct andT cr acting on the propeller around axis oy (Chap. 8). The precession torques T in and T am act on the propeller. The airplane flies along the curve, which creates the forced angular velocity of precession around axis oy that is as follows: \u03c9y = V L = 300000(m)/3600(s) 80(m) = 1.04 rad s . (B.1.1) Appendix B: Applications of Gyroscopic Effects in Engineering 239 The gyroscopic torques acting on the propeller are generated by the action of the common inertial forces and the change in the angular momentum around axis oz (Fig. A.6b, Appendix A). The flight of an aeroplane does not allow for acquiring the angular velocity around axes oz and ox. Hence, the torques generated by the centrifugal and Coriolis forces are deactivated around axis oy (Sect. A.5, Appendix A). The bending moment acts only around axis oz. The equation of the mass moment of inertia of the propeller should be rearranged and represented by the equation of the propeller\u2019s gyration radius. The mass moment of the propeller\u2019s inertia is J = Mr2g , where M is mass and rg is the radius of gyration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure1.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure1.1-1.png",
        "caption": "Fig. 1.1 Euler angles. Definition (a) and application in a two-gimbal suspension (b)",
        "texts": [
            "3 Euler Angles 7 Calculations with nine direction cosines subject to six constraint equations are cumbersome. In the present section and in following sections the elements of the direction cosine matrix are formulated in various ways in terms of either three coordinates without constraint equations or in terms of four coordinates with one constraint equation. In the present section so-called Euler angles are introduced. The final position e2 of the body-fixed basis is the result of three successive rotations (Fig. 1.1a ). In the initial position prior to the first rotation the body-fixed basis coincides with e1 . The first rotation is carried out through an angle \u03c8 about the axis e13 (in the usual right-handed sense). It carries the body-fixed basis into an intermediate position e2 \u2032\u2032 . The second rotation is carried out through an angle \u03b8 about the axis e2 \u2032\u2032 1 . It carries the body-fixed basis into a new intermediate position e2 \u2032 . The third rotation is carried out through an angle \u03c6 about the axis e2 \u2032 3 . It carries the body-fixed basis into the final position e2 . A characteristic feature of Euler angles is that the second and the third rotation are carried out about axes which are the result of the previous rotation (or rotations). Another characteristic feature is the sequence (3,1,3) of rotation axes. The desired expression for the matrix A12 in terms of the three angles is obtained from the transformation Eqs.(1.5) for the individual rotations. Figure 1.1a yields the equations e1 = A\u03c8e 2\u2032\u2032 , e2 \u2032\u2032 = A\u03b8e 2\u2032 , e2 \u2032 = A\u03c6e 2 (1.26) with 8 1 Rotation about a Fixed Point. Reflection in a Plane A\u03c8 = \u23a1 \u23a2\u23a3 cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1 \u23a4 \u23a5\u23a6 , A\u03b8 = \u23a1 \u23a2\u23a3 1 0 0 0 cos \u03b8 \u2212 sin \u03b8 0 sin \u03b8 cos \u03b8 \u23a4 \u23a5\u23a6 , A\u03c6 = \u23a1 \u23a2\u23a3 cos\u03c6 \u2212 sin\u03c6 0 sin\u03c6 cos\u03c6 0 0 0 1 \u23a4 \u23a5\u23a6 . (1.27) From (1.26) it follows that A12 = A\u03c8A\u03b8A\u03c6 . When this is multiplied out and use is made of the abbreviations c\u03c8 , c\u03b8 , c\u03c6 for cos\u03c8 , cos \u03b8 , cos\u03c6 and s\u03c8 , s\u03b8 , s\u03c6 for sin\u03c8 , sin \u03b8 , sin\u03c6 , the matrix is obtained in the form A12 = \u23a1 \u23a2\u23a3 c\u03c8c\u03c6 \u2212 s\u03c8c\u03b8s\u03c6 \u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 s\u03c8s\u03b8 s\u03c8c\u03c6 + c\u03c8c\u03b8s\u03c6 \u2212s\u03c8s\u03c6 + c\u03c8c\u03b8c\u03c6 \u2212c\u03c8s\u03b8 s\u03b8s\u03c6 s\u03b8c\u03c6 c\u03b8 \u23a4 \u23a5\u23a6 . (1.28) The advantage of having only three coordinates and no constraint equation is paid for by the disadvantage that the direction cosines are complicated functions of the three coordinates. There is still another problem. Figure 1.1a shows that in the case \u03b8 = n\u03c0 (n = 0,\u00b11, . . .) the axis of the third rotation coincides with the axis of the first rotation. This has the consequence that \u03c8 and \u03c6 cannot be distinguished. Euler angles can be illustrated by means of a rigid body in a two-gimbal suspension system (Fig. 1.1b ). The bases e1 and e2 are attached to the material base and to the suspended body, respectively. The angles \u03c8 , \u03b8 and \u03c6 are, in this order, the rotation angle of the outer gimbal relative to the material base, of the inner gimbal relative to the outer gimbal and of the body relative to the inner gimbal. With this device all three angles can be adjusted independently since the intermediate bases e2 \u2032\u2032 and e2 \u2032 are materially realized by the gimbals. For \u03b8 = n\u03c0 (n = 0, 1, . . .) the planes of the gimbals coincide (gimbal lock)",
            " With the abbreviations c1 = cos\u03c61 and s1 = sin\u03c61 these formulas are written in the forms cos \u03c6\u03021 = c1 \u2212 \u03b5u1s1 , sin \u03c6\u03021 = s1 + \u03b5u1c1 . Hence A\u0302 12 1 = \u23a1 \u23a3 1 0 0 0 c1 \u2212s1 0 s1 c1 \u23a4 \u23a6+ \u03b5u1 \u23a1 \u23a3 0 0 0 0 \u2212s1 \u2212c1 0 c1 \u2212s1 \u23a4 \u23a6 . (3.83) The same result is obtained from (3.61) with r1 = u1 , r2 = r3 = 0 . The dual part is calculated from the primary part by the rule of dual differentiation. In what follows, the same idea is applied to the direction cosine matrix A12 expressed as function of Euler angles \u03c8 , \u03b8 and \u03c6 (see (1.28)). Euler angles are defined in Fig. 1.1a . They are angles of subsequent rotations about the axes e13 , e2 \u2032\u2032 1 and e2 \u2032 3 = e23 . Each of these three rotations is replaced by a screw displacement about the respective axis. The three dual screw angles are denoted \u03c8\u0302 = \u03c8+ \u03b5u\u03c8 , \u03b8\u0302 = \u03b8+ \u03b5u\u03b8 and \u03c6\u0302 = \u03c6+ \u03b5u\u03c6 , respectively. They are dual Euler angles. The dual direction cosine matrix A\u0302 12 is obtained from the direction cosine matrix A12 by the rule of dual differentiation: 3.10 Principle of Transference 109 A\u0302 12 = \u23a1 \u23a2\u23a3 c\u03c8c\u03c6 \u2212 s\u03c8c\u03b8s\u03c6 \u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 s\u03c8s\u03b8 s\u03c8c\u03c6 + c\u03c8c\u03b8s\u03c6 \u2212s\u03c8s\u03c6 + c\u03c8c\u03b8c\u03c6 \u2212c\u03c8s\u03b8 s\u03b8s\u03c6 s\u03b8c\u03c6 c\u03b8 \u23a4 \u23a5\u23a6 +\u03b5 \u239b \u239du\u03c8 \u23a1 \u23a3\u2212s\u03c8c\u03c6 \u2212 c\u03c8c\u03b8s\u03c6 s\u03c8s\u03c6 \u2212 c\u03c8c\u03b8c\u03c6 c\u03c8s\u03b8 c\u03c8c\u03c6 \u2212 s\u03c8c\u03b8s\u03c6 \u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 s\u03c8s\u03b8 0 0 0 \u23a4 \u23a6 +u\u03b8 \u23a1 \u23a3 s\u03c8s\u03b8s\u03c6 s\u03c8s\u03b8c\u03c6 s\u03c8c\u03b8 \u2212c\u03c8s\u03b8s\u03c6 \u2212c\u03c8s\u03b8c\u03c6 \u2212c\u03c8c\u03b8 c\u03b8s\u03c6 c\u03b8c\u03c6 \u2212s\u03b8 \u23a4 \u23a6 +u\u03c6 \u23a1 \u23a3\u2212c\u03c8s\u03c6 \u2212 s\u03c8c\u03b8c\u03c6 \u2212c\u03c8c\u03c6 + s\u03c8c\u03b8s\u03c6 0 \u2212s\u03c8s\u03c6 + c\u03c8c\u03b8c\u03c6 \u2212s\u03c8c\u03c6 \u2212 c\u03c8c\u03b8s\u03c6 0 s\u03b8c\u03c6 \u2212s\u03b8s\u03c6 0 \u23a4 \u23a6 \u239e \u23a0 ",
            " There, it is shown that the motion of the central cross in a Hooke\u2019s joint is the inverse of the motion studied here. A plane normal to the body-fixed line 0P2 intersects the moving cone in the circle (x = x\u2032/ cos\u03b1 ) (x\u2032 \u2212 1 2 sin\u03b1) 2 + y2 = ( 12 sin\u03b1) 2 . (10.20) 10.3 Bryan Angles 333 In the case \u03b1 1 both cones are circular cones with the curves (x\u2212 \u03b1 2 ) 2 + y2 = (\u03b12 ) 2 , X2 + Y 2 = \u03b12 . (10.21) The smaller circle is rolling inside the fixed circle which is twice as big. These circles are met again in Sect. 15.1.2 (Fig. 15.4a). End of example. Figure 1.1a yields for the angular velocity vector \u03c9 the expression \u03c9 = \u03c8\u0307e13 + \u03b8\u0307e2 \u2032 1 + \u03c6\u0307e23 . (10.22) The vectors are decomposed in basis e2 . With the help of (1.26) this results in the coordinate equations\u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 = \u23a1 \u23a3 sin \u03b8 sin\u03c6 cos\u03c6 0 sin \u03b8 cos\u03c6 \u2212 sin\u03c6 0 cos \u03b8 0 1 \u23a4 \u23a6 \u23a1 \u23a3 \u03c8\u0307 \u03b8\u0307 \u03c6\u0307 \u23a4 \u23a6 . (10.23) Inversion yields the desired differential equations:\u23a1 \u23a3 \u03c8\u0307 \u03b8\u0307 \u03c6\u0307 \u23a4 \u23a6 = \u23a1 \u23a3 sin\u03c6/ sin \u03b8 cos\u03c6/ sin \u03b8 0 cos\u03c6 \u2212 sin\u03c6 0 \u2212 sin\u03c6 cot \u03b8 \u2212 cos\u03c6 cot \u03b8 1 \u23a4 \u23a6 \u23a1 \u23a3\u03c91 \u03c92 \u03c93 \u23a4 \u23a6 . (10.24) These equations are nonlinear",
            "81) are the solutions of Euler\u2019s dynamics equations of motion for a classical problem of rigid body dynamics, namely, the motion of an inertia-symmetric body about its center of mass in the absence of external torques (Wittenburg [6, 8]). The angular momentum vector of the body has constant magnitude and direction in an inertial reference basis e1 . This additional condition requires the Euler angles to be the special solutions \u03c6(t) = \u2212\u03c90t , \u03c6\u0307 \u2261 \u2212\u03c90 = const , cot \u03b8 \u2261 \u03bc+ \u03c90 \u03a9 = const , \u03c8\u0307 \u2261 \u03a9 sin \u03b8 = const . \u23ab\u23ac \u23ad (10.83) These results are interpreted as follows (see Fig. 1.1). The motion of basis e2 is the superposition of two rotational motions. One is rotation with \u03c8\u0307 = const about e13 in the position \u03b8 = const., and the other is rotation with \u03c6\u0307 = const about e23 . This means that the body-fixed axis e23 is moving on the cone with axis e13 and with semi apex angle \u03b8 . The fixed herpolhode cone generated by \u03c9 is another circular cone also with the axis e13 . The vector \u03c9 along the line of contact of polhode and herpolhode cone is permanently in the plane spanned by e23 and e13 "
        ],
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    },
    {
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        "original_path": "designv10-12/openalex_figure/designv10_12_0001548_s10846-014-0040-y-Figure1-1.png",
        "caption": "Fig. 1 Controlled variables and reference axes at t0",
        "texts": [
            " The scalar ub is the external controller of the global system; each subsystem represented by the state \u03bel (l = 1, . . . , k \u2212 1) is controlled by the virtual control input \u03bel+1. In this work fixed-wing aircraft dynamics are considered, they are described by three vectorial differential equations: force equation, moment equation and attitude equation [19]. The manipulation of the equations of motion allows the building of the desired cascade form under some assumptions and for a limited number of states: angle of attack \u03b1, sideslip angle \u03b2 and stability-axes roll rate ps , see Fig. 1. The aim is to design a controller so that \u03b1 = \u03b1ref , ps = p ref s and \u03b2 = 0. The idea behind the proposed backstepping approach is to directly control the stability-axes angular velocities \u03c9s = (ps, qs, rs) T so that, in cascade, \u03b1 and \u03b2 follow the reference signal. This direct control is achieved through the relationship \u03c9\u0307s = uc, where uc = (u1, u2, u3) T is the control vector. The dynamics of \u03b1 and \u03b2 are obtained from the force equation written in wind axes, the complete derivation is available in [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002677_j.vacuum.2019.109009-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002677_j.vacuum.2019.109009-Figure1-1.png",
        "caption": "Fig. 1. Diagram of the electron beam freeform fabrication",
        "texts": [],
        "surrounding_texts": [
            "Microscopic observation specimens were cut perpendicular to the deposition using a wire-cut electric discharge machining (EDM). Subsequently, each specimen was polished using a series of SiC emery papers with 200 to 5000 grit sizes in succession with water, and then polished by a 0.05 \u00b5m diamond paste. To reveal the microstructure, the aquaregia (75% HCl + 25% HNO3) and the solution of 5 ml FeCl3 + 50 ml HCl + 100 ml water were used as the etchants for 304SS and copper side, respectively. The etched samples were studied under the optical microscope (OM) (Keyence: VHX1000), and the polished samples and the fracture were investigated under the scanning electron 3 microscope (SEM) (Zeiss: Merlin Compact). Analysis of the crystallographic textures was carried out by the SEM-based electron back scatter diffraction (EBSD) (FEI: Quanta 200FEG). For shear tests, the electronic universal material testing machine (Shimadzu: AG- 20 kN) were used."
        ]
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure5-1.png",
        "caption": "Fig. 5 Two panels connected by an elastic hinge. a The initial, b an intermediate and c the final configurations predicted by the 8-node solid-shell element model SC8R. The crease element A1A2A3A4 is defined using nodes on the faces of the two panels",
        "texts": [
            " It also serves to compare the convergence of different elements used to model the panels. The dimensions of the panels are: L = 2, W = 1 and H = 0.05. Practically, no strain will be induced in the panels. The nonlinearity of the problem mainly comes from the large displacement and rotation experienced by the elements. Here, four modelling methods are considered. In the first method of modelling, the panels are modelled by ABAQUS\u2019s SC8R solid-shell element model which possesses no rotation dof. Eight elements are employed as shown in Fig. 5. B1 to B5 are pinned. C1 and C2 are restrained from moving along the Xdirection. An elastic hinge is realized by having four nodes along A1A3 common to the two panels. The crease element A1A2A3A4 with initial fold angle ho = p, see Fig. 5a, provides the elastic effect to the hinge. A rest angle loading with hrest = 0 is applied to unfold the panels. An intermediate configuration at h & 2p/3 and the final configuration at h = 0 are shown in Fig. 5b, c, respectively. The animation video is given in Online Resource 1. In the second method of modelling, A2 and A4 that define the crease element are then changed to nodes on the side edges of the panels, See Fig. 6. In other words, the crease element is initially flat (ho = 0) and fully folded in the final configuration (hrest = p). The animation video is given in Online Resource 2. In the third method of modelling, the S4R shell element model in ABAQUS is employed, see Fig. 7. The element possesses 4-node on the mid-surface of the plate/shell and each node has 3 translational and 3 rotational dofs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.29-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.29-1.png",
        "caption": "Fig. 17.29 Slider-crank (a) and inverted slider-crank (b)",
        "texts": [
            " (17.106) The position d = \u2212 r is always possible, the position d = + r only if the four-bar is a crank-rocker. It is left to the reader to show that the positions d = \u2212 r and d = + r of a crank-rocker yield identical values of y if the parameters satisfy the condition r2+ 2 cot2 \u03b2 = 4a2 cos2 \u03b2 . In this case, 606 17 Planar Four-Bar Mechanism the coupler curve has a quadruple point on the circle of singular foci. In Fig. 17.28 these conditions are satisfied. The slider-crank mechanism shown in Fig. 17.29a is derived from the four-bar in Fig. 17.19 by moving the point B0 in y-direction to \u2212\u221e . This has the effect that the endpoint B of the coupler of length a is guided along the straight line y = h = const. In the inverted slider-crank mechanism of Fig. 17.29b the coupler of length a has become the fixed link, while the fixed link with the parameter h has become the moving coupler. The parameter h can be positive or zero or negative. Arbitrarily, it is considered as positive in both figures. In both figures the crank angle \u03d5 is the input variable, and the inclination angle \u03c7 of the coupler and the position s of the slider are output variables. Every value of \u03d5 is associated with two positions of the mechanism. In Fig. 17.29a the two values of \u03c7 and s are determined by the equations sin\u03c71,2 = h\u2212 r sin\u03d5 a , s1,2 = r cos\u03d5\u00b1 \u221a a2 \u2212 (h\u2212 r sin\u03d5)2 . (17.107) In Fig. 17.29b the output variables are obtained from two equations expressing the fact that the slider has the coordinates x = a and y = 0 : r cos\u03d5+ h cos\u03c7+ s sin\u03c7 = a , r sin\u03d5+ h sin\u03c7\u2212 s cos\u03c7 = 0 . (17.108) Decoupling produces the equations 17.9 Slider-Crank. Inverted Slider-Crank 607 (r cos\u03d5\u2212 a) cos\u03c7+ r sin\u03d5 sin\u03c7 = \u2212h , s = r sin\u03d5 cos\u03c7\u2212 (r cos\u03d5\u2212 a) sin\u03c7 . } (17.109) The first equation has two solutions cos\u03c71,2 and sin\u03c71,2 . The associated solutions s1,2 are obtained from the second equation. In both figures the equivalent to Grashof\u2019s Theorem 17.1 is Theorem 17.3. The link with the shorter of the two lengths a and r is fully rotating relative to all other links if h2 \u2264 (a\u2212 r)2 . (17.110) Coupler curves: In both figures the coupler-fixed point C is specified by constant parameters b1 , b2 and \u03b2 . In Fig. 17.29a the notation is the same as in Fig. 17.19, whereas in Fig. 17.29b b2 and \u03b2 are defined differently. Implicit equations for coupler curves in the form f(x, y, r, b1, b2, \u03b2) = 0 are obtained from two linear equations for the sine and cosine of the auxiliary variable angle \u03b1 . For both figures (17.78) and (17.79) are valid. Hence also the resulting Eq.(17.80) is valid: 2b1(x sin\u03b1+ y cos\u03b1) = x2 + y2 + b21 \u2212 r2 . (17.111) In Fig. 17.29a the second linear equation for cos\u03b1 and sin\u03b1 is y = h+ b2 cos(\u03b2 \u2212 \u03b1) . (17.112) In Fig. 17.29b the coordinates of point E satisfy the three equations xE = x\u2212 b2 sin(\u03b1\u2212 \u03b2) , yE = y \u2212 b2 cos(\u03b1\u2212 \u03b2) , xE = a\u2212 yE cot(\u03b1\u2212 \u03b2) . (17.113) 608 17 Planar Four-Bar Mechanism Elimination of xE and yE produces the desired second linear equation: (x\u2212 a) sin(\u03b1\u2212 \u03b2) + y cos(\u03b1\u2212 \u03b2) = b2 . (17.114) To this equation and to (17.112) addition theorems are applied. Following this, the two sets of equations, one for Fig. 17.29a and one for Fig. 17.29b, are solved for cos\u03b1 and sin\u03b1 . As in Eqs.(17.83) for the four-bar these solutions have the forms cos\u03b1 = U/\u0394 and sin\u03b1 = V/\u0394 with the pertinent coefficient determinants U , V and \u0394 . The desired implicit equations of the coupler curves are the equations cos2 \u03b1 + sin2 \u03b1 = 1 , i.e., U2 + V 2 = \u03942 . The equation \u0394 = 0 determines the locus of double points and cusps of coupler curves. Omitting elementary intermediate steps only the final equations are documented. Figure 17.29a: The equation of the coupler curve is the quartic[ b2(x 2 + y2 + b21 \u2212 r2) sin\u03b2 \u2212 2b1x(y \u2212 h) ]2 + [ b2(x 2 + y2 + b21 \u2212 r2) cos\u03b2 \u2212 2b1y(y \u2212 h) ]2 = 4b21b 2 2(x cos\u03b2 \u2212 y sin\u03b2)2 . (17.115) The equation \u0394 = 0 defines the straight line (line f in Fig. 17.29a) y = x cot\u03b2 . (17.116) Since a straight line intersects a quartic in at most four real points, the maximum number of double points and of cusps is two. In the context of Fig. 17.18b the existence of two cognate slider-crank mechanisms producing one and the same coupler curve has been proved. Figure 17.29b: The equation of the coupler curve is the tricircular sextic{ (x2 + y2 + b21 \u2212 r2)[y sin\u03b2 + (x\u2212 a) cos\u03b2]\u2212 2b1b2x }2 + { (x2 + y2 + b21 \u2212 r2)[y cos\u03b2 \u2212 (x\u2212 a) sin\u03b2]\u2212 2b1b2y }2 = 4b21 { x[y cos\u03b2 \u2212 (x\u2212 a) sin\u03b2]\u2212 y[y sin\u03b2 + (x\u2212 a) cos\u03b2] }2 . (17.117) The equation \u0394 = 0 defines the circle of singular foci (circle c in Fig. 17.29b)( x\u2212 a 2 )2 + ( y \u2212 a 2 cot\u03b2 )2 = ( a 2 sin\u03b2 )2 . (17.118) This equation is formally identical with Eq.(17.87) for the four-bar. Both a and denote the length of the fixed link. The definitions of \u03b2 are different, 17.10 Planar Parallel Robot 609 however. The maximum number of double points and of cusps of coupler curves on the circle is three. It can be shown that the third singular focus coincides with the singular focus A0 . This has the consequence that there are no cognate inverted slider-crank mechanisms",
            " , n) defined by each such n -tuple represent the positions of a suitable crank in the positions \u03a31, . . . , \u03a3n of the coupler plane \u03a3 . Two arbitrarily chosen n -tuples of this kind define two suitable cranks and, thus, a four-bar. Whether a four-bar thus determined produces the prescribed positions in the prescribed order remains to be seen. The problem of order is the subject of Sect. 17.14.4 . In what follows, n homologous points on a circle are called circle points, and the center of the circle is called center point. The slider-crank mechanism in Fig. 17.29a is a degenerate four-bar in that one center point Q0 is at infinity. The circle is a straight line. The elliptic trammel in Fig. 15.4 has two sliders. In the inverted slider-crank mechanism in Fig. 17.29b and in the inverted elliptic trammel the sliders are pivoted at center points Q0 fixed in \u03a30 . The associated circle points Q1, . . . ,Qn are at infinity. In the mechanism shown in Fig.15.9 one slider is pivoted in the frame \u03a30 and the other in the coupler \u03a3 . This mechanism equals its inverse. Three prescribed positions can be generated by four-bars of all types including the previously listed degenerate forms. Three prescribed positions determine a pole triangle (P12 ,P23 ,P31 ). Since three points are always located on a circle, one out of three circle points Q1 , Q2 , Q3 can be chosen arbitrarily"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003254_s11431-020-1588-5-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003254_s11431-020-1588-5-Figure3-1.png",
        "caption": "Figure 3 (Color online) Gait topology patterns of the six-legged robot. (a) 3-3 gait; (b) 2-4 gait; (c) 1-5 gait; (d) 0-6 gait.",
        "texts": [
            " The quasi-static gaits of a six-legged robot are investigated in this paper. When the amount of supporting legs is larger than 3, and the projection of the mass center of a six-legged robot along the gravity direction is located in supporting polygon, a six-legged robot walks on terrains using such gaits called the quasi-static gaits. Therefore, 0-6 gaits, 1-5 gaits, 2-4 gaits and 3-3 gaits are likely to quasi-static gaits. A six-legged robot can maintain static stability when using quasi-static gaits (see Figure 3). According to the leg permutations of legs, a six-legged robot has 42 kinds of quasistatic gaits at most. Conversely, when the amount of supporting legs is less than 3, the supporting points of a sixlegged robot cannot form a supporting polygon. So that a sixlegged robot cannot maintain static stability. Therefore, 4-2 gaits, 5-1 gaits, 6-0 gaits are dynamic gaits, totally 22 kinds of dynamic gaits. When walking on the continuous-nondifferentiable terrain, stability and collision prevention are necessary to six-legged robots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001335_j.apm.2013.05.056-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001335_j.apm.2013.05.056-Figure2-1.png",
        "caption": "Fig. 2. Assembly of rack cutter, rotors, and worm-shaped tool.",
        "texts": [
            " The geometric relationships between axial feed Ld, tangential feed Kd, and rotor offset angle D/r can be expressed as follows: D/r \u00bc jr Ld pr \u00fe nw nr Kd pw : \u00f02:6\u00de The setting of the feed is usually based on machine specifications and machining requirements, and can be expressed as a polynomial of time: Kd\u00f0t\u00de \u00bc Xi\u00bck i\u00bc0 ct;iti; Ld\u00f0t\u00de \u00bc Xi\u00bcq i\u00bc0 ca;iti; Ed\u00f0t\u00de \u00bc E0 \u00fe DEd \u00bc E0 \u00fe Xi\u00bcm i\u00bc0 cr;iti; \u00f02:7\u00de where k, q, and m are the polynomial order of the tangential, axial, and radial feed, respectively; ct , ca, and cr are the polynomial coefficients of tangential, axial, and radial feed, respectively; and DEd is the increment of radial feed. As shown in Fig. 2, generation of the screw rotors from the worm-shaped tool is usually simplified as a rack generation model by translating the rack and rotating the rotors correspondingly. Further, a pair of conjugated rotors can be generated by the same rack. In general design, as the equation of sectional rotor profile is known, the shape of the worm-shaped tool can be generated directly from it with the relative motion of a pair of crossed helical gears or indirectly obtained from a rack generated by it. The related methods were proposed in the past references (see [1], [4], [6], [9] and [11])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003120_tia.2020.3033262-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003120_tia.2020.3033262-Figure23-1.png",
        "caption": "Fig. 23. Mesh of the CFD model with precise 3-D stator structure.",
        "texts": [
            " Because the stator core losses of the HM are higher than the AM, the total losses of the two motors are comparable. Due to high-speed operation, the power of the two motors is very high. The difference in efficiency between them is very small. The criterion to evaluate the two motors is the temperature rise. In this article, water-cooled method is used. Hence, a computational fluid dynamic (CFD) software Star CCM+ is applied. To consider the temperature difference of the windings at different positions, precise three-dimensional model is built and the mesh of the model is presented in Fig. 23. To improve the cooling performance, the stator is encapsulated with highthermal conductivity epoxy resin. In the simulation models, the ambient and the inlet water temperatures are 300 K (26.85 ). The inlet water velocity is 1 m/s. The temperature distributions of the two motors at maximum speed and rated torque are compared in Fig. 24. Because the losses of copper windings close to the air gap are higher than those at the bottom of slots and the cooling condition at the bottom is better, the windings close to the air gap is much hotter than the bottom windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000275_978-1-4020-8600-7_35-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000275_978-1-4020-8600-7_35-Figure1-1.png",
        "caption": "Fig. 1 2-DoF parallel mechanism in unstable static equilibrium.",
        "texts": [
            " The Cartesian stiffness matrices found in the literature can be easily obtained from the matrix presented here. The matrices for serial mechanisms [1, 4] in which there are no passive joints and no internal wrenches such that KI = 0. As well as the matrices in which the external wrench is not taken into account [2, 4] such that KE = 0. 337 C. Quennouelle and C.M. Gosselin The stiffness matrix of a compliant mechanism can be positive definite, semipositive definite or non-positive definite. The 2-DoF mechanism presented in the configuration shown in Figure 1 is used to illustrate this property. The articular coordinates of this mechanism are \u03b8a , \u03b8b, \u03c1a and \u03c1b, while the pose of the platform is x = [ x, y ]T . The two base points of the legs, noted A and B, are defined by vectors a = (0, 0) and b = (L, 0). The revolute joints are not compliant while both prismatic compliant joints are identical, the free length of their equivalent linear spring is noted \u03c10 and their stiffness coefficient is noted k\u03c1 . In the configuration presented in Figure 1, the parameters are \u03b8a = 0, \u03b8b = \u03c0 , \u03c1a = \u03c1b = L/2 and the external wrench f = 0. The coordinates of leg a are arbitrarily chosen as the generalized coordinates of the mechanism, noted \u03c7 . Then, the pose and the Jacobian matrix can be expressed as x = { \u03c1a cos \u03b8a \u03c1a sin \u03b8a and J = [\u2212\u03c1a sin \u03b8a cos \u03b8a \u03c1a cos \u03b8a sin \u03b8a ] . (31) The two kinematically constrained joints, noted \u03bb, are \u03b8b and \u03c1b. The geometric constraints that represent the condition of rigidity of the platform, are then written 338 Stiffness Matrix of Compliant Parallel Mechanisms as xa \u2212 xb = 0 \u21d4 { \u03c1a cos \u03b8a \u2212 (\u03c1b cos \u03b8b + L) = 0, \u03c1a sin \u03b8a \u2212 \u03c1b sin \u03b8b = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure8.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure8.8-1.png",
        "caption": "Fig. 8.8 Direct and quadrature flux/current diagram in steady-state. (a) d-axis flux/current diagram. (b) q-axis current diagram",
        "texts": [
            "5 Direct and quadrature field-oriented symbolic model with zero leakage inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 Fig. 8.6 Generic representation of a current source fed field-oriented induction machine model, with zero leakage inductance . . . . . . . . . 227 Fig. 8.7 Transient response of field-oriented model with zero leakage inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Fig. 8.8 Direct and quadrature flux/current diagram in steady-state. (a) d-axis flux/current diagram. (b) q-axis current diagram . . . . . . 229 Fig. 8.9 Three inductance, IRTF based induction machine model . . . . . . . . . 229 Fig. 8.10 Universal, IRTF based induction machine model, with ITF module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Fig. 8.11 Comparison of vector diagrams for original and universal induction machine model",
            "7 shows a typical transient response for a machine in its current form, without a mechanical load, in terms of the torque Tm, shaft speed \u03c9m, slip frequency \u03c9sl, and electrical frequency \u03c9s. In this example, a current isd = 4.0 A is applied at t = 0 and a quadrature stator current step isq = 0 \u2192 4.0 A is made at t = 0.8 s. The results shown are obtained with the model given in the tutorial (see Sect. 8.6.4). The reader is referred to Sect. 8.6.4 for further details of the simulation model. Flux/Current Diagram Further insight with regard to this type of model can be obtained by considering the flux/current diagram of the machine taken at a particular instance in time. Figure 8.8 shows the flux lines \u03c6d linked with the flux linkage \u03c8m. A current distribution in the stator windings and squirrel-cage rotor is shown for both cases. The current and flux distributions tied to the dq-plane rotate at speed \u03c9s, while the rotor rotates with a shaft speed \u03c9m. The direct axis flux distribution (Fig. 8.8a) shows the d-axis which is aligned with the flux linkage vector \u03c8m. The current isd is shown in distributed form on the stator side. Note that the rotor component shows no current, i.e. ird = 0. The quadrature model, see Fig. 8.8b, shows the flux distribution \u03c6d and the stator and rotor current distributions which correspond to isq and irq, respectively. It is noted that the two current distributions are in opposition in the actual machine given, while the model assumes the condition isq = irq. The reason for the supposed discrepancy is linked to the choice of input/output power conventions of the IRTF model. The 228 8 Induction Machine Modeling Concepts resultant current distribution in the stator is formed by the two stator components shown in Fig. 8.8. In practical machines, not all the magnetic flux linkage is fully coupled between the stator windings and the rotor squirrel-cage. The so-called leakage flux paths are present on the stator and rotor side of the machine which in modeling terms are represented by leakage inductances L\u03c3s and L\u03c3r, respectively. In this section, the IRTF and field-oriented modeling approach used in the previous section is extended to accommodate magnetic flux leakage of the machine. In this context, a universal field-oriented (UFO) approach will be introduced, which will prove to be instrumental for the development of a field-oriented controller in the next chapter [3]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003296_j.jsv.2020.115712-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003296_j.jsv.2020.115712-Figure8-1.png",
        "caption": "Fig. 8. DDS platform.",
        "texts": [
            " Sun gear Planet gear Ring gear Number of planet gears Numbers of teeth 28 36 100 4 Fig. 9. Considered different sun gear health scenarios. (a) Healthy; (b) Tooth missing; (c) Root crack; (d) Distributed wearing. The experimental studies are all conducted on a Dynamic Drivetrain Simulator (DDS) platform at the University of Electronic Science and Technology of China (UESTC), Equipment Reliability and Prognostic and Health Management Laboratory (ERPHM). Configuration of the DDS platform is shown in Fig. 8 : Mainly including a 2.24kW(3HP) three-phase electric motor to supply the power; a one-stage planetary gearbox; a parallel shaft gearbox; a magnetic brake with a torque range of 1\u201365 lb.ft for loading. An accelerometer (With a frequency measurement range of 0-10kHz and sensitivity of 100mV/g) was vertically mounted on the housing of the PG to collect the vibration signals. The assembled parameters of the PG are listed in Table 3 . Four different health scenarios of the sun gear faults and planet gear faults will be studied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure2.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure2.1-1.png",
        "caption": "FIGURE 2.1. Direct Stresses in Cylindrical Coordinates.",
        "texts": [
            " Jazar, Vibrations of Thick Cylindrical Structures DOI 10.1007/978-0-387-75591-5_2, \u00a9 Springer Science+Business Media, LLC 2010 16 2. Governing Equations of stress, strain, and displacement in cylindrical coordinates. The following sections provide a succinct review of essential topics needed for the establishment of the governing elasto-dynamic equations. 2.1 State of Stresses at a Point A three dimensional state of stress in an infinitesimal cylindrical element is shown in the following three figures. Figure 2.1 depicts such an element with direct stresses, dimensions, and directions of the cylindrical coordinate. Figure 2.2 represents the direct and shear stresses in the radial and transverse directions (r and \u03b8), and the variation of direct and shear stresses in these two directions. Figure 2.3 shows direct and shear stresses associated with the planes perpendicular to the r and z directions, as well as their variations along these directions. In the above graphical representations the changes in direct and shear stresses are given by considering the first order infinitesimal term used in Taylor series approximation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001772_1.4027166-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001772_1.4027166-Figure4-1.png",
        "caption": "Fig. 4 Coordinate systems for the hobbing of work gear with longitudinal crowning teeth",
        "texts": [
            " (1)\u2013(5), the locus and unit normal of the right-hand side rack cutter can be attained as r3 \u00bc \u00bdx3\u00f0u1; v1;w1\u00de; y3\u00f0u1; v1;w1\u00de; z3\u00f0u1; v1;w1\u00de; 1 T (6) and n3 \u00bc \u00bdnx3\u00f0u1; v1;w1\u00de; ny3\u00f0u1; v1;w1\u00de; nz3\u00f0u1; v1;w1\u00de T (7) where u1 \u00bc sin aon\u00f0 ro1w1 \u00fe v1 sin bo1\u00de cos bo1 (8) x3 \u00bc \u00f0ro1 \u00fe u1 cos aon\u00de cos w1 \u00fe \u00f0ro1w1 \u00fe u1 cos bo1 sin aon v1 sin bo1\u00de sin w1 (9) y3 \u00bc \u00f0ro1 \u00fe u1 cos aon\u00de sin w1 \u00fe \u00f0 ro1w1 u1 cos bo1 sin aon \u00fe v1 sin bo1\u00de cos w1 (10) z3 \u00bc v1 cos bo1 \u00fe u1 sin bo1 sin aon (11) nx3 \u00bc sin aon cos w1 cos aon cos bo1 sin w1 (12) ny3 \u00bc cos aon cos bo1 cos w1 \u00fe sin aon sin w1 (13) and nz3 \u00bc cos aon sin bo1 (14) The tooth profile and its unit normal of the standard involute helical gear (i.e., standard hob) are defined by considering Eqs. (5), (6) and (7), simultaneously. The definitions of axes on a gear hobbing machine are shown in Fig. 3. The coordinate systems for the hobbing of helical gears with longitudinal crowning teeth are shown in Fig. 4, where coordinate systems S1\u00f0x1; y1; z1\u00de and S2\u00f0x2; y2; z2\u00de are rigidly connected to the hob and work gear, respectively, while the coordinate system Sa\u00f0xa; ya; za\u00de is rigidly connected to the frame of hobbing machine, and Sb\u00f0xb; yb; zb\u00de, Sc\u00f0xc; yc; zc\u00de, Sd\u00f0xd; yd; zd\u00de, Se\u00f0xe; ye; ze\u00de, and Sf \u00f0xf ; yf ; zf \u00de are auxiliary coordinate systems. On a modern gear hobbing machine, there are three hob\u2019s movements: traverse movement along the axis of the work gear za(t) (i.e., Z-axis movement, as shown in Fig",
            "org/about-asme/terms-of-use c \u00bc bo16bo2 (15) where the \u201c6\u201d sign indicates the same/opposite direction of helices between the hob cutter and work gear. The crossed angle of the hob and work gear is usually fixed during the gear\u2019s hobbing process. The operating center distance E0 between the hob and work gear is also presented in the literatures [1,9], it can be expressed as follows: Eo \u00bc ro1 \u00fe ro2 (16) For conventional longitudinal tooth crowing of a hobbed work gear, it is accomplished by modifying the radial feed-in Eo to a second order polynomial, such as Et \u00bc Eo az2 a\u00f0t\u00de, as shown in Fig. 4. However, this modification causes a tooth flank twist on the helical gear. For this reason, this study proposes a novel hobbing method to obtain anti-twist tooth flanks on the crowned helical gear. The diagonal feed is set as a linear function of the hob\u2019s traverse feed (i.e., Eq. (17)), and the rotating angle of work gear /2\u00f0/1; za\u00f0t\u00de\u00de is set as a function of both the hob\u2019s rotation angle /1 and the amount of hob\u2019s traverse feed za(t) (i.e., Eqs. (32) and (33)). The relationship between the hob\u2019s diagonal feed zs(t) and traverse movement za(t) is proposed as follows: zs\u00f0t\u00de \u00bc cza\u00f0t\u00de (17) According to Fig. 4 and Eq. (17), the hob is shifted diagonally in the process of gear hobbing if c 6\u00bc 0. The position vector r1 and unit normal n1 of the hob cutter equal the position vector r3 and unit normal n3 of the rack cutter, respectively, as defined in Eqs. (6) and (7). By applying the homogeneous coordinate transformation matrix equation, the locus of hob cutter can be represented in coordinate system S2 as follows: r2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de \u00bcM21\u00f0/1; za\u00f0t\u00de\u00de r1\u00f0v1;w1\u00de (18) where M21 \u00bcM2c Mc1 (19) M2c \u00bc cos /2 sin /2 0 \u00f0Eo az2 a\u00f0t\u00de\u00de cos /2 sin /2 cos /2 0 \u00f0Eo az2 a\u00f0t\u00de\u00de sin /2 0 0 1 za\u00f0t\u00de 0 0 0 1 2 666664 3 777775 (20) and Mc1 \u00bc cos /1 sin /1 0 0 cos c sin /1 cos c cos /1 sin c cza\u00f0t\u00de sin c sin c sin /1 sin c cos /1 cos c cza\u00f0t\u00de cos c 0 0 0 1 2 666664 3 777775 (21) After some mathematical operations, the locus of hob cutter can be simplified as r2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de \u00bc \u00bdx2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de; y2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de; z2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de; 1 T (22) where x2 \u00bc cos /2\u00f0 Eo \u00fe az2 a\u00f0t\u00de \u00fe x1 cos /1 \u00fe y1 sin /1\u00de \u00fe sin /2\u00bd\u00f0cza\u00f0t\u00de \u00fe z1\u00de sin c\u00fe cos c\u00f0 y1 cos /1 \u00fe x1 sin /1\u00de (23) y2 \u00bc cos /2\u00bd\u00f0cza\u00f0t\u00de \u00fe z1\u00de sin c\u00fe cos c\u00f0 y1 cos /1 \u00fe x1 sin /1\u00de \u00fe sin /2\u00f0 Eo \u00fe az2 a\u00f0t\u00de \u00fe x1 cos /1 \u00fe y1 sin /1\u00de (24) and z2 \u00bc za\u00f0t\u00de \u00fe \u00f0cza\u00f0t\u00de \u00fe z1\u00de cos c \u00fe \u00f0y1 cos /1 x1 sin /1\u00de sin c (25) Since the hobbing process has two independent motion parameters, /1 and za(t), there are two equations of meshing between the hob and work gear that can be obtained and expressed as follows: f3\u00f0v1;w1;/1; za\u00f0t\u00de\u00de \u00bc n2 d/1 dt @ @/1 x2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de y2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de z2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de 2 64 3 75 T 0 BB@ 1 CCA0 (26) and f4\u00f0v1;w1;/1; za\u00f0t\u00de\u00de \u00bc n2 dza\u00f0t\u00de dt @ @za\u00f0t\u00de x2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de y2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de z2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de 2 64 3 75 T0 B@ 1 CA \u00bc 0 (27) where n2\u00f0v1;w1;/1; za\u00f0t\u00de\u00de \u00bc L21\u00f0/1; za\u00f0t\u00de\u00de nx1\u00f0v1;w1\u00de ny1\u00f0v1;w1\u00de nz1\u00f0v1;w1\u00de 2 64 3 75 (28) and the transformation matrix L21\u00f0/1; za\u00f0t\u00de\u00de is the submatrix of M21, as expressed in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000414_tac.2007.902750-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000414_tac.2007.902750-Figure6-1.png",
        "caption": "Fig. 6.",
        "texts": [
            " Without loss of generality, we may assume that x0 = (0; 0)T , and g1(x 0) = 0. Let x1;\"(x2; a) [x1(x2; a)] be the unique solution of (dx1)=(dx2) = h\"(x1; x2) [(dx1)=(dx2) = h(x1; x2)], with x1;\"(0; a) = a [x1(0; a) = a], then the corresponding C1 differential homeomorphism T\" : (a; x2) ! (x1;\"(x2; a); x2) [the one-to-one map T : (a; x2) ! (x1(x2; a); x2)] transforms the parallel straight-lines x01 = a in the (x01; x 0 2) plane to the integral curves x1 = x1;\"(x2; a) [x1 = x1(x2; a)] in the (x1; x2) plane as shown in Fig. 6 (see [31]). Now, for any point P 0 not on the x02-axis, we can define a straightline k = ( k1; k2); k1 6= 0 which connects the origin with P 0 as shown in Fig. 6. The differential homeomorphism T\" will then map k to k = Jacobian(T\") k = exp( x 0 @h (x ; ) @x d ) h\"(x1; x2) 0 1 k1 k2 : (20) Note that ~g = (1; h(x1; x2)) T is a normal vector field of the equation (dx1)=(dx2) = h(x1; x2), we then have hk; ~gi = k1 exp x 0 @h\"(x1; ) @x1 d + k2[h\"(x1; x2) h(x1; x2)]: (21) Therefore, hk; ~gi 6= 0 for \" small enough. It is easy to verify that the transformations T\" converge uniformly to T as \" tends to zero. Then for any point x1 not on the trajectory x1(x2; 0), it is not difficult to convince oneself that x01\" T 1 \" (x1) will tend to x01 T 1(x1) as \" tends to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001146_j.pnucene.2011.12.008-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001146_j.pnucene.2011.12.008-Figure1-1.png",
        "caption": "Fig. 1. A schematic of UTSG.",
        "texts": [
            " Section 5 illustrates the computer simulations and the comparative results with respect to the gain scheduled dynamic slidingmode controller presented in (Ansarifar et al., 2011). Finally, Section 6 concludes the paper. In this section, a description of the water level control problems and a mathematical model for UTSG are given. UTSG is thermal-hydraulic component in PWR type nuclear power plants for exchange of heat between the primary and secondary circuits and provides the necessary steam for generating electricity. As shown in Fig. 1, two types of water level measurements are provided: Narrow Range Level (NRL) and Wide Range Level (WRL) (Kothare et al., 2000). For the SG in a Nuclear Power Plant (NPP), the main goal of control system is to maintain the narrow range water level at a desired value by regulating the feed water flow rate. Difficulties in designing a nuclear steam generator water level controller arise from some issues summarized below: (1) The UTSG is an open loop unstable system. (2) reverse thermal dynamic effects of \u2018\u2018shrink and swell\u201d, which are more prominent at startup and low power range of operation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003289_j.rcim.2020.102055-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003289_j.rcim.2020.102055-Figure8-1.png",
        "caption": "Fig. 8. Visualizations of the optimized robot path ( = 10 3).",
        "texts": [
            " For this scenario, = 10 3 makes a reasonable trade-off between path length and internal force reduction. Fig. 6 shows a series of snap shots of the initial robot motion and the optimized robot motion corresponding to = 10 3. The robot stays away from the pillar (highlighted in red) and the contact between the dress pack and robot link 4 is resolved in order to reduce the internal forces actuated at the attachment points during the optimized robot motion. Furthermore, the joint configurations in the initial path and the optimized robot path are plotted in Fig. 8a respectively, showcasing that the path length is indeed reduced in the optimized robot path. A sweep of the dress pack for the optimized robot motion (Fig. 8b) illustrates that the occupied space of the dress pack during the motion does not intersect with the pillar geometry. The optimization problem was solved with the interior-point method IPOPT (see also Section 4.6) on a PC with an 8-core AMD processor (3.70 MHz). Fig. 9a shows how the computation time scales with the size of the problem in terms of rod model resolution and number of discrete time steps. The plots suggest that the computational time for the solver scales at worst linearly with both the number of grid points in the rod model and the number of discrete time steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002848_s12555-019-0023-7-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002848_s12555-019-0023-7-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed frame and body-fixed frame.",
        "texts": [
            " Then, for every x \u2208 R, there are the following inequalities:[ min {x:V1(x)=1} V\u03042(x) ] [V\u03041(x)] l2/l1 \u2264 V\u03042(x)\u2264 [ max {x:V1(x)=1} V\u03042(x) ] [V\u03041(x)] l2/l1 . (4) Lemma 4 [29]: For any x \u2208 R, y \u2208 R, d1 > 0 and d2 > 0, |x|d1 |y|d2 \u2264 d1|x|d1+d2/(d1 +d2)+d2|y|d1+d2/(d1 +d2). Lemma 5 [30]: For any xi \u2208 R, i = 1,2, . . . ,n, and a real number y \u2208 (0, 1], (\u2211n i=1 |xi|)y \u2264 \u2211n i=1 |xi|y \u2264 n1\u2212y(\u2211n i=1 |xi|)y. 2.2. Mathematical model of ship motion In order to establish mathematical modeling of the DPM system, it is necessary to introduce a reasonable coordinate system. The ship movement reference coordinate system is established as shown in Fig. 1. In general, we mainly use two space coordinate systems, including the earth-fixed coordinate system (North-East-down coordinate system) and the body-fixed coordinate system. The frame OXY is the earth-fixed coordinate system and ObXbYb is the body-fixed coordinate system. For positioning ships, we only consider the three degrees of freedom of motion in the horizontal plane which is surge, sway and yaw. In general, the parameter matrix of the ship is difficult to obtain accurately. Consider the uncertainty of the system matrices, the nonlinear mathematical model of DPM vessel is given as \u03b7\u0307 = R(\u03c8)\u03c5 , M\u03c5\u0307 +D(\u03c5)\u03c5 = \u03c4 + \u03c4moor +dex (t)+\u03c9 (\u03c5) , (5) where \u03b7 = [x y \u03c8]T is the generalized position vector defined in earth-fixed frame, x is the north position, y is the east position and \u03c8 is the heading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003803_s12540-021-01021-7-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003803_s12540-021-01021-7-Figure15-1.png",
        "caption": "Fig. 15 The compression fatigue fracture mechanism of the SLM Ti\u20136Al\u20134V cellular solid with the COH unit cell",
        "texts": [
            " However, the compressive force on the cellular structure could squeeze the unit cell and increase the distance between the neighboring central nodes, which induced tensile stress in the transverse struts and thus the fracture of the struts. Tensile stress has previously been found in the struts perpendicular to the direction of compressive stress in an SLM commercial-purity Ti cellular solid by FEM [16]. The FEM result in Fig.\u00a014b also demonstrates that tensile stress was present in the horizontal struts along the X axis. According to the previous results on deformation/fracture behaviors, the fatigue fracture mechanism can be deduced, as shown in Fig.\u00a015. Figures\u00a09, 10,\u00a012, and 13 show that the fatigue fracture mechanisms of the SLM and HIP specimens were identical. However, Figs.\u00a08 and 11 indicate that the HIP specimen exhibited better compression fatigue performances than the SLM specimen. The HIP treatment played a positive role in the compression fatigue properties of the SLM sample, even though the uniaxial yield strength of the HIP sample was slightly lower. For the AM cellular Ti\u20136Al\u20134V , several factors, including unit cell design, porosity, surface roughness, and microstructure, have been found to affect the compression fatigue performance [15, 16, 18\u201323]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000423_tmag.2009.2012540-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000423_tmag.2009.2012540-Figure2-1.png",
        "caption": "Fig. 2. Stator and rotor end cores and the rotor end windings.",
        "texts": [
            " In this paper, the problem is investigated with the following assumptions: \u2022 quasi-stationary time harmonic field; \u2022 the field is solved as steady-state; \u2022 the three spatial current density components are consid- ered; \u2022 the geometric configuration of the end zone is real 3-D; \u2022 relations between all input electric and magnetic variables are taken into account in the solution. By applying 3-D FEM using the program Comsol Multiphysics 3.4, it is possible to represent an accurate 3-D geometry with its real complexity and to find more exact solution of the electromagnetic field even in the vicinity of the end core region. An application example is given, referring to a 200 MW turbine generator. The 3-D geometry of the machine is presented in Fig. 2 showing the stator and the rotor core with the rotor end windings. The complete model of the machine end zone is shown in Fig. 3. Because of the whole model complexity and especially the too large number of elements in the whole domain, in Fig. 4 is presented the stator core mesh only. There are described the number and the kinds of the elements for the stator core discretization. The technical characteristics of the investigated object are presented by its specification in Table I. The force densities are calculated using Maxwell stress tensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure8.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure8.1-1.png",
        "caption": "Fig. 8.1 Stewart-Gough-platform",
        "texts": [
            " Suh C H (1969) On the duality in the existence of RR-links for three positions. Eng. f.Ind. 91:129\u2013134 12. Tsai L W (1972) Design of open-loop chains for rigid-body guidance. PhD thesis Stanford 276 7 Two-Joint Chains 13. Tsai L W, Roth(1972) Design of dyads with helical, cylindrical, spherical, revolute and prismatic joints. Mechanism Machine Theory 7:85\u2013102 Chapter 8 Stewart Platform A Stewart platform (or Gough platform; Stewart [9]) is a rigid body which is connected to a supporting frame by six telescopic legs with spherical joints at both ends (Fig. 8.1). The spherical joints Qi on the frame have position vectors Ri in a frame-fixed basis e1 , and the joints Pi on the platform have position vectors i in a platform-fixed basis e2 (i = 1, . . . , 6). Neither the six points on the platform nor those on the frame are coplanar or otherwise regularly arranged. In a general position five legs of given constant lengths determine a linear complex (see Sect. 2.7.4) giving the platform a single degree of freedom, namely, instantaneously a screw motion about the axis of the actual linear complex"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure4.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure4.4-1.png",
        "caption": "Fig. 4.4 Planar mechanism with 7 bodies and 9 revolute joints (a) before and (b) after eliminating rod 6",
        "texts": [
            " The platform is said to be shaky in this position. In exceptional cases a platform is mounted on more than five rods in such a way that large motions are possible. This requires an arrangement where every position in the course of motion satisfies the condition that all rods are complex lines of a single linear complex. The platform-fixed endpoint of each rod is moving on the sphere having its center at the other endpoint of the rod. In Sect. 6.8 such systems are investigated. 4.2 Illustrative Examples 143 In Fig. 4.4a a planar multiloop mechanism with n = 7 bodies (fixed body 0 plus bodies 1, . . . , 6) and with m = 9 revolute joints is shown (the connection of bodies 2 , 4 and 5 represents two joints). To be determined is the degree of freedom F . Solution: Equation (4.2) yields F = d . Hence the degree of freedom is F > 0 only if at least one constraint is dependent. In order to find out whether this is the case, rod 6 is eliminated and, thereby, a single constraint forcing the endpoints P16 and P36 to have identical velocity components in the direction of rod 6 . The mechanism without rod 6 is shown in Fig. 4.4b . If in this system with degree of freedom F = 1 P16 and P36 have identical velocity components in the direction of the eliminated rod 6 , this rod 6 is unnecessary which means that d = 1 . Velocities are determined with the help of Theorem 15.3 by Kennedy and Aronhold. The condition to be satisfied is that the pole P13 is located on the line P16P36 . This pole P13 is found as intersection of the lines P10P30 and P12P23 . The poles P12 and P23 are determined as intersections of the lines P10P20 and P14P24 and of the lines P20P30 and P25P35 , respectively. In the present case, P13 is, indeed, located on the line P16P36 . However, this is true only in the instantaneous position of the mechanism. Hence the conclusion: In the position shown the mechanism in Fig. 4.4a has the degree of freedom F = 1 . Neighboring positions cannot be assumed. In statics the system is called an infinitesimally mobile or shaky truss. Gru\u0308bler\u2019s formula and the formula used for checking statical determinacy of trusses are directly related. 144 4 Degree of Freedom of a Mechanism The planar system shown in Fig. 4.5 can be interpreted in different ways. For one thing, it is a multiloop system with m = 12 bodies (the shaded bodies plus eight rods) and with n = 16 revolute joints each joint having the individual degree of freedom f = 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure9-1.png",
        "caption": "Fig. 9. The tooth profile with k2 = 0.3.",
        "texts": [],
        "surrounding_texts": [
            "The contact ratio can be defined as the average number of teeth of each gear in contact. It can also be defined as the ratio of the angle rotated by the gear between starting and end points of contact to the angle between two adjacent teeth which (the latter angle) is equal to 2\u03c0 divided by the number of teeth [19]. As illustrated in Fig. 13, B presents the intersection point between the line of action and the addendum circle of the driven gear and C is the intersection point between the line of action and the addendum circle of the driving gear. Assuming that the driving gear rotates in a clockwise direction, two gears would firstly engage at B, and finally separate at C. The contact ratio of the gear drive can be expressed as where \u03b5 \u00bc \u03a8 2\u03c0=z1 \u00f055\u00de \u03a8 denotes the angle between O1B and O1C . The parameters are set with the same values as those in examples 1 and 2. According to Eq. (55), the corresponding contact ratio of the gears with different parameters of k1 and k2 are listed in Table 1. Under the same parameters, the contact ratio of an involute gear drive is also listed in Table 1. From the obtained numerical results, the following conclusions can be made. (i) From Figs. 2 and 3, it can be seen that the greater k1 and k2, the closer the parabola to the x0-axis. From Figs. 9 and 10, the closer the parabola to x0-axis, the greater the corresponding angle \u03c8 will be. Thus, according to Eq. (55) the values of the contact ratio will increase with increased parameters k1 and k2. This has been confirmed by the results shown in Table 1. (ii) The contact ratio of the proposed gear drive varies from 1.3738 to 1.5694 in the example. The lowest value is nearly 10% less than that of the involute gear drive. Such gear drives can be applied in gear pumps since less contact ratio is advantageous to ease the trapping phenomenon [20,21]. However, low contact ratio will decrease the combined gear bending strength when more than one simultaneous contact points are considered."
        ]
    },
    {
        "image_filename": "designv10_12_0000148_tia.2006.873670-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000148_tia.2006.873670-Figure5-1.png",
        "caption": "Fig. 5. Schematic representation of the q- and d-axes stator current components, in the estimated and actual rotor flux (d-axis) reference frame, and resulting back-EMF voltage (only motoring operation is shown).",
        "texts": [
            " First, the controller\u2019s reference frame is not aligned with the actual rotor flux, and the amount of misalignment changes as a function of the q-axis current (12b). This effect is shown in Fig. 4(a). Second, misalignment of the controller\u2019s reference frame from the actual rotor flux causes the actual d-axis current to change with respect to its commanded value. This causes the rotor flux level (13) to change when the torque command is changed, as shown in Fig. 4(b). These changes in the orientation and magnitude of the rotor flux cause the back EMF voltage orientation and magnitude to also change. This is schematically shown in Fig. 5. The fact that the back-EMF voltage varies when the slip gain is mistuned and a change in torque command takes place can be used to detect the mistuning. The variation in the back-EMF voltage will follow the relative slow dynamics of the rotor flux (3). When a change in torque is commanded, the current regulators, usually reaching steady state in less than a few milliseconds, will govern the stator currents\u2019 dynamics. This is much faster than the rotor flux dynamics. Following this reasoning, the change in the back-EMF voltage, labeled as \u2206vd and \u2206vq in Figs. 2 and 5, between the instant when the stator current reaches steady state (t = t1 in Fig. 2) and the instant when the rotor flux reaches steady state (t = t2 in Fig. 2) contains information on the correctness of the slip gain estimate. From Fig. 5, it can be observed that the signs of the \u2206vd and \u2206vq voltages depend on whether the estimated slip gain is larger or smaller than the actual slip gain. The magnitudes of \u2206vd and \u2206vq indicate the degree of mistuning and their combined sign the direction in which the slip gain needs to be changed. The signs of \u2206vq and \u2206vd also depend on whether the machine is motoring or generating. Note that Fig. 5 is for motoring operation, and a similar figure can be developed ex- From (15), it can be seen that \u2206vq is more sensitive to changes in the rotor flux magnitude than to changes in the rotor flux orientation, i.e., cos(\u2206\u03b8rf ) does not change significantly over the range of \u2206\u03b8rf typically seen. In contrast, \u2206vd is more sensitive to changes in the rotor flux orientation than it is to changes in the rotor flux magnitude, i.e., sin(\u2206\u03b8rf ) changes significantly. Since \u2206vq is more sensitive to changes in rotor flux magnitude, it also is more sensitive to the effects of saturation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.4-1.png",
        "caption": "Fig. B.4 Gyroscopic device with counterweight",
        "texts": [
            "4 Gyroscopic Torques Acting on a Rotor with CounterWeight The 3.0 kg rotor with the mass moment of inertia about a spin axis is 0.1 \u00d7 10\u22124 kg m2 rotates with constant angular velocity \u03c9 = 50.0 rad/s in the counterclockwise direction. The rotor locates on 300 mm from the spherical pivot. The disc-type counterweight has a mass 4.0 kg, and by adjusting its position b from the spherical pivot can change in the precession of the rotor about its supporting spherical pivot while the shaft remains horizontal (Fig. B.4). The mass moment of inertia around axis ox of the rotor is 4.0 \u00d7 10\u22124 kg m2 and the counterweight is 5.0 \u00d7 10\u22124 kg m2. Determine the position b that enables the rotor to have a constant precession \u03c9p = 0.5 rad/s around the pivot. Neglect the weight of the shaft and friction forces in the pivot. The origin of the coordinate system oxyz is located at the fixed-point o. In the conventional sense, the oz axis is chosen along the axis of precession and the axis of the spin. Since the precession is steady, the equation of the gyroscopic device motion around axis ox is presented by the following system (Chap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002725_j.mechmachtheory.2015.04.014-Figure2-1.png",
        "caption": "Fig. 2. Description of the overlap between the particles.",
        "texts": [
            " The designation \u201cdiscrete element\u201d recalls that the model comes from granular media [6]. The ball bearing is considered as a ball chain. By using the DEM, the contact forces between particles are described with a contact model depending on elastic force displacement law, Coulomb friction and viscous damping coefficient. The principle of the calculation is based on dynamic considerations. If contact is detected, so \u03b4n = Rij \u2212 Ri \u2212 Rj b 0, the springs are activated; here \u03b4n denotes the normal overlap, as suggested by Fig. 2. The equivalent model of the contact is given by Fig. 3, where 4 parameters and \u03bc, the dry friction coefficient, are introduced. Kn and Kt respectively represent the normal stiffness and the tangential stiffness. Nevertheless, stiffnesses are not sufficient to describe the contact correctly, and a viscous damping force is also considered. To dissipate energy and move towards a steady state system, dampers are introduced in the normal direction, Cn and in the tangential direction, Ct. The force F "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000943_tmag.2009.2034021-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000943_tmag.2009.2034021-Figure2-1.png",
        "caption": "Fig. 2. Rotor of machine (b) with its 28 prismatic NdFeB magnets.",
        "texts": [
            " This winding presents concentrated, nonoverlapping coils allowing short end connections with reduction of copper losses and leakage reactances. The coils are allocated around the teeth and connected to obtain four coils in series for each winding, as shown in Fig. 1. The windings were made with enameled copper wire, thermal class, with a cross section of 1 mm . The number of turns per coil is 130. A class resin was used to impregnate the stator coils, therefore the maximum stator temperature is 120 C. The AFPMSM rotor consists of 28 PMs mounted onto a core as shown in Fig. 2. Table I shows main data of the two machines. The different rated currents will result from the thermal characterization of Section V. As the saturation point of SMC is lower than that of iron, the SMC rotor back core is thicker. No further difference between the rotor exists. The phase resistance at room temperature is (1) whereas at rated temperature (2) 0018-9464/$26.00 \u00a9 2010 IEEE The inductance was determined combining no-load and load tests [11]. An incremental encoder is connected to machine shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure2-1.png",
        "caption": "Fig. 2 Mesh results for the solid model of the bearing-axle assembly that was used to perform the finite element analysis in this study",
        "texts": [
            " Additional embedded heaters could have been used, but it would have added greatly to the complexity of the experimental setup and instrumentation, not to mention the time and effort involved in conducting these experiments. Numerical simulations tend to be a more economical means of obtaining prompt results and an efficient way to overcome the experimental challenges and limitations. Hence, ALGOR 20.3TM was utilized to develop a finite element (FE) model for a class K taperedroller bearing mounted to an axle, as shown in Fig. 2. The findings of the previous experimental and analytical work performed by Tarawneh et al. [2] and [3] were used to devise the FE model and validate its accuracy. The FE model was then utilized to run several different bearing heating simulations that provided definitive answers as to whether it is possible for rollers to heat to high temperatures without heating the cup surface to a sufficient temperature necessary to trigger any HBD alarms. The paper presented here provides a thorough summary of the results attained from the aforementioned steady-state thermal finite element analysis (FEA)",
            " Once the model was completed, it was imported into ALGOR 20.3TM and discretized into 68,086 elements with a mesh size of 4.0 mm, which is the largest element size that can be used without jeopardizing the convergence of the FE model while keeping the computational time relatively low ( 20 min on a DELL OPTIPLEX 755 Minitower, Core 2 Duo E8200/2.66 GHz processor). The convergence analysis run on the model revealed that the attained results varied by less than 0.7% when the mesh size was changed by 610%. The final meshed model is illustrated in Fig. 2. The ALGOR \u201cbricks and tetrahedral\u201d solid mesh type option was used since it generates the most accurate mesh utilizing the fewest elements. Even though the use of brick and hexahedral elements can sometimes yield better results [33], the generated mesh contains many more elements, which substantially increases the analysis time. In this study, the use of hexahedral elements resulted in an insignificant improvement on the acquired results (<0.5%) while more than tripling the analysis time. Note that, while the mesh contained six-node wedge, five-node pyramid, and four-node tetrahedral elements toward the center of the model, the majority of the solid mesh consisted of eight-node brick elements",
            " Thus, the bearing is connected to a semi-infinite body of metal and can conduct heat to the axle through the inner cones and to the side-frame through the cup surface in contact with the adapter. The model utilized in this investigation uses a bearing that is pressed onto the middle of a 2.2 m axle in order to provide comparable heat conduction paths to the ones the bearing experiences in service, without the added complexity that the actual setup would impose on the FEA. Furthermore, the bearing overall heat transfer coefficients used in this study were acquired utilizing an experimental setup similar to the one depicted by the FE model (Fig. 2) with a full-load applied to the bearing through the adapter using a hydraulic cylinder (Tarawneh et al. [3]). Hence, based on the above discussion, the FE model devised for this investigation is assumed to approximate the actual setup of a bearing in service. Boundary Conditions. The validity of the FE model depends greatly on the correctness of the BCs applied when running the simulations. With this in mind, the BCs used for this study were derived from previously conducted experimental efforts (Tarawneh et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001130_10402004.2011.582571-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001130_10402004.2011.582571-Figure7-1.png",
        "caption": "Fig. 7\u2014Schematics showing definition of speeds and dent position points.",
        "texts": [
            " 6 (two-disc test with about zero slip) showing similar micropitted areas at the trailing edge of the contact. This experimental observation coincides with the calculated results to be presented next, which show higher pressures and higher risk of fatigue failure for the trailing edge of the dent for a significant amount of slip, 2\u20133%, and also for nominal zero slip conditions of the contact. Before describing the modeling results, the velocity nomenclature used in the present article and the location points in the dent are provided. Figure 7 shows the upper surface as the dented surface with a velocity u2 moving from left to right; therefore, the back (trailing edge) of the dent is at the left-hand side and the front (leading edge) is at the right-hand side in Fig. 7. The lower smooth surface moves with a velocity u1. Some theoretical results with the use of the semi-analytical model are presented. All dent geometries used here either in simulations or experiments are summarized in Table 1 and the operating conditions are given in Table 2. All of the dent geometries in Table 1 except the geometry no. 4 represent idealizations of actual dents produced on bearing steel (AISI 52100) with a Rockwell C indenter and different loads. Dent geometry 4 represents a shallower dent suitable for use with the semi-analytical model, because typical EHL operating conditions in Table 2 do not show actual negative pressures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001513_tec.2014.2353133-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001513_tec.2014.2353133-Figure1-1.png",
        "caption": "Fig. 1. Cross-sectional view of an axial flux surface mounted PMSM.",
        "texts": [
            "ndex Terms\u2014Finite-element analysis (FEA), measurement techniques, measurement uncertainty, permanent magnet losses, permanent magnet machines, rotor losses. I. INTRODUCTION DUE TO its high-power density and good efficiency, the surface mounted permanent magnet synchronous machine (PMSM) is a popular electrical machine topology [1], [2]. Fig. 1 shows an axial flux PMSM, which was the topology used as a case study in the present paper; details of the machine are given in Table I. This particular machine uses Nd-Fe-B magnets, consequently its performance is highly dependent on the temperature of the permanent magnets, as this changes both its electrical and magnetic properties [3]. These changes can be so drastic that demagnetization can occur at elevated temperatures. Causes of magnet temperature rise include the losses generated in the magnets due to hysteresis and eddy currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure10-1.png",
        "caption": "Figure 10 Rotation from v1s to v1t around two vectors",
        "texts": [
            " Thus, we haveP 0 1 \u00bc Mco Msot Moc P1, specifically, P 0 1 \u00bc 1 0 0 1 0 XC 0 YC 0 0 0 0 1 ZC 0 1 2 664 3 775 1 0 0 cosa 0 0 sina 0 0 sina 0 0 cosa 0 0 1 2 664 3 775 cosb 0 0 1 sinb 0 0 0 sinb 0 0 0 cosb 0 0 1 2 664 3 775 cosc sinc sinc cosc 0 0 0 0 0 0 0 0 1 0 0 1 2 664 3 775 1 0 0 1 0 XC 0 YC 0 0 0 0 1 ZC 0 1 2 664 3 775 P1 (3) Process planning for five-axis wire Fusheng Dai, Haiou Zhang and Runsheng Li Rapid Prototyping Journal To calculate Msot, we should look at the second step of the transformation. The second step, rotating v1s to v1t around O, is able to be carried out via two vectors of vx, vy, and vz, which is proved in the following. As shown in Figure 10, v1s is rotated to v1t by rotating v1s to vectorCQ (XQ,YQ, ZQ) via one axis, then rotatingCQ to v1t via another axis. If we choose vx and vz as axes in Figure 10(a), we have: XQ \u00bc Xv1t ZQ \u00bc Zv1s YQ \u00bc 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xv1t 2 Zv1s 2 q c \u00bc atan2 YQ;XQ\u00f0 \u00de atan2 Yv1s ;Xv1s\u00f0 \u00de b \u00bc 0 a \u00bc atan2 Zv1t ;Yv1t\u00f0 \u00de atan2 ZQ;YQ\u00f0 \u00de There is no real solution ifXv1t 2 1Zv1s 2 > 1. If we choose vy and vz as axes in Figure 10(b), or vx and vy as axes in Figure 10(c), we will get similar result. There must be at least one real solution, because Xv1t 2 1Zv1s 2 1 Yv1t 2 1Zv1s 2\u00de1 Yv1t 2 1Zv1s 2 k3. Then it is proved that v1s can be rotated aroundO to v1t via 2 vectors of vx, vy, and vz. We can get P 0 1 XP 0 1 ; YP 0 1 ; ZP 0 1 when putting the values of c, b and a into equation (3). However, the five-axis platformmay not have these two rotating axes. Solution 1 tells us that, there could be no real solutions when rotating v1s to v1t via two axes of vx, vy, and vz, so a vector vz(0,0,1) is introduced as a transition, shown in Figure 11, where v1s is firstly transformed to vz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure5.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure5.4-1.png",
        "caption": "FIGURE 5.4. Torsional Mode and the First Three Related Thickness Modes, n = 0.",
        "texts": [],
        "surrounding_texts": [
            "Axially symmetric vibration occurs only in breathing mode with radial displacement (Markus 1988). Longitudinal modes occur with axial displacement, and torsional modes with transverse displacement around the circumference of the cross section. Figures 5.4 through 5.6 depict the three axisymmetric modes associated with the corresponding first three thickness modes of vibrations."
        ]
    },
    {
        "image_filename": "designv10_12_0002506_j.jsv.2017.08.029-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002506_j.jsv.2017.08.029-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of forces acting on the cage.",
        "texts": [
            "mi is the mass of inner ring, \u20acxi, \u20acyi and \u20aczi are displacement accelerations of inner ring, Iix, Iiy, and Iiz are moments of inertia of inner ring, uix, uiy, uiz, _uiy, _uiz are angular velocities and accelerations of inner ring, Fx, Fy, Fz, My, Mz are external loads, rij is the rolling radius and can be expressed as rij \u00bc 0:5dm 0:5DWgi cos aij (8) where dm is the pitch diameter of bearing, gi is the inner ring raceway curvature radius coefficient. The contact between the balls and the cage leads to friction and impact noise, the contact between the jth ball and the cage is shown in Fig. 3. In Fig. 3, ec is the distance of O and Oc in plane OYZ, and shows the eccentricity of the cage center. fc is the deviation angle between coordinates {O;Y,Z} and {Oc;Yc,Zc}, Qcj shows the impact force between the jth ball and cage, Qcxj, Qcyj and Qczj are decomposition components along axes OcXc, OcYc and OcZc. PRhj and PRxj are frictional forces acting on the cage in plane OcYcZc and OcXcZc, respectively. Fc is the hydrodynamic force acting on the cage, Fcx and Fcy are decomposition components along OcYc and OcZc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure8-1.png",
        "caption": "Fig. 8. (a) Contact lines on worm wheel tooth flank in Example B. (b) Contact lines in (o1; jo1, ko1) in Example B.",
        "texts": [],
        "surrounding_texts": [
            "Six numerical examples with various basic designs and technological parameters, which are given in Table 1, are considered in this section. The primary geometrical design is carried out by using the current formulae for the Hindley hourglass worm drive and the toroid enveloping worm drive with double conical generatrices."
        ]
    },
    {
        "image_filename": "designv10_12_0002383_1.4035079-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002383_1.4035079-Figure9-1.png",
        "caption": "Fig. 9 The envelope surface of the cutter upper surface: (a) for convex tooth surface and (b) for concave tooth surface",
        "texts": [
            " Then we have oh\u00f0u;b\u00de \u00bc pm jomqmj nm \u00fe \u00f0h\u00f0b\u00de jomocj\u00de l (37) vh is obtained as the derivative of oh with respect to u as vh u; hq\u00f0 \u00de \u00bc dpm du djomqmj du nm jomqmj dnm du \u00fe h b\u00f0 \u00de jomocj\u00f0 \u00de dl du \u00fe djomocj du l (38) where djomocj du \u00bc sec ac sec ag dhm du (39) Subsequently, the envelope surface generated by the cutter surface can be obtained. For the previous example, the envelope surfaces of the cutter upper surface for flank milling the convex and concave tooth surfaces, respectively, are obtained as shown in Fig. 9. Consequently, the 3D gear model with simulate machined tooth surfaces is obtained in CATIA V5, and it will be used to compare with the designed model, as shown in Fig. 10. Journal of Manufacturing Science and Engineering JUNE 2017, Vol. 139 / 061004-7 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/936000/ on 02/03/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5.1 The Geometric Deviation Analysis of the Proposed Designed Model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001293_0954406214543490-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001293_0954406214543490-Figure3-1.png",
        "caption": "Figure 3. (a) Mesh points on the sun\u2013planet when there is no misalignment error and (b) 3D view of sun\u2013planet mesh with carrier misalignment error.",
        "texts": [
            " The characteristic of planetary gear system due to pinhole position error has been investigated sufficiently.13\u201316 So, this paper focuses on the characteristic analysis on the tilting of carrier with point O fixed. For the point E on the line OG in Figure 2, with z coordinate z0, the x and y coordinate values are x0 \u00bc z0 tan y0 \u00bc z0 tan = cos \u00f01\u00de at UNIV CALIFORNIA SAN DIEGO on February 16, 2016pic.sagepub.comDownloaded from Perfect pinion-sun mesh when there is no misalignment error is shown in Figure 3(a). Each contact line in the base plane is discretized into several potential contact points. As the carrier is titling, all planets are assumed to incline in the same degree regardless of the effect of the bearing clearance as shown in Figure 3(b). For individual mesh point, arbitrary crosssection I perpendicular to the rotational axis is selected as shown in Figure 4. In Figure 4, Opn is the center of the circle of the perfect planet and G is the center of the circle of the planet section after the carrier is titled. The whole section I of the nth planet all move along the vector OpnG. It can be observed that the original in meshing state will shift to a new condition. It should be further analyzed whether the new state is just in mesh, in separation, or in penetration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.12-1.png",
        "caption": "Fig. 15.12 Six-link door mechanism with permanent center of rotation P50",
        "texts": [
            " An equation for the moving centrode km is obtained as follows. In the coupler-fixed system the pole P has the polar coordinates \u03d5 = (ABB0) and r\u2032 =BP= \u2212R and with the above expression for R r\u2032 = (2\u2212 r/a) . Hence r = a(2 \u2212 r\u2032/ ) . Substitution into (15.28) results in the desired equation for km : r\u2032 = 2 a a2 \u2212 2 (a+ cos\u03d5) . (15.29) This is a limac\u0327on of Pascal with the double point B and with the line of symmetry BA . The equation is obtained directly from (15.28) by interchanging and a . Example 6 : Door mechanism In Fig. 15.12 the labeled six-body linkage of an airplane door is shown in the position door closed. The body of the airplane is the frame 0 , and the door is body 5 . All revolute joints are instantaneous centers with labels as shown. The joints of bodies 0 , 1 , 2 , 3 form a parallelogram 1 , and the joints of bodies 5 , 3 , 2 , 4 form another parallelogram 2 . Both parallelograms share bodies 2 and 3 and the joint P23 . About which point P50 does the door rotate relative to the frame in the position shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure9-1.png",
        "caption": "Fig. 9 Thermal FE analysis results for three consecutive hot rollers (heating scenario 8 in Table 2)",
        "texts": [
            "org/about-asme/terms-of-use motivation behind this simulation is to determine the roller temperature and heat rate associated with a bearing cup temperature of 90 C, which is still about 40 C below the hot-box alarm threshold assuming an ambient temperature of 25 C. The results indicate that, in order to produce a 90 C bearing cup temperature, the two hot rollers must generate a heat rate of 489 W if the remaining 44 rollers are assumed to be operating normally (producing 11.5 W each). The roller temperature associated with this heat rate is about 292 C, which is hot enough to produce distinct roller discoloration without triggering the HBDs. In the heating scenario \u201cthree hot rollers\u201d (simulation 8 in Table 2), shown in Fig. 9, it is assumed that three adjacent rollers are caught misaligned while entering the loaded zone of the bearing, thus, heating abnormally to an elevated temperature of 232 C. The main goal of this simulation is to determine the bearing cup temperature associated with this hypothetical heating scenario. The results of this simulation demonstrate that the average bearing cup temperature is 88.5 C even though there are three hot rollers operating abnormally at an elevated temperature that can cause distinct discoloration in these rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure5.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure5.5-1.png",
        "caption": "Fig. 5.5 Geometrical parameters of the gyroscope components",
        "texts": [
            "4 demonstrates the angular speed of the spinning rotor is decreasing on average around 67 revolutions per second. The drop in the frequency of the rotor spinning changes the angular velocities of gyroscope precessions and the value of the gyroscope resistance and precession torques. The gyroscope with one side free support is suspended from the flexible cord. The gyroscope weight generates the load torque T that resulting in the gyroscope precessions about the centre o of coordinate system oxyz (Fig. 5.5). The object of the tests is to determine practically the precession angular velocities of the gyroscope around axes ox and oy and validate the mathematical model for the gyroscope motions. Equations (5.5) of the gyroscope motions contain technical parameters and the initial numerical data of the gyroscope components. The rotor disc mounted on the shaft of the gyroscope and represented the complex formwith the different radii of its components. The radius of the location of the centre mass elements and the conventional external radius of the rotor are calculated. The Fig. 5.4 Angular velocity for the spinning rotor versus time components i of the gyroscope are represented by the number 1, \u2026, 5 in Fig. 5.5, which masses are calculated by the following equation: mi = \u03c1\u03c0 ( r2out\u2212r2in ) h (5.18) where \u03c1 is density, rin is the inner radius, rout is the outer radius, h is the length or width, and other parameters are as specified above. The gyroscope frame is represented the ribbed spherical frame and for simplification is presented as the thin sphere of radius r5 and mass m5. The mass moment of inertia of the gyroscope frame about the axis ox or oy is the same and calculated by the following equation: Jy5 = (2/3)m5r 2 5 (5",
            " The new mathematical model of the internal forces acting on a gyroscope is represented by four components, namely the centrifugal, common inertial and Coriolis forces and the change in the angular momentum of the spinning rotor (Table 3.1). The external torque applied to the gyroscope generates the resistance and precession torques acting about two axes. The tests on the acting forces of gyroscope precession about axis oy were conducted on the base of the Super Precision Gyroscope \u201cBrightfusion LTD\u201d (Fig. 5.5), which the technical data are represented in Table 5.2. The gyroscope with one side free support is suspended from the flexible cord. The gyroscope weight generates the load torque T that results in the gyroscope precessions about the point o of the support (Fig. 5.5). The defined gyroscope\u2019s parameters are represented in Table 5.3 and enable for calculating the value of torques by the equations represented in Table 3.1. The action of inertial torques is displayed on the motion of the gyroscope suspended from the flexible cord. The equation of gyroscope motion around axis ox at the horizontal location (\u03b3 = 0) is represented by Eq. (5.29) of Sect. 5.3. Theweight of the gyroscope and inertial torques are acting on the one side free support of the flexible cord"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003759_09544062211016889-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003759_09544062211016889-Figure1-1.png",
        "caption": "Figure 1. Construction of a cycloidal transmission.",
        "texts": [
            " Thirdly, the influence of backlash on the form of the force distri- bution and contact pressures appearing at the point of the bushings\u2019 contact with the holes of the planet wheel, which are components of the output mechanism, was determined. Finally, using the carried out analysis, exemplary calculations of backlash, forces and contact pressures were made while, taking into account the differing operational deviations of the elements forming the mechanism. The machining tolerances were selected in order to obtain different backlash distributions, namely the force distributions and contact pressures. Figure 1 shows a typical cycloidal planet transmis- sion. The basic elements are two planet wheels (1a, 1b) mounted eccentrically on the input shaft (7), as well as the central wheel (2), in which there are rollers (3) cooperating with the planet wheels (1a, 1b). The central wheel (2) also acts as a body in which the planet wheels (1a, 1b) are closed. The planet wheels (1a, 1b) are identical, mounted eccentrically, by means of the central bearings (4a, 4b), on the shaft. There are rotated 180 in relation to each other, and together with the rollers (3) they form a planet mechanism",
            " These elements constitute starting mech- anism for transmitting rotational motion from the input shaft (7), through cycloidal meshing, to the output shaft (8). Both shafts are coaxial with each other. Thus, the center of the radius of the bushing (5) together with the pins (6) is in the axis of rotation of the input and output shaft. The rotating input shaft (7) causes rotation of the bearings (4a, 4b) mounted eccentrically on it, which forces the rolling wheels (1a, 1b) to roll around the perimeter of the stationary central wheel (2) with rollers (3) (Figure 1). While the planet wheels (1a, 1b) roll to one side inside the central wheel (2) with the rollers (3), they simultaneously rotate round their own axis in the opposite direction to the input shaft (7). This rotation round its own axis is caused by the mashing of the consecutive teeth of the planet wheels (1a, 1b) with the rollers (3) and center wheel (2). The rotational movement of the planet wheels (1a, 1b) around their own axis is transmitted to the output shaft (8) by means of the output mechanism as follows: the rotating planet wheels (1a, 1b), through the holes made in them, press on the bushings placed in them (5) mounted on the pins (6), whose ends are pressed into the shield of the output shaft (8), in turn causing its rotation",
            " rolling radius, hmax\u00bcRwk; dj \u2013 displacement; dmax \u2013 max. displacement. The displacements dj, at the places of forces Qj, as already mentioned, result from the deflection of the pins with the bushings and the deformation of the bushings in contact with the holes of the planet wheel; the displacement can be determined using the following equation: dj \u00bc fj \u00fe ddj (14) where: fj \u2013 the arrow of the pin and bushing deflection; ddj \u2013 displacement due to deformation of the bushing in contact with the planet wheel hole. The pin (Figure 1, pos.6) mounted to the disc of the output shaft (Figure 1, item 8) is treated as a rigid beam for which: fj \u00bc 64 Qj0 l3 3 Es p d4s (15) where: Qj0 \u2013 force acting in the output mechanism, free of backlash; l \u2013 distance of force Qj0 from the rigid connection; Es \u2013 Young\u2019s modulus of elasticity of the material from which the pin is made; ds \u2013 diameter of the pin. The maximum displacement ddmax in the bushings contact with the planet wheel hole can be determined using expression (16):22\u201325 dmax \u00bc Qmax0 p B \u00bd 1 2k Ek 1 3 \u00fe ln 4 Rotwj c \u00fe 1 2t Et 1 3 \u00fe ln 4 Rtzj c (16) where: k \u2013 Poisson\u2019s number of the material from which the planet wheel is made; t \u2013 Poisson\u2019s number of the material from which the bushing is made; Ek \u2013 elastic modulus (Young\u2019s) of the material from which the planet wheel is made; Et \u2013 Young\u2019s modulus of elasticity of the material from which the bushing is made; B \u2013 planet wheel width; Qmax0 \u2013 max"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002734_1.4032579-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002734_1.4032579-Figure3-1.png",
        "caption": "Fig. 3 Coordinate systems applied in the generation of surface R2",
        "texts": [
            "org/about-asme/terms-of-use Dw2 \u00bc a0 \u00fe a1w1 \u00fe a2w 2 1 \u00fe a3w 3 1 \u00fe a4w 4 1 \u00bc XYT (5) The coefficients could be determined by 1 w11 w2 11 w3 11 w4 11 1 w12 w2 12 w3 12 w4 12 1 w13 w2 13 w3 13 w4 13 0 1 2w12 3w2 12 4w3 12 0 1 2w13 3w2 13 4w3 13 2 66666664 3 77777775 a0 a1 a2 a3 a4 2 6666664 3 7777775 \u00bc AX \u00bc Dw21 0 Dw23 0 s 2 6666664 3 7777775 \u00bc B (6) where Dw2j, w1j (j\u00bc 1, 2, 3) are used to control the shape of transmission errors [31]. 2.3 Redesign of Tooth Surface of the Face Gear. The coordinate systems applied in generating of the face gear by the application of a shaper s proposed by Litvin and Fuentes is represented by Fig. 3 [32]. The shaper and the face gear rotate about axes zs and z2 with angles us and u2, respectively. They are related by m2s \u00bc Ns=N2 \u00bc u2=us (7) in which N2 is the teeth number of the face gear, m2s is the transmission ratio. The localization of the bearing contact is obtained by setting Ns larger than N1, usually, Ns N1\u00bc 1, 2, 3 [33]. The teeth of the face gear can be generated by the cutting edges of the shaper, the tooth surface R2 of the face gear is expressed by the envelope to the family of the generating surface Rs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003755_wemdcd51469.2021.9425634-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003755_wemdcd51469.2021.9425634-Figure15-1.png",
        "caption": "Fig. 15: Flux density maps at 15000 rpm of PRC-2 and PRC-8 motors",
        "texts": [
            " The efficiency of the PRC-8(\u21d3) motor results higher at rated point but once the reduction of the flux begins, the PRC-8(\u21d1\u21d3) reach higher values of efficiency (for higher speeds) as shown in Fig. 11. A comparison of all the configurations is carried out in terms of power in Fig. 12, torque in Fig. 13 and efficiency in Fig. 14. It is possible to recognize that at low speeds the IPM motor exhibits slightly better efficiency. The PMs magnetization is always in the limits of de-magnetization, also at the speed of 15 000 rpm as shown in Fig. 15 for all the machines. However, at speed higher than the rated speed its benefit disappears and the HEPM motor shows a higher torque and power behaviour. The PRC-8 HEPM motor 14 Authorized licensed use limited to: Dalhousie University. Downloaded on May 25,2021 at 12:27:18 UTC from IEEE Xplore. Restrictions apply. configuration with the possibility to increase and to reduce the rotor flux exhibits the highest performance parameters, in comparison with the other solutions described above. The maximum efficiency reached by PRC-8 is 96% and along all the speed range is always higher than 93%"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.3-1.png",
        "caption": "Fig. 17.3 Limit positions of a four-bar",
        "texts": [
            " Its dependency on \u03d5 is obtained as follows. The length of the diagonal starting from A is expressed by means of the cosine law once in terms of cos\u03d5 and once in terms of cos\u03bc . The identity of these expressions results in cos\u03bc = 2r1 cos\u03d5\u2212 (r21 + 2) + r22 + a2 2r2a . (17.25) Extremal values of \u03bc are obtained from (17.1) by interchanging (r1, ) and (r2, a) : cos\u03bcstat = r22 + a2 \u2212 ( \u2213 r1) 2 2r2a . (17.26) In positions with these extremal values the input link and the fixed link are collinear (see Fig. 17.3). In phases of motion in which the coupler is required to transmit a large torque to the output link the transmission angle \u03bc should differ from \u03c0/2 as little as possible. In other words: | cos\u03bc| should be as small as possible. The angular velocity ratio i = \u03d5\u0307/\u03c8\u0307 is called transmission ratio of the fourbar. In what follows, the inverse value 1/i = \u03c8\u0307/\u03d5\u0307 is represented in geometric and in analytical form. The geometric form is obtained from (15.6). Let the fixed link, the input link and the output link be links 0 , 1 and 2 , respectively, so that \u03c910 = \u03d5\u0307 and \u03c920 = \u03c8\u0307 (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000768_j.1475-1305.2008.00558.x-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000768_j.1475-1305.2008.00558.x-Figure3-1.png",
        "caption": "Figure 3A\u2013D: Definition of meshing angle at various engagement positions",
        "texts": [
            " In gears with contact ratios lower than 2, which represent the majority of geared power transmissions based on the 20 involute system, contact takes place either between a single pair of teeth or two pairs of teeth. In the latter case, the total transmitted load is shared between the meshing tooth pairs and this is quantified by means of a non-dimensional factor termed \u2018load-sharing factor\u2019 (LSF) given by the equation: LSF \u00bc Pi P (7) where Pi is the load carried by the pair and P the total load along the path of contact. The LSF is dependent on tooth compliance, which in turn is a function of gear position and load, and is hence a nonlinear quantity. Referring to Figure 3, a tooth pair load cycle can be described as follows: Step 1. A new tooth pair (shaded teeth) engages in such a manner that the root of the driving gear contacts the tip of the driven gear. This position is herein set as x \u00bc 0. As can be seen in Figure 3A, two pairs of teeth are simultaneously engaged after this position. Step 2. At position x \u00bc hLPSTC (Figure 3B) the previ- ous pair disengages, and single-tooth contact commences. This condition defines the lowest point of single tooth contact (LPSTC) on the engaged tooth of the driving gear. Step 3. At position x \u00bc hHPSTC (Figure 3C) the next tooth pair engages, so that double tooth contact is resumed. This condition defines the highest point of single tooth contact (HPSTC) on the engaged tooth of the driving gear. Step 4. The load cycle ends at x \u00bc h (where h is the total meshing angle), at which point the tooth pair disengages as the tip of the driving gear contacts the root of the driven gear. The meshing cycle described in steps 1\u20134 is characterised by double tooth contact at the intervals 0 < x < hLPSTC and hHPSTC < x < h and single tooth contact at the interval hLPSTC < x < hHPSTC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001946_j.matdes.2018.05.032-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001946_j.matdes.2018.05.032-Figure7-1.png",
        "caption": "Fig. 7. (a) Published habit plane for \u03b2 \u2192 \u03b1 transformation in Ti alloy (b) The diagra",
        "texts": [
            " In the process of laser additive manufacturing, the final stable \u03b1 phase inherit the crystallographic orientation of martensite transition phase formed during thermal cycling, as shown in Fig. 3, but the specific mechanism still needs to be studied in depth. So the habit plane is used to locate the \u03b1 lath boundary. able zone of large columnar grain, (c\u2013f) Themicrostructure of themiddle transition zone of According to the literatures, the habit planes in Ti alloy are always within 10\u00b0 of the {111} plane as shown in Fig. 7 (a), for example, {8 9 12} [35], {8 8 11} [33], {334} [36], and {344} [37] et al. That is to say, the actual habit plane of \u03b2\u2192 \u03b1 in Ti alloy is not the {112} plane in Burgersmodel, but one plane intersectingwith {112} plane at a small angle. So, a schematic diagram of the spatial crystallographic relationship between the \u03b1 lath and the \u03b2 matrix can be plotted as in Fig. 7(b). The gray translucent film is a \u03b1 lath, and the green plane is the (112) plane of \u03b2 matrix with parallel to the (1100) plane of the \u03b1 lath. And the crystallographic orientation between the \u03b1 lath and \u03b2 matrix obey Burgers OR. In the paper, themethod of single \u201cedge-on\u201d trace analysis is used to calculate the habit plane of \u03b1 phase as shown in Fig. 8 [38]. The specimen is tilted to the \u2329110\u232a\u03b2 direction of \u03b2 matrix as shown in Fig. 8(b), and the\u03b1 lath with [0001] \u03b1 // b110N\u03b2, as shown in Fig. 8(c), is selected to calculate the habit plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.32-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.32-1.png",
        "caption": "Fig. 2.32 Principle layout of the radar cruise mechatronic control [Toyota; AMEMIYA 2004].",
        "texts": [
            " Compared also with a steer-by-wire (SBW) all-wheel-steered (AWS) conversion mechatronic control system, here reliability of the steering function is directly related to safety. Radar Cruise Control (RCC) (Low-velocity following mode included) - At values of vehicle velocity lower than 30 km/h, if the preceding vehicle stops, a warning through display and alarm is given to stimulate the driver to press on the brake, as well as in the incident where the driver is late in pressing the brakes, stops the automotive vehicle (see Fig. 2.32) [AMEMIYA 2004]. Automotive Mechatronics 178 Radar Cruise Control (RCC) (Brake mechatronic control built-in) - Because of the information from the laser radar sensor located inside the bumper and so on, thus preserving a distance proportional to the vehicle velocity, within the cruise vehicle velocity set by the vehicle in front, uses the brake for deceleration (see Fig. 2.33) [AMEMIYA 2004]. Lane Monitoring Control (LMC) - When driving on a highway, the distance between the vehicle and the white (yellow) lines on the roads is continuously measured using a colour CCD camera for guidance monitoring to the rear (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000768_j.1475-1305.2008.00558.x-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000768_j.1475-1305.2008.00558.x-Figure1-1.png",
        "caption": "Figure 1: Hertzian stress distribution between two elastic bodies in contact",
        "texts": [
            " A special test rig has been designed and constructed at the Laboratory of Machine Elements of the National Technical University of Athens (NTUA) for testing multi-tooth gear models and the infrastructure of the Laboratory of Strength of Materials of NTUA has been used to perform the caustics measurements. The experimental findings are compared with the prevailing gear standards International Organisation for Standardisation (ISO) 6336 [20] and ANSI American Gear Manufacturers Association (AGMA) B88 [21]. In gear tooth contact, the individual teeth in mesh can be treated as a pair of perfectly elastic bodies, 1 and 2, each with a local curvature of R1 and R2, respectively, subjected to a normal load per unit width equal to P as in Figure 1. Assuming a contact width equal to 2l, the Hertzian pressure distribution is (Johnson [22]): p\u00f0s\u00de \u00bc pmax ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 s l 2 r for s \u00bc l! \u00fel (1) The half-width l of the contact area is liked to the applied load through the relation [22]: l \u00bc ffiffiffiffiffiffiffiffiffiffiffi 2kRP p r (2) where k \u00bc (1 ) m2)/pE, assuming the same Young\u2019s modulus and Poisson\u2019s ratio for the bodies in contact, R \u00bc R1R2/(R1 + R2) is the equivalent radius of curvature and P \u00bc Z l l p\u00f0s\u00deds is the applied load per unit width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001959_access.2018.2845134-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001959_access.2018.2845134-Figure2-1.png",
        "caption": "Fig. 2; b is the lift coefficient; and k is the moment scaling factor of the force.",
        "texts": [
            " The conclusions of this paper are presented at the end. Because a quadrotor is unstable and underactuated, it is challenging to design a controller to realize QH-1 stability and robust flying performance in a real-world setting. Many factors can affect the controller performance, including wind disturbance, body vibration, inner model uncertainty, and electromagnetic interference. To resolve these problems, a reliable model must be built before designing a controller. The schematic configuration of QH-1 in Fig. 1 is shown in Fig. 2. Here, o-x-y-z represents the body coordinates, and its origin is the center of mass of the body; the earth coordinate is represented by O-X-Y-Z; the four thrust orientations are along the o-z axis. The roll, pitch, and yaw angles are denoted by  T    , and the angular rates are denoted by  Tb p q r  in the body frame. The translation relationship between  and b can be expressed as = bR  According to Newton-Euler equation, the dynamic equations can be obtained: 2 3 4 ( ) + ( ) + ( ) = + y z r x x x z x r y y y x y z z I I J L U I I I I I J L U I I I I I U I I                                                     (3) where 1 2 3 4=    ; Jr is the propeller inertial coefficient; L is the distance from the body center to a rotor; xI , yI and zI are the QH-1 inertial values along the body frame axis; 1= x k I  , 2= y k I  and 3= z k I  are the equations of 2169-3536 (c) 2018 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.3-1.png",
        "caption": "Fig. 15.3 Theorem of Kennedy and Aronhold",
        "texts": [
            "4) In addition, \u03c9ik = \u03c9ij + \u03c9jk is valid and, consequently, 454 15 Plane Motion \u03c9ij + \u03c9jk + \u03c9ki = 0 . (15.5) In multi-link mechanisms it frequently happens that for less than two points of some link the directions of the velocities are known. In such cases, the geometric construction of the instantaneous center requires Theorem 15.3. (Kennedy/Aronhold)1 The instantaneous centers Pij , Pjk and Pki of three bodies i , j , k in plane motion relative to each other are collinear. Proof: Suppose the centers Pik and Pjk are known (Fig. 15.3). The center Pij is the point at which body i and body j have equal velocities v relative to body k . This establishes the equation \u03c9ik \u00d7 PikPij = \u03c9jk \u00d7 PjkPij . The two vector products are collinear only if PikPij and PjkPij are collinear. This ends the proof already. In addition, the equation requires the two vector products to be equal in magnitude and in sense of direction. If PikPij and PjkPij have equal directions (opposite directions), also \u03c9ik and \u03c9jk have equal directions (opposite directions)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001137_tmag.2012.2197404-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001137_tmag.2012.2197404-Figure9-1.png",
        "caption": "Fig. 9. The equipment for testing torque.",
        "texts": [
            " To demonstrate the effect of this method, a slotless prototype machine with two ends is fabricated, which is derived by a little ripple motor at a constant speed. An ergometer between the two motors will record the variation of the torque. The tested end cogging force is shown in Fig. 8. It is noted in Fig. 8 that after the central angle between two stators is optimized, the component of the first harmonic has been removed, and the magnitude has decreased from 2.5 N m to 0.8 N m. To validate the optimization results, an experiment was carried out to test the torque ripple of Arc PMLSM. The experimental equipment is shown in Fig. 9. The Arc PMLSM was controlled at a constant low speed (0.01 /s), and an ergometer between the Arc PMLSM and the mass block will record the variation of torque. The value of the ergometer was sampled at a frequency of 250 Hz. The tested torque of primary Arc PMLSM and the optimized Arc PMLSM is shown in Fig. 10. The experimental results show that the peak-to-peak torque of the primary Arc PMLSM changed from 75 Nm to 80 Nm, and the torque ripple equals 3.2%. While the peak-to-peak torque of the optimized Arc PMLSM changed from 77 Nm to 78 Nm, the torque ripple equals 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001749_s12239-014-0053-3-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001749_s12239-014-0053-3-Figure7-1.png",
        "caption": "Figure 7. Refined model: (a) repetitive slice and (b) ful model generated by revolving.",
        "texts": [
            " The fluctuation of roling angular velocity is beyond the reasonable range. To limit the fluctuation to an acceptable level (see figure 6) requires the localy refined mesh. A double fine mesh is applied to the region of tread and the localy refined tread elements are combined to the main body by using the \u201ctie\u201d constraint to D1 0.01C10 C01+( )\u2044= tstable\u2206 2 \u03c9max 1 \u03b52+ \u03b5\u2013( ) -------------= EI EV EFD EW\u2013 EPW\u2013 ECW\u2013 EMW Etotal cons ttan= =\u2013+ + EI EE EP ECD EA+ + += connect the adjacent surfaces of two parts, depicted as figure 7. The total element number after refinement rises from the initial 27840 to 48960. Thus, the fluctuation amplitude of roling angular velocity is controled within 1%, which is remarkably improved. A recent general trend in wear prediction by computer simulation is the usage of Archard wear model (Archard, 1953; Archard, 1980). The model is expressed mathematicaly as folows: (5) where V denotes the volume lost during wear, s the sliding distance, K the dimensionless wear coeficient, H the Brinel hardness of the softer material, and FN the applied normal force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002664_j.mechmachtheory.2019.103608-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002664_j.mechmachtheory.2019.103608-Figure3-1.png",
        "caption": "Fig. 3. Planar prismatic joint.",
        "texts": [
            " At this moment, the pose error is represented by x pra = ( \u03b8 , 0, 0) T , and the corresponding group element, similar to Eq. (8) , is g pra = exp( x \u2227 pra). In general, the offset of a rotating motor complies with the normal distribution, i.e. \u03b8 \u223c N ( \u03b8 ; 0 , ( to l pr 6 )2 ) (13) where N ( \u00b7) denotes a univariate Gaussian distribution and tol pr is the driving tolerance. Therefore, the covariance of g pra is pra = Diag ( ( to l pr 6 )2 , 0 , 0 ) . (14) 2.2. Planar prismatic joint As shown in Fig. 3 , a mobile frame is attached on the slider. Suppose x ppc = ( \u03b8 , 0, y ) T represents the pose deviation of the aforementioned frame with respect to the one fixed on the rail due to the play. The slider can not only translate along the nominal axis of the rail but also perform a small translation perpendicular to the axis and a tiny rotation on the plane as long as the geometric constraint of the joint is satisfied, which is given as \u2223\u2223\u2223y + 1 2 L s sin \u03b8 \u2223\u2223\u2223 \u2264 r pp (15) where r pp = 0.5 \u00b7( t s \u2013 t r )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure18.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure18.3-1.png",
        "caption": "Fig. 18.3 Spherical four-bar with coupler point C in the coupler triangle (A,B,C) . Schematic view with great-circle arcs shown as straight lines. All lengths are angles. Geographical coordinates u , v . Auxiliary angles \u03b1 , \u03b5 , \u03b4",
        "texts": [
            " Like planar four-bars also spherical four-bars fall into the categories of crank-rockers, double-cranks, double-rockers and foldable four-bars. A spherical four-bar is foldable if \u03b1min + \u03b1max = \u03b1\u2032 + \u03b1\u2032\u2032 . Every point C fixed on the coupler of a moving spherical four-bar traces a coupler curve which is located on a sphere. Without loss of generality the point C is chosen on the unit sphere. Together with the endpoints A and B of the coupler the point C creates a coupler-fixed spherical triangle (A,B,C). In Fig. 18.3 arcs of great circles are schematically represented by straight lines. As parameters of the coupler triangle the angles \u03b15 , \u03b16 and \u03b17 are chosen. They are equivalent to the parameters b1 , b2 and \u03b2 of the coupler triangle of the planar four-bar in Fig. 17.19. As coordinates of the coupler point C its geographical longitude u and its geographical latitude v are used (A0 and B0 lie in the equatorial plane; u = 0 at A0). The meridian passing through C defines the point D on the equator. 644 18 Spherical Four-Bar Mechanism To be determined is an implicit equation of the coupler curve in the form f(u, v, \u03b11, \u03b13, \u03b14, \u03b15, \u03b16, \u03b17) = 0 ",
            " This projection produces the principal-axes equation of the curve shown in Fig. 18.5: (\u03be2 + \u03b62)2 sin(\u03b14 \u2212 \u03b17)\u2212 8(\u03be2 \u2212 \u03b62) sin\u03b17 \u2212 16 sin(\u03b14 + \u03b17) = 0 18.3 Coupler Curves 655 great-circle arcs of lengths \u03b11 , \u03b15 and of \u03b13 , \u03b16 are pairwise co-tangent. In any such configuration the base A0B0 is seen from C either under the angle \u03b17 or under the angle \u03c0\u2212\u03b17 . This proves again that cusps lie on the curve \u03c4 . The four configurations are shown by Fig. 17.24 if the straight lines are interpreted as great-circle arcs and if the notations are changed according to Fig. 18.3. The cosine law applied to the spherical triangles (A0,B0,C) and (A,B,C) yields the equations C4 = cos(\u03b11 + \u03b15) cos(\u03b13 + \u03b16) + sin(\u03b11 + \u03b15) sin(\u03b13 + \u03b16)C7 , C2 = C5C6 + S5S6C7 . } (18.47) Elimination of C7 = cos\u03b17 results in a condition for the existence of cusps. With the help of addition theorems it can be given the form C1S3S5(C5 \u2212 C2C6) + S1C3S6(C6 \u2212 C2C5) + S1S3(C 2 5 + C2 6 \u2212 C2C5C6 \u2212 1) + S5S6(C4 \u2212 C1C2C3) = 0 . (18.48) With reference to Fig. 17.24 the combination (S1, S3) can be replaced by any of the combinations (\u2212S1, S3) , (S1,\u2212S3) and (\u2212S1,\u2212S3) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002734_1.4032579-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002734_1.4032579-Figure1-1.png",
        "caption": "Fig. 1 Simulation of a pinion meshing with a face gear",
        "texts": [
            " The generating surfaces Rs, RE, respectively, are generated by the reciprocating motion of the cutting edges of shapers s and E and tooth surfaces R1 of involute pinion 1 meshes with the face gear will be employed in the paper, and their position and normal vectors are represented by Rk (uk, lk) and nk (uk, lk), respectively, where (k\u00bc s, E, 1), and uk, lk are surface parameters in the profile and longitudinal directions Rk\u00f0uk; lk\u00de \u00bc rbk sin\u00f0uk \u00fe u0k\u00de uk cos\u00f0uk \u00fe u0k\u00de\u00bd rbk cos\u00f0uk \u00fe u0k\u00de \u00fe uk sin\u00f0uk \u00fe u0k\u00de\u00bd lk 1 2 664 3 775 (1) nk \u00bc @Rk @uk @Rk @lk @Rk @uk @Rk @lk \u00bc cos uk \u00fe u0k\u00f0 \u00de sin uk \u00fe u0k\u00f0 \u00de 0 0 2 664 3 775 (2) where rbk is the radius of the base circle of gear k, and u0k\u00bcp/ (2Nk) tana\u00fe a, a is pressure angle, Nk is the teeth number of gear k [1]. 2.2 Predesign of Transmission Errors. The simulation of pinion 1 meshing with the face gear 2 is shown in Fig. 1. The coordinate systems S2, S1, and Sf are rigidly connected to the face gear, the pinion, and the frame of the face gear drive, respectively. When the pinion rotates about axis z1 with angle w1, the face gear rotates about axis z2 with angle w2 pushed by the pinion. Theoretically, the rotational angles w1 and w2 obey the following function: w2 \u00bc w1 N1=N2 \u00bc w1 m21 (3) Because of misalignments, deflections, etc., Eq. (3) should not be satisfied. The real rotation angle of the face gear is regarded as the function of w1 and is represented by w2 (w1), which, upon subtracting the theoretical rotation angle, is determined to be the function of the transmission errors, that is Dw2 \u00bc w2\u00f0w1\u00de w1m21 (4) This function is a periodic function with period T\u00bc 2p/N1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001806_tasc.2016.2524026-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001806_tasc.2016.2524026-Figure3-1.png",
        "caption": "Fig. 3. The principle of generating the suspension force in 12/10-pole BFSPM motor.",
        "texts": [
            " And shorter length magnets in the radial direction are employed to save space for the accommodation of the added suspending windings. In addition, 12/14-pole BFSPM motor has an additional suspension tooth to place suspending windings. I 1051-8223 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The principle of generating the suspension force in 12/10- pole BFSPM motor is illustrated in Fig. 3. It can be seen that the flux density direction excited only by x-axis suspension winding current are identical with that of PMs in air gap 1 and opposite in air gap 2. Hence, the flux density is increased in air gap 1 and decreased in air gap 2. Then, the radial suspension force Fx is generated toward the positive direction in the x-axis. Similarly, the suspension force generated principle of the 12/14 pole BFSPM motor is shown in Fig. 4. In this section, the electromagnetic performances of the two BFSPM motors are calculated and compared using 2-D FEA, including the magnetic saturation, torque, suspension force, coupling and loss"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.16-1.png",
        "caption": "Figure 5.16. Schema for the equipollent moment condition in a parallel, variable gravity field.",
        "texts": [
            "63) , the distribution of the weight of a body in a parallel, but variable gravitational field is equipollent to the single force W(gj). In addition, for any assigned point Q in the Earth frame <1> = {F;Ik } shown in Fig . 5.16, the moment MQ about Q of the weight distribution dw(P) = ndw(P) in the parallel Earth field is equipollent to the moment about Q of the total weight W (913) = nW(913) acting at a point C along its line of action in <1> . The unknown position vector of C from Q is denoted by xQ(913) in Fig 5.16. Thus, the equipollent moment condition (5.29) is (5.65) wherein xQ(P) is the position vector of a material parcel of weight dw(P) at P. With dw = dwn and use of (5.64) , (5.65) yields W(913)xQ x n = J9'! xQ(P)d w(P) x n. For simplicity, let us discard the subscript Q, and note that in general the position vectors may vary with time t , as suggested in Fig. 5.16 . Then, with these adjustments, since Qmay be chosen arbitrarily and n is a fixed 48 Chapter 5 direction , we may satisfy this equation by choosing the point at xdefined by W(~)x(~, t )=1x(P , t )dw(P ) 9B (5.66) to provide the location from Q of the point C at which the weight of ~ acts to produce a moment about Q equal to that of its distribution. The point of the body ~ defined by x(~, t) in (5.66) is called the center ofgravity of .9c3. The location of the center of gravity will depend on the variable gravitational field strength g(P) and the orientation of the body, which also might be nonhomogeneous"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001981_s11665-018-3563-8-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001981_s11665-018-3563-8-Figure3-1.png",
        "caption": "Fig. 3 Schematic of AM 4043 aluminum alloy: (a) location of the metallographic, ratcheting and tensile specimens, and (b) the shape",
        "texts": [
            " The walking speed of the ABB robot welding gun was 5.2 mm/s, and the printing path is shown in Fig. 1. When each layer of metal was printed, a 120-s cooling time was employed before printing the next layer. When the second layer was printed, the welding gun automatically rose 4.5 mm according to a pre-set program and continued to print the same length along the previous layer. A total of 8 layers were printed to fabricate a 4043 aluminum alloy wall specimen with dimensions of 90 9 7.5 9 38 mm. As shown in Fig. 3(a), three specimens were cut from the AM 4043 aluminum alloy to study the microstructure of the interlayer and the interlayer junctions. The size of the specimens was 10 9 8 9 5 mm. The surfaces of the specimens were polished until no obvious scratches remained on the surface before etching in Kelley s solution for 15 s to permit examination in an optical microscope (model: 4XCJZ). According to the report from D. Rouchard et al., the relationship between the secondary dendrite spacing (SDAS) and the cooling rate of the 4043 aluminum alloy is expressed by Eq 1, where B is the fitting factor for the 4043 aluminum alloy, with B = 50 lm (K s 1) and the constant n = 0",
            " Cooling rate \u00bc SDAS B 1=n \u00f0Eq 1\u00de Microhardness measurements for the printed aluminum alloy were performed using a Vickers microhardness tester (model: HXD-1000TMSC/LCD) under a load of 100 g and a dwell time of 15 s. Microhardness measurements were taken along the length of the specimen from top to bottom. The interlayer hardness test interval was 0.2 mm. However, by observing the microstructure changes, when the near-interlayer joints were approached, the hardness at the interlayer joints was measured at a slightly adjusted test interval, making the interval value vary slightly from 0.2 mm. Tensile test specimens were produced from the material according to the ISO 4136:2001 standard, as shown in Fig. 3(b). The long axes of the tensile specimens were perpendicular to the print direction, and the thickness of the specimens was 1 mm. The size of the parallel segment was 10 9 2 9 1 mm. The ratcheting and tensile specimens had the same size. Tensile tests were performed under strain control via an in situ bidirectional tension\u2013compression testing system (model: IBTC-300). All the tensile tests were performed at a rate of 0.01 mm/s. Fracture analysis of the broken tensile specimens was performed using a scanning electron microscope (model: 3400 N)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000758_1.4001600-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000758_1.4001600-Figure6-1.png",
        "caption": "Fig. 6 Rendered triangulation",
        "texts": [
            "org/ on 04/25/201 However, the surface can be represented, for instance, by means of a Non Uniform Rational B-Splines NURBS approximation to the resulting cloud of points. A MAPLE R application has been developed to assess the cloud of points with various levels of accuracy N in order to map the surface, as follows: A i = i R i = i M i = i i = \u2212 N . . . N 21 This is done in such a way that all possible combinations are chosen, resulting in 2N+1 3 points. The cloud of points is represented in Fig. 5 for N=20 68,921 points and Fig. 6 shows a rendered triangulation of the resulting surface. The points near the coordinate planes are also represented in Figs. 7\u20139. In Eq. 21 , the parameters A, R, and M are real values varying from \u2212 to . Each value has a direct correspondence in the FA /C0a , FR tan /C0a , M /d /C0a coordinate system. According with Eq. 3 , the variation range of A, R, and M would be similar to the variation range of a, r, and , and one can think that very large values for these displacements would not be realistic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003074_rpj-01-2020-0001-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003074_rpj-01-2020-0001-Figure12-1.png",
        "caption": "Figure 12 Transformation to vz(0,0,1) via two axes",
        "texts": [
            " We first deal with the problem of rotating v1s to vz around C, which has such three steps, translating from C to O, then rotating v1s to vz around O, and translating from O to C, corresponding to three transformation matrixes, Mco, Msoz and Moc respectively, while rotating matrix Msoz is equal to the matrixes of rotating around vz(1,0,0), vy(0,1,0) and vx(0,0,1) by angles g , b anda respectively, thus we have: Msz \u00bc 1 0 0 1 0 XC 0 YC 0 0 0 0 1 ZC 0 1 2 664 3 775 1 0 0 cosa 0 0 sina 0 0 sina 0 0 cosa 0 0 1 2 664 3 775 cosb 0 0 1 sinb 0 0 0 sinb 0 0 0 cosb 0 0 1 2 664 3 775 cosg sing sing cosg 0 0 0 0 0 0 0 0 1 0 0 1 2 664 3 775 1 0 0 1 0 XC 0 YC 0 0 0 0 1 ZC 0 1 2 664 3 775 (4) To calculate Msoz, look at the second step. v1s can be rotated to vz through mere two axes. Here we choose the xaxis and z-axis as an example shown in Figure 12(a), firstly rotating v1s around the z-axis by g until it is on yOz plane and then rotating around x-axis to vz by a. tan g\u00f0 \u00de \u00bc Yv1s Xv1s ; cos a\u00f0 \u00de \u00bc Zv1sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xv1s 2 1Yv1s 2 1Zv1s 2 p \u00bc Zv1s . By rotating v1s around the z-axis, y-axis and x-axis successively, we get g \u00bc atan2 Yv1s ;Xv1s\u00f0 \u00de, b = 0, a = acos Zv1s\u00f0 \u00de. It is similar if we choose the y-axis and z-axis shown in Figure 12(b). As forMzt in the process of rotating vz to v1t aroundC, it can be written asMzt =Mco *Mzot *Moc, whereMzot is the rotating matrix from vz to v1t around O. As an inverse process of rotating v1t to vz around O, it can be performed by rotating around x-axis, y-axis and z-axis by angles a 0, b 0 and g 0 respectively, presented as follows: Process planning for five-axis wire Fusheng Dai, Haiou Zhang and Runsheng Li Rapid Prototyping Journal Mzot \u00bc cosg 0 sing 0 sing 0 cosg 0 0 0 0 0 0 0 0 0 1 0 0 1 2 664 3 775 cosb 0 0 0 1 sinb 0 0 0 0 sinb 0 0 0 0 cosb 0 0 0 1 2 6664 3 7775 1 0 0 cosa 0 0 0 sina 0 0 0 sina 0 0 0 cosa 0 0 0 1 2 664 3 775 (5) where a 0 \u00bc acos Zv1t\u00f0 \u00de b 0 \u00bc 0 g 0 \u00bc atan2 Yv1t ;Xv1t\u00f0 \u00de The whole transformation is achieved by merging these two processes, then we have P 0 1 \u00bc Mco Msoz Moc\u00f0 \u00de Mco Mzot Moc\u00f0 \u00de P1 \u00bc Mco Msoz Mzot Moc P1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002700_j.jmapro.2019.12.016-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002700_j.jmapro.2019.12.016-Figure5-1.png",
        "caption": "Fig. 5. Distribution of the lines of grinding contact observed from testing: (a) machining of the worm; (b) scratches on the worm tooth surface; (c) contact lines on the worn roller.",
        "texts": [
            " The values of the error parameters were maximum values observed and recorded from testing this device, which are \u0394\u03c62 = \u0394\u03b1 = \u0394\u03b2=0.1\u00b0, and \u0394a = \u0394c = \u0394d = \u0394R=0.1mm. From above plots it can be seen that the line of grinding contact is significantly affected by the error in radius of the grinding rod and the overall error. The other error parameters mainly changed the contact pattern between the grinding rod and the worm blank, whose influences on the contact line are smaller. Practical phenomena observed during the machining of the worms agreed very well with what was predicted by our theoretical model. Fig. 5 shows a rejected worm caused by a manufacturing error in machining its tooth surface (Fig. 5a). Scratches on the tooth surface (Fig. 5b) is a consequence of poor engagement due to the abrasive wear of the grinding rod (\u0394R). Fig. 5c displays the worn grinding rod. From that figure it can be found that the contact lines on the upper half of the rod are very close to the lines plotted in Fig. 4h. In order to minimize the effects of the error parameters during the machining process and improve the fineness of grind of the worm tooth surface so as to reduce the toughness of such surface, we performed topography analyses on the grinding rod using a metallurgical microscope. Several measures were suggested to improve the machining of the worm tooth surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure3-1.png",
        "caption": "Figure 3. Piston regions for conjugated HT-FEA 3D-CFD modeling",
        "texts": [
            " In addition, moving the cooling gallery to the periphery instead of the center will allow optimization of the first ring groove position thereby reducing the crevice volume that will, in turn, help to reduce pollutant emissions [7]. In order to perform the heat transfer analysis on the gasoline piston, it has been decided to use the CFD software Star-CCM+ 8.06.007 [8] due to its ability to model heat transfer accurately. The piston model has been divided into the following components shown in Figure 3: Piston top land (up to the first ring groove), rings region, piston skirt, cooling gallery, pin hole region (where pin bore is joined to the connecting rod), piston undercrown, and piston bottom. Due to the complexity of defining a full 3D-CFD conjugate heat transfer simulation including the combustion chamber flow field, it was decided to impose heat transfer coefficients obtained from previous research at the different piston elements. Consistent values have been obtained from different references [9, 10, 11, 12]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000011_978-3-540-73890-9_14-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000011_978-3-540-73890-9_14-Figure2-1.png",
        "caption": "Fig. 2. Three-dimensional bipedal robot",
        "texts": [],
        "surrounding_texts": [
            "In this section we construct a control law that results in stable walking for a simple model of a 3D bipedal robotic walker. In order to achieve this goal, we shape the potential energy of this model via feedback control so that when hybrid functional Routhian reduction is carried out, the result is the 2D walker H s 2D introduced in the previous section. We utilize Theorem 2 to demonstrate that this implies that the 3D walker has a walking gait on flat ground (in three dimensions). This is the main contribution of this work. 3D biped model. We now introduce the model describing a controlled bipedal robot walking in three dimensions on flat ground, i.e., we will explicitly construct the controlled hybrid system describing this system: H3D = (D3D, G3D, R3D, f3D). The configuration space for the 3D biped is Q3D = T2\u00d7S and the Lagrangian describing this system is given by: L3D(\u03b8, \u03b8\u0307, \u03d5, \u03d5\u0307) = 1 2 ( \u03b8\u0307 \u03d5\u0307 )T ( M2D(\u03b8) 0 0 m3D(\u03b8) )( \u03b8\u0307 \u03d5\u0307 ) \u2212 V3D(\u03b8, \u03d5), where m3D(\u03b8) is given in the Table 1. Note that, referring to the notation introduced in Section 3, M\u03b8(\u03b8) = M2D(\u03b8) and M\u03d5(\u03b8) = m3D(\u03b8). Also note that L3D is nearly cyclic; it is only the potential energy that prevents its cyclicity. This will motivate the use of a control law that shapes this potential energy. Using the controlled Euler-Lagrange equations, the dynamics for the walker are given by: M3D(q)q\u0308 + C3D(q, q\u0307)q\u0307 + N3D(q) = B3Du, with q = (\u03b8, \u03d5) and B3D = ( B2D 0 0 1 ) . These equations yield the control system: (q\u0307, q\u0308) = f3D(q, q\u0307, u) := fL3D(q, q\u0307, u). We construct D3D and G3D by applying the methods outlined in Section 2 to the unilateral constraint function h3D(\u03b8, \u03d5) = h0 2D(\u03b8) = cos(\u03b8s)\u2212 cos(\u03b8ns). This function gives the normalized height of the foot of the walker above flat ground with the implicit assumption that \u03d5 \u2208 (\u2212\u03c0/2, \u03c0/2) (which allows us to disregard the scaling factor cos(\u03d5) that would have been present). The result is that h3D is cyclic. Finally, the reset map R3D is given by: R3D(\u03b8, \u03b8\u0307, \u03d5, \u03d5\u0307) = ( S2D\u03b8, P2D(\u03b8)\u03b8\u0307, \u03d5, p3D(\u03b8)\u03d5\u0307 ) where p3D(\u03b8) is given in Table 1. Note that this map was again computed using the methods outlined in Section 2 coupled with the condition that the stance foot is fixed. Control law construction. We now proceed to construct a feedback control law for H3D that makes this hybrid system an almost-cyclic unilaterally constrained Lagrangian hybrid system, H \u03b1 3D. We will then demonstrate, using Theorem 2, that H \u03b1 3D has a walking gait by relating it to H s 2D. Define the feedback control law parameterized by \u03b1 \u2208 R: u = K\u03b1 3D(q) := B\u22121 3D \u2202 \u2202q ( V3D(q)\u2212 V \u03b3 2D(\u03b8) + 1 2 \u03b12\u03d52 m3D(\u03b8) ) Applying this control law to the control system (q\u0307, q\u0308) = f3D(q, q\u0307, u) yields the dynamical system: (q\u0307, q\u0308) = f\u03b1 3D(q, q\u0307) := f3D(q, q\u0307,K\u03b1 3D(q)), which is just the vector field associated to the almost-cyclic Lagrangian L\u03b1 3D(\u03b8, \u03b8\u0307, \u03d5, \u03d5\u0307) = 1 2 ( \u03b8\u0307 \u03d5\u0307 )T ( M2D(\u03b8) 0 0 m3D(\u03b8) )( \u03b8\u0307 \u03d5\u0307 ) \u2212 V \u03b1 3D(\u03b8, \u03d5), where V \u03b1 3D(\u03b8, \u03d5) = V \u03b3 2D(\u03b8) \u2212 1 2 \u03b12\u03d52 m3D(\u03b8) . That is, f\u03b1 3D = fL\u03b1 3D . Let H \u03b1 3D := (D3D, G3D, R3D, f\u03b1 3D), which is a unilaterally constrained Lagrangian hybrid system. Applying hybrid functional Routhian reduction. Using the methods outlined in Section 3, there is a momentum map J3D : TQ3D \u2192 R given by: J3D(\u03b8, \u03b8\u0307, \u03d5, \u03d5\u0307) = m3D(\u03b8)\u03d5\u0307. Setting J3D(\u03b8, \u03b8\u0307, \u03d5, \u03d5\u0307) = \u03bb(\u03d5) = \u2212\u03b1\u03d5 implies that \u03d5\u0307 = \u2212 \u03b1\u03d5 m3D(\u03b8) . The importance of H \u03b1 3D is illustrated by: Proposition 1. H \u03b1 3D is an almost-cyclic unilaterally constrained Lagrangian hybrid system. Moreover, the following diagram commutes: Rk G3D R3D J3D|G3D D3D J3D|D3D G2D \u03c0 R2D D2D \u03c0 Therefore, H s 2D is the functional Routhian hybrid system associated with H \u03b1 3D. This result allows us to prove\u2014using Theorem 2\u2014that the control law used to construct H \u03b1 3D in fact results in walking in three dimensions. Theorem 4. \u03c7H \u03b1 3D = (\u039b, I, {(\u03b8i, \u03b8\u0307i, \u03d5i, \u03d5\u0307i)}i\u2208\u039b) is a hybrid flow of H \u03b1 3D with \u03d5\u03070(\u03c40) = \u2212 \u03b1\u03d50(\u03c40) m3D(\u03b80(\u03c40)) , (3) if and only if \u03c7H s 2D = (\u039b, I, {\u03b8i, \u03b8\u0307i}i\u2208\u039b) is a hybrid flow of H s 2D and {(\u03d5i, \u03d5\u0307i)}i\u2208\u039b satisfies: \u03d5\u0307i(t) = \u2212 \u03b1\u03d5i(t) m3D(\u03b8i(t)) , \u03d5i+1(\u03c4i+1) = \u03d5i(\u03c4i+1). (4) To better understand the implications of Theorem 4, suppose that \u03c7H \u03b1 3D = (\u039b, I, {(\u03b8i, \u03b8\u0307i, \u03d5i, \u03d5\u0307i)}i\u2208\u039b) is a hybrid flow of H \u03b1 3D. If this hybrid flow has an initial condition satisfying (3) with \u03b1 > 0 and the corresponding hybrid flow, \u03c7H s 2D = (\u039b, I, {\u03b8i, \u03b8\u0307i}i\u2208\u039b), of H s 2D is a walking gait in 2D: \u039b = N, lim i\u2192\u221e \u03c4i = \u221e, \u03b8i(\u03c4i) = \u03b8i+1(\u03c4i+1), then the result is walking in three dimensions. This follows from the fact that \u03b8 and \u03b8\u0307 will have the same behavior over time for the full-order system\u2014the bipedal robot will walk. Moreover, since Theorem 4 implies that (4) holds, the walker stabilizes to the \u201cupright\u201d position. That is, the roll \u03d5 will tend to zero as time goes to infinity since (4) essentially defines a stable linear system \u03d5\u0307 = \u2212\u03b1\u03d5 (because m3D(\u03b8i(t)) > 0 and \u03b1 > 0), which controls the behavior of \u03d5 when (3) is satisfied. This convergence can be seen in Fig. 3 along with a walking gait of the 3D walker."
        ]
    },
    {
        "image_filename": "designv10_12_0002151_1350650115574869-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002151_1350650115574869-Figure2-1.png",
        "caption": "Figure 2. FZG efficiency gear test rig.",
        "texts": [
            " The sum velocity v and the sliding velocity vg are defined as v \u00bc v1 \u00fe v2 \u00f02\u00de vg \u00bc v1 v2 \u00f03\u00de All running-in experiments are performed under line contact condition with cylindrical discs having a diameter of 80mm and a width of 5mm. The discs are made from case-carburized steel (16MnCr5E) and axially ground. The initial surface roughness in terms of arithmetic mean roughness Ra, measured perpendicular to the grinding direction, is approximately Ra\u00bc 0.5 m (section \u2018\u2018Surface roughness\u2019\u2019). For the investigations of running-in at gears a modified FZG back-to-back gear test rig - the FZG efficency gear test rig10 - shown in Figure 2 is used. Thereby, two matching pairs of spur gears type C11 are mounted in the test and in the slave gear box. The geometrical data of spur gear type C is shown in Table 1. Table 1. Geometrical data of spur gear type C11 (no profile modification, no helix modification, no crowning). Symbol Pinion (1) Wheel (2) Unit Centre distance a 91.5 mm Face width b 14 14 mm Pitch diameter dw 73.2 109.8 mm Tip diameters da 82.45 118.35 mm Module m 4.5 mm Number of teeth z 16 24 \u2013 Addendum modification factor x 0",
            ",13 the direct alignment of roughness measurements of the same measuring point before and after running-in of an individual disc pair is shown. Each value in Figure 5 is a mean of six single roughness measurements per disc pair. Although no clear correlation of Ra, Rpk, and Rsk with x0 has been found (x0 decreases from left to right in Figure 5), a notable influence of the Hertzian pressure pH as found in Wang et al.,4 Cavatorta and Cusano,5 and Roy Chowdhury,6 has been observed (cf. Figure 5, subfigure 2 and 3). Thereby, the influence of #Oil on the reduction of the roughness parameters is rather secondary (cf. Figure 5, subfigure 3 and 4). A comparison of the lubricants shows that FVA3\u00fePD features the lowest reduction of roughness parameters for each running-in condition although the reduction of the coefficient of friction is highest (Figure 4). Just as Figure 5 shows a large effect of the runningin on the skewness roughness parameter Rsk, Figure 6 compares the asperity height distribution before and after running-in at pH\u00bc 1300N/mm2, v \u00bc 1m/s, vg\u00bc 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure1-1.png",
        "caption": "Fig. 1. The topological structure of parallel manipulators with configurable platforms.",
        "texts": [
            " For parallel manipulators, to achieve better orientation performance and large workspace, the configurable platforms are expected to connect fewer legs as much as possible [26] . The number of active joints is equal to the dimension of the task space. And the active joints are installed on or next to the fixed base. Therefore, the multi-drive hybrid limbs are urgently desired to design full-controlled parallel manipulators with configurable platforms. The diagram of the topological structure for this kind of parallel manipulators is drawn in Fig. 1 . This paper, however, not oriented at CPMs, but aims at presenting a systematic method for designing parallel mechanisms with configurable platforms. A novel class of GPMs with configurable platforms is presented in this study. In Section 2 , the closed-loop linkages are designed to form configurable platforms with integrated end-effectors. In Section 3 , various serial limbs that exert different constraints on the end-effector are synthesized according to the screw theory. Then the multi-drive hybrid limbs are obtained through composing closed-loop chains and the serial limbs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.31-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.31-1.png",
        "caption": "Figure 2.31 Schematic illustration of DM3D\u2019s patented closed-loop feedback control system. courtesy: DM3D Technology.",
        "texts": [
            "30 shows images taken from Concept Laser\u2019s QMcoating module which captures visual images of the powder layer after the recoating process and indicates any anomaly through visual contrast differences in the images [70]. 3. Meltpool monitoring\u2014Direct sensing of the meltpool through photodiode, pyrometer, or camera-based monitoring provides direct information about the heat source and powder metal interaction. DM3D technology employs a patented closed-loop feedback control technology that uses a high-speed CCD camera to measure the layer height during the deposition process and modulates laser power and/or nozzle speed to obtain the desirable layer thickness [71] (Fig. 2.31). DMLS technology employs meltpool monitoring based on photodiodes. Signals from the meltpool can be collected with off-axis or on-axis sensors and the presence of a defect is reflected through an anomaly in the signal when compared to a standard reference signal (Fig. 2.32) [72]. The above concept of process monitoring can be taken one step further in process control. Another monitoring system employed in EOS machines is Exposure OT [72]. This is a camera-based system with specially designed optics to gather high-resolution and high-focal depth images in the NIR wavelength range from the entire build platform during laser processing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003776_j.rcim.2021.102193-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003776_j.rcim.2021.102193-Figure4-1.png",
        "caption": "Fig. 4. Illustration of the tool orientation deviation error.",
        "texts": [
            " The final transition length lpe of the position spline and loa, lob of the orientation spline are optimized by satisfying the constraints of the smoothing error for tool position and tool orientation and ensuring the C3 synchronization of the tool orientation path with respect to the tool position path, which will be discussed in the following two sections. The tool-axis vector is fixed in the tool frame {tb}. Without loss of generality, denote the tool-axis vector in the tool frame as Ob \u2208 R3, \u2016 Ob \u2016 = 1. Since the orientation linear path is smoothed at the corners, the actual tool axis O\u2032 b will deviate from the desired one, resulting in the orientation smoothing error as shown in Fig. 4. Generally, the orientation smoothing error is defined as the minimal angle deviation between the tool-axis vectors at the corner point r2 and at the inserted orientation spline O(u), which is difficult to calculate directly. Nevertheless, in literature, the orientation smooth error is usually estimated by the upper bound limit which is defined as the angle between the tool-axis vectors at the corner point r2 and the middle point O(0.5). As shown in Fig. 3(b), the deviation between the middle point of the inserted B-spline at u =0",
            "5) = 3 8 (loau1 \u2212 lobu2) (9) where u1 and u2 are the unit vectors along the line r1r2 and line r2r3, respectively. Then, the differential rotational displacement of the tool represented in the tool frame with regard to the deviation \u0394r in the rotation parametric space can be calculated by wb = A(r2)\u0394r (10) where A(r2) is the Jacobian matrix represented as [27] A(r2) = I \u2212 1 \u2212 cos\u2016 r2 \u2016 \u2016 r2 \u20162 [r2] + \u2016 r2 \u2016 \u2212 sin\u2016 r2 \u2016 \u2016 r2 \u20163 [r2] 2 (11) According to Eq. (10), the magnitude of the deviation \u0394O shown in Fig. 4 can be estimated as \u2016 \u0394O \u2016=\u2016 wb \u00d7Ob \u2016=\u2016 [Ob]A(r2)\u0394r \u2016 (12) From Eqs. (9) \u2013 (12), to comply with the user-defined orientation error tolerance limit, \u03b5\u2217o, Eq. (13) should hold \u2016 \u0394O \u2016= 2sin(\u03b5o / 2) \u2264 2sin ( \u03b5\u2217o / 2 ) \u21d2loa \u2264 16sin ( \u03b5\u2217o / 2 ) 3 \u2016 [Ob]A(r2)(u1 \u2212 ku2) \u2016 (13) J. Peng et al. Robotics and Computer-Integrated Manufacturing 72 (2021) 102193 where k = lob /loa is a constant, and its value will be determined in section 2.4. After local smoothing, the generated smooth tool path consists of the remaining linear segments and spline segments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure1-1.png",
        "caption": "Fig. 1. Structure drawing of the mechanism.",
        "texts": [
            " Meanwhile, for the parallel six-axis force sensing mechanisms integrating flexible elements, the precise force mapping analytical modeling between the six-dimensional external force and the axial tension/compression of the flexible measurement limbs is seldom studied, which confines for the configuration optimization design of flexible parallel six-axis force sensing mechanism. Consider the above problems, starting from the flexibility matrix of basic flexible elements, the flexibility matrix of the flexible series branches and the stiffness matrix of the force sensing mechanism are derived in this paper. On this basis, the theoretical derivation of the force mapping relation is also obtained. The structure drawing of the six-component force sensing mechanism is shown in Fig. 1. From this drawing, the structure of the mechanism is a spoke structure with hybrid branches and can be divided into four parts: an outside platform called fixed platform, an inside platform called measuring platform, 8 flexible measuring branches and 4 load-bearing branches. The 8 flexible measuring branches can be divided into four symmetrical groups, in which group the angles of the two branches are opposite. The two ends of each flexible measuring branch are provided with two right circular flexible spherical joints and two flexible thin beams, and the middle is connected into a whole by a flexible rectangular beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure20-1.png",
        "caption": "Fig. 20. Stress results of dangerous positions.",
        "texts": [
            "2 are recognized to be suitable to predict the fatigue life of the two wheels. The simulation processes of the stamping and the cornering fatigue test of the two wheels are similar with above. The model of wheel 1 is 16 6 J with five bolt holes, and the stress distributions of wheel 1 is shown in Fig. 19 under the load applied at 0-deg. The dangerous area locates at the connecting position between the bolt hole and the strengthening rib, as shown in Fig. 18. One typical point in this area (Point B in Fig. 20) is selected to calculate the operating stress, and this point suffers an approximate cosine form of alternating stress in one cycle (Fig. 21). A comparison of the operating stress in one cycle before and after the superposition of the residual stress is shown in Fig. 21. The corresponding fatigue life is estimated by Eq. (16), as shown in Table 7. The experimental fatigue life of this steel wheel on the fatigue test machine is 1.79 million revolutions and the cracking position is consistent with the simulation results, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002249_iros.2017.8206400-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002249_iros.2017.8206400-Figure7-1.png",
        "caption": "Fig. 7. Vehicle configuration and nomenclatures of elevons",
        "texts": [
            " The control algorithm can be written as MT = Kpw e b +Ki \u222b we bdt+Kd dwe b dt + w\u0302bJbwb (9) where MT = [ MTx MTy MTz ]T \u2208 R3 is the moment vector, Kp, Ki, and Kd are positive diagonal gains for the PID controller, we b = wd b \u2212 wb is the angular velocity error. After getting the trust and moment, a tail-sitter mixer is used to allocate them to the proper actuators. As mentioned in Section II-A, we further incorporate a pair of elevons to enhance the stability for level and transitional flight. The configuration of our vehicle is shown in Fig. 7. \u03b4i is the elevon deflection angle. fl and fr are respectively the lift forces produced by the left wing and right wing, and l1 is the distance between the lift forces, which acts on the mean aerodynamic chord (MAC), and longitudinal axis. According to [24], fl and fr can be represented as fl = 1 2 \u03c1V 2Sl (CL0 + CL\u03b1\u03b1+ CL\u03b4 \u03b41) fr = 1 2 \u03c1V 2Sr (CL0 + CL\u03b1\u03b1+ CL\u03b4 \u03b42) (10) where Sl and Sr are respectively the left and right wing area. Because of symmetry, Sl and Sr are the same. CL0 is the lift coefficient when \u03b1 = 0 and \u03b4i = 0, CL\u03b1 and CL\u03b4 are respectively two lift coefficient terms derived with respect to the angle of attack and elevons deflection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002076_j.triboint.2014.09.014-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002076_j.triboint.2014.09.014-Figure14-1.png",
        "caption": "Fig. 14. Bearing failed due to cage fracture; the cage lost its original shape and the balls were clustered together.",
        "texts": [
            " We did not find any spalls, which indicated that fatigue was not a dominant failure mechanism for the bearings in our study. The bearing cage was susceptible to physical degradation. The tolerances between the cage and balls were increased after bearing failure. Wear on the contact surfaces of the cage against the balls was the most severe among the contact surfaces of other bearing elements made of steel (i.e., the balls, the inner race, and the outer race). All the failed bearings from tests no. 4\u201312 showed deformation of the cage. As presented in Fig. 14, the bearing from test no. 11 was an extreme case in which the cage was fractured, which caused the bearing to cease rotating due to the increase in the friction force in the bearings. Many of the leading original equipment manufacturers (OEMs) in the electronics industry are interested in the reliability of ball bearings, which are known to contribute to low-power electric motor failure. In this paper, the failure mechanisms of ball bearings were investigated under lightly loaded, non-accelerated usage conditions, which better emulated bearing failures under the actual operating conditions of most commercial electronics than in previous studies",
            " Although the grease in the life tests was stressed for 9,120 hours (E one year) on average, no oxidation products were detected in the infrared spectral analysis. This indicated that chemical deterioration of the grease was insignificant under the loading condition. The reduction in lubricating ability caused severe damage in the glass-fiber reinforced polyamide cages. The cage materials were not as hard as the other bearing elements made of steel, which caused them to wear preferentially. In an extreme case, the bearing cage was fractured, which caused the bearing to cease rotating due to the increase in friction (see Fig. 14). Bearing elements made of steel, including the balls and inner and outer races, did not show any spalling, although numerous pits and transfer film layers were observed on their contact surfaces. Thus, the fatigue of bearing steel was not a failure mechanism for the ball bearings in this study. Wear performance of the cage should be improved to enhance the reliability of ball bearings, as the cages were more susceptible to wear than any other bearing elements made of steel. However, unintended consequences must be considered before changing cage materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001420_s11431-013-5433-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001420_s11431-013-5433-9-Figure2-1.png",
        "caption": "Figure 2 Nine basic kinds of planar four-bar linkages.",
        "texts": [
            " Therefore, the planar four-bar phase in Figure 1(b) has a translational output. Next, planar five-bar linkages meeting these requirements are enumerated. Since adding a joint to a planar four-bar linkage generates a planar five-bar linkage, attention is paid to planar four-bar linkages according with the phase in Figure 1(b). Considering that link 3 in Figure 1(b) has a translational motion and joint C is a revolute joint, three planar four-bar linkages, shown in Figure 3, are selected from nine basic types of planar four-bar linkages in Figure 2. Figure 3(a) shows a planar four-bar parallelogram that is a special case of the linkage in Figure 2(a). It is ob- vious that joints D and C have the same instantaneous translational motion perpendicular to link 4(2), which determines that link 3 has a translational output with changeable direction. Planar five-bar metamorphic linkages can be obtained by inserting appropriate joint A between joints B and E of the planar four-bar linkages in Figure 3. Some necessary conditions should be taken into consideration. For the planar four-bar parallelogram in Figure 3(a), the additional joint A can be either a revolute joint or a prismatic joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001128_9781118562857.ch1-Figure1.28-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001128_9781118562857.ch1-Figure1.28-1.png",
        "caption": "Figure 1.28. Schematic arrangement of the LRM process domain",
        "texts": [
            " However, Inconel-625 clad does not show any significant improvement in the erosion wear resistance at higher impact angles compared to that of the substrate material (AISI 304L steel). A possible reason for the lack of improvement in the erosion wear resistance of the clad layer may be the higher degree of dilution and insignificant improvement in the micro-hardness of the clad layer [MAN 00]. Experimental investigations on the erosion wear behavior of the LRM surface of Colmonoy-6 and Inconel-625 on SS316L and SS304L were carried out, and showed improvement in the surface properties of engineering materials. Figure 1.28 presents the schematic arrangement of the LRM process domain. The physical domain of the LRM process consists of a substrate, deposited material, a powder stream and a laser beam. To model the process, the laser beam specifications, material deposition, laser beam-powder interactions and heat transfer throughout the process domain should be integrated in a dynamic fashion. Figure 1.29 presents various interaction zones (involving laser, powder, shielding gas and substrate) and their effects. The total interaction process can be divided into two interaction zones, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002903_cdc40024.2019.9029417-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002903_cdc40024.2019.9029417-Figure2-1.png",
        "caption": "Fig. 2. Robosimian coordinates for optimization in MuJoCo [7], shown here for skate 1, where skate numbering is clockwise. \u03b8 is the rotation about the z axis, which points out of the page for the world, body, and skate frame coordinates.",
        "texts": [
            " Section II describes modeling details for a simplified Robosimian system to be used in the trajectory optimization framework, the latter of which is outlined in detail in Section III. Section IV presents results from using this framework to efficiently skate forward, skid and turn around simultaneously, and skate with different gaits. A brief conclusion and future outlook is given in Section V. We first ignore all internal degrees of freedom for the full Robosimian model and consider a free floating body with floating skate end effectors, whose coordinate frames are as shown in Figure 2. Throughout this work we will assume no pitch or roll from any body. In the figure, (xw,yw,zw) are the fixed world frame coordinates for the global origin, and thus (xb,yb,zb) are the robot\u2019s body center coordinates relative to the fixed world frame. \u03b8b represents the counterclockwise (CCW) rotation of the body x-axis, relative to the fixed world frame x-axis xw. Each skate\u2019s coordinates (xi,yi,zi) are relative to the body frame, where i\u2208{1,2,3,4}, starting with the front right skate (shown), and proceeding clockwise (so skate 2 is the rear right, skate 3 is the rear left, skate 4 is the front left, when viewed from above)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002003_tfuzz.2018.2883369-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002003_tfuzz.2018.2883369-Figure3-1.png",
        "caption": "Fig. 3. A two links manipulator robot.",
        "texts": [
            " The consequent parameters are determined through the PI adaptive laws (20) and (21), and they are initialized as follows: , for , for j=1,...,81. The control parameters are chosen as follows: The initial conditions are chosen as: The disturbances are taken as square signals with an amplitude of and a frequency of 1/ . The simulation results are depicted in Fig.2. It can be seen from this figure that the system successfully tracks its reference signals and the control input signals are admissible and bounded. Example 2: Consider the dynamical equations of a two-link rigid manipulator robot, as shown in Fig.3 [8]: with and where and Fig.2. Simulation results for a 2 DOF polar manipulator robot (example 1) : (a) Tracking of , (b) Tracking of (c) Tracking of , (d) Tracking of , (e ) Tracking errors and , (f ) Tracking errors and , (g ) Norm of fuzzy parameters: and , (h) Control signals: u1 and u2. 1063-6706 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure4.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure4.7-1.png",
        "caption": "Fig. 4.7 Directions of ball spin and the Magnus force on various pitched balls, as viewed by the batter and pitched by a right hand pitcher. Gravity pulls the ball downward in all cases. The Magnus force acts in a direction perpendicular to the spin axis, in the directions shown, causing the ball to break left or right as well as up or down. There is no Magnus force on a gyroball",
        "texts": [
            " And both sports have a richly documented variety of pitched ball types. In cricket, there are inswingers, outswingers, reverse swingers, legspinners, legbreaks, offbreaks, flippers, doosras, bouncers, zooters, and googlies. Some of those terms refer to the flight through the air and some refer to the bounce off the pitch before the ball reaches the batter. In baseball there are curveballs, fastballs (two-seam and fourseam), cutters, sliders, sinkers, changeups, knuckleballs, screwballs, and gyroballs plus a few others [2\u20134] (Fig. 4.7). It is difficult to find clear definitions of each pitch type in terms of physical properties, such as the inclination of the spin axis, partly because the forward or backward tilt of the spin axis is difficult to measure. Cricket balls and baseballs have almost the same weight and diameter and both have a leather cover. The main difference concerns the stitching used to attach the cover. In cricket, there are several parallel rows of stitches running around the equator. The stitching used in a baseball follows the same curved path as the seam in a 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001654_s00170-017-1048-9-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001654_s00170-017-1048-9-Figure8-1.png",
        "caption": "Fig. 8 Geometry of ball end mill (a\u2013d). Chip thickness regeneration (e)",
        "texts": [
            " Equation 10 shows the relation between different force components [39, 41]: dFt z; \u03b8\u00f0 \u00de \u00bc Kteds\u00fe Ktch \u03c8; \u03b8;\u03ba\u00f0 \u00dedb \u00f010A\u00de dFr z; \u03b8\u00f0 \u00de \u00bc Kreds\u00fe Krch \u03c8; \u03b8;\u03ba\u00f0 \u00dedb \u00f010B\u00de dFa z; \u03b8\u00f0 \u00de \u00bc Kaeds\u00fe Kach \u03c8; \u03b8;\u03ba\u00f0 \u00dedb \u00f010C\u00de where \u03a8 is the helix lag angle in global coordinates between the tip of the cutter (z = 0) and the cutting edge point (z), ds is the length of an infinitesimal curved cutting edge segment and db is the infinitesimal cutting flute in the direction along the cutting velocity. In Eq. 11A\u2013C, Ktc, Krc and Kac are the tangential, radial and axial cutting force coefficients (force/area) and Kte, Kre and Kae are the tangential, radial and axial edge force coefficients (force/length) respectively (see Fig. 8). ds and db are calculated according to Eqs. 11 and 12. ds \u00bc drj j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R 0 \u03c8\u00f0 \u00de2 \u00fe R \u03c8\u00f0 \u00de2 \u00fe R2 0cot 2i0 r d\u03c8 \u00f011\u00de db \u00bc dz=sin\u03ba \u03ba \u00bc sin\u22121 R \u03c8\u00f0 \u00de=R0\u00f0 \u00de\u21d2db \u00bc dzR0 R \u03c8\u00f0 \u00de \u00f012\u00de where i0 is the helix angle at the ball-shaped flute and shank meeting point measured from the y-axis (CW). R(\u03a8) is the tool radius in the x-y plane at a point defined by \u03a8, and its derivate is obtained from the following equations",
            " \u00f028\u00de EI \u22024\u03c9 \u2202z4 \u00fe Fa z; \u03b8\u00f0 \u00de \u2202 2\u03c9 \u2202z2 \u00fem \u22022\u03c9 \u2202\u03b82 \u2212 \u03c1I\u00fe mEI \u03baAG \u22024\u03c9 \u2202z2\u2202\u03b82 \u00fe \u03c1I \u03baAG \u22024\u03c9 \u2202\u03b84 \u00bc KreR0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u03c8Cot i0\u22121\u00f0 \u00de2Cot2 i0 1\u2212 \u03c8Cot i0\u22121\u00f0 \u00de2 \u00fe 2\u03c8\u2212\u03c82Cot i0 \u00fe Cot i0 Cot i0 s\" # d\u03c8\u00fe Krcdb Rc Kz; t\u00f0 \u00de\u2212Rs Kz;m; t h i dz\u00fe \u03c1I \u03baAG \u22022Fr \u2202\u03b82 \u2212 EI \u03baAG \u22022Fr \u2202z2 \u00f029\u00de In Eq. 13, the value of the radical should be zero or positive: 1\u2212 \u03c8cot i0\u22121\u00f0 \u00de2\u22650\u21d22\u2265\u03c8cot i \u00f030\u00de In this experiment, the helix angle was 30\u00b0; therefore, the maximum value of \u03a8 becomes \u03c8\u22641:15rad \u03c8\u226466:11\u00c5 \u00f031\u00de According to Fig. 8c\u2013e, T2T3 is obtained by using sin laws: sin900 4 \u00bc sin330 T2T3 \u21d2T2T3 \u00bc 2:17mm \u00f032\u00de Rsm is the maximum radial depth of cut/finishing allowance that is calculated from the following equations: T1T3 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 c \u03c8\u00f0 \u00de\u2212R2 big q \u00bc 3:354mm \u00f033\u00de Rsm \u00bc Rc \u03c8\u00f0 \u00de\u2212T1T3 \u00bc 0:645mm \u00f034\u00de Tool deflection for static cutting forces for two tests with different feed rates: \u03b4t \u00bc Fc\u03be \u00fe D 1\u2212 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe B2 p ! \u00bc m dvcm dt \u03be \u00fe D 1\u2212 1ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe B2 p "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003357_0954406220911966-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003357_0954406220911966-Figure10-1.png",
        "caption": "Figure 10. Oscillating motion of the bearing and the oscillating amplitude. Figure 11. Oscillating load acting on the bearing.",
        "texts": [
            " Qc,M,N indicates the basic dynamic load rating of a roller which is expressed as9 Qc,M,N \u00bc 1 l Cr,N 0:378Zr7=9 cos N 1\u00fe 1:038 1 1\u00fe 143=108 \" # 9=28< : 9= ; 2=9 , M \u00bc 1, 2 andN \u00bc i, o\u00f0 \u00de \u00f022\u00de In equations (21) and (22), the upper and lower signs are used for the inner and outer rings, respectively. r represents the number of rows, r\u00bc 2. The reduction factors l \u00bc 0:83 and \u00bc Dmcos\u00f0 N\u00dedm are adopted from the literature.9 Here, Dm and dm are the mean roller diameter and pitch diameter of the bearing, respectively. The basic dynamic radial load rating of the DTRB is given by Cr,N \u00bc bmfc rlwe cos N\u00f0 \u00de 7=9Z3=4D29=27 m \u00f023\u00de where the value of fc can be found by9 fc \u00bc 0:483B10:377l 2=9 1 \u00f0 \u00de 29=27 1\u00fe \u00f0 \u00de 1=4 1\u00fe 1:04 1 1\u00fe 143=108 \" #9=2 8< : 9= ; 9=2 \u00f024\u00de Figure 10 shows the schematic of a bearing under oscillating motion. The amplitude of the oscillation is . According to Harris et al.,28 when the oscillation amplitude is higher than a certain critical angle ( crit), the oscillation speed factor is given by aosc n \u00bc 2 \u00f025\u00de If is smaller than crit, the oscillation speed factor is determined by aosc n \u00bc 2 2=9 Z0:0277 p \u00f026\u00de where p\u00bc 10/3 is for roller bearing, and the critical angle is calculated by crit \u00bc 2 Z 1 \u00f0 \u00de \u00f027\u00de The oscillation factor in equation (26) is applicable for the case when the oscillation angle is larger than the so-called dither angle ( dith)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure5.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure5.3-1.png",
        "caption": "FIGURE 5.3. The geometrical properties of a cylinder.",
        "texts": [
            " For visco-elastic materials, the modal loss-factor \u03b7 can be defined as: \u03b7 = =\u03c92 <\u03c92 (5.40) In this text, the frequency factor, \u2126, as defined by Armenakas et al. (1969), is implemented, which is: \u2126 = <\u03c9 \u03c9s (5.41) where, \u03c9s = \u03c0v2 H (5.42) and v2 is the velocity of the distortional wave for the inner layer v2 = r \u03bc \u03c1 (5.43) and H is the total thickness of the layered cylinder. 5.8 Sample Calculations for One Layered Cylinder Consider a single layer steel cylinder with thickness of H = 0.35294 in, density of \u03c1 = 0.000725 lb s2/ in4, and shear modulus of \u03bc = 1.1538\u00d7 107 lb/ in2. Figure 5.3 depicts the geometrical properties of the considered single layer cylinder, which has the following specifications: 5. Vibration of Multi-Layer thick cylinders 89 inner radius: a = 1 in. outer radius: b = 1.35294 in. mean radius: R = (a+ b)/2 = (1 + 1.35294)/2 = 1.17650 in. thickness of the cylinder H: H = b\u2212 a = 1.35294\u2212 1 = 0.35294 in. thickness to radius ratio of H/R: H/R = 0.35294/1.17650 = 0.3. Assuming the thickness to length H/L = 0.1. The axial wave length \u03b6 was defined in section 4.4 by equation (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003355_j.matpr.2020.02.542-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003355_j.matpr.2020.02.542-Figure1-1.png",
        "caption": "Fig. 1. Original beam",
        "texts": [
            " In this study, FEA (Finite Element Analysis) technique has been considered to carry out the structural and modal analysis to matrix determine the natural frequency of vibration of the beam and deformation and stress distribution over the beam under tensile and compressive loading condition. To perform the modal and structural analysis of beam, Chicken Feather Fibre (CFF) with the Epoxy-Resin (CY-230) matrix is considered. Mechanical properties of the material are taken from literature review [5] and are provided in Table 1. Original picture of Chicken Feather Fibre (CFF) specimen with Epoxy-Resin (CY-230) matrix is given in Fig. 1. Beam of CFF-Epoxy Resin (CY-230) matrix has been modelled using SolidWorks 2018. The dimension of the beam structure is (60 12.7 7.9) mm. CAD model of beam is imported into ANSYS 18 and meshing is done using quadratic elements. Total number of nodes and elements are 29,215 and 6240 respectively. CAD model and mesh model of the beam is shown in Fig. 2. Table 1 Mechanical properties of CFF-Epoxy Resin (CY-230) Matrix. Material Modulus of Elasticity (E) (MPa) Poisson\u2019s Ratio Density (q) (kg/m3) CFF-Epoxy Resin Matrix 800"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000603_s0022112010004465-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000603_s0022112010004465-Figure2-1.png",
        "caption": "Figure 2. (Colour online) Conformal mapping from interior of unit disk to the unbounded fluid region exterior to a wall with a single gap.",
        "texts": [
            " Building on an idea originally developed by the authors in Crowdy & Samson (2010), we now introduce a conformal mapping from the interior of the unit \u03b6 -disk to the fluid region just described. It is given by z(\u03b6 ) = 2\u03b6 \u03b6 2 + 1 . (6.1) The point \u03b6 = i maps to infinity in the upper half-plane while \u03b6 = \u2212 i maps to infinity in the lower half-plane. This map can be obtained by considering a composition of the two conformal maps: \u03b7 = 1 2 (\u03b6 \u22121 + \u03b6 ), z = 1 \u03b7 . (6.2) The first map takes the interior of the unit \u03b6 -disk to the unbounded region exterior to the slit [\u22121, 1]; the second map takes this slit region to the required flow domain since it maps \u03b7 =0 to z = \u221e. Figure 2 shows a schematic of the mapped regions. If a point swimmer is at a position zd in the fluid domain, the pre-image of this point will be called \u03b6d so that zd = z(\u03b6d). (6.3) It is possible to invert the map (6.1) explicitly to give \u03b6 (z) = 1 \u2212 (1 \u2212 z2)1/2 z . (6.4) This function has square-root branch points at z = \u00b11 (corresponding to the two edges of the walls). It will be convenient to consider the two-sheeted Riemann surface associated with this inverse map (i.e. (6.4)): one of the sheets corresponds to the physical fluid domain (the \u2018physical sheet\u2019) but there also exists a second sheet (which we refer to as the \u2018non-physical sheet\u2019)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002146_1464419313519612-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002146_1464419313519612-Figure6-1.png",
        "caption": "Figure 6. Localized defect in bearing at inner race and at outer race.",
        "texts": [
            "16,23 In modeling as shown in Figures 2 and 3 the rolling element bearing is considered as a spring mass damper system having nonlinear spring and nonlinear damping. In this work outer race is fixed in a rigid support and inner race is held rigidly in the shaft. A constant radial load is acting on the bearing which is contact stiffness that can be calculated using Hertz theory and dissipating forces at contact point are modeled with nonlinear damping. Contact stiffness for roller bearings On inner race and on outer race localized defect is inserted with nonconventional machining processes as shown in Figure 6. Shaft is inserted in the bearing by press fit. In Figure 1, Dm is a pitch diameter of the bearing; Dr1 and Dr2 are diameters of the outer race and inner race, respectively; and Pd/4 is a radial clearance of the bearing. Palmgren24 developed empirical relation from laboratory test data which define relationship between contact force and deformation for line contact for roller bearing as \u00bc 3:84 10 5 Q0:9 l0:8 \u00f01\u00de Contact length is divided into k lamina, each lamina of width w, and rearranging the above equation to define q yields q \u00bc 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f02\u00de Edge stresses are not considered in equation (2), obtained only over small areas, here localized defect is modeled as a half sinusoidal wave, amplitude of outer race defect and inner race defect are defined as Go \u00bc A1 \u00fe Dh sin Ro DL "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001611_0278364917691114-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001611_0278364917691114-Figure1-1.png",
        "caption": "Fig. 1. Planar 2R robot mechanism representing an inverted double pendulum actuated at joint 2",
        "texts": [
            " However, there is an important difference: a template typically describes a simplified mechanical system, whereas the model presented here describes the exact dynamics of balancing expressed in its simplest form. A good example of the former is the springloaded inverted pendulum template for hopping and running (Blickhan, 1989; Full and Koditschek, 1999), in which the leg is assumed to be massless. This assumption simplifies the dynamics considerably, but at the expense of ignoring all effects due to the non-zero mass of a physical leg. In contrast, the model presented here expresses the essence of balancing behaviour without ignoring any dynamic effect. Figure 1 shows a planar 2R mechanism representing an inverted double pendulum. Joint 1 is passive and represents the point contact between the foot of the mechanism and a supporting surface (the ground). It is assumed that the foot neither slips nor loses contact with the ground. The state variables of this robot are q1, q2, q\u03071 and q\u03072. The total mass of the robot is m; the coordinates of its centre of mass (CoM) relative to the support point are cx and cy; and it is assumed that the support point is stationary, i",
            "2) we have H01 = sT 0 Ic 1s1 and H11 = sT 1 Ic 1s1, where s0 = [0 1 0]T, s1 = [1 0 0]T and Ic 1 = \u23a1 \u23a3 I \u2212mcy mcx \u2212mcy m 0 mcx 0 m \u23a4 \u23a6 (18) (planar vectors and matrices: see Featherstone (2008, \u00a72.16)). It therefore follows that H01 = \u2212mcy and H11 = I , implying that T2 c = \u2212H11 gH01 (19) On comparing this with Equation (12) it can be seen that T2 c = \u2212Y2 Y1 (20) The linear velocity gain of a robot mechanism, Gv, as defined in Featherstone (2015a), is the ratio of a change in the horizontal velocity of the CoM to the change in velocity of the joint (or combination of joints) that is being used to manipulate the CoM. For the robot in Figure 1 the velocity gain is Gv = c\u0307x q\u03072 (21) where both velocity changes are caused by an impulse about joint 2. The value of Gv can be worked out via the impulsive equation of motion derived from Equation (8): \u23a1 \u23a3\u03b90 0 \u03b92 \u23a4 \u23a6 = \u23a1 \u23a3H00 H01 H02 H10 H11 H12 H20 H21 H22 \u23a4 \u23a6 \u23a1 \u23a3 0 q\u03071 q\u03072 \u23a4 \u23a6 , (22) where \u03b92 is an arbitrary non-zero impulse. Solving this equation for \u03b90 gives \u03b90 = H01 q\u03071 + H02 q\u03072 = ( H02 \u2212 H01H12 H11 ) q\u03072 = \u2212D H11 q\u03072 (23) But \u03b90 is the ground-reaction impulse in the x direction, which is the step change in horizontal momentum of the whole robot; so we also have \u03b90 = m c\u0307x, and the velocity gain is therefore Gv = c\u0307x q\u03072 = \u03b90 m q\u03072 = \u2212D mH11 (24) The two plant gains can now be written in terms of Tc and Gv as follows: Y1 = 1 mgT2 c Gv , Y2 = \u22121 mgGv (25) and another interesting formula for Y1 is Y1 = cy IGv (26) Equation 20 suggests a small modification to the plant model in Figure 2, in which Y2 is replaced with T2 c as shown in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002821_1.5096115-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002821_1.5096115-Figure6-1.png",
        "caption": "FIG. 6. Experimental setup for the shear test of the hybrid samples. Reproduced with permission from Schaub et al., Key Eng. Mater. 611\u2013612, 609\u2013614 (2014). Copyright 2014, Trans Tech Publications Ltd.",
        "texts": [
            " Laser power, Pl 250W 400W 400W 1000W Scan speed, vs 900 mm/s 900 mm/s 300 mm/s 400 mm/s Spot diameter, ds 110 \u03bcm 110 \u03bcm 110 \u03bcm 680 \u03bcm Hatch distance, h 120 \u03bcm 120 \u03bcm 120 \u03bcm 400 \u03bcm Layer thickness 50 \u03bcm 50 \u03bcm 50 \u03bcm 100 \u03bcm Line energy 0.28 J/mm 0.44 J/mm 1.33 J/mm 2.5 J/mm Volume energy 46.3 J/mm3 74.1 J/mm3 222.2 J/mm3 62.5 J/mm3 J. Laser Appl. 31, 022318 (2019); doi: 10.2351/1.5096115 31, 022318-3 \u00a9 2019 Laser Institute of America universal testing machine walter + bai FS-300 with a maximum force of 300 kN was used. The tool setup for the shear tests shown in Fig. 6 was presented in prior investigations regarding the characterization of hybrid components.20 Based on these investigations, the punch velocity was set to 5 mm/min. Prior to the testing, the samples were heat treated at 850 \u00b0C for 2 h followed by furnace cooling to mitigate the residual stress induce by the LBM process and to adjust the microstructure of the LBM elements. This heat treatment was investigated by Vrancken et al.21 for LBM parts and already applied in the previous work on hybrid parts from LBM and sheet metal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001958_tmag.2018.2841874-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001958_tmag.2018.2841874-Figure2-1.png",
        "caption": "Fig. 2. Rotor model. (a) Unsegmented PM. (b) Axial segmentation number N = 2. (c) Axial segmentation number N = 3. (d) Axial segmentation number N = 4.",
        "texts": [
            " In this section, a 12-slots/10-poles SPMSM with different winding layouts and axial segmentation number is introduced. MMF of different winding layouts is analyzed. Stator winding layout of 12-slots/10-poles SPMSM is generally classified into the following several categories: TP single-layer (TP-SL) winding layout in Fig. 1(a); TP doublelayer (TP-DL) winding layout in Fig. 1(b); DTP-DL winding layout in Fig. 1(c); TP-FL winding layout in Fig. 1(d); and DTP-FL winding layout in Fig. 1(e). Rotor model adopts surface-mounted PM considering different axial segmentation numbers as shown in Fig. 2, and the conductivity of PM is 6.67e5 (Simens/m). 0018-9464 \u00a9 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Main parameters of a 24-kW SPMSM are given in Table I. Current source is applied to stator winding, thus the normalized winding MMF is obtained by finite element method (FEM), which neglects the effect of flux leakage. The winding MMF of five types of winding layout by the tooth star map method and FEM are shown as in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003295_s12555-019-0796-8-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003295_s12555-019-0796-8-Figure1-1.png",
        "caption": "Fig. 1. Trailer mobile robot with monocular camera.",
        "texts": [
            " The remainder of this paper is as follows: In Section 2, the kinematic model of tractor-trailer system with input delay and its chained model are proposed. In Section 3, an adaptive control method based on RBFNN and sliding mode control is designed, and the stability of the closedloop system is strictly proved by Lyapunov stability theory. Simulation results are included in Section 4. Finally, the conclusions of this paper are drawn in Section 5. 2. PROBLEM STATEMENT 2.1. System configuration Fig. 1 shows a robot-camera system. The pinhole camera is fixed on the ceiling. Three coordinate frames are given for the convenience of description: the inertial frame X\u2212Y\u2212Z, the image frame u\u2212o\u2212v and the camera frame x\u2212y\u2212 z. Suppose that the u\u2212o\u2212v plane is parallel to the the plane of the x\u2212 y plane. C is the intersection point between the optical axis of the camera and the X\u2212Y coordinate. Its coordinate on X\u2212Y plane is (cx,cy). The original point of the camera frame is represented by (Oc1,Oc2) coordinates with the u\u2212 o\u2212 v plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003713_tec.2021.3062501-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003713_tec.2021.3062501-Figure2-1.png",
        "caption": "Fig. 2. Flux paths on (a) aligned position, and (b) unaligned position. (c) Magnetic equivalent circuits of the proposed SRM.",
        "texts": [
            " At the fully unaligned position, the C-core teeth of the relevant stator phase are exactly placed between two teeth of the rotor; in this case, the reluctance of the magnetic flux path is maximized; following the phase excitation and placing the rotor in the aligned position, the reluctance of the magnetic flux path is minimized. In the proposed structure, the magnetic flux tends to close its path as such that the reluctance of the path has its lowest value. Therefore, the main part of the flux closes its path inside the C-core. This results in a shorter flux path and consequently lower core losses; this enhances the mean torque and improves the efficiency. Fig. 1b shows the cross-section of the conventional structure for a fair comparison. Table I presents the major parameters of both motors. Fig. 2 shows the magnetic flux paths in the proposed SRM for two aligned and fully unaligned positions. The main paths of the flux and paths with lower flux are easily observed in the figure. Fig. 2c presents the MEC model of the motor. The elements of the MEC model including stator yoke, rotor yoke, stator teeth, rotor teeth, airgaps permeances and magnetomotive force (MMF) of the stator windings are determined based on the structure presented in Fig. 3 and Table A1 in appendix A. To obtain the varying air gap permeance, when motor rotates from the fully aligned position to the unaligned position, the relevant region is divided into five sections. Each Authorized licensed use limited to: University of Prince Edward Island",
            " According to this algorithm, first, an initial value is assumed for permeability at different parts of the stator and rotor cores and then permeances of the air gap and different parts of the stator and rotor are determined. Then, MMF is obtained as follows: where Tpole is the number of turns per stator pole and Iph is the excitation current of each phase. In this model, equations have been written as Kirchhoff's current law (KCL). For more simplification, nodal equations of the MMF source are considered in series with the stator tooth permeance as shown in Fig. 2c. The magnetic flux source in parallel with the stator tooth permeance is as follows: f sp fP F  (20) After completing the MEC model as shown in Fig. 2b, and obtaining their permeances, the equations, they are solved by applying the Kirchhoff current law (KCL) and node equations, here the number of these equations is 16 as follows: 1,1 1, 1,161 1 .1 , ,16 16,1 16, 16,1616 16 j i i j ii i j P P P F P P P F P P P F                                                         (21) where Pi,j is the permeance between nodes i and j. If i=j, Pi,j is equal to the sum of permeances connected to i nodes, if i\u2260j, the minus sum of the existing permeances between node i and node j, and if i\u2260j, and there is no permeance between these two nodes, Pi,j=0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000414_tac.2007.902750-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000414_tac.2007.902750-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [
            " Without loss of generality, we may assume that the origin is in Side-B. Now, for any x0 = (x01; x 0 2) T on , there is a neighborhood U(x0) of x0 such that the segment of the curve in U(x0) can be rewritten as x2 = (x1) (or x1 = (x2)), since the vector field of the control curve is nonzero. Now, let the normal vector which points to Side-A of be denoted as p(x0) = (p1(x 0); p2(x 0))T . Without loss of generality, we assume that p2(x0) > 0 (since other cases can be treated similarly). Then as shown in Fig. 3, the point (x1; x2)T in the Side-A of and in U(x0) satisfies x2 > (x1). Now we prove it by considering two cases as follows. Case 1. det(f(x0); g(x0)) 6= 0. Then for any control function u(t); f(x0) + g(x0)u(t0) 6= 0. Without loss of generality, we suppose f1(x 0) + g1(x 0)u(t0) 6= 0. When f1(x 0) + g1(x 0)u(t0) > 0, we can further suppose that f1(x) + g1(x)u(t) > 0; t0 t < T and p2(x) > 0 in U(x0). Then, by the assumption about the control curve , we know that on hf(x) + g(x)u(t); p(x)i = [f1(x) + g1(x)u(t)]p1(x) + [f2(x) + g2(x)u(t)]p2(x) 0: Hence, by simple calculation, we have dx2 dx1 = f2(x) + g2(x)u(t) f1(x) + g1(x)u(t) d (x1) dx1 ; x 2 \\ U(x0): (17) Since the positive semitrajectory 'u(x0; t); t > 0 of (2) under control function u(t)with initial pointx0 satisfies the left-hand side (LHS) of (2), which can also be rewritten the form '(x1) in the neighborhood U(x0); '(x1) (x1); x1 2 [x01; x 1 1), where x01 < x11 (see [33])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure1.46-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure1.46-1.png",
        "caption": "Fig. 1.46 Image of a proof-of-concept intelligent vehicle [UEKI ET AL. 2004].",
        "texts": [
            "45), mounted inside the intelligent vehicle to avoid dirt spattering, may take high-resolution pictures of the course, while computer algorithms \u2018learned\u2019 the terrain and mapped out an optimal driving on/off road surface [CHEN 2003]. The unmanned intelligent vehicle\u2019s brains -- for example, multi-PentiumM microcomputers -- may be located in the boot. The machines ought to be shock-mounted to survive the bumps on the on/off road surface, and the E&IN mechatronic control system ought to have multiple copies of every computer program. A thick spinal column of electrical wires connects the microcomputers to a mechatronically controlled brake, throttle, and E-M motor-driven steering column. Figure 1.46 shows a proof-of-concept intelligent vehicle with the RBW or XBW integrated unibody or chassis motion mechatronic control hypersystem developed by Hitachi Ltd. The aim of this intelligent vehicle is to improve vehicle dynamics and layout [UEKI ET AL. 2004]. Since a large proportion of traffic accidents are caused by the driver (namely, human error), adaptive driver-assistance systems -- which stop human-error accidents before they occur or alleviate damage by taking mechatronic control of the automotive vehicle just before an accident occurs -- have been actively developed, and some systems have already been implemented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001662_j.ijleo.2017.11.053-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001662_j.ijleo.2017.11.053-Figure1-1.png",
        "caption": "Fig. 1. TRMS system configuration.",
        "texts": [
            " In Section 3, the decomposed model of the TRMS is introduced. The non linear observer is designed in Section 4. The fuzzy sliding mode controller based on non linear observer is presented in Section 5, Section 6 presents the simulation results. the experimental results to validate the effectiveness of the proposed approach is presented in Section 7. Finally we arrive to the conclusion of the whole work in Section 8. 2. Model description of the 2-DOF helicopter (TRMS) The behaviour of a nonlinear TRMS [23], Fig. 1, in certain aspects resembles that of a helicopter. It can be well seen as a static test rig for an air vehicle with formidable control challenges. This TRMS consists of a beam pivoted on its base in such a way that it can rotate freely in both its horizontal and vertical planes. There are main and tail rotors driven by DC motors, at each end of the beam. The two rotors are controlled by variable speed electric motors enabling the helicopter to rotate in a vertical plan (pitch noted ) and horizontal plane (yaw noted \u03d5)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001976_j.promfg.2018.07.110-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001976_j.promfg.2018.07.110-Figure1-1.png",
        "caption": "Figure 1. CAD model for SLM experiment (dimensions in mm).",
        "texts": [
            " The melt pool sizes were estimated based on the obtained liquidus-solidus transition point. Moreover, width of the single tracks formed at the top of the part were measured using white light interferometer, which was then compared with the melt pool width estimated using thermal analysis. In addition, the cylindrical samples with enclosed single track at different scanning speeds were built to study the internal features such as pores using CT scanner. In this study, EOS M270 machine was used to fabricate the part whose CAD design is shown in Figure 1(a). The part has dimensions of 66\u00d730\u00d715 mm (x\u00d7y\u00d7z) with two rectangular holes defined in middle so as to determine the spatial resolution. Default EOS M270 scanning parameters were used for the part body. In addition, single tracks are defined over the part, with gap of 1 mm in between them as shown in Figure 1. Single tracks are formed at each alternate layer as indicated in Figure 1(b) and they are nothing but the support structures with user defined power and scanning speed. There is no single tracks, which are indicated by red arrows, in the intermediate layer between two layers with singe tracks. The single track scanning and default EOS scanning in the part is performed simultaneously in the layers where single track is formed: single track is scanned first and then default scanning is performed. The SLM machine settings for single track and thermal camera settings used have been summarized in Table 1",
            " The binary image clearly presents the model edges which are suitable for resolution calculation. The directional spatial resolutions can be calculated from the top to bottom edge distance (L1) and the notch distance (L2) as well as the horizontal and vertical pixel values, as shown Figure 3(b). The resolution is calculated to be 49.66 \u00b5m/pixel in horizontal direction and 62.85 \u00b5m/pixel in vertical direction. In addition, separate semi-hollow cylindrical parts with enclosed single tracks were built. The procedure of forming single track is similar as discussed in Figure 1(b). Scanning speeds used in this case were 200 mm/s, 400 mm/s, 600 mm/s and 800 mm/s and the detail dimensions of the part is shown in Figure 4. Skyscan 1173 was used to take CT scan of built part at 7.1 \u03bcm magnification. The voltage and power used were 130 kV and 8 Watts respectively. Brass filter of 0.25 mm thickness was used to absorb X-rays with energy below 60kV. CT scanning was performed to observe the interior defects such as porosity at different scanning speed as it can differentiate materials based on density"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003346_s12206-020-0104-9-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003346_s12206-020-0104-9-Figure1-1.png",
        "caption": "Fig. 1. Gear modeling.",
        "texts": [
            " Using the NewtonRaphson method, the total load of the loaded rolling elements is converged to the external force of bearings. The bearing stiffness can be obtained by substituting the converged radial displacement into Eq. (2). Driving and driven spur gears are modelled with the rigid cylinder of the base diameter and connected with the mesh stiffness as well as the damping along the line of action. Spur gears are supported with the stiffness and the damping of bearings, and the four DOF modelling is shown in Fig. 1. Gear deformation is obtained by the translational displace- ment, the rotational displacement, and the static transmission error as follows: 1 2 1 1 2 2= - + - -b b\u03b4 y y r \u03b8 r \u03b8 e . (3) The static transmission error e is given by manufacturing errors, profile wear, and profile modification. If gears have the backlash, the mesh force is classified as the gear deformationbacklash conditions as follows: ( )( ) ( )( ( ) )= - +g d\u03b4 tF t k t \u03b4 t b c dt If ( ) >\u03b4 t b , (4a) ( ) 0=gF t If ( ) \u00a3\u03b4 t b , (4b) ( )( ) ( )( ( ) )= + +g d\u03b4 tF t k t \u03b4 t b c dt If ( ) < -\u03b4 t b "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002952_s12555-018-0400-7-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002952_s12555-018-0400-7-Figure8-1.png",
        "caption": "Fig. 8. Payload test: (a) wire-driven continuum robot used in payload test, (b) experimental setup for payload test with continuum robot driven by wire.",
        "texts": [
            " Each experiment was repeated 10 times to improve reliability. Fig. 7 shows the measured and simulated twist deformation of each wire. The results show that twist deformation in the nitinol wire with a lower Young\u2019s modulus is greater than that in the steel wire. In addition, although some errors occurred, we confirmed that the proposed sag effect model predicted the twist deformation with an accuracy of 1.0\u25e6. 4.3. Payload test To measure the twist deformation in an actual continuum robot, we developed a continuum robot with spherical joint, as shown in Fig. 8(a). The developed robot has two DOFs, including two bending motions, except for the grasping motion of the forceps. The robot consists of general spherical joints and four steel wires were used for two bending motions. The parameters of the robot used in the experiment were r = 5.5 mm, Ns = 18, Ls = 6.5 mm, dw = 0.8 mm, and dc = 0.85 mm. At the center of the spacer, flexible forceps with a diameter of 6 mm were inserted into the robot. The robot was actuated via three rotary motors (MX-64R, Robotis Corp",
            ", Seoul, Korea) including the grasping motion of the forceps; most parts of the robot were machined from aluminum and the motor housing was fabricated with a rapid prototyping machine (Eden 250TM, Stratasys Ltd., Rehovot, Israel). The twist deformation was measured by applying a load at the end effector of the forceps as a manipulation of the organ. We conducted an experiment to measure the twist deformation in an actual robot in which clearance and sag effects occur simultaneously, as shown in Fig. 8(b). To measure the twist deformation when a load is applied at the end effector of the robot, a marker was attached to the end effector and a Polaris infrared tracker system, provided by NDI (Canada, Ontario, Waterloo), was used as the measurement device. The experiment was conducted in three postures, as shown in Fig. 9: pose 1 without bending, pose 2 with a bending angle \u03b8 = 45\u25e6, and pose 3 with a bending angle \u03b8 = 90\u25e6. Further, based on the consideration by Blanc et al. [33] that end-effector external loads of \u00b13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.9-1.png",
        "caption": "Figure 8.9. Gravity induced free vibrations of a system of two particles .",
        "texts": [
            "95c) for the total potential energy of our new system, and the total kinetic energy is given by (8.95d) . Let the reader consider the force s that act on the free bodies involved in these additional models and write down the separate equations of motion for the particles of the respective systems. Try to derive the additional forces from their potential energy functions. Now let us tum to another example and apply the theory directly . Example 8.8. Two small blocks of weight WI and W2 are connected by a perfectly flexible and inextensible cable of negligible mass, as shown in Fig. 8.9. The weight WI rests on a smooth horizontal surface and is attached to a linear spring of stiffness k fastened to a rigid wall. The cable is free to slide over a smooth pulley at P and suspends the weight W2 .The system is at rest initially when W2 is displaced vertically and released. (i) Find the total energy of the system. (ii) Derive the equation of motion and determine the frequency of the vibration. (iii) Describe alternative formulations of these issues . Solution of (i). The physical system is modeled as a system of two particles of masses m I and m2 for each of which the free body diagram is shown in Fig. 8.9a. The weight WI and the normal, smooth surface reactions at WI and at P do no work in the motion . The cable has negligible mass, so its motion around the smooth pulley may be ignored , and hence the oppositely directed, internal cable tensions T I and T2 have equal magnitude T, say. The cable is inexten sible and perfectly flexible, so the total internal potential energy of the system is zero: B = 0, and WI and W2 share the same displacement so that x =Y.In the equilibrium state, Xo=Yo is the static displacement of WI and W2 so that kxo = m2g",
            " The kinetic energy is unchanged in (8.96b), while the total potential energy may be written as 1 2 V(f3) = ix . (8.96f) This procedure, however, cannot be used when the spring is nonlinear, whereas the earlier method leading to (8.96a) can. The principle of conservation of energy (8.86) yields 1 1 \"2m(f3)x2 + \"2kx2 = E . (8.96g) Differentiation of this equation with respect to x (or t) returns (8.96e) . Another approach starts with the separate equations of motion for each particle. With reference to the free body diagrams in Fig. 8.9a, we find easily WI = N . (8.96h) Dynamics of a Systemof Particles 335 Eliminating T and introducing the inextensibility constraint y = x and the equilibrium condition m-ig= kxo, we recover (8.96e). The equations of motion also may be formulated relative to the static state :mi x = T - kx , m2Y = -T, which again lead to (8.96e). Suppose the cable in the previous example has elasticity characterized by a force-elongation equation S = k20+ k303, in which k2 and k3 are constants and ois the cable elongation measured from its natural unstretched state . To model this case, the vertical portion of the cable in Fig. 8.9 is replaced with a nonlinear spring characterized by S, the remaining part of the cable being inextensible and perfectly flexible . Of course, now x i= y . In view of the nonlinear character of the cable spring, it is best to measure the respective particle displacements X == x + Xo and Y == Y + Yo from the natural state of the springs, then the cable elongation 0 = Y - X.We wish to derive the energy equation of the system for 0 ::: O. Afterwards, the equations of motion for the linear system with k3 = 0 are described"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure7-1.png",
        "caption": "Fig. 7 Two panels connected by an elastic hinge. a The initial, b an intermediate and c the final configurations predicted by the 4-node shell element model S4R",
        "texts": [
            " An intermediate configuration at h & 2p/3 and the final configuration at h = 0 are shown in Fig. 5b, c, respectively. The animation video is given in Online Resource 1. In the second method of modelling, A2 and A4 that define the crease element are then changed to nodes on the side edges of the panels, See Fig. 6. In other words, the crease element is initially flat (ho = 0) and fully folded in the final configuration (hrest = p). The animation video is given in Online Resource 2. In the third method of modelling, the S4R shell element model in ABAQUS is employed, see Fig. 7. The element possesses 4-node on the mid-surface of the plate/shell and each node has 3 translational and 3 rotational dofs. The boundary conditions prescribed to Bis and Cis are the same as those in SC8R. To avoid coupling the rotational dofs of the elements modelling the two panels, the two panels are created separately. The translational dofs of Eis and Fis are then tied by using the Multi-Point Constraint of PIN type in ABAQUS so that Eis and Fis share the same translational dofs. The crease element E2A2E4A4 with initial fold angle ho = p\u20130",
            " It should be remarked that the more natural setting ho = p is not used because it would cause all Bis and Cis lying on the same vertical line. The two fully folded panels can spin freely about the vertical line leading to the singular of the initial global stiffness matrix. Again, rest angle loading with hrest = 0 is employed to unfold the panels. After the first few time increments, the time increments of ABAQUS remain to be * 0.0014 throughout the simulation, see Table 2. An intermediate configuration h & 2p/3 and the final configuration are shown in Fig. 7b, c, respectively. The animation video is given in Online Resource 3. In the fourth method of modelling, the M3D4 3D membrane element model in ABAQUS, the Q4 bending element and crease elements are employed. The initial mesh is same as the one shown in Fig. 7a whilst the two panels share the same nodes at the elastic hinge. In other words, nodes Eis and Fis in Fig. 7b are identical and they need not be separately defined. Again, E2A2E4A4 is the crease element providing the elastic hinge effect. For 20 common element edges shared by adjacent elements within each panel, crease elements with a large stiffness (k = 1000) are defined to maintain the coplanarity of the panels. The predicted configurations are identical to those of the S4R shell element model in Fig. 7. The animation video is given in Online Resource 4. The numbers of time increment and the CPU time consumed by the four methods of modelling are summarized in Table 2. The result echoes that the discussion in Sect. 1 on the relative convergence of the elements with and without rotational dofs. S4R shell element model consumes far more computing resource than the SC8R solid-shell element model which, in turn, is less computationally efficient than using the membrane element and the developed elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001128_9781118562857.ch1-Figure1.19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001128_9781118562857.ch1-Figure1.19-1.png",
        "caption": "Figure 1.19. (a) Schematics of the cross-thin-wall fabrication strategy; and (b) a LRM porous structure of ~20% porosity",
        "texts": [
            " A comparison between them with respect to their internal geometry, pore size and part density, using a range of techniques including micro-tomography were reported by Ahsan et al. [AHS 11]. At our laboratory, the porous structures were laser rapid manufactured using a cross-thin-wall fabrication strategy and structures up to 60% porosity was achieved. The mechanical properties of these structures were also investigated. In a cross-thinwall fabrication strategy, the porous material is fabricated by depositing the material in mutually orthogonal directions in successive layers. Figure 1.19a presents a schematic of the cross-thin-wall fabrication strategy. The investigation indicated that the properties of LRM porous structures were governed by the major processing parameters involved, i.e. laser energy per unit transverse length, powder fed per unit transverse length and transverse traverse index [PAU 12]. The response surface method using the Box-Behken design of experiments was employed to investigate the effect that these three important processing parameters have on the porosity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure8.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure8.1-1.png",
        "caption": "Fig. 8.1 Four-pole induction machine with squirrel-cage rotor, showing a two-layer winding and rotor with rotor bars",
        "texts": [
            " This universal model is the stepping stone to the universal fieldoriented (UFO) machine model which gives a basic understanding of the transient behavior of induction machines [4]. Furthermore, this model forms the cornerstone for the development of field-oriented control algorithms. At the end of this chapter, attention is given to single-phase induction machines. These machines are widely used in domestic appliances and as such it is important to have access to dynamic and steady-state models. A set of tutorials is provided which allows the user to interactively explore the concepts presented in this chapter. Figure 8.1 shows the cross-section of an induction machine with a so-called squirrel-cage rotor. The squirrel cage consists of a set of conductors, i.e. rotor bars, (shown in red), which are short-circuited at both ends by a conductive ring. The cage \u00a9 Springer Nature Switzerland AG 2020 R. W. De Doncker et al., Advanced Electrical Drives, Power Systems, https://doi.org/10.1007/978-3-030-48977-9_8 221 222 8 Induction Machine Modeling Concepts is embedded in the rotor lamination as may be observed from Fig. 8.1. A three-phase two-layer winding is housed in the stator of a four-pole machine. A rotating field created by the stator winding is penetrating the rotor. If the rotor is rotating asynchronously to the stator field (which means it is rotating at a different speed), alternating currents are induced in the squirrel cage. These currents, together with the stator field, are responsible for the torque production of the machine. This is why asynchronous machines are commonly known as induction machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure1.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure1.17-1.png",
        "caption": "Fig. 1.17 Structural and functional diagram of RBW or XBW [SNU 2000].",
        "texts": [
            " Advanced mechatronic control systems and the RBW or XBW infrastructure may enable potential active safety improvements. Summing up, RBW or XBW integrated unibody or chassis motion mechatronic control hypersystems consist of DBW AWD propulsion and BBW AWB dispulsion, SBW AWS conversion as well as ABW AWA suspension mechatronic control systems, and so on (Fig. 1.16) [SNU 2000]. 1.3 RBW or XBW Philosophy 37 Automotive Mechatronics 38 This R&D may consider a target RBW or XBW integrated unibody motion mechatronic control hypersystem (see Fig. 1.17) with mechatronic control systems, such as DBW AWD propulsion and BBW AWB dispulsion, SBW AWS conversion as well as ABW AWA suspension mechatronic control systems, and so on [SNU 2000]. If RBW or XBW integrated unibody or chassis mechatronic control hyper-systems are to deliver on the safety promise of reducing deaths and injuries in accidents, the RBW or XBW integrated unibody or chassis motion mechatronic control hypersystems in a vehicle must be able to communicate with one another. That means there must be a communication network that may enable RBW or XBW integrated unibody or chassis motion mechatronic control hypersystems to work individually and together, smoothly, safely, and efficiently"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003214_j.measurement.2020.107897-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003214_j.measurement.2020.107897-Figure2-1.png",
        "caption": "Fig. 2. Three possible t",
        "texts": [
            " The remaining parts of this article are organized as follows: Section 2 introduces the scheme of determining the motion period of the sun gear\u2019s fault meshing positions; Section 3 analyzes the effect and the integrity of embracing fault information about the motion period; Experimental studies are demonstrated in Section4. Finally, Section 5 concludes the article. When the sun gear\u2019s faulty tooth is meshing with a planet gear, the fault-induced vibration may travel through three possible transfer paths to the vibration sensor [16,27,31], as is shown in Fig. 2. In Fig. 2, the transfer path 2 (yellow dashed line) and transfer path 3 (blue dashed line) do not time-varying [16, 27]; therefore, the attenuation effects through these two transfer paths can be identically deemed for all the meshing positions. The attenuation effect of the remaining transfer path 1 (black dashed line), which relies on the positions of fault-meshing, should be mainly focused. Some possible fault-meshing positions (solid dot) and their corresponded propagating distances through transfer path 1 to the fixed sensor are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003067_j.ymssp.2020.107022-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003067_j.ymssp.2020.107022-Figure1-1.png",
        "caption": "Fig. 1. Helicopter schematic.",
        "texts": [
            " The system identification method in [34] requires as many datasets as possible in every case. Combining the measurement and system identification methods can yield a reliable model that incorporates the strong points of one method to offset the weaknesses of the other. The kinematic model consists of translation motion and rotation motion and is based on the assumption of a north-eastdown (NED) inertial system. The direction of the NED and the direction of the body coordinate system both point in the same direction, as shown in Fig. 1. The equations for translation motion are shown below: h \u00bc Pned z _Pned x _Pned y _Pned z T \u00bc RB u v w\u00bd T ( \u00f01\u00de where Pned x, Pned y and Pned z represent the corresponding displacement in the local NED coordinate system; h is the flight height; and u, v, and w are the velocity components in the body axis system. The rotation matrix, translated from the NED system to the body system, is expressed as follows: RB \u00bc ChC/ C/Cw S/ S/ShCw C/Cw S/ShSw \u00fe ChCw C/Sh S/ChSw \u00fe ShSw S/ChCw ShCw C/Ch 2 64 3 75 \u00f02\u00de where C , T and S represent the cosine, tangent and sine functions, respectively",
            " 5272\u20135277. [34] Q. Bian, K. Zhao, X. Wang, R. Xie, System identification method for small unmanned helicopter based on improved particle swarm optimization, J. Bionic Eng. 13 (3) (2016) 504\u2013514. [35] A.J. van der Schaft, L2-gain analysis of nonlinear systems and nonlinear state-feedback H1 control, IEEE Trans. Autom. Control 37 (6) (1992) 770\u2013784. [36] E.D. Sontag, Mathematical Control Theory, Springer, New York, New York, NY, 1998. [37] M. Quigley et al, ROS: An open-source robot operating system no. Figure 1, Icra, 2009, p. 5. [38] M. He, J. He, A real-time H1 cubature Kalman filter based on SVD and its application to a small unmanned helicopter, Optik (Stuttg) 140 (2017) 96\u2013 103."
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.10-1.png",
        "caption": "Figure 10.10. Free body diagram of the rotating plate.",
        "texts": [
            " The torque about the bearing axle j' is related to the applied drive torque T, and the remaining components, which arise from the asymmetrical distribution of mass about the plate diagonal , are restraining torques supplied by the bearings at A and B. 0 Exercise 10.6. Determine the moment of inertia tensor components referred to cp' , which is not a principal reference frame . Note that w = wj',W = wj', and apply (10.65) to derive (10.79f). 0 Solution of (iii). Wenext explore the role of the static bearing reaction forces . The free body diagram of the plate is shown in Fig. 10.10. When the plate is at rest , each shaft bearing support exerts an equal force As = Bs = -(W)/2 on the plate at A and B, equal to one-half its weight W . These static loads are equipollent to zero, and therefore they contribute nothing to the total force or to the total torque about the center of mass C in the dynamics problem. Henceforward, these statically balanced forces may be ignored . Now let us relate the drive torque T = Tj' to the rotational motion and determine the resultant dynamic bearing reaction forces A = Aki~ and B = Bk( , exerted by the shaft at A and B, respectively, and which we shall suppose, for simplicity, act at the comers of the plate in Fig. 10.10. Euler's first law (10.26) requires that A + B = ma* = 0; thus, A = -B, so the bearing reaction force system forms a couple with moment arm 2x = (e2 + w 2)1/2j' , where x is the position 446 Chapter 10 vector of A from C. Therefore, the total applied torque on the plate about C is (10.79g) Equating the corresponding components in (10.79f) and (1O.79g), we obtain an equation relating the drive torque to the rotation and two relations for the dynamic bearing reaction force components: wmw2\u00a32 T = --;:---::- 6(\u00a32+ w2) ' (10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.12-1.png",
        "caption": "Figure 7.12. Propulsive motion of a slider block.",
        "texts": [
            "81a) Hence , the total energy is constant if and only if the noncon servative part of the force does no work in the motion or, trivially, when nonconservative forces are absent. It is useful to distinguish conservative and nonconservative forces, if possible ; but if the nature of a force is uncertain, the ambiguous force is considered nonconservative until proven otherwise. The following example illustrates the straightforward application of the general energy principle (7.80). Example 7.13. A propulsive force P of constant magnitude moves a slider S of mass m in a smooth circular track in the vertical plane, as shown in Fig. 7.12. The slider starts from rest at the horizontal position A . Determine the speed of S as a function of e.What is its angular speed after n complete turns? Solution. The total force that acts on S in the Fig. 7.12 consists of the workless normal reaction force N exerted by the smooth tube, the conservative gravitational force Fe = mg, and the nonconservative propulsive force FN = P = Pt which always is tangent to the path of S. The change in the potential energy of S is t:,.V =mg R sin e, the datum being at A, and the change in the kinetic energy from the initial rest posit ion at A is t:,.K = !mv2\u2022 Therefore, with t:,.@= t:,.K + t:,. V and FN \u2022 dx = Pds, the general energy principle (7.80) yields 1 iRe-mv2 +mgR sin e = P ds = PRe , 2 0 and hence the speed of S as a function of e is given by vee) = J2: cee - mg sine)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003170_j.apor.2019.102028-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003170_j.apor.2019.102028-Figure2-1.png",
        "caption": "Fig. 2. The BODY and NED reference frames.",
        "texts": [
            " A matrix with all zero elements of order n is denoted by 0n and a identity matrix of order n is denoted by In. Consider a robotic USV called as CSICET-DH01, with a length of 120 cm and a width of 40 cm, shown in Fig. 1. The USV is equipped with a GNSS receiver and a 9-axis IMU instrument consisting of 3-axis rate gyro, 3-axis accelerometer and 3-axis magnetometer. Two reference frames are used to describe the motion of USV, namely bodyfixed (BODY) reference frame and North-East-Down (NED) reference frame. The explicitly reference frames are shown in Fig. 2 and the nomenclature of USV is given in Table 1. By ignoring the motion in heave, roll and pitch [12,37], the model of an USV can be described as follows [4,38\u201340] =\u03b7 R \u03c8 \u03bd\u02d9 ( ) ,t n t t b (1) =\u03bd a\u02d9 ,t b t b (2) where R(\u03c8t) is a rotation matrix from BODY to NED reference frame defined as follows From the model in (1) and (2), it is clear that the rotation matrix and the velocity can be obtained using the heading \u03c8t and inertial acceleration from the IMU sensor. The position can be obtained by the integration of velocity, but there will be a drift problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001307_iet-epa.2012.0342-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001307_iet-epa.2012.0342-Figure1-1.png",
        "caption": "Fig. 1 Flux tube connecting the stator and rotor in a salient-pole machine",
        "texts": [
            " In the stationary reference frame, for a rotating coil, the winding function N is a function of \u03c6 and \u03b8, whereas for a stationary coil it is only a function of \u03c6. Equation (4) is used to find inductances in machines where the air gap is small or characterised by small variations. It will be shown here that (4) can be used to calculate the winding inductances in a salient-pole machine where the air gap is small under poles but is considerably larger in inter-polar region. Consider a flux tube connecting the stator and rotor as shown in Fig. 1. The cross-sectional area of the flux tube at a distance l along the flux tube is sL where L is the axial length of the stator. Assume that the flux within the vanishingly small flux tube is d\u03a6. The MMF along a small differential portion of the flux tube will be dF = dF dR (5) IET Electr. Power Appl., 2013, Vol. 7, Iss. 5, pp. 391\u2013399 doi: 10.1049/iet-epa.2012.0342 The total MMF drop along the entire flux tube is F0 = \u222bF0 0 dF = dF \u222bR0 0 dR (6) where F0 and R0 are the MMF and reluctance of the complete overall flux tube",
            " In practice roughly ten flux tubes need to be identified from a flux plot of the interpolar region. Each of these tubes should be divided into a number of segments depending upon the accuracy desired, for example, n segments. The average normalised width s/s0 of each segment can then be calculated and a modified segment length calculated. With n segments the equation defining this process is for the flux tube located at the spatial angle \u03c6 geff (f) = g n \u2211n k=1 save s0 ( )\u22121 k (18) where save is the average value of the flux tube width for the kth segment. Again see Fig. 1 for the definition of s0, g and \u03c6. When n is sufficiently large the width varies essentially linearly so that the average value is simply the algebraic average of the width at the entrance and exit of the flux tube, so that, finally geff (f) = g n \u2211n k=1 sk\u22121 + sk 2s0 ( )\u22121 (19) It is important to point out that the approach converges to the exact answer as the number of flux tubes and tube segments increase without bound. The method of analysis which was described in previous section can be obtained by first calculating a field plot of the region of interest for the winding function and plotting selected flux lines and also lines of constant magnetic potential (MMF)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure13.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure13.4-1.png",
        "caption": "Fig. 13.4 Model used to describe the collision between a ball and the wall of a hollow bat",
        "texts": [
            " The wall on the opposite side of the impact point will tend to remain circular during the impact, although it will start vibrating in and out after the ball bounces off the bat. The mass of the wall that is in direct contact with the ball is hard to estimate precisely, but we can at least make a reasonable estimate that it will be somewhere in the range from about 100\u2013300 g for a typical aluminum or composite bat. The actual value makes a big difference to the batted ball speed, as we will now show. The elastic behavior of the ball and the wall can be modeled as shown in Fig. 13.4. The ball is represented by a mass m1 connected to a spring S1 of spring 13.3 Trampoline Calculations for a Bat 227 constant k1. The wall in contact with the ball is represented by a mass m2, and is connected elastically to a mass m3 by a spring S2 with spring constant k2. The total mass of the bat at the impact point, m2 C m3, will be taken as the effective mass of the bat so that the speed of the bat and the ball after the collision will be consistent with results obtained previously in Chaps",
            " The COR continues to increase as the ball becomes stiffer, provided the mass of the front wall is less than the mass of the ball, as indicated by the result when m2 D 0:1 kg. However, if m2 is equal to or larger than the mass of the ball then the COR will decrease as the ball stiffness is increased. Given that m2 can be decreased by making the wall thinner and more flexible, the design problem in producing a high performance bat is to ensure that the wall is not so thin that the bat will break. The mass-spring model in Fig. 13.4 can also be used to describe the collision of a ball with a wood bat. In the case of a wood bat, m2 C m3 in Fig. 13.4 is equal to the effective mass of the bat at the impact point and k2 is determined by the frequency of the fundamental vibration mode, about 170 Hz for most bats. The model provides an accurate description of the collision when the fundamental mode is the dominant mode, as it is when the impact speed is low or when the bat strikes the ball at the node of the second mode. A more complicated model would be needed, with additional springs and masses, if higher frequency modes contribute to energy losses",
            " If the ball has kinetic energy E1 when it collides with the bat, then the total elastic energy stored in the bat and the ball will be given by E1 D Eball C Ebat D Ebat 1 C k2 k1 so Ebat D k1E1 k1 C k2 Similarly, Eball D k2E1 k1 C k2 If we assume that the ball loses 75% of its stored energy and the bat loses only 5% of its stored energy, then the total kinetic energy remaining after the collision is E2 D .0:25k2 C 0:95k1/E1 k1 C k2 Since the bat is clamped, it has no kinetic energy after the collision, so E2 is the kinetic energy of the ball after the collision. If r D k1=k2 then E2 E1 D 0:25 C 0:95r 1 C r The ratio E2=E1 is plotted as a function of r in Fig. 13.2. Appendix 13.2 Trampoline Model 233 Appendix 13.2 Trampoline Model The collision between a ball and the elastic wall of a bat can be modeled as shown in Fig. 13.4, assuming that part of the front wall of the bat, of mass m2, moves radially towards the rear wall, of mass m3. The total wall mass, m2 C m3 is equal to the equivalent mass of the bat at the impact point. During the compression phase, the force F1 on spring S1 is F1 D k1.x y/ and the force F2 on spring 2 is given by F2 D k2.y z/ where k1 is the stiffness of the ball, k2 is the stiffness of the bat, x y is the compression of the ball and y z is the compression of the bat. F1 acts to the left on the ball and to the right on the front wall, while F2 acts to the left on the front wall and to the right on the rear wall"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure7-1.png",
        "caption": "Fig. 7. Tooth profiles and rack cutter profiles of CRC gear and involute gear.",
        "texts": [
            " When Z 1 \u2208 [5, 10], undercut happens if Z 2 \u2264 18. When Z 1 \u2208 [11, 18], the minimum tooth number of Z 2 for non-undercut are 17,16,15,14,13,12,11,10, respectively. If Z 1 \u2265 19, undercut never occurs. 4. Evaluation of gear drive In this section, performance of the CRC gear drive is evaluated by comparison with that of the involute gear drive. The geometry parameters for the gear drives are given in Table 1 . Tooth profiles and rack cutter profiles of the CRC gear and involute gear are displayed in Fig. 7 a and b, respectively. The differences of two tooth shapes are that tooth thickness of the CRC gear tooth is slightly larger than that of the involute gear above the pitch circle, and the opposite is the case below the pitch circle. The reason is that their rack cutter profiles are different. Unlike those of the involute gear, the working parts of cutter profile for CRC gear are not straight lines, which may cause problems in manufacture. As shown in Fig. 8 , for the CRC gear drive, the relative curvature at any contact point is almost invariable during a whole meshing period, while the significant change in the relative curvature of involute gear drive can be found, especially, the difference between the value of the start point and that of the end point is large",
            " As shown as Fig. 10 , the dangerous section can be obtained by 30-degree-tangent method. During the single-tooth-pair period, the maximum bending stress is as follows \u03c3F = M F W s = 6 F n h F cos \u03b1F Bs 2 F (48) Where M F is the bending moment caused by the normal contact force; W s is the anti-bending section factor of the dangerous section. \u03b1F is the pressure angle when the tooth tip meshes. There are little difference in h F and s F between CRC gear tooth profile and involute gear tooth profile (See Fig. 7 ). But the values of \u03b1 are different, specifically, \u03b1 = 26 . 638 4 \u25e6, \u03b1 = 21 . 326 5 \u25e6. Thus \u03c3 = ( cos \u03b1 / cos \u03b1 ) \u03c3 = 1 . 0421 \u03c3 . The F F i Fc Fc Fc F i F i F i maximum root bending stress of the CRC gear is higher by about 4%. The result shows that the CRC gear can remain about the same bending strength as the involute gear. 4.3. Sliding coefficient The relative sliding between tooth profiles can induce wear or even scoring on tooth surfaces, which affects the stability and accuracy of transmission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000084_j.triboint.2005.12.005-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000084_j.triboint.2005.12.005-Figure4-1.png",
        "caption": "Fig. 4. Half ball contacted by partial: (a) inner ring and (b) outer ring.",
        "texts": [
            " Thus, before solving a contact problem by using the penalty method, it must be verified by calculations for the searching of an appropriate or optimal penalty parameter. Initially, a small penalty parameter is used, and the penalty parameter will be increased step by step until the solution converges. For time saving in determination of ball deformation for various bearings, a simplified approach by using partial model is needed. For a bearing with N balls, two axissymmetrical models as shown in Fig. 4 are constructed, which consist of a half ball contacted by the 1/N partial inner ring or by the 1/N partial outer ring. Their boundary conditions are (a) G1: all nodal degrees of freedom (d.o.f.) on both ends of the inner and outer rings are constrained in tangential direction, (b) G2: both lines between the contact points of the inner ring, outer ring and the center of the half ball, respectively, are constrained in both horizontal directions and (c) G3: all nodal d.o.f. on the inner edge of the inner ring and the outer edge of the outer ring are constrained in all directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003214_j.measurement.2020.107897-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003214_j.measurement.2020.107897-Figure11-1.png",
        "caption": "Fig. 11. Considered sun gear health scenarios.",
        "texts": [
            " More detailed information can be found in Ref. [4]. The Geometry parameters of the planetary gearbox are listed in Table 2. The experiments operated on the planetary gearbox and the rotational frequency was set up with 30 Hz, data length of 13.8 s, and the sampling frequency is set to be 7680 Hz. Once the value of rotational frequency is known, the values of some characteristic frequency can be calculated [4], we list them in Table 3. Four sun gear health scenarios will be studied, as is shown in Fig. 11. The frequency spectra of the above four considered health scenarios are plotted in Fig. 12. In Fig. 12, the dominant frequency components: f m; f m f shaft and f m f sun are annotated with arrows. These components are predicted by the original model within sun gear tooth damage in Ref. [27]. Furthermore, the sidebands induced by the relaxed tidal period are highlighted and indicated by arrows, namely f m f rt ; f m f sun f rt and f m f shaft f rt . All the scenarios in Fig. 12 demonstrate the amplitude modulation effect caused by the motion period of the fault meshing positions",
            " Additionally, Some trends of these exisiting sidebands may indicate different fault symptoms and should become a meaningful future research directions. The experimental studies also conducted on the planetary gearbox of DDS platform (shown in Fig. 10). According to the assembled parameters listed in Table 2, the sun gear\u2019s rotations to be a tidal and relaxed-tidal period can be calculated based on expressions of ns t and ns rt , as are given in Table 4. Table 4 tells that ns t is 4 times of ns rt for the studied planetary gearbox. 28 groups of the four sun gear scenarios (Fig. 11) were collected under the rotational frequencies of 30 Hz and 50 Hz, respectively. All the data was captured with the time duration of 13.8s and the sampling frequency of 7680 Hz. Each signal was sliced with the pace length of a relaxed-tidal period. The time duration of a relaxed-tidal period and a tidal period can be determined by the rotational frequency and Table 4, as are listed in Table 5 and 6. For each same length of the sliced signals, two indicators are selected for the statistical analysis: the root means square (RMS) and Kurtosis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000766_te.2008.2011542-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000766_te.2008.2011542-Figure5-1.png",
        "caption": "Fig. 5. Mobile robot follower.",
        "texts": [
            " The two regular wheels were driven using separate stepper motors. A set of two infrared sensors were mounted in the front of the vehicle suitably oriented for optimal coverage of the space in front of the robot. The objective was to get the vehicle to follow a target (in this case a cardboard plane) at a fixed distance. The infrared sensors provided information on the distance of the target. This information was used in a simple control algorithm to command the stepper motors to turn the wheels forward or backward as needed to maintain target distance. Fig. 5 is a picture of the vehicle that was successfully demonstrated. 2) Automated windshield wiper system: This project connects with the automated systems that have started to appear in some high-end automobiles, whereby the sweep rate of the windshield wipers is set based on the wetness of the windshield (as established by the volume of rain). Fig. 6 shows a picture of the scaled-down mockup that was constructed to represent the above application. An optical sensor enables the wetness of the windshield to be assessed through changes in the scattering of light, while a servo motor is used to actuate the sweep of the wipers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.152-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.152-1.png",
        "caption": "Fig. 2.152 Brushless-type AC-DC/DC-AC macrocommutator-based hyposynchronous (induction) squirrel-cage-rotor dynamotor [FIJALKOWSKI 1985B; 1987].",
        "texts": [
            " Protective functions are implemented in a separate system that co-operates with the microcomputer-based mechatronic control system. For this tri-mode HE DBW 4WD propulsion mechatronic control system, the entire system approach centres on the new concept of the integral AC-DC/DC-AC macrocommutator-based dynamotorised transaxle shown in Figure 2.151. This essentially replaces the conventional dynamotor/transaxle assembly of a conventional frontwheel-drive (FWD) HE DBW 4WD propulsion mechatronic control system. The brushless AC-DC/DC-AC macrocommutator hyposynchronous (induction) squirrel-cage rotor dynamotor (Fig. 2.152) that consists of just a stator and a rotor, has a hollow dynamotor shaft with an M-M differential case placed on the end of the shaft to serve as the input for the limited slip M-M differential [FIJALKOWSKI 1985B, 1987]. Automotive Mechatronics 346 The AC-DC/DC-AC macrocommutator-based brushless-type dynamotorised transaxle has the following advantages [FIJALKOWSKI 1985B]: It functions automatically and is very rapid (during starting and slipping, the wheel can perform maximum 1 revolution); It fully utilizes the forces of wheel adhesion; It does not lead to the hazard of destructive transaxle components operating overloads); It does not demand special cooling and lubrication oils; It has great durability",
            "153 shows the main functions and signal routes of the transaxle\u2019s brushless AC-DC/DC-AC macrocommutator squirrel-cage rotor asynchronous (induction) dynamotor [FIJALKOWSKI 1985B, 1987, 1996A]. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 347 The mechatronic control equipment is divided into a \u2018Higher-Level Propulsion Controller\u2019 and a \u2018Lower-Level Macrocommutator Controller\u2019. Both sets of equipment are located in the macrocommutator housing. The macrocommutator controller incorporates circuits for controlling and monitoring the stator-field application-specific integrated matrixer (ASIM) as shown in Figure 2.152). In principle, the input signal to the macrocommutator controller is a torque reference (set point) that is compared with a torque signal obtained by means of suitable control of stator-field ASIM. The propulsion controller incorporates circuits for controlling and monitoring the transaxle driven by the AC-DC/DC-AC macrocommutator dynamotor. The control mode used is angular velocity control. The reference (set point) for the controlled variable is formed in the onboard microprocessor-based highest-level HEV controller (see Figs 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002053_j.ijnonlinmec.2014.11.015-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002053_j.ijnonlinmec.2014.11.015-Figure1-1.png",
        "caption": "Fig. 1. Non-linear mechanic model of gear pair on deformable bearings.",
        "texts": [
            "015i Also, these two of the machine elements have a completely different construction, function and physical attributes. The nonlinear dynamic models of spur gear and ball bearing are explained in order to identify the qualitative and mathematical analogies. One of the typical mechanical systems with non-linear dynamic characteristics is the gear pair model supported by rolling element bearings. This mechanical system exists in almost all machines and machine systems. The model of this mechanical system is shown in Fig. 1 [15]. It consists of a spur gear pair (pinion and wheel) and bearings with rolling elements. Gears are modeled with two disks coupled with non-linear mesh stiffness and mesh damping [4\u20136,16,17]. In this model gears have masses m1 and m2, mass moments of inertia I1 and I2 and base circle radii r1 and r2. The deformations of pinion and wheel during gears rotation are displacements of pinion tooth and wheel tooth in direction of the line of contact and are labeled with x1 and x2. The pinion torque and wheel torque are labeled with M1 and M2, while Fb1 and Fb2 refer to radial forces applied to the center of the pinion and the wheel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003738_s41403-021-00228-9-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003738_s41403-021-00228-9-Figure7-1.png",
        "caption": "Fig. 7 a LDED set-up b Zr-4 tube and its cross-section",
        "texts": [
            "6\u00a0mm thick \u00d7 100\u00a0mm length Zircaloy tube were carried. LDED process parameters were optimised and it was observed that selection of appropriate processing parameters is critical to get homogeneity, uniformity and defect-free deposition. During initial trials, it was observed that the lower thickness (~ 400\u00a0\u03bcm) of Zr-4 tubes is a major challenge as it yields excessive dilution or thermal damage/burning. The control of excessive dilution and thermal damage/burning is achieved by cooling the tube from inside by flowing Ar gas (20\u00a0l/min) Figure\u00a07a presents the experimental arrangement used for depositing SiC layers. The optimized parameter yielding defect-free SiC cladding (refer Fig.\u00a07b) is laser power density of 4.52\u00a0kW/cm2, powder feed rate 2.71\u00a0g/min and scan speed 325\u00a0mm/min (Rai et\u00a0al. 2020). Copper (Cu) is known for its higher thermal and electrical conductivity, which attract its deployment in several engineering applications. However, processing of pure Cu through LAM is challenging due to issues related to its higher thermal conductivity and higher reflection to the laser beam. In one of our works, the process window is developed for LDED of Cu bulk structures using a combined parameter called \u201claser energy per unit powder feed (LEPF)\u201d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001806_tasc.2016.2524026-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001806_tasc.2016.2524026-Figure2-1.png",
        "caption": "Fig. 2. Topology of 12/14-pole BFSPM motor.",
        "texts": [
            " Based on the FSPM motor, a type of novel bearingless FSPM (BFSPM) motors with the single winding are proposed and investigated [9]. The purpose of this paper is to compare the configurations and electromagnetic performances of a 12-stator-slot/10-rotorpole BFSPM motor and a 12-stator-slot/14-rotor-pole BFSPM motor. In Section II, the configurations and operating principles of the two motors will be described. In Section III, the electromagnetic characteristics of both motors will be analyzed and compared using the finite element analysis (FEA). Finally, conclusion will be drawn in Section IV. Fig. 1 and Fig. 2 show the configurations of three-phase 12/10-pole and 12/14-pole BFSPM motors, respectively. In Fig. 2, the stator contains 12 segments of \u201cE\u201d-shape magnetic cores, between which 12 pieces of magnets are sandwiched. The magnets are magnetized circumferentially in alternative opposite directions. The concentrated armature coils are wound around the adjacent teeth and PM, and suspending coils are wound around the middle teeth. The key difference between the two motors is that the \u201cU\u201d-shaped magnetic cores are adopted in 12/10-pole motor. And shorter length magnets in the radial direction are employed to save space for the accommodation of the added suspending windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001851_gt2016-56084-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001851_gt2016-56084-Figure11-1.png",
        "caption": "Figure 11. (\u0430) The wireframe model of the blade and views of",
        "texts": [
            " In this study several set-ups were considered, but the final one was as follows: minimization of the potential energy of deformation as an objective, and at least double reduction of the design space volume as a constraint. The value range of the first six eigenfrequencies was also used as a constraint for the design space. Since stress values are highly sensitive to mesh quality and concentrations, value range checked only after the TO and stress constraints were not applied. As a result of TO, design of a blade with reduced weight, satisfying strength (Fig. 11), and eigenfrequency requirements with the constant airfoil surface was obtained. its section in (b) radial and (c) transverse directions. Blade # V was \u201cprinted\u201d by SLM on a small scale using Mlab Cusing equipment (Fig. 12). The minimum wall thickness was 0.15 mm. A blade of this design would be very difficult to produce by casting. There are tomographic images of some blade sections shown in Fig. 13. Results show good geometrical correlation between the CAD-model and the blade produced by SLM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure4.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure4.5-1.png",
        "caption": "Fig. 4.5 Location of the spinning disc with the inner gimbal at the process of the turn of the outer gimbal",
        "texts": [
            "4 Test stand of Super Precision Gyroscope \u201cBrightfusion LTD\u201d gimbal 2 on the small angle \u03b3 = 2\u25e6 55\u2032 71\u2032\u2032 around axis oy, under the action of the resulting torque (T \u2212 T p\u00b7x \u2212 T r\u00b7y), turns the gimbal 1 in the clockwise direction around axis ox on the maximal angle \u03d5 = 164,841101855\u00b0 around axis ox. The following turn of the gimbal 2 does not turn the gimbal 1 that keeping the vertical location of the spin axis that coincides with axis oy. The final location of the gimbals is represented in Fig. 4.3b. The practical test of the gimbal motions was conducted for the horizontal location of the spinning disc and its following turn until vertical. At the starting condition, the location of the spinning disc and the outer gimbal represented in Fig. 4.5a. The minor turn of the outer gimbal in the counterclockwise direction around the vertical axis oy on the angle \u03b3 leads to the big turn of the inner gimbal in the clockwise direction around the horizontal axis ox on the angle \u03d5 (Figs. 4.4 and 4.5b).The inner gimbal turns until the vertical location of the spinning disc axis with the minor turn of the outer gimbal on the angle \u03b3 (Fig. 4.5c). The following turn of the outer gimbal does not turn the inner gimbal (Fig. 4.5d). The practical measurement of the angles of the turn for the gimbals by load torque conducted manually by the Mitutoyo Universal Bevel Protractor. The angle of the turn of the inner gimbal on \u03c9yt = 90\u00b0 from horizontal location implements by the minor turn of the outer gimbal on the angle \u03c9xt = \u03b3 and the motion of the inner gimbal on \u03d5 = \u03d5max \u2212 90o = 164.841101855\u00b0 \u2212 90\u00b0 = 74.841101855\u00b0 that defined by Eq. (4.13). 90o = [ 2\u03c02 + 8 + (2\u03c02 + 9) cos 74.841101855\u25e6 2\u03c02 + 9 \u2212 (2\u03c02 + 8) cos 74.841101855\u25e6 ] \u03b3 and \u03b3 = 1",
            "2), other components are as specified above. Substituting defined parameters into Eq. (5.50) and transformation yields the following result: 5.3 The Practical Test of Gyroscope Motions 101 \u03b5x = Tx Jx = 1.461887255 \u00d7 10\u22127/9.81 1.9974649 \u00d7 10\u22124 = 7.460461885 \u00d7 10\u22125 rad/s2 (5.51) \u03b5y = Ty Jy = 1.297409209 \u00d7 10\u221211/9.81 1.9974649 \u00d7 10\u22124 = 6.621079654 \u00d7 10\u22129 rad/s2 (5.52) The theoretical reactions of the forces Fi acting on the flexible cord along axis oy and ox are calculated by the following formula: Fi = Ti l (5.53) where l = 0.0325 m (Fig. 4.5, Chap. 4), other components are as specified above. Substituting defined parameters into Eq. (5.53) and transformation gives the following result: Fy = Tx l = 1.461887255 \u00d7 10\u22127 0.0325 = 4.498114630 \u00d7 10\u22126 N = 4.585234077 \u00d7 10\u22124 g (5.54) Fx = Ty l = 1.297409209 \u00d7 10\u221211 0.0325 = 3.992028335 \u00d7 10\u221210 N = 3.992028335 \u00d7 10\u22127 g (5.55) The calculated values of the gyroscopic forces acting along axis oy can be measured and validated by the practical test. The test of the gyroscope with one side free support and the measurement of the force acting on the flexible cord were conducted on the stand that represented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.74-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.74-1.png",
        "caption": "Fig. 2.74 Schematic diagram of a contemporary CVT (A) and its single segmented metal drive-belt (B) [Van Doorne Transmissie BV; NEWTON ET AL. 1989].",
        "texts": [
            " The simplest form had the driven disc set on a shaft at right angles to the driving disc. 2.3 M-M DBW AWD Propulsion Mechatronic Control Systems 227 The driving disc may be slid along its splinted axle to contact the driven friction discs at different distances from its centre [HOMANS 1910]. The speed ratio of such a design is simply the radius of the driving disc divided by the distance from the contact point to the centre of the driven discs. Many of the automotive vehicle manufacturers still perform research in this area. From Figure 2.74 it can be seen that a contemporary CVT is particularly suitable for FWD vehicles. Automotive Mechatronics 228 A centrifugal clutch, top left, transmits the drive to the primary pulley and, through a quill drive, to a M-F pump, top right, the adjustable flanges of both the primary and secondary \u2013 driving and driven \u2013 pulleys slide axially on linear ballbearing splines, that of the primary one being controlled by fluidical pressure in the cylinder to the left of it, while the secondary one is closed by the coil spring plus fluidical pressure in the smaller diameter cylinder on its right"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure9-1.png",
        "caption": "Figure 9. Top ring groove position modification",
        "texts": [
            " It has been found that at engine normal operative conditions, crevice size slightly effects HC emissions. Nevertheless as the piston crevice volume is increasing its size for engine cold conditions, HC emissions increases too during engine warm-up. According to Wentworth's work [17], HC emissions are decreased by 20% to 40% with an 86% decrease in the piston top-land volume. In this paper, different scenarios of modifying top ring groove position have been analyzed. Two iterations have been analyzed, first moving the groove up by 1mm and later 2mm as is depicted on Figure 9. Finite element analysis has been performed to determine mechanical stresses distribution on piston design due to the ring movement. On Figure 10 it can be observed von-Mises stress distribution as well as the safety factor for the first groove region. Table 6 reflects safety factor and von-Misses stress for the different scenarios studied. As it can be observed, the ring groove fatigue strength improves as this region is approximately 50\u00b0C cooler than at the standard piston. Also, as the groove is moved up, the wall section increases where it is not directly adjacent to the cooling gallery thus improving the stress condition further"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000205_978-1-4615-9882-4_40-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000205_978-1-4615-9882-4_40-Figure1-1.png",
        "caption": "Figure 1 Co-ordination of walking system",
        "texts": [
            " Plane walking As for biped walking robots, a control device and/or power source was not installed on the body, and its gait was almost all straight walking. But in the near future, when the practical walking robots should be widely used, it is necessary that these robots have independent hardware and are able to do plane walking. From this point of view, we made it the main target for our study to make plane walking on the level of static or quasi-dynamic walking, and to install the control device on the body as the first step to hardware independence. We set the Cartesian co-ordinate axes of x-y-z, as shown in Figure 1, for walking robot to be treated mathematically. Therefore, the x-z plane forms a sagittal plane, the y-z plane forms a lateral plane and the x-y plane forms a floor plane. Plane walking is a form considered to be man's usual walking. He may walk straight as well as diagonally or from side-to-side. As space for walking is restricted to a floor, there are totally 3 DOF for walking adding 2 DOF of x-y plane and 1 DOF of rotation around z axis. In connection with these 3 DOF, we call the walking on x axis 'straight walking', the walking on y axis is called 'sideway walking' and the rotation around z axis 'turning'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001570_j.ifacol.2015.09.584-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001570_j.ifacol.2015.09.584-Figure3-1.png",
        "caption": "Fig. 3. Different types of coupling used in the experiment.",
        "texts": [
            " In order to measure the vibrations at the motor DE bearing the rotor DE and NDE bearing, accelerometers were mounted in the vertical direction. However, these accelerometers measure the bearing vibrations at the housing only. So, in order to measure the NDE bearing vibration, a single point PDV 100 laser vibrometer was focused on a spot on the outer stationary race of the NDE bearing in the axial direction. Figure 2 shows a view of the experimental setup with all the measurement devices. The three types of coupling, helical, gear and rigid used in the present study are shown in Figure 3. A B&K PULSE system was used for the vibration analysis of the signals from the accelerometers and the laser vibrometer. In order to introduce parallel misalignment in the system, the DE and NDE housings were displaced in the horizontal direction by 2.12 mm. An angular misalignment was introduced by introducing shims below the NDE bearing of 1.90 mm thickness, which gave rise to an angular misalignment of 0.30. In our study both the misalignment types were present simultaneously. For measuring the temperature at the DE, NDE bearings and the coupling the thermal imaging camera was focused on them from a distance of 1 m and the temperature data logged at a rate of 30 image frames per second",
            " With the addition of the heavy loads it was observed that the time taken to reach the steady speed was almost the same. Thus the angular accelerations in the rotor system with and without the loaders were the same. The electrical power drawn by the motor was estimated by measuring the current drawn using a hall-effect current sensor and the supply voltage. There was no noticeable difference in the electrical power even in comparison to the case of the misaligned system. The rotor-rig basically consisted of two major configurations, one with the two heavy bearing loaders as shown in Figure 3 and one without. For each of the case, two types of couplings were used between the motor and the rotor shaft, namely flexible and rigid. The gear coupling was used as a flexible coupling, however when misalignment was introduced in the system, the gear coupling was replaced by a flexible helical coupling, since helical coupling by flexing could only take up the severe shaft misalignment as shown in Figure 4. While the rotor rig was in operation the temperatures of the coupling, DE and NDE bearings were measured by a FLIR Initially once the rotor-rig was switched on it was observed that the temperatures at the couplings and bearings rise exponentially and reach a steady state value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001013_s12283-012-0102-y-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001013_s12283-012-0102-y-Figure2-1.png",
        "caption": "Fig. 2 JAXA\u2019s 60 cm magnetic suspension balance system (MSBS): a coil arrangement, b suspended archery arrow",
        "texts": [
            " It is one of the long lasting subjects in fluid mechanics to fully understand the physical mechanism of the boundary layer transition. We will see later that the study of arrow-aerodynamics is not a straightforward application of fluid mechanics, but it casts another puzzle on the subject. 2.1 MSBS wind tunnel experiments The Magnetic Suspension and Balance System (MSBS) of the JAXA\u2019s 60 cm wind tunnel provides an ideal way of supporting a thin arrow for wind tunnel tests, because the force supporting the arrow is generated by magnetic fields which are controlled by 10 coils arranged outside the test section. Figure 2 illustrates the coil arrangement. We insert 10 pieces of cylindrical neodymium magnet of diameter 4 mm and length 30 mm, inside the arrow shaft and the magnetic field is adjusted to balance the gravity by controlling the electric currents flowing through the coils. When the wind is flowing, we further adjust the magnetic field to compensate the aerodynamic forces exerted on the arrow, i.e., we control the electric currents so that the arrow remains at a fixed position with an initially specified attitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.1-1.png",
        "caption": "Figure 2.1. Planar 1-dof parallel mechanism (four-bar linkage)",
        "texts": [
            " In flight simulators, for instance, the mass of the platform is usually very large and powerful actuators are required to support the weight of the moving links. In such a system, static balancing can be used to eliminate the need for the actuators to support the weight of the links. This can be accomplished using Equation (2.5). In order to provide more insight into this problem, two examples are now provided. First, the simplest case of a planar mechanism is addressed and then a sixdof general parallel mechanism is analysed. A planar one-dof mechanism is shown in Figure 2.1. This mechanism is commonly referred to as a four-bar mechanism. It is studied here mainly for illustration purposes. As shown in the figure, the length of the ith link is noted li, its mass, mi and the position of its centre of mass is defined using angle i and distance ri. The latter two quantities are expressed in a local frame attached to the link. Variable 1 is the angle of the actuated link with respect to the fixed link and is therefore referred to as the actuated joint variable. Angles 2 and 3 are associated with unactuated joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000714_1.3157159-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000714_1.3157159-Figure10-1.png",
        "caption": "Fig. 10. The effect of table friction on the cue ball path for an oblique collision from Ref. 2 . a The parameters involved in an oblique collision. b The cue ball path for different precollision cue ball speeds under rolling conditions.",
        "texts": [
            "org/authors/copyright_permission C. Impact between balls If the approaching and separating velocities of two balls lie along the line connecting the centers of the balls, then the impact is said to be frontal or head-on. Impacts occur in two dimensions in billiards as oblique collisions, and the frontal impact is a special case. Amateur billiards players use the 90\u00b0 rule9,10 to visualize the postcollision trajectories of the colliding balls. It states that the balls will separate at 90\u00b0 after an oblique collision see Fig. 10 for the predicted ideal directions of travels . It is also assumed that the cue ball will immediately stop after a frontal collision. In snooker the cue ball and all object balls have the same mass. It can be easily shown by momentum conservation that the 90\u00b0 rule only holds when the coefficient of restitution between the balls is one that is, the balls are purely elastic . The angular velocity of the cue ball in the form of the side/top spin when it collides with the object ball also affects the postcollision velocities and the directions of separation for the balls",
            " The tracked results for the cue ball and an object ball collision are shown in Fig. 11. We see that the temporal resolution of the tracking is sufficient to capture the deflections in its postimpact trajectory. The reason for the curvature in the path of the cue ball is that it starts to slip immediately after the impact a similar slipping phenomenon was 792 Am. J. Phys., Vol. 77, No. 9, September 2009 Downloaded 19 Oct 2012 to 136.159.235.223. Redistribution subject to AAPT also observed in the ball collision with a cushion; see Fig. 10 a . Figure 10 b gives an idea of how this behavior is influenced by the incident velocity of the cue ball. Similarly, the object ball also starts to slip immediately after the impact. Once the slipping phase has stopped, both balls go into rolling motion, and the curved path of the cue ball is then directed along the tangent line to the curve. Reference 2 analyzed this phenomenon and showed that the velocities for the postcollision and postsliding phases of the object ball are see their notation in Fig. 10 VO = 5 7V cos , O = , 1 and for the cue ball is VC = 5 7V 9 5sin2 + 4 25 , C = tan\u22121 sin cos sin2 +2 5 . 2 They defined =b /D as the fractional impact parameter, where D is the ball diameter and b is the separation of the ball centers in the direction perpendicular to the incident ball velocity V. Also note that =sin . Plots of angles o, c, and o+ c versus the impact parameter are shown in Fig. 12. The experimental values agree with the theoretical predictions in most instances, but o deviates more from its theoretical value at high fractional impact values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002102_s00170-015-6915-7-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002102_s00170-015-6915-7-Figure11-1.png",
        "caption": "Fig. 11 Cross section of face gear and shaper by plane \u03a0",
        "texts": [
            "3 Numerical verification of envelope residual The residual values of the tooth surface in the experiment are unavailable due to lack of measurement instruments. In order to verify the value of the envelope residuals, an envelope simulation for face gear tooth profile is performed with software AutoCAD with the following steps: 1. Plot the cross section of the face gear and shaper by plane \u03a0 (Fig. 4a). The profile of the shaper is firstly plotted by involute equations. The profile of the face gear is considered as a straight line because the tooth number is very large [19]. As shown in Fig. 11, point I is the instantaneous center. Line IN is tangent to the base circle of the shaper, and it is perpendicular to the profile of the shaper at M. rbs is the radius of the base circle of the shaper. \u03c9s is the angular velocity of the shaper and v2 is the line velocity of the face gear on plane\u03a0. The meshing angle \u03b1 can be determined by \u03b1 \u00bc arccos rbs rIs \u00bc arccos 0:5Nsmncos\u03b1n rIs \u00bc 35:30879\u2218 \u00f014\u00de Then, the profile of the face gear can be drawn according to \u03b1, point M, addendum ha, and dedendum hd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001818_978-3-319-19740-1_15-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001818_978-3-319-19740-1_15-Figure5-1.png",
        "caption": "Fig. 5 A kinematic model of hypoid generators",
        "texts": [
            "\u00fe cm4q 4 \u00fe cm5q 5 \u00fe cm6q 6 j \u00bc j0 \u00fe j1q\u00fe . . .\u00fe j4q4 \u00fe j5q5 \u00fe j6q6 i \u00bc i0 \u00fe i1q\u00fe . . .\u00fe i4q4 \u00fe i5q5 \u00fe i6q6 ; 8>>>>>>< >>>>>: \u00f012\u00de Here, q is the cradle rotational increment; Ra is the ratio of generating roll; Xb is the sliding base; sr is the cutter radial setting; Em is the offset; Xp is the work head setting; cm is the root angle; j is the swivel angle; and i is the cutter head tilt angle. The machine setting parameters represent corresponding kinematic elements of the hypoid generator illustrated in Fig. 5. The geometry of the tooth surfaces of a pair of mating pinion and gear can be generally represented by the position vector, unit normal and unit tangent in the coordinate systems S1 and S2 that are rigidly connected to the pinion and the gear, respectively, as follows, Pinion : r1 \u00bc r1\u00f0u1; h1;u1\u00de n1 \u00bc n1\u00f0u1; h1;u1\u00de t1 \u00bc t1\u00f0u1; h1;u1\u00de f1\u00f0u1; h1;u1\u00de \u00bc 0 8>>< >: ; \u00f013\u00de Generated gear : r2 \u00bc r2\u00f0u2; h2;u2\u00de n2 \u00bc n2\u00f0u2; h2;u2\u00de t2 \u00bc t2\u00f0u2; h2;u2\u00de f2\u00f0u2; h2;u2\u00de \u00bc 0 ; 8>< >: \u00f014\u00de Formate gear : r2 \u00bc r2\u00f0u2; h2\u00de n2 \u00bc n2\u00f0u2; h2\u00de t2 \u00bc t2\u00f0u2; h2\u00de 8< : : \u00f015\u00de Step 3: Assembly of the pinion and gear members in their running position, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.14-1.png",
        "caption": "Fig. 17.14 Shears (a), (b), (c) with parameters 1 , . . . , 4 and shears (d) with instantaneous centers of rotation open and closed (e)",
        "texts": [
            " Solution: Since x1 and x2 describe relative positions, it is unnecessary to declare any particular link as fixed link. In Table 17.1 the velocities x\u03071 and x\u03072 are expressed in terms of relative angular velocities (positive counterclockwise). These expressions are obvious from the figures. In each expression the two relative angular velocities are related through a constraint equation. These equations have the following forms. (a) x\u03073 = \u2212 2\u03c910 = \u2212 3\u03c923 , (b) The constraint x\u03073 = 0 means that 2\u03c910 \u2212 ( 2 + 3)\u03c920 = 0 , (c) x\u03073 = \u2212 3\u03c910 = \u2212( 2 + 3)\u03c923 , (d) In Fig. 17.14d instantaneous centers are shown. From (15.6) it follows that \u03c910/\u03c930 = L4/L3 and \u03c923/\u03c930 = L1/L2 and, consequently, \u03c910/\u03c923 = L2L4/(L1L3) . With these constraint equations the final results shown in Table 17.2 are obtained. 17.7 Transmission of Forces and Torques 589 Comparative evaluation: Figures 17.14a,b,c are drawn with identical lengths 1 = 35 , 2 = 3.5 , 3 = 6 , 4 = 9 . With these lengths F2/F1 \u2248 6.7 for the shears (a), F2/F1 \u2248 11.6 for the shears (b) and F2/F1 \u2248 3.3 for the shears (c). Shears (c) are the only ones in which the object to be cut can be placed in the position 4 = 0 ",
            " Then, F2/F1 \u2248 6.4 . With parameters of commercially available pruning-shears of this kind a ratio F2/F1 = 15 is possible. Compared with all other devices these shears have the advantage that for a given width of the object to be cut the opening angle between the shearing blades is the smallest. 590 17 Planar Four-Bar Mechanism In shears (d) the lengths L2 and L3 are constant. The lengths L4 and L1 depend very much on the opening angle. Both of them decrease monotonically in the process of closing the blades. Figure 17.14e shows the blades fully closed. The dimensions should be chosen such that in this position the instantaneous centers P13 , P10 and P20 are almost collinear as shown. In this case, the ratio L4/L1 is > 1 in every position, and it increases monotonically when the blades are closing. With shears of this kind reinforcement steel rods of 15 mm diameter can be cut by hand. Every point fixed in the plane of the coupler traces a coupler curve when the four-bar is moving through its entire range. It is the complexity of these curves to which the four-bar owes much of its importance in engineering (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001827_1350650116649889-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001827_1350650116649889-Figure11-1.png",
        "caption": "Figure 11. Nondimensional fatigue life factor of TRB as a function of the number of defective rollers ( D\u00bc 2mm).",
        "texts": [
            " However, for the purpose of investigating the effect of the number of defective rollers on TRB performance, the following conditions were introduced: (1) all defective rollers were assumed to have an D value of 2 mm, and (2) three configurations of defective rollers were considered: case 1: roller #1, case 2: rollers #1 and 5, and case 3: rollers # 1, 5, and 9. Figure 10 shows the TRB stiffness that was dependent upon the number of defective rollers. The average stiffness of the TRB decreased with increasing number of defective rollers. Figure 11 indicates the fatigue life factor of the TRB as a function of the number of defective rollers. The fatigue life factors of bearings for the three different cases of defective rollers were reduced by 9.55%, 33.28%, and 42.87% in the axially loaded case, and 36.00%, 40.50%, and 43.83% in the case of combined loads, respectively. The maximum contact forces between the roller and raceways increased as the number of defective rollers increased. Figure 12 illustrates the time varying maximum contact force between the roller and inner raceway for the TRB with and without defective rollers. Increasing the number of defective rollers consequently increased the interval time subject to the at Middle East Technical Univ on May 18, 2016pij.sagepub.comDownloaded from higher contact loads. In other words, for the same amount of running time, the TRB with a larger number of defective rollers sustained a longer time with higher roller contact forces. Consequently, the TRB fatigue life decreased, as demonstrated in Figure 11. Effect of defective roller locations This section analyzes the effect of defective roller configuration on the TRB performance. Four cases of defective roller positions were considered with increasing distance angle \u2019 between consecutive defective rollers. Figure 13 illustrates these four cases of defective roller configurations, including 13a defective rollers #1, #2, and #3 (\u20191,2\u00bc \u20192,3\u00bc 18.95 ), 13b defective rollers #1, #3, and #5 (\u20191,3\u00bc \u20193,5\u00bc 37.89 ), 13c defective rollers #1, #5, and #9 (\u20191,5\u00bc \u20195,9\u00bc 75"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003357_0954406220911966-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003357_0954406220911966-Figure3-1.png",
        "caption": "Figure 3. The five DOF model of DTRB: (a) the global coordinate system; (b) the angular misalignment of the inner ring; (c) the load zone and the local coordinate system at a particular roller.",
        "texts": [
            " In this section, the contact loads of rollers will be determined by solving the relevant equilibrium equations of DTRB using a quasi-static model. The detailed description of the DTRB model was presented in literature25 without considering the bearing clearances. This section briefly develops the bearing model particularly with the inclusion of radial and axial clearances. Figure 2 shows the cross-section of a DTRB with some basic geometric parameters and clearances. The inner ring of DTRB is subjected to a load vector {F}, which causes a displacement vector {d} (Figure 3(a) and (b)) Ff gT \u00bc Fx,Fy,Fz,Mx,My \u00f01\u00de f gT \u00bc x, y, z, x, y \u00f02\u00de where the superscript T represents the transpose of a vector. Figure 3(c) shows the local coordinate system \u00f0r; ; z\u00de located at the inner ring cross-section at a particular roller of azimuth angle . A cross-section view of the inner ring under the local coordinate system is shown in Figure 4(a). The displacement vector of the inner ring cross-section, displacement vector of roller, and the inner ring contact load vector are expressed respectively as uMf g T \u00bc uM,r, uM,z, M \u00bc RM\u00bd f g \u00f03\u00de vMf g T \u00bc vM,r, vM,z, M \u00f04\u00de QM T \u00bc QM,r,QM,z,TM \u00f05\u00de where the subscript M is the row index, M\u00bc 1 represents the right row, and M\u00bc 2 the left row"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003384_s12555-019-0904-9-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003384_s12555-019-0904-9-Figure2-1.png",
        "caption": "Fig. 2. Sketch of the PVP.",
        "texts": [
            " However, the stable control of planar Pendubot has been realized by employing NA model and that of planar Acrobot has been achieved by using angle constraint. Motivated by the above stable control strategies of two kinds of two-link systems, we divide the planar APA system into two parts to control by analyzing its mechanical structure. When the angle and the angular velocity of the third link of the planar APA system are controlled to zero, that is, q3 = 0 and q\u03073 = 0, the last two links can be regarded as a virtual passive link. In this case, the planar APA system is treated as a PVP. The PVP is shown as Fig. 2, where we mainly implement the control objective of the FAL. When the angle of the first link of the planar APA system is kept at a constant, the planar APA system is treated as a PVA. The PVA is shown as Fig. 3, where we mainly realize the control objectives of the SUL and TAL. 3. CONTROLLER DESIGN FOR PVP We achieve the control objective of FAL for the PVP in this section, and make the system be reduced to a PVA with all links stopping rotating. 3.1. Target angle solution of the FAL This subsection uses a geometry method to get the FAL\u2019s target angle corresponding to the target value of end-point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.70-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.70-1.png",
        "caption": "Fig. 2.70 Eight-velocity range-change manual transmission (MT) [Scania\u2019s MT - GR801-8].",
        "texts": [
            " Automotive vehicle M-M transmissions are classified into different categories: Classical 4-6 velocity manual transmissions (MT) that in turn can be divided into: Unsynchronised, constant-mesh manual transmission (CMT); Synchronised, synchronised manual transmission (SMT); Semi-automatic transmissions (SAT). Automotive Mechatronics 224 Fully automatic transmission (FAT) that, in turn, can be divided into Automatic power-shift transmissions (APS); Automatic manual transmission (AMT); Mechano-mechanical (M-M) continuously variable transmission (CVT). Manual Transmissions (MT) - The manual gearbox consists of different gearwheels that are engaged and disengaged (Fig. 2.70). In conventional MTs, the driver is involved in the process of changing gears. The driver changes gears and performs the process of engaging and disengaging the master clutch. The MT is synchromesh and fitted with helical gears that result in easy gear shifting and avoidance of wear and unpleasant noise. Semi-Automatic Transmissions (SAT) -- In SATs, one of the operations of engaging the clutch and changing gear is automatic, for example, the driver chooses the gear and the transmission performs the clutch manoeuvre"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001450_s1560354715050056-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001450_s1560354715050056-Figure1-1.png",
        "caption": "Fig. 1. Realization of the Suslov problem.",
        "texts": [
            " Highly efficient numerical experiments were conducted using the software package \u201cComputer Dynamics: Chaos\u201d by means of a computational cluster of the laboratory LATNA of the National Research University Higher School of Economics. 2. EQUATIONS OF MOTION Consider the motion of a heavy rigid body with a fixed point in the presence of the nonholonomic constraint (\u03c9, e) = 0, (2.1) where \u03c9 is the angular velocity of the body and e is the unit vector fixed in the body. The constraint (2.1) was introduced by G. K. Suslov in [8, p. 593]. The realization of the constraint (2.1) by means of wheels with sharp edges rolling over a fixed sphere was proposed by V. Vagner [9] (see Fig. 1). The sharp edges of the wheels prevent the wheels from sliding in the direction perpendicular to their plane. Choose two coordinate systems: \u2014 an inertial (fixed) coordinate system Oxyz; \u2014 a noninertial (moving) coordinate system Ox1x2x3 rigidly attached to the rigid body in such a way that Ox3\u2016e and the axes Ox1 and Ox2 are directed so that one of the components of the tensor of inertia of the body vanishes: I12 = 0. REGULAR AND CHAOTIC DYNAMICS Vol. 20 No. 5 2015 To parameterize the configuration space, we choose a matrix of the direction cosines Q \u2208 SO(3) the columns of which contain the unit vectors \u03b1, \u03b2 and \u03b3 of the fixed axes Ox, Oy and Oz projected onto the axes of the moving coordinate system Ox1x2x3 Q = \u239b \u239c\u239c\u239c\u239d \u03b11 \u03b21 \u03b31 \u03b12 \u03b22 \u03b32 \u03b13 \u03b23 \u03b33 \u239e \u239f\u239f\u239f\u23a0 \u2208 SO(3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002503_sibcon.2017.7998581-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002503_sibcon.2017.7998581-Figure1-1.png",
        "caption": "Fig. 1. Concept design of the walking in-pipe robot; 1-3 \u2013 legs, forming the forward leg triplet, 4-6 \u2013 legs, forming the backward leg triplet, 7 \u2013 robot\u2019s body",
        "texts": [
            " Many of these results are applicable to the in-pipe robots. This is discussed in more detail in the following sections. II. DESCRIPTION OF THE SIX-LEGGED IN-PIPE ROBOT In this paper, we consider a walking type in-pipe robot with six legs. Each leg consists of two links connected via actuated rotational joints. The legs are attached to the robot\u2019s body in such way that they form two symmetrical triplets, one behind the other. Each triplet assumes a T-shaped form when the legs are stretched out. Figure 1 shows a concept design of the robot. It should be noted that the algorithms described in this paper are not exclusive for six-legged in-pipe robots and would work with a wide range of mechanical designs. The algorithms can be easily extended to handle different number of legs. It would also work for legs with a different structure compared to the one presented in fig. 1. The links that are supposed to come in contact with the inner surface of the pipe have contact pads mounted on their tips. In fig. 2 we use the following notation: iK are contact pads represented as a single point ( 6,1=i ), iC and iD are actuated rotational joints, C is the center of mass of the body link of the robot and i\u03c8 and i\u03b8 are angles that describe the relative orientation of the links that form robot\u2019s legs. III. GEOMETRIC DESCRIPTION OF THE PIPELINE The algorithms presented in this paper rely on a certain geometric description of the pipeline where the motion takes place"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.20-1.png",
        "caption": "Fig. 15.20 Sawtooth construction",
        "texts": [
            " Graphical constructions have the advantage of making things visible. But they have the disadvantage of relying on intersections of lines which, frequently, are either almost parallel or intersecting outside the available sheet of paper. 15.3 Curvature of Plane Trajectories 483 First, a method known as sawtooth construction is explained. As preparatory step, the Euler-Savary Eq.(15.73) in combination with (15.69), R = + r , and with (15.78), s = rW , is written in the form (rW \u2212 r) = r2 . (15.80) Consider Fig. 15.20 which is in part a copy of Fig.15.18. The relationships between the points P1 , Q , M and W on a line e can be expressed geometrically as follows. Let P\u2217 be an arbitrarily chosen auxiliary point. Lines P\u2217M and P\u2217P1 are drawn and parallel to these lines the lines g1 through P1 and g2 through W . Proposition: The point of intersection W \u2217 of g1 and g2 lies on the line P\u2217Q . Proof: The triangles (Q,M,P\u2217) and (Q,P1,W \u2217 ) are similar, and the triangles (Q,P1,P \u2217) and (Q,W,W\u2217 ) are similar. Therefore, QP\u2217 : QW\u2217 equals : r as well as r : (rW \u2212 r) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002975_tvt.2019.2943414-Figure18-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002975_tvt.2019.2943414-Figure18-1.png",
        "caption": "Fig. 18. Liquid-cooled PMR prototype.",
        "texts": [
            " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. change of permeability is 0.22, while that for the proposed model without considering the change of permeability is 0.46 V. TEST BENCH The main components of the test bench are the high-power driving motor (350 kW), the electric control cabinet, the transmission, the cooling system, the data acquisition system, and the torque sensor installed between the PMR and the driving motor, as shown in Fig. 17 and 19. Fig. 18 shows the liquid-cooled PMR prototype. The cooling system includes a water pump, a cooling tank, and a water pipe. Two thermocouple sensors used for measuring water temperature were fixed on the water inlet and outlet, respectively. The materials of the magnet are sintered Nd-Fe-B(N38SH). To reduce the influence of the high temperature, the flow rate of water in the cooling water pipe is approximately 150 L/min, and the retarder must be completely cooled to the environment temperature prior to the next test"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002520_access.2017.2772319-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002520_access.2017.2772319-Figure1-1.png",
        "caption": "FIGURE 1. Communication graph between the follower spacecraft.",
        "texts": [
            " ILLUSTRATIVE EXAMPLE In this section, an example is provied to illustrate the effectiveness of the proposed control laws using NFTSM and CNN in this paper. The mass of the leader and the follower spacecraft are ml = 1kg, and mif = 1kg, (i = 1, 2, 3) respectively. The input control force is ui \u2264 umax = 2N , (i = 1, 2, 3). For simplicity, the leader spacecraft is assumed in a circular reference orbit of radius 6728km and ith (i=1,2,3) follower spacecraft is represented by \"Sat i\u2018\u2018. The communication graph between the follower spacecraft is shown in Figure 1. The information exchange among follower spacecraft is described by a weighted adjacency matrix A de ned by A = [aij]3\u00d73 =  0 1, 1 1.1 1.1 0 1.1 1, 1 1.1 0  . (50) The initial states and desired states of the individual follower spacecraft are shown in Table 1 and Table 2. The parameters of NFTSM controller are taken as g = 1.2, h = 1, p = 10, q = 9,a = 0.002, b = 0.2, \u03ba1 = 10, \u03ba2 = 2, \u03b6 = 0.01, Ki1 = diag(0.2, 0.2, 0.2), Ki2 = diag(0.02, 0.02, 0.02), \u03b9i = 0.008, \u03c3i1 = 100, \u03c3i2 = 0.001, (i = 1, 2, 3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure3.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure3.7-1.png",
        "caption": "Fig. 3.7 Schematic of the spinning thin ring",
        "texts": [
            " Analysis of the expressions of inertial torques acting on the spinning cylinder demonstrates that all of them are the same as for the spinning disc and can be used for the modelling of motions for the spinning objects that have the same surfaces. The analysis of the inertial torques acting on the spinning thin ring with a constant angular velocity \u03c9 is considered the location of its mass elements m on the middle radius R. The action of centrifugal forces on a ring spinning around axis oz with an angular velocity of \u03c9 in a counterclockwise direction is considered in Fig. 3.7. The rotation of mass elements generates the plane of centrifugal forces, which disposes of perpendicular to the axis of the spinning ring. The action of an external torque on the spinning ring inclines the plane of the rotating centrifugal forces that resist the action of the external torque. The following analysis of acting forces and motion of the spinning ring is similar as for rotation disc represented in Sect. 3.1, this chapter. There is a minor difference in the presentation of location of the mass elements of the ring R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002981_icecct.2019.8869179-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002981_icecct.2019.8869179-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of the cart -pole pendulum system.",
        "texts": [
            " This paper is ordered as follow: section II describes the dynamic model of cart pole pendulum, section III suggests the structure of considered adaptive observer taking into account the main properties used in design development, section IV focuses on the design of adaptive observer-based backstepping of cart-pole pendulum system, and section V includes the stability and analysis of the closed-loop system using Lyapunov function. In the final section VI, the effectiveness of the observer-based control design algorithm is verified using simulated results within the MATLAB environment. II. SYSTEM MODEL AND DYNAMIC The schematic representation of cart-pole pendulum systems is shown in Fig. 1 [6, 15]. The dynamic equation of under-actuated system can be written in matrix form as follow [9]: (1) where , , are the position, velocity and acceleration, respectively, and represents the control vector with input components. The matrices , and are given by , , , \u03b4 is zero matrix. where G(q) is the vector of gravity, is the Coriolis and Centripetal force matrix, \u03b4 is the damping matrix and M(q) is the inertia matrix, which is a symmetrical and positive definite matrix, is the mass of the pendulum, is the mass of the cart, is the distance between the axis of rotation and the center of mass, is the moment of inertia of pendulum, is the angle of pendulum and is the displacement of the cart"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001523_tmag.2014.2364264-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001523_tmag.2014.2364264-Figure20-1.png",
        "caption": "Fig. 20. Topologies of multi-tooth VFRMs, n=4, Nr = nNs \u00b1 1 or Nr = nNs \u00b1 2.",
        "texts": [
            " Among the 6-stator pole VFRM and different n, 4-tooth VFRMs exhibits the largest average torque at the conditions of rated 30W total copper loss and same stator outer radius according to Nr=nNs\u00b11 as shown in Fig. 8. Hence, the main stator and rotor pole combinations of 4-tooth VFRM with 6- stator pole will be compared in this section. A. Main Stator and Rotor Pole Combinations while n=4 The main stator and rotor pole combinations of 4-tooth VFRM with 6-stator pole as Nr=nNs\u00b11 and Nr=nNs\u00b12 are shown in Fig. 20. Meanwhile, the main parameters of all the machines which are optimized for maximum average torque under rated copper loss are also listed in Table I. As shown in Fig. 20, the coil connections of 4-tooth VFRMs with Nr=nNs\u00b11 or Nr=nNs\u00b12 are satisfied with (3), by which the coils A1 and A2 belong to the same phase are connected in series with 180 electric degree shifting (opposite polarity) when Nr=nNs\u00b11 but with same polarity when Nr=nNs\u00b12. B. Flux-linkage and Back-EMF Waveforms The open-circuit phase flux-linkages of four machines are compared in Fig. 21 and Table II. It can be seen that the phase flux-linkages of 4\u00d76/23 and 4\u00d76/25 stator/rotor pole (Nr = nNs \u00b1 1) VFRMs are bipolar while those of 4\u00d76/22 and 4\u00d76/26 stator/rotor pole (Nr = nNs \u00b1 2) VFRMs are unipolar, which are consistent with the conclusion of single tooth VFRMs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001532_j.procir.2014.10.023-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001532_j.procir.2014.10.023-Figure9-1.png",
        "caption": "Fig. 9. Setup and position of monitoring points.",
        "texts": [
            " However, this appears to be not expedient for industrial application because the amount of load steps needed for modelling the build-up process would increase in a way that the calculation times and the result file sizes are larger than accepted by the users. In general, taking the scan pattern into account (CLI- or pattern-based) leads to an increase in load steps compared to the application on a whole layer. For that reason it is advisable to foresee a modular structure of the simulation system and let the user decide whether an increase in both calculation time and result accuracy is acceptable and desired or the calculation time efficient way is preferred. 4.2. Simulation results Figure 9 illustrates the utilized simulation setup. Thereby, the simplified turbine blade (cf. CAD-model in figure 3) is modelled with its real dimensions (height 30 mm) and a layer compound height of 250 \u03bcm, which equals 12,5 real layers. The part is meshed by hexahedral elements with varying dimensions below or equal 1 mm. The base plate is modelled with the dimensions of 250 x 250 x 50 mm3 in order to accurately model the process environment and meshed by tetrahedral elements. The preheating of the base plate is modelled by a block structure underneath the base plate, which represents the surrounding machine structure with an included heating unit. Applied simulation parameters are: preheating temperature 80 \u00b0C (on machine structure only) load temperature 1250 \u00b0C (solidus temperature of IN 718) time for applying a new layer (cool down time) 14 s The following diagrams in figure 10 and 11 show the temperature-time-curve for the monitoring points highlighted in figure 9. Thereby, two approaches for heat input are compared. One data set is based on a uniform heat input on the whole layer within one load step whereas the other one is premised on a CLI-based heat input. For the latter, all scan vectors were exemplarily comprised to Nareas,layer = 3 (cf. formula 4). Moreover, the scan information of one layer per layer compound was applied as load on the Z2-level with each position in the middle of the compound (position (Z2-Z1)/2), figure 8). Figure 10 illustrates the temperature-time-curve of the monitoring point in the massive part area (cf. figure 9) until 20 seconds process time (equals the solidification of two layer compounds). It can be seen that the investigated monitoring point is located within the first out of three scan areas in the CLIbased heat input of the first layer compound because the highest peak is right at the beginning of the curve. Furthermore, for this configuration two more rises in temperature are existent due to the heat transfer from neighbouring scan areas. Thereby the third scan area has a shorter distance to the monitoring point compared to the second one because the corresponding peak exhibits a higher temperature (about 130 \u00b0C vs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002146_1464419313519612-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002146_1464419313519612-Figure2-1.png",
        "caption": "Figure 2. Displacement of inner ring center relative to outer ring center.",
        "texts": [],
        "surrounding_texts": [
            "Contact deformation between races and roller gives a nonlinear force deformation relation, which is derived using Hertz contact theory.16,23 In modeling as shown in Figures 2 and 3 the rolling element bearing is considered as a spring mass damper system having nonlinear spring and nonlinear damping. In this work outer race is fixed in a rigid support and inner race is held rigidly in the shaft. A constant radial load is acting on the bearing which is contact stiffness that can be calculated using Hertz theory and dissipating forces at contact point are modeled with nonlinear damping. Contact stiffness for roller bearings On inner race and on outer race localized defect is inserted with nonconventional machining processes as shown in Figure 6. Shaft is inserted in the bearing by press fit. In Figure 1, Dm is a pitch diameter of the bearing; Dr1 and Dr2 are diameters of the outer race and inner race, respectively; and Pd/4 is a radial clearance of the bearing. Palmgren24 developed empirical relation from laboratory test data which define relationship between contact force and deformation for line contact for roller bearing as \u00bc 3:84 10 5 Q0:9 l0:8 \u00f01\u00de Contact length is divided into k lamina, each lamina of width w, and rearranging the above equation to define q yields q \u00bc 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f02\u00de Edge stresses are not considered in equation (2), obtained only over small areas, here localized defect is modeled as a half sinusoidal wave, amplitude of outer race defect and inner race defect are defined as Go \u00bc A1 \u00fe Dh sin Ro DL !c\u00f0 \u00det\u00fe 2 j 1\u00f0 \u00de z \u00f03\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from Gi \u00bc A1 \u00fe Dh sin Ri DL !c !2\u00f0 \u00det\u00fe 2 \u00f0 j 1\u00de z \u00f04\u00de Roller raceway deformation considering contact deformation due to ideal normal loading, radial defection due to thrust loading, radial internal clearance, and localized defect can be given by j \u00bc j \u00fe w 1 2 j Pd 2 G0 Gi For k no. of lamina qjk \u00bc X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 1:24 10 5 kw\u00f0 \u00de0:11 \u00f05\u00de Depending on degree of loading and misalignment, all laminae in every contact may not be loaded; in equation (5), k is the number of laminae under load at roller location j. Total roller loading is given by Qj \u00bc X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 1:24 10 5 k\u00f0 \u00de0:11 w0:89 \u00f06\u00de For determining the individual roller loading, it is necessary to satisfy the requirement of static equilibrium for radial load Fr 2 Xj\u00bcZ 2\u00fe1 j\u00bc1 jQj cos j \u00bc 0 \u00f07\u00de j\u00bc angular position of the jth roller\u00bc 2 j 1\u00f0 \u00de z \u00fe !ct where j\u00bc loading zone parameter for jth rolling element j\u00bc 0.5 for j\u00bc (0, P), j\u00bc 1 for j 6\u00bc (0, P) Fr\u00bc applied radial load, substituting equation of Qj in equation (7) we get 0:62 10 5Fr w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j cos j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 \u00bc 0 \u00f08\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from For applied thrust load equilibrium equation: Fa 2 Pj\u00bcZ 2\u00fe1 j\u00bc1 jQaj \u00bc 0 Where, Qaj\u00bc total roller race way loading for length (l) for jth roller in axial direction. At each roller location, thrust couple is balanced by radial load couple caused by skewed axial load distribution. Therefore, h 2 Qaj \u00bc Qjej, where h\u00bc roller thrust couple moment arm, therefore equation becomes as Fa 2 2 h Xj\u00bcZ 2\u00fe1 j\u00bc1 jQjej \u00bc 0 \u00f09\u00de where ej is the eccentricity of the loading for jth roller and given by ej \u00bc P \u00bck \u00bc1 q j 1 2 wP \u00bck \u00bc1 q j l 2 Substituting Qj and ej in equation (9), we get 0:31 10 5Fa h w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j k0:11 X \u00bck \u00bc1 j 1:11 1 2 w ( l 2 X \u00bck \u00bc1 j 1:11) \u00bc 0 \u00f010\u00de The sum of the relative radial movements of the inner and outer rings at each roller azimuth minus the radial clearance is equal to the sum of inner and outer raceway maximum contact deformation at same azimuth a l D \u00fe r cos j Pd 2 2 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G \u00bc 0 \u00f011\u00de The set of simultaneous equations (6), (8), (10), (11) can be solved by using Newton\u2013Raphson method for solution of j, j, a, and r. The simultaneous equations are as follows f1\u00f0Dj, fj, da, dr\u00de \u00bc Qj \u00bc w0:89 1:24 10 5k0:11 X \u00bc11 \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 2 f2\u00f0Dj, fj, da, dr\u00de \u00bc 0:62 10 5Fr w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j cos j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11 f3\u00f0Dj, fj, da, dr\u00de \u00bc 0:31 10 5Fa h w0:89 Xj\u00bcz 2\u00fe1 j\u00bc1 j k0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11( 1 2 w l 2 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 1:11) \u00bc 0 f4 Dj, fj, da, dr \u00bc da l D \u00fe drcosWj Pd 2 2 Xk\u00bck k\u00bc1 Dj \u00fe w k 1 2 fj Pd 2 G From the theory of Newton\u2013Raphson method, function and Jacobean matrix for nonlinear stiffness can be defined as follows F j, j, a, r \u00bc f1 j, j, a, r f2 j, j, a, r f3 j, j, a, r f4 j, j, a, r 2 66664 3 77775 \u00f012\u00de J j, j, a, r \u00bc @ @ j f1 j, j, a, r @ @ j f1 j, j, a, r @ @ a f1 j, j, a, r @ @ r f1 j, j, a, r @ @ j f2 j, j, a, r @ @ j f2 j, j, a, r @ @ a f2 j, j, a, r @ @ r f2 j, j, a, r @ @ j f3 j, j, a, r @ @ j f3 j, j, a, r @ @ a f3 j, j, a, r @ @ r f3 j, j, a, r @ @ j f4 j, j, a, r @ @ j f4 j, j, a, r @ @ a f4 j, j, a, r @ @ r f4 j, j, a, r 2 66666666664 3 77777777775 \u00f013\u00de at Purdue University on June 7, 2015pik.sagepub.comDownloaded from Radial contact stiffness and axial stiffness are defined as follows K\u00bcQj= j \u00bc w0:89 1:24 10 5 k\u00f0 \u00de0:11 P \u00bck \u00bc1 j\u00few 1 2 j Pd 2 G 1:11 P \u00bck \u00bc1 j\u00few 1 2 j Pd 2 G \u00f014a\u00de ka \u00bc w0:89 1:24 10 5 k\u00f0 \u00de0:11 X \u00bck \u00bc1 j \u00fe w 1 2 j Pd 2 G 0:11 1 2 l 2 2 h \u00f014b\u00de After solving above nonlinear simultaneous equation iteratively with Newton\u2013Raphson method, program is made to calculate contact stiffness (K) in radial directions and axial direction (ka). Algorithm for n-nonlinear simultaneous equation for contact force calculations is given in Appendix 3. Nonlinear contact forces can be calculated in radial vertical and axial direction as below. Qry \u00bc XZ I\u00bc1 K x cos i\u00fe y sin i\u00f0 \u00de B\u00feAsin \u00f0 t i\u00de 1:11 sin i \u00f015\u00de Qry \u00bc XZ I\u00bc1 K x cos i\u00fe y sin i\u00f0 \u00de B\u00feAsin \u00f0 t i\u00de 1:11 cos i \u00f016\u00de Qa \u00bc 1 ka Xj\u00bcz j\u00bc1 Qaj \u00f017\u00de a\u00bc (size of local defect/raceway radius), K\u00bc contact stiffness If the defect is at inner race, t\u00bc (oc\u2013 o2)*t\u00fe 2p/z (z\u2013i), where i\u00bc 11 to 1 If the defect is at outer race, t\u00bc (oc)*t\u00fe 2p/z (z\u2013i), where i\u00bc 11 to 1 Dissipative force for roller bearing In formulation for dissipation of energy the lubrication behavior assumed in a Newtonian way and here viscous damping model is assumed in which dissipative forces are proportional to time derivative of mutual approach. According to Upadhyay et al.,17 a nonlinear damping formula, correlating the contact damping force with the equivalent contact stiffness and contact deformation rate is given by Fd \u00bc c \u00f0 \u00de _ p \u00f018\u00de where c(d) is a function of contact geometry, material properties of elastic bodies, the properties of contact surface velocities, and properties of lubricant. Hence total dissipation force can be calculated as given in Appendix 6 where c is equivalent viscous damping factor between outer race/inner race with the roller is assumed 646N s/m.15 It is assumed that equivalent viscous damping factor of roller inner race contact and roller outer race contact is equal. Fdin \u00bc Cin Keq _ in 1.11 and Fdout \u00bc Cout Keq _ ou 1.11 Fd \u00bc Qdjr \u00bc 9 19 c\u00f0 \u00de\u00f0k\u00de 19 9 \u00f0 _ \u00de1:11 Qdry \u00bc 1=z Xj\u00bcz j\u00bc1 Qdjr sin 2 \u00f0 j 1\u00de z \u00fe !c t \u00f019\u00de where \u00bc \u00f0xcos i\u00feysin i\u00de B\u00feAsin \u00f0 t i\u00de Assuming dissipative forces are similar in y and z direction, Qdry\u00bcQdrz Dynamics model of a rigid rotor system Mathematical representation for motion of rigid rotor roller bearing system is defined as \u00bdM \u20acX\u00fe \u00bdC _X\u00fe \u00bdK X \u00bc f \u00f0x, t\u00de \u00f020\u00de where [M], [C], and [K] are the mass vector of system, damping vector of system, and stiffness matrices for the system. \u20acX, _X, X refers to the acceleration, velocity, and displacement vectors, respectively, and f(t) is a force vector. Nonlinear contact stiffness and nonlinear damping between the inner race/outer race and roller is considered while modeling of equations (21) and (22). m \u20acY\u00feQry\u00feQdry\u00bcFy can be rewritten as follows m \u20acY\u00fe 1=Z XZ I\u00bc1 K \u00f0xcos i\u00fe ysin i\u00de B\u00feA sin \u00f0 t i\u00de 1:11 sin i at Purdue University on June 7, 2015pik.sagepub.comDownloaded from m \u20acZ\u00feQrz\u00feQdrz\u00bcFz can be rewritten as follows. m \u20acZ\u00fe 1=Z XZ I\u00bc1 K \u00f0x cos i\u00fe y sin i\u00de B\u00feAsin \u00f0 t i\u00de 1:11 cos i \u00fe 1=z Xj\u00bcz j\u00bc1 Qdjr sin 2 \u00f0 j 1\u00de z \u00fe!c t \u00bc Fz \u00f022\u00de where Fy is a force vector on the bearing in horizontal direction and Fz is a force vector in vertical direction, m is a mass of the rotor; Newmark-b method is used for solution of differential equations of motion and the transient responses at every time increment are obtained. Algorithm for solution of nonlinear differential equation of motion is given in Appendix 4."
        ]
    },
    {
        "image_filename": "designv10_12_0002381_j.measurement.2015.12.006-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002381_j.measurement.2015.12.006-Figure6-1.png",
        "caption": "Fig. 6. Measurement of the curve-face gear artefact.",
        "texts": [],
        "surrounding_texts": [
            "To sum up, the relationship between the moving coordinates S01\u00f0X 0 1Y 0 1Z 0 1\u00de and S02\u00f0X 0 2Y 0 2Z 0 2\u00de can be depicted as\nx20 y20 z20\n1\n2 6664 3 7775 \u00bc\nR cosu2 R sinu2\nr\u00f00\u00de r\u00f0u1\u00de 1\n2 6664\n3 7775 \u00bc M x10 y10\nz10\n1\n2 6664 3 7775 \u00bc M r\u00f0u1\u00de cosu1 r\u00f0u1\u00de sinu1\n0 1\n2 6664\n3 7775\n\u00f08\u00de where\nM\u00bc\nsinu1 sinu2 cosu1 sinu2 cosu2 Rcosu2 cosu2 sinu1 cosu1 sinu2 sinu2 Rsinu2\ncosu1 sinu1 0 r\u00f00\u00de 0 0 0 1\n2 6664\n3 7775\n\u00f09\u00de In order to ensure the curve-face gear pair can achieve continuous rotary motion, the pitch curve of curve-face gear must be closed, that is, within the scope of 0 2p, its teeth change n2 cycles (n2 is a integer), described as follows\n2p n1n2\n\u00bc Z 2p n1\n0 1 i12 du1 \u00bc 1 R\nZ 2p n1\n0 r\u00f0u1\u00dedu1 \u00f010\u00de\nThus\nR \u00bc n2\n2p\nZ 2p n1\n0 r\u00f0u1\u00dedu1 \u00bc 71:29 mm \u00f011\u00de\nFinally, the equation of the pitch curve of curve-face gear can be expressed as\nx2 \u00bc n2 2p cos\u00f0u2\u00de R 2p n1 0 r\u00f0u\u00dedu\ny2 \u00bc n2 2p sin\u00f0u2\u00de R 2p n1 0 r\u00f0u\u00dedu z2 \u00bc r\u00f00\u00de r\u00f0u1\u00de\n8>>< >>:\n\u00f012\u00de\n3. Processing of gear pair\nThe tooth profile of non-circular gear is obtained by doing generating motion on its elliptical pitch curve by generating method. While the surface is that, when gear pair engages with each other, postulate the non-circular gear is meshing with a small spur gear at the same time. Therefore, at the moment the curve-face gear engages with the non-circular gear, it can be seen as the small spur gear meshes with the curve-face gear to take advantage of the known spur gear tooth profile can enveloping the surface of the tooth profile.\nSince each tooth profile of the present curve-face gear is different, and the teeth distribute in space pitch curve, it needs more than 3-axis Simultaneous Motion Machine tools in order to be processed. Therefore, in accordance with the existing equipment, the production is processed by the DMU 60mono BLOCK five-axis machining center of German DMG machine tools group to carry on the processing, the basic parameters (see Table 1), and the specific processing steps are as follows: blank rough machining, cogging machining, semi-finishing, finishing (see Figs. 2 and 3).\nPitch deviation reflects the inhomogeneity of gear teeth which relative to the center of gyration, and it\u2019s a major evaluation item of geometrical eccentricity and movement eccentricity.\nThe study about the pitch deviation measurement of non-circular gear is rare and there is no uniform error",
            "detection item. Currently, the major item of error detection about the non-circular gear is the angular error, which mainly caused by the pitch deviation and the pitch cumulative error. However, there isn\u2019t any special measuring instrument about the angular error detection. And the general measurement methods are meshing with standard gear or measuring its absolute coordinates by the coordinate measuring machine. Similarly, for curve-face gear there is no practical possibility for a reliable metrological traceability to national or international measurement standards can be provided. Thus, this paper defines that the pitch of curve-face gear is the arc length of the pitch curve between two adjacent corresponding flanks (see Fig. 4).\nThese experiments use the contour scanning software of the German Klingelnberg P26 automatic CNC controlled gear measuring center to measure the coordinates of the gear pair (see Figs. 5 and 6). The main work flow is shown in Fig. 7.\nDuring the experiments, the following rules must be conformed\n1. In order to avoid the probe intervenes with the under test or the adjacent flanks, the probe must be chosen appropriately, i.e. the intersection angle of the probe and the intersecting line which was formed of the tangent plane and pitch plane at the measuring point must be greater than zero, moreover, be small as far as possible. 2. In order to avoid the calculation error of the measuring data during the coordinate transformation, the Vertex\u2013 Edge\u2013Face Location Principle (that is three points on the datum plane; two points on the datum line and one\ndatum point) is used to set up the inspected artefact\u2019s coordinate system at the start. It\u2019s the most important and difficult step throughout the experiment.",
            "5. Pitch deviation calculation and analysis\n5.1. Preprocessing of the measured data\nThe processing benchmarks are coincident with the design during the processing. But before the measurement, the inspected gears need second installation. These undoubtedly will cause the misalignment of measurement datum and design. The work pieces\u2019 coordinates are not concentric with the workbench coordinate are the concrete manifestations.\nMatrix M0 represents the coordinate transformation from the work pieces\u2019 coordinates to the workbench coordinate, which includes a rotating transformation represents as Matrix M1 and a shifting transformation represents as Matrix M2.\nM1 \u00bc\ncos d sin d 0 0\nsin d cos d 0 0\n0 0 1 0\n0 0 0 1\n2 666664\n3 777775\n\u00f013\u00de\nM2 \u00bc\n1 0 0 0\n0 1 0 0\n0 0 1 z\n0 0 0 1\n2 666664\n3 777775\n\u00f014\u00de\nM0 \u00bc M1 M2 \u00bc\ncos d sin d 0 0\nsin d cos d 0 0\n0 0 1 z\n0 0 0 1\n2 666664\n3 777775\n\u00f015\u00de\nTransform the measurement coordinate data which got from the measurement experiments according to the above method. Afterwards, import the results into the three-dimensional design software Solidworks as shown below (see Fig. 8).\n5.2. Pitch deviation calculation and analysis\nThe pitch of the curve-face gear pair is defined as the arc length of the pitch curve between two adjacent corresponding flanks in this paper. Therefore, it can be expressed as follows p1i \u00bc Z u12\nu11\n\u00bdr2\u00f0u1\u00de \u00fe r02\u00f0u1\u00de 1=2 du1 \u00f016\u00de\np2i \u00bc Z u22\nu21\n\u00bdv2\u00f0u2\u00de \u00fe w2\u00f0u2\u00de \u00fex2\u00f0u2\u00de 1=2 du2 \u00f017\u00de\nThe nominal pitch of the non-circular gear and the curve-face gear pair are the same.\npt1 \u00bc pt2m \u00bc L1 z1 \u00bc pm \u00bc 12:5664 mm \u00f018\u00de The individual pitch deviation Df pt \u00bc p0 t pt \u00f019\u00de\nThe pitch accumulative error\nDFp \u00bc Xn 1 Df pt \u00f020\u00de\nIn accordance with the definition of pitch, the measured coordinates which are corresponding with the theoretical can be confirmed as the intersections of the pitch curves and the curves made up of the measurement coordinate data. And the theoretical coordinates are obtained by theoretical calculation. Moreover, as the thickness of the teeth of the curve-face gear is inequality, and in order to verify the accuracy of the measurement results, more measurement experiments were needed. Thus, the authors pick three different positions uniformity along the length of the teeth to complete the measurement.\nConsequently, the pitch deviations of the gear pair turned out to be as shown in Figs. 9 and 10.\nAs shown in Fig. 9, the maximal value of single pitch deviation is\njDf pt1maxj \u00bc 23:8 lm\nAnd the accumulative pitch deviation is\nDFp1 \u00bc 23:2\u00fe 23:8 \u00bc 47:0 lm\nThe maximal value of single pitch deviation at the inner, medial and outboard flanks of the curve-face gear shown in Fig. 10 is"
        ]
    },
    {
        "image_filename": "designv10_12_0000085_j.cma.2005.05.055-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000085_j.cma.2005.05.055-Figure1-1.png",
        "caption": "Fig. 1. Illustration of: (a) transmission functions 1 of a misaligned gear drive and linear function 2 of an ideal gear drive without misalignment; (b) periodic functions D/2(/1) of transmission errors formed by parabolas.",
        "texts": [
            " \u00f04\u00de Here, r \u00f02\u00de f represents the surface that is in mesh with curve r \u00f01\u00de f ; or \u00f01\u00de f oh1 is the tangent to the curve of the edge. Application of TCA allows to discover both types of meshing, surface-to-surface and surface-to-curve. Computerized simulation of meshing is an iterative process based on numerical solution of nonlinear equations [8]. By applying double-crowning to one of the mating surfaces, it becomes possible to: (i) avoid edge contact, and (ii) obtain a predesigned parabolic function [7] (Fig. 1). Application of a predesigned parabolic function is the precondition of reduction of noise. Application of double-crowning allows to assign ahead that function of transmission errors is a parabolic one, and allows to assign as well the maximal value of transmission errors as of 6\u2013800. The expected magnitude of the predesign parabolic function of transmission errors and the magnitude of the parabolic plunge of the generating tool have to be correlated. Fig. 2 shows the case wherein due to a large magnitude of error of misalignment, the function of transmission errors is formed by two branches: dP 1P 2 of surface-to-surface contact and dP 2P 3 of surface-to-curve contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003369_tcsii.2020.2987980-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003369_tcsii.2020.2987980-Figure2-1.png",
        "caption": "Fig. 2: IPE with rigid belt configuration [24]",
        "texts": [
            " Hence, V\u0307 can be written as, V\u0307 \u2264 \u2212\u00b5min{Q}(\u2016x1(t)\u2016 \u2212 2\u03b1 \u2016PA12C \u22121 2 \u2016 \u00b5min{Q} )\u2016x1(t)\u2016 (16) Hence, x1(t) remains bounded stable given by \u2016x1(t)\u2016 \u2264 2\u03b1 \u2016PA12C \u22121 2 \u2016 \u00b5min{Q} . Since \u2016s(t)\u2016 and x1(t) is bounded, x2(t) is also bounded. Hence, when the system (1) is contained with in the PSMB, the system is uniformly ultimately bounded stable. In this section, a simulation study of the proposed SDISMC is done on the industrial plant emulator (IPE) set up [24]. The IPE setup represents a scaled down version of industrial plant mechanisms like the conveyor belts, drives, servomechanisms and assembly machines, etc. The IPE setup in Fig. 2 consists a load disk coupled to drive disk which is driven by a drive motor. The rigid body configuration of the IPE set up is considered in this study [24]. The proposed SDISMC is applied to the IPE model and the results is compared with the existing control methods such as SMC [2] [1], Event triggered SMC [13],[14] and adaptive SMC [21]. Authorized licensed use limited to: McMaster University. Downloaded on May 03,2020 at 03:10:52 UTC from IEEE Xplore. Restrictions apply. 1549-7747 (c) 2020 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001547_iros.2013.6696825-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001547_iros.2013.6696825-Figure23-1.png",
        "caption": "Figure 23. Experiment environment.",
        "texts": [
            " As shown in the table, the unit length became its shortest so that the unit can grasp the elbow, enabling the robot to pass smoothly through an elbow. The locomotion speed of the robot is 10.2 mm/s in a 1-inch acrylic pipe, using Motion 4-1-1 with a time interval of 0.2 s. Air pressure of 0.12 MPa was applied to the unit. As the unit length became short, the length contraction of in the pipe increase. Therefore, the locomotion speed in a pipe increases compared to a low-friction robot. We conducted an experiment in which the developed robot attempts to pass through (narrow) continuous elbows. Figure 23 shows an image of the experimental environment and connected elbows. This array is the same as that encountered in real-life environments. If the pressure in the pipes that is connected to both ends of an elbow differs, the elbow may be broken by the pressure of the pipe and the expansion and contraction of pipe. To prevent this, an elbow and a street elbow are combined. This experiment is conducted in a 1-inch acrylic pipe (made based on pipe manufactured by Sekisui Chemical Company) using Motion 4-1-1 with a time interval of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002718_978-3-319-17043-5_13-Figure21-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002718_978-3-319-17043-5_13-Figure21-1.png",
        "caption": "Fig. 21. Structure of haptic scanner. Fig. 22. Structure of haptic display.",
        "texts": [],
        "surrounding_texts": [
            "TELESAR V (TELExistence Surrogate Anthropomorphic Robot) is a telexistence master\u2013slave robot system that was developed to realize the concept of telexistence. TELESAR V was designed and implemented with the development of a high-speed, robust, full upper body, mechanically unconstrained master cockpit, and 53 degrees-offreedom (DOF) anthropomorphic slave robot. The system provides an experience of our extended \u201cbody schema,\u201d which allows a human to maintain an up-to-date representation in space of the positions of his/her various body parts. Body schema can be used to understand the posture of the remote body and to perform actions with the belief that the remote body is the user\u2019s own body. With this experience, users can perform tasks dexterously and perceive the robot\u2019s body as their own body through visual, auditory, and haptic sensations, which provide the most simple and fundamental experience of telexistence. The TELESAR V master\u2013slave system can also transmit fine haptic sensations such as the texture and temperature of a material from an avatar robot\u2019s fingers to a human user\u2019s fingers [24, 25]. As shown in Figs. 19 and 20, the TELESAR V system consists of a master (local) and a slave (remote). A 53-DOF dexterous robot was developed with a 6-DOF torso, a 3-DOF head, 7-DOF arms, and 15-DOF hands. The robot also has Full HD (1920 \u00d7 1080 pixels) cameras for capturing wide-angle stereovision, and stereo microphones are situated on the robot\u2019s ears for capturing audio from the remote site. The operator\u2019s voice is transferred to the remote site and output through a small speaker installed in the robot\u2019s mouth area for conventional verbal bidirectional communication. On the master side, the operator\u2019s movements are captured with a motion-capturing system (OptiTrack) and sent to the kinematic generator PC. Finger bending is captured to an accuracy of 14 DOF with the \u201c5DT Data Glove 14.\u201d The haptic transmission system consists of three parts: a haptic scanner, a haptic display, and a processing block. When the haptic scanner touches an object, it obtains haptic information such as contact force, vibration, and temperature. The haptic display provides haptic stimuli on the user\u2019s finger to reproduce the haptic information obtained by the haptic scanner. The processing block connects the haptic scanner with the haptic display and converts the obtained physical data into data that include the physiological haptic perception for reproduction by the haptic display. The details of the scanning and displaying mechanisms are described below [26\u201329]. First, a force sensor inside the haptic scanner measures the vector force when the haptic scanner touches an object. Then, two motor-belt mechanisms in the haptic display reproduce the vector force on the operator\u2019s fingertips. The processing block controls the electrical current of each motor to provide the target torques based on the measured force. As a result, the mechanism reproduces the force sensation when the haptic scanner touches the object. Second, a microphone in the haptic scanner records the sound generated on its surface when the haptic scanner is in contact with an object. Then, a force reactor in the haptic display plays the transmitted sound as a vibration. This vibration provides a high-frequency haptic sensation. Therefore, the information should be transmitted without delay. For this purpose, the processing block transfers the sound signals by using circuits with no transformation. Third, a thermistor sensor in the haptic scanner measures the surface temperature of the object. The measured temperature is reproduced by a Peltier actuator placed on the operator\u2019s fingertips. The processing block generates a control signal for the Peltier actuator. The signal is generated based on a PID control loop with feedback from a thermistor located on the Peltier actuator. Figures 21 and 22 show the structures of the haptic scanner and the haptic display, respectively. Figure 23 shows the left hand of the TELESAR V robot with the haptic scanners, and the haptic displays set in the modified 5DT Data Glove 14. Figure 24 shows TELESAR V conducting several tasks such as picking up sticks, transferring small balls from one cup to another cup, producing Japanese calligraphy, playing Japanese chess (shogi), and feeling the texture of a cloth."
        ]
    },
    {
        "image_filename": "designv10_12_0002444_j.proeng.2016.08.864-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002444_j.proeng.2016.08.864-Figure3-1.png",
        "caption": "Fig. 3. Orientation of specimen to the build direction (Z \u2013 axis) a) orientation a; b) orientation b; c) orientation c",
        "texts": [
            " In this study a stress relieving at 380 \u00b0C for 8 hours was carried out. To protect the oxidization of the surface heat-treatment was undertaken in a vacuum furnace. 2.3. Orientation of specimens to the build direction The specimens for fatigue crack growth testing were manufactured according to ASTM E 647-08 Standard. The characteristic specimen dimension w was 30 mm and the thickness 6 mm. The CT specimens were manufactured in such a way that the build direction Z was either laying in the macroscopic fatigue crack plane, Fig. 3 a, b, or it was perpendicular to this plane, Fig. 3 c. Thus, the testing of these three types of specimens, denoted a, b and c types can reveal the potential effect of material anisotropy on fatigue crack growth behavior. The fatigue crack growth testing was conducted on a Roell/Amsler HFP 5100 resonant testing machine under load control. The loading asymmetry, i.e. the ratio of the minimum to maximum stress in a loading cycle was R = 0.1. The loading frequency was dependent on the crack length (i.e. on the stiffness of the specimen and grip system) and was in the interval 80 - 50 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002223_s1560354717030042-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002223_s1560354717030042-Figure6-1.png",
        "caption": "Fig. 6. Trajectory of the point P for the fixed parameters \u03b4 = 1.2, \u03bd = 0.8, j1 = 1, j2 = 2, c1 = 3, c2 = 4, \u03bc = 1 and the initial conditions \u03d5(0) = 0, \u03d1 = 4.11, \u03c8(0) = 0, x(0) = 0, y(0) = 0.",
        "texts": [
            " Numerical experiments (see Fig. 5) show that the phase portrait on the thorus T 2 in this case consists only of equilibrium points x(i) i = 1, . . . , 4 and trajectories asymptotically tending to them. However, the absence of limit cycles on the thorus T 2 remains unproved. This issue is complicated by the fact that the system (3.1) has a large number of parameters. At the above-mentioned equilibrium points, \u03c8 = \u03c80 = const, therefore, they correspond to the straight-line motion of the roller racer (see Fig. 6): x(\u03c4) = \u00b1 cos \u03c80\u03c4 + x0, y(\u03c4) = \u00b1 sin\u03c80\u03c4 + y0, where the upper sign corresponds to x(1), x(2) and the lower sign corresponds to x(3), x(4). Thus, the following proposition holds: Proposition. All trajectories of the roller racer are not compact when \u03b4 = 0 and, as \u03c4 \u2192 +\u221e (or \u03c4 \u2192 \u2212\u221e), asymptotically tend to straight-line motion. Remark. If this hypothesis is correct, then from the known solution \u03d1(\u03c4) of the reduced system (3.1) with \u03b4 = 0, the system (3.2) defines the scattering map (see, e. g., [7, 9]), which is apparently regular (since the reduced system describes the vector field on the thorus T 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure10.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure10.2-1.png",
        "caption": "Fig. 10.2 2/2 single-phase switched reluctance motor",
        "texts": [
            "34 Simulation results for induction machine drive with rotor flux oriented UFO controller and field weakening controller . . . . . 334 Fig. 9.35 Simulation results for induction machine drive with rotor flux oriented UFO controller and field weakening controller . . . . . 336 Fig. 10.1 Radial flux switched reluctance machine examples, showing a Nph = 3 phase machine with a 6/4 stator/rotor configuration. (a) Unaligned position (phase A). (b) Aligned position (phase A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Fig. 10.2 2/2 single-phase switched reluctance motor . . . . . . . . . . . . . . . . . . . . . . 343 Fig. 10.3 Single-phase equivalent circuit of a switched reluctance machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Fig. 10.4 Magnetization curves for the linear and non-linear case. (a) Linear case: Te = 1 2 T\u0303e. (b) Non-linear case: Te \u2248 T\u0303e . . . . . . . . . . . . . 348 xxxiv List of Figures Fig. 10.5 Energy flow in SR machine ",
            "2 Operating Principles 343 The basic operating principles of the switched reluctance machine are discussed on the basis of a single-phase machine. A single-phase model is representative because even in multi-phase SRMs mutual coupling between electrical phases can be neglected. Consequently, the development of generic models for this single-phase machine is directly applicable to multi-phase concepts. The machine under consideration is a 2/2 configuration, i.e., two stator and two rotor teeth as shown in Fig. 10.2. In the given example the rotor is displaced by an angle \u03b8m from the stator teeth. An angle dependent current source i(\u03b8m) as shown in Fig. 10.2 is connected to the N -turn phase winding, which consists of two concentrically wound coils located on each of the two stator teeth. The inter-pole arc \u03c4rp is in this example equal to 180\u25e6 mechanical. This angle is also equal to one electric period of the two-pole rotor. If the rotor is displaced by an angle \u03b8m = \u03c4rp, a single torque pulse will result, provided the appropriate phase excitation conditions are met. The number of torque pulses, defined by the variable Npu for this machine equals two",
            " This torque multiplication process, which is referred to as the vernier principle in electrical machines, leads to increased switching losses in the converter and core losses in the SR machine, given the need for a higher electrical frequency (see Eq. (10.6)). However, the presence of this vernier principle in SR machines is fundamental to its ability to produce a torque that is an average similar, if not higher, than that of an induction machine of the same frame size. In terms of choosing a higher or lower number of rotor teeth with respect to the stator teeth number, it is prudent to choose the latter, given that this leads to comparatively lower core and switching losses. The terminal voltage equation for this machine is according to Fig. 10.2 and Kirchhoff\u2019s voltage law of the form u(i, \u03b8m) = R i (\u03b8m) + d\u03c8 (i, \u03b8m) dt , (10.7) where R represents the phase coil resistance and \u03c8(i, \u03b8m) the flux linkage depending on phase current and rotor angle, otherwise referred to as the magnetization characteristics of the machine. The simplicity of the doubly salient machine structure (see Fig. 10.2) may give the impression that understanding the nature of torque production and energy conversion principles is equally simple. Unfortunately, this is not the case as will become apparent in this section. Initially, the single-phase machine model is examined to ascertain the energy flows that are present between the supply source, magnetic energy in the air-gap and energy supplied to the shaft. In this process, 10.2 Operating Principles 345 the role of magnetic saturation is duly explored. Iron losses and copper losses will inevitably affect the overall machine performance but do not significantly affect the torque and energy conversion principles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003715_tpel.2021.3064184-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003715_tpel.2021.3064184-Figure2-1.png",
        "caption": "Fig. 2 Cross section of the twelve-phase SPM and the phase winding numbering convention.",
        "texts": [
            "TWELVE-PHASE SPM DRIVE WITH CPS APPLIED This paper uses a twelve-phase surface permanent magnet motor (SPM) drive as an example to study the effect of carrier phase shifting. But the same analysis process can be applied to motors with different phases and winding configurations. The twelve-phase SPM drive is shown in Fig. 1. Twelve-phase windings of the SPM can be divided into four sets of three-phase windings which are apart by 15 electric degrees. Each motor phase is fed by an H-bridge VSI with carrier-based SPWM. The studied motor features full-pitch concentrated windings, with each phase occupying one slot, as shown in the cross-section view in Fig. 2. For convenience, all phases are numbered consecutively. Parameters of the studied motor are shown in Table I. To avoid unnecessary complications to the analysis, subtle geometric features of stator teeth, such as the wedge holder near the slot opening, are neglected. Hence, stator teeth have perfectly straight edges. Authorized licensed use limited to: Carleton University. Downloaded on June 01,2021 at 00:13:46 UTC from IEEE Xplore. Restrictions apply. 0885-8993 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission",
            " Besides, three CPS modes are studied and compared in this paper. Specifically, shifting the PWM carrier for only one phase is denoted as \u201cone phase\u201d mode. Shifting the PWM carriers for a full set of three-phase windings is denoted as \u201cone set\u201d mode. Similarly, shifting the PWM carriers for two sets of non-adjacent three-phase windings is denoted as \u201c two sets\u201d mode. For all three CPS modes, the numbers of phase windings that have their carriers shifted are summarized in Table II, where the numbering convention of phases is the same as Fig. 2. To analyze high-frequency stator EM forces induced by PWM, this section introduces a method based on the concept of permeance distribution function (PDF)[24]. The method is orders of magnitude faster than finite-element analysis while almost as accurate. The overall framework of the method is shown in Fig. 4. It is crucial to calculate motor current harmonics accurately since they are the cause of high-frequency vibrations. Normally, current harmonics can be obtained by circuit simulation, but this approach is too time consuming as many simulation runs are needed to study the effect of CPS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003293_s40430-020-02645-3-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003293_s40430-020-02645-3-Figure9-1.png",
        "caption": "Fig. 9 Experimental results of the tracking performance Fig. 10 Tracking performance of SMC controlled robot for different mass values",
        "texts": [
            "\u00a08, the controller voltages and total power used by PID and SMC controllers are presented for experimental (24)AverageSection = 1 \u0394ti ti+1 \u222b ti |e|dt (25)Average Total = 1 \u0394t 5\u2211 i=1 ti+1 \u222b t1 |e|dt Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:561 1 3 561 Page 8 of 13 and numerical results. It shows that the PID controller is trying to track the trajectory by generating higher control voltages even on the straight line. It is understood that the SMC controller needs lower voltages both in sharp turns and straight lines on the path. Moreover, it seems that the sliding mode controller is more stable and requires lower voltage values than PID controller during the entire path. The visual experimental results of the tracking performance of two controllers are presented in Fig.\u00a09. Although SMC responds faster and provides better tracking performance than PID controller in sharp turns, both SMC and PID controllers are successful on the road with low disturbance. Yet, it is seen that the SMC controller is more effective on the road with dashed lines (Section\u00a02\u20133) consumes less energy and finishes the track at a considerably shorter time. Note that robot with SMC completes the track in 1 3 29.5\u00a0s, whereas the PID controlled robot barely completes the track in 32.7\u00a0s. In order to visualize the robust behaviour of the sliding mode controlled robot, for different robot mass values, the numerical solution of the tracking performance of the line following robot is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.140-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.140-1.png",
        "caption": "Fig. 2.140 HEV driving circumstances during normal driving [DRIESEN 2006].",
        "texts": [
            " Changing the operating range of the ICE to high speed and low load for the equivalent power output enables recirculation to be avoided, but it also reduces the ICE\u2019s energy efficiency. An exemplary series/parallel HEV layout with an ICE and two electrical machines is shown in Figure 2.138 [DRIESEN 2006]. In Figure 2.139 is shown the HEV driving circumstances during starting when the ICE remains off to save liquid fuel and the E-M motor drives the series/parallel HEV. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 336 In Figure 2.140 HEV driving circumstances are shown during normal driving when the ICE starts and may drive the series/parallel HEV and produce electrical energy for the E-M motor or is charging the CH-E/E-CH storage battery. In Figure 2.141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 337 In Figure 2.142 HEV driving circumstances are shown during deceleration and braking the E-M motor is turned into a M-E generator to charge the highvoltage CH-E-CH storage battery"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.18-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.18-1.png",
        "caption": "Fig. 15.18 Inflection circle with normal poles P1 and P2. On a line e a point Q fixed in \u03a32 , the center of curvature M of the trajectory of Q and the second point of intersection W with the inflection circle",
        "texts": [
            " The result for n = 3 states that the two pairs of poles P1 , P2 and P\u2217 3 , P3 are the 15.3 Curvature of Plane Trajectories 479 parallel sides of a trapezoid and that the ratio of the lengths of these sides is 1 : 3 . From the sequence of Eqs.(15.67) continued for n > 3 the following explicit expression for rP\u2217 n is deduced: rP\u2217 n = n\u2211 k=1 ( n k ) (\u22121)k\u22121rPk . (15.68) The proof by induction is left to the reader. In this section the curvature of trajectories is investigated. An important role is played by the inflection circle shown in Fig. 15.18. As is known from Fig. 15.17 the circle is determined by the normal poles P1 and P2 . It is the geometric locus of all points of \u03a32 the trajectories of which have, instantaneously, an inflection point and a tangent passing through the normal pole P2 which has the coordinate (see (15.45)) y2 = a0/\u03d5\u0307 2 , a0 being the acceleration of the point of \u03a32 coinciding with P1 . For simplifying the figure the case y2 < 0 is illustrated.The tangent to the inflection circle in P1 is also the tangent to the centrodes which are in rolling contact at P1 ",
            "76) in combination with (15.74) it follows that s1 sin(\u03b12 \u2212 \u03b13) + s2 sin(\u03b13 \u2212 \u03b11) + s3 sin(\u03b11 \u2212 \u03b12) = 0 . (15.77) Given the constants s1 and s2 on two lines e1 , e2 and the direction of a third line e3 relative to these two, the equation determines the constant s3 on line e3 . The tangent to the centrodes as line of reference is not needed for this purpose. The equation was first formulated by Fayet [9] without, however, explicitly referring to (15.76). From the right-angled triangle (P1,W,P2) in Fig. 15.18 it follows that rW = y2 sin\u03b1 . This proves the identity of s with the polar coordinate rW : s = rW . (15.78) This follows also directly from (15.73). At the inflection point W the center of curvature is at infinity. Hence R = \u221e and s = rW . Euler-Savary Equation of the Inverse Motion In the inverse motion, trajectories in \u03a32 produced by points Q fixed in \u03a31 are considered. Let M\u2217 be the center of curvature with the position vector R\u2217e . In the inverse motion a0 is replaced by \u2212a0 (see Theorem 9",
            " Graphical constructions have the advantage of making things visible. But they have the disadvantage of relying on intersections of lines which, frequently, are either almost parallel or intersecting outside the available sheet of paper. 15.3 Curvature of Plane Trajectories 483 First, a method known as sawtooth construction is explained. As preparatory step, the Euler-Savary Eq.(15.73) in combination with (15.69), R = + r , and with (15.78), s = rW , is written in the form (rW \u2212 r) = r2 . (15.80) Consider Fig. 15.20 which is in part a copy of Fig.15.18. The relationships between the points P1 , Q , M and W on a line e can be expressed geometrically as follows. Let P\u2217 be an arbitrarily chosen auxiliary point. Lines P\u2217M and P\u2217P1 are drawn and parallel to these lines the lines g1 through P1 and g2 through W . Proposition: The point of intersection W \u2217 of g1 and g2 lies on the line P\u2217Q . Proof: The triangles (Q,M,P\u2217) and (Q,P1,W \u2217 ) are similar, and the triangles (Q,P1,P \u2217) and (Q,W,W\u2217 ) are similar. Therefore, QP\u2217 : QW\u2217 equals : r as well as r : (rW \u2212 r) ",
            " Once the tangent to the centrodes is known, the theorem can be used for constructing the center of curvature M3 associated with an arbitrarily chosen point Q3 . This is done in the following steps. 15.3 Curvature of Plane Trajectories 485 1. Draw the line h\u2032 through P1 under the angle \u03b11 (known by now) against the line P1Q3 . 2. Construct the point A\u2032 as point of intersection of h\u2032 with the line Q1Q3 . 3. The desired point M3 is the point of intersection of the lines M1A \u2032 and P1Q3 . In Fig. 15.21 the points Q and M on an arbitrary line e are those of Fig. 15.18. In the figure also the centrode k2 fixed in \u03a32 and the centrode k1 fixed in \u03a31 together with their point P1 of rolling contact are shown. The centers of curvature of the centrodes at P1 are denoted Mp 1 and Mp 2 , respectively. They are located on the common normal to the centrodes. Let en be the unit vector directed from P1 toward Mp 2 . The radii of curvature 1 and 2 are defined by expressing the vector from P1 to Mp i (i = 1, 2) in the form ien . This means that always 2 > 0 , whereas 1 is positive or negative depending on whether the two centrodes are curved toward the same side or toward opposite sides"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.4-1.png",
        "caption": "Figure 2.4 Left: CAD model of the part and process head. Right: simulated toolpath for five-axis deposition using DMDCAM software [4]. Courtesy: DM3D Technology.",
        "texts": [
            " The next steps involve slicing the model into multiple layers and CAM toolpathing for each layer. Powder bed fusion (PBF) technologies slice the solid model in horizontal 2D layers (Fig. 2.3) [6], directed energy deposition (DED) technologies can use horizontal 2D layers as well as 3D layers following 3D surfaces. This becomes particularly important while adding metal to existing parts or components for remanufacturing and/or surface-coating applications or hybrid manufacturing. 14 Science, Technology and Applications of Metals in Additive Manufacturing Fig. 2.4 shows a typical deposition toolpath simulated on a CAD model for a five-axis deposition process using DMDCAM software [4]. In PBF systems, parts are fully built from scratch in a single setup. Therefore proper part geometry orientation is a critical step. In addition, these systems also rely on support structures for building overhangs and designing the proper support structure is an essential part of a successful build strategy [7]. Various software, such as Magics from Materiallise, are available that are dedicated to strategizing part orientation and building support structures for PBF systems [8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003094_j.addma.2020.101550-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003094_j.addma.2020.101550-Figure5-1.png",
        "caption": "Fig. 5. mechanical design of the hybrid SLM/CNC milling machine developed in this study.",
        "texts": [
            " With a tilting spindle, the spindle axis can rotate over x-axis and the milling capacity can be greatly enhanced. For the third type, the hybrid system is equipped with a multiple axes rotary spindle and hybrid SLM/5-axis CNC milling can be obtained. With a multiple axes rotary spindle, the milling capacity can be further enhanced. However, for hybrid SLM/CNC milling process, the milling procedures is executed every 5 ~ 10 layers and there are no imperative requirements for tilting spindle or multiple axes rotary spindle. Therefore, a fixed spindle mounted on a 3-axis moving platform was selected. Fig. 5 shows the hybrid SLM/CNC milling machine developed in this study. The key modules include: a 3-axis CNC milling module, a building chamber and overflow module to recycle the excessive powder, a laser scanning module, a powder supply module using the \u201ctop-down\u201d approach and a powder coating module. As for the CNC milling module, an ATC (automatic tool change) module with 16 milling tools was included. In order to avoid structural interference with the moving spindle of CNC milling, the laser scanning system should be adapted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000917_j.fss.2011.04.004-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000917_j.fss.2011.04.004-Figure2-1.png",
        "caption": "Fig. 2. The inverted pendulum system.",
        "texts": [
            " The objective of the two-mode operating scheme is to reduce the computational burden of the adaptive fuzzy systems while maintaining an acceptable level of performance. However, the performance may deteriorate during the operating mode because the parameters of the two fuzzy systems are not continuously updated. Because the tracking error may be influenced by bigger approximation errors, the size of the tracking error in the operating mode is another important performance index of adaptive fuzzy systems that must be considered. In the next section, this index will be investigated through a case study. Consider the benchmark nonlinear system in Fig. 2 x\u03071 = x2 where x1 = is the angular position of the pendulum, x2 = \u0307 is the angular velocity of the pendulum, m and mc are the mass of the pendulum and the cart, respectively, and l is the half-length of the pole. The parameters of the system used in this study are shown in Table 1. The objective is to drive the angular position to track the reference signal ym(t) = ( /30) sin(t) under the assumption that f (x) and g(X) are unknown. The control tasks employed to assess the proposed controller are identical to those used in the existing literature to provide a common basis for comparison"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.90-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.90-1.png",
        "caption": "Fig. 2.90 Rear ICE, M-M clutch, MT and live-axle M-M transmission arrangement for the M-M DBW 2WD propulsion mechatronic control system [NEWTON ET AL.1989].",
        "texts": [
            " The drive is twisted through much less than \u03c0/2 rad from the propeller shaft at both its final drive and transfer drive ends that returns to the first principles of design of both pairs of gears. A problem with this arrangement is the housing of the long ECE or ICE, MT (gearbox) and transfer drive within the comprehensive width of the vehicle. That is why some vehicle manufacturers have mounted their ECEs or ICEs longitudinally behind the rear axle. Automotive Mechatronics 258 This arrangement is shown in Figure 2.90, where the MT (gearbox) is installed independently in front of the axle [NEWTON ET AL. 1989]. As the FJs, UJs or CVJs on the coupling shaft between the ECE or ICE and MT (gearbox) have to assist only comparative movements due to deflections of the mountings and vehicle frame or construction \u2013 instead of movements of the axles \u2013 they can be of a basic design. CVJs are indispensable, however, on the short propeller shaft. In Figure 2.91 again, independently mounted transverse ECE or ICE and MT units are used, but the M-M differential can be closer to the centre of the axle [NEWTON ET AL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure14-1.png",
        "caption": "Fig. 14. The 5-DOF and 6-DOF parallel manipulators: (a) 2T2R + 1-DOF (b) 3T2R + 1-DOF.",
        "texts": [
            " They are the L 1 F 1 C -limb and L 0 F 0 C -limb, L 1 F 1 C -limb and L 0 F 1 C -limb, L 1 F 1 C -limb and L 1 F 0 C -limb, L 1 F 0 C -limb and L 1 F 0 C -limb, L 1 F 0 C -limb and L 0 F 1 C -limb. With the topological arrangements in Figs. 8 (d), the L 0 F 1 C -limb and the L 1 F 1 C -limb are synthesized. The constraint-couple of the L 0 F 1 C -limb is parallel to the constraint-couple of the L 1 F 1 C -limb. Two groups of parallel revolute kinematic joints are assigned on the platform to achieve high rotation capability [14] . Then the 2T2R parallel mechanism that can output large angles in two directions is obtained, as shown in Fig. 14 (a). After consolidating the configurable platforms, 6-DOF parallel manipulators with configurable platforms can degenerate into 5-DOF manipulators. The wrench system of 3T2R parallel mechanisms is a constraint-couple. Two combinations are adequate for the wrench system. They are the L 0 F 1 C -limb and L 0 F 0 C -limb, L 0 F 1 C -limb and L 0 F 1 C -limb. For the manipulators with two L 0 F 1 C -limbs, the constraint-couples are parallel. Afterward, the 3T2R parallel mechanism with the planar fourbar platform is obtained, as shown in Fig. 14 (b). For 2T3R parallel manipulators, the wrench system only consists of one constraint-force. The valid combinations to realize one constraint-force can be the L 1 F 0 C -limb and L 0 F 0 C -limb, L 1 F 0 C -limb and L 1 F 0 C -limb. It is noteworthy that two parallel constraint-forces generate a constraint-couple with the direction vertical to the plane defined by the constraints. When three-drive L 1 F 0 C -limbs are adopted to build the 2T3R parallel manipulators, the two constraint-forces must be collinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003143_j.ijfatigue.2020.106100-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003143_j.ijfatigue.2020.106100-Figure1-1.png",
        "caption": "Fig. 1. Schematic of coupon build orientations, crack planes and FCG direction.",
        "texts": [
            " Moreover, the aim is to limit orientation specific NASGRO parameters, to formulate a more generalised modelling parameters that may not necessarily, as discussed later, require the consideration of anisotropy. Experimental data was acquired through testing of CT test coupons fabricated on an EOSINT M280 (EOS GmbH, Krailling, Germany) LPBF machine. Coupons were printed in three build orientations namely: XZY, ZXY and YXZ according to ISO/ASTM52921, hereafter referred to as Flat, Vertical and Edge based on the orientation of the crack and build direction (presented in Fig. 1). The raw powdered material used in print being Ti-6Al-4V (ELI) with measured chemical composition constituting of Ti combined with 6.43% Al, 3.94% V, 0.25% Fe, 0.006% N, 0.082% O, with a particle size distribution of d10 = 23 \u00b5m, d50 = 33 \u00b5m and d90 = 46 \u00b5m. Printing parameters implemented are presented in Table 1. Argon gas was used to flood the building chamber, and the oxygen level was maintained below 0.12% during the fabrication process. Individual coupons were printed in a near-net shape at similar height from the baseplate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000050_j.jsv.2007.05.010-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000050_j.jsv.2007.05.010-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the moving parts of a Roots blower vacuum pump, illustrating the parallel arrangement of rotors, shafts and gears.",
        "texts": [
            " We shall derive a model with specific reference to N&V problems in the gearing mechanism of Roots blower vacuum pumps. However, we believe that the equations derived here are applicable to much wider classes of backlash oscillators. A Roots blower pump [8\u201310] is made up of two involute steel rotors (denoted by X and Y), rigidly attached to two counter-rotating parallel shafts. One shaft (the X-shaft) is driven by means of a motor, while the other (the Y-shaft) is driven only by means of a gearing mechanism between the two shafts. A schematic diagram is shown in Fig. 1. Note that contact is through the gears only, not through the lobes of the rotors. When the gear teeth are in contact, we suppose that each assembly deforms according to Hooke\u2019s law, and that the restoring torque (normal reaction force on the meshing teeth) is proportional to the relative rotational displacement. Moreover, we neglect the so-called transmission error effect by taking a time-independent linear stiffness coefficient. More sophisticated gear models use a periodic stiffness function operating at the meshing frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001335_j.apm.2013.05.056-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001335_j.apm.2013.05.056-Figure6-1.png",
        "caption": "Fig. 6. Machining simulation result: (a) assembly chart, (b) single cutting line, and (c) cutting locus over a rotor groove.",
        "texts": [
            " Table 1 lists the design parameters used in the example, where the machined male rotor was a right-hand screw with a helix angle of 46 , 5 teeth (6 teeth with the female rotor), a screw length of 183.022 mm, a pitch diameter of 72.727 mm, an outer diameter of 113.067 mm, and an inner diameter of 70.4 mm. The worm-shaped tool was a right-hand screw with a lead angle of 2.316 , a single start, 3 threads, and pitch diameter of 250 mm. The initial assembly center distance was 161.364 mm between the rotor and the worm-shaped tool. The worm-shaped tool feed path can be controlled by appropriately giving values to the polynomial coefficients of the tangential, axial, or radial feed. As shown in Fig. 6, the datum rotor and its worm-shaped tool were assembled and constructed in the developed numerical program to check the correctness of the relative position, single cutting line and cutting trace (presented per 50 rounds) solved by the proposed mathematical model of the worm-shaped tool machining approach. These nearly coincided with the datum rotor surface from different viewing angles, which were generated by an arbitrary single cutting edge at a rotation speed of 300 rpm for the worm-shaped tool and an axial feed machining speed of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureA.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureA.3-1.png",
        "caption": "Fig. A.3 Schematic the spinning paraboloid of revolution",
        "texts": [
            "1 Centrifugal Forces Acting on a Spinning Paraboloid The paraboloid\u2019smass elementsm are located on the arbitrary radius r which forming the rotating paraboloid around axes oz. The focus of the parabola locates at the point o of the system coordinate oxyz. The rotating mass elements of the spinning paraboloid are located on the paraboloid surface which maximal radius is the 2/3 radius of the base of the paraboloid. The analysis of the acting inertial forces generated by the mass element of the paraboloid is considered on the arbitrary planes that parallel to the plane of the base of the paraboloid (Fig. A.3) that is the same as the plane of the thin disc represented in Fig. 3.2 of Chap. 3. The rotating centrifugal Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 207 forces of the paraboloid\u2019s mass elements is declined and resisted opposite to the action of external torque. The analytical approach for the modelling of the acting centrifugal forces generated by the mass elements of the spinning paraboloid is the same as represented for the spinning cone in Sect. A.2.4. Similar resistance torques are generated by the mass elements located on the planes of the paraboloid that parallel to the plane xoy (Fig. A.3). The resistance torque T ct produced by the centrifugal force f ct.z of the paraboloid\u2019s mass element is expressed by the following equation: Tct = fct.z ym (A.3.1) where ym is the distance of the paraboloid\u2019s mass element\u2019s location at the arbitrary plane relatively to axis ox. The equation for the axial component of the centrifugal force for the arbitrarily chosen plane of the paraboloid is as follows: fct.z = fct sin \u03b1 sin \u03b3 = mr\u03c92 sin \u03b1 sin \u03b3 (A.3.2) where fct = mr sin \u03b1\u03c92 is the centrifugal force of the mass element m; m = (M/2\u03c0b) \u03b4 b, M is the mass of the paraboloid; b is the length of the line that forms the paraboloid surface of the mass element\u2019s location; b is the line part of the mass element\u2019s location; \u03b4 is the sector\u2019s angle of the mass element\u2019s location on the plane that parallel to plane xoy; r is the radius of the arbitrary circle plane of the paraboloid where the mass elements located; \u03c9 is the constant angular velocity of the paraboloid; other components as specified above. 208 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects Substituting defined parameters into Eq. (A.3.2) yields the following equation: fct.z = M 2\u03c0b r\u03c92 sin \u03b1 \u03b4 b \u03b3 (A.3.3) The simple equation of the parabola, y2 = z. The maximal radius of the paraboloid is as follows:y = R = \u221a z = \u221a L , where L = R2 (Fig. A.3). The equation for the parabola line of mass elements is as follows (2/3)y = \u221a z where (2/3) is the factor of the mass elements location or y = (3/2) \u221a z. The maximal radius of the parabola line of mass elements is as follows y = r = (2/3)R. The length b of the parabola line where the mass elements locate is computed by the following equation [10] and by substituting parameters defined above: b = L\u222b 0 \u221a 1 + y\u20322(z)dz (A.3.4) The derivative of y = (3/2) \u221a zis as follows: y\u2032 = 3 4 \u221a z , and then substituting into Eq",
            "4) and transforming emerges in the following expression: b = L\u222b 0 \u221a 1 + 9 16z dz = L=R2\u222b 0 \u221a 9/16 + z 0 + z dz (A.3.5) Integral Eq. (A.3.5) presents the tabulated one [10].\u222b \u221a a+x b+x dx = \u221a (a + x)(b + x) + (a \u2212 b) ln \u2223\u2223\u221aa + x + \u221a b + x + C \u2223\u2223 with the following solution: b = \u221a( 9 16 + z ) z + 9 16 ln \u2223\u2223\u2223\u2223\u2223 \u221a 9 16 + z + \u221a z \u2223\u2223\u2223\u2223\u2223 \u2223\u2223\u2223L=R2 0 giving rise for the following result b = \u221a( 9 16 + R2 ) R2 + 9 16 ln (\u221a 9 16 + R2 + \u221a R2 ) \u2212 9 16 ln 3 4 = R \u221a 9 16 + R2 + 9 16 ln [ 4 3 (\u221a 9 16 + R2 + R )] (A.3.6) The part of the line b (Fig. A.3) for the mass element m is expressed by the following equation: Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 209 b = \u221a ( z)2 + ( y)2 = \u221a( 8 9 y y )2 + ( y)2 = y \u221a( 8 9 y )2 + 1 = r \u221a( 8 9 r )2 + 1 (A.3.7) where z is expressed from the equation (4/9)y2 = z by the following solution (Fig. A.3): (4/9)y2 \u2212 (4/9)(y \u2212 y)2 = (z + z) \u2212 z, which solving yields z = (8/9)y y, where y = r, and ( y)2 = 0 is accepted due to the small value. Substituting the defined parameters into Eq. (A.3.3) and transforming yield the following equation: fct.z = ( M\u03c92 sin \u03b1 2\u03c0b ) \u03b4 \u03b3 \u239b \u239d \u221a( 8 9 r )2 + 1 \u239e \u23a0r r (A.3.8) where all components are as specified above. The centre mass of the paraboloid locates at the distance zcm = (2/3)L from its vertex [10]. The radius of the paraboloid plan of mass elements passes through the centre mass and presented by the expression y = r = \u221a (2/3)R that is defined from proportion R = y2 = L and r = y2r = (2/3)L. ym is the distance of the location of the paraboloid\u2019s mass elements at the plane of the centre mass along with axis oz, and relative the axis ox (Fig. A.3) is presented by the following expression: ym = \u221a 2 3 \u00d7 2 3 R sin \u03b1. (A.3.9) Substituting Eqs. (A.3.7), (A.3.8) and (A.3.9) and all defined components above and transforming yield the following equation: yA = \u222b \u03c0 \u03b1=0 \u222b (2/3)R r=0 fct.z ymd\u03b1dr\u222b \u03c0 \u03b1=0 \u222b (2/3)R r=0 fct.zd\u03b1dr = \u222b \u03c0 \u03b1=0 \u222b (2/3)R 0 ( M\u03c92 sin \u03b1 2\u03c0b ) \u03b4 \u03b3 (\u221a( 8 9r )2 + 1 ) r r \u00d7 \u221a 2 3 2 3 R sin \u03b1d\u03b1dr \u222b \u03c0 \u03b1=0 \u222b (2/3)R 0 ( M\u03c92 sin \u03b1 2\u03c0b ) \u03b4 \u03b3 (\u221a( 8 9r )2 + 1 ) r r = M\u03c92 2\u03c0b \u03b4 \u03b3 M\u03c92 2\u03c0b \u03b4 \u03b3 \u00d7 \u222b (2/3)R r=0 (\u221a( 8 9r )2 + 1 ) r rdr \u222b (2/3)R r=0 (\u221a( 8 9r )2 + 1 ) r rdr \u00d7 \u221a 2 3 2 3 R \u222b \u03c0 \u03b1=0 sin 2 \u03b1d\u03b1\u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 = \u221a 2 3 2 3 R \u222b \u03c0 \u03b1=0 sin 2 \u03b1d\u03b1\u222b \u03c0 \u03b1=0 sin \u03b1d\u03b1 (A",
            " Analysis of the inertial torques acting on the spinning paraboloid demonstrates differences in the results compare with other spinning objects. A.3.5 Working Example The paraboloid has a mass of 3.0 kg, the radius of 0.1 m at the end and the length of 0.2 m. The paraboloid is spinning at 3000 rpm. An external torque acts on the paraboloid, which rotates with an angular velocity of 0.05 rpm. These data are used to determine the value of the resistance and precession torques generated by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum of the spinning paraboloid (Fig. A.3). Solving this problem is based on the equations in Table A.3. Substituting the initial data into the aforementioned equations and transforming yield the following result: Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 217 218 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects = \u239b \u239c\u239c\u239c\u239c\u239d 16 {\u221a[( 4 9 \u00d7 0.1 )2 + ( 98)2 ]3 \u2212 ( 98)3 }\u221a 2 3\u03c0 2 27 { 0.1 \u221a 9 16 + 0.12 + 9 16 ln [ 4 3 (\u221a 9 16 + 0.12 + 0.1 )]} 0.1 + 1 \u239e \u239f\u239f\u239f\u239f\u23a0 \u00d7 3.0 \u00d7 0.12 6 \u00d7 3000 \u00d7 2\u03c0 60 \u00d7 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000433_s0022112007005514-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000433_s0022112007005514-Figure2-1.png",
        "caption": "Figure 2. Schematic of coupled droplets pinned at tube ends of radius r . V1 and V2 are protuding volumes. Typical equilibria for (a) V1 + V2 < (4/3)\u03c0r3 and (b) V1 + V2 > (4/3)\u03c0r3. Equilibrium occurs for menisci with equal curvatures, R1 = R2.",
        "texts": [
            " The emergence of a linear, low-frequency centre-of-mass oscillation in a related problem has been reported by Strani & Sabetta (1984). The translational mode introduced by the pinned circular constraint has not been studied before, however, as far as we are aware. The above geometry-of-constraint is generalized in two ways in our study. First, two sub- or super-hemispherical caps can be joined at the constraining circle giving a non-spherical overall shape. Second, the pinning circle can be \u2018inflated\u2019 to be a cylindrical tube of length 2L with spherical caps pinned to each of the tube ends (figure 2). This family of undeformed capillary surfaces is characterized by two control parameters: the sum of spherical-cap volumes (V1 + V2) and the connection half-length L. Figure 2 shows symmetric and antisymmetric equilibria (inter-droplet pressures equal) distinguished by V1 + V2 < (4/3)\u03c0r3 (figure 2a) or V1 + V2 > (4/3)\u03c0r3 (figure 2b). The translational motion of the droplet\u2013droplet system is modelled by restricting to spherical-cap shapes. The benefit of this approximation is that finite-amplitude dynamics become tractable. The motions are described by a two-dimensional system while Rayleigh\u2019s infinitesimal motions are described by a partial differential equation. For the purposes of this paper, the validity of the approximation is tested by comparing with experiment. Motivation for this study comes from practical applications",
            " For these, understanding the dynamics of the droplet\u2013droplet configuration and especially the lowest frequency mode is important. Droplet motions dominated by inertia and surface tension are generally also influenced by liquid viscosity. Even though the Reynolds number is order one hundred, viscous effects are non-negligible according to experiment. The proposed inviscid model of the translational-mode dynamics is readily modified to include viscous damping. Let zc be the centre-of-mass for the total liquid volume (figure 2), in the tube and both droplets, VT = V0 + V1 + V2. Newton\u2019s law takes the form d dt ( \u03c1VT dzc dt ) = F\u03c3 + F\u00b5. (2.1) Owing to axisymmetry, the net force F = F\u03c3 + F\u00b5 acting on the control volume is in the axial direction, F e = \u222b \u2202VT Tn dA, where T = \u2212p1 + 2\u00b5D is the stress tensor, \u00b5 is the viscosity, D the symmetric part of the velocity gradient tensor, e the axial unit vector and n the unit normal. The net force splits into a capillary F\u03c3 and a viscous part F\u00b5 according to the split between pressure and deviatoric stress using the assumption of a stress-free liquid/gas interface",
            "2) where Re\u22121 \u2261 (\u00b5/\u03c1)(\u03c1/r\u03c3 )1/2 represents the ratio of viscous to inertial forces. Inviscid behaviour dominates the dynamics and we put Re\u22121 = 0 for now in order to obtain a closed-form equation for the dissipationless motions. Viscous effects are discussed in \u00a7 4. The magnitude of the centre-of-mass for each droplet zi has a closedform expression in terms of droplet height hi and length L, zi = L+(1/2)hi(2+h2 i )/(3+ h2 i ). Droplet radii are given by 2Ri = (hi + 1/hi) and volumes by Vi = (1/8)hi(3 + h2 i ) (figure 2). System centre-of-mass is related to component centre-of-mass by zcVT = \u2212z1V1 + z2V2 where the tube volume drops out since its centre-of-mass stays fixed at z =0. Substituting these relationships into (2.2), two second-order systems, each in terms of dependent variables h1 and h2, emerge. In view of the constantvolume constraint, h1 and h2 are not independent and therefore the more convenient variables are (\u0398, \u03bb) \u2261 (V1 \u2212 V2, V1 + V2). In order to express (2.2) in terms of (\u0398, \u03bb), mappings between coordinate pairs (h1, h2), (V1, V2) and (\u0398, \u03bb) are needed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003321_j.matpr.2020.11.415-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003321_j.matpr.2020.11.415-Figure2-1.png",
        "caption": "Fig. 2. Geometric model in ANSYS.",
        "texts": [
            " It works better way while using Solid elements, Shell elements, Beam/rod/tie, Anisotropic materials, and Composites [14,15]. Table 1 Mechanical properties of the materials. Sr. No. Material (Spring Steel) Brinell Hardness (BHN) Modulus of Elasticity (GPA) Fatigu Streng (MPa) 1 ASTM-A228 Music Wire 710 190 1280 2 ASTM-A231 Chrome- Vanadium 540 190 1000 3 ASTM-A401 Chrome-Silicon 540 200 1055 4 ASTM-A227 Carbon-Spring 640 190 1160 Now, the process before FEA, the 3D modeled design was exported in ANSYS from SolidWorks. Fig. 2 shows the imported three-dimensional model in ANSYS. Thereafter, the material assigning stage is performed. First of all, the ASTM-227 steel spring is assigned with its mechanical properties in the ANSYS as a crucial stage of FEA. The second stage is discretization also well known as meshing is performed. Meshing means dividing the whole model into multiple elements that leads to a uniform distribution of load in the element. The tetrahedral kind of meshing is performed having 13,574 elements. This process is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure4-1.png",
        "caption": "Fig. 4. Modified versions of the HALF* parallel manipulator with (PRR)2R-PRC chain.",
        "texts": [
            " Figure 2(b) shows the HALF* parallel manipulator with revolute actuators, where the R joints fixed to the base platform are active. Notably, the actuating direction of all sliders in the HALF* parallel manipulator with prismatic actuators may be inclined at an \u03b1 angle with respect to the vertical line as shown in Fig. 3(a). Figure 3(b) illustrates a typical example when the actuating direction is horizontal. For the manipulator shown in Fig. 2(a), as previously mentioned, the collinear axes for the two revolute joints lead to the motivation of redesigning Legs 1 and 2, as shown in Fig. 4. In these two designs, the two revolute joints are combined to one revolute joint. In Fig. 4(a), the first and second legs are connected to the moving platform through one common revolute joint. In Fig. 4(b), the first and second legs have the PRR chains, which are connected to a constant orientation bar that is linked to the mobile platform by a revolute joint. If the kinematics chain for the manipulator shown in Fig. 2(a) is denoted as (2-PRU)PRC, it will be (PRR)2R-PRC for the two designs shown in Fig. 4. This modification, which has no negative influence on the kinematics and rotational capability of the manipulator, can be also extended to the HALF* parallel manipulator with revolute actuators shown in Fig. 2(b). It is noteworthy that in the HALF* parallel manipulators the universal joints connected to the mobile platform can be replaced by spherical joints. Figure 5 shows the HANA parallel manipulator introduced in ref. [15], which is also one member of the family presented in ref. [13]. In the HANA manipulator, two legs (the first and second legs) consist of parallelogram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002085_tec.2014.2326301-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002085_tec.2014.2326301-Figure7-1.png",
        "caption": "Fig. 7. First quadrant of the permanent-magnet machine.",
        "texts": [
            " In order to ease assembly of the root Jacobian matrix J in (38) and gradient vector f in (39), the positions of the rotor are restricted to those in which the nodes along the shared boundary can be made to align. For this reason, the nodes within the air-gap are evenly spaced. One-degree resolution is provided by using 360 nodes along this boundary, which is shown to be sufficient for calculation of both torque and back-EMF of this machine. Rotation is implemented during assembly of the root Jacobian or gradient by shifting a ring buffer of indices mapping nodes along the boundary from the rotor to the stator. Fig. 7 shows the first quadrant of the machine\u2019s mesh and a close-up of a section of the air-gap is shown in Fig. 8. VI. VALIDATION AND RESULTS The accuracies of the PFEM when used to predict the mechanical or electrical properties of a device are identical to that of the FEM because the underlying node potential solutions used to calculated those properties are also identical. The PFEM makes exactly the same approximations that are made in the FEM, and therefore, the only difference in their final solutions are the negligible differences due to roundoff errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002694_j.msea.2019.138785-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002694_j.msea.2019.138785-Figure2-1.png",
        "caption": "Fig. 2. a) Arcam EBM A2X and b) schematic illustration of segmentation of build platform.",
        "texts": [
            " Most powder particles show a spherical shape and only few satellite particles are attached, as highlighted in Fig. 1. Further analysis of powder particles revealed good powder quality, e.g. a low fraction of internal pores (not shown). The calculation of the particle size distribution was carried out by using the software ImageJ based on the calculation of the mean feret diameter of 837 particles. The mean feret diameter is the mean value from the min and max distance of one powder particle measured by means of a caliber. An Arcam A2X machine (Fig. 2a, EBM control software version 4.2.76) was used to manufacture specimens in this study. All specimens were fabricated by using the Arcam standard melting scheme for IN718. For initial sintering the plate was heated by a defocused electron beam to 1025 \ufffdC (measured by a thermocouple below the build plate), where the temperature was hold after reaching the target temperature for 30 min. Each EBM cycle consists of 5 steps: 1) the pre-heating of the individual powder layer by a defocused electron beam, 2) the contour melting of the build, 3) the hatch melting of the interior of the build, 4) the post heating of the processed layer, and 5) the deposition of a new powder layer upon lowering the build plate by 75 \u03bcm",
            " Hatch melting was conducted at a hatch distance of 125 \u03bcm, a scanning speed of 4530 mms 1, a speed function of 63, and a current of 15 mA. For hatching the line order was set to 1. For each layer the hatch was rotated by 90\ufffd, while the initial start angle was set to 0\ufffd. As scanning strategy snake was chosen. The auto-functions were activated as recommended by Arcam. For investigating the influence of different positions on the finally resulting mechanical properties, the build platform was divided into 30 sections as is shown in Fig. 2b. Specimens were numbered individually. Specimens with an uneven number always had a diameter of 5 mm, whereas specimens with even number had a diameter of 3 mm. Surface roughness for a certain number of specimens was determined using a Surface Roughness Tester M 300 C (Mahr Gruppe, Goettingen, Germany). Roughness was always determined for the BD. Since every specimen was intended to be used for mechanical testing, semidestructive basic characterization had to be conducted on the top surface of the specimen",
            " Rather, it has been in focus of interest if the specimen position on the build platform can lead to similar effects, even if less pronounced. For Arcam standard parameters a strongly anisotropic microstructure characterized by pronounced <001> texture in BD and elongated grains evolves (Fig. 7e and f). Since both specimens were manufactured using the same process parameters, different thermal gradients could only result from the specimen location on the base plate. Specimen 17 was placed in the middle of the base plate surrounded by other specimens from all sides, while specimen 29 was placed at the lower edge as shown in Fig. 2b. Since both specimens show the same grain morphology, grain dimensions and texture, potential differences in thermal gradient are not strong enough to alter texture and grain morphology. In comparison to other powder based manufacturing methods offering a high flexibility in terms of geometry, i.e. IN718 parts produced by powder injection molding as discussed by \u20acOzg\u00fcn et al. [13], the E-PBF process results in relatively coarse and elongated instead of equiaxed grains, which can be attributed to melting and solidification and epitaxial growth of grains up to the uppermost layer of the build in the E-PBF processes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.151-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.151-1.png",
        "caption": "Fig. 2.151 Integral AC-DC/DC-AC macrocommutator dynamotorised transaxle [FIJALKOWSKI 1985B, 1990].",
        "texts": [
            "8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 345 The highest-level HEV controller acts as the modern microcomputer-based control centre for all of the new concept HEV functions - monitoring driver demands through the shift lever, accelerator and brake foot-pedal position signals, and controlling transmission shifting of the ICE propelled axis and regenerative braking operations, as well as the HE DBW 4WD propulsion mechatronic control system \u2018status quo\u2019, display and bookkeeping functions. The mechatronic control, monitoring, and automation functions have been integrated into a hierarchical microcomputer-based mechatronic control system. Protective functions are implemented in a separate system that co-operates with the microcomputer-based mechatronic control system. For this tri-mode HE DBW 4WD propulsion mechatronic control system, the entire system approach centres on the new concept of the integral AC-DC/DC-AC macrocommutator-based dynamotorised transaxle shown in Figure 2.151. This essentially replaces the conventional dynamotor/transaxle assembly of a conventional frontwheel-drive (FWD) HE DBW 4WD propulsion mechatronic control system. The brushless AC-DC/DC-AC macrocommutator hyposynchronous (induction) squirrel-cage rotor dynamotor (Fig. 2.152) that consists of just a stator and a rotor, has a hollow dynamotor shaft with an M-M differential case placed on the end of the shaft to serve as the input for the limited slip M-M differential [FIJALKOWSKI 1985B, 1987]. Automotive Mechatronics 346 The AC-DC/DC-AC macrocommutator-based brushless-type dynamotorised transaxle has the following advantages [FIJALKOWSKI 1985B]: It functions automatically and is very rapid (during starting and slipping, the wheel can perform maximum 1 revolution); It fully utilizes the forces of wheel adhesion; It does not lead to the hazard of destructive transaxle components operating overloads); It does not demand special cooling and lubrication oils; It has great durability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000858_978-1-4419-1126-1_8-Figure8.19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000858_978-1-4419-1126-1_8-Figure8.19-1.png",
        "caption": "Fig. 8.19 Distributed approach of automating services in the operating room. CAD rendering of a gross positioning arm (macro arm) carrying a surgical robotic arm (micro) replacing it own tool (a) or picking its own supply (b). A design of a macro arm named the \u201cC-arm\u201d (c). CAD rendering showing the Raven system (micro) carried by the C-arm (macro)",
        "texts": [
            " A far as services to the surgical robot are concerned (tool change and equipment dispensing) centralized solution was used in a form of a single surgical nurse. As a result the performance of the entire system in providing these two services is dictated by the performance of the surgical nurse alone. An alternative approach in which each surgical robot is attached to another robotic arm in a micro\u2013macro configuration, allows each surgical robot to be an independent unit that may serve itself (replacing it own tools and picking its own supplies) \u2013 Fig. 8.19. In this configuration the nurse function is distributed among all the robotics arms allowing each one to function autonomously. The micro\u2013macro approach to surgical robotics in which a gross manipulator carry a high dexterous manipulator is inspired by the human arm and hand in which the human arm serves as the gross manipulator positions the wrist in space for high dexterity manipulation by the hand. This approach may allow to design small and fast responding manipulator with high manipulability in a limited workspace which occupy only a subset of the surgical site (micro) and mount it on a land slow manipulator with a large workspace (macro)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.42-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.42-1.png",
        "caption": "Fig. 15.42 Rectangle of unit length in a space defined by \u03b1 and P0 in cases \u03b1 > \u03c0/2 (a) and \u03b1 < \u03c0/2 (b). Initial position I , intermediate positions with position angle \u03d5 and final position II",
        "texts": [
            " 514 15 Plane Motion In all four references the maximum length of the rectangle for a given width is determined. This statement of the problem results in a sixth-order polynomial equation for the unknown length. In the present section the problem is stated differently. The length of the rectangle is given. The maximum possible width is the unknown. This approach leads to a fourth-order polynomial in the case \u03b1 \u2265 \u03c0/2 and to a sixth-order polynomial in the case \u03b1 < \u03c0/2 . For achieving the maximum possible width corner points of the rectangle must be guided along g1 and g2 . In the case \u03b1 \u2265 \u03c0/2 shown in Fig. 15.42a , the motion of the rectangle consists of three phases, namely, of translation along g1 until B is at 0 , of a motion with the position variable \u03d5 in the interval 0 \u2264 \u03d5 \u2264 \u03c0 \u2212 \u03b1 and of translation along g2 . These phases are numbered 1 , 3 and 5 . In the case \u03b1 < \u03c0/2 shown in Fig. 15.42b , phase 3 is restricted to the interval \u03c0/2\u2212\u03b1 \u2264 \u03d5 \u2264 \u03c0/2 . In the interval 0 \u2264 \u03d5 \u2264 \u03c0/2\u2212\u03b1 between phases 1 and 3 a phase 2 occurs with A moving along g1 and with B\u2032 moving along g2 . Between phases 3 and 5 a phase 4 occurs with A\u2032 moving on g1 and with B on g2 . The translatory motions in phases 1 and 5 are trivial. The other motions in phases 2 , 3 and 4 are known from the elliptic trammel in Sect. 15.1.2 . They are called elliptic motions because trajectories of body-fixed points are ellipses. The inverse motion is known, too",
            " First, it is determined in which domain \u0393 \u2032 k P0 is located. Then, the single equation fk(x0, y0, b) = 0 is solved. Its smallest root is Bmax . The domains \u0393 \u2032 i (i = 1, . . . , 5) are determined by their boundaries. Let Gij = Gji (i, j = 1, . . . , 5 ; i = j ) be the boundary between \u0393 \u2032 i and \u0393 \u2032 j . By definition, for every point (x, y) on Gij there exists a real value of b satisfying the equations fi(x, y, b) = 0 and fj(x, y, b) = 0 . Elimination of b from these equations yields an equation for Gij . This is the case \u03b1 \u2265 \u03c0/2 . Figure 15.42a shows that the curve E5(b) in phase 5 is the line y \u2261 b for x \u2265 0 . The curve E1(b) is the reflection of E5(b) in g . It is the line parallel to g1 at the distance b . Its equation is x sin\u03b1\u2212 y cos\u03b1\u2212 b = 0 (x cos\u03b1+ y sin\u03b1 \u2265 0) . (15.160) From this it follows that the domain \u03935 is the first quadrant of the x, y-plane, and that \u03931 is the reflection of \u03935 on g . Furthermore, the symmetry axis g is the boundary G15 between the domains \u0393 \u2032 1 and \u0393 \u2032 5 . Next, a parametric equation is given for the curve E3(b) in phase 3 of the motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001335_j.apm.2013.05.056-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001335_j.apm.2013.05.056-Figure3-1.png",
        "caption": "Fig. 3. Schematic of cutting edge plane of a worm-shaped tool.",
        "texts": [
            " This paper topic focuses on the process of generating machining and starts from a predesigned worm-shaped tool surface, which is generated by a given rack equation as r0\u00f0u\u00de \u00bc \u00bdx0\u00f0u\u00de; y0\u00f0u\u00de , can be represented in a general form as the following equation: rt\u00f0u; h\u00de \u00bc \u00bdxt ; yt; zt \u00bc \u00f0x0 rpwh\u00de cos h\u00fe \u00f0y0 \u00fe rpw\u00de sin h; \u00f0y0 \u00fe rpw\u00de cos h \u00f0x0 rpwh\u00de sin h; pwh ; \u00f02:8\u00de where u and h are the profile parameters of the worm-shaped tool, pw is the tool lead given for unit tool rotation. The normal vector, Nw, and unit normal vector, nw, of the worm-shaped tool surface can be derived from the following equation: Nw\u00f0u; h\u00de \u00bc @rw @u @rw @h ; nw\u00f0u; h\u00de \u00bc Nwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nw Nw p : \u00f02:9\u00de For further solving the cutting lines on the machined rotor surface with the tool moves in the machining simulation, the cutting edge of the worm-shaped tool should be solved first. As shown in Fig. 3, the equation of the position vector of plane Rc , which is on the same plane as plane zw\u2013yw, can be expressed as follows: rc \u00bc \u00bd0; yc rpw; zc : \u00f02:10\u00de The cutting edge can be obtained by solving the simultaneous equations, as shown in Fig. (2.11), with respect to the plane equation rc and the equation of the worm-shaped tool helicoid rw, given the parameter u. xw\u00f0u; h\u00de \u00bc 0 yw\u00f0u; h\u00de \u00f0yc rpw\u00de \u00bc 0 zw\u00f0u; h\u00de zc \u00bc 0 8>< >: : \u00f02:11\u00de As indicated in Fig. 4, the points solved in the cutting edge curves are discrete"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000144_ip-b.1987.0046-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000144_ip-b.1987.0046-Figure3-1.png",
        "caption": "Fig. 3 Geometrical details",
        "texts": [
            "ist of principal symbols A \u2014 stator slot area Ac = aspect ratio of transformer core (= axial length/radial thickness) B = maximum airgap flux density from magnet Bb = maximum flux density in backing iron Bs = maximum flux density allowed in magnetic circuit Bt = maximum tooth flux density Ca = transformer core area Dc = diameter of transformer primary wire / = supply frequency h = slot opening depth H = slot depth J = peak current density averaged over stator slot \u2022Ji> ^2 = peak current density in transformer primary and secondary windings, respectively k = multiplying factor for tooth tip permeance Ku K2 = rare earth magnet material constants LT = length of transformer section N = number of stator slots bi\u00bb 'bo \u00bb ci > ' co ' i \u00bb o \u00bb defined in Fig. 3b Rb = radius of stator bore Ro = overall radius of stator lamination s = core stacking factor t = dimension from stator bore to magnet surface T = peak torque per unit axial length Vh = RMS stator bar voltage due to magnet Ws = width of slot opening W, = tooth width Paper 5628B (PI), first received 16th April and in revised form 1st July 1987 The authors are with the Department of Electronic and Electrical Engineering, University of Manchester, Manchester M13 9PL, United Kingdom 286 rp = transformer dimensions WT = transformer weight X = slot permeance factor 0 = torque angle A desired specification for a motorised handpiece is 10 W output at 150000 rev/min",
            " The single-turn secondary windings each thread one core and are connected to a common end ring at the rear of the transformer section. The heat sink can be advantageously connected to the secondary circuit at this end-ring as shown in Fig. 8. To obtain a compact arrangement for the secondary connecting bars, these are formed into arcs which surround the two cores they do not thread. The bar arcs each span nominally one third of the core periphery and the primary supply leads can be conveniently routed between these arcs as shown in Fig. 3b. The main advantages of this form of transformer construction over the previous transformer [3] is the ease of winding formation and the absence of a precision ground sliding joint in the magnetic circuit. The toroidal construction, combined with the high permeability of mumetal leads to a high magnetising impedance which is essential for motor synchronisation at low frequency. In operation, the handpiece is fed from an electronically generated variable frequency supply ranging from 20 to 2500 Hz",
            " The combination of the constructional and synchronising requirements was sufficient in itself to indicate copper as the favoured secondary circuit material for both the motor and the transformers. The 2-dimensional design procedure for the motor follows a development of the method outlined in Reference 4 for trapezoidally slotted laminations. Account must be taken of constraints which are associated with the general arrangement of this miniature motor and the basic design procedure for a 2-pole machine illustrated by Fig. 3a is as follows. The equations for the maximum tooth and backing iron flux densities which are given in Reference 4 are for the most unfavourable combination of magnet and leakage fluxes. Designs resulting from these equations are more conservative than is necessary for the present application and the incorporation of a torque angle at which the design is to be optimised allows some relaxation in the magnetic circuit geometry. A torque angle 6 may be defined as the angle between the fields produced individually by the stator and rotor",
            " When Bb is set to the maximum value permitted in the stator core, Bs say, the normalised form of eqn. 1 becomes Ro Ro \\\\BSRJ \\ROBJ (2) IEE PROCEEDINGS, Vol. 134, Pt. B, No. 6, NOVEMBER 1987 Similarly, for a torque angle 0, the maximum tooth flux density can be shown to be 2 sin (n/N) Wt + 2(BRb)bi0JAA)cosO}112 (3) so that with Bt = Bs, the normalised form of eqn. 3 becomes w- B 1/2 (4) It will be seen that when 0 = 0, eqns. 1 and 3 may be reduced to their counterparts in Section 3.1 of Reference 4. For the slot geometry shown in Fig. 3a, the slot leakage flux will be small relative to the tooth tip leakage. However, both the slot leakage and bore flux produced by the stator winding can be taken into account by allowing the tooth tip leakage to be increased by some factor k, say. The trapezoidal slot permeance factor specified by eqn. 30 of Reference 4 can then be simplified to (5) The peak torque/unit length of the motor can be written [4] in the form T = BJR{mm, (6) where the slot area A can be calculated from lamination geometry, so that in normalised terms (7) where fx indicates a function of the variables listed in the brackets",
            " 6, NOVEMBER 1987 The case temperature rise was not to exceed 17\u00b0C on a 50% duty cycle but as the anticipated thermal time constant is longer than the duty periods this thermal specifi- cation may be thought of as a 34\u00b0C temperature rise on a 100% duty cycle. Within the electrical and temperature specification the design method for the transformer unit as a whole attempts to determine the major geometrical data for each transformer which is consistent with the most favourable combination of overall weight, diameter and axial length. 4.2 Design procedure The cross-section of an individual transformer with connecting bars from the other transformers is shown in Fig. 3b. The design method starts from the centre and works outwards allowing 0.2 mm for insulation between the windings, the core and the case. In addition it is assumed Jhat a constant cross-section of secondary copper will be necessary through this winding and that skin effect, where appropriate, will modify the secondary circuit resistance accordingly. An arbitrary choice was made initially for the diameter of the central assembly hole such that r, = 1.4 mm. The first design parameter for the transformer is the secondary circuit peak current density (J2) on the basis of uniform current distribution. As the required secondary current is already specified by the motor as 80 A, the radius to the inner of the primary winding is then known as a function of J2 by rp = 0.2 + n J-, + 1.4 mm when 0.2 mm allowance is made for insulation and J2 is given in A/mm2. The form of the primary winding is as shown in Fig. 3b with two internal layers and one external layer. The first internal layer is arranged to have N\\ touching turns say, so that the total primary turns will be 3NJ2. Experience has shown that it is desirable to allow a distance of two wire diameters for the primary winding between the insulation surfaces of the inner core and the secondary. Two simultaneous equations can now be obtained subject to the introduction of a second design parameter {JJJ2). This second parameter in effect specifies the primary current density Jx because J2 is already specified by the first parameter",
            ": Torque availability from small synchronous motors using high coercivity magnets', IEE Proc. B, Electr. Power Appl, 1985,132, (5), pp. 279-288 5 HESMONDHALGH, D.E., and TIPPING, D.: 'Slotless construction for small synchronous motors using samarium cobalt magnets', ibid., 1982,129, (5), pp. 251-261 6 HESMONDHALGH, D.E., and TIPPING, D.: 'Relating instability in synchronous motors to steady-state theory using the HurwitzRouth criterion', ibid., 1987,134, (2), pp. 79-90 The normalised slot area given by the function/x in eqn. 7 can be determined from the lamination geometry of Fig. 3a as f A (R\u00bb, H Jl-R*0-\\R RR. ( 7 t ~ g i ) 2Rn Rb h\\2/n fr-gj /?\u201e Rj \\N 2 3 A x 2 R. (19) where 0Ll = 2 C O S \" 1 WJRO 2(Ufc + H)/K( IEE PROCEEDINGS, Vol. 134, Pt. B, No. 6, NOVEMBER 1987 295 and a2 = 2 cos\"1 2{Rb + h)/R0 It is seen from eqns. 6, 7 and 8 that and elimination of WJ2R0 from the expression for fx using eqn. 9 then gives the function / 3 directly from f2. The function/4 is deduced from eqn. 2 using eqns. 5, 7 and 9 as K B,R B, Ro/\\ Bs where fx is given by eqn. 19. The inner radius of the transformer core rci is obtained from the simultaneous solution of two equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000894_j.triboint.2010.03.016-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000894_j.triboint.2010.03.016-Figure8-1.png",
        "caption": "Fig. 8. Schematic of the lubricated contact as a multi-layer fluid. The surface layer of thickness h0 has a viscosity ZL and a Newtonian limit t0L while the fluid has a viscosity under pressure Z and a Newtonian limit t0H.",
        "texts": [
            " However, the transition appears at similar shear rate and shear stress as shown in Fig. 7a. The \u2018thermal effects\u2019 hypothesis does not seem sufficient to explain the observed experimental behaviour. This tends to demonstrate that surface phenomena contribute to the friction response even if there is no solid contact. This is why a rheological modelling based on Ree\u2013Eyring theory and integrating such a contribution has been proposed. In order to take into account this surface effect, the contact of thickness, h, is depicted in Fig. 8 as a multi-layer interface: a layer of viscosity, ZL, and Newtonian limit, t0L, of thickness h0 is present on both surfaces. This surface layer corresponds to the adsorbed layer at the liquid/solid interface whose existence is often referred to in the literature [24,25,29,30]. It results from a segregation of the additives near the surface the lubricant separating these surface layers has a viscosity Z in the contact that obeys Eq (3) and a3 Newtonian limit is t0H. As shown in Fig. 8, the shear flow is supposed to be heterogeneous and the sliding velocity DU is given by DU \u00bc 2U1\u00feU2 \u00bc 2 _g1h0\u00fe _g2\u00f0h 2h0\u00de \u00f07\u00de that is to say, using a Ree\u2013Eyring model to describe the rheology of each layer _g \u00bc 2h0 h t0L ZL sinh t t0L \u00fe h 2h0 h t0H Z0exp\u00f0aP\u00de sinh t t0H \u00f08\u00de If h0\u00bc0, Eq. (8)-Eq. (2): this corresponds to the conventional Ree\u2013Eyring\u2019s model. In this case, there is no adsorbed layer at the liquid/solid interface. If h0\u00bch/2, Eq. (8)-Eq. (2) with a specific lubricant at the interface whose properties are ZL and t0L"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.6-1.png",
        "caption": "Figure 2.6 Schematic showing direct metal deposition (DMD) technology. Courtesy: DM3D Technology.",
        "texts": [
            " Liquid metal infil- tration can be used to densify the parts further, adding another process step and increasing the processing time \u2022 Post-sintering and infiltration also leads to some amount of shrinkage that needs to be considered during part design. DED technologies use material feedstock injection into the meltpool. The meltpool can be created using various energy sources, such as laser, electron beam, plasma arc, and gas-metal arc, and material feedstock can use metal powders or metal wires. Fig. 2.6 shows a schematic of the DMD technology (laser-based metal deposition). The process steps for DED are: 1. A substrate or existing part is placed on the work table. 2. Similar to PBF, the machine chamber is closed and filled with inert gas (for laser processing) or evacuated (for electron beam processing) to reduce the oxygen level in the chamber to the desired level (AMS 4999A specifies below 1200 ppm). The DMD process also offers local shielding and does not require an inert gas chamber for metals less reactive than titanium, such as, steels, Ni alloys, and Co alloys"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000918_j.fss.2011.06.001-Figure25-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000918_j.fss.2011.06.001-Figure25-1.png",
        "caption": "Fig. 25. Double pendulum system.",
        "texts": [
            " 24 shows that the proposed state observer can generate the estimated states very quickly and accurately. The simulation results in this case demonstrate that the tracking trajectories of the actual outputs y1 and y2 also follow very well the reference signals ym1 and ym2, respectively, even when an additional load is added after 10 s. The simulation results shown in Figs. 20\u201324 demonstrate that the proposed method is robust against load changes. Example 3. We consider a two-degree-of-freedom double pendulum shown in Fig. 25 [39]. The two rods rotate in the vertical plane. Torque control is applied at two connecting joints. The rods are rigid bodies and all frictional forces are ignored. We define x11 = , x12 = \u0307, x21 = and x22 = \u0307, and the dynamic equations are then given as (35) x\u030711 = x12 x\u030712 = f11(x)M1(x, u1) + f12(x)M2(x, u2) + f13(x) x\u030721 = x22 x\u030722 = f21(x)M1(x, u1) + f22(x)M2(x, u2) + f23(x) (35) where f11( , ) = 12 l2 1[4m1 + 12m2 \u2212 9m2 cos2( \u2212 )] f12( , ) = 12l2 + 18l1 cos( \u2212 ) l2 1l2[9m2 cos2( \u2212 ) \u2212 4m1 \u2212 12m2] f21( , ) = 18 cos( \u2212 ) l1l2[9m2 cos2( \u2212 ) \u2212 4m1 \u2212 12m2] f22( , ) = 12m1 + 36m2 l2 2m2[4m1 + 12m2 \u2212 9m2 cos2( \u2212 )] f13( , \u0307, , \u0307) = 9gm2 sin(2 \u2212 ) l1[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] \u2212 9l1m2\u0307 2 sin(2 \u2212 2 ) l1[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] + 12l2m2\u0307 2 sin( \u2212 ) l1[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] \u2212 (15gm2 + 12gm1) sin( ) l1[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] and f23( , \u0307, , \u0307) = 12l1\u0307 2 sin( \u2212 )(m1 + 3m2) l2[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] \u2212 9l2m2\u0307 2 sin(2 \u2212 2 ) l2[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] \u2212 9g sin( \u2212 2 )(m1 + m2) l2[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] + 3g sin( )(m1 + 6m2) l2[15m2 + 8m1 \u2212 9m2 cos(2 \u2212 2 )] In this example, the parameter values are m1 = m2 = 1 kg, l1 = l2 = 1 m, and g = 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure6.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure6.3-1.png",
        "caption": "Fig. 6.3 Torques acting on the gyroscope with one side support and motions",
        "texts": [
            " Besides that, the analysis of the torques and motions acting on the gyroscope with one side support is conducted by the following peculiarities: The values of resulting torques acting on the supports and pivot of the gyroscope are very small (Sect. 5.3.1, Chap. 5); the reactive forces of the supports and pivot do not generate the sensitive frictional torques and can be neglected. This fact should be taken into account when compiling mathematical models of acting torques on the gyroscope and motions. Analysis of the torques acting on the gyroscope demonstrates the following features. The external load torque T that is produced by the gyroscope weight W generates the frictional and inertial torques acting around axes ox and oy (Fig. 6.3). The inertial torques are represented by the interrelated components that well described in Sect. 5.1, Chap. 5. The action of the frictional torques on the test stand is represented by the following components: (a) The gyroscopeweightW produces the external frictional torquesTf.W.x andTf.W.y acting on the supports of the inner gimbal and pivot of the outer gimbal around axes ox and oy, respectively; (b) The frictional torque Tf.W.y decreases the value of the load precession torques Tp.x, and the resistance torque Tcr",
            "y acting on the supports and pivot around axes ox and oy, respectively; (g) The rotation of the gyroscope around axis ox and oy of the test stand has occurred with low angular velocities that give the small values of high order for the inertial forces generated by the gyroscope centre mass that can be neglected; (h) The decrease in values of inertial torques acting around two axes is equal because the inertial torques express the parts of the kinetic energy of the spinning rotor; (i) The resulting torques acting on the gyroscope do not generate the sensitive reactive forces on its supports and pivot and can be neglected. The action of the external and inertial torques on the gyroscope and motions is represented on the diagram of the test stand that represented in Fig. 6.3. The action of interrelated external and inertial torques represented in Chaps. 4 (Eq. 4.9) and 5 enables to formulating the mathematical models for the gyroscope motions around two axes that are expressed by the following Euler\u2019s differential equations [14, 16, 17]: JEx d\u03c9x dt = T cos \u03b3 + Tx .ct.y \u2212 T f.x \u2212 Tct.x \u2212 Tcr.x \u2212 Tam.y\u03b7 (6.1) JEy d\u03c9y dt = Tin.x cos \u03b3 + Tam.x cos \u03b3 \u2212 Tcr.y cos \u03b3 \u2212 Ty.cr.y \u2212 T f.y (6.2) \u03c9y = \u2212 [ 2\u03c02 + 8 + (2\u03c02 + 9) cos \u03b3 2\u03c02 + 9 \u2212 (2\u03c02 + 8) cos \u03b3 ] \u03c9x (6.3) where \u03c9x and \u03c9y are the angular velocity of the gyroscope around axes ox and oy, respectively; Tct",
            " 3); \u03b7 is the coefficient of the change in the inertial torque due to the action of the frictional torques on the pivot; Tx.ct.y and Ty.ct.y are the torques generated by the centrifugal force of the rotating gyroscope centre mass around axis ox and oy acting around axis ox, respectively; Tf.x and Tf.y are the frictional torques acting on the supports B and D and the pivot C, respectively; and other components are as specified above. The running gyroscope produces the system of external and inertial torques acting around two axes of the gyroscope test stand that demonstrated in Fig. 6.3. The defined external and inertial torques are expressed by the following equations: (a) The weight W of the gyroscope inclined on the angle \u03b3 produces the torque T acting around axis ox in the counterclockwise direction: T = Mglcos\u03b3 (6.4) whereM is the gyroscopemass; g is the gravity acceleration, l is the distance between the centre mass of the gyroscope and axis of the centre beam (Fig. 6.3), \u03b3 is the angle of the gyroscope axle inclination. (b) The torque generated by the centrifugal force of the rotating gyroscope centre mass around axis oy acting in the counterclockwise direction around axis ox: Tx .ct.y = Ml(cos \u03b3 )\u03c92 y(l sin \u03b3 ) = Ml2\u03c92 y cos \u03b3 sin \u03b3 (6.5) where \u03c9y is the angular velocity of the gyroscope around axis oy and other components are as specified above. (c) The centrifugal force of the rotating gyroscope centremass around axis ox acting along the gyroscope axle (Fig. 6.3) Fz.ct.x = Ml\u03c92 x (6.6) where \u03c9x is the angular velocity of the gyroscope around axis. (d) The frictional torques acting on the supports B and D are represented by the following equation: T f.x = T f.x .E .x + T f.x .cr.y + +T f.z.ct.x + T f.x .ct.y (6.7) where: (e) The frictional torque acting on the supports B and D (Fig. 6.2) in the clockwise direction around axis oy generated by the centrifugal force of the rotating gyroscope centre mass around axis oy: T f.x .ct.y = Ml cos \u03b3\u03c92 y ( d f 2 cos \u03b4 ) (6",
            "581o is the angle of the action of Coriolis force on the sliding bearing, and other components are as specified above. (h) The frictional torque acting on the sliding bearing of the supports B and D in the clockwise direction around axis ox generated by the gyroscope weight with the centre beam E: T f.x .E .x = (Eg sin \u03b3 + Ml\u03c92 x) d f 2 cos \u03b4 (6.11) (i) where E is the mass of the gyroscope with the centre beam (Table 6.1), Fy.ct.x = Ml\u03c92 x is the centrifugal force of the rotating gyroscope centre mass around axis ox acting along axis oy (Fig. 6.3), and other components are as specified above. The expression of the total frictional torque (Eqs. (6.2)\u2013(6.4)) acting on the supports B and D is represented by the following equation: T f.x = Eg sin \u03b3 d f 2 cos \u03b4 + Ml\u03c92 x d f 2 cos \u03b4 + Ml\u03c9y\u03c9x (sin \u03b3 ) l h d f 2 cos(\u03b4 \u2212 \u03c4) + Ml\u03c92 y cos \u03b3 d f 2 cos \u03b4 (6.12) The torque generated by Coriolis force of the rotating gyroscope centre mass around axes oy and ox and acting in the clockwise direction around axis oy: Ty.cr.y = (Ml\u03c9y sin \u03b3 )(\u03c9x l sin \u03b3 ) = M\u03c9y\u03c9x (l sin \u03b3 )2 (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002271_tie.2018.2809463-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002271_tie.2018.2809463-Figure1-1.png",
        "caption": "Fig. 1 12-slot/10-pole dual three-phase machines with different rotors. (a) 12-slot stator, (b) Tile rotor, (c) Sinusoidal field shaped rotor, (d) Sinusoidal with harmonics field shaped rotor.",
        "texts": [
            " Section III analyzes the effects of harmonics into the outer frame of the PM and injected into the phase current on the increment of the output torque, and the mutual influence between PM shape and current, both utilizing harmonics, are given. The electromagnetic performance of the dual threephase PM machine with the harmonics into the outer frame of PM is predicted by the FE method in Section IV. Finally, in Section V, the prototype machine is built and measured to verify the analytical and FE analysis. The dual three-phase PM machine with 12-slot stator and 10-pole rotor is given in Fig. 1, where the two sets of the threephase windings are spatially shifted by 30 electrical degree in order to utilize the harmonics [8]-[10]. All the machines share the identical stator outer diameter of 90mm, the stator inner diameter of 53mm, the stator yoke thickness of 5mm, the opening slot width of 2mm, the teeth width of 9mm, and the axial length of 50mm, as given in TABLE I. The dual threephase PM machines have different rotors, characterized by the different PM shapes. These rotors are designated as Tile rotor, Sinusoidal field rotor, and Sinusoidal with harmonics field rotor, respectively, and the PM parameters are given in TABLE I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.116-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.116-1.png",
        "caption": "Fig. 2.116 Elementary wiring connection for axleless, full-time DBW 4WD E-M transmission arrangement with the torque proportioning front-wheel drive and rear-wheel drive as well as centre-wheel drive electro-mechanical differentials [FIJALKOWSKI 1997C].",
        "texts": [
            " For AEVs intended mainly for operation on soft ground, the CWD E-M differential may be omitted from the drive E-M powertrain line, but some means of disengaging DBW 4WD propulsion, leaving only a single pair of SM&GWs to do the driving, is generally provided for use if the AEV is required to operate on metalled roads. As it is well known from the principle of Ackermann\u2019s SBW 2WS conversion, the front SM&GWs always tend to roll further than the fixed-geometry rear SM&GWs, because their radius of turn is always larger, a parallel electrical connection (cabling) can be interposed between the EES as well as FWD and RWD units and the CWD E-M differential may be omitted from the E-M powertrain line drive (see Fig. 2.116). In practise, this usually takes the form of two separate FWD and RWD units, single on each front and rear SM&GWs on which there are rotary controls that can be locked by the driver, but the driver has to stop and alight to do so. As soon as the driver again drives the AEV on firm ground, however, the driver must remember to unlock the FWD and RWD units. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 303 Should the rear SM&GWs lose traction, on the other hand, and therefore tend to rotate further than the front ones, the drive may be automatically transferred to the front SM&GWs, even if they are in the freewheeling mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure3-1.png",
        "caption": "Fig. 3. Definition of positive of curvature.",
        "texts": [
            " (21) gives: k 1 = x \u2032 1 y \u2032\u2032 1 \u2212 x \u2032\u2032 1 y \u2032 1 ( x \u2032 1 2 + y \u2032 2 1 ) 3 2 = r 1 cos \u03b1 d \u03b1 dr + 1 r ( r 1 cos \u03b1 d \u03b1 dr + 1 ) + r 1 sin \u03b1 (29) Likewise, the curvature of 2 at any point can be calculated as k 2 = x \u2032 2 y \u2032\u2032 2 \u2212 x \u2032\u2032 2 y \u2032 2 ( x \u2032 2 2 + y \u2032 2 2 ) 3 2 = r 2 cos \u03b1 d \u03b1 dr \u2212 1 r 2 sin \u03b1 + r ( r 2 cos \u03b1 d \u03b1 dr \u2212 1 ) (30) Thus the relative curvature of 1 and 2 at any meshing point can be calculated as follows K r = | k 1 \u2212 k 2 | (31) Positive and negative of the curvature need to be defined to establish the design condition regarding relative curvature. As depicted in Fig. 3 , t is the tangential vector of a curve at point A , and \u03b1 is included angle between line oA and the positive direction of x-axis. If t points to the direction of increased \u03b1, the positive normal vector n can be defined as follows: Turning t counterclockwise about point A by 90 \u00b0, if the center of curvature at point A for the curve is on the positive normal vector n , the corresponding curvature is positive. Otherwise when the center of curvature is on the other side of n , the corresponding curvature is negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure6.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure6.5-1.png",
        "caption": "Fig. 6.5 Internal torques and motions when the load torque Ty acts in the clockwise direction around axis oy",
        "texts": [
            " Under this condition, the actions of the gyroscope internal torques and motions are as follows: \u2022 The load torque Ty generates the resistance torque Try, which acts in a counterclockwise direction around axis oy and the precession torque Tpy, which acts around axis ox in a counterclockwise direction. This coincides with the action of the load torque T. \u2022 The action of the torque produced by the gyroscope weight T generates the resistance Trx and precession Tpx torques. The resistance torque Trx acts in a clockwise direction around axis ox. The precession torque Tpx acts in a counterclockwise direction around axis oy as the torque T. All acting torques and motions of the gyroscope with one side support are illustrated in Fig. 6.5. For the simplification of the computation is accepted the horizontal location of the gyroscope (\u03b3 = 0\u00b0). The equations of the gyroscope torques and motions around axes ox and oy are represented by the following expressions: Jy d\u03c9y dt = \u2212Ty + Tct.y + Tcr.y + Tam.x\u03b7 (6.60) Jx d\u03c9x dt = T + Tin.y + Tam.y \u2212 Tcr.x (6.61) where the sign (\u2212) indicates clockwise movement. All other components are as specified above. The coefficient \u03b7 represents the increase of the precession torque Tp.x around axis oy. The coefficient \u03b7 is expressed as the ratio of the sum of the precession Tp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001137_tmag.2012.2197404-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001137_tmag.2012.2197404-Figure1-1.png",
        "caption": "Fig. 1. The basic model of Arc PMLSM.",
        "texts": [
            " First, the harmonic components of the current caused by the asymmetry of three-phase winding was analyzed, and then a method for getting symmetry three-phase winding was introduced to decrease the torque ripple. Second, the torque ripple caused by the end cogging force was analyzed, and then a method for counteracting the end cogging force by changing the structure of the motor was introduced. The analysis was based on a test model of Arc PMLSM used on the next generation large telescope. As shown in Fig. 1, the Arc PMSM is composed of three stators (S1, S2, S3) and one rotor. Specifically, the stator consists of steel core and coil, and the rotor is comprised of yoke and 64 poles magnets. Permanent magnets are embedded on the top of yoke, which provide a flux return path. These stator units are laminated by arc discs with slots facing the rotor, and the three phase windings are located in the slots in sequence. The specification of the motor is listed in Table I. From another point of view, the Arc PMLSM is composed of three unit linear motors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002528_1350650117750806-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002528_1350650117750806-Figure2-1.png",
        "caption": "Figure 2. Schematic diagram of the test rig used in the Pouly study.",
        "texts": [
            "20 developed an accurate thermal network for an angular ball bearing under oil\u2013air lubrication in high speed applications. In this network, power losses are located on the contacts between balls and rings, and on the oil mist into the REB. Thermal resistances simulate heat transfer by conduction, convection and radiation through REB. The oil properties are defined by using an oil fraction in the oil\u2013air mixture. Thermal network\u2019s results are compared with experimental data. To this end, a test rig is used. The schematic diagram of this test rig is presented in Figure 2. The test rig presented in Figure 2 is composed of one driving shaft supported by two preloaded angular-contact ball bearing. To eliminate any force and moment transfer, the driven shaft is isolated from the driven shaft by revolute and prismatic joint. REB is loaded via a hydraulic jack imposing a control axial thrust. To measure friction torque, the REBtested outer ring is mounted in a separate housing equipped with strain gauges (accuracy 10%). Some thermocouples are located on fixed parts of the system (housing, inner rings, lubricant) and other on rotating parts (inner ring and shaft) via a telemetry system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003776_j.rcim.2021.102193-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003776_j.rcim.2021.102193-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the linear robot path in the reference frame.",
        "texts": [
            "1, the tool orientation parameterization based on exponential coordinates of rotations is described followed by the tool path smoothing in Section 2.2. Section 2.3 presents an analytical way to derive the tool orientation smoothing error constraint. The improved C3 synchronization of the tool position path and tool orientation path is presented in Section 2.4. Section 3 validates the correctness and effectiveness of the proposed method through simulation and experiments. Conclusions are given in Section 4. J. Peng et al. Robotics and Computer-Integrated Manufacturing 72 (2021) 102193 As shown in Fig. 1, the robot path is usually defined by a series of discrete tool poses, {Ti|Ti = (pi,Ri) \u2208 SE(3),i \u2208 {1,\u22ef,N}}, where pi \u2208 R3 and Ri \u2208 SO(3) denote the tool tip position and the tool orientation in the reference frame {s}, respectively. The linear path is assumed to be far away from the singularity. To conveniently control the smoothing errors, the robot path is preferred to be smoothed in a decoupled way. In this work, the position path that consists of linear segments of the tool tip position commands is directly smoothed in the reference frame while the orientation path is smoothed in the rotation parametric space based on the exponential coordinates of rotations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002381_j.measurement.2015.12.006-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002381_j.measurement.2015.12.006-Figure1-1.png",
        "caption": "Fig. 1. Pitch curves of the curve-face gear pair. 1-non-circular gear, 2-curve-face gear, a = 35.822, k = 0.1, n1 = 2, n2 = 4.",
        "texts": [
            " The pitch curve of non-circular gear must be closed in order to ensure the continuity of motion transmission, thus it must satisfy the following equation: r\u00f00\u00de \u00bc r 2p n1 \u00bc r\u00f02p\u00de \u00f02\u00de Furthermore, the teeth of the non-circular gear must be distributed uniformly on the pitch curve, consequently, the perimeter of the pitch curve is: L \u00bc Z 2p 0 \u00bdr2\u00f0u\u00de \u00fe r02\u00f0u\u00de 1=2du \u00bc z1p \u00bc z1pm \u00f03\u00de Finally, according to the given value of the eccentricity, number of teeth, module, the value of the semi-major axis of elliptic pitch curve can be calculated as a \u00bc mz1p 2n1\u00f01 e2\u00de R p n1 0 f \u00f0u1\u00dedu1 \u00f04\u00de where f \u00f0u1\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2e cos\u00f0n1u1\u00de \u00fe e2\u00bd\u00f01\u00fe \u00f0n2 1 1\u00de sin\u00f02n1u1\u00de q \u00bd1 e cos\u00f0n1u1\u00de 2 \u00f05\u00de 2.2. Pitch curve of the curve-face gear In the process of curve-face gear pair meshing transmission, two pitch curves are doing pure rolling for specific performance. Hence, according to the spatial meshing theory and coordinate relation, the complex pitch curve of curve-face gear can be deduced from the readily available non-circular gear. The pitch curve of non-circular gear is elliptic, as shown in Fig. 1. The coordinates of each point on the pitch curve in static coordinate S1\u00f0X1Y1Z1\u00de is certain, it\u2019s moving coordinate S01\u00f0X0 1Y 0 1Z 0 1\u00de, which is rigidly connected to the noncircular gear, rotates company with gear around axis O1Z1 with an angular velocity of x1 in clockwise direction. And coordinates S1, S 0 1 are overlapped at the initial time. Likewise, the moving coordinate S02\u00f0X0 2Y 0 2Z 0 2\u00de is rigidly connected to the curve-face gear, which rotates around axis O2Z2 with an angular velocity of x2 in counter-clockwise direction, and overlapped with the static coordinate S2\u00f0X2Y2Z2\u00de in the initial time as well. In Fig. 1, point P1 is a point on the pitch curve of the non-circular gear; point P2 is a point on the pitch curve of the curve-face gear. They are overlapped at point P when the non-circular gear rotates an angle of u1 in clockwise direction and the curve-face gear rotates an angle of u2 in counter-clockwise direction. And the two pitch curves are tangent, hence r\u00f0u1\u00de x1 \u00bc R x2 \u00f06\u00de Afterwards, the value of /2 can be calculated as u2 \u00bc Z u1 0 1 i12 du \u00bc Z u1 0 x2 x1 du \u00bc Z u1 0 r\u00f0u\u00de R du \u00f07\u00de In the light of the movement relationship between the two gears of the curve-face gear pair, a relationship about the axis O1Z1 of rotation exists between the static coordinate S1\u00f0X1Y1Z1\u00de and the moving coordinate S01\u00f0X 0 1Y 0 1Z 0 1\u00de, so do the curve-face gear about axis O2Z2",
            " It was confirmed that these artefacts were manufactured with high accuracy. 5.3. Angular deviations calculation The pitch angle refers to the angle between two adjacent corresponding pitch points which were defined as the intersections of the flank profile with the pitch curve. And the angular deviations are equivalent to the tangential composite errors of spur gear. As for the curve-face gear pair in this article, the non-circular gear rotates around axis O1Z1, and the curve-face gear rotates around axis O2Z2 as shown in Fig. 1. Hence, the angular deviations of the gear pair, i.e. the rotation angular deviations within the coordinate plane XOY. The pitch angle can be described as follows h \u00bc h2 h1 \u00bc tan 1 y2 x2 tan 1 y1 x1 \u00f021\u00de where h1; h2 represent the polar angles of the pitch points P1; P2 in Spherical coordinate. Finally, the angular deviations are depicted as As is shown in Figs. 11 and 12, the angular deviations of the curve-face gear pair are very small, and the changes of the values of curve-face gear at the three different positions which were picked uniformity along the length of the teeth are similar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003329_j.mechmachtheory.2019.103753-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003329_j.mechmachtheory.2019.103753-Figure1-1.png",
        "caption": "Fig. 1. An anti-parallelogram unit.",
        "texts": [
            " This paper will deal with the construc- tion and analysis of Bricard-like mechanism, and the paper is organized as follows: Section 2 introduces the simplification of the new Bricard-like mechanism. In Section 3 , the kinematic of the Bricard-like mechanism is analyzed, and the degree of freedom and the kinematic paths are proposed. The prototype of the triangular prism deployable mechanism is fabricated to verify the proposed analysis and the configurations in Section 4 . Section 5 concludes the whole paper. As shown in Fig. 1 , an anti-parallelogram unit consists of four links (link AB, link CD, link AD, link BC) and four revolute joints, links AB and CD cross each other. The mechanism has one degree of freedom and its parameters satisfy AD = BC, AB = CD. After investigating the anti-parallelogram unit, we found that it can be simplified to a two bars linkage with variable links\u2019 lengths. As shown in Fig. 2 , the anti-parallelogram unit ABCD can be simplified as a mechanism P 1 S 2 P 3 , S 2 represents revolute joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.37-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.37-1.png",
        "caption": "Fig. 3.37 Series HE AWD DBW \u00d7 BBW AWB \u00d7 AWA ABW \u00d7 AWS SBW HEV termed a Poly-Supercar [FIJALKOWSKI 2000B].",
        "texts": [
            " Automotive Mechatronics In the nearest future, automotive vehicle manufacturers may be compelled to manufacture ultra-low-emission vehicles (ULEV) and virtual-zeroemission vehicles (VZEV) for the global market that offer emission-free and moderate vehicle velocity in certain areas [FIJALKOWSKI AND KROSNICKI 1994, For instance, an ultralight (600 kg), 4 -- 5 passenger, high-performance, allround energy-efficient, HEV termed a Poly-Supercar with the series hybridelectric (HE) AWD DBW propulsion, enhanced anti-lock and/or anti-spin BBW AWB dispulsion, predictive and adaptive ABW AWA suspension and dual-mode hybrid SBW AWS conversion mechatronic control systems and simplified design, may achieve 1.5 -- 4.5 l/100 km. Automotive E-M components for full-time AWD DBW propulsion, BBW AWB dispulsion, ABW AWA suspension and SBW AWS conversion mechatronic control systems of the Poly-Supercar that is a VZEV, as shown in Figure 3.37, may be well suited to help reduce local air pollution emissions. Automotive E-M components for full-time DBW AWD propulsion, BBW AWB dispulsion, ABW AWA suspension, and SBW AWS conversion mechatronic control systems of the Poly-Supercar that is a VZEV, as shown in Figure 3.35, may be well-suited to help reduce local air pollution emissions. The electrical energy required to dispel such VZEV is generated by the clean-burning, hydrogen fuelled gas turbine-generator/motor (GT-G/M) that is based on the Fijalkowski turbine boosting (FTB) system or the Fijalkowski engine \u2013generator/motor (FE-G/M) with the brushless AC-DC/ DC-AC macrocommutator flywheel-disc generator/motor that directly converts into electrical energy the mechanical energy supplied to the pistons by the combustion of gaseous hydrogen, installed on board a VZEV",
            " The former may be effectively controlled by independently distributing the braking forces to the left and right rear SM&GWs; the latter can be controlled by adopting a method for preventing SM&GW lockup. This chapter presents a novel enhanced anti-lock/or and anti-spin BBW AWB dispulsion mechatronic control system for also controlling the braking forces between the inner and outer SM&GWs independently in a hard turn. Significant bettering has been seen in cornering performances in recent years as a result of advances achieved in tyre and AWA ABW suspension technology. Due to these improvements, Poly-Supercar (see Fig. 3.37) handling characteristics during braking has taken on an added importance. The analytical results show that decreasing the yaw moment before SM&GW locking or spinning occurs is effective in achieving stable handling. An effective approach to decreasing the yaw moment is to control the braking forces between the inner and outer SM&GWs. An independent braking force control subsystem for regulating the distribution of brake application voltages to the left and right rear SM&GWs include examples that combine linkage loadsensing input and a lateral acceleration-sensitive input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000684_12_2009_22-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000684_12_2009_22-Figure3-1.png",
        "caption": "Fig. 3 A typical situation in which wrinkles occur in the presence of a macroscopic stress is schematically depicted: A thin sheet is exposed to a uniaxial macroscopic deformation (1). As a consequence, the sheet is compressed in the direction perpendicular to the elongation axis and the reacts by a buckling instability. Wrinkles are formed, which however relax as the macroscopic strain is released (2), unless plastic deformations occur in the macroscopically stressed state",
        "texts": [
            " In addition, if micron- and sub-micron wavelengths are desired, the film thickness should be controllable on the nanoscale. In most of the work, polydimethylsiloxane (PDMS) was used as elastomeric substrate. Experimentally, both transient wrinkles, which only exist when macroscopic strains are applied, and \u201cpermanent\u201d wrinkles, which remain in the absence of macroscopic strains, can be produced. Both cases are illustrated in Figs. 3 and 4 for the simplest situation of a uniaxial deformation. In Fig. 3 the sheet is macroscopically stretched as indicated by the arrows. As a consequence, transversal contraction takes place perpendicular to the stretching direction. Wrinkles will appear in the macroscopically stretched state and \u2013 provided the system is linearly elastic and no plastic deformations occur \u2013 disappear upon relaxation [22]. In Fig. 4 the film was wrinkle-free in the macroscopically stretched state (e.g., it could be prepared on a stretched substrate, as in some of the cases explained below)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000568_j.polymertesting.2010.12.005-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000568_j.polymertesting.2010.12.005-Figure1-1.png",
        "caption": "Fig. 1. Honeycomb structure with double thickness walls.",
        "texts": [
            " l\u00fe sinq t l (15) Gxz upper \u00bc 1 2 h . l\u00fe 2sin2q h . l\u00fe sinq cosq t l Gs (16) Gxz lower \u00bc h . l\u00fe sinq 1\u00fe 2h . l cosq t l Gs (17) Gxz \u00bc Gxz lower \u00fe 0:787 b . l Gxz upper Gxz lower Gs (18) Ez \u00bc t l 1\u00fe h . l h . l\u00fe sinq cosq Es (19) where l and h indicate the length of the hexagon face; b indicates the height; t indicates the thickness of the face; q indicates the semi-angle between two faces; and Es and Gs indicate the Young\u2019s modulus and shear stiffness of the honeycomb material, respectively, as shown in Fig. 1. The honeycomb was modelled by FEM according to the geometry of Fig. 1. The analysis was carried out by imposing known displacements. Depending on the elastic property evaluated, the displacement applied was angular or longitudinal. The opposite face to the applied displacement was fixed and then forces were obtained. The required elastic moduli were obtained by measuring the linear slope of the stress-strain curve. The honeycomb core structure was made of Polypropylene Honeycomb Core \u2013 OpenThermHex , while the skins were made of 1 mm thick aluminiumMagnealtok 30- H111. The thickness of the core structure was 15 mm and the cell size of the honeycomb structure was 9.6 mm. Two specimens, S1 and S2, were cut in the two principal directions of orthotropy of the honeycomb core in order to obtain shear modulus corresponding to both directions. S1 was cut having as longitudinal direction the x axis, parallel to the double wall direction of the material and S2 having the y axis, perpendicular to the double wall direction: These directions are indicated in Fig. 1. The whole thickness was 16.9 mm and the width was 80 mm in both cases. Both specimens were tested on an INSTRON 4206 testing machine at spans of 120, 160, 200, 240, 300, and 340 mm. Results obtained by regression according to Eqs. (10) and (11) are shown in Table 1. Young\u2019s modulus of the aluminiumwas Eal\u00bc 70 GPa and the equivalent modulus of the sandwich panel was calculated according to Eq. (3), being Eeq \u00bc 22027 MPa. In addition, indentation tests were carried out for both specimens in order to obtain an estimate of the stiffness of the system, which gave a value of k/w \u00bc 60 MPa"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003024_s00202-020-00955-2-Figure23-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003024_s00202-020-00955-2-Figure23-1.png",
        "caption": "Fig. 23 Flux density in LSPMSM without CPQI",
        "texts": [
            " If inertia is increased to 3 JwithmaximumCPQI, LSPMSMrefuses to start and synchronize but SCIM operates at the speed of 1352 rpm. Since there is an increase in inertia, the torque ripple is reduced in both the motors, as shown in Fig. 21. Based on the nature of application, the load inertia may vary. Figure 22 shows the maximum load torque and maximum inertia applied to the motor under normal supply and maximum CPQI. Total loss in motor is segregated into stator, rotor and mechanical loss. The mechanical loss of the motor is 44 W which is identified from the reduced voltage test. Figure 23 illustrates the magnetic flux density in stator teeth of LSPMSM under pure sine waveform. The flux density in the motor should not exceed the prescribed limit; else saturation would occur in the core, so that it can reduce efficiency, power factor and overload capacity of the motor. It is observed that flux density in teeth without CPQI is around 1.35 Tesla. And for the maximum CPQI, flux density is increased to 1.4 Tesla in middle of the teeth. Figure 24 shows there is a slight saturation in the tip around 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure13.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure13.6-1.png",
        "caption": "Fig. 13.6 Alternative model used to describe the collision between a baseball and the walls of a hollow bat. This model includes a series dashpot to account for energy losses in the ball",
        "texts": [
            "2) These relations can be solved numerically assuming that the bat is initially at rest, with dy=dt D dz=dt D 0 and that the ball is incident at speed dx=dt D vo. The initial coordinates can be taken for convenience as x D y D z D 0. If spring S1 begins to expand during the collision, we can let F1 D k3.x y/7 so that the ball has a COR D 0.5 when it impacts on a rigid wall. At maximum compression, when x y D so, the peak force F1 D k1so D k3s7 o , so k3 D k1=s6 o . The area enclosed by the ball hysteresis curve in this case then indicates that 75% of the stored elastic energy in the ball is lost and that the COR is therefore 0.5. Figure 13.6 shows an alternative model that can be used to account for energy loss in the ball. In this case, a series dashpot is included. The force on the dashpot is the same as the force on the spring S1 so k1.x w/ D kd d.w y/=dt where s D x w is the compression of the spring and w y is the compression of the dashpot. We can solve to find s using the relations d2s dt2 D d2x dt2 d2w dt2 d.w y/ dt D k1s kd d2w dt2 d2y dt2 D k1 kd ds dt 234 13 The Trampoline Effect so d2s dt2 D d2x dt2 d2y dt2 k1 kd ds dt Since m1 d2x dt2 D k1s m2 d2y dt2 D k1s k2",
            "y z/ which describes a damped oscillation with a forcing term. The corresponding equations for y and z are m2 d2y dt2 D k1s k2.y z/ m3 d2z dt2 D k2.y z/ The damping term kd can be chosen so that the ball bounces with COR D 0.5 off a very stiff bat, and the equations for s, y and z can be solved numerically to find the COR when the ball bounces off a flexible bat. The two different ball models give essentially the same results. The results in Fig. 13.5 were obtained using the slightly more complicated dashpot model depicted in Fig. 13.6. 1. D.A. Russell, Hoop frequency as a predictor of performance for softball bats, in Proceedings of the 5th International Conference on the Engineering of Sport, vol. 2 (UC Davis, CA, 2004), pp. 641\u2013647 2. A.M. Nathan, D.A. Russell, L. Smith, The physics of the trampoline effect in baseball and softball bats, in Proceedings of the 5th International Conference on the Engineering of Sport, vol. 2 (UC Davis, CA, 2004), pp. 38\u201344 3. A.M. Nathan, Dynamics of the baseball bat collision. Am. J. Phys. 68, 979\u2013990 (2000) Chapter 14 Some of the longest home runs I\u2019ve hit, I didn\u2019t actually realize they were going that far"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure3.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure3.4-1.png",
        "caption": "Fig. 3.4 Schematic of the acting forces, torques and motions of the spinning disc",
        "texts": [
            " In classical mechanics, Coriolis acceleration and force are products of the linear motion of a mass on a rotating disc and its angular velocity. The action of the Coriolis acceleration and force generated by mass elements is revealed in the spinning rotor when its plane turns around the axis perpendicular to the disc\u2019s axle. The resulting action of Coriolis force produced by the rotating mass elements of the disc is expressed as the integrated resistance torque counteracting the external torque [10]. Figure 3.4 depicts the mass element m that ravels in a circle on the disc, which turns on the plane yoz in precession angle \u03b3 around axis ox. This turn leads to a change in the direction of the tangential velocity of mass elements and produces the acceleration and Coriolis forces of the rotating mass elements. The turn of the disc\u2019s plane around axis ox leads to a non-identical change in the directions of the tangential velocity vectors. The maximal changes in direction result in the velocity vectors V* of the mass element being located on the line of axis ox (Fig. 3.4). The two vectors do not have any changes in tangential velocity V,whose directions are parallel, to the line of axis ox, that is, located on 90\u00b0 and 270\u00b0 from axis ox. These variable changes in tangential velocity vectors are represented by the vector\u2019s components Vz whose directions are parallel to the rotor\u2019s axle oz. Changes in velocity are represented by an acceleration of the mass elements and are hence inertial forces. The resistance torque generated by the Coriolis force of the rotating mass element is expressed by Tcr = \u2212 fcrym = \u2212mazym (3",
            "22) and transformation yields the following equation. Tcr = \u2212M \u03b4 2\u03c0 \u00d7 2 3 R\u03c9\u03c9x cos\u03b1 \u00d7 yC = \u2212MR\u03c9\u03c9x \u03b4 3\u03c0 cos\u03b1 \u00d7 yC (3.24) The Coriolis forces represent the distributed load along the circumference where the disc\u2019s mass elements are disposed. Figure 2.4 depicts the locations of Coriolis forces generated by the motion of rotating mass elements m around axes oz and ox. A distributed load can be equated with a concentrated load applied at a specific point along the semicircle. The location of the resultant force is the centroid (point C, Fig. 3.4) of the area under the Coriolis force\u2019s curve calculated by Eq. (3.4) but with its symbols. Substituting the defined parameters into Eq. (3.4) and transformation yields the following equation. 44 3 Inertial Forces and Torques Acting on Simple Spinning Objects yC = \u222b \u03c0 \u03b1=0 fct\u00b7z ymd\u03b1\u222b \u03c0 \u03b1=0 fct\u00b7zd\u03b1 = \u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 3\u03c0 cos\u03b1 \u00d7 2 3 R sin \u03b1d\u03b1\u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 3\u03c0 cos\u03b1d\u03b1 = \u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 3\u03c0 cos\u03b1 \u00d7 2 3 R sin \u03b1d\u03b1\u222b \u03c0/2 0 MR\u03c9\u03c9x \u03b4 3\u03c0 cos\u03b1d\u03b1 = MR2\u03c9\u03c9x \u03b4 3\u03c0 \u222b \u03c0/2 0 2 3 cos\u03b1 sin \u03b1d\u03b1 MR2\u03c9\u03c9x \u03b4 3\u03c0 \u222b \u03c0/2 0 cos\u03b1d\u03b1 = \u222b \u03c0/2 0 1 3 sin 2\u03b1d\u03b1\u222b \u03c0/2 0 cos\u03b1d\u03b1 (3",
            "15) where az = dV z/dt is Coriolis acceleration of the mass element along axis oz; V z = V cos\u03b1 sin \u03b3 = (2/3)R\u03c9 cos\u03b1 sin\u03b2 sin \u03b3 is the change in the tangential velocity V of the mass element; other components are represented in Sect. A.1.1. Substituting defined data into the expression of Coriolis force (Eq. 1.14) is represented by the following expression: fcr = M \u03b4 4\u03c0 2 3 R\u03c9\u03c9x cos\u03b1 sin \u03b2 = MR \u03b4 6\u03c0 \u03c9\u03c9x cos\u03b1 sin \u03b2 (A.1.16) Substituting defined parameters into Eq. (1.16) and transforming yield the following equation: Tcr = MR\u03c9\u03c9x \u03b4 6\u03c0 cos\u03b1 sin \u03b2 \u00d7 ym (A.1.17) The location of the resultant force is the centroid (point C, Fig. 3.4, Chap. 3) of the area under the Coriolis force\u2019s curve calculated by Eq. (A.1.4), but with symbols of the sphere. The centroid point C is defined for the resultant force acting around axis oz. yC = \u222b \u03c0 \u03b1=0 \u222b \u03c0 \u03b2=0 fcrymd\u03b1d\u03b2\u222b \u03c0 \u03b1=0 \u222b \u03c0 \u03b2=0 fcrd\u03b1d\u03b2 = \u222b \u03c0 \u03b1=0 \u222b \u03c0 \u03b2=0 MR\u03c9\u03c9x \u03b4 6\u03c0 cos\u03b1 sin \u03b2 \u00d7 2 3 R sin \u03b1 sin \u03b2d\u03b1d\u03b2\u222b \u03c0 \u03b1=0 \u222b \u03c0 \u03b2=0 MR\u03c9\u03c9x \u03b4 6\u03c0 cos\u03b1 sin \u03b2d\u03b1d\u03b2 = MR\u03c9\u03c9x \u03b4 6\u03c0 \u222b \u03c0 \u03b1=0 2 3 R sin \u03b1 cos\u03b1d\u03b1 \u00d7 \u222b \u03c0 0 sin2 \u03b2d\u03b2 MR\u03c9\u03c9x \u03b4 6\u03c0 \u222b \u03c0 \u03b1=0 cos\u03b1d\u03b1 \u00d7 \u222b \u03c0 0 sin \u03b2d\u03b2 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 197 = 2 3 R \u222b \u03c0 0 sin \u03b1d sin \u03b1 \u00d7 \u222b \u03c0 0 sin2 \u03b2d\u03b2\u222b \u03c0 0 cos\u03b1d\u03b1 \u00d7 \u222b \u03c0 0 sin \u03b2d\u03b2 = 2 3 R \u222b \u03c0 0 sin \u03b1d sin \u03b1 \u00d7 1 2 \u222b \u03c0 0 (1 \u2212 cos 2\u03b2)d\u03b2\u222b \u03c0 0 cos\u03b1d\u03b1 \u00d7 \u222b \u03c0 0 sin \u03b2d\u03b2 (A",
            " Substituting defined parameters into the expression of Coriolis force fcr and transforming yield the following expression: fcr = 3M 4\u03c0R \u03c9\u03c9x \u03b4r r cos\u03b1 = 3M 4\u03c0R \u03c9\u03c9xr r \u03b4 cos\u03b1 (A.2.16) Substituting these defined parameters into Eq. (A.2.14) and transforming yield the following equation: 204 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects Tcr = 3M\u03c9\u03c9x 4\u03c0R cos\u03b1 \u00d7 r r \u03b4 \u00d7 yC (A.2.17) The Coriolis forces represent the distributed load applied along the length of the circle and the cone forming line where the cone\u2019s mass elements are located. The location of the resultant force is the centroid (point C, Fig. 3.4, Chap. 3) of the area under the Coriolis force\u2019s curve calculated by Eq. (A.2.4), but with its own symbols. The centroid is expressed by the following equation: yC = \u03c0\u222b \u03b1=0 (2/3)R\u222b r=0 fcr ymd\u03b1dr \u03c0\u222b \u03b1=0 (2/3)R\u222b r=0 fcr d\u03b1dr = \u03c0\u222b \u03b1=0 3M\u03c92 4\u03c0R \u03b4 \u03b3\u00d7cos\u03b1\u00d7 4 9 R sin \u03b1 cos\u03b1d\u03b1\u00d7 (2/3)R\u222b r=0 rdr \u03c0\u222b \u03b1=0 3M\u03c92 4\u03c0R \u03b4 \u03b3 cos\u03b1d\u03b1\u00d7 (2/3)R\u222b r=0 rdr = 3M\u03c92 4\u03c0R \u03b4 \u03b3 cos\u03b1\u00d7 (2/3)R\u222b r=0 rdr\u00d7 4 9 R \u03c0\u222b \u03b1=0 sin \u03b1 cos\u03b1d sin \u03b1 3M\u03c92 4\u03c0 \u03b4 \u03b3\u00d7 (2/3)R\u222b r=0 rdr\u00d7 \u03c0\u222b \u03b1=0 cos\u03b1d\u03b1 = 4R \u03c0\u222b 0 sin \u03b1 cos\u03b1d sin \u03b1 9 \u03c0\u222b 0 cos\u03b1d\u03b1 (A.2.18) where the expression 3M 4\u03c0R\u03c9\u03c9x \u03b4 is accepted as constant for Eq",
            " 214 Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects Defined parameters enable for the expression Coriolis force generated by themass elements: fcr = M 2\u03c0b \u03b4 br\u03c9\u03c9x cos\u03b1 = M\u03c9\u03c9x 2\u03c0b \u03b4 r \u239b \u239d \u221a( 8 9 r )2 + 1 \u239e \u23a0r cos\u03b1 (A.3.29) where b is presented by Eq. (A.3.7) Substituting Eq. (A.3.29) into Eq. (A.3.27) and transforming yield the following equation: Tcr = M\u03c9\u03c9x 2\u03c0b cos\u03b1 \u00d7 \u239b \u239d \u221a( 8 9 r )2 + 1 \u239e \u23a0r r \u03b4 b \u00d7 ym (A.3.30) where \u03b4 and b is the angular and axial location of themass element, yC is presented by Eq. (A.3.10) (Sect. A.3.1, Appendix A). The location of the resultant force is the centroid (point C, Fig. 3.4, Chap. 3) of the area under the Coriolis force\u2019s curve calculated by Eq. (A.3.4) of Chap. 3, but with its own symbols. The centroid point C is defined for the resultant force by the following equation: yC = \u222b \u03c0 \u03b1=0 \u222b (2/3)R r=0 fcrymd\u03b1dr\u222b \u03c0 \u03b1=0 \u222b (2/3)R r=0 fcrd\u03b1dr = \u222b \u03c0 \u03b1=0 M\u03c9\u03c9x 2\u03c0b \u03b4 cos\u03b1 \u00d7 (\u221a( 8 9r )2 + 1 ) r r \u00d7 \u221a 2 3 2 3 R sin \u03b1d\u03b1dr \u222b \u03c0 \u03b1=0 M\u03c9\u03c9x 2\u03c0b \u03b4 cos\u03b1 (\u221a( 8 9r )2 + 1 ) rdrd\u03b1 = M\u03c9\u03c9x 2\u03c0b \u03b4 \u00d7 \u222b (2/3)R r=0 (\u221a( 8 9r )2 + 1 ) rdr \u00d7 \u221a 2 3 2 3 R sin \u03b1 cos\u03b1d\u03b1 M\u03c9\u03c9x 2\u03c0b \u03b4 \u222b (2/3)R r=0 (\u221a( 8 9r )2 + 1 ) rdr \u222b \u03c0 \u03b1=0 cos\u03b1d\u03b1 = \u222b \u03c0 \u03b1=0 \u221a 2 3 2 3 R sin \u03b1 cos\u03b1d\u03b1\u222b \u03c0 \u03b1=0 cos\u03b1d\u03b1 = \u222b \u03c0 \u03b1=0 \u221a 2 3 R 3 sin 2\u03b1d\u03b1\u222b \u03c0 \u03b1=0 cos\u03b1d\u03b1 (A",
            " Substituting defined parameters into an expression of f cr and transforming yield the following: fcr = M n n\u03c9\u03c9xr cos\u03b1 (A.5.17) Substituting these defined parameters into Eq. (A.5.15) and transforming yields the following equation: Tcr = M n n\u03c9\u03c9xr cos\u03b1 \u00d7 yC (A.5.18) Appendix A: Mathematical Models for Inertial Forces Acting on Spinning Objects 233 The Coriolis forces represent the distributed load applied along the length of the circle and the cone forming line where the cone\u2019s mass elements are located. The location of the resultant force is the centroid (point C, Fig. 3.4, Chap. 3) of the area under the Coriolis force\u2019s curve calculated by Eq. (3.4) of Chap. 3 but with its own symbols. The centroid is expressed by the following equation: yC = \u03c0\u222b \u03b1=0 fcr ymd\u03b1 \u03c0\u222b \u03b1=0 fcr d\u03b1 = \u03c0\u222b \u03b1=0 M n n\u03c9\u03c9xr cos\u03b1 \u00d7 r sin \u03b1d\u03b1 \u03c0\u222b \u03b1=0 M n n\u03c9\u03c9xr cos\u03b1d\u03b1 = M n n\u03c9\u03c9xr2 \u03c0\u222b \u03b1=0 sin \u03b1 cos\u03b1d\u03b1 M n n\u03c9\u03c9xr \u03c0\u222b \u03b1=0 cos\u03b1d\u03b1 = r \u03c0\u222b 0 sin \u03b1 cos\u03b1d\u03b1 \u03c0\u222b 0 cos\u03b1\u03b1d\u03b1 (A.5.19) where the expression M n n\u03c9\u03c9xr is accepted as constant for Eq. (A.5.19), the expression 2 sin \u03b1 cos\u03b1 = sin 2\u03b1is a trigonometric identity that is replaced in the equation, and other parameters are as specified above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000205_978-1-4615-9882-4_40-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000205_978-1-4615-9882-4_40-Figure2-1.png",
        "caption": "Figure 2 Inverted pendulum model",
        "texts": [
            " Control method The control method is a program control with a preset walking pattern. It is pre designed before walking as angle data of each DOF by computer simulation. Walking is achieved by the appropriate time interval output of interpolated preset walking pattern which is stored in a control computer on the machine model. Therefore, the way of walking pattern design is the essential point to realize walking. We regard the machine model as an inverted pendulum, and analyse its movement on a phase plane shown in Figure 2. The change-over movement of last machine model WL-9DR started only by hind-leg's kick in the first stage, after that two legs were kept in a locked state, and finished as shown in Figure 3. This method has an advantage in simplifying a walking pattern design, but has the problems that walking becomes unstable by the occurrence of a strong impact at every floor contact of heels or toes and, still more, a machine model is damaged quickly. So we realize low impact and smooth walking with precise movement on two ankles in change-over phase as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.101-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.101-1.png",
        "caption": "Fig. 2.101 Parallel hybrid fluidic vehicle: Fluidic launch assist (FLA) augments the conventional drivetrain [HASKELL; HAWKINS 2008]",
        "texts": [],
        "surrounding_texts": [
            "276\nTo all intents and purposes, the expression HFV deals with a large variety of automotive vehicles that include a minimum of two energy sources to power their drive trains. Unlike the pure F-F accumulator-powered AFVs that had a real range of less than 80 km (50 mi) prior to requiring recharging, hybrids have a great deal more flexibility close to that of conventional automotive vehicles.\nHybrids also do not depend exclusively on their ECEs or ICEs for all the mechanical energy they need to run; so they have enhanced fuel economy and lower greenhouse exhaust gas emissions when compared with equivalent conventional automotive vehicles [FIJALKOWSKI 1985B, 1986, 1996A, 2000C; CHAN AND CHAU 2001; CHAN 2002; WOUK 1997, 2000; VALENTINE TECHNOLOGIES INC., USA; HAWKINS 2008]. What is a hybrid-fluidic (HF) system? Synthesis between a primary energy source (PES), for example, an ECE or ICE, and/or even FC and a secondary energy source (SES), for example, an F-F accumulator or motorised and/or pumped flywheel (M&PF) that supplies or absorbs an F-M/M-F motor/pump \u2013 attaining different functions because of changed energy arrangements.\nThe typical configurations of different ICE HE DBW AWD propulsion mechatronic control systems are shown in Figures 2.101 and 2.102 [FIJALKOWSKI 1985B; VALENTINE TECHNOLOGIES INC., USA; HAWKINS 2008].\nIn a parallel design, the ESD and F-M propulsion system are connected directly to the vehicle wheels. The primary ICE or ECE is used for highway driving; the F-M motor provides added power during hill climbs, acceleration, and other periods of high demand.\nIn a series design, the primary ICE or ECE FC is connected to a mechanofluidical (M-F) pump that produces fluidicity which charges the low- and/or highpressure F-F accumulators driving a F-M motor that powers the wheels. HFVs can also be built to use the series configuration at low speeds and the parallel configuration for highway driving and acceleration. Unlike AFVs, the F-F accumulators in HFVs do not need to be plugged into a charger. Instead, they are recharged using regenerative braking or by an on-board M-F pump. The HF transmission arrangement for HF DBW AWD propulsion mechatronic control systems leads to drastically improved HFV concepts [VALENTINE TECHNOLOGIES INC., USA].\nThe main advantages are greatly improved SFC, emission, functionality and simplicity. It is based on a fluidostatic CVT, a fluidic energy store (FES), i.e., an F-F accumulator or a mechanical energy store (MES) namely, an M-M flywheel, and an E-TMC ECU or a central powertrain controller (CPC) that controls all HF transmission components. This technique permits low polluting and efficient production and use of energy. The expected average improvements are:\nFuel saving \u2013 60%; Pollution reductions \u2013 75%.\n2.6 ECE/ICE HF DBW AWD Propulsion Mechatronic Control Systems",
            "277\nAutomotive Mechatronics",
            "278\nFurther alterations that may be directly noticed by the driver are a more comfortable drive due to fast and shiftless acceleration from zero to maximum velocity. A fully active HF DBW AWD propulsion mechatronic control enhances the com-fort and safety noticeably.\nThe simplicity of the HF transmission arrangement, as shown in the following pages, is visible when comparing number and size of the HF transmission components and their arrangement in a conventional \u2018M-M transmission\u2019 and a new concept \u2018HF transmission\u2019 HFV [VALENTIN TECHNOLOGIES INC., USA]. M-M Transmission Arrangement\nMT (gearbox); M-M clutch; drive shafts; M-M differential; Starter.\nHF Transmission Arrangement wheel-hub F-M motors; fluidic energy store (FES) that is F-F accumulator, or mechanical energy\nstore (MES) that is M-M flywheel; ECE or ICE driven M-F pump; F valves, tubes, hoses.\nAn ECE or ICE, a cooling system, a tank, a CH-E/E-CH storage battery and an on-board M-E generator are less than half of its present size. These results in mass reductions of approximately 15% for a medium-size passenger vehicle with a curb mass of 1,500 kg (3,400 lbs).\nThe components of the HF transmission can be arranged alongside each other with a great degree of freedom, allowing the best use of space and distribution of mass. The best distribution of axle loads, for example 50 : 50%, and a reduced height of the barycentre (centre of gravity) can be easily achieved. This and the reduced unsprung mass of the wheels amount to increased safety and driving comfort.\nThe functionality of the automotive vehicle may be increased without additional cost and dimension due to the ease of controllability of the HF transmission and other components. The fluidostatic M-F pump driven by a significantly smaller and simplified ECE or ICE, charges the FES (F-F accumulator) with a pressurised oily-fluid. The ECE or ICE may be cut-off by the E-TMC ECU or CPC when the latter is filled.\nThe FES (F-F accumulator) provides the wheel-hub F-M motors on each wheel with energy in the form of a pressurised oily-fluid to accelerate and drive the HFV. During braking and cornering (pivot skid steering), the in-wheel-hub F-M motors become M-F pumps and transmit the braking and cornering energy back to the FES. The size of the wheel-hub F-M motors are such that they can provide sufficient braking torque to lock the wheels under all circumstances and very high torque to accelerate the HFV at all values of vehicle velocity.\n2.6 ECE/ICE HF DBW AWD Propulsion Mechatronic Control Systems"
        ]
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure3-1.png",
        "caption": "Fig. 3. HALF* parallel manipulators: (a) with inclined angle \u03b1 and (b) with horizontal actuators.",
        "texts": [
            " 2(a), the self-calibration can be implemented by attaching the sensors to the two revolute joints and the cylinder joint that are connected to the mobile platform. Hereby, the accuracy of the HALF* parallel manipulator can be improved. Therefore, compared with the old version, the new manipulator will be more popular in practical applications. Figure 2(b) shows the HALF* parallel manipulator with revolute actuators, where the R joints fixed to the base platform are active. Notably, the actuating direction of all sliders in the HALF* parallel manipulator with prismatic actuators may be inclined at an \u03b1 angle with respect to the vertical line as shown in Fig. 3(a). Figure 3(b) illustrates a typical example when the actuating direction is horizontal. For the manipulator shown in Fig. 2(a), as previously mentioned, the collinear axes for the two revolute joints lead to the motivation of redesigning Legs 1 and 2, as shown in Fig. 4. In these two designs, the two revolute joints are combined to one revolute joint. In Fig. 4(a), the first and second legs are connected to the moving platform through one common revolute joint. In Fig. 4(b), the first and second legs have the PRR chains, which are connected to a constant orientation bar that is linked to the mobile platform by a revolute joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure12.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure12.9-1.png",
        "caption": "Fig. 12.9 Pitch quadric defined by three lines n1 , n2 , n3 . Body moving instantaneously with independent angular velocities (zero-pitch velocity screws) about these lines regardless of constraint forces (zero-pitch force screws) along transversals",
        "texts": [
            " The hyperboloid associated with p = 0 (real only if pz and px are of different sign) is referred to as pitch quadric. It has the equation x2 pypz + y2 pzpx + z2 pxpy = \u22121 . (12.90) Zero-pitch screws about generators of one regulus are reciprocal to zero-pitch screws about generators of the other regulus. Hence Theorem 12.7. Pure rotation of an hyperboloid about a generator of regulus 1 has the effect that every point P of the hyperboloid has a velocity normal to the generator of regulus 2 through P 384 12 Screw Systems The practical significance of this theorem is illustrated in Fig. 12.9 . The body with a spherical head is the terminal body of a chain with three revolute joints along skew axes n1 , n2 and n3 . In the absence of the support of the spherical head the body is free to move instantaneously with independent angular velocities (zero-pitch velocity screws) about the three lines. Through these lines a hyperboloid is determined on which the lines belong to one regulus (regulus 1). The other regulus 2 is the manifold of all transversals t1 , t2 , t3 etc. of the three lines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003784_s11012-021-01372-w-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003784_s11012-021-01372-w-Figure5-1.png",
        "caption": "Fig. 5 Coordinate relationship between HD components",
        "texts": [
            " Therefore, we take the FS tooth profile to obtain the CS tooth profile as an example to show how to design the exact conjugate tooth profile of HDs. Based on the kinematics principle [26], the contact point on a couple tooth profiles must satisfy the following condition: N V12 \u00bc 0; \u00f030\u00de where N and V12 are the common normal vector and the relative velocity vector at the contact point, respectively. For convenience, we calculate Eq. (30) in the coordinate system fixed on the CS. Before this, some coordinate systems need to be established first, as shown in Fig. 5. The stationary coordinate system, {XOY}, is fixedly connected to the CS, X coincides with the symmetric axis of the CS tooth space, andO is located at the CS center. One moving coordinate system, {x1o1y1}, is fixedly connected to the WG, x1 coincides with its major axis, and o1 is located at the WG center. The other moving coordinate system, {x2o2y2}, is fixedly connected to the FS, x2 coincides with the symmetric axis of the FS tooth, and o2 is located at a point on the neutral curve. Suppose that a coordinate transformation matrix from {x2o2y2} to {XOY} are M21 and a normal vector transformation matrix from {x2o2y2} to {XOY} are W21"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001513_tec.2014.2353133-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001513_tec.2014.2353133-Figure5-1.png",
        "caption": "Fig. 5. Single-phase circuit representation of a surface mounted PMSM, circuit parameter values are given for a machine temperature of 50 \u00b0C.",
        "texts": [
            " 4) it would take a large number of thermocouples embedded in the magnet to resolve the distribution of the loss field. Indeed, it could be argued that the presence of an embedded sensor would disrupt the eddy current flow and render the measurement meaningless, especially in small machines where the relative size of the sensor is large. Surface measurement techniques, such as infrared thermometry suffer from similar conceptual uncertainties. A single-phase circuit representation of the electrical machine is shown in Fig. 5 [11]. This circuit representation considers the voltage measured across the phase to be comprised of resistive iR, reactive j\u03c9Lsi, and back electromotive force e voltage drops. During each loss measurement, the voltage constant was calculated from measured variables using (3), a steady-state ac equation derived from the equivalent circuit. Subsequently (4) was used to calculate the magnet temperature rise ken = \u221a v2 \u2212 (\u03c9Lsi)2 \u2212 iR \u03c9 (3) where v is the fundamental phase-neutral voltage (V), Ls is the synchronous inductance (H), i is the fundamental current (A), and R is the phase resistance (ohm) \u03b8m = \u03b1(ke1 \u2212 ke2 ) (4) where \u03b1 is the calibration coefficient from Fig",
            " The equation could be recast in terms of iq and id in order to apply it to measurements taken in the field weakening range; rotor position would have to be measured in order to decompose i into iq and id . In order to use (3) to determine the voltage constant during a magnet loss test, and hence calculate the magnet temperature from (4), the parameters R and Ls must be known a priori. In this study, these parameters were measured using the standard techniques described in [12]; the measured values are shown in Fig. 5. The method used to measure ohmic resistance assumes that the ac and dc resistances of the winding are the same. Equation (5) has been used to calculate the skin depth of the current flowing in the winding \u03b4 = \u221a 2 \u03c9\u03c3\u03bco\u03bcr (5) where \u03b4 is the skin depth (m), \u03c3 is the conductivity (S/m), \u03bco is the permeability of free space (H/m), and \u03bcr is the relative permeability (H/m). The radius of the copper wires in the winding was 0.25 mm, a skin depth below this would indicate a skin effect influence on resistance",
            " This demonstrates the importance of these measurements as, assuming a linear thermal system, this would lead to an increase in magnet temperature rise of 32%. Future investigations will include extending the method to enable it to take measurements in the field weakening region of the machine\u2019s operation. In order to do this (3) will be recast in terms of in terms of iq and id . Rotor position will be measured in order to decompose i into iq and id . The method could also be modified to enable it to take measurements of magnet losses from inset or interior PMSMs. This would require the synchronous inductance in Fig. 5 to be decomposed into Lq and Ld components, which may or may not be functions of phase current. The authors would like to thank Dr. T. Allen and P. Mitchell for their contributions during the construction of the experimental setup. REFERENCES [1] H. Polinder and M. J. Hoeijmakers, \u201cEddy-current losses in the permanent magnets of a PM machine,\u201d in Proc. IEEE Int. Conf. Elect. Mach. Drives, Cambridge, MA, USA, 1997, pp. 138\u2013142. [2] H. Toda, Z. Xia, J. Wang, K. Atallah, and D. Howe, \u201cRotor eddy-current loss in permanent magnet brushless machines,\u201d IEEE Trans"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002879_tie.2019.2952801-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002879_tie.2019.2952801-Figure1-1.png",
        "caption": "Fig. 1. Structure and configuration of 6/4 SRM.",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Index Terms\u2014 Current profile, harmonic current injection method, reluctance machine, torque density. I. INTRODUCTION WITCHED reluctance machines (SRMs) are developed as one kind of rare-earth magnet free machines. The operation principle of SRMs is well illustrated in [1] and [2]. They have doubly salient cores and compact windings, as shown in Fig. 1. Thanks to the simple and robust structure, SRMs have high reliability and are able to operate in a harsh environment [3-6]. However, compared with most permanent magnet machines, SRMs also suffer from low torque density, large torque ripple, large core loss and high acoustic noise. To improve the performance of SRMs, one solution is the optimal design of stator and rotor cores. Several attempts have been made in the existing literature, e.g. relative eccentricity of the stator and rotor poles [7], rotor flux barriers [8], rotor notches [9], slant stator pole face [10][11], skewed rotor poles [12]",
            " 3 is bipolar, which requires the application of H-bridge or open-winding control inverter [26], as shown in Figs. 5(a) and (b). However, in the conventional SRM drive systems, the asymmetric bridge inverter (see Fig. 5(c)) is most frequently used. Hence, the optimal current profiles are further improved in this part. For better illustration of the proposed method, the H2 current profile is chosen as an example and the finite element analysis (FEA) results of a 6/4 SRM is presented. The topology and the main specification of the 6/4 SRM are given by Fig. 1 and Table II, respectively. The rated current is 4A, which is derived based on the thermal consideration of this scaled machine (the copper loss for continuous working should not exceed 30W). This machine will be used throughout the investigations and the validations of this paper. Fig. 6(a) shows the original H2 current profile and its corresponding single-phase torque production. It can be observed that the main positive part contributes to the majority of the total torque, whereas the torque produced by the minor fluctuations is negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003517_tie.2021.3050369-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003517_tie.2021.3050369-Figure4-1.png",
        "caption": "Fig. 4. One pole-pair finite element model built according to the specifications of the 75 kW prototype.",
        "texts": [
            " The surface temperatures of the conductor rotor were measured by means of an infrared thermometer. The eddy current coupling is normally operated at small slips while the increasing slip speed will cause the drastic rise in the eddy current loss and the temperature. Therefore, the measurement was conducted within a narrow slip range to prevent possible machine overheating and break-downs. A 3-D finite element (FE) analysis is also conducted in this work. To reduce the computational cost, the one pole-pair FE models, one of which is exhibited in Fig. 4, are constructed in exact accordance with the specifications of the corresponding prototypes. By imposing the periodic boundary conditions, the interactions between magnetic poles can be effectively taken into account. Since the 3-D FE model can produce the results approximate to the actual values, its results are taken as the reference values provided that no measured results are available. In the following analytical and FE predictions, the impact of the temperature on the conductor conductivity has been taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003713_tec.2021.3062501-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003713_tec.2021.3062501-Figure7-1.png",
        "caption": "Fig. 7. Magnetics (a) flux paths and (b) flux density of the proposed SRM with 5A excited current.",
        "texts": [
            " 0885-8969 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.     21 , , . 2cW y i L y i i (24) Therefore, electromagnetic torque under a fixed excitation current is as follows:    , , c i const W y i T y i y     (25)    21 , . 2 dL y T y i i dy  (26) In this section, the performances of the proposed and conventional SRM are analyzed using 2D FEM. Fig. 7 presents the magnetic flux and flux density counters of both SRM at rated excitation current of 5 A, at aligned and half unaligned and unaligned positions. The trend of magnetic flux lines passing the air gap is close to the proposed model with acceptable accuracy which shows the high precision of the model. It is observed that the path of the main part of the magnetic fluxes in the proposed SRM is shorter than that of the conventional SRM. In this structure, there is almost no flux reversal in the stator core, the reason is its unique topology which reduces the core losses of the motor. Besides, there is no negative torque, and all these factors lead to the improvement of the efficiency of the proposed SRM. Fig. 7b shows the magnetic flux density of the proposed SRM showing that the main part of the magnetic fluxes is inside of the Ccore; and at the aligned position, the magnetic flux density in the stator yoke in the C-core is close to the knee of the magnetization characteristic and is equal to 1.727 T. Fig. 8 presents the magnetic flux density of the yoke and the tooth of the stator pole versus the stator excitation current for different angles of the rotor movement for both motors. As seen, for the nominal excitation current of 5A, the flux density is located near the knee of the BH-curve of core in both motors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure2-1.png",
        "caption": "Fig. 2 a Initial, corotated and deformed configurations of the Q4 bending element, b P and Q are along the diagonals in the initial configuration",
        "texts": [
            " The presence of the adjacent non-coplanar facets allows one to assume that the creases are straight due to the large membrane stiffness. The assumption implies the T3 facet cannot be bent and it is not necessary to consider its bending deformation. For the Q4 facet, the following subsection will derive a method to quantify the bending deformation under large displacement large rotation but small strain and small curvature assumption using a corotational consideration. 2.2 Bending deformation of quadrilateral facet Figure 2 shows the initial, corotated and deformed configurations of a quadrilateral facet. In the initial configuration, the element is flat whilst P and Q are the overlapping points along the straight lines 1\u20133 and 2\u2013 4, respectively. The deformed and corotated configurations are obtained from initial configuration through respectively the displacement U and a rigid body displacement Uc defined with respect to the global coordinate (X, Y, Z). The location of node/point i (= 1, 2, 3, 4, P and Q) in the two configurations are denoted by i\u2019 and ic",
            " Thus, elastic energy of the Q4 bending element is Ub \u00bc 1 2 D Z\u00fe1 1 Z\u00fe1 1 o2w=o2xc o2w=o2yc 2o2w=oxcoyc 8>< >: 9>= >; 1 m 0 m 1 0 0 0 \u00f01 m\u00de=2 2 64 3 75 o2w=o2xc o2w=o2yc 2o2w=oxcoyc 8>< >: 9>= >;jdndg \u00bc De 2 \u00f0Dw\u00de2 \u00f08\u00de where D = Eh3/(1-m2)/12 is the bending rigidity, E is the elastic modulus E, m is the Poisson\u2019s ratio, h is the paper thickness and De \u00bc 2D\u00bd2\u00f0b3b1 \u00fe a3a1\u00de2\u00fe \u00f01 m\u00dej20 =j30. More complicated material models can also be considered. A physical interpretation of Dw in (7) is then identified by referring to points Pc and Qc in Fig. 2b. As a point of remark, Pc is along 1c\u20133c, Qc is along 2c\u2013 4c and the two points are intersecting. It can be solved that xc P yc P \u00bc xc Q yc Q \u00bc xP yP \u00bc xQ yQ \u00bc 1 j0 a0j0 a1j1 a3j2 b0j0 b1j1 b3j2 : \u00f09\u00de Now, u of Pc is linearly interpolated from those at 1c and 3c whilst the displacement of Qc is linearly interpolated from those of 2c and 4c. Thus, uP uQ \u00bc uP uQ vP vQ wP wQ 8< : 9= ; \u00bc l1Pu3 \u00fe lP3u1 l13 l2Qu4 \u00fe lQ4u2 l24 \u00bc M1u1 \u00fe M2u2 \u00fe M3u3 \u00fe M4u4 \u00f010\u00de where lij \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xi xj\u00de2 \u00fe \u00f0yi yj\u00de2 q and M1 \u00bc lP3 l13 ; ;2 \u00bc lQ4 l24 ; M3 \u00bc l1P l13 ; M4 \u00bc l2Q l24 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003616_16878140211034431-Figure18-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003616_16878140211034431-Figure18-1.png",
        "caption": "Figure 18. Schematic of friction surfacing additive manufacturing process.",
        "texts": [
            " The ultimate strength was 278MPa at the top and 231MPa at the bottom, while the elongation exhibited the opposite trend, with the largest value of 14.8% at the bottom and 10.4% at the top. Compared with the base material, the tensile strength was significantly improved and the elongation was slightly decreased. The distribution of ultimate tensile strength gradually decreased from the top to the bottom. Friction surfacing additive manufacturing The principle of friction surfacing AM is shown in Figure 18. Through the high-speed friction between the consumable rod and the substrate, enough heat is generated to plasticize the rod material. Because the temperature gradient of the substrate and the rod is different, the plasticized material cools faster on the side of the substrate, thereby forming a coating.63 The heat dissipation at the rod is slow, which leads to excessive plasticization of the rod and flashes under the action of axial force.64 Through the lateral movement of the consumable, a continuous additive material is left on the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003220_j.addma.2020.101174-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003220_j.addma.2020.101174-Figure4-1.png",
        "caption": "Fig. 4. Columnar grain morphology of three orthogonal surfaces in which the analytical surface is discussed in detail.",
        "texts": [
            " The EBSD sample preparation process included wire cutting, mechanical polishing and electrolytic polishing. The test areas of the EBSD were determined based on the observation results under OM. Each test area had a range of 250 \u03bcm\u00d7 250 \u03bcm and a step size of 0.5 \u03bcm. The test areas were selected to explore whether there is a difference in the microtexture in the columnar grains that exhibited different characteristics in the OM and SEM images. The representative microstructure of the Ti-6.5Al-2Zr-Mo-V titanium alloy fabricated by DED consists of columnar grains. As shown in the OM images in Fig. 4, areas with different degrees of brightness represent different columnar grains. The columnar grains were formed during the DED process, where the growth direction is parallel to the deposition direction. The measured results show that the axis of the columnar grains was not strictly parallel with the deposition direction, the angle between the columnar grain axis and the deposition direction did not exceed 15\u00b0 in the T\u2013S direction, and the S\u2013T and T\u2013L directions had an angle of 5\u201310\u00b0. The length of the columnar grains varies greatly, with a range of approximately 8.98\u201325.43 mm, and there is a large difference in length between different sampling directions. In this paper, the average width of a columnar grain is 855 \u03bcm. In addition, the molten pool line perpendicular to the columnar grains can be observed in Fig. 4. The formation of the molten pool line is related to the characteristics of the layer-by-layer melting process during DED. The distance between molten pool lines was 600 \u03bcm theoretically, and it was measured to be 646.9\u2013739.7 \u03bcm. The metallographic features (including the type and size of the \u03b1 phase) of the three sections, namely, X\u2013Y, X\u2013Z, and Y\u2013Z, observed with high-magnification OM are similar. Only the analytical surface (as shown in Fig. 4) is discussed here. In the region away from the molten pool line, the metallographic characteristics are mainly dominated by acicular \u03b1, as shown in Fig. 5(a). The acicular \u03b1 has a width of 0.4\u20131.7 \u03bcm and an aspect ratio up to 50:1. The distribution of the \u03b1 phases is disordered. At the molten pool line, the acicular \u03b1 has grown because of the remelting effect, as shown in Fig. 5(b). The metallographic features of this area are acicular \u03b1, with a width of approximately 1.0\u20132.3 \u03bcm and an aspect ratio that reaches only 15:1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.20-1.png",
        "caption": "Fig. 3.20 Anti-lock EFMB BBW AWB dispulsion mechatronic control system [Mercedes-Benz; BERGER 2002].",
        "texts": [
            " Based on driver input (such as steering angle), the motion of the vehicle (actual values of the wheel velocity, yaw), the g forces acting on it, ECE or ICE shaft angular velocity, and transmission gear selected, the controller drives the modulator\u2019s fluidical valves to produce the optimum brake fluid or air pressure at each individual wheel. For example, if a driver enters a turn too fast and brakes, the mechatronics may apply most of the brake force to the two wheels on the outside of the turn to reduce the chance of skidding. The result is effectively a four-way split in braking functions as opposed to the twin, diagonally split systems, used on conventional automotive vehicles with completely FMBs or PMBs (see Fig. 3.20). With no fluidics to feed oily-fluid or air (gas) pressure back into the brake pedal when the ABS function kicks in during a panic stop, the pedal remains vibration free. And how's this for mechatronic legerdemain: In such an emergency stop, sensors detect the quick removal of the driver's foot from the accelerator pedal and signal the controller to prime the system with higher oily-fluid or air (gas) pressure and move the pads lightly against the discs (this is imperceptible to the driver). As soon as the driver\u2019s foot presses the pedal, full brake force is applied using the high-pressure fluidic accumulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001589_j.phpro.2015.11.049-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001589_j.phpro.2015.11.049-Figure6-1.png",
        "caption": "Fig. 6. Surface reconstruction of Pipe 3 and deviation (left) from the original 3D model (right). Cold (blue to green) colors for negative difference and warm (yellow to red) colors for positive difference with maximum value of \u00b10.2 mm (values higher or visually saturated).",
        "texts": [
            " Surface reconstructions of the pipes were oriented using the Rapidform Transform Scan Data tool and cut to 5 mm pieces using the Split tool. Comparing and evaluating the original 3D model and the actual CT scanned specimen (Table 3.), several key differences could be identified. All the comparisons were done from full volumetric 3D data (Fig 5.). Variation between the different 3D parts was partly due testing with slightly different scan settings and density thresholds. Surface area was increased (Fig. 6.), both on the inner and outer pipe surfaces, mainly due to the finish roughness of additive manufacturing technique. On the whole surface, relative surface area (relief) was from ~1.4 to 2.0 times greater, on the inner surface ~1.7 to 3.0 times greater and on the outer surface ~1.1 to 1.4 times greater. Also, the original polygon model had 4 degree perimeter intervals, which was clearly visible in the finished specimen as surface texture. Average deviation was ~0.1 mm inwards from the modelled outer surface and approximately even with the inner surface; even with no difference on the inner surface, surface roughness and thus difference in local distances, has to be taken into consideration when evaluating the actual specimen surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure6-1.png",
        "caption": "Fig. 6. Residual stress measurement of the wheel disc.",
        "texts": [
            " The X-ray diffractometer is made by Rigaku Corporation, and its model is MSF-2M. The area of measured point is /5 mm. Since the X-ray penetration depth is very small for general metal plate (about 10 lm), the residual stress component in the normal direction of the surface is not taken into account. A local coordinate system is set up for each measured point, of which the X-axis along the radial direction and the Y-axis along the circumferential direction. The residual stresses on two directions are measured, as shown in Fig. 6. In the test process, the X-ray emitter and receiver rotate at a certain angle (depending on the tested materials) along the specific direction of the residual stress. A great bending deformation near the measured points may cause that the X-ray emitter and receiver impact the wheel disc. Therefore, the principle of choosing the measured points is: there is no great bending deformation near the measured points. So some representative points of three processes are selected to be shown in Figs. 7\u20139, of which three points, four points and six points are selected in the first, second and third stamping processes, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure3.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure3.7-1.png",
        "caption": "Fig. 3.7 Resultant of two screw displacements in the screw triangle",
        "texts": [
            " Screw Triangle 95 Consider now the displacement of a body which is the result of two successive screw displacements (S1,n1, \u03d51, s1) (first screw displacement) and (S2,n2, \u03d52, s2) . According to Chasles\u2019 theorem the resultant displacement is itself a screw displacement called the resultant screw displacement (Sres,nres, \u03d5res, sres) . This resultant is geometrically constructed by applying Halphen\u2019s theorem several times. First, the general case is considered in which the screw axes S1 and S2 are skew. Let g1 be the common perpendicular of S1 and S2 (see Fig. 3.7). Each of the two screw displacements 1 and 2 is represented as resultant of two reflections. For the line of the second reflection of screw displacement 1 and also for the line of the first reflection of screw displacement 2 the common perpendicular g1 is chosen. These two reflections cancel each other. Hence the resultant screw displacement is the resultant of the first reflection of screw displacement 1 and of the second reflection of screw displacement 2 . The lines of these two reflections are called g3 and g2 ",
            "11 and 3.12 analytical relationships are developed for the screw triangle. When in the given screw displacements 1 and 2 s1 and s2 are changed (all other parameters held fixed), then the lines g2 and g3 undergo lateral displacements. This has no effect on \u03d5res whereas all other parameters of the resultant screw displacement are effected. In Fig. 3.8 the special case s1 = s2 = 0 is shown, i.e., the resultant of two pure rotations about skew axes ( S1 , n1 , \u03d51 , S2 , n2 , \u03d52 and g1 are the same as in Fig. 3.7). The points A1 and A2 coalesce in a single point A , and B1 and B2 coalesce in a single point B . Remark: In 1848 Cayley [7],v.1 gave analytical solutions for the resultant of two successive screw displacements as well as for the inverse problem of decomposing a given screw displacement into two screw displacements with prescribed characteristics. He did not consider the special case of screw displacements with 180\u25e6 rotation angles which was the subject of Halphen\u2019s paper [17] almost half a century later",
            "104) the relationship between these vectors is \u2217 = + 2[q\u00d7 (q\u00d7 ) + q0q\u00d7 ] + 2(q0q \u2032 \u2212 q\u20320q+ q\u00d7 q\u2032) . (3.105) The dualized form of Theorem 1.4 is Theorem 3.5. The dual quaternion D\u0302res of the resultant of two subsequent screw displacements with dual quaternions D\u03021 (first screw displacement) and D\u03022 is the product D\u0302res = D\u03022D\u03021 . (3.106) Applications of the above equations see in Sect. 3.11 and in Chap. 8 . Additional material see in Ravani/Roth [41]. Halphen\u2019s geometrical construction of the resultant of two screw displacements resulted in the spatial hexagon shown in Fig. 3.7 . Extracting analytical expressions for the unknowns \u03d5res , sres and Sres from this figure is difficult. Explicit solutions are most easily obtained on the basis of Theorem 3.5. The quaternion equation Dres = D2D1 for the resultant (nres, \u03d5res) of two successive rotations (n1, \u03d51) (first rotation) and (n2, \u03d52) resulted in the explicit coordinate-free Eqs.(1.118) and (1.119). Decomposition of vectors in the basis shown in Fig. 1.4 led to Eqs.(1.120) \u2013 (1.122): n1,2 = e1 cos \u03b1 2 \u2213 e2 sin \u03b1 2 , (3",
            " For specifying the location of the resultant screw axis the perpendicular u = nres\u00d7wres from point 0 onto the screw axis is needed. The cross-product of the vectors in (3.109) and (3.111) is 2u sin2 \u03d5res/2 where sin2 \u03d5res/2 is determined by (3.108). The result of this multiplication is4 u sin2 \u03d5res 2 = \u2212e1 sin 2 \u03b1 2 [( s1 sin 2 \u03d52 2 \u2212 s2 sin 2 \u03d51 2 ) cos \u03b1 2 + sin \u03d51 2 sin \u03d52 2 sin \u03d51 \u2212 \u03d52 2 sin \u03b1 2 ] +e2 cos 2 \u03b1 2 [( s1 sin 2 \u03d52 2 + s2 sin 2 \u03d51 2 ) sin \u03b1 2 + sin \u03d51 2 sin \u03d52 2 sin \u03d51 + \u03d52 2 cos \u03b1 2 ] + 1 4 e3 [ (s2 sin\u03d51 \u2212 s1 sin\u03d52) sin\u03b1+ (cos\u03d51 \u2212 cos\u03d52) ] . (3.112) In accordance with Fig. 3.7 this equation shows that, in general, the resultant screw axis does not intersect the common perpendicular e3 of the screw axes 1 and 2 . The resultant screw displacement has scalar measures pD and pP defined by (3.18) and (3.19). They are written in the forms pD = sres sin\u03d5res = sres sin \u03d5res 2 2 sin2 \u03d5res 2 cos \u03d5res 2 , pP = pD cos2 \u03d5res 2 . (3.113) With (3.108) and (3.110) both measures are expressed in terms of s1 , \u03d51 , s2 , \u03d52 , \u03b1 and . The quantities s1 and s2 appear only in the numerator expressions",
            " It has internal angles \u03d51/2 and \u03d52/2 at P1 and P2 , respectively, and the external angle \u03d5res/2 at P3 . The vector ( /2)e3 + u is \u2212\u2212\u2212\u2192 P1P3 , and (e2 sin \u03d51 2 + e3 cos \u03d51 2 ) is the unit vector in the direction of \u2212\u2212\u2212\u2192 P1P3 . The equation expresses the sine law in the triangle. In the special case \u03d52 = \u2212\u03d51 , (3.108) yields \u03d5res = 0 . This indicates that the resultant of the two screw displacements is a translation. No further information is obtained from (3.109) \u2013 (3.112). Both magnitude and direction of the translation are obtained from Fig. 3.7. In the case of parallel screw axes n1 = n2 and with \u03d52 = \u2212\u03d51 , the lines g2 and g3 are parallel. In Fig. 3.14b the screw axes and the lines are shown in projection along the axes as in Fig. 3.14a . The component (s1+s2)e1 of the displacement is normal to the plane. The in-plane component is illustrated by the displacement of the point which prior to the first screw displacement is located at A . It is displaced via B to C . The total translatory displacement vector is sres = (s1+s2)e1+ \u2212\u2192 AC = (s1+s2)e1+ [\u2212 sin\u03d51 e2+(1\u2212cos\u03d51)e3] ",
            "12 Equations for the Screw Triangle 119 (n31, \u03d531) executed in this order or in any order produced by cyclic permutation carry a body via two intermediate positions back into its initial position. Each rotation is the inverse of the resultant of the previous two. Application of the sine and cosine laws led to (1.134): tan \u03d531 2 = n12 \u00d7 n23 \u00b7 n31 (n12 \u00d7 n31) \u00b7 (n23 \u00d7 n31) . (3.130) Analogously, two successive screw displacements followed by the inverse of the resultant of these two carry a body via two intermediate positions back into its initial position. The figure analogous to the rotation triangle is the spatial hexagon shown in Fig. 3.7 with \u03d5res and sres replaced by \u2212\u03d5res , \u2212sres . This analogy explains the name screw triangle of the hexagon. Let the three screw displacements be newly labeled 12 , 23 and 31 . Then, according to the principle of transference, (3.130) is valid in the form tan \u03d5\u030231 2 = n\u030212 \u00d7 n\u030223 \u00b7 n\u030231 (n\u030212 \u00d7 n\u030231) \u00b7 (n\u030223 \u00d7 n\u030231) (3.131) with \u03d5\u0302ij = \u03d5ij + \u03b5sij , n\u0302ij = nij + \u03b5wij , n2 ij = 1 , nij \u00b7wij = 0 (3.132) (ij) = (12), (23), (31) . The vectors nij and wij are the Plu\u0308cker vectors of the screw axis ij in a reference frame with arbitrary origin 0 ",
            "140) yields for s31 the final result s31 2 = 1 (n23 \u00d7 n31)2 [n31 \u00b7 n23 \u00d7w23 + (n23 \u00b7 n31)n23 \u00b7 n31 \u00d7w31] \u2212 1 (n12 \u00d7 n31)2 [n31 \u00b7 n12 \u00d7w12 + (n12 \u00b7 n31)n12 \u00b7 n31 \u00d7w31] . (3.148) The vectors n12 \u00d7w12 , n23 \u00d7w23 and n31 \u00d7w31 are the perpendiculars from the reference point onto the three screw axes. The scalar products of 122 3 Finite Screw Displacement unit vectors can be expressed through the angles \u03b11 and \u03b13 in Fig. 1.6 : n12 \u00b7 n31 = cos\u03b11 , (n12 \u00d7 n31) 2 = sin2 \u03b11 , n23 \u00b7 n31 = cos\u03b13 , (n23 \u00d7 n31) 2 = sin2 \u03b13 . } (3.149) Tsai and Roth [48] deduced (3.148) geometrically from Fig. 3.7 . See also Bottema/Roth [5]. In this section Eqs.(3.109) \u2013 (3.112) for the resultant of two screw displacements are evaluated in the special case of infinitesimal screw displacements. Let p1 , p2 and pres be the pitches of the three screw displacements so that si = pi\u03d5i (i = 1, 2) , sres = pres\u03d5res . (3.150) In what follows, the index res is omitted. For Eq.(3.109) a Taylor series expansion up to 1st-order terms is made. When (3.107) is taken into account, this results in the parallelogram rule for small rotations (see Fig",
            ", basis e2 , through prescribed positions 1 , 2 , . . . , m in basis e0 . In addition, the joint variables in these positions are to be determined. Problem 2 is a relaxed form of Problem 1 : Position 1 is not prescribed. Only the m \u2212 1 screw displacements leading from position 1 to positions 2 , . . . , m are prescribed. Problem 2 has been the subject of intensive research (Roth [6, 8], Suh [10, 11], Tsai [12], Tsai/Roth [13], Huang [3], Perez Gracia/McCarthy [4]). Tsai and Roth based their analysis on the geometry of the screw triangle (Fig. 3.7). They proved that at most three positions relative to each other can be prescribed arbitrarily. The analysis led to ten coupled second-order equations for ten unknowns which were then reduced to a bicubic equation with a single real and positive root. This root proved the existence of two chains RR . It was shown that these chains form a Bennett mechanism. In view of what has been said at the end of Sect. 6.2, this result had to be expected. Perez Gracia/McCarthy [4] combined the analysis of the screw triangle with properties of the Bennett mechanism, in particular with the fact that finite displacement screws of the coupler form a cylindroid (Huang [3])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001557_s12206-014-0804-0-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001557_s12206-014-0804-0-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of a rolling element bearing.",
        "texts": [
            " When a bearing mounted on a shaft rotates at some speed, the rolling elements orbit the bearing axis and simultaneously revolve about their own axes (refer Fig. 2). The rotational speed of the cage is given by . (1) The angular velocity of the cage is . (2) Angular velocity of balls is defined by the following rela- tion: . (3) Bearing load distribution (refer to Fig. 3) with respect to angular position of ball is calculated by Eq. (4): (4) where In general, the deflection of the ith ball located at any angle q is calculated by following expression (refer to Fig. 4): . (5a) x and y are the deflections along X and Y direction respectively and g is the internal radial clearance which is the clearance between an imaginary circle, which circumscribes the balls and the outer race. At the time of impact at the defect, a pulse of short duration is produced and it is accounted for by the term D i.e. additional deflection. Hence, Eq. (5a) is modified by adding D to internal radial clearance and is given by . (5b) The restoring force generated by ball-race contact deformation of the ball is of nonlinear nature because of the Hertzian contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001975_1.4040268-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001975_1.4040268-Figure1-1.png",
        "caption": "Fig. 1 Coordinate system for gear skiving",
        "texts": [
            " Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 27, 2017; final manuscript received April 28, 2018; published online June 1, 2018. Assoc. Editor: Mohsen Kolivand. Journal of Mechanical Design AUGUST 2018, Vol. 140 / 084502-1Copyright VC 2018 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use where rc refers to the pitch radius of the cutter, and at is the end pressure angle of the cutter. As shown in Fig. 1, ug is the angle of the gear, uc is the angle of the cutter, E is the center distance between the gear and the cutter, and sf is the feeding distance. Four coordinate systems are established to illustrate the kinematic relations in gear skiving: Coordinate system S0 is fixed on the ground, in which the origin is the gear center, and z0-axis is along the gear axis; coordinate system Sg is attached on the gear with an angle ug relative to S0; Coordinate system S1 is also fixed on the ground, of which the origin is the cutter center, and z1-axis is along the cutter axis; Coordinate system Sc is attached on the cutter with an angle uc relative to S1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000525_ichr.2010.5686851-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000525_ichr.2010.5686851-Figure3-1.png",
        "caption": "Fig. 3. Details of the cross four-bar joint and position of the Instantaneous Center of Rotation (ICR)",
        "texts": [
            " To compare the performance of the planar bipedal robot in function of the knee joint, we use the same characteristics of length, mass and inertia for both bipeds. The bipedal robots are depicted in compass gait fig.1 with the two structures of the knee joint, see fig.2. Table (I) presents the physical data of the biped which are issued from the hydroid bipedal robot [18]. 978-1-4244-8690-8/10/$26.00 \u00a92010 IEEE 379 The dimensions of the four-bar structure are chosen with respect to the human characteristics measured by J. Bradley et al. by radiography in [19]. Figure 3 represents the cross four-bar knee structure. This parallel structure needs just one actuator on the drive angle \u03b11. Let us introduce \u0393m = [\u0393p1 ,\u0393p2 ,\u03931,\u03932,\u03933,\u03934] T 1 of the applied joint torques vector. During the single support phase, the stance foot is assumed to remain in flat contact on the ground, i.e., no sliding motion, no take-off, no rotation (qp1 = 0). So, we can use the general form of the dynamic model for a polyarticular system, which is independent from the reaction force of the gait on the stance foot: A(X)X\u0308 +H(X, X\u0307) = D\u0393\u0393m (1) where X is the vector of the generalized coordinated of the different segments of the bipedal robot",
            " For the sake of clarity let us consider only knee 1 to detail the principle of the calculation: la cos(q1)\u2212 lb sin(qg11) + lc cos(q2) + ld sin(qg12 ) = 0 la sin(q1) + lb cos(qg11)\u2212 lc sin(q2)\u2212 ld cos(qg12 ) = 0 (6) These constraint equations and their derivatives are used to obtain the vectors qg = [qg11 , qg12 ] T , q\u0307g , and q\u0308g of the knee\u2019s segment orientations with respect to the orientation of the tibia and the femur. By using the virtual work principle, these constraints equations can be expressed in the dynamic model by adding the Lagrange multipliers. A(X)X\u0308 +H(X, X\u0307) = D\u0393\u0393 + JT 1 \u03bb (7) Here J1 is the 2x10 Jacobian matrix calculated from the geometrical constraints (6) and \u03bb = Fc1 = [Fx1 , Fz1 ] T defines the two Lagrange multipliers vector associated to the constraint equations. These multipliers represent the exerted forces on point A of the knee joint to respect the closed loop constraints (Fig.3). We apply the same principle for the knee joint 2. So, we obtain the dynamic model of the bipedal robot with the cross four-bar knees: A(X)X\u0308 +H(X, X\u0307) = [ D\u0393 JT 1 JT 2 ] [ \u0393m Fc ] (8) with the constraints equation: [ J1 J2 ] X\u0308 + [ J\u03071 J\u03072 ] X\u0307 = 0 (9) Here Fc = [FT c1 , FT c2 ]T . To calculate the applied joint torques, which are used to obtain the energy consumption of each bipedal robot during the optimization process, we use the dynamic model (1) for the biped with rotoide knees and the dynamic model (8) for the biped with cross four-bar knees"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002847_s00170-019-04096-0-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002847_s00170-019-04096-0-Figure12-1.png",
        "caption": "Fig. 12 Schematic of residual stress measurement",
        "texts": [
            " Note that residual stress computation in simulation does not involve the removal of parts from the base plate, in that doing so could lead to significant amount of stress relief in the parts. This practice was carefully followed in the experiment to ensure the results on residual stress are comparable. Therefore, after the SLM process, the samples were kept on the base plate without any wire EDM sectioning or post treatment. The residual stress measurement was directly carried out on the samples attached to the base plate. To measure the in-depth residual stress, electropolishing method was employed, as illustrated in Fig. 12. Seven measurement depths were taken at 2.0, 1.9, 1.8, 1.7, 1.6, 1.5, and 1.4 mm, respectively, in which the depth of 2.0 mm actually means the top surface of the sample. A PROTO MG2000 XRD system, with Mn target, was used for residual stress instrument. The measurements were obtained under the following conditions: U = 18.0 KV 0, I = 4 mA, and Bragg Angle = 152.80. Each measurement was repeated twice, and the averages of the two readings were recorded. Note that we were able to obtain fairly consistent residual stress results from the ten specimens produced, and thus only the results of two specimens, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure7.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure7.1-1.png",
        "caption": "FIGURE 7.1. Coordinates and displacements of a typical thick visco-elastic cylindrical panel.",
        "texts": [
            " In the case of having linear visco-elastic material for the panel, the modal loss factors can also be computed for the breathing and flexural modes, and their respective thickness modes for different material damping factors. The cylindrical panel with different panel angles can also be modeled using finite element method. 7.2 Objectives of the Present Chapter The general two-dimensional plane strain model is used to investigate the harmonic wave propagation in a visco-elastic cylindrical panel. The cylindrical panel shown in figure 7.1, is assumed to be homogeneous, isotropic, linearly visco-elastic and infinitely long. The employed mathematical model is based on the reported work of Hamidzadeh (1997). He extended his research work on vibration analysis of thick cylindrical structures to develop the two-dimensional solution for the visco-elastic cylindrical panels. In this chapter, a solution is developed to determine the modal stresses and displacements for any point in the medium for panels with any angle. The mathematical model is presented for the governing equations of motion",
            " The chapter also presents computed natural frequency factors for several panel angles for breathing and flexural modes, as well as, their corresponding thickness modes for a wide range of thickness to radius ratios. Also, the computation is conducted to study the effect of structural damping on the natural frequencies and the modal loss factors for panels. In addition to the results from the analytical modeling, results from the the finite element model are also presented for the non-dimensional natural frequencies. Figure 7.1 depicts the geometry of the panel, where a and b indicate the inner and outer radius of the cylindrical panel respectively. r is the radius of the any point on the panel and \u03c8 is the panel angle. ur and u\u03b8 are the radial and transverse displacements of the panel. H is defined as the thickness of the panel. 7. Vibrations of Partial Cylindrical Panels 155 7.3 Harmonic Vibrations of Cylindrical Panels This section presents an analytical solution to the harmonic response of an infinitely long elastic cylindrical panel with internal damping subjected to flexural forced vibration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.16-1.png",
        "caption": "Figure 6.16. Motion of a charged particle in uniform and oppositely directed electric and magnetic fields.",
        "texts": [
            "The following exampleof a particlemoving in an electromagnetic field exhibits a motion that is periodic but not oscillatory. The solution procedure, however, is the same. 6.8. Motion of a Charged Particle in an Electromagnetic Field A particle of charge q and massm is ejected from an electronicdevice,with initial velocityVo = vj at the place Xo = Ri in an inertial frame <f> = {F; ikl . The chargemoves under the influence of constant and oppositelydirectedelectric and magnetic fields that are parallel to the axis of the gravitational field, as shown in Fig. 6.16. The total body force acting on q is F = Fe + Fm+W; hence, with (6.18), the equationof motionmay be written as dx- eX x B = -(x - cx x B) = cE + g, dt where in c == q /m. This vectorequationis readily integratedto obtain the velocity 142 Xas a function of x and t ; thus, x= cx x B + (cE + g)t + Co. Chapter 6 (6.75b) The constant vector of integration is fixed by the initial data x(O)= xo, x(O)= Vo , so that Co = Vo - cXo x B. (6.75c) Although (6.75b) cannot be integrated further, its use in (6.75a) leads to another integrable result"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001272_1.4024103-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001272_1.4024103-Figure2-1.png",
        "caption": "Fig. 2 Position of the three loading points equivalent to the normal force at the ball-ring contact. The gray dashed line represents the deformed shape of the ring, including the contact deformation.",
        "texts": [
            " For each contact point, and for a given mesh, the purpose is to find an equivalent load leading to a satisfactory estimation of the displacement near the contact ellipse. Applying one nodal force is not possible since it requires a node at the contact point, with a time consuming re-meshing process. Thus, three nodal forces are used to create a resultant that will be in accordance with the intensity, direction, and position of the contact normal effort Q. In order to choose the expression of the three normal forces, ~F1; ~F2; and ~F3 (see Fig. 2), three conditions must be satisfied: (1) ~Q \u00bc ~F1 \u00fe ~F2 \u00fe ~F3 (2) load symmetry with respect to the major axis of the contact ellipse and around the contact point (3) all forces are parallel with ~Q The second point induces that the moment created by ~F1; ~F2, and ~F3 is null; this defines the contact center position. If the contact area is considered as a circle, these criteria lead to the repartition described by the left-hand picture in Fig. 2. Symmetry around the contact point implies that the three equivalent loads are on a 031402-2 / Vol. 135, JULY 2013 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 06/05/2014 Terms of Use: http://asme.org/terms concentric circle spaced by a 2p/3 angle with equal intensity. The radius has to be chosen as a compromise between the accuracy of the raceway displacement far from the contact ellipse and the displacement at the edge of the contact ellipse. This is the only parameter set as arbitrary, with all other characteristics being driven by the three criteria",
            " Using three forces decreases the relative difference of the displacement outside the contact ellipse, compared to only one central point force. The relative difference outside [\u20131.1a;1.1a] is 8% for three nodal forces while it reaches 40% for a single nodal force placed at the contact center. Data inside the contact ellipse are unusable due to the singularities created by the punctual forces. The radius of the nodal force location is set to be as large as possible while limiting the error outside the contact area. A value set as 3a/4 (see Fig. 2) is a good compromise. 2.2 New Geometry Computation. The conformity, the axial, and radial positions of the curvature center describe the geometry of a given ball bearing raceway. As the raceway deforms differently from one contact point to another, all contact points must be investigated. The local geometry will now be considered, and the method to obtain the new raceway discussed in what follows next. Knowing the deformed geometry of each ring, the aim is now to find the new raceway characteristics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure20-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure20-1.png",
        "caption": "Fig. 20. The test principle of worm drive backlash.",
        "texts": [
            " 16 , the structure and testing site of backlash test is considered in Fig. 19 (a) and (b). Driven by the AC servo motor, the OPE hourglass worm rotates the IHB gear at a certain angle, and then turns back. Due to the backlash of the worm drive, the position has a certain deflection with the initial position. The measuring rod is fixed at the output of the worm drive to amplify the deflection, and the effective length l m of the measuring rod is 300 mm. The dial gauges is used to measure the deflection. The test principle of the worm drive backlash is shown in Fig. 20 . The specific test steps are as follows: (a) The measuring rod is in the initial position 1 \u00a9. (b) The OPE hourglass worm is rotated 200 \u25e6 by the AC servo motor, and the measuring rod moves to the position 2 \u00a9, then lay out the dial gauges and return the pointer to zero. (c) The OPE hourglass worm continues to rotate 200 \u25e6 by the AC servo motor, and the measuring rod moves to the position 3 \u00a9. (d) The OPE hourglass worm is driven by the AC servo motor to rotate 200 \u25e6 in the reverse direction, and the measuring rod back to the position 2 \u00a9, record the dial gauges reading e "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003049_tia.2020.2993525-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003049_tia.2020.2993525-Figure1-1.png",
        "caption": "Fig. 1. Cross section of the SynRM with the related direct (x) and quadrature (y) axis",
        "texts": [
            " Experimental results achieved with the proposed MTPA have been compared firstly with those achievable with the classic MTPA (\ud835\udc56\"# = %\ud835\udc56\"&%) and secondly with those achievable with the real MTPA, with aim of highlighting the advantages in terms, from one side, of the of torque increase capability with respect to the classic MTPA and, from another side, the limited torque loss with respect to the real MTPA. This paper is an improvement and extension of [13]. II. COMPLETE MAGNETIC MODEL OF THE SYNRM A novel complete magnetic model of the SynRM has been proposed in [12], where specific original flux versus current functions have been deduced, permitting both the self and cross-saturation effects to be accounted for. In the following, this model is briefly described. For the detailed version of the model, the reader can refer to [12]. As for the adopted notation of the axis, Fig. 1 shows the cross section of a typical SynRM, where the direct (x) and quadrature (y) axis are clearly highlighted. If \ud835\udf13\"#, \ud835\udf13\"& are the stator direct (x) and quadrature (y) flux components in the rotor reference frame, and isx, isy are the corresponding stator current components, the flux versus current functions can be written as: \ud835\udf13\"#*\ud835\udc56\"#, \ud835\udc56\"&, = \ud835\udefc(1 \u2212 \ud835\udc5223456) + \ud835\udefd\ud835\udc56\"# \u2212 \ud835\udefe ;<2=>?@56@5AB 456 , \ud835\udf13\"&*\ud835\udc56\"#, \ud835\udc56\"&, = \ud835\udeff*1 \u2212 \ud835\udc522D45A, + \ud835\udf00\ud835\udc56\"& \u2212 \ud835\udefe ;<2=>?@56@5AB 45A (1 a, b) The entire magnetic behavior of the machine can be, therefore, described by functions requiring the knowledge of 8 model parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.7-1.png",
        "caption": "Fig. 3.7 Disc (a), ring (b) and drum (c) brakes [FIJALKOWSKI AND KROSNICKI 1997].",
        "texts": [],
        "surrounding_texts": [
            "The torque produced by the brake functions to generate a braking force at the ground and to decelerate the wheels and driveline components is t wwb b R JT F \u03b1\u2212 = , (3.25) where: Fb - brake force [N]; Jw - angular inertia of wheels and driveline components [kg m2]; \u03b1w - angular deceleration of wheels [rad/s2]; Rt - rolling radius of the wheel-tyre [m]. Except during a wheel lockup process, \u03b1w is related to the deceleration of the automotive vehicle through the radius of the wheel-tyre, i.e., \u03b1w = ax/Rt , and Jw may be simply lumped in with the vehicle mass for convenience in calculation. In that circumstance, the braking torque and braking force are related by the relationship t b b R T F = . (3.26) Disc and/or Ring Brakes -- In disc and/or ring brakes, force is applied equally to both sides of a rotor (in the form of a disc or ring), and the braking function is achieved through the frictional action of inboard and outboard brake pads against the rotor (disc or ring). The pads are contained within a calliper, as is the wheel fluidical or pneumatical cylinder. 3.3 Basics of Automotive Vehicle Braking 447 Although not a high-gain type of braking, disc and/or ring brakes have the advantage of providing relatively linear braking with lower susceptibility to fading than drum brakes. Force applied to the rotor by the pads is a function of fluid or air pressure in the BBW AWB dispulsion mechatronic control system and the area of the wheel fluidical or pneumatical cylinder (or cylinders, as the design dictates). Static brake torque Tbs can be computed using the following equation: Tbs = Eb Ac pa Rb , (3.27) where Eb - brake effectiveness factor: ratio of the disc or ring rubbing surface force to the input force on the shoes; Ac - wheel fluidic or pneumatic cylinder area [m2]; pa - application fluid or air pressure [Pa]; Rb - brake radius [m]. Drum Brakes - Historically, drum brakes have seen common usage because of their high value of the braking factor and the easy incorporation of parking brake features. On the negative side, drum brakes may not be as consistent in torque performance as disc and/or ring brakes. The lower values of the brake factors of disc brakes require a higher value of actuation effort, and development of integral parking brake features has been required before disc brakes could be used at all wheel positions. The brake factor has mechanical advantages that can be used in drum brakes to minimise the actuation effort required. For instance, the drum brake consists of two shoes pivoted at the bottom. The application of an actuation force pushes the lining against the drum generating a friction force whose magnitude is the normal load times the coefficient of friction of the lining material against the drum. The moment of rotation about the pivot point produced by the friction force on the \u2018leading\u2019 shoe functions to rotate it against the drum and increase the friction force developed. This \u2018self-servo\u2019 function yields a mechanical advantage characterised as the \u2018brake factor\u2019, a \u2018trailing\u2019 shoe on which the friction force functions to reduce the application force. The brake factor is much lower, and higher application forces are required to achieve the desired braking torque. For example, using two leading shoes, two trailing shoes, or one of each can obtain different values of the brake factor. The \u2018duo-servo\u2019 brake has two leading shoes coupled together to obtain a very high value of the brake factor. The consequence of using high values of the brake factor is sensitivity to the lining coefficient of friction, and the possibility of more noise and squeal. Small changes in the lining coefficient of friction due to thermal energy (heating), wear, or other factors cause the drum brake to behave more erratically. Since disc brakes lack this self-actuation effect, they generally have better torque consistency, although at the cost of requiring more actuation effort. Automotive Mechatronics 448 The differences between the three types of brakes can usually be seen in their braking torque properties during a stop. On drum brakes, the braking torque may often exhibit a \u2018sag\u2019 in the intermediate portion of the stop. It has been hypothesised that the effect is the combination of temperature fade and vehicle velocity effects (braking torque increases as vehicle velocity decreases). Disc and/or ring brakes normally show less braking torque variation in the course of a stop. With an excess of these variations during a brake application, it can be difficult to maintain the proper balance between front and rear braking effort during a maximum\u2013effort stop. Ultimately, this can show up as less consistent deceleration performance in braking manoeuvres resulting in longer stopping distances [GILLESPIE 1992]. The torque from the drum or ring brake normally increases almost linearly with the actuation effort, but the levels that vary with the vehicle velocity and the thermal energy (heat) absorbed through the temperature generated. Thus ),,( tab EvFfT = , (3.28) where Tb - braking torque [Nm]; Fa - actuation effort [N]; v - vehicle velocity in forward sense of longitudinal direction [m/s]; Et - thermal energy [Ws]. In drum brakes, force is applied to a pair of brake shoes in a variety of configurations, including leading/trailing shoe (simplex), duo-simplex, and duo-servo. Drum and/or ring brakes feature high gains relative to disc and/or ring brakes, but some configurations tend to be more non-linear and sensitive to fading and other brake-lining coefficient-of-friction changes. The static brake torque relationship expressed by Eq. (3.24) presented for disc and/or brakes are equally applicable to drum brakes with design-specific changes for drum-brake radius and effectiveness factor. By design, the brake or ring radius for a drum or ring brake is one-half the drum or ring diameter. The effectiveness factor represents the major functional difference between drum and/ or disc brakes; the geometry of drum and/or ring brakes may allow a torque to be produced by the friction force on the shoe in such a manner as to rotate it against the drum and increase the friction force developed. This function may yield a mechanical advantage that significantly increases the gain of the drum brake and the effectiveness factor as compared with disc brakes. The dynamic brake-force calculation for drum and disc and/or ring brakes is more complex since the brake-lining coefficient of friction is a function of temperature; as the lining heats during a braking manoeuvre, the effective coefficient friction increases and less fluid or air pressure or electric voltage is needed to maintain a constant brake torque. 3.3 Basics of Automotive Vehicle Braking 449 Booster and Master Cylinder - Figure 3.8 is a schematic diagram of a brake pedal, a vacuum booster, and a master cylinder. In actual practice, in passenger vehicles, as well as light and medium trucks the mechanical force gain due to the brake-pedal geometry is usually 3 to 4 and the gain through a vacuum booster is typically 5 to 9 after the booster reaches its crack point and before run-out occurs. Therefore, force applied by the driver may be multiplied by a factor of 12 to 36 at the master cylinder in order to achieve the fluid or air pressure necessary for braking. The resulting fluid or air pressure in the master cylinder pmc is as follows: Automotive Mechatronics 450 p sbbmghd mc A FkkF p \u2212 = \u03b7 , (3.29) where \u03b7 - mechanical energy efficiency; Fdriver - driver force on the brake pedal [N]; kmg - mechanical gain primarily related to the brake pedal assembly geometry and the instantaneous return spring force; kbb - brake booster gain, a function with the non-linearities of a mini- mum crack force being necessary to initiate boost and a run-out phenomenon resulting in a decreased force gain after a given input force is applied; Fs - return spring force [N]; Ap - area in the master cylinder on which the force is acting (chamber piston area) [m2]. Master cylinders are separated into primary and secondary chambers to better safety by avoiding total BBW AWB dispulsion mechatronic control system loss in the case of a failure in one portion of the sphere. The most common configuration is shown in Figure 3.8 with two chambers in a single bore [ROMANO 2000]. Proportioning Fluidical or Pneumatical Valve - Due to the dynamic vehicle mass transfer (shift), as shown in Eq. (3.16), brake fluid or air pressure that are appropriate for high-deceleration braking on front wheels usually are too high for the rear wheels; the result is that the rear wheels may tend to lock during braking. This problem can be decreased significantly through the use of proportioning fluidical or pneumatical valves. Standard proportioning for fluidical or pneumatical valves allow equal front and rear brake oily-fluid or air (gas) pressure during low input pressures (corresponding to low deceleration rates and little dynamic vehicle mass shift) but decrease the gain through the fluidical or pneumatical valve to less than one when a fixed input pressure (crack oily-fluid or gas pressure) is reached. More complex mass-sensing fluidical or pneumatical valves are used in some applications when necessary, such as when dynamic vehicle mass transfers (shifts) and vehicle-mass changes are wide enough to make a fixed proportioning fluidical or pneumatical valve become insufficient for proper braking in all conditions. Mass-sensing fluidic or pneumatic valves feature a means to measure the mass on the rear wheels and adjust the gain through the fluidical or pneumatical valve accordingly. Figure 3.9 shows a layout of the two most common passenger vehicle as well as light and medium truck 4WB BBW dispulsion mechatronic control systems including proportioning fluidical (hydraulical or pneumatical) valves [CAGE 1994]. 3.3 Basics of Automotive Vehicle Braking 451 mechatronic control systems [CAGE 1994]. The vertically split 4WB BBW dispulsion mechatronic control system typically used on rear-wheel drive (RWD) vehicles and the diagonally split 4WB BBW dispulsion mechatronic control system is typically used on frontwheel drive (FWD) vehicles. Widespread use of diagonally split 4WB BBW dispulsion mechatronic control systems has been a direct result of the popularity of FWD vehicles. Current law requires a half-system (fluidical or pneumatical) failure stopping rate that is difficult to meet if the half system is the rear brakes (on a vertically split 4WB BBW dispulsion mechatronic control system) and the vehicle mass is significantly shifted towards the front as it is in FWD automotive vehicles. Diagonally split 4WB BBW dispulsion mechatronic control systems afford the use of one front brake regardless of the half-system failure, and FWD automotive vehicles can be made to pass the legal requirements despite the large difference between the mass on the front and on the rear wheels. However, diagonally split 4WB BBW dispulsion mechatronic control systems require two proportioning fluidic or pneumatic valves and tend to require more sophisticated plumbing than the vertically split 4WB BBW dispulsion mechatronic control systems. Automotive Mechatronics"
        ]
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.13-1.png",
        "caption": "Fig. 13.13 Homokinetic coupling with contacting symmetrical curves (a) and with a ball-in-track joint (b)",
        "texts": [
            " The triangle can rotate full cycle if A2 +B2 \u2212R2 \u2265 0 for 0 \u2264 \u03d5 \u2264 2\u03c0 . This is the condition 1\u2212 cos2 \u03b3 cos2 \u03b2 sin2 \u03d5 \u2265 0 . (13.41) This requires cos\u03b2 \u2265 cos \u03b3 or \u03b2 \u2264 \u03b3 \u2264 \u03c0/2 . The inclination angle between the two shafts is \u03b1 = \u03c0 \u2212 2\u03b3 . Thus, the condition is 2\u03b2 \u2264 \u03c0 \u2212 \u03b1 . With 2\u03b2 = 90\u25e6 inclination angles \u03b1 up to 90\u25e6 are possible. The symmetrical five-d.o.f. chains essential for all previously described shaft couplings have the disadvantage of being structurally complex. Much simpler realizations are shown in Figs. 13.13a and b . The shafts in Fig. 13.13a are connected by a spherical joint. The shafts as well as the symmetrical curves 13.4 Homokinetic Shaft Couplings 405 of arbitrary shape drawn in thick lines are in the plane of the drawing. Imagine these curves to be rigid and rigidly attached to the shafts. Due to the symmetry the point of contact is in the bisecting plane \u03a3 . Both symmetry with respect to and contact in the bisecting plane are maintained when the inclination angle \u03b1 between the shafts is changed and also, when both shafts are rotated through arbitrary identical angles into positions in which the two curves are no longer coplanar",
            " However, since point contact is transmitting force from one shaft to the other in only one sense of direction of rotation, a second pair of rigid curves for the opposite sense of direction is necessary. This is the pair drawn in dashed lines in the same plane. Repeating the arguments at the beginning of the previous section the shaft coupling continues to be homokinetic if the central spherical joint is replaced by two additional sets of curves in planes placed at intervals of 120\u25e6 . Engineering realizations see in Kutzbach [10]. The contacting curves are edges of bodies. Single-point contact of curves is unsatisfactory. A much better design is the so-called ball-in-track joint shown in Fig. 13.13b . The role of the contact point is played by the center C of a spherical ball of arbitrary diameter. Motion of C relative to the shafts along prescribed symmetric curves is realized by appropriately curved shallow grooves referred to as tracks in which the ball is constrained to move. Each track is rigidly attached to one of the shafts. The element composed of a ball enclosed between two crossing tracks is called ball-in-track joint. It is a five-d.o.f. joint. Homokinetic shaft couplings with ball-in-track joints have many advantages such as small size, small dynamic unbalance and distribution of contact forces among a large number of balls"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000007_978-1-4613-2811-7_7-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000007_978-1-4613-2811-7_7-Figure2-1.png",
        "caption": "Figure 2. Lattice planes Jar a simple part.",
        "texts": [
            " It is advan tageous to keep the internal details of the resulting cells simple; the positioning of the lattice planes has been implemented to achieve this. The cells are derived from the boundary representation of the part. Infinite planes are then posi tioned coincident with each plan ar face and tangential to each cylindrical half space. This particular method is appropriate to the PADL-l domain. In a larger geometrie domain it is likely that each plane would be positioned to pass through each vertex and line of tangency of the component. The lattice planes for a simple part are illustrated in Figure 2. Slices through the resulting decom position, normal to the vertieal axis, are shown in Figure 3. ReJerences pp. J 5 3- J 54 For the present implementation, the stock is assumed to be a rectilinear block, so each resulting cell is represented as one of the following: \u2022 Stock cello The cell contains only stock material, all of which must be re moved. Any of the six cell boundary faces may be of type stock when it lies on the face of the stock, part when it lies on the face of the part and internal when it does not correspond to any real surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure13.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure13.1-1.png",
        "caption": "Fig. 13.1 Hooke\u2019s joint with frame-fixed bases e1 , e2 in position \u03d51 = 0 , \u03d52 = \u2212\u03c0/2",
        "texts": [
            " However, as will be seen in the following section, \u03c91 = const in shaft 1 does not cause \u03c92 \u2261 \u03c91 = const in shaft 2 . Shaft couplings allowing changes of relative position while maintaining the identity \u03c92 \u2261 \u03c91 are called homokinetic. The general theory of homokinetic couplings is the subject of Sect. 13.4. The engineering importance and a simple example were explained in Sect. 4.2.6. 387 J. Wittenburg, Kinematics, DOI 10.1007/978-3-662-48487-6_ 13 \u00a9 Springer-Verlag Berlin Heidelberg 2016 388 13 Shaft Couplings In the plane of Fig. 13.1 two shafts 1 and 2 are mounted in bearings such that the shaft axes intersect at point 0 under a constant angle \u03b1 . The shafts are coupled by a Hooke\u2019s joint. Its essential element is a cross-shaped central body. Each shaft is connected to this body by a revolute joint the axis of which is normal to the shaft. On the central body the two joint axes intersect orthogonally at 0 . In the figure the system is shown in a position in which one axis of the central body is in the plane of the drawing, while the other axis is perpendicular to it. The central body and the two revolute joints together constitute Hooke\u2019s joint. The angle \u03b1 is a free parameter which in Fig. 13.1 is prescribed by the other two revolute joints connecting the shafts to a frame. The entire system composed of frame, shafts, central body and of four revolute joints represents a spherical four-bar with center 0 . From Chap. 4 it is known that the degree of freedom is one. Thus, Hooke\u2019s joint transmits a rotation from shaft 1 to shaft 2 . Let \u03d51 and \u03d52 be the angles of rotation of shaft 1 and of shaft 2 , respectively, relative to the frame. They are related by a constraint equation f(\u03d51, \u03d52) = 0 . In what follows, this equation is formulated. Subsequently, various other kinematical relationships are derived from this equation. In Fig. 13.1 e1 and e2 are two reference bases fixed on the frame. Their common basis vectors e13 = e23 are normal to the plane of the two shafts, and e11 and e21 are directed along the respective shaft axes. The bases are related by the constant transformation matrix A12 = \u23a1 \u23a3 cos\u03b1 \u2212 sin\u03b1 0 sin\u03b1 cos\u03b1 0 0 0 1 \u23a4 \u23a6 . (13.1) Let n1 and n2 be unit vectors fixed on the central body along the joint axes. In the position shown in Fig. 13.1 n1 = e12 . Let this be the position \u03d51 = 0 of shaft 1 and the position \u03d52 = \u2212\u03c0/2 of shaft 2 . This means that \u03d52 = 0 is the position when n2 = e22 . In a position \u03d51 (arbitrary) n1 has 13.1 Hooke\u2019s Joint 389 in basis e1 the coordinate matrix n1 1 = [0 cos\u03d51 sin\u03d51] T . Similarly, in a position \u03d52 (arbitrary) n2 has in e2 the coordinate matrix n2 2 = [0 cos\u03d52 sin\u03d52] T . (13.2) Transformation yields the coordinate matrix n1 2 = A12n2 2 in basis e1 . The coordinate matrices n1 1 and n1 2 determine the coordinate matrix n1 3 = n\u03031 1n 1 2 of the vector n3 = n1 \u00d7 n2 ",
            " The three coordinate matrices are n1 1 = n1 2 = n1 3 =\u23a1 \u23a3 0 cos\u03d51 sin\u03d51 \u23a4 \u23a6 , \u23a1 \u23a3\u2212 sin\u03b1 cos\u03d52 cos\u03b1 cos\u03d52 sin\u03d52 \u23a4 \u23a6 , \u23a1 \u23a3\u2212 cos\u03b1 sin\u03d51 cos\u03d52 + cos\u03d51 sin\u03d52 \u2212 sin\u03b1 sin\u03d51 cos\u03d52 sin\u03b1 cos\u03d51 cos\u03d52 \u23a4 \u23a6 . (13.3) From the first two matrices the desired relationship f(\u03d51, \u03d52) = 0 is obtained. Orthogonality of the vectors n1 and n2 requires that n1 \u00b7 n2 = 0 . This is the equation f(\u03d51, \u03d52) = cos\u03d51 cos\u03b1 cos\u03d52 + sin\u03d51 sin\u03d52 = 0 or tan\u03d52 tan\u03d51 = \u2212 cos\u03b1 . (13.4) This relationship was first published in 1824 by Jean Victor Poncele\u0301t (1788- 1867) (see also Poncele\u0301t [15]). The output angle \u03d52 is an odd, \u03c0-periodic function of the input angle \u03d51 . It is independent of the sign of \u03b1 . In view of Fig. 13.1 this had to be expected. The equation yields the expressions cos\u03d52 = 1\u221a 1 + tan2 \u03d52 = sin\u03d51\u221a 1\u2212 sin2 \u03b1 cos2 \u03d51 , sin\u03d52 = \u2212 cos\u03b1 cos\u03d51\u221a 1\u2212 sin2 \u03b1 cos2 \u03d51 . \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (13.5) Differentiation of (13.4) with respect to time results in the equation (\u03d5\u03072/ cos 2 \u03d52) tan\u03d51 + (\u03d5\u03071/ cos 2 \u03d51) tan\u03d52 = 0 . This yields for the angular velocity ratio the expression \u03d5\u03072 \u03d5\u03071 = \u2212 sin\u03d52 cos\u03d52 sin\u03d51 cos\u03d51 . (13.6) Elimination of \u03d52 by means of (13.5) leads to the final formula \u03d5\u03072 \u03d5\u03071 = cos\u03b1 1\u2212 sin2 \u03b1 cos2 \u03d51 . (13",
            " Relative to each pair 2 Stanislo Fenyi, Forschungszentrum Karlsruhe 394 13 Shaft Couplings of trunnions the ring executes a screw motion. It is assumed that shaft 1 is in pure rotation relative to the frame (angle of rotation \u03d51 ). In order to function properly the bearings of shaft 2 must allow shaft 2 to execute a screw motion composed of a rotation \u03d52 and a translation z . In the special case \u03b1 = 0 , the joint is the Oldham coupling shown in Fig. 15.6 . In the special case = 0 , the joint is Hooke\u2019s joint shown in Fig. 13.1 , and all screw displacements are pure rotations. The following kinematics investigation is based on the principle of transference. The rotational part of the problem is identical with that of a Hooke\u2019s joint with parameter \u03b1 . The principle of transference is applied to Eq.(13.4): tan\u03d52 tan\u03d51 = \u2212 cos\u03b1 . (13.22) The angle \u03b1 is replaced by \u03b1\u0302 = \u03b1 + \u03b5 , and the angle \u03d52 is replaced by \u03d5\u03022 = \u03d52+\u03b5z . The angle \u03d51 is not effected because shaft 1 is, by assumption, in pure rotation. Thus, the dual form of (13",
            " This equation leads to cos2 \u03d51 = 1/(1+ cos2 \u03b1) , sin2 \u03d51 = cos2 \u03b1/(1+ cos2 \u03b1) and sin\u03d51 cos\u03d51 = cos\u03b1/(1+ cos2 \u03b1) . When this is substituted into (13.24), the maximum range of the translatory displacement of shaft 2 is found to be 13.2 Fenyi\u2019s Joint 395 zmax \u2212 zmin = 2zmax = tan\u03b1 . (13.25) The central ring is executing a periodic spatial motion without a fixed point. The periodically moving instantaneous screw axis is the generator of two closed raccording axodes. In what follows, parameter equations with \u03d51 as parameter are developed for these axodes. On the frame the basis e1 known from Fig. 13.1 is fixed. Its origin A is the point where the axis of shaft 1 intersects the first axis of the ring. On the ring the basis n with basis vectors n1, n2, n3 known from Fig. 13.1 is defined. It has its origin at the point of intersection M of the two ring axes. By writing the vector from A to M in the form z1n1 the coordinate z1 = z1(\u03d51) is defined. Let u(\u03d51) be the perpendicular from A onto the instantaneous screw axis (ISA) of the ring, and let, furthermore, \u03c9(\u03d51) be the angular velocity of the ring relative to the frame. With a dimensionless parameter \u03bb the vectors from A and from M to an arbitrary point P(\u03bb) on the ISA are rAP(\u03d51, \u03bb) = u(\u03d51) + \u03bb \u03d5\u03071 \u03c9(\u03d51) , rMP(\u03d51, \u03bb) = u(\u03d51) + \u03bb \u03d5\u03071 \u03c9(\u03d51)\u2212 z1(\u03d51)n1 ",
            " The present section is devoted to the following problem. A chain of shafts 1, . . . , n is interconnected by Hooke\u2019s joints 1, . . . , n\u2212 1 . The shafts labeled 1 and n are referred to as input shaft and as output shaft, respectively. The entire system between these two shafts represents a single joint. To be formulated are necessary and sufficient conditions guaranteeing the angular velocity ratio \u03d5\u0307n/\u03d5\u03071 \u2261 1 . First, the case n = 3 is investigated, i.e., the case of Hooke\u2019s joints 1 and 2 coupling shafts 1 , 2 and 3 . The parameter \u03b1 of Fig. 13.1 associated with Hooke\u2019s joint 1 is now called \u03b11 . The parameter \u03b12 associated with Hooke\u2019s joint 2 is the constant angle between shafts 2 and 3 . Until further below it is assumed that shafts 1 , 2 and 3 are coplanar. Since they are coplanar, only two configurations are possible in which shafts 1 and 3 intersect at an angle which is either \u03b11 + \u03b12 or \u03b11 \u2212 \u03b12 . The cross of each of the two Hooke\u2019s joints is rotating relative to shaft 2 about an axis which is perpendicular to shaft 2 . Let \u03b22 be the constant angle between these two perpendiculars"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003033_tie.2020.2982102-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003033_tie.2020.2982102-Figure4-1.png",
        "caption": "Fig. 4. Rotor structures of LSVPM machines with different rotor starting unit. (a) Rotor structure with no rotor starting unit. (b) Rotor structure with squirrel cage. (c) Rotor structure with wound winding.",
        "texts": [
            " Moreover, the Peth MMF cannot be induced in the not only the wound winding but also squirrel cage. The proper wound winding pole-pair number can be expressed as {Pr|Pr = Pslot or Pr = Pe}. (11) Some FEA Models are built to validate the earlier analysis , and the only difference is the rotor starting unit. The parameters of the LSVPM machine are given in Table IV. The steady performance of the LSVPM machine with no rotor starting unit should be investigated as a reference, and the rotor structure is shown in Fig. 4(a). The rotor structures with the rotor starting units of the squirrel cage and wound winding are also shown in Fig. 4(b) and (c), respectively. Fig. 5(a) shows the air gap flux density waveforms in steady state of LSVPM machines with different rotor starting units when electrical load is 208.4 A/cm, and the spectrum of flux density is shown in Fig. 5(b). As shown in Fig. 5, the flux density harmonics in the air gap are abundant. The flux density amplitudes of each harmonic remain constant when rotor winding pole-pair numbers are 2 and 5. The steady torque waveforms and average values of the LSVPM machine with different rotor starting units are shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002261_s12555-016-0545-1-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002261_s12555-016-0545-1-Figure1-1.png",
        "caption": "Fig. 1. The over ground gait training robot with the exoskeleton.",
        "texts": [
            " The effects of the vertical GRF on the hip and knee joint torque are formulated for the inverse-dynamicsbased muscular torque estimation. The EMG has been used for evaluation and analysis of the muscular torque [18] and the proposed method of the estimating the muscular torque is evaluated by comparing the EMG measurements of muscle efforts with the estimated torque. 2. ESTIMATION OF THE USER\u2019S ACTIVE MUSCULAR TORQUE DURING WALKING 2.1. Rehabilitation robot considered for over-ground gait training As shown in Fig. 1(a), a rehabilitation robot has been developed for over-ground gait training. The device features a lower limb exoskeletal robot connected to a free mobile base. The mobile base has four free-spinning wheels and carries all heavy peripherals such as batteries, motor drivers, and a controller. The base is expected to be used on a flat surface and maintains the user\u2019s balance during the over-ground walking. The exoskeletal robot provides the assistive joint torques via electric motors in the sagittal plane at the hip and knee joints. These motors can generate 75 Nm peak torques at each joint. The range of motion at the hip and knee joint is -20\u201370 degrees and 0\u201390 degrees, respectively. The lower limb is connected to the exoskeleton at three attachment points: the thigh, shank, and foot. The length of the thigh and shank in the exoskeleton can be manually adjusted to fit the user\u2019s leg length. The exoskeleton can support the user\u2019s body weight in part by the spring module shown in Fig. 1(a). Fig. 1(b) shows the sensor configuration of the exoskeletal robot. The exoskeleton is equipped at each joint with a BLDC motor with an encoder, and the joint torque sensor locates between the motor and link (\u2018torque sensor\u2019 in Fig. 1(b)). The technical specifications of the torque sensor are the sensing range of \u00b1120 Nm, resolution of 0.015 Nm, non-linearity of 0.03% full scale and repeatability of 0.02% full scale. The hip and knee joints have the same configuration. The smart shoe which is equipped with the pressure sensors is installed at the exoskeleton foot to measure the vertical GRF. The following section presents the method for calculating the vertical GRF with the smart shoe. 2.2. Measurement of vertical GRF with the insole pressure sensors A smart shoe with the insole pressure sensors measures the vertical GRF during over-ground walking",
            " The external torque, \u03c4EXT , is the applied torque from the environment which can be expressed by subtracting the torque needed to move the exoskeleton from the torque generated by the robot actuators as: \u03c4EXT = \u03c4R \u2212 ( MR(\u03b8)\u03b8\u0308 +VR(\u03b8 , \u03b8\u0307)+GR(\u03b8) ) + \u03c4GRF , (3) where \u03c4R \u2208 R2 is the vector of the actuator torque applied at the joint, MR(\u03b8) \u2208 R2x2 is the symmetric positive definite inertial matrix of the exoskeleton, VR(\u03b8 , \u03b8\u0307) \u2208 R2 is the vector of the Coriolis and centrifugal torques of the exoskeleton, GR(\u03b8) \u2208 R2 is the vector of the gravitational torques of the exoskeleton, and \u03c4EXT is the vector of the torque induced by the vertical GRF. The torque sensor mounted at the exoskeleton\u2019s joint (Fig. 1(b)) measures the reaction torque of \u03c4R. From Equation (3), the measured torque, \u03c4s, can be described as follows: \u03c4S =\u2212 \u03c4R =\u03c4M + \u03c4GRF \u2212 ( MHR(\u03b8)\u03b8\u0308 +VHR(\u03b8 , \u03b8\u0307)+GHR(\u03b8)+P(\u03b8) ) , (4) where the index HR represents the combined humanexoskeleton system, i.e., MHR =MH +MR, VHR =VH +VR, and GHR = GH +GR. The active muscular torque of the human user can be estimated by the measured torque \u03c4S as follows: \u03c4\u0302M = \u03c4S \u2212 \u03c4\u0302PAS \u2212 \u03c4\u0302GRF , (5) where \u03c4\u0302PAS =\u2212 ( M\u0302HR(\u03b8)\u03b8\u0308 +V\u0302HR(\u03b8 , \u03b8\u0307)+ G\u0302HR(\u03b8)+ P\u0302(\u03b8) ) , (6) and \u201chats\u201d are placed on the parameters to denote the estimated values",
            " During phase 2 (6-14 s), the magnitude of the measured torque is greater than that of the phase 1; and the pattern is not repetitive because it includes active muscular torque in addition to the passive one. Figs. 5(c) and 5(d) show the measured vertical GRF and computed GRF-induced joint torque, respectively. The computed GRF-induced torques are close to zero in the swing phase, whereas they significantly affect each joint in the stance phase. The maximum vertical GRF is under 600 N due to the body weight support by spring module as shown in figure 1(a). The gray regions show the loading response phase (0-10% of one gait cycle) and pre-swing phase (50-60% of one gait cycle) where the maximum magnitude of the horizontal GRF (Less or equal to 10 percent of vertical GRF) locates. Since the horizontal GRF is not ignorable during the loading response phase and pre-swing phase, the vertical GRF is considered reliable at the end of the mid-stance phase (30% of one gait cycle) where the minimum magnitude of the horizontal GRF (Less or equal to 2 percent of vertical GRF) locates [16]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001420_s11431-013-5433-9-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001420_s11431-013-5433-9-Figure14-1.png",
        "caption": "Figure 14 3T configuration.",
        "texts": [],
        "surrounding_texts": [
            "A class of reconfigurable parallel mechanisms can be obtained by connecting a moving platform and a base with three identical reconfigurable limbs. Figure 12 shows the 3(R1PR1R2-5R) reconfigurable parallel mechanism constructed with three reconfigurable limbs, where number 3 denotes the number of R1PR1R2-5R limbs. When the planar five-bar metamorphic linkages evolve into R phases as shown in Figure 13, an important characteristic of the reconfigurable parallel mechanisms in this class is that all the axe of joints RC and R2 intersect at a common point O. With the planar five-bar metamorphic linkages in different phases, the parallel mechanism has various configurations. Different constraints will be exerted on the moving platform and the mechanism has different degrees of freedom. The number of the planar five-bar metamorphic linkages in source phase, in T phase, in R phase, the constraint exerted by the reconfigurable limbs, and the degrees of freedom of the parallel mechanism in corresponding configurations are listed in Table 3. In the description of DoF (degrees of freedom) of the mechanism, T represents translational motion and R represents rotational motion. The 3(R1PR1R2-5R) reconfigurable parallel mechanism in 3R configuration and 3T configuration are illustrated in Figures 13 and 14."
        ]
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure7-1.png",
        "caption": "Fig. 7 Thermal FE analysis results for twisted cage bar (heating scenario 4 in Table 2)",
        "texts": [
            " The results indicate that the operating temperature of the welded rollers was about 76 C, which is 21 C ( 38 F) hotter than the temperature of a roller in normal operation, yet, the average cup temperature of the bearing with six welded rollers was only 9 C above that of a normally operating bearing. The latter provides initial proof that a number of rollers within a bearing may experience considerable heating events without affecting the average cup temperature significantly since the bearing cup averages all the roller temperatures. Further evidence of the aforementioned can be seen in the following FE model simulation. The \u201ctwisted cage\u201d heating scenario (simulation 4 in Table 2), shown in Fig. 7, simulates the test in which one of the cage bars in a steel cone assembly was bent toward the cone race forcing two adjacent rollers to misalign and rub against the cage bar producing Journal of Thermal Science and Engineering Applications SEPTEMBER 2012, Vol. 4 / 031002-7 Downloaded From: http://thermalscienceapplication.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use excessive frictional heating. The simulation results illustrate how the two misaligned rollers reach an operating temperature of 218"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003006_j.ijfatigue.2020.105483-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003006_j.ijfatigue.2020.105483-Figure3-1.png",
        "caption": "Fig. 3. Definition of four different semicircular notch surfaces obtained by layer-wise construction (Note for Type B: (i) contour and hatch patterns rather than layers are shown and (ii) build direction is perpendicular to page).",
        "texts": [
            " If the part is subjected to fatigue, then such locations will be characterized by the notch fatigue phenomenon i.e. selective fatigue crack initiation at the notch root [4]. The aim of this section is the definition of an interpretative framework of the notch fatigue behavior on the base of the quality of curved PBF surfaces in the as-built state. Therefore, the orientation of the same generic curved surface is systematically changed and qualitatively characterized in terms of segmentation and surface orientation. Fig. 3 shows four different ways of producing the same curved surface by the PBF process although surface orientation and segmentation are expected to impact differently the final surface quality. The four types of curved surfaces of Fig. 3 will be the notches of test specimens whose PBF fabrication phase will be detailed in the next section. They are arbitrarily denominated as follows: Type A- has the notch with the detailed representation of Fig. 2 (i.e. down-skin); Type A+ notch is the up-skin version of Type A- notch; Type B notch is obtained only by contouring (i.e. no stair stepping); layers of Type C notch are perpendicular to build direction. When investigating notch fatigue behavior, crack initiation will occur at the notch root. Therefore, local surface quality at the notch root is of paramount importance [14,24]. To clarify this aspect, Fig. 3 shows the direction of applied stress \u03c3 at the notch root. The stress of Type A- and Type A+ notches acts parallel to the layers while the notch stress of Type C specimen is perpendicular to the layers. The stress at Type B notch is parallel to the layer, as in Type A specimens, but acts on the contour that is typically produced with different process parameters compared to hatching [1]. Table 1 summarizes all these factors contributing in different degrees to the final quality of the four types notched specimens shown in Fig. 3. It is noted that notch root of Type A specimens is affected very significantly by the step-wise approximation of circular geometry. The layer thickness is also expected to give an increasing negative contribution in fatigue. On the other hand, the notch root geometry of Type B specimens is not affected by the layer-wise fabrication. The contour and hatch strategy typically used defines accurately the circular notch geometry by contouring. Finally, the notch root of Type C specimens is globally affected by the step-wise approximation of circular geometry but the notch root is affected the least",
            " Type C notches are of Grade II because affected slightly only by stair stepping. Type A+ notches are of Grade III because significantly affected by stair stepping while Type A- notches are of Grade IV because are down skin in addition of being significantly affected by stair stepping. This qualitative ranking of the notch surface quality (where Grade 1 is best and Grade IV is worst) will be investigated and quantified by actual fatigue testing of specimens containing notches schematically shown in Fig. 3 on the hypothesis that the better the surface quality the better the notch fatigue behavior. The stress direction with respect to layer at the notch root is an additional test variable defined in the last row of Table 1. The experimental program described here combines the previous description of the notch generation by PBF and a novel fatigue test method based on the use of miniature specimens [26]. Fatigue testing investigated the fatigue behavior of Ti6Al4V fabricated with the L-PBF process in the presence of notches of different severity, but in all cases, with as-built surfaces",
            " Apparently, the notch severity affects the nominal stress applicable to initiate a crack. According to the classical definition of notch fatigue factor (i.e. ratio of un-notched nominal fatigue strength/notched nominal fatigue strength) and using the smooth fatigue behavior as a reference (i.e. continuous line in Fig. 8), Kf is estimated as Kf = 1.11 for Kt = 1.63 and Kf = 2.2 for Kt = 4.95. Type C specimens. The notch root geometry of Type C specimens is minimally affected by segmentation, see Fig. 3, while it differs from specimen Type B because stress are perpendicular instead of parallel to the layers. So the local stress concentration is close to the analytical prediction although affected by the roughness of as-built surfaces. Fig. 9 shows the three sets of well-behaved fatigue data. The sharp notch is associated to larger scatter in cycles to failure. The notch severity affects the nominal stress applicable to initiate a fatigue crack. Again using the smooth fatigue behavior as a reference (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001765_s12161-014-0041-2-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001765_s12161-014-0041-2-Figure2-1.png",
        "caption": "Fig. 2 Cyclic voltammograms of the Nafion/TB/catalase/AuE in a 0.10 M phosphate buffer (pH 7.0) solution in the absence a and presence b of 0.20 mM H2O2. c As a and d as b for a Nafion/TB/ AuE and e and f as b for Nafion/AuE and bare AuE, respectively. Scan rate, 20 mV s\u22121",
        "texts": [
            "3 s\u22121 for Nafion/TB/AuE, respectively. These values of\u03b1 and ks are comparable to those reported for a modifier that has a hydroquinonemoiety (Nasirizadeh et al. 2011; Zare et al. 2012; Nasirizadeh et al. 2013a, b). Electrocatalytic Reduction of H2O2 In order to test the potential electrocatalytic reduction of different modified electrodes, the cyclic voltammetric responses of a Nafion/TB/catalase/AuE, Nafion/TB/AuE, Nafion/AuE, and a bare AuE were obtained in the absence and presence of a 0.20 mMH2O2 solution. Figure 2 shows the cyclic voltammetric responses from the electrochemical reduction of 0.20 mM H2O2 at the Nafion/TB/catalase/AuE (curve b), Nafion/TB/AuE (curve d), Nafion/AuE (curve e), and bare AuE (curve f). In the absence of H2O2, a pair of welldefined redox peaks of Nafion/TB/AuE (curve c) can be observed. Upon the addition of H2O2, there was a drastic enhancement of the cathodic peak current, and no anodic peak current was observed (curve d). This observation confirms that Nafion/TB/AuE is possessing electrocatalytic ability in reduction of H2O2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.8-1.png",
        "caption": "Fig. 3.8 Layout of the brake pedal, vacuum booster, and master cylinder [How Stuff Works; ROMANO 2000].",
        "texts": [
            " This function may yield a mechanical advantage that significantly increases the gain of the drum brake and the effectiveness factor as compared with disc brakes. The dynamic brake-force calculation for drum and disc and/or ring brakes is more complex since the brake-lining coefficient of friction is a function of temperature; as the lining heats during a braking manoeuvre, the effective coefficient friction increases and less fluid or air pressure or electric voltage is needed to maintain a constant brake torque. 3.3 Basics of Automotive Vehicle Braking 449 Booster and Master Cylinder - Figure 3.8 is a schematic diagram of a brake pedal, a vacuum booster, and a master cylinder. In actual practice, in passenger vehicles, as well as light and medium trucks the mechanical force gain due to the brake-pedal geometry is usually 3 to 4 and the gain through a vacuum booster is typically 5 to 9 after the booster reaches its crack point and before run-out occurs. Therefore, force applied by the driver may be multiplied by a factor of 12 to 36 at the master cylinder in order to achieve the fluid or air pressure necessary for braking",
            "29) where \u03b7 - mechanical energy efficiency; Fdriver - driver force on the brake pedal [N]; kmg - mechanical gain primarily related to the brake pedal assembly geometry and the instantaneous return spring force; kbb - brake booster gain, a function with the non-linearities of a mini- mum crack force being necessary to initiate boost and a run-out phenomenon resulting in a decreased force gain after a given input force is applied; Fs - return spring force [N]; Ap - area in the master cylinder on which the force is acting (chamber piston area) [m2]. Master cylinders are separated into primary and secondary chambers to better safety by avoiding total BBW AWB dispulsion mechatronic control system loss in the case of a failure in one portion of the sphere. The most common configuration is shown in Figure 3.8 with two chambers in a single bore [ROMANO 2000]. Proportioning Fluidical or Pneumatical Valve - Due to the dynamic vehicle mass transfer (shift), as shown in Eq. (3.16), brake fluid or air pressure that are appropriate for high-deceleration braking on front wheels usually are too high for the rear wheels; the result is that the rear wheels may tend to lock during braking. This problem can be decreased significantly through the use of proportioning fluidical or pneumatical valves. Standard proportioning for fluidical or pneumatical valves allow equal front and rear brake oily-fluid or air (gas) pressure during low input pressures (corresponding to low deceleration rates and little dynamic vehicle mass shift) but decrease the gain through the fluidical or pneumatical valve to less than one when a fixed input pressure (crack oily-fluid or gas pressure) is reached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003255_s00170-020-05766-0-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003255_s00170-020-05766-0-Figure13-1.png",
        "caption": "Fig. 13 The treatment of scanning modal. a Before repairing. b After repairing. c NUBRS surface",
        "texts": [
            " The typical steps for a failed crankshaft die\u2019s WAAM process are shown in Fig. 12. The location datum is crucial for determining the relative position between the additive remanufacturing area and the initial module. Moreover, the accuracy of the location datum can also influence the aligning error between the scanning modal (after carbon arc gouging) and the standard modal in target modal\u2019s reconstruction. The scanning modal of the die cavity is a triangle-patch model in STL format which cannot be used directly, as shown in Fig. 13a. After treatments such as filling, smoothing, and streamline removing, a modified STL modal is obtained. And then the STL model is converted into a NURBS surface to facilitate the processing in commercial software, shown in Fig. 13c. The difference between the scanning modal and the standard modal is the area for WAAM process. Before calculating the target model, the inner cavity area and the outer non-cavity area should be segmented in the scanning model, as shown in Fig. 14b. Then by segmenting the standard model with the newly generated inner-cavity patch and the cavity boundary patch, as shown in Fig. 14c, the target model can be obtained. By importing the target model into the self-developed filling path planning software and by inputting the optimal WAAM parameters of welding materials, the filling path of the target model can be generated layer-by-layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001278_j.engfailanal.2013.02.030-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001278_j.engfailanal.2013.02.030-Figure7-1.png",
        "caption": "Fig. 7. Definition of outer ring support deformation in the FEM-model (a), analysed support deformation profiles (b).",
        "texts": [
            " In numerical calculations the Young\u2019s modulus E = 201 GPa for the raceway (steel 42CrMo4) and E = 207 GPa for the rollers (steel 100Cr6) were considered, while the Poisson\u2019s ratio m = 0.3 was the same for both materials. In the \u00bd symmetry model the same material parameters were used for the rings. To analyse the influence of the bearing clearance on the internal contact force distribution in the discussed example, different positive values ranging from c = 0 mm to c = 0.8 mm were considered. Additionally, the influence of the outer ring support deformation was analysed (Fig. 7a). The deformation shape was presumed to be gradual in form of sinusoidal function (manufacturer recommendation, see reference [18]), with different deformation amplitude (A), considering two different orientations in respect to the external load \u2013 MT (Fig. 7b). Fig. 8 shows the dependence between the contact force Q and the maximum von Misses stress value rMis,max in the raceway for the investigated roller types and sizes. The location of the maximum stress for particular roller types is shown in Fig. 6. While the Q\u2013rMis,max responses of the logarithmic and ZB-profile roller are similar, the cylindrical roller shows a clearly different behaviour and the maximum von Misses stress value is considerably higher at given contact force, which can be correlated to the edge effect",
            " The difference between the results is explainable with the fact, that in the analytical calculation model rings do not deform additionally because of the loading of the bearing. To prove this concept, results of an additional FEM analysis are shown, where the rings are modelled as rigid. In Fig. 10 the internal contact force distribution is presented for the case of zero bearing clearance (c = 0) at two different magnitudes of outer ring support deformation (A), considering two different possible deformation orientations, as defined in Fig. 7b. As it can be seen from the results, the support deformation negatively influences the contact force distribution as it increases the maximum contact force in either the carrying or supporting row. As a reference the contact force distribution of the non-deformed ring support is shown. In Fig. 11 the combined influence of the bearing clearance (c = 0.8 mm) and different magnitudes and orientations of ring support deformations on the internal contact force distribution are presented. Contact force distribution in a bearing with non-deformed ring support is shown as a reference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001849_10402004.2016.1163759-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001849_10402004.2016.1163759-Figure1-1.png",
        "caption": "Figure. 1 Cross section of a radial cylindrical roller bearing",
        "texts": [
            " Above model can be used to detect the frequency spectrum having peaks at the bearing defect frequencies. In experimental work defect on inner race and on outer race is produced using Electro Discharge Machining. In experimental work data is acquired using data acquisition ACCEPTED MANUSCRIPT 9 system with relevant software (omnitrend). Simulated results are compared with the experimental results. In derivation of the equation for dynamics characteristics of a rotor bearing system, the nonlinear contact forces should be determined. Figure.1 shows the cross section of a roller bearing with a roller, an inner race and an outer race. In Figure.1, D is a pitch diameter of the bearing, and Do and Di are diameters of the outer race and inner race respectively, Dc is a Diameter clearance of the bearing. In fig (2) displacement of inner ring centre relative to outer ring centre is caused due to the radial loading, Lundsberg et al.(2,24) developed empirical relation which defines relationship between contact force and deformation for line contact for roller bearing as below. [1] Contact length is divided into \u00a3 lamina, each lamina of width b, Then, Equation[1], can be written as, [2] Radial defection due to thrust loading, radial internal clearance can be given by, = + [3] [4] ACCEPTED MANUSCRIPT 10 Where, = Total roller race way contact loading per length for jth roller and\u03bbth lamina"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003527_j.mechatronics.2021.102498-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003527_j.mechatronics.2021.102498-Figure1-1.png",
        "caption": "Fig. 1. Schematics of the sweep process of CHMs.",
        "texts": [
            " The vision-based navigation system of microrobot in dynamically changing environments remains challenging because the underlying mechanisms, the interaction between microrobot and external environment, and highly flexible adjustment strategies for collective state transitions are still being studied. Here, we put forward a magnetically actuated CHM with micron dimension for microblocks and impurities sweep in a liquid environment vailable online 30 January 2021 957-4158/\u00a9 2021 Elsevier Ltd. All rights reserved. E-mail address: xiehui@hit.edu.cn (H. Xie). ttps://doi.org/10.1016/j.mechatronics.2021.102498 eceived 25 May 2020; Received in revised form 2 January 2021; Accepted 14 Jan uary 2021 under the VMD system, as shown in Fig. 1. The velocity and direction of the CHM were modulated by the rotating magnetic field, which was adjustable in frequency, intensity, and direction. The CHM can move steadily on a predetermined trajectory and climb over barriers. The friction generated by rolling CHM mainly gives it the climbing ability through the fluid flow fields simulation experiments. This magnetic CHM can trip, transport, and release microblock approximately 200 times the volume of it. The VMD system provides two collective states: rotating CHMs pairs and rows of CHMs to address environmental changes or multitask requirements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002063_j.triboint.2015.01.024-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002063_j.triboint.2015.01.024-Figure12-1.png",
        "caption": "Fig. 12. 3D shear stress distribution of oil film at ZEV for Ree\u2013Eyring fluid.",
        "texts": [
            " However, it disappears again if the entraining velocity is altered. Wang and Yang [16] thought that the immobile oil layer was a product of special kinematic condition and participated into the lubrication. Fig. 11 shows 3D shear stress distributions of oil film for Newtonian fluid. Similar as the velocity and temperature distributions, two tiny ears also occur in the shear stress distribution of Fig. 11(c). With the increase of surface velocity, the shear stress decreases and two ears disappear. Fig. 12 gives the 3D shear stress distributions of oil film for Ree\u2013 Eyring fluid under ZEV. For Ua\u00bc Ub\u00bc0.88, the shear stress for Ree\u2013Eyring fluid gives the same appearance as that of Newtonian fluid, shown in Fig. 11(a). With the decrease of the surface velocity, the shear stress increases. For Ua\u00bc Ub\u00bc0.77\u20130.22, there are two ears appeared. The value of two ears at Ua\u00bc Ub\u00bc0.66 is remarkably larger than that of Newtonian fluid in Fig. 11(c) due to the rheological behavior. In Fig. 12(f), the two ears disappear. Fig. 13 shows the comparison of central and minimum films for Newtonian and Ree\u2013Eyring fluids. For Newtonian fluid, with increasing surface velocity, central film decreases and minimum film increases. For Ree\u2013Eyring fluid, the central and minimum film thicknesses have a distinct growth under low velocity. Then the trend of central and minimum films for different fluids is the same as that of those by Newtonian fluid model. The value of central film for Ree\u2013Eyring fluid is always lower than that of Newtonian fluid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure11.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure11.3-1.png",
        "caption": "Fig. 11.3 Two cranks of a planar four-bar connecting bodies i and b(i) . Articulation point Pi",
        "texts": [
            "4) The scalars \u03a9i ( = 1, 2, 3) are the coordinates of \u03a9i in basis ei, and the vectors pi ( = 1, 2, 3) are the basis vectors themselves. The Euler-Rodrigues parameters and the coordinates \u03a9i are related through the kinematical differential Eqs.(10.35). 5. Cylindrical joint: As articulation point an arbitrary point on the joint axis is chosen. Furthermore, the axial unit vector p fixed on both bodies, the cartesian coordinate q1 along the axis and the angle of rotation q2 about the axis are defined. With these definitions cb(i)i = pq1 + const , vi = pq\u03071 , ai = pq\u03081 , Gi = Gi(q2) , \u03a9i = pq\u03072 , \u03b5i = pq\u03082 . } (11.5) 6. In Fig. 11.3 two cranks of a planar four-bar constitute a 1-d.o.f. joint connecting bodies i and b(i) . As joint variable the crank angle \u03d5 is chosen and as articulation point Pi the endpoint of this crank. The figure explains the unit vector e along the crank, the unit vector p normal to the plane and the inclination angle \u03c7 of body i . For every value of \u03d5 two (not necessarily real) angles \u03c71,2 are determined by (17.21) and (17.22): A cos\u03c7+B sin\u03c7 = C , (11.6) A = \u22122a( \u2212r1 cos\u03d5) , B = 2r1a sin\u03d5 , C = 2r1 cos\u03d5\u2212(r21+ 2+a2\u2212r22) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002130_s12206-015-1233-4-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002130_s12206-015-1233-4-Figure2-1.png",
        "caption": "Fig. 2. Mechanical equilibrium of high-speed angular contact ball bearing.",
        "texts": [
            " o i a X o i Y O O Asin O O Acos \u03b1 \u03b4 \u03b1  = +  = (1) And the ball-inner raceway and ball-outer raceway contact deformation i\u03b4 and o\u03b4 can be expressed as Eq. (2)\uff0cwhere the subscript X represents axial projection of the line segment, and the subscript Y represents radial projection of the line segment. 2 2 ' ' ' ' 0.5 0.5 ' ' ' 2 ' ' ' 2 ( ) ( 0.5) ( ) ( 0 ( .5 ) ) i i i i b X Y o o i i o i i X X Y Y o b OO OO f D O O OO O O OO f D \u03b4 \u03b4  = + \u2212 \u2212    = \u2212 + \u2212    \u2212 \u2212 . (2) In addition, according to the Hertz contact theory, i\u03b4 and o\u03b4 can be also expressed as Eq. (3) [26]. 2 3 2 3 ( / ) ( ./ ) i i i o o o Q K Q K \u03b4 \u03b4  =   = (3) Fig. 2 shows the mechanical equilibrium of high-speed angular contact ball bearings. The gyroscopic moment Mg and the centrifugal force cF of rolling element can be expressed as Eqs. (4) and (5) [5]. 2 20.5 ( )m c mF md \u03c9 \u03c9 \u03c9 = (4) 2( )( ) sin .m RMg J \u03c9 \u03c9 \u03c9 \u03b2 \u03c9 \u03c9 = (5) Considering the equilibrium of forces in the horizontal and vertical directions, the mechanical equilibrium of rolling element can be expressed as Eq. (6). And the equilibrium equations of bearing outer ring can be expressed as Eq. (7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002727_1.1716777-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002727_1.1716777-Figure2-1.png",
        "caption": "FIG. 2. Cross section of both sticks at the completion of a \"cut.\"",
        "texts": [
            " After the crystal is rough-cut to a sphere by any convenient method, the finishing process is started by rotating one stick in a small lathe and hand holding the other against the crystal which rotates between the two sticks. Silicon carbide (280) mixed with thin oil or water does the cutting. Since the crystal tends to settle down to a position in which the soft direction is perpendicular to the axis of lathe rotation, the sphere must be removed frequently with fingers and placed in a new arbitrary position. This method differs from that of Bond in that the cutting is continued with these sticks until they come in contact and the sphere lies inside (Fig. 2). The crystal must again be moved with the fingers and the cutting continued until the sticks touch. This is repeated until it is evident that all the high points are removed, and the sticks can touch with the crystal inside in any position. Next, a set of somewhat smaller 5ticks is made, and the whole process is repeated with 400 silicon carbide. If a higher polish is desired, one may go to 600, and finer polishes, but since the cutting with these abrasives is too slow to allow the spheroid to form, one may use the more convenient method of Bond in which the sticks are smaller and do not come in contact at all (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003131_0309524x20968816-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003131_0309524x20968816-Figure6-1.png",
        "caption": "Figure 6. Slot induced eddy voltages with tilted strands.",
        "texts": [
            " The standard analysis is performed in Ringland and Rosenberg (1959), where the strands are not tilted. All the assumption mention by Ringland and Rosenberg (1959) kept as it is except the analysis is been performed for the tilted strand case. Stator bar side current assumed as, Imax coswt:Imax = ffiffiffi 2 p I , where I is the rms amperes. The leakage flux per inch of core length threading between a strand at the bottom of the stator bar and the point y from the bottom can be shown to be presented in Figure 6 [ 0 y = 0:4p ffiffiffi 2 p 2:54I coswt\u00f0 \u00de Ws y+ y2 2Y cos u \u00f01\u00de The voltage induced per inch of length of any tilted strand at position y will be ey 0 = dfy 0 dt 10 8 = 0:4p ffiffiffi 2 p 2:54Isinwt\u00f0 \u00de Ws108 y+ y2 2Y sinu \u00f02\u00de The voltage induced in strand length dx as compared with the hypothetical strand along the bottom of the stator bar side will be de 0 = 0:4p ffiffiffi 2 p 2:54Isinwt\u00f0 \u00de Ws108 y+ y2 2Y sinudx \u00f03\u00de A tilted strand selected beginning at position nY up from the bottom (where n is the starting elevation of the typical strand as fraction of stator bar height), as presented in Figure 7",
            " Usually, to assure thermal integrity of the insulation system, various qualification measure like thermal cycling test need to be performed (Istad et al., 2011) but is not the scope of this paper. One of the components, that is, responsible for the safe operation of the system of stator bar, is the air vent tube. Air vent tubes are usually used in high voltage stator bars. Air vent tubes are meant to flow the coolant in between the stator bar, to overcome the issue of the heated strand. Strands get heated due to high current flow. Ideally, the vent should look like, as presented in Figure 6. Manufacturing defect and use of soft metal for vent tube, during stator bar formation leads to vent tubes deformation. Once the formed stator bar goes to the process of vacuum pressure impregnation, resin occupies the available area. The stator bar then passes through an oven for heating, and resin turns into hard. Figure 8 represents an example of a deformed vent tube. The area affected by the deformed vent tube has been circled with red. Although deformation of vent tube known for the manufacturing industry but presented here in relation with strand tilt study"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003321_j.matpr.2020.11.415-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003321_j.matpr.2020.11.415-Figure1-1.png",
        "caption": "Fig. 1. Design in",
        "texts": [
            " The steel is also hardened by chromium and vanadium. Abrasion, oxidation, and corrosion resistance also benefit Chromium. Both chromium and carbon will increase elasticity. Table 1 shows the mechanical properties of Chromium-vanadium steel [12]. Chromium-Silicon steel is also a category of alloys of steel. Chromium has the same work to do in this alloy. While silicon is used as a deoxidizer. Table 1 shows the mechanical properties of Chromium-silicon steel [13]. The design of the helical spring (Fig. 1) was prepared in the 3d Modeling software named SolidWorks. The dimensions of the spring were the same as of spring used in the i10 Car i.e. the free length is 280 mm, wire diameter is 30 mm and the pitch is 46.67 mm. Thereafter, Finite Element Analysis (FEA) of the Model was done using ANSYS workbench 18.1. The reason behind using ANSYS workbench 18.1 has its own advantages over other software that is discussed here in a very brief manner. Ansys has a better Graphical geometry modeler, Graphical manual meshing, and a good CAD importer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001224_icra.2011.5980498-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001224_icra.2011.5980498-Figure7-1.png",
        "caption": "Fig. 7. Reference ZMP position and stability region during turning.",
        "texts": [
            " Based on the anthropometric data, a turning motion is generated to rotate each foot around the toe and the heel. Fig. 6 (b) illustrates a robot\u2019s toe trajectory of a turning pattern generated. The origin of this figure is the moving coordinate system fixed to the robot\u2019s waist, and the direction of the X axis signifies the frontal direction of the robot\u2019s waist. Fig. 6 (b) is similar to the human\u2019s toe trajectory. Reference ZMP is fixed at the midpoint between the toe and the heel during turning as shown in Fig. 7. Fig. 8 shows a turning simulation. But if the turning pattern is output to a robot, the robot falls down during turning due to a model error of the robot. So, we have developed a turning stability control as described in the following chapter. Although a robot\u2019s turning motion is generated based on a human\u2019s motion by utilizing the slip between the feet and the ground (right foot: heel contact, left foot: toe contact), the robot falls down during turning motion due to a model error and so on. Therefore, we have developed a turning stability control to inhibit the robot from falling down"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure5-1.png",
        "caption": "Fig. 5 Thermal FE analysis results for normal operation conditions. Axle was suppressed from the visual results to provide a better temperature visualization of the bearing surface (heating scenario 1 in Table 2).",
        "texts": [
            " The FE model simulation replicating the latter normal heating scenario indicates that the total heat input, Qtotal, needed to attain the 50 C cup temperature is about 529 W (within 1% of the experimentally obtained value), which translates into a roller heat input, Qroller, of 11.5 W (for each of the 46 rollers), and a maximum average roller temperature of 55 C. Thus, under normal operating conditions, the temperature of the rollers is only about 5 C (9 F) hotter than the average cup temperature. Figure 5 shows the results of the simulation along with the temperature distribution. Note that the axle was suppressed from the visual results to provide a better temperature visualization of the bearing surface. In the heating scenario \u201csix welded rollers\u201d (simulation 3 in Table 2), the FE model simulation presented in Fig. 6 replicates the laboratory dynamic test in which six rollers in one cone assembly were welded to the steel cage bars causing them to slide on the cup raceway rather than rotate. The results indicate that the operating temperature of the welded rollers was about 76 C, which is 21 C ( 38 F) hotter than the temperature of a roller in normal operation, yet, the average cup temperature of the bearing with six welded rollers was only 9 C above that of a normally operating bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000133_med.2008.4602174-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000133_med.2008.4602174-Figure3-1.png",
        "caption": "Fig. 3. The experimental quadrotor UAV",
        "texts": [
            " An important part of the UAV is the power supply system. Its basic element is the battery, that should be of high capacity while it can represent light weight; Lithium Polymer (LiPOL) batteries are used to fulfil the requirements. The power-supply sub-system produces the necessary supply voltages to the other units, furthermore monitors the battery charge, and produces alarms in the case of shortage or faults, that are sent to the main computer via CAN communication. The experimental quadrotor UAV that has been built can be seen in Figure 3. Some details of the implementation are as follows: \u2022 Four small size BLDC motors of outrunner type \u2014 with diameter 28 mm, rotation speed 1469rpm/V, maximal current 6A, and efficiency 80% \u2014 have been used. \u2022 The main power supply consist of a 3-cell LiPOL battery of capacity 4100 mAh and weight 160 g. An additional smaller battery serves as a power source for the on-board electronics. \u2022 Two normal and two reverse pitch propellers of diameter 18 cm are used as rotors. \u2022 A uniquely constructed chassis of dimensions 380 mm x 380 mm built up of light carbon and epoxy materials has been realized"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002407_1.4033387-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002407_1.4033387-Figure7-1.png",
        "caption": "Fig. 7 Coordinate systems of generating face-gear based on the multistep method",
        "texts": [
            " When the final range is greater than the range of [us min\u00f0 \u00de, us max\u00f0 \u00de], the entire working part can be grinded out completely by the worm as shown in Fig. 5. Therefore, the grinding process can be divided into multiple steps which can be superimposed together to obtain the complete tooth surface of the face-gear. 3.2 Generation of Face-Gear Surface Based on Multistep Method. The coordinate systems of generating the face-gear by a worm based on the multistep method are established, as shown in Fig. 7. Coordinate systems Ow and O2 are rigidly connected to the worm and the face-gear, respectively, and Ow0, Om, Os0, Od, and O20 are fixed coordinate systems. Ews is the shortest distance between the axis zw and xs. Parameter lw of the translational motion is provided as collinear to the axis of the shaper. ud is the additional swing angle of the worm and the shaper. The position vector of the face-gear surface is determined by the worm with the multistep method as r2 hs;us;uw; lw\u00f0 \u00de \u00bcM2w uw; lw\u00f0 \u00derw hs;us\u00f0 \u00de Nw hs;uw\u00f0 \u00de v w2;lw\u00f0 \u00de w \u00bc f 1\u00f0 \u00de w2 hs;us;uw; lw \u00bc 0 Nw hs;uw\u00f0 \u00de v w2;uw\u00f0 \u00de w \u00bc f 2\u00f0 \u00de w2 hs;us;uw; lw \u00bc 0 8>>< >>: (11) where the matrix M2w describes the coordinate transformation from Ow to O2",
            " 10(a). The detailed coordinate transformation mapping of the VERICUT model is shown in Fig. 10(b). The movable coordinate systems OA;OB;OC are rigidly connected to the worm, the face-gear, and the machine model, respectively, and rotate around their axes, respectively. At the same time, the coordinate systems OA0; OB0; OC0 are fixed in the relative part of the machine model. MB;A is the coordinate transformation matrix from OA to OB. M2;w is the coordinate transformation matrix from Ow to O2 (Fig. 7). The motion relationship of each axis in the VERICUT model can be obtained due to MB;A \u00bcM2;w. 4.2 Verification of Integrity of Tooth Surface During the Grinding Process 4.2.1 Simulation of the Original Grinding Method. From the analysis above, it is clear that the whole working part may not be covered completely by the worm tool when the original method is used during the grinding process. In order to verify the correctness of the theoretical analysis, the simulation of the original method is carried out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure4.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure4.3-1.png",
        "caption": "Fig. 4.3 Motions and locations of the spinning disc under the action of the external torque T applied to the gimbal",
        "texts": [
            " The spinning disc with the angular velocity \u03c9 located symmetrically regarding its supports of the gimbal 1, which rotates on supports of the gimbal 2 and later one rotates on pivots of the platform 4 (Figs. 4.3a and 4.4). The action of the external torque is applied to outer gimbal 2 of the gyroscope manifests the motions of the inner gimbal 1 around axis ox of the coordinate \u2211 oxyz. These motions of the gimbals around axes are expressed by the mathematical model of ratio for the angular velocities (Eq. 4.9). The torque T and inertial torques acting on the spinning disc start to turn the gimbal 2 in the counterclockwise direction around axis oy (Fig. 4.3a). The resulting inertial torques (T p\u00b7y \u2212 T r\u00b7x) generated by the spinning disc turn intensively the gimbal 1 in the clockwise direction around axis ox by the ratio of Eq. (4.10). The turn of the Fig. 4.4 Test stand of Super Precision Gyroscope \u201cBrightfusion LTD\u201d gimbal 2 on the small angle \u03b3 = 2\u25e6 55\u2032 71\u2032\u2032 around axis oy, under the action of the resulting torque (T \u2212 T p\u00b7x \u2212 T r\u00b7y), turns the gimbal 1 in the clockwise direction around axis ox on the maximal angle \u03d5 = 164,841101855\u00b0 around axis ox. The following turn of the gimbal 2 does not turn the gimbal 1 that keeping the vertical location of the spin axis that coincides with axis oy. The final location of the gimbals is represented in Fig. 4.3b. The practical test of the gimbal motions was conducted for the horizontal location of the spinning disc and its following turn until vertical. At the starting condition, the location of the spinning disc and the outer gimbal represented in Fig. 4.5a. The minor turn of the outer gimbal in the counterclockwise direction around the vertical axis oy on the angle \u03b3 leads to the big turn of the inner gimbal in the clockwise direction around the horizontal axis ox on the angle \u03d5 (Figs. 4.4 and 4.5b).The inner gimbal turns until the vertical location of the spinning disc axis with the minor turn of the outer gimbal on the angle \u03b3 (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002127_cjme.2015.0710.091-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002127_cjme.2015.0710.091-Figure2-1.png",
        "caption": "Fig. 2. Spatial thirteen-links mechanism with double loops",
        "texts": [
            " Obviously, the eight screws are linearly dependent and six of them are independent, which indicates the rank of the screw system is six. So there is no constraint screw and no over-constraint, i.e. 0 = . Based on Eq. (1), there is ( )6 1 6(4 4 1) 8 0 2.iM n g f = - - + + = - - + + =\u00e5 (3) The mobility of the mechanism is two, including one local freedom of link BC, which can rotate freely around its own axis. That occurrence is because of a linearly dependence of the screw system in Eq. (2). This mechanism as Fig. 2 shows contains thirteen links and fourteen kinematic pairs, which forms two loops. The first loop, ABCGA, has seven revolute pairs, where four of them are parallel to each other, and the other three are also parallel to each other. But the axes of the two group screws are perpendicular to each other. The second loop, CDEHNC, has ten kinematic pairs, but only seven of them belong to the second loop independently, and the axes H, I, J are parallel to that of L, M, N. CHINESE JOURNAL OF MECHANICAL ENGINEERING \u00b73\u00b7 (1) For the first loop, under the coordinate system A-XYZ, four axes of kinematic pairs A, B, F, G are all along Y-axis and the axes of other three pairs are along Z-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001288_tec.2013.2245332-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001288_tec.2013.2245332-Figure2-1.png",
        "caption": "Fig. 2. Main flux saturation characteristic and FC function.",
        "texts": [
            " Specifically, neglecting stator and core losses, the measured rms stator line currents Ias,NL and rms line-to-neutral voltages Vas,NL are related to \u03bbm and im by \u03bbm \u2248 \u221a 2 (Vas,NL \u2212 \u03c9eIas,NLLls) \u03c9b (15) im \u2248 \u221a 2Ias,NL (16) where \u03c9e and \u03c9b are the operating and base frequencies, respectively. Thereafter, curve-fitting techniques such as piecewise linear interpolates, polynomials, arctangent functions [31], etc., can be used to represent the saturation characteristic. Regardless of the method, for the purpose of this paper, this characteristic is represented by the function (lookup table) im = F (\u03bbm ) (17) or conversely, \u03bbm = F\u22121 (im ) . (18) The relationship between the saturated main flux \u03bbm and magnetizing current im is qualitatively depicted in Fig. 2 (right-hand side), wherein an unsaturated flux is also shown as a straight line. C. Implicit FC Method The basic idea of the FC approach is to define the correction function f(\u03bbm ) as the difference between the saturated and unsaturated curves as shown in Fig. 2 [4]. Extending this approach to qd-axes, the corrected (saturated) flux linkages in each axis become \u03bbmq = Lmu (iqs + iqr ) \u2212 fq (\u03bbm ) (19) \u03bbmd = Lmu (ids + idr ) \u2212 fd (\u03bbm ) (20) where for a symmetrical induction machine fq (\u03bbm ) = \u03bbmq \u03bbm f (\u03bbm ) (21) fd (\u03bbm ) = \u03bbmd \u03bbm f (\u03bbm ) . (22) Substituting (5), (7), (21) in (19) and (6), (8), (22) in (20), and solving for \u03bbmq and \u03bbmd yields \u03bbmq = Laqu ( \u03bbqs Lls + \u03bbqr Llr ) \u2212 Laq Lmu \u03bbmq \u03bbm f (\u03bbm ) (23) \u03bbmd = Ladu ( \u03bbds Lls + \u03bbdr Llr ) \u2212 Lad Lmu \u03bbmd \u03bbm f (\u03bbm ) (24) where Laqu = Ladu = ( 1 Lmu + 1 Lls + 1 Llr )\u22121 ",
            " 5 as \u03bbm = \u221a( \u03bbmq m )2 + \u03bb2 md (59) im = \u221a (imqm)2 + i2md. (60) After this rescaling, the d-axis saturation function (57) is applied to the main flux saturation as im = Fd (\u03bbm ) (61) or conversely \u03bbm = F\u22121 d (im ) . (62) As it can be seen from (58)\u2013(60), this formulation automatically covers both salient-pole and round-rotor machines. For the latter case, m = 1, and the equations become similar to those presented in Section II-B. C. Implicit FC Method For the implementation of saturation in the model, the FC function f(\u03bbm ) depicted in Fig. 2 is redefined using the synchronous machine saturation characteristic (61). It is then possible to write the corrected (saturated) magnetizing flux for each axis as \u03bbmq = Lmqu (iqs + ikq1 + ikq2) \u2212 m \u00b7 fq (\u03bbm ) (63) \u03bbmd = Lmdu (ids + if d + ikd) \u2212 fd (\u03bbm ) (64) where fq (\u03bbm ) = \u03bbmq m \u00b7 \u03bbm f (\u03bbm ) (65) fd (\u03bbm ) = \u03bbmd \u03bbm f (\u03bbm ) . (66) Substituting (47), (50), and (65) into (63) and (48), (51), and (66) into (64), and solving for \u03bbmq and \u03bbmd yields \u03bbmq = Laqu ( \u03bbqs Lls + \u03bbkq1 Llkq1 + \u03bbkq2 Llkq2 ) \u2212 Laq Lmqu \u03bbmq \u03bbm f (\u03bbm ) (67) \u03bbmd = Ladu ( \u03bbds Lls + \u03bbf d Llf d + \u03bbkd Llkd ) \u2212 Lad Lmdu \u03bbmd \u03bbm f (\u03bbm ) (68) where Laqu = ( 1 Lmqu + 1 Lls + 1 Llkq1 + 1 Llkq2 )\u22121 (69) Ladu = ( 1 Lmdu + 1 Lls + 1 Llf d + 1 Llkd )\u22121 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.15-1.png",
        "caption": "Fig. 17.15 Roberts/Tschebychev theorem",
        "texts": [
            " In this case, the ratio L4/L1 is > 1 in every position, and it increases monotonically when the blades are closing. With shears of this kind reinforcement steel rods of 15 mm diameter can be cut by hand. Every point fixed in the plane of the coupler traces a coupler curve when the four-bar is moving through its entire range. It is the complexity of these curves to which the four-bar owes much of its importance in engineering (see Fig. 17.2). In the following sections properties of coupler curves are investigated. The curvature of coupler curves was the subject of Sect. 15.3.3 (see Fig. 15.19). Figure 17.15 is started by drawing the four-bar A0A1B1B0 and a point C fixed in the plane of the coupler A1B1 . This plane is represented by the coupler triangle (A1,B1,C). Subject of investigation is the coupler curve generated by C . To this basic figure lines A0A2C and B0A3C are added thus creating two parallelograms. In the next step, triangles similar to the coupler triangle are drawn as shown with bases A2C and A3C . This results in points B2 and B3 . Finally, another parallelogram defining the point C0 is drawn",
            "16 a position is shown in which the links of four-bar A0A1B1B0 are stretched out in the line A0A\u03031B\u03031B\u03030 . The new positions of the remaining points (denoted by the symbol tilde) are determined by the three parallelograms not shaded and by the three similar coupler triangles (shaded). In this position all three fourbars have their links stretched out. The triangle (A0B\u03030C\u03030) is similar to the coupler triangles. It is this figure from which all lengths of the other two four-bars are most easily obtained. Figure 17.15 is particularly simple if the coupler point C in the fourbar A0A1B1B0 is located on the line A1B1 of the coupler. This case is characterized by \u03b1 = 0 or \u03c0 and z real. From this it follows that in all three four-bars C is located on the coupler line. The positions of C0 , A2 , B2 , A3 and B3 are determined by the equations C0 = B0z , A2 = (B1 \u2212 A1)z , B2 = B1z , B3 = C + (B0 \u2212 A1)z with real z . Figure 17.17 explains how to proceed geometrically when the four-bar A0A1B1B0 and point C on the coupler are given. As in Fig. 17.15 A2 and A3 are constructed by drawing the parallelograms A0A1CA2 and B0B1CA3 . Next, B2 and B3 are constructed, the former as point of intersection of the lines A0B1 and CA2 and the latter as point of intersection of the lines B0A1 and CA3 . Finally, C0 is constructed as in Fig. 17.15 by drawing the parallelogram B2CB3C0 . In what follows, the general case shown in Fig. 17.15 is considered again. The parallelity of lines in parallelograms in combination with the rigidity of coupler triangles has the consequences: If one of the links A0A1 , A2B2 and 17.8 Coupler Curves 593 C0B3 is fully rotating, all three of them are fully rotating, and if any one of them is not fully rotating, none of them is fully rotating. The same statements apply to the links B0B1 , A3B3 and C0B2 . The combination of these arguments leads to the following statements: 1. If four-bar A0A1B1B0 is a double-rocker of second kind, the other two four-bars are double-rockers of second kind as well",
            " Identical angular velocities are produced also by means of three gears with centers fixed in the base according to Fig. 17.18a . The two outer gears have arbitrary, but equal diameters, and each of them is rigidly connected with one of the two links. The central gear has arbitrary diameter and arbitrary location. When the central gear is set into motion, C is generating the same coupler curve that is generated by the three four-bars. The linkage shown in Fig. 17.18b is composed of some of the links in Fig. 17.15 . The degree of freedom is two. The parallelogram is free to rotate as rigid body about A0 . It may also deform. Hence it is possible to guide B1 along an arbitrarily prescribed curve (within a certain workspace). From (17.73), B2 = B1z , it follows that B2 generates the same curve rotated through the angle \u03b1 and multiplied by the factor |z| = A1C/A1B1 . This linkage is called Sylvester\u2019s plagiograph [38], v.3 . If, in particular, B1 is guided along a straight line f1 (arbitrary), B2 is moving along a straight line f2 which is rotated counter-clockwise against f1 through \u03b1 ",
            " Given three circles a , b , c and a triangle (A,B,C), there exist six (not necessarily real) positions of the triangle in which A lies on a , B on b and C on c . This result is important for Sect. 17.10 on planar robots. The equation \u0394 = 0 can be written in the form( x\u2212 2 )2 + ( y \u2212 2 cot\u03b2 )2 = ( 2 sin\u03b2 )2 . (17.87) It is the equation of the circle shown in Fig. 17.21 . The circle passes through A0 and B0 . It has the central semi-angle \u03b2 and, hence, the peripheral angle \u03b2 . It was shown that \u03b2 is also the angle at C0 in the triangle (A0,B0,C0) of Fig. 17.15 . Therefore, also C0 is located on the circle. From this fact Roberts concluded Theorem 17.2 on the existence of three cognate four-bars generating one and the same coupler curve. The three centers A0 , B0 and C0 are referred to as singular foci, and the circle itself is called circle of singular foci. Since \u0394 equals zero on the circle, cos\u03b1 and sin\u03b1 are indeterminate if the coupler point is located on the circle. Indeterminate means that at least two different positions of the four-bar generate one and the same point of the coupler curve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000421_cec.2007.4424647-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000421_cec.2007.4424647-Figure6-1.png",
        "caption": "Fig. 6. (a) The first prototype of the robot capable for selfassembling in a multi-robot organism; (b) The worm gears connecting integrated motors and wheels.",
        "texts": [
            " The most critical operation for multi-robot organism is the self-assembling from separate robots into one organism. For this we tested possibility and accuracy of docking approach with current Jasmine IIIp robots. Robots are lead by IR light, emitted by the first robots. The second robots, by following this light, try to dock to the first robots, see Fig. 5. As demonstrated by many experiments, accuracy of docking is about +-5mm. Based on these experiments we developed the first prototype of the robots capable for selfassembling, shown in Fig. 6(a). Each robot has three female docking connectors and one male docking connector in the front of the robot. Two female docking connectors are placed in the wheels, so that robots have individual locomotion based on a differential drive. These docking connectors can rotate. The third female docking connector is placed behind and is capable for vertical rotation. It has a strong motor. Male docking connector has a hook-based lock mechanism. All female connectors and hook-based lock are driven by DC motors, integrated into plastic chassis. Transmission between motors and wheels is done by a worm gear, as shown in Fig. 6(b). Advantage of the worm gear is that this can fix the position of wheels, so that it can statically keep the required position (configuration of the organism) and does not consume energy in this mode. In this way, each robot has two degrees of freedom: one vertical-plane rotation behind with strong forces and one rotation around the wheel axis. IV. THE FIRST TOPOLOGICAL EXPERIMENTS Before further development of self-assembling robots, we performed a series of topological experiments. They are related to capabilities of planar self-assembling and demonstrated 3D topologies; a relation between individual degrees of freedom (DOF) and collective DOF for the organism; locomotion principles and finally encountered open points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.6-1.png",
        "caption": "Fig. 3.6 Arbitrary forces acting on an automotive vehicle [GILLESPIE 1992].",
        "texts": [
            " An Euler--Lagrange IInd order differential equation for dynamic braking performance can be obtained from Newton's second law written for the x-axis longitudinal direction. The sum of the external forces acting on a vehicle body in a given direction is equal to the product of its mass and the acceleration in that direction. Automotive Mechatronics 438 Relating this law to straight-line automotive vehicle braking, the significant factors are shown in Eq. (3.2) and the sum of the forces acting on the vehicle is shown in Figure 3.6 [WONG 1978; GILLESPIE 1992]. \u03a3Fx = mv ax = mv dx = Fxf + Fxr + Dxa + mv g sin \u0398 + fr mv g cos \u0398 , (3.2) where mv - mass of the automotive vehicle [kg]; ax - linear acceleration in the forward sense of longitudinal direction [m/s2]; g - linear acceleration due to gravity [m/s2]; dx = ax - linear deceleration in the forward sense of longitudinal direction [m/s2]; Fxf - front-wheel brake (FWB) force [N]; Fxr - rear-wheel brake (RWB) force [N]; Dxa - aerodynamic drag (considered to be acting at a point) [N]; fr = (Rxf + Rxr)/mv g cos \u0398 - rolling resistance coefficient; \u0398 - uphill grade (angle of on/off road surface) [rad]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure9.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure9.6-1.png",
        "caption": "Fig. 9.6 Bevel differential (a) and angular velocity diagram (b)",
        "texts": [
            " The geometrical construction just demonstrated for two wheels is applicable to arbitrarily complicated bevel gear trains with degrees of freedom F \u2265 1 . All wheel axes as well as all generators of all pitch cones are passing through a common point. Every wheel axis and every generator common to the cones of two wheels determines the direction of a relative angular velocity. 9.7 The Ancient Chinese Southpointing Chariot 307 This fact in combination with (9.71), (9.72) or (9.73) determines all angular velocities if F angular velocities are arbitrarily prescribed. Example: In the bevel differential shown in Fig. 9.6a with bodies 0, . . . , 4 the gear box 4 can rotate relative to the frame 0 . The bevel differential has the degree of freedom F = 2 . The lines with indices ij determine the directions of the angular velocities \u03c9ij (i, j = 0, . . . , 4 ; j = i ) . Any two angular velocities can be prescribed arbitrarily. Then the remaining ones are uniquely determined. In Fig. 9.6b the angular velocity diagram is shown. End of example. Subject of this section is an engineering problem. In Needham [7] it is reported that in China possibly as early as 3000 years ago and with certainty at about 200 a.C. during imperial processions two-wheel chariots were displayed on which a rotating wooden statue pointed its arm due south independent of driving maneuvers. In a rather detailed description dated 1107 a gear train connecting the wheels of the chariot to the vertical axis of the statue is described"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002672_j.measurement.2019.107096-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002672_j.measurement.2019.107096-Figure1-1.png",
        "caption": "Fig. 1. Sectional view of a 3D model of gearbox sy",
        "texts": [
            " Compared with only considering the gears subsystem, the solution of the dynamic force, especially the bearing force of the heavy-duty gearbox, is more accurate, which is of positive significance to further improve the bearing failure status of the heavyduty system such as shearer. System modeling considering the flexibility of the box provides theoretical support for its lightweight design. In addition, the paper also illustrates the different effects of internal and external excitation on the dynamic behavior of coupled systems. The gearbox system studied in this paper includes multistage parallel-shaft spur gears transmission subsystem, two-stage planetary gears transmission subsystem and box substructure system. Fig. 1 is a cross-sectional view showing a 3D model of the gearbox in a continuous miner. Fig. 2 is a simplified model of the coupling system between the gears-rotors and the box. In the Fig. 2, shaft 1 ~ shaft 7 are the drive shafts of the multistage parallel-shaft transmission subsystem. In the modeling of multistage parallel-shaft gears rotors subsystem, referring to references [7,8], the modeling of transmission shaft 1 ~ shaft 7 is simulated by beam element. Referring to reference [8], the spring element is used to simulate the bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure1.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure1.5-1.png",
        "caption": "Fig. 1.5 Example of commercial converter unit and integrated semiconductor module which can be used to build an inverter [16]",
        "texts": [
            " Left, a very small (less than 1 W) drive. Right, a high power (in excess of 10 MW) example [17] . . . . . . . . 3 Fig. 1.3 Example of commonly used machine configurations. (a) Induction machine. (b) Synchronous machine. (c) Switched reluctance machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Fig. 1.4 Useful lifetime of insulation material versus operating temperature (class H). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Fig. 1.5 Example of commercial converter unit and integrated semiconductor module which can be used to build an inverter [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Fig. 1.6 Example of modern inverter technology with standard communication interfaces [25] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Fig. 1.7 Example of an electrical vehicle propulsion unit which utilizes a liquid cooled AC\u2013DC converter and 55 kW switched reluctance machine [6, 8] ",
            " \u2022 Availability of compact high-performance digital processors with extensive I/O capabilities that can be readily interfaced with the equally compact power electronic drive circuitry required to control the switching devices. 1.2 Drive Technology Trends 7 \u2022 Design and manufacturing improvements in passive devices most notably in capacitors which play a key role in terms of overall voltage source converter sizing and costs. The culmination of the improvements indicated above is exemplified by the availability of building blocks as shown in Fig. 1.5, to construct a complete inverter and \u201coff-the-shelf\u201d commercial inverters, as shown in Fig. 1.6, which can be readily interfaced to electrical machines. Note that the term inverter refers to a dc to ac converter, as shown in Fig. 1.1. In this section, the emphasis has been predominantly placed on improvements in volumetric power density. However, improvements in converter technology leading to the ability to operate at much higher electrical fundamental frequencies have also been instrumental in realizing high speed drives"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002102_s00170-015-6915-7-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002102_s00170-015-6915-7-Figure2-1.png",
        "caption": "Fig. 2 Coordinate systems for deducing interpolations",
        "texts": [
            " According to this machining principle, face gears can be grinded on a machine tool with 5 degrees of freedom, and the axes of A, B, X, and Z must be linked. 2.2 CNC interpolation algorithm The grinding disk swings around the axis of the virtual shaper when a face gear is being grinded. But, the rotation center OB of the machine axis B is not on the axis O's of the virtual shaper; interpolations must be applied here for determining the feed displacements of the grinding disk on each axis. As shown in Fig. 2, point O2 is on the locating surface of the workpiece; point Ob is the intersection of the disk symmetry plane and the spindle axis; system Sf (Of, Xf, Yf, Zf) is the machine coordinate system, and the original point Of is the intersection point of axis A and the vertical plane through point Ob. The workpiece can move along axis Xf, the rotary rack can move along axis Zf and Yf, and the grinding disk and the spindle can rotate along with the rotary rack together. The axis (Os) of the virtual shaper is stationary relative to the face gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003264_tvt.2020.3013342-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003264_tvt.2020.3013342-Figure3-1.png",
        "caption": "Fig. 3. Transient electromagnetic field of the ECB. (a) Mesh. (b) Joule loss density P(r,z,\u03b1n) on the stator.",
        "texts": [
            " By utilizing the principle of lumped heat transfer method and the working characteristics of the ECB, the improved transient coupling model simplifies the time-consuming sequential calculation of the electromagnetic field analysis of the standard model into parallel calculations. The 3D transient electromagnetic field can be modeled by the finite element method (FEM) to obtain the distribution of the eddy current density and braking torque of the ECB [15]. The model consists of a stator, a rotor and a set of coils, as shown in Fig. 3(a). Since the ECB is cyclically symmetric in the circumferential direction, it is modeled by one period. The computational domain space is divided by the tetrahedral mesh. Considering the influence of the skin effect, the gradient of eddy current density on the stator\u2019s surface is large, and the mesh on it needs to be denser. The material of the stator and the rotor is 20# steel, and the coils are made by copper. After defining the rotor\u2019s speed and magnetic potential excited by coils, the transient electromagnetic field calculation by FEM is performed",
            " 4 that the steady-state braking torque of the ECB is quickly reached, after the coils provide a constant current. Therefore, the response time of the electromagnetic field can be ignored during the coupling calculations. When the braking torque stabilizes, the calculation ends, and the eddy current density and the braking torque are output as the analysis results. The quasi-stationary distribution of the joule loss density (P(r,z,\u03b1n)) generated by the eddy current on the arc (l(r,z)) could be obtained after the calculation, as shown in Fig. 3(b). The joule lose density is numerically the same as the heat generation rate in the heat transfer model. Because of the high speed of the rotor, the average P(r,z,\u03b1n) on l(r,z) can be taken as the heat generation rate (QFEM(r,z)) in the thermal analysis by (8). max 1 1 1 FEM 1 2 max ( , , ) ( , ) , ( , ) 2 2 n n n n P r z L L Q r z r r r z n          (8) where nmax is the total number of elements on l(r,z). The QFEM\u2019(r) can be obtained by averaging QFEM(r,z) in the axial direction for comparison with the results obtained by analytical calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002777_iceeot.2016.7754868-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002777_iceeot.2016.7754868-Figure1-1.png",
        "caption": "Fig. 1 quadrotor structure",
        "texts": [
            " The quadrotor also possesses more advantages compared to standard helicopters in terms of small size, efficiency, and safety. In this paper linearised model of quadrotor is considered while applying optimal control to the uncoupled states of the quadrotor and full dynamic model is considered while designing PD controller. Simulations are done using MATLAB and quadrotor outputs are analysed. II. STRUCTURE OF QUADROTOR The quadrotor is assumed to be symmetric with respect to the x and y axes. A general structure is presented in fig.1. The model analyzed in this paper assumes the following: \u2022 The structure is rigid. \u2022 The structure is symmetrical. \u2022 The center of gravity and the body fixed frame origin coincident. \u2022 The propellers are rigid. \u2022 Thrust and drag are proportional to the square of propeller\u2019s speed. III. QUADROTOR DYNAMICS The orientation of quadrotor is determined by roll angle (\u03c6), pitch angle ( ) and yaw angle ( ).The angles are depicted in the fig.2 The control inputs for guiding and stabilizing the quadrotor are mapped from the four independent motor thrusts to one force and three torques: the total thrust force, roll torque, pitch torque, and yaw torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure13-1.png",
        "caption": "Fig. 13. Pressure distribution in the oil film for Db = 0.9 tilt angle change.",
        "texts": [],
        "surrounding_texts": [
            "On the basis of the presented theoretical background a computer program has been developed. By using this program, the influence of machine settings for pinion finishing as are: the sliding base setting (c), basic radial (e), basic offset setting (g), basic tilt angle (b), basic swivel angle (d), machine root angle (c1), velocity ratio in the kinematic scheme of machine tool (ig) and basic cradle angle (w0) (Fig. 2), on maximum oil film pressure (pmax) and temperature (Tmax), EHD load carrying capacity (W), and on power losses in the oil film (fT) was investigated. In this paper, the term of \u2018\u2018EHD load carrying capacity\u201d is used for the load calculated by Eq. (17) for a prescribed value of the minimum oil film thickness. The investigation was carried out for the hypoid gear pair of the design data given in Table 1. The starting machine tool setting parameters for the generation of pinion tooth blanks are given in Table 2, and the lubricant characteristics and operating parameters in Table 3. The obtained results are presented in Figs. 3\u201318. Factors kpmax , kTmax , kW and kfT represent the ratios of the maximum oil pressure and temperature, EHD load carrying capacity, and power losses in the oil film, calculated for varied machine tool setting parameters, and the same EHD characteristics obtained for the basic set of machine tool settings for pinion teeth finishing, given in Table 2. The pressure and temperature distributions in the oil film for the basic set of machine tool setting parameters are shown in Figs. 3 and 4. The maximum temperatures across the oil film are plotted. As it was mentioned earlier, a modified hypoid gear pair with theoretical point contact is treated. The investigations have shown [45] that as the tooth surface modifications are relatively small and the conjugation of the mating surfaces is relatively good, thus the point contact under load spreads over a surface along the whole or part of the \u2018\u2018potential\u201d contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal. In Figs. 3 and 4, this line of minimal separations is plotted. It can be noted that the crest of the pressure surface corresponds to this line. The influence of sliding base setting (c) on EHD lubrication characteristics is shown in Fig. 5. Several observations can be made: a small change in sliding base setting causes sharp increase in the maximum oil pressure and a moderate improvement of the EHD load carrying capacity. The change of the friction factor is quite opposite than that of the EHD load carrying capacity: with an increase in W the friction factor is reduced, and vise versa. Finally, the change in sliding base setting appears to have very little influence on maximum oil temperature. From Fig. 6, it can be seen that a sliding base setting change of Dc = 0.125 mm causes an increase in maximum oil pressure of 21% and 7% in EHD load carrying capacity, and also a reduction in friction factor of 4%. The influence of basic radial setting (e) is similar to that for sliding base setting (Figs. 7\u20139), but there is a significant drop in maximum oil pressure and EHD load carrying capacity for negative values of De, followed by a significant increase in power losses. Therefore, such a change of basic radial setting worsens the conditions of EHD lubrication and it should be avoided. The basic offset setting (g) of the head-cutter has a significant influence on the EHD lubrication characteristics, by its decrease the EHD load carrying capacity can be considerably improved and the friction factor reduced (Figs. 10 and 11). The adjustment of the basic tilt angle (b) should be made very carefully: a small decrease in its value significantly improves the EHD load carrying capacity, but its bigger change sharply reduces W and increases the friction factor (Figs. 12 and 13). The effects of the change of basic swivel angle (d, Figs. 14 and 15) and of machine root angle (c1, Fig. 16) are very similar to that of basic tilt angle. The other two machine tool setting parameters, the velocity ratio in the kinematic scheme of machine tool (ig, Fig. 17) and the basic cradle angle (w0, Fig. 18) have an almost identical effect on EHD lubrication as the other machine tool setting parameters: a small change in their adjustment moderately improves the load carrying capacity and reduces the friction factor, but their bigger changes have a negative effect on EHD lubrication."
        ]
    },
    {
        "image_filename": "designv10_12_0002001_icstc.2018.8528714-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002001_icstc.2018.8528714-Figure1-1.png",
        "caption": "Fig. 1. Design parameter for analytic calculation.",
        "texts": [
            " For this study, h was assumed to have an equal value to water depth height (d) in a channel, therefore: h = d () After the blade height (h) and outer diameter (Do) were calculated, the following calculation was used to determine the inner diameter (Di): Di = Do \u2013 2h () The angular distance between blades () was calculated using:  = () Then, the blades number (Z) proportional to the undershot waterwheel\u2019s dimensions could be determined: Z = ) Equations (5) and (6) were adapted from the Pelton turbine design principle. This was needed to calculate the second blade position right above the water surface and assumed that maximum hydrostatic pressure was acting on the vertical blade. The geometric relationship between (1) and (5) can be seen in Fig. 1. After the blade\u2019s geometry was determined, further analysis was conducted to calculate potential value of hydrostatic pressure, rotation per minute (RPM), and output power for this operation. Senior, Wiemann, and M\u00fcller [19] generated an equation for hydrostatic pressure on a vertical blade, thus leading to theoretical output power of the system. As shown in Fig. 2, hydrostatic force (FR) acts along the vertical blade. Where water depth upstream (d1), water depth downstream (d2), and width of blade (W), gravity (g), and water density (r)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002113_j.bios.2015.11.074-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002113_j.bios.2015.11.074-Figure2-1.png",
        "caption": "Fig. 2. Electrical configurations used for the EFCs cascade in the device D1. A: top view of the D1, showing the entry, middle and exit anode and cathode electrode pairs, leading respectively to EFC1, EC2 and EFC3. B: top view of D2. The electrochemical performance of the fuel cells in the cascade was tested in the case of independent electrical connection (C), and of parallel connection (D).",
        "texts": [
            " To prevent any activity loss due to storage, the hPG electrodes were therefore used right after the enzyme immobilization. Two single-channel devices were tested and their performance compared. The first configuration, D1, was characterized by three pairs of anode and cathode, which led to a cascade of three EFCs, due to the laminar flow in the channel. The resulting fuel cells have been indicated as: EFC1, EFC2 and EFC3. The fuel cells were operated in two different electrical configurations, as represented in Fig. 2. In one configuration (Fig. 2C) each EFC was connected independently to a fixed resistor and a voltmeter. This configuration allowed the individual analysis of the performance of each EFC. In the second configuration (Fig. 2D), the EFCs were electrically connected in parallel to a resistor and a voltmeter. A second device, D2, was also tested for comparison. D2 was characterized by the same geometry and cross-sectional area of D1, but had a shorter channel to host only one pair of electrodes, leading to a control fuel cell, named as EFCc. Both D1 and D2 were operated in continuous mode and fed with an aerated PBS solution of glucose (27 mM) at a flow rate of 0.35 ml min 1. Fig. 3A shows the power generated by the fuel cells in the two devices over 15 hours of operation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003324_b978-0-12-821350-6.00007-x-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003324_b978-0-12-821350-6.00007-x-Figure19-1.png",
        "caption": "Fig. 19 Conceptual representation of configurable modular robots inside the stomach (Nakadate and Hashizume, 2018), used under CC BY 3.0.",
        "texts": [
            " The EndoWrist SP instruments and camera have joggle joints in combination with snake-like wrist joints that mimic the human wrist, shoulder, and elbow. Also, the wrist joint allows for seven degrees of freedom and the elbow joint maintains intracorporeal triangulation. A more remarkable feature is the instrument guidance system, which tracks the locations of the robot camera, port, and instruments within the operational field and simultaneously repositions the instruments. With this system, it is possible to operate efficiently in a narrow space without clashing the instrument. Fig. 19 shows a new conceptual design for microrobots to be developed for NOTES. For these robots, the tools are attached directly to the magnetic joint, which is coupled to the external magnetic handle. The advantage of the design lies in its simple structure and compact size. Each modular robot has an ingestible size and can be ingested/inserted into the lumen through the natural orifices/endoscope channels. After reaching the working space, the robots start the self-assembly process by magnetic force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure7.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure7.7-1.png",
        "caption": "Fig. 7.7 Torques and angular velocities of the gyroscope motions around axis ox in clockwise (a) and counterclockwise (b) directions",
        "texts": [
            "x and precession torques Tp.y that act in the clockwise direction. The gyroscope starts to turn up under the action of surplus resistance inertial torques around axis ox in the clockwise direction. The following actions of external and internal torques are the same as described in sections (a1, a2) and (b1, b2). The gyroscope nutation is repeated with the continuous action of changeable inertial torques. The action of the external and internal torques on the gyroscope for the conditions described above is presented in Fig. 7.7. The gyroscope motions are presented by the corresponding equations that are described in several publications [13, 14]. The equations for stages (a1, a2 and b1, b2) of the gyroscope nutation are presented below. (a1) The equation for the gyroscope motion from the low position to the angle where the resistance torque resets to zero (Tr.x = 0) is as follows (Chaps. 5 and 6): Jx d\u03c9x dt = Mglm cos \u03b3 \u2212 ( 2\u03c02 + 8 9 ) J\u03c9\u03c9x + ( 2\u03c02 + 9 9 ) J\u03c9\u03c9y (7.63) 7.3 The Gyroscope Nutation 155 Jy d\u03c9y dt = \u2212 ( 2\u03c02 + 9 9 ) J\u03c9\u03c9x cos \u03b3 + ( 2\u03c02 + 8 9 ) J\u03c9\u03c9y cos \u03b3 (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure2.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure2.5-1.png",
        "caption": "Fig. 2.5 The pencil of complex lines in the null plane with null point P is normal to the helix through P",
        "texts": [
            " Cross- and dot-multiplying this equation by a and using the orthogonality a \u00b7u = 0 one gets for u and for p the expressions 72 2 Line Geometry u = a\u00d7 b a2 , p = a \u00b7 b a2 . (2.29) The axis has the Plu\u0308cker vectors a and u\u00d7a = (a\u00d7b)\u00d7a/a2 = b\u2212pa . In a reference basis having its origin on the axis of the complex the same linear complex has the second Plu\u0308cker vector u\u00d7a = 0 . In this reference basis the linear complex (a;b) is the complex (a; pa) . For better understanding the relationships between axis, constant p , null point and null plane points of a single line perpendicular to the axis are considered (Fig. 2.5). The foot of this perpendicular is chosen as origin 0 so that (2.29), (2.27) and (2.26) have the forms u = 0 , b = pa , n = a\u00d7 r+ pa , (2.30) a \u00b7 [r\u00d7 r\u2032 + p (r\u2032 \u2212 r)] = 0 . (2.31) Let P with position vector r be an arbitrarily chosen null point on the line. The associated null plane contains the line because (2.31) is satisfied with every position vector r\u2032 collinear with r . The figure shows the pencil of complex lines in this null plane. The null plane is inclined against the axis of the complex by an angle \u03b1 for which the triangle at P yields the formula (with r = |r|) tan\u03b1 = p r ",
            " If the null planes are known for two null points on one reciprocal polar, the other reciprocal polar is the line of intersection of these null planes. Two pairs of reciprocal polars determine a linear complex. According to Theorem 2.2 its axis is the common perpendicular of the common perpendiculars of the two pairs. According to Fig. 2.6 a single pair determines the null plane associated with an arbitrary null point on one of the polars. The axis, this null plane and this null point determine the radius r and the inclination angle \u03b1 shown in Fig. 2.5. According to (2.32) the pitch of the linear complex is p = r tan\u03b1 . 2.8 Linear Congruence 77 A congruence is the manifold of all lines (v , w) which are subject to two constraint equations. In this section linear congruences are briefly treated. This is the special case of the intersection of two linear complexes (see (2.25)): C1 = a1 \u00b7w + b1 \u00b7 v = 0 , C2 = a2 \u00b7w + b2 \u00b7 v = 0 . (2.45) The lines (v , w) of the congruence are complex lines common to both C1 and C2. Through every point in space a line of the congruence is passing, namely, the line of intersection of the null planes of C1 and C2 associated with this null point",
            " The defect d is determined as follows. According to Chasles\u2019s Theorem 3.1 an infinitesimal displacement of a rigid body is a screw displacement with a certain screw axis and a certain pitch (this includes as special cases pure translation and pure rotation). The infinitesimal displacement of an arbitrary body-fixed point is directed along the helix through this point. Every line perpendicular to the helix is a complex line of the linear complex with this screw axis and with this pitch (see the comment on Fig. 2.5). From this it follows that the normals to the five surfaces at the points Pi (i = 1, . . . , 5) are complex lines. Let ri (i = 1, . . . , 5) be the position vectors of the points Pi in a reference basis fixed on the frame. In this basis the normals have Plu\u0308cker vectors vi = ni and wi = ri \u00d7 ni (i = 1, . . . , 5) . From five independent complex lines the vectors a and b of a linear complex (a ;b) are determined by Eqs.(2.38): wi \u00b7 a+ vi \u00b7 b = 0 (i = 1, . . . , 5) . (4.6) The screw axis has the direction of a ",
            " The unit line vector n\u0302 along the ISA and the velocity screw are written as dual vectors. The former is composed of the Plu\u0308cker vectors of the ISA and the latter is defined as \u03c9\u0302 = \u03c9 + \u03b5v : n\u0302 = n+ \u03b5a\u00d7 n , (9.35) \u03c9\u0302 = \u03c9 + \u03b5v = \u03c9[n+ \u03b5(a\u00d7 n+ pn)] . (9.36) These dual vectors are related through the equation (to be verified by multiplying out again) \u03c9\u0302 = \u03c9(1 + \u03b5p)n\u0302 . (9.37) Comparison with (2.29) shows that Eqs.(9.23) define the axis and the pitch of the linear complex (\u03c9 ; vA) . It is called linear complex of velocity. From Fig. 2.5 it is known that the complex lines of this linear complex are normals of the helices, i.e., of the velocities v . Let z be the first Plu\u0308cker vector of 1 The name velocity screw is used instead of twist 9.3 Instantaneous Screw Axis. Pitch. Velocity Screw. Linear Complex of Velocity 297 a complex line passing through the point with position vector and with velocity v = vA +\u03c9 \u00d7 . Orthogonality requires that v \u00b7 z = 0 . This is the equation (vA +\u03c9\u00d7 ) \u00b7 z = 0 or \u03c9 \u00b7 \u00d7 z+vA \u00b7 z = 0 . In this equation the defining Eq",
            " The null plane is intersected orthogonally by a helix at its null point P . Hence also g is intersected orthogonally. A simpler proof makes use of the rigid-body property. Body-fixed points located on g have identical velocity components along g . So, if one point has a zero velocity component, all points have. End of proof. Theorem 9.3 explains the names null plane and null point. The null plane associated with a null point P is the locus of points which have zero velocity components toward P (see Fig. 2.5 ). Imagine in Fig. 2.5 a sphere of arbitrary radius a centered at the point P with coordinates [ r , 0 , 0 ] . From Theorem 9.3 it follows that the great circle in which the null plane associated with P intersects the sphere is the locus of points on the sphere which have velocities tangent to the sphere. This is independently verified as follows. An arbitrary point [x, y, z] on the sphere has the velocity coordinates (9.25), v = \u03c9[ \u2212y x p ] and the local normal with coordinates [ x \u2212 r y z ] . The orthogonality condition is ry + p z = 0 ",
            " Since g3 is intersected by the pencil of complex lines in \u03a31 and also by the pencil of complex lines in \u03a32 , the line g3 reciprocal to g3 , too, is intersected by these pencils of complex lines. Hence g3 is the line of intersection of \u03a31 and \u03a32 . It is passing through Q0 . For the same reason the line g1 reciprocal to g1 is the line of intersection of \u03a32 and \u03a33 also passing through Q0 . According to Theorem 2.2 the axis of the linear complex is the common perpendicular of the common perpendiculars of the pairs g3 , g3 and g1 , g1 . The pitch of the instantaneous screw is calculated from (2.32), p = r tan\u03b1 . The quantities r and \u03b1 are explained in Fig. 2.5 where P and its nullplane are any of the pairs Pi , \u03a3i (i = 1, 2, 3). The trajectories of three body-fixed points in the course of an arbitrary general motion are curves satisfying the condition stated in Theorem 9.4 not only instantaneously, but continuously. At the beginning of Sect. 2.7.5 on reciprocal polars (p1,q1) and (p2,q2) of a linear complex it was shown that the absolute value of p1 in (2.39) can be chosen such that in (2.41) \u03bc = 1 . Let this be the case. Applied to the linear complex (\u03c9 ; v) Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003225_tec.2020.2995433-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003225_tec.2020.2995433-Figure1-1.png",
        "caption": "Fig. 1. Structure of the baseline 6PIM: (a) 24-slot stator, (b) 18-bar cage rotor, (c) two-pole DW, and (d) two-pole conventional CW as reported in [22].",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. been implemented on the baseline motor. Then, motor performances have been compared with the one-layer DW and the two-layer conventional CW [22]. The analytical calculations, time-stepping finite element analyses and experimental measurements have been used to investigate the proposed layout performance characteristics. A 90W induction motor with a 24-slot stator (Fig. 1 (a)) and an 18-bar squirrel-cage rotor (Fig. 1 (b)) has been considered as the baseline motor. Table I shows the main geometrical dimensions of the baseline motor. The utilized symmetrical six-phase system is made up of two three-phase systems shifted by 60 o . However, from the air gap point of view, this six-phase system behaves similar to a conventional threephase on and adds redundancy to enhance the fault-tolerant capability. For the baseline 6PIM, the one-layer DW and the conventional two-layer CW have been used as the reference windings. This winding layout (Fig.1 (c)) is applied to the baseline motor. By supplying the motor with the rated phase voltage (14V), simulation results of the finite element analysis (FEA) have been obtained as reported in Table II. According to simulation results, the no-load current is 1.45A rms and the full-load current is 1.82A rms. In comparison, the experiment has reported 1.41 A rms and 1.78 A rms respectively[6]. Moreover, FEA simulation results show that the rotor nominal speed and torque are 2822rpm and 0.3N.m respectively at rated condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001381_j.molliq.2012.04.013-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001381_j.molliq.2012.04.013-Figure1-1.png",
        "caption": "Fig. 1. CVs of (a) unmodified CPE in 0.1 M phosphate buffer solution (pH 7.0) at scan rate of 10 mV s\u22121; (b) as (a)+0.2 mM CD; (c) as (a) at the surface of MCNPE; (d) as (b) at the surface of CNPE; (e) as (b) at the surface of MCPE; (f) as (b) at the surface of MCNPE.",
        "texts": [
            "01 g of CA with 0.89 g graphite powder and 0.1 g CNTs with a mortar and pestle. Then, ~0.7 mL of paraffin was added to the above mixture and mixed for 20 min until a uniformly-wetted paste was obtained. The paste was then packed into the end of a glass tube (ca. 3.4 mm i.d. and 10 cm long). A copper wire inserted into the carbon paste provided the electrical contact. When necessary, a new surface was obtained by pushing an excess of the paste out of the tube and polishing with a weighing paper. Fig. 1 depicts the CV responses for the electrochemical oxidation of 0.2 mM CD at unmodified CPE (curve b), CNPE (curve d), MCPE (curve e) and MCNPE (curve f). As it is seen, while the anodic peak potential for CD oxidation at the CNPE, and unmodified CPE is 710 and 790 mV, respectively, the corresponding potential at MCNPE and MCPE is ~120 mV. These results indicate that the peak potential for CD oxidation at the MCNPE and MCPE electrodes shifts by ~590 and 670 mV toward negative values compared to CNPE and unmodified CPE, respectively. However, MCNPE shows much higher anodic peak current for the oxidation of CD compared to MCPE, indicating that the combination of CNTs and the mediator has significantly improved the performance of the electrode toward CD oxidation. In fact, MCNPE in the absence of CD exhibited a wellbehaved redox reaction (Fig. 1, curve c) in 0.1 M phosphate buffer (pH 7.0). However, there was a drastic increase in the anodic peak current in the presence of 0.2 mM CD (curve f), which can be related to the strong electrocatalytic effect of the MCNPE towards this compound [82] (Scheme 1). The effect of scan rate on the electrocatalytic oxidation of CD at the MCNPE was investigated by cyclic voltammetry (Fig. 2). As can be observed in Fig. 2, the oxidation peak potential shifted to more positive potentials with increasing scan rate, confirming the kinetic limitation in the electrochemical reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002660_tia.2019.2920923-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002660_tia.2019.2920923-Figure7-1.png",
        "caption": "Fig. 7. Finite element model of the motor: (a) original prototype motor, (b) pole with varied-width",
        "texts": [
            " 6 shows the amplitude of radial force and bending moment for different width difference  when the pole width of the first segment is kept as 9. It reveals that both the amplitude of radial force and bending moment can reach the minimum when the width difference  is equal to 1. It should be noted that in this case, the average pole arc width of one PM pole is 8.5. If there is other pole arc width which is usually determined by the demand of voltage and power of one motor, the optimum pole width difference  can also be derived from (5) and (8). Fig.7 shows the structural finite element model of the motor, and a motor with skewed slots on the rotor and straight PM pole on the stator is used for comparison. In order to fully consider the spatial distribution characteristics of electromagnetic force, in Fig.7 (a), one PM pole of the origin prototype is evenly divided into 6 segments along the axial direction and 17 pieces in circumferential direction. In this case, every segment include 17 equal-sized pieces, such as piece 1, piece 2, and piece 17. Every piece faces half of tooth pitch in this case. In Fig.7 (b), one PM pole of the proposed motor is also evenly divided into 6 segments along the axial direction. The segment 1, segment 3, segment 5 of one PM pole include 18 pieces and the rest segments of one PM pole include 16 pieces. Special attention is needed to the same area of one PM pole in the original and proposed motor. Fig.8-10 show the electromagnetic pulsating forces acting on the proposed motor at speed of 1500r/min. In Fig.8, the force acting on piece 8 is presented. It can be seen that the dominant frequencies of force are the integer multiples of the product of the slot number and the rotation mechanical frequency rf ( / 60rf n ), that is 1 24 rf , 2 24 rf , 3 24 rf , 4 24 rf , which are usually called 1st-order, 2nd-order, 3rdorder, 4th-order slot frequency, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001213_10402004.2012.729298-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001213_10402004.2012.729298-Figure1-1.png",
        "caption": "Fig. 1\u2014Roller geometry and coordinate system.",
        "texts": [
            " Results are 88 D ow nl oa de d by [ U ni ve rs ity o f T en ne ss ee A t M ar tin ] at 0 9: 00 0 7 O ct ob er 2 01 4 NOMENCLATURE b = phRx E\u2032 = Half-width of Hertzian contact cp = Thermal capacity of oil E = Modulus of elasticity E\u2032 = 2( 1\u2212\u03bd2 1 E1 + 1\u2212\u03bd2 2 E2 )\u22121 = Reduced modulus of elasticity er = Stepwise discrepancy FN = Applied normal force H = Dimensionless film height H\u2217 = h/Rx105 = Dimensionless film height Hmin = Dimensionless minimum film height h = Film height k = Solids thermal conductivity L1 = Roller length L2 = Length of the cylindrical part of the roller p, P = Real, dimensionless pressure ph = 2FN \u03c0bL1 = Maximum Hertzian pressure Rx, Ry = Reduced radius of curvature along the x and y directions S = 2 u1\u2212u2 u1+u2 = Slide-to-roll ratio S1,2 = Surface profile T, T\u0304 = Real, dimensionless temperature T0 = Reference temperature u = Velocity along the x-axis uref = Reference velocity v = Velocity along the y-axis w = Velocity along the z-axis X, Y, Z = Dimensionless coordinates \u03b3\u0307 = Shear rate \u03b7 = Viscosity \u03b70 = Viscosity at reference pressure and temperature \u03b8 = Fractional film content \u03bboil = Thermal conductivity of oil \u03c1 = Density \u03c10 = Density at reference pressure and temperature \u03c4 = Shear stress \u03c40 = Shear stress at ambient pressure \u03c4L = Limiting shear stress Subscripts 1, 2 = Solid 1, solid 2 in = Inlet, boundary condition shown and discussed for a filleted, chamfered, and profiled roller pressed against a semi-infinite body. THEORY The model consists of a roller (solid 1) pressed against a semiinfinite body (solid 2). The radius of the roller is Rx and the fillet radius is Ry, as shown in Fig. 1. u1 and u2 are the velocities along the x direction of the surfaces of the two solids. Governing Equations The following form of the Reynolds equation is used. Its derivation can be found in the Appendix. \u2202 \u2202x ( m2 \u2202p \u2202x ) + \u2202 \u2202y ( m2 \u2202p \u2202y ) \u2212 \u2202m4 \u2202x = 0 [1] where m1 = \u222b h 0 ( \u03c1 \u222b z 0 Fdz ) dz, m2 = f 1m1 f 0 \u2212 \u222b h 0 ( \u03c1 \u222b z 0 zFdz ) dz, m3 = \u222b h 0 \u03c1dz m4 = \u03b8 ( m1 f 0 (u2 \u2212 u1) + u1m3 ) f 0 = \u222b h 0 Fdz, f 1 = \u222b h 0 zFdz F stands for a function describing the non-Newtonian shear thinning behavior of the lubricant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000700_s11044-009-9145-7-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000700_s11044-009-9145-7-Figure2-1.png",
        "caption": "Fig. 2 The lower manipulator with kinematics parameters and it force situation",
        "texts": [
            " In the 2(SP + SPR + SPU) manipulator, the number of links is g0 = 13 for the platform m1 with a cylinder, the composite platform m/c with a cylinder, the base B,4 cylinders, and 6 piston-rods; the number of joints is g = 16 for 6 prismatic joints, 2 revolute joints, 6 spherical joints, and 2 universal joints. The DOF M of this manipulator is calculated as below [1, 2]: M = 6(g0 \u2212 g \u2212 1) + g\u2211 i=1 mi = 6 \u00d7 (13 \u2212 16 \u2212 1) + (8 \u00d7 1 + 6 \u00d7 3 + 2 \u00d7 2) = 6. (1) 3.1 Displacement of the lower manipulator A lower manipulator with kinematic parameters and its force situation are shown in Fig. 2. The position vectors B i (i = 1,2,3) of points Bi on B in {B}, the position vectors mbi of points bi on m in {m}, the position vectors bi of bi on m in {B}, and the position vector o of point o on m in {B} can be expressed as follows [1, 2]: B i = \u23a1 \u23a3 XBi YBi ZBi \u23a4 \u23a6 , mbi = \u23a1 \u23a3 xbi ybi zbi \u23a4 \u23a6 , bi = \u23a1 \u23a3 Xbi Ybi Zbi \u23a4 \u23a6 , o = \u23a1 \u23a3 Xo Yo Zo \u23a4 \u23a6 , (2) B mR = \u23a1 \u23a3 xl yl zl xm ym zm xn yn zn \u23a4 \u23a6 , bi = B mRmbi + o, where, (Xo,Yo,Zo) are the components of o in {B}; B mR is a rotational transformation matrix from {m} to {B}; (xl, xm, xn, yl, ym, yn, zl, zm, zn) are 9 orientation parameters of m, their constrained equations can be obtained from references [1\u20133]",
            " When given ri (i = 1,2,3), (\u03b1,\u03bb) are solved from (11) as follows: \u03bb = 2arctan (\u22122qr1E \u2213 \u221a (2qr1E)2 + 36E2e2 \u2212 [r2 1 + 3(E2 + e2) \u2212 r2 2 ]2 r2 1 \u2212 r2 2 + 3(E2 + e2) + 6Ee ) (12) \u03b1 = 2arctan ( \u22123E(qes\u03bb + 2roc\u03bb) \u2213 D 2r2 1 + 6(E2 + e2) + 2qEr1s\u03bb \u2212 3Eec\u03bb \u2212 2r2 3 + 9Ee ) , D = \u221a 81E2e2 + 9E2(qes\u03bb + 2roc\u03bb)2 \u2212 [ 2r2 1 + 6 ( E2 + e2 ) + 2qEr1s\u03bb \u2212 3Eec\u03bb \u2212 2r2 3 ]2 . (13) Thus, (Xo,Yo, Zo) can be solved from (6) and (10)\u2013(13) as follows: Xo = 2r2 3 \u2212 r2 1 \u2212 r2 2 \u2212 3e2 \u2212 3Ee(c\u03bb \u2212 2c\u03b1) 6E , Yo = r2 1 \u2212 r2 2 + 3e2 \u2212 3eEc\u03bb 2Eq , (14) Zo = [2r2 3 \u2212 r2 1 \u2212 r2 2 \u2212 3e2 \u2212 3Ee(c\u03bb \u2212 2c\u03b1)]c\u03b1 \u2212 3E2c\u03b1 + 3Ee 6Es\u03b1 . 3.2 Geometric constraints of the constrained forces of the lower manipulator The force situation of the lower manipulator is shown in Fig. 2(b). The whole workloads can be simplified as a wrench (F , T ) applied upon m at o. (F ,T ) includes the inertia wrench and the gravity of m, and inertia wrench and the gravity of the active legs which can be mapped into a part of (F ,T ), and the external working wrench. F is a concentrated force and T is a concentrated torque. (F ,T ) are balanced by 3 active forces F ai (i = 1,2,3) and 3 constrained forces F f i . Here, F ai is applied on and along ri at Bi , its unit vector \u03b4i is the same as that of ri "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003693_tie.2021.3051547-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003693_tie.2021.3051547-Figure13-1.png",
        "caption": "Fig. 13 Saturation distribution factor.",
        "texts": [
            " The resultant air-gap flux density (B\u2019g) fully considering the saturation effects is obtained with the original linear air-gap flux density divided by the saturation distribution factor: \ud835\udc35\u2032 \ud835\udf03 \ud835\udc35 \ud835\udf03 /\ud835\udc3e \ud835\udf03 (23). In order to obtain the high accuracy, a simple iteration based on the flowchart shown in Fig. 12 can be applied to identify Ksat at each rotor position. With the square-wave current with 24A amplitude and 60\u00ba current angle, the saturation distribution factors over the half of the air-gap circumference during one electric period are illustrated in Fig. 13, which are actually determined by the air-gap permeance and the original flux density distributions. Afterwards, the air-gap field distributions considering the nonlinear characteristics can be predicted and the results are summarized in Fig. 14. The air-gap field at the initial rotor position is shown in Fig. 14(a), where the AM and FEM predicted flux densities are both included and the good agreement is observed. Meanwhile, by comparison of the linear air-gap flux density in Fig. 9(a) and the nonlinear result in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.7-1.png",
        "caption": "Figure 10.7. A belt driven pulley system.",
        "texts": [
            " Euler's laws in (10.26) and (10.65) are the fundamental equations for study of all rigid body dynamics problems. Their solution for several special problems of practical interest are explored below. 440 10.12.1. Application to a Belt Driven Machine Chapter 10 Example 10.7. A homogeneous cylindrical pulley of radius a and mass m, initially at rest, is driven by a belt of negligible mass. During the start-up period, the drive belt exerts a constant torque T on the pulley about its axle at C , as shown in Fig. 10.7. Determine the pulley's angular speed wet) . Solution. The homogeneous pulley rotates with angular velocity w(t ) = w(t) e3 about a fixed principal body axis e3 = K at its center of mass C in Fig. 10.7. The constant belt torque about C is Me = T = TK, and Euler's equation in (10.75) require s Me = lew =lewK. Hence , equat ing components, the angular speed wet) during startup is determined by lew = T. (I0.77a) Integration of (I0.77a) with w(O) = Wo initially yields the angular speed, T w(t) = Wo+ -1. (I0.77b) Ie Since the pulley starts from rest, we set Wo = 0 to obtain w(t) = Tt l Ie. 0 The result shows that the angular speed varies inversely with the pulley properties through Ie . Suppose the pulley is modeled as a homogeneous thin disk for which, by (9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure8.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure8.6-1.png",
        "caption": "Fig. 8.6 Vectorial diagram of the velocities and acceleration of the gyroscope with spinning disc",
        "texts": [
            " These motions express the work of the potential energy of the gyroscope weight and kinetic energy of the spinning disc along axes of motions. The kinetic energy of the spinning disc is expressed by the action of the change in the angular momentum around axis oz and by the action of the inertial torques generated by the centrifugal, common inertial and Coriolis forces around axes ox and oy. The action of all inertial torques around axes is interrelated. The vectorial diagram of the angular velocities and acceleration of the spinning disc and the gyroscope around axes are presented in Fig. 8.6. All rotational motions of the gyroscope around axes are in the counterclockwise directions if considered from the tips of the coordinate axes. The blocking of the turn of the running gyroscope around axis oy causes rotation to stop the acceleration and rotation around this axis, i.e.\u03c9\u03c9x = \u03b5y =0. Since the angular velocity of the spinning disc \u03c9 is constant, the angular velocity of the precession around axis ox is an absence \u03c9x = 0. It means all inertial torques (Eq. 8.47) have the zero values Ti = 0, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure6-1.png",
        "caption": "Figure 6. Temperature distribution on a gasoline cooled piston (top), and non-cooled (down)",
        "texts": [
            " In order to analyze the influence of introducing a cooling gallery near the top land in a gasoline engine piston, a heat transfer analysis has been repeated for the same piston model with and without the insert of a cooling gallery. Heat transfer study results have been analyzed in terms of temperature and heat flux ratios at each of the piston regions. In order to simplify the results analysis, both parameters have been integrated across the studied surfaces and compared with results from previous works [9, 11, 12, 13, 14, 15]. In Figure 6, temperature distribution across a gasoline piston has been shown for the original piston model (without cooling gallery) and for the modified piston by introducing an oil cooling gallery. In order to simplify the analysis, same color scale has been used for both cases. As it can be observed, temperature differences between both models are evident, appearing the higher temperature at piston top land and rings for the non-cooled case as it was expected. The lower temperature observed at those regions for the cooled piston is beneficial since they can prevent from abnormal combustion events such as knocking or pre-ignition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003293_s40430-020-02645-3-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003293_s40430-020-02645-3-Figure14-1.png",
        "caption": "Fig. 14 Electronic and mechanical parts of the robot",
        "texts": [],
        "surrounding_texts": [
            "The purpose of this study is to design a successful controller for line following robots. Therefore, the non-chattering sliding mode controller was designed and compared with PID 1 3 one. A complicated test path was used for this purpose. The test path consists of five sections having different tracking difficulties. Two different controllers are applied to robot. First, PID controller, which is one of the commonly used control methods in industry is designed for comparison. Then, SMC and PID parameters were obtained in numerical analysis before experimental tests. Both computer simulation and experimental study were presented in figures together with the trajectory tracking errors of them. When the experimental data are examined, it is observed that the SMC controller recovers the robot faster in sharp turns. It is also understood that it has less trajectory tracking errors in the dashed line section on which it is hard to follow. It is generally deduced that the SMC controller is much more successful than PID controller in terms of tracking performance. Moreover, it is also seen that the SMC controller is consuming less energy and finishes the trajectory more quickly than PID one. As a result, SMC finishes the track % 10.83 faster, produces error % 31.60 lower, consumes 1 3 energy % 16.38 less on the track. Afterwards, the robustness of the SMC controlled robot has been tested for different robot masses resulting in expected success. Then, SMC and PID controlled robots have been run on a harder track resulting in superior performance of SMC one. Then, experimentally SMC and PID controlled robots have been started on a faulted track line, and it has been verified that SMC controlled robot finishes the track having very low average tracking error compared with the other controller. Finally, it has been concluded that non-chattering SMC controlled line following robot proposed in this study has a very satisfactory tracking performance under all hard working conditions. Appendices A1 See Table\u00a03. Fig. 13 Experimental tracking errors and average total errors of SMC and PID controlled robots after a faulted start line Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:561 561 Page 12 of 13"
        ]
    },
    {
        "image_filename": "designv10_12_0000268_tmag.2008.921097-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000268_tmag.2008.921097-Figure3-1.png",
        "caption": "Fig. 3. Mutual coupling in SRM due to leakage flux.",
        "texts": [
            " 2, motor phases are numbered in counterclockwise direction. This is also the sequence of excitation when rotor rotates clockwise. The rated speed of the motor is 1420 rpm and the dc bus voltage is 280 V. When one phase is excited in an SRM, the major part of the resultant flux is linked by the excited phase. However, a small part of the flux, called mutual flux, is linked by other phases. In fact, the origin of mutual flux in SRM comes from leakage flux developed between the energized phase and other phases [9]. In Fig. 3, phase1 is excited by current equal to 2 A in unaligned position. As seen, some of the flux produced by phase1 is linked by phases 2 and 4 (the flux linked by phase3, which is quadrant to phase 1, is very lower than the ones linked by two adjacent phases of the excited phase). Considering 2-D FEA, fluxes are present only in X and Y directions, while currents and magnetic potential vectors are present only in Z direction. Then, flux linkage per unit length of each pole of every phase, , is computed as follows [10]: (2) where and stand for the average values of the magnetic potential vectors over the area of each \u201cgo\u201d (a) and \u201creturn\u201d (b) pole winding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003495_iros45743.2020.9341743-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003495_iros45743.2020.9341743-Figure3-1.png",
        "caption": "Fig. 3. Inertial and link frames of the virtual model in relation to the real robot. (a) The location of the stance feet dictate the axis about which the joints of the virtual model rotate (dotted line), which is orthogonal to the plane where the virtual model lies. (b) Location of coordinate frames of the virtual model and its corresponding joint variables yp and yh.",
        "texts": [
            " To exploit the balance controller on a quadruped robot, we define the motion constraints that define a lower dimensional operational space, which corresponds to the two degrees of freedom of the pendulum. We call kinematic mapping the function transforming the state variables from the quadruped to the pendulum space. The mapping allows us to apply the controller in pendulum space, and convert its output into signals suitable for the actual robot. The derivation of the mapping is described in the following paragraphs. First, consider a quadruped standing on a single pair of diagonal legs, with the other leg pair retracted (lifted up from the ground), as shown in Fig. 3(a). Project a virtual inverted pendulum moving in the vertical plane perpendicular to the line of contact defined by the two stance feet. The pendulum consists of two links, the leg and the torso, and two revolute joints, the pivot and the hip (see Fig. 3(b)). The pivot joint is passive and its axis coincides with the line of contact of the quadruped; the hip joint is actuated and its axis is parallel to the previous one, at a distance equal to the length of the virtual leg link. The virtual torso link is composed of the real robot torso and the retracted legs, thus they have the same inertia and undergo the same motion (see Fig. 3(a)). We attach three reference frames to the virtual pendulum: vbase is an inertial frame with origin at the pivot contact point with its xaxis coinciding with the pivot axis; vleg is a frame attached to the virtual leg and also its x-axis coincides with the pivot axis; vtorso is attached to the virtual torso and its x-axis coincides with the virtual hip axis. The origins of vtorso and of the real torso frame (rtorso) coincide, and their zaxes are aligned. The frames only differ by a relative rotation of \u03c6t radians about their local z-axis",
            " From \u03c6t we can compute the rotation matrix that transforms 3D vectors from rtorso to vtorso coordinates, E\u03c6t \u2208 SO(3). At this point, simple geometric observations yield some of the relations between sensor data and the state of the virtual pendulum. For example, we have that y\u0307p + y\u0307h = (E\u03c6t \u03c9)x (2) where (\u00b7)x indicates the x-component of the vector inside the parenthesis; we also have that yp + yh = sin\u22121 ( E\u03c6t \u2192 up ) y (3) 3651 Authorized licensed use limited to: University of Prince Edward Island. Downloaded on June 07,2021 at 00:23:55 UTC from IEEE Xplore. Restrictions apply. With reference to Fig. 3(b), we also observe that the pivot point in the vtorso frame, denoted by (py, pz), allows us to calculate the virtual hip joint angle: yh = tan\u22121 ( py pz ) (4) and by differentiating (4) w.r.t. time, it follows that y\u0307h = pzvy \u2212 pyvz p2y + p2z (5) Hence, at each time instant, the virtual states y and y\u0307 are found by solving (2) - (5). The purpose of this phase is to determine the coefficients of the following motion constraint equations: q\u0307 = Gjy\u0307 q\u0308 = Gjy\u0308 + gj (6) where Gj \u2208 Rn\u00d72 and gj = G\u0307jy\u0307 relate the motion of the pendulum to the exact desired motion of the real robot (cf"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.44-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.44-1.png",
        "caption": "Fig. 15.44 Domain \u03933 (shaded), evolute K and curves E3(b) for several values of b in the case \u03b1 = 110\u25e6 . Curves E3(b) with \u22122 cot\u03b1 < b < bS have cusps on K",
        "texts": [
            " With the length p = xP cos\u03b2 of the perpendicular from 0 onto the line AB and with \u03b2 = \u03d5+ \u03b1\u2212 \u03c0/2 this becomes( x\u2212 sin\u03d5 sin\u03b1 ) sin(\u03d5+ \u03b1)\u2212 y cos(\u03d5+ \u03b1)\u2212 b = 0 . (15.161) On E3(b) this equation as well as its partial derivative with respect to \u03d5 is satisfied: x cos(\u03d5+ \u03b1) + y sin(\u03d5+ \u03b1)\u2212 sin(2\u03d5+ \u03b1) sin\u03b1 = 0 . (15.162) The solutions of these two equations for x and y are parameter equations of E3(b) : 15.6 Rectangle Moving Between two Lines and a Point 517 x(\u03d5, b) = b sin(\u03d5+ \u03b1) + sin\u03d5+ cos\u03d5 sin(\u03d5+ \u03b1) cos(\u03d5+ \u03b1) sin\u03b1 , y(\u03d5, b) = \u2212b cos(\u03d5+ \u03b1) + cos\u03d5 sin2(\u03d5+ \u03b1) sin\u03b1 \u23ab\u23aa\u23ac \u23aa\u23ad (0 < \u03d5 < \u03c0 \u2212 \u03b1) . (15.163) Figure 15.44 shows parallel curves E3(b) for several values b \u2265 0 in the case \u03b1 = 110\u25e6 . The lines n1 and n2 are the normals n(\u03d5 = 0) and n(\u03d5 = \u03c0 \u2212 \u03b1) , respectively. The curves E3(b) are symmetric with respect to g . The endpoints for \u03d5 = 0 and for \u03d5 = \u03c0 \u2212 \u03b1 are located on n1 and n2 , respectively. The endpoint on n2 has the coordinates x = 1 , y = b . The curve E3(b = 0) is the envelope of all lines AB. When P0 is located on E3(0) , the maximum admissible width of the rectangle is Bmax = 0 . For points P0 in the domain between g1 , g2 and E3(0) no rectangle can be moved from position I to position II",
            " Let K be the curve connecting all cusps. It is the evolute of all E3(b) and also the envelope of the normals n(\u03d5) . The equation of n(\u03d5) is Eq.(15.162). On K this equation as well as its partial derivative with respect to \u03d5 is satisfied: \u2212x sin(\u03d5+ \u03b1) + y cos(\u03d5+ \u03b1)\u2212 2 cos(2\u03d5+ \u03b1) sin\u03b1 = 0 . (15.164) The solutions of these two equations for x and y are parameter equations of K : 518 15 Plane Motion x(\u03d5) = 3 sin\u03d5\u2212 sin(3\u03d5+ 2\u03b1) 2 sin\u03b1 y(\u03d5) = 3 cos\u03d5+ cos(3\u03d5+ 2\u03b1) 2 sin\u03b1 \u23ab\u23aa\u23ac \u23aa\u23ad (0 < \u03d5 < \u03c0 \u2212 \u03b1) . (15.165) In Fig. 15.44 the evolute K is shown. It is symmetric with respect to g . Its endpoints associated with \u03d5 = 0 and with \u03d5 = \u03c0 \u2212 \u03b1 are the points Q1 on n1 and Q2 on n2 , respectively. At these points K merges tangentially with n1 (with n2 ). The point Q2 has the coordinate y = \u22122 cot\u03b1 . The tip S of K belonging to the central value \u03d5 = (\u03c0 \u2212 \u03b1)/2 has the coordinates xS = 1/ sin(\u03b1/2) , yS = 1/ cos(\u03b1/2) . Its distance from 0 is 2/ sin\u03b1 , i.e., twice the radius of the pole circle. The width b = bS associated with the special curve E3(b) through S is obtained from the first Eq.(15.161) with x = xS and \u03d5 = (\u03c0\u2212\u03b1)/2 . It is bS = (3\u2212cos\u03b1)/(2 sin\u03b1) . From this it follows that the curve E3(b) has cusps if b is in the interval \u22122 cot\u03b1 \u2264 b \u2264 bS . The domain \u03933 of definition of curves E3(b) is the shaded domain in Fig. 15.44 . In what follows, the boundary G35 between the domains \u0393 \u2032 3 and \u0393 \u2032 5 is determined. By definition, every point of G35 is the intersection point of two curves E3(b) and E5(b) with identical b . Since both curves have the point with coordinates x = 1 , y = b in common, the normal n2 is part of G35 . Figure 15.44 shows that a curve E3(b) with cusps and the line E5(b) for the same value of b have a second point of intersection located between the lines n2 and K (in the small figure this is shown schematically). Also this point is part of G35 . A parameter equation for G35 is found as follows. For E3(b) Eqs.(15.161) and (15.162) are used (in the interval (\u03c0 \u2212 \u03b1)/2 \u2264 \u03d5 \u2264 \u03c0 \u2212 \u03b1 describing the branch below the symmetry line g ). In both equations b is replaced by y because E5(b) has the equation y = b . This results in two linear equations for x and y : x sin(\u03d5+ \u03b1)\u2212 y[1 + cos(\u03d5+ \u03b1)] = sin\u03d5 sin(\u03d5+ \u03b1) sin\u03b1 , x cos(\u03d5+ \u03b1) + y sin(\u03d5+ \u03b1) = sin(2\u03d5+ \u03b1) sin\u03b1 \u23ab\u23aa\u23ac \u23aa\u23ad (\u03c0 \u2212 \u03b1 2 \u2264 \u03d5 < \u03c0 \u2212 \u03b1 ) ",
            "6 Rectangle Moving Between two Lines and a Point 519 x\u2217 = 1 + sin \u03b1 2 2 sin \u03b1 2 , y\u2217 = 1 + sin \u03b1 2 2 cos \u03b1 2 = 1 2 tan \u03c0 + \u03b1 4 . (15.168) The other endpoint associated with \u03d5 = \u03c0\u2212\u03b1 is the point Q2 on n2 . In Fig. 15.45 this branch of the boundary G35 is shown. The results are summarized as follows. The domain \u0393 \u2032 3 has the symmetry axis g . The part below g is bounded by the section 0 \u2264 x \u2264 1 of the x-axis, by the section of n2 between the points (x = 1 , y = 0) and Q2 and by the section of G35 between Q2 and S\u2217 . That the section of n2 above Q2 does not play a role is seen in Fig. 15.44 from the curves E3(b) and E5(b) terminating on this section of n2 . Figure 15.45 shows also the domains \u0393 \u2032 1 , \u0393 \u2032 3 and \u0393 \u2032 5 , the line g and the curve E3(0) . The three domains have the point S\u2217 in common. If P0 is located at S\u2217 , all three motion phases 1 , 3 and 5 yield one and the same maximum width Bmax . This implies that S\u2217 has equal distances from g1 , from g2 and from the curve E3(0) . The maximum width is Bmax = y\u2217 with y\u2217 from (15.168). Next, equations determining Bmax are formulated for the three domains \u0393 \u2032 1 , \u0393 \u2032 3 and \u0393 \u2032 5 ",
            " P0 is located in \u0393 \u2032 5 : The equation of E3(b) is y = b . Hence Bmax = y0 . P0 is located in \u0393 \u2032 3 : E3(b) is represented by (15.161) and (15.162). With x = x0 , y = y0 these equations are 520 15 Plane Motion b(\u03d5) = ( x0 \u2212 sin\u03d5 sin\u03b1 ) sin(\u03d5+ \u03b1)\u2212 y0 cos(\u03d5+ \u03b1) , x0 cos(\u03d5+ \u03b1) + y0 sin(\u03d5+ \u03b1)\u2212 sin(2\u03d5+ \u03b1) sin\u03b1 = 0 \u23ab\u23aa\u23ac \u23aa\u23ad (0 < \u03d5 < \u03c0 \u2212 \u03b1) . (15.169) For every root \u03d5 of the second equation the associated solution b(\u03d5) is calculated from the first equation. On the number of solutions the following statement can be made. Consider in Fig. 15.44 the curve E3(b) with the cusp shown in the enlarged inset. A neighboring curve E3(b + \u0394b) with a sufficiently small \u0394b intersects the curve E3(b) at two points, one of them located between G31 and n1 and the other between G35 and n2 . Hence the conclusion: Two solutions b exist if P0 is located either between G31 and n1 or between G35 and n2 . A single solution exists if P0 is located elsewhere in \u0393 \u2032 3 . For solving the second Eq.(15.169) the terms cos(\u03d5+\u03b1) , sin(\u03d5+\u03b1) and sin(2\u03d5+\u03b1) are expressed in terms of functions of individual angles by means of addition theorems",
            " It starts with b = 0 at the point Q0 and it terminates with b = cot\u03b1 at the point R0 . Elimination of the parameter b yields the explicit equation x = \u221a 1\u2212 y2 + (1/y) cot\u03b1 (valid for sin\u03b1 \u2264 y \u2264 1 ) . The domain \u03932 is the shaded area in Fig. 15.48 . Of its boundary only the small section is still unknown on which the curves E2(b) have cusps. This section is called e2 . For a given value of b (arbitrary) all normals n(\u03d5) envelope a curve K(b) . This curve K(b) is found by the same method that was used for the curve K of Fig. 15.44 . Starting point is Eq.(15.173) of the normal n(\u03d5) . On K(b) this equation as well as its partial derivative with respect to \u03d5 is satisfied: \u2212x sin(\u03d5+\u03b1) + y cos(\u03d5+\u03b1)\u2212 2 cos(2\u03d5+ \u03b1)\u2212 b sin(2\u03d5+ \u03b1) sin\u03b1 = 0 . (15.176) At the cusp of E2(b) Eqs.(15.172), (15.173) and (15.176) have the quantities b , x , y and \u03d5 in common. Summation of (15.172) and (15.176) eliminates x and y . The resulting equation is solved for b : b = 3 cos(\u03d5+ \u03b1) cos\u03d5\u2212 cos\u03b1 3 cos(\u03d5+ \u03b1) sin\u03d5+ sin\u03b1 . (15.177) Substitution of this expression into (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002130_s12206-015-1233-4-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002130_s12206-015-1233-4-Figure6-1.png",
        "caption": "Fig. 6. The expression of the bearing contact curvature.",
        "texts": [
            " 2/3 n n n K Q\u03b4 = (21) 2 2 2 2 3 2 ( ) 1 3 1 1 [ ( )] 8 2 b n n n a b n K e K Q m E E \u00b5 \u00b5 \u03c1 \u03c0 \u2212 \u2212 = + \u2211 (22) / 2 2 2 0 ( ) 1 [1 ]sin d K e k \u03c0 \u03d5 \u03d5 = \u2212 \u2212 \u222b (23) /2 2 2 0 ( ) 1 [1 ]sinL e k d \u03c0 \u03d5 \u03d5= \u2212 \u2212\u222b (24) 23 2 ( ) / ( ) a m L e k\u03c0= (25) / .k b a= (26) The above five equations can be used to solve the Hertz contact stiffness between bearing rolling element and the inner or outer raceway. According to the analysis in Sec. 3.1, an increase of bearing temperature leads to a change of raceway contact curvature. Table 1 shows the calculation formula of the bearing contact curvature, which can be expressed in Fig. 6. According to Eqs. (18) and (19), the rise of bearing temperature will change the curvature coefficient of inner and outer raceway, which leads to the change of bearing contact curvature, and affects the Hertz contact stiffness between rolling element and raceway. Fig. 7 shows the effect of temperature on the Hertz contact stiffness. The rising bearing temperature leads to the increase of contact stiffness between rolling element and the inner and outer raceway ( iK and oK ), which enlarges the axial stiffness of angular contact ball bearing directly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.3-1.png",
        "caption": "Fig. 2.3 Basic mechanical layout of the rear ICEs driving the rear wheels [Polski Fiat \u2013 126p; DUFFY 2008].",
        "texts": [],
        "surrounding_texts": [
            "As a generalisation, the rear ECE or ICE layout, that is, rear-wheel-drive (RWD) tends to make an automotive vehicle light and inexpensive but unstable in side winds, whereas the front-wheel-drive (FWD) arrangement gives more inherent stability, but transmitting mechanical energy to steered and driving wheels adds mass and cost. All kinds of DBW AWD propulsion mechatronic control systems have been use on automotive vehicles, including thermo-mechanical (TH-M) steam engines, as well as fluido-mechanical (F-M), that is hydro-mechanical (H-M) or pneumo-mechanical (P-M) or electro-mechanical (E-M) motors. These latter run from ECE- or ICE-driven mechano-fluidical (M-F) pumps, mechanopneumatical (M-P) compressors, or mechano-electrical generators or even chemo-electrical/electro-chemical (CH-E/E-CH) storage batteries or fuel cells (FC), respectively. 2.1 Introduction 151 Due to many factors such as cost to buy and to run, ease of driving, reliability, quick availability, quietness, freedom from smell, and good power-to-mass ratio, the four-stroke petrol ICE has come to dominate the scene. It is an ICE that has a wide but not unlimited crankshaft angular-velocity range, having a minimum as well as a maximum useful rotational velocity that results in it needing some sort of gradually-engaged M-M clutch to be able to start an automotive vehicle from rest, and change \u2013 velocity gearing to suit various values of the vehicle velocity and gradients while running. Like so many technologies nowadays, DBW AWD propulsion mechatronic control systems are primarily a response to tightening emission standards. As with fuel injection and integrated engine management controllers (EMC), these systems improve ECE or ICE energy efficiency while cutting exhaust emissions. They do this by replacing clunky and inaccurate M-M, F-M or P-M systems with highly advanced and precise electronic sensors. Currently, DBW AWD propulsion applications are being used to replace the throttle-cable system on newly developed vehicles. These systems work by replacing conventional throttle valve control (TVC) systems. Instead of relying on a mechanical cable that winds from the back of the accelerator pedal, through the automotive vehicle firewall, and onto the throttle body, a DBW AWD propulsion mechatronic control system consists of a sophisticated pedal-position sensor (PPS) that closely tracks the position of the accelerator pedal and sends this information to the EMC. This is superior to a cableoperated throttle system for the following reasons: By eliminating the M-M elements and transmitting an automotive vehicle\u2019s throttle position mechatronically, DBW AWD propulsion greatly reduces the number of moving parts in the throttle system; this means greater accuracy, reduced mass, and, theoretically, no service requirements (like oiling and adjusting the throttle cable). Automotive Mechatronics 152 The greater accuracy not only improves the driving experience (increased responsiveness and consistent pedal feel regardless of outside temperature or pedal position), but it allows the throttle position to be tied closely into EMC information like fuel pressure, engine temperature, and exhaust gas recirculation (EGR); this means improved fuel economy and power delivery as well as lower exhaust emissions. With the pedal inputs reduced to a series of electronic signals, it becomes a simple matter to integrate a vehicle\u2019s throttle with non-engine specific items like ABS, gear selection and traction control; this increases the effectiveness of these systems while further reducing the amount of moving parts, service requirements, and vehicle mass. But what may occur if the \u2018wire\u2019 in the DBW AWD propulsion mechatronic control system, breaks? In other words, what if a mechatronic malfunction disrupts the flow of information between the TPSs and the EMC? It could give a whole new meaning to the term \u2018sticking throttle\u2019, couldn\u2019t it? The reality is that, just like fuel injection and an anti-lock braking system (ABS), a DBW AWD propulsion mechatronic control system is only as good as its programmers and manufacturers. While the first generation of fuel-injected ICEs had its share of technical gremlins, the fuel system of the average 2005 model is far more accurate, and dependable, than any carburettor-equipped vehicle from 25 years ago. Because DBW technology was first used on civil and military aircraft over 20 years ago (except it was termed fly-by-wire (FBW) back then), consumers can be assured that its reliability under less-than-ideal circumstances has been tested. It is now used on everything from industrial equipment (like heavy-duty machines) to cutting-edge ground-assault vehicles (like the future Grizzly tank). Speaking of aircraft (air-plane), many of modern jets use FBW technology for turning and braking, in addition to throttle mechatronic control. Could the same thing sooner or later be subjected to automotive vehicles? Could an unsophisticated joystick in the future substitute a vehicle\u2019s steering hand wheel, accelerator pedal, and brake pedal? That would be like suggesting that sooner or later vehicles may be able to drive themselves without any driver input [BRAUER 2004]. To achieve an overall improvement in vehicle safety, a fully-controlled powertrain is necessary. For instance, the technical objective of a powertrain equipped with intelligent technologies (PEIT) project [PEIT 2004] might be thus to build up an integrated self-stabilising powertrain that provides an interface to add all accident prevention and driver assistance functions of the vehicle. The powertrain interface may make it possible to integrate DBW AWD propulsion, BBW AWB dispulsion, ABW AWA suspension, and SBW AWS conversion mechatronic control systems and fail operative energy management into the RBW or XBW integrated unibody or chassis motion mechatronic control system, for example as shown in Figure 2.4 [PEIT 2004] 2.1 Introduction 153 To connect the functionalities and their mechatronically controlled devices, a failure tolerant system architecture is developed with two or even three central electronic control units (ECU) derived from the avionics industry co-ordinating the powertrain functions. Thus, only a single input, the motion vector providing the information of vector length and vector angle for acceleration/deceleration and yaw angle, respectively, vehicle body sideslip angle, may be necessary to control the whole motion task. The integrated engine-transmission management control (E-TMC) system is responsible for the coordination of safety and redundancy functionality. This key technology function may serve as a new standard in the automotive industry to coordinate a powertrain\u2019s automotive mechatronics. DBW AWD propulsion mechatronic control systems could eventually use joystick-like mechatronic controls that would eradicate the necessity for a steering wheel as well as accelerator and brake pedals, freeing up room in the interior for other potential innovative advancements. Besides, DBW AWD propulsion mechatronic control systems allow faster, more accurate interfacing with vehicle stability control (VSC) systems, as well as \u2018smart\u2019 ACC and ATC, and they also leave room for future active safety measures like collision-avoidance systems and park-assist gadgets. DBW AWD propulsion mechatronic control systems allow a level of integration not possible with M-M systems. For instance, a vehicle\u2019s airbag system could take into account the throttle position at the time of impact (or release the throttle on impact), an automatic suspension system could stiffen in response to a punch of the gas, or the steering system could take the throttle position into account when deciding how much boost to give [HALVORSON, 2004]. Automotive Mechatronics 154 There are many advantages in replacing a vehicle\u2019s M-M, F-M and/or P-M hyposystems with mechatronic ones (for example, sidebar, \u2018DBW AWD\u2019, and so on). Mechatronic control systems are inherently more reliable, more efficient, add less mass to an automotive vehicle, and can offer more functionality than M-M systems can. Lighter mass and more efficiency equate to better fuel economy -- an average of 5% improvement over traditional systems, a factor on everyone\u2019s mind in recent times of skyrocketing fuel prices. However, the mechanical-to-electrical shift is hampered by several factors, including the inertia of the automotive industry and a vehicle\u2019s available power source [LIPMAN 2004]. In not-too-distant automotive vehicles, in place of the steering hand wheel (HW) and floor acceleration and brake pedals mechatronic control systems may be used. The accelerator, gear shifting, and clutch actuator, as well as brakes and steering may be mechatronically controlled by DBW AWD technology. DBW AWD propulsion mechatronic control systems may be mechatronically controlled by the proof-of-concept driver interface shown in Figure 1.5 [SAE INTERNATIONAL, 2004; CITRO\u00cbN 2005]. Gearshift and clutch operation are so closely coupled that the systems may be considered together. The gearbox for the automotive vehicle may be based on an existing production unit employing a conventional H-pattern manual shift configuration. However, to accomplish the second-third and fourth-fifth movements of the selector mechanism inside the gearbox, more precise linear and rotational movements may be required. Up and down shifts are handled via the \u2018+\u2019 and \u2018-\u2018 buttons on the right-side side of the driver interface, with neutral being a logical \u20180\u2019. 2.1 Introduction 155 Reverse is selected via a dedicated button and is protected from inappropriate application by algorithms in the actuator control unit. Both clutch and gearshift-actuating units may be on a conventional 14 VDC or future 42 VDC energy-and-information network (E&IN). For the BBW AWB dispulsion mechatronic control systems, compact E-M actuating units may be coupled with brake calliper and braking design. At its current, interim stage of development, the braking system is said to rival conventional F-M arrangements in performance. Significant progress has been made in mass and size reductions during development, with the complete mechatronic brake calliper assembly now being a compact unit with a mass comparable to that of the conventional F-M design it replaces. Control of the braking mechatronic control system is duplicated on both the left and right driver interface yokes and is enabled by squeezing the handgrips. The M-M design incorporates a progressive resistance and a small, discernible free-play at the beginning of the movement to provide the driver with a tactile indication when the brakes begin to operate. The system controls each brake as an individual subsystem under an umbrella control for the complete vehicle braking system. The driver interface\u2019s left and right steering control yokes are linked mechanically and have a full movement of just 20 deg. Movement of the vehicle\u2019s front wheels is aided by full logic mechatronic control, with feedback to the driver being provided by a high-torque motor. driver \u2018feel\u2019 is programmable, as is the relationship between yoke and front-wheel movement. A next-generation steering actuator fits easily into the front subframe assembly of the future production automotive vehicle. The vehicle of the future gives the impression of being just similar to this: it has no ECE or ICE, no steering column, and no brake pedal. It needs no petrol (gasoline), emits no pollution (only a little water vapour) and hitherto handles similarly to a high-performance vehicle. It might seem not unlike an ecologist\u2019s imagination, in place of an ICE, for example, the vehicle of the future may be energised by fuel cells (FC) similar to those used in the orbiting space station [HM-MILTON, 2002]. Electrical energy is generated by an electro-chemical (E-CH) reaction of hydrogen and oxygen that submits only thermal energy (heat) and water (H2O) as its side-effect. No smelly exhaust, no smog, no greenhouse gases. Misplaced too are the cables and mechanical links that have held together automotive vehicles since the beginning of the automobile age a century ago. As a substitute, the steering and braking are fully mechatronically controlled; using techniques originated in FBW aircraft cockpits. Instead of a steering column there is a miniature colour screen and two handgrips, as shown in Figure 2.6 [THIESEN 2003, SCHMIDT 2004]. Automotive Mechatronics 156 To accelerate, drivers twist the grips. To have an effect on the brakes, drivers squeeze them. To turn left or right, drivers reposition the grips up or down. In place of a rear-view mirror, there is a video camera that visualises an image of the road travelled, along with such driving data as vehicle velocity and hydrogen-fuel levels. For the reason that the automotive vehicle is properly programmable, drivers can adjust their performance preferences. (Brakes ought to be soft or hard? ECE or ICE sporty or fuel saving?) Eradicating all the mechanical controls frees up the space where an ECE or ICE would normally dwell; for example, in the automotive vehicle of the future, drivers can watch straight through the front of the vehicle. Without a steering column, vehicle designers can locate the mechatronic controls anywhere in the vehicle for maximum comfort and safety, even in the backseat. The core of the vehicle of the future, however, is an aluminium, skateboardlike chassis that runs the length of the automotive vehicle. Incorporated within it are the FCs, an electro-mechanical (E-M) motor, tanks of compressed hydrogen and all the mechatronics. Since the fibreglass body is principally a shell, different models can be exchanged similar to cell-phone covers. Consequently drivers could in theory drive a sports car on the weekends and alter it into a minivan to take the children to school. For one thing, the roadside infrastructure that fuels and services nowadays \u2018gas guzzlers\u2019 would have to be modified to distribute hydrogen and reprogram out-of-order mechatronic control systems. However, if the effect may be a fleet of safe, fuel-efficient, non-polluting vehicles that downgraded or eradicated the world\u2019s dependence on fossil fuel, it would be worth the effort. 2.1 Introduction 157 Automotive engineers and scientists seek future enhancements to the automotive vehicles of the future to principally approach from systems engineering efficiencies prior to breakthroughs in specific components. For example, separated wheel E-M motors are likely may be made possible by fully integrating the brake, suspension, and wheel into an optimised corner module. Although part of the concept platform was unveiled some time ago, such technology is not on the driveable automotive vehicle of the future that features a central electrical system to power the wheels. But the automotive vehicle manufacturers maintain their goal remains to put an in-wheel-hub E-M motor at each wheel -- if it can find a way to fit them into the skateboard-chassis along with the FC system, drivetrain, storage tanks, and various mechatronics. Some vehicle manufacturers are working on a solid-state system that uses sodium alienate hydride material to store hydrogen. The system can store a relatively large amount of hydrogen but it currently takes too long to infuse the hydride and release the hydrogen. Another challenge is reducing the amount of expensive precious metals from the FC stack and costly carbon fibre in the fuel tank. It is estimated that three-quarters of the cost of the tank may be attributed to the carbon fibre shell [AUTOTECH 2003]. All of the emerging automotive vehicle\u2019s working parts may reside in a skateboard-chassis of less than a foot thick. The chassis may contain, for example, the FC, hydrogen tanks and E-M motors to drive the front and rear wheels. What appears to be a kind of video game to a conventional driver is actually a unique innovation based on a revolutionary concept known as \u2018DBW AWD\u2019. This new system not only offers improved safety, comfort, and ergonomics, but also provides extra advantages in terms of vehicle design and production. It\u2019s all made possible by a mechatronic control system that replaces the mechanical and fluidical connections linking the steering wheel and pedals with the steering, drive, and brakes. Designed so that it can only be moved to the left or right, a unique sidestick (see Fig. 2.7) enables drivers to steer with high precision. Automotive Mechatronics 158 At the same time, an integrated E-M motor gives them a more realistic feeling of steering resistance. A two-dimensional force-measuring sensor that reacts to forward or backward hand pressure, registers commands to accelerate or brake. The DBW AWD propulsion mechatronic control system takes over control of the ECE or ICE plus the braking and steering functions. In this manner, it can control the automotive vehicle as the driver would wish, even in a situation where the driver might not be able to react in time. Today, there are in normal driving operations \u2018DBW AWD\u2019 automotive vehicles of the future without steering hand wheels, acceleration or brake pedals that are steered only by sidesticks, as shown in Figure 2.8. Appearances can be deceiving: The easy-to-use sidestick is based on a complex mechatronic system with redundant safeguards. A DBW AWD propulsion mechatronic control system consists of sensors and control elements connected by a redundant data bus (black). The driving dynamics controller plays an important role here, actively taking over when the driver loses control of the vehicle. All mechatronic components have a backup system to ensure maximum safety. To achieve this ambitious objective, automotive scientists and engineers disconnected the fluidical and mechanical connections and replaced them with E-M servomotors and electronic switching elements. Both types of mechatronic components are controlled by a fault-tolerant microcomputer system. The latter receives its data not only from the driver, who issues commands to the system, but also from sensors that continually monitor the vehicle\u2019s status. \u2018DBW AWD\u2019 automotive vehicles of the future may offer numerous benefits: Their safety systems react automatically to potentially dangerous driving situations within fractions of a second; The push of a button on a sidestick (side-mounted joystick) may be sufficient to make parking and other difficult manoeuvres child\u2019s play; The advanced concept may also enable designers to completely revamp automobile interiors. 2.1 Introduction 159 High values of the vehicle velocity, tight curves, and wet cobblestones -- even experienced race car drivers would struggle with the steering under such conditions. As far as automotive scientists and engineers are concerned, two fingers are sufficient to control the vehicle; the driver is driving with a hand-sized sidestick, or side-mounted joystick. The driver\u2019s left elbow may be supported against the centrifugal force by the arm console in the door and the right elbow may rest on the centre console. The driver literally has a handle on the automotive vehicle. The most important driving operations -- accelerating, braking, steering, signalling, and honking the horn -- are integrated, for instance, in two sidesticks in the vehicle\u2019s armrests, as shown in Figure 2.9. [DaimlerChrysler]. Much like a modern jet fighter, the automotive vehicle can be accelerated by lightly pushing forward the compact joysticks that are linked electronically. Automotive Mechatronics 160 Once the vehicle is on its way, the integrated ACC automatically maintains vehicle velocity. When the driver wants to brake, he or she simply pulls back the side-stick (see Fig. 2.10). by lightly pushing forward the compact joysticks that are linked electronically [DaimlerChrysler]. A significant safety feature of DBW AWD is that, unlike the electronic stability program (ESP) currently in use, it can be extended to act on the steering as well as on the brakes (see Fig. 2.11), even sceptical drivers end up delighted by the system. While the sidestick is held comfortably in the hand that sets the course, the wheels dance over wet, slippery cobblestones, controlled by microcomputers that automatically compensate for every bump with a corrective steering adjustment. 2.1 Introduction 161 [DaimlerChrysler]. A test procedure in which strong winds are directed at the side of a vehicle also demonstrates the effectiveness of the stabilising algorithms. When the wind corridor is reached, a conventional vehicle immediately swerves off course and the driver must steer accordingly to counteract its effect. With DBW AWD, drivers hardly notice the wind at all. This is because the sensors immediately register the deviation it causes, while the computer already \u2018knows\u2019 the direction that the driver wants to take due to the position of the sidestick. As a result, the wheels are automatically turned in the right direction to offset the effect of the side wind. With the stabilising algorithm of DBW AWD, however, sensors, computers, and actuators react so quickly that the vehicle neither skids nor swerves out of the lane. Instead, it maintains the desired course. Passive Safety - Integrating driving functions into a sidestick offers additional passive safety benefits, too. It is well known that, if there is no steering column, then there is also no danger of the chest injuries often caused in an accident and if the driver\u2019s foot can no longer get caught in one of the pedals during a collision, then the number of foot injuries may also be reduced. Braking Speed - But the sidestick concept\u2019s ace in the hole is braking speed. In order to brake, drivers of conventional vehicles require an average of 0.2 s to move their feet from the acceleration to the brake pedal. At a speed of circa 50 km/h (30 mph), this translates into an additional braking distance of roughly 2.9 m (9.5 feet). The quicker reaction time of the sidestick system could therefore prevent many collisions [DAIMLERCHRYSLER 1998-2004]. Automotive Mechatronics 162 Automatic Vehicle Velocity Adjustion - DBW AWD -- whether by means of sidestick or mechatronic steering wheel -- also offers a general advantage. Because there is no longer a direct mechanical or fluidic (hydraulic) connection between the driver and the wheel, the steering ratio can be automatically adjusted to the vehicle\u2019s velocity."
        ]
    },
    {
        "image_filename": "designv10_12_0003006_j.ijfatigue.2020.105483-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003006_j.ijfatigue.2020.105483-Figure6-1.png",
        "caption": "Fig. 6. Elastic stress at the point of fatigue crack initiation under cyclic bending loading with R = 0, \u03c3n = b \u00d7 h2/6.",
        "texts": [
            " The severity of the notch was varied defining (i) a semicircular notch with radius c, Fig. 5 top; and (ii) a semi elliptical notch, Fig. 5 bottom, with a c/a ratio equal to 4 where c is the major semi-axis and a is the minor semi axis of the ellipse. The notch depth c was the same for the two geometries and defined the same minimum cross-section (5 mm \u00d7 5 mm) for nominal stress calculation. Details of the two notched specimen geometries are summarized in Table 2. The miniature specimens of Fig. 5 were tested under cyclic bending [26]. Fig. 6 shows different ways to apply a bending moment M to the specimens. Therefore, the reference nominal stress \u03c3n is computed as M/W where W is the section modulus of the minimum cross section. The bending moment generates tensile stress at desired locations in the specimen: i.e. at the notch root or at the flat surface opposite to the round notch. A detailed elastic finite element analysis of the two specimen geometries and loading conditions shown in Fig. 6 provided the stress concentration factors Kt of the two notches in bending: a mild notch effect Kt = 1.63 is associated to the semicircular geometry of Fig. 5 top, while a severe notch effect of Kt = 4.95 is obtained for the semielliptical geometry shown in Fig. 5 bottom. In addition, a stress correction factor (i.e. Cmg = 0.91) for the first kind of specimen loading was computed [26]. It is used for the nominal stress correction in order to determine the smooth (i.e. un-notched) fatigue behavior of the material using mild notched miniature specimens, i"
        ],
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    },
    {
        "image_filename": "designv10_12_0002734_1.4032579-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002734_1.4032579-Figure5-1.png",
        "caption": "Fig. 5 Determination of points Pi3, Pi4 to define the ease-off surface of the pinion: (a) determination of points Pi1, bi1, ai1, Pi3, (b) illustration of points Pi, ai1, ai2, and (c) ease-off topography and Pi Pi3 Pi4",
        "texts": [
            " The third equation for the determination of these three unknowns is the equation of meshing f2s\u00bc 0. The meshing of surfaces R1r and R2r is expected to reproduce Dw2 represented by Eq. (5), so us, u2 are correlated by Eq. (10). Considering Eqs. (14), f2s\u00bc 0, (15), and (10) simultaneously allows the determination of parameters (us, ls, us) at points Mi. The solutions of (us, ls, us) at Mi are denoted by (usi, lsi, usi). By substituting usi, lsi (i\u00bc 1, 2,\u2026, 2l 1) into Eq. (1) of the shaper s, a desired contact path P1P2l 1 on Rs can be attained, as shown in Fig. 5. 3.2 Redesign of the Tooth Surface of the Pinion. Surfaces R2r and R1 (or Rs) are in line contact at every instant. Hence, the aim of this part is to localize bearing contact between R2r and R1 (or Rs), and control the length of the major axis. The procedure is (1) By selecting a point Mi1 (Mi1 is not coincident with Mi) on contact path M1M2l 1, by applying Eqs. (8) and (10), it is possible to determine the conjugate point Pi1 of Mi1 on surface Rs. (2) In plane Pt that is tangent to point Pi1, an infinite contact ellipse (represented by 2a, f, and g) can be determined [32], as shown in Fig. 5(a), where g and f are the direction vectors of the major and minor axes of the contact ellipse, respectively, and 2a is the length of the major axis. L21 is the contact line between R2r and Rs (or R1) at point Pi1, and Pn is the normal plane of point Pi1. (3) A point bi1 locates on the major axis g, so the length of the major axis could be controlled by the distance jPi1bi1j \u00bc a, where a is a predesigned value, the position vector of point bi1 is represented by Rsbi1 \u00bc RsPi1 \u00f0us; ls\u00de \u00fe a g (16) where RsPi1 is the position vector of point Pi1 in coordinate system Ss",
            "org/ on 03/14/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use R2rzMi1 \u00f0us; ls;us\u00de Rl \u00bc tan \u00f0c\u00fe h\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 2rxMi1 \u00f0us; ls;us\u00de \u00fe R2 2ryMi1 \u00f0us; ls;us\u00de q Ll (18) (ii) To facilitate calculation, point ai1 is chosen to be located on the straight line kk that passes through point Pi (Fig. 5(b)), which is expressed by Eq. (19). Rsxai1, Rsyai1, Rsx, Rsy in Eq. (19) are the projections of the position vector Rs of point ai1 and Pi on axes xs, ys. It must be reiterated that parameters usi and lsi have been determined for point Pi in Sec. 3.1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 sxai1 \u00f0us; ls\u00de \u00fe R2 syai1 \u00f0us; ls\u00de q \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 sx\u00f0usi; lsi\u00de \u00fe R2 sy\u00f0usi; lsi\u00de q (19) (iii) Because of the identity of R1 and Rs, ai1 is also a point on surface R1",
            "00635 mm, here, surfaces R2r and R1 contact along curve L21, the length of the major axis is infinitely great, the elastic deformations at Pi1 and ai1 are equal or very approximate, so the materials at ai1 must be removed, and the cutting depth in normal direction is jai1Pi3j \u00bc d. The position vector of point Pi3 is expressed by RsPi3 \u00bc RsPi1 \u00f0us; ls\u00de \u00fe a g\u00fe \u00f0dp \u00fe d\u00de nsPi1 \u00f0us; ls\u00de (21) By the same procedures of (1)\u2013(5), points Pi2, bi2, ai2, Pi4 can be determined on the other side of the contact path P1P2l 1, as shown in Figs. 5(b) and 5(c), In Fig. 5, l\u00bc 3. In this manner, the points of three columns are determined: Pi, Pi3, and Pi4 (i\u00bc 1, 2,\u2026, 2l 1). Figure 6 shows that a parabolic curve k0k0 passing through Pi3, Pi, and Pi4 is tangent to Pi, Hence, if the all parabolas at P1, P2,\u2026, P2l 1 are applied to construct a new ease-off surface R1r (Fig. 5(c)) of the pinion, point contact between R1r and R2r is foreseeable. 4 Manufacturing of Pinion With Tooth Surface R1r 4.1 Manufacturing Method. To generate R1r, there are some materials on R1 that need to be cut. It can be seen from Figs. 5(c) and 6 that: the maximum cutting depth may occur at either endpoints B or D on surface R1; the material along P1P2l 1 does not require removal; the material that needs cutting at A and C on surface R1 is very small, as shown in Fig. 7. Point contact between surface R1r and its generating cutter is required to avoid the point generated on surface R1r being further cut when the cutter generates the current point",
            " The equations of meshing between surfaces R1r and Rg are represented by fgu\u00f0uE; hg; ug\u00de \u00bc ng\u00f0uE; hg\u00de v \u00f0g1;ug\u00de g \u00f0ug\u00de \u00bc 0 (26) fgL\u00f0uE; hg; Lg\u00de \u00bc ng\u00f0uE; hg\u00de v\u00f0g1; Lg\u00de g \u00f0Lg\u00de \u00bc 0 (27) where vector v \u00f0g1;ug\u00de g (v \u00f0g1;Lg\u00de g ) represents the relative velocity between the grinding disk and the pinion determined under the condition that the parameter ug (Lg) of motion is varied and the other parameter Lg (ug) is held at rest, both vectors of relative velocity are represented in Sg. The normal vector to surface R1r is n1r \u00bcM1g ng (28) The envelope to the family of Rg is determined as the ease-off surface R1r of the pinion by simultaneous consideration of Eqs. (25)\u2013(27). 4.3 Representation of the Moving Trajectory of the Grinding Disk. Now, the determination of parameter Eg is considered. First, comparing Fig. 5(c) to Fig. 5(b), the difference between k0k0 (Pi3 Pi Pi4) and kk is very small, angle ugi is assumed to be a constant no matter which point on k0k0 is generated by the grinding disk; hence, parameter Eg can be defined as the function of parameter Lg as Eg \u00bc c1 \u00fe c2 Lg \u00fe c3 L2 g (29) where coefficients c1, c2, and c3 require determination. For generating R1r, only one spindle movement of the machine tool has to be adjusted to obey the motion rule represented by Eq. (29), which can be regarded as special case in which multiple spindles\u2019 movement need adjusting for modifying the tooth surface of the hypoid gear drive [13]"
        ],
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    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.13-1.png",
        "caption": "Figure 10.13. Stable and unstable principal axes of inertia for a homogeneous block.",
        "texts": [
            " Also, for an admissible point Q on the axis i l of an axisymmetric body for which 122= 133, (10.88) holds for the principal axes at Q. In particular, the steady rotation about every principal axis at the center of mass of a body of revolution is infinitesimally stable . The torque-free rotational instability of a rigid body may be demonstrated physically by carefully tossing a uniform rectangular block into the air while imparting to it a constant spin initially about one of its principal axes at its center of mass, as shown in Fig. 10.13. When the block is rotated about axes el and e2 456 Chapter 10 of its smallest and largest principal moments of inertia at its center of mass, the block is observed to rotate in a fairly steady, stable manner. But when the block is set spinning about its intermediate axis e3 at its center of mass, it is observed that the block wobbles from its initial spin axis. See Problem 10.45. 10.14.2. Discussion of the General Torque-Free Steady Rotation of a Rigid Body The problem of the stability of the torque-free motion of a rigid body concerns the steady rotation about a principal axis, which is one of several solutions of the homogeneous system (10"
        ],
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    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure12.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure12.4-1.png",
        "caption": "Fig. 12.4 A ball impacting near the tip of a stationary bat causes the tip to bend to the right. If the ball impacts near the middle of the bat then the tip bends to the left. An impact at the vibration node causes the bat to rotate without vibrating",
        "texts": [
            " Vibrations of a bat are largest in amplitude when the ball is struck right at the tip of the bat. Such an impact usually stings the hands. Vibrations are weakest when the bat strikes the ball at one or other of the two node points about 6 in. from the tip of the bat. These are the sweet spots on the bat. In the sweet spot region between the two node points, vibrations are reduced to such a low level that the batter is almost unaware of the fact that he or she actually struck the ball. The existence of a node point can be explained in a slightly oversimplified manner with reference to Fig. 12.4. We show in Fig. 12.4a a bat in a position at rest, with a ball approaching from the left. An impact near the tip of the bat will bend the tip to the right, as shown in Fig. 12.4b, and the bat will rotate away from the ball. An impact near the middle of the bat will bend the tip to the left, without any rotation of the bat if the impact is at the bat center of mass (CM). The whole bat will just recoil away from the ball without rotating. An impact at the node point about half way between the tip and the CM bends the bat locally at the impact point, but as the bending wave propagates toward each end, the bat quickly straightens out. The end result of an impact at the node point is that the bat translates and rotates away from the ball without vibrating. In each case shown in Fig. 12.4 we have ignored the manner in which the bend develops and changes over time. The whole bat does not bend instantly into the positions shown. Rather, the bend occurs locally around the impact point while the rest 212 12 Bat Vibrations of the bat remains straight. The local bend then propagates as a wave away from the impact point. As it does so, the bat assumes the shapes shown in Fig. 12.4. Some of the bending energy ends up as rotation of the bat, some as recoil motion of the whole bat and some as vibration of the bat. The energy that remains is retained by the ball as it bounces off the bat. If the bat is initially at rest then the ball bounces off the bat at only about 1=5th of its incident speed at most, depending on the impact point. The high frequency ping of an aluminum bat is due to a change in bat shape around the circumference of the barrel. The barrel is circular in cross-section, but the shape of the barrel changes when it strikes a ball due to the large force acting on the barrel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000444_s12206-008-0110-9-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000444_s12206-008-0110-9-Figure9-1.png",
        "caption": "Fig. 9. Photograph of structural modal test setup.",
        "texts": [
            " When one of the frequencies of the excitation forces coincides with the structural or acoustic resonant frequency, resonance occurs resulting in excessive acoustic noise. When the frequency components of the noise are proportional to the motor RPM, noise emission is related to electromagnetic excitation forces. However, when the frequency components of the noise are not related to the motor RPM, noise phenomena are related to structural or acoustic mode. A structural modal test was performed by random excitation with a shaker to examine the structural frequency response of the motor and its test setup is shown in Fig. 9. The frequency response function of the motor is shown in Fig. 10, where no resonance is observed near 650 Hz. Therefore, the noise component of 650 Hz seems not to be related to the mechanical resonance. To examine the acoustic characteristics of the motor internal airspace, white noise excitation by a horn driver is applied to the motor at standstill through a 25 mm diameter hole introduced on the rotor frame, and the noise is measured by a microphone as shown in Fig. 11. The acoustic frequency response function is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003776_j.rcim.2021.102193-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003776_j.rcim.2021.102193-Figure6-1.png",
        "caption": "Fig. 6. The five-point path of the simulation in the reference frame.",
        "texts": [
            " To minimize the feedrate fluctuation, the parametric interpolation method in Ref. [31] is adopted. Finally, the reference drive commands can be obtained through the inverse kinematics of the robot. Two different tool paths are utilized in the simulation and the experiment respectively to show the advantages of the proposed method. All the algorithms are implemented in Matlab 9.7 on a personal PC with an Intel Core i7-6700HQ CPU of 2.6 GHz and 8G RAM. In this section, the five-point robot path as shown in Fig. 6 is utilized for the simulation. The original position linear path is directly represented based on the coordinates of the tool tip positions in the reference frame while the orientation linear path is represented based on the exponential coordinates in the rotation parametric space as shown in Fig. 7. The five-point path contains three corners. Then, both the direct transition scheme based on Eq. (20) and (23) and the proposed adaptive transition scheme based on Eq. (28) in Section 2 can be utilized to smooth the corners"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000806_j.mechatronics.2010.04.009-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000806_j.mechatronics.2010.04.009-Figure1-1.png",
        "caption": "Fig. 1. Illustration of forces and moments acting on a small scale helicopter.",
        "texts": [
            " The position and velocity of the helicopter center of gravity are respectively given by Pi = [x y z]T and mi = [mx my mz]T with respect to the inertial frame in North\u2013East\u2013Down (NED) orientation (with an upper subindex i). The helicopter angular rate vector xb = [xx xy xz]T and the Euler angle vector Hb = [/ h w]T defined in the roll-pitch-yaw sequence are with respect to its body frame (with an upper sub-index b). Furthermore, R\u00f0H\u00de is the helicopter\u2019s rotation matrix from the body axes to the inertial axes and sk(xb) means the skew-symmetric matrix of the body angular rate. The principle force and moments exerting on the rigid body are illustrated in Fig. 1. The four independent inputs to this model are one lift force control, denoted by ub T \u00bc Tmreb 3, and three directional torque controls, denoted by ub M \u00bc \u00bdLmr Mmr Ntr T 2 R3. Both ub T and ub M are applied along the body frame. Qmr and Qtr respectively represent the antitorques on the main rotor and tail rotor. J is related to the helicopter mechanical characteristics and expressed by J \u00bc 1\u00fe kb Tmr hmr 0 0 0 1\u00fe kb Tmrhmr 0 0 0 1 2664 3775 \u00f05\u00de where hmr denotes the height of rotor head above the helicopter centre of gravity (c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000632_s10846-010-9445-4-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000632_s10846-010-9445-4-Figure8-1.png",
        "caption": "Fig. 8 Aerosonde UAV",
        "texts": [
            " Also, because of the reduction on the switching the control becomes implementable. The hardware, servos, will be able to keep up with the control necessities. The simulation was done by using SIMULINK in conjunction with the Aerosim library. The library contains all of the necessary blocks to simulate different airplane Table 3 Aerosonde specifications Wingspan 116 in 2.9 m Wing area 878.4 in2 0.57 dm2 Length 68 in 1.7 m Height 24 in 0.60 m models. It also comes with an Aerosonde UAV preloaded model [9]. The Aerosonde UAV (see Fig. 8) was used to test the control algorithm since it contains certain similarities with the real airplane. The Fig. 9 shows the block containing the dynamic function representation of the UAV model. Only the States, Sensors and Euler outputs of the UAV are used to test the control algorithm. Figure 10 shows all of the inputs that go into the control algorithms. The simulation begins with the airplane at an altitude of 1,000 m, and an initial velocity of 27 m/s, the rest of the variables are set to zero for t = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002383_1.4035079-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002383_1.4035079-Figure2-1.png",
        "caption": "Fig. 2 The circular lengthwise curve of the crown gear",
        "texts": [
            " 139, JUNE 2017 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/936000/ on 02/03/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use choice than the others. The corresponding design procedure can be applied to the other choices of the lengthwise curve. For a crown gear, the circular lengthwise curve is a given arc in the reference plane. The reference plane becomes the pitch cone when the crown gear is spindled into a spiral bevel gear. Figure 2 is a partial view about the intersection of the crown gear tooth flanks with the reference plane. qoMqi _ is the circular lengthwise curve, which can be defined with the given mean point M and arc center point ol. To define M and ol, a coordinate system Sg\u00f0og; xg; yg; zg\u00de fixed in the reference plane is established as shown in Fig. 2. og is the intersection point of the gear axis with the reference plane. zg is the unit normal direction of the reference plane, and it directs from pitch cone apex to back cone apex. M is defined in Sg by the given mean cone distance Am and an initial angle hmc. ol is defined in Sg by the given ht and rc. ht is the commentary to spiral angle, which is given in gear design and defined as the angle between Mog and the tangent direction of the lengthwise curve at M. In conventional methods, rc is the cutter radius chosen based on gear design and manufacturing methods",
            " Assuming that the angle from ogM to ogqc is represented with hc, we also have qc\u00f0u\u00de \u00bc rq \u00bd cos hc sin hc 0 (3) where rq \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2 cx \u00fe q2 cy q ; hc \u00bc arctan qcy qcx hmc Geometrically, a spiral bevel gear can be obtained from the crown gear, while the reference plane of the crown gear is spindled into the pitch cone of the spiral bevel gear. Subsequently, the circular lengthwise curve of the crown gear is spindled into a new lengthwise curve on the pitch cone. As shown in Fig. 3(a), the new lengthwise curve is q0oMq0i _ . While q0oMq0i _ is projected in the plane xgogyg, as shown in Fig. 3(b), hms and hs are two angles in this plane related to hmc and hc in Fig. 2, respectively. According to Ref. [41], we have hms \u00bc hmc cscC; hs \u00bc hc cscC (4) where C is the gear pitch angle. Generally, the pitch cone in Sg\u00f0ogxg; yg; zg\u00de can be parametrically represented as P\u00f0r; h\u00de \u00bc r \u00bd sin C cos h sin C sin h cos C (5) Subsequently, a point qs on the new lengthwise curve q0oMq0i _ can be represented in Sg as qs\u00f0hs\u00de\u00bc rq \u00bd sinC cos\u00f0hms\u00fehs\u00de sinC sin\u00f0hms\u00fehs\u00de cosC (6) where rq is obtained as Eq. (3); hms and hs are calculated as Eq. (4). Since rq; hms, and hs are the functions with respect to parameter u, the parametric expression of the new lengthwise curve can also be treated as the representation with respect to parameter u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001565_0954406214562632-Figure19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001565_0954406214562632-Figure19-1.png",
        "caption": "Figure 19. The illustration of VHG.",
        "texts": [
            " Figures 15 and 16 show the processing of gear cutting in YH606 CNC Curved Tooth Bevel Gear Generator made by Tianjin Jing Cheng Machine Co., Ltd of China. The gear and pinion after processing are as shown in Figures 17 and 18, which completely meet the required design precision. Figure 13. The smooth tooth surface. Figure 12. The uneven assembly drawing of spiral bevel gear. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from To better illustrate the problem, other related experiments have also been conducted. The illustration of VHG is shown in Figure 19. H is the movement along the pinion axis, while G is the movement along the gear axis, and V is the offset of the gear set. When doing the experiments of contact pattern for spiral bevel gear set, keep the offset (V) at the value of 0, and the true backlash for the gear is set at 0.22mm. Each time, only change the value of H from 0.2 to \u00fe0.2. In this way, three experiments have been done, setting the value of H as \u00fe0.2, 0, and 0.2, respectively. The transmitted torque of contact patterns experiment was 20Nm according to at UNIVERSITY OF WINDSOR on September 29, 2015pic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.8-1.png",
        "caption": "Fig. 17.8 Four-bar F and the associated four-bar F\u2217 with link lengths r1 and interchanged",
        "texts": [
            "9) the substitutions \u03c8 = \u03c0 \u2212 \u03b1 and = r1 + r2 \u2212 a are made. Following this, a Taylor expansion up to second-order terms is made. The result is a quadratic equation for \u03bb = \u03b1/\u03d5 = x/( \u2212 x) . The solutions \u03bb1,2 are identical with those in (17.18): \u03bb1,2 = r1r2 \u00b1 \u221a r1r2a r2(r2 \u2212 a) , x1,2 = \u03bb1,2 \u03bb1,2 + 1 . (17.19) Examples: The link lengths of Fig. 17.6a yield x1 \u2248 5.17 , x2 \u2248 10.8 and those of Fig. 17.6b yield x1 \u2248 4.64 , x2 \u2248 2.21 . These are the points M1 and M2 shown in the figure. End of examples. 576 17 Planar Four-Bar Mechanism In Fig. 17.8 the four-bar A0ABB0 with link lengths , r1 , a , r2 is called four-bar F . Dashed lines parallel to the fixed link and to the input link define the point P . The quadrilateral B0PAB is drawn one more time in dotted lines. The dotted quadrilateral is called four-bar F\u2217 . Its fixed link has length r1 , and its input link has length . Both four-bars have the same coupler and the same output link. If F is a foldable four-bar, also F\u2217 is foldable. If F is a double-rocker of first kind (of second kind), also F\u2217 is a double-rocker of first kind (of second kind). If F is a double-crank, F\u2217 is either a double-crank or a crank-rocker. If F is a crank-rocker, F\u2217 is either a double-crank (if fixed link and crank are interchanged) or a crank-rocker (if fixed link and rocker are interchanged). Example: Let F be the crank-rocker in Fig. 17.4b . Interchange of fixed link and crank produces the double-crank of Fig. 17.4a . In Fig. 17.8 F and F\u2217 have one and the same input angle \u03d5 . The relation between the output angles \u03c8 and \u03c8\u2217 is seen to be \u03c8 + \u03c8\u2217 \u2261 \u03d5+ \u03c0 . (17.20) For a given angle \u03d5 Eqs.(17.12) determine in the four-bar F two angles \u03c81 and \u03c82 and in the four-bar F\u2217 with coefficients A\u2217 = 2r2(r1 \u2212 cos\u03d5) , B\u2217 = \u22122 r2 sin\u03d5 , C\u2217 = C two angles \u03c8\u2217 1 and \u03c8\u2217 2 . The coordination of the pairs of angles is as follows: \u03c81+\u03c8\u2217 2 \u2261 \u03d5+\u03c0 . This is verified by substituting 17.4 Inclination Angle of the Coupler. Transmission Angle 577 A , B ,C and A\u2217 , B\u2217 , C\u2217 into the equation cos\u03c81 cos\u03c8 \u2217 2 \u2212 sin\u03c81 sin\u03c8 \u2217 2 \u2261 \u2212 cos\u03d5 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure9-1.png",
        "caption": "Fig. 9. (a) Contact lines on worm wheel tooth flank in Example C. (b) Contact lines in (o1; jo1, ko1) in Example C.",
        "texts": [],
        "surrounding_texts": [
            "Six numerical examples with various basic designs and technological parameters, which are given in Table 1, are considered in this section. The primary geometrical design is carried out by using the current formulae for the Hindley hourglass worm drive and the toroid enveloping worm drive with double conical generatrices."
        ]
    },
    {
        "image_filename": "designv10_12_0000144_ip-b.1987.0046-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000144_ip-b.1987.0046-Figure8-1.png",
        "caption": "Fig. 8 Cross-section of driving transformers",
        "texts": [
            " 6, NOVEMBER 1987 287 and 8. Essentially each transformer consists of a mumetal core constructed from the same material as the motor laminations. The core is evenly wound with one phase of the 3-phase primary winding and the supply leads routed to the centre of the heat sink. The single-turn secondary windings each thread one core and are connected to a common end ring at the rear of the transformer section. The heat sink can be advantageously connected to the secondary circuit at this end-ring as shown in Fig. 8. To obtain a compact arrangement for the secondary connecting bars, these are formed into arcs which surround the two cores they do not thread. The bar arcs each span nominally one third of the core periphery and the primary supply leads can be conveniently routed between these arcs as shown in Fig. 3b. The main advantages of this form of transformer construction over the previous transformer [3] is the ease of winding formation and the absence of a precision ground sliding joint in the magnetic circuit",
            " The primary winding turns and wire diameter are not, of course, continuous variables and the final design values represent the closest possible fit to the continuously variable solution. Here the solution of the two simultaneous equations in wire diameter and number of primary turns gives an available wire size and an integer, respectively. It was found that when the closest fit was obtained to the design values shown in Fig. 7, the primary windings of the transformers each have 62 turns of 0.633 mm diameter wire. A scaled cross-section of the chosen transformer design is shown in Fig. 8. Also shown in Fig. 8 is the 292 IEE PROCEEDINGS, Vol. 134, Pt. B, No. 6, NOVEMBER 1987 connection of the motor and the heat sink to the transformer unit. The transformer end ring is arranged to be a press fit in the rear of the outer case and the heat sink ro = 11 mm, case temperature rise = 34\u00b0C on 100% duty cycle D = design value oiJJJ2 screws into the centre of the end ring. The primary leads enter the connection area through the centre of the transformer end ring. 5 Experimental results 5.7 Equivalent circuit The per-phase equivalent circuit of the motortransformer combination at 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.4-1.png",
        "caption": "Figure 10.4. Motion of a rigid log on a conveyor belt.",
        "texts": [],
        "surrounding_texts": [
            "F2 =W2+ T + b21 = - . (l0.31d) dt Adding (l0.31c) and (l0.31d) and noting (l0.31b), we reach A A d F 1+ F2 = F(a'l, t) + N + b21 = dt (PI + P2). (l0.31e) However, by (5.11), p(a'l, t) == pea'll U a'l2, t) = p(a'l] , t) + P(a'l2, t), and hence the far right-hand side of (l0.31e) is the total force F(a'l , t) on a'l . Therefore, N +b21 = 0, i.e. b21= -N. In conclusion, note also thatdp(a'l, t) /dt = dp(a'll, t) /dt + dp(a'l2, t) /dt = m(a'l])a*(a'll, t) +m(a'l2)a*(a'l2, t) . For the current case, since a*(a'l] , t) = a*(a'l2, t) = a*(a'l, t) and m(fJIJ) = mea'll) +m(a'l2), we confirm that F(a'l, t) = dp(a'l, t) /dt = m(a'l)a*(a'l, t). This example illustrate s in specific terms the analysis used in the construction ofthe mutual action principle for bodies . Obviously, there is no need to repeat these details in each problem solution. 0 Example 10.2. A 2 ft diameter log weighing 3220 lb is moved steadily on a large conveyor belt shown in Fig. lOA. At shutdown the belt speed decreases at the rate of 2 ft/sec2, and the log is observed to roll without slipping. At an instant of interest to, the log has an angular speed w which is increasing at the rate OJ = 1 rad/sec? relative to the belt, and g = 32.2 It/sec\". Find the total force acting on the log at the instant to. 422 Chapter 10 Solution. The total force acting on the log is determined by (l 0.26). The mass of the log is m(:?l3) = 3220/g = 100 slug; therefore, F(:?l3, t) = 100a*(:?l3, t). (l0.32a) We choose a reference frame rp fixed in the belt, as shown in Fig. lOA. Since there is no rotation of rp, the absolute acceleration of the center of mass of :?l3 in the ground frame <I> is determined by a\" == aCF = aco + aOF , (l0.32b) wherein aoF = - 2i ft/sec2 \u2022 Since the log rolls on the belt without slipping, with w = wk and x = lj ft, we find vco = VCD = W x x = -wi for all t . Therefore, at the moment of interest, aco = -wi = -Ii ft/sec2 relative to the belt frame , and (l0.32b) yields a* = -Ii - 2i = -3i It/sec\" . Hence , by (l0.32a) , the total force acting on the log at the time to is F(:?l3, t) = -30Oi lb. D"
        ]
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.29-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.29-1.png",
        "caption": "Fig. 7.29 Deployable mechanisms could be the size of a credit card to fit into a wallet for emergencies. Examples include (a) an adrenaline injector or (b) an inhaler",
        "texts": [
            " A deploying desk and chair could eliminate the need for an extra room for a home office, making them more available to the general population. International barge containers could be collapsed during return transport to reduce the cost associated with shipping empty space. Temporary structures could be LEMs, allowing innovative,deploying camping shelters, green houses, and field medical rooms. Many deployable devices could be the size of a credit card and easily carried in a wallet for unexpected situations (see Fig. 7.29). A compact blood lancet for blood testing would be useful for diabetes patients. Credit card sized adrenaline injectors could be useful for people with serious allergies. A small inhaler could easily be carried by asthma patients for use in case of emergencies. Even a single-exposure, disposable camera could fit inside a wallet in case of unplanned photograph opportunities. Compliant mechanisms provide significant benefits for motion applications. They can be compatible with many fabrication methods, may not require assembly, have friction-free and wear-free motion, provide high precision and high reliability, and they can integrate multiple functions into fewer components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002071_s12206-014-1032-3-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002071_s12206-014-1032-3-Figure5-1.png",
        "caption": "Fig. 5. Illustration of design variables.",
        "texts": [
            ", the upper region of the front left pillar. And it can be seen that the fatigue life is also comparable between the simulation and experimental test as summarized in Table 3. In this study, we aimed to maximize the fatigue life of the cab without increasing the mass. Thus the optimization problem can be formulated mathematically as, ( ) ( ) 1 2 11 min . . 475.20kg =[ , ,..., ] L U F s t m x x x \u00ec - \u00ef \u00a3 \u00ef \u00ed \u00a3 \u00a3 \u00ef \u00ef \u00ee x x x x x x (11) where F(x) and m(x) are the log of fatigue life and mass of the cab structure, respectively. Fig. 5 presents 11 thickness design variables whose ranges are all from 0.6 mm to 2.0 mm in this study. The surrogate model is to construct an approximate function from a series of sampling points, which are typically determined using design of experiment (DoE) methods. In this study, 100 sets of sampling data were generated using the optimal latin hypercube sampling (OLHS) approach [16, 36- 41]. Since the mass of the cab follows a linear relationship to the panel thicknesses, m(x) is thus fitted by a linear function of the thickness variables"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001264_we.1530-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001264_we.1530-Figure6-1.png",
        "caption": "Figure 6. Frame of reference and nomenclature.",
        "texts": [
            " Afterwards, several combinations of axial, radial and angular displacements for which the most loaded ball reaches the statically allowable interference or elastic deflection are arranged (as deduced from ISO 76:200610); these interference combinations define the acceptance surface in the interference space. Finally, the force and moment equilibrium equations are applied, and as a result, the allowable axial, radial and moment load combinations are calculated from the aforementioned allowable interferences; these load combinations define the acceptance surface in the load space. Figure 6 shows the reference frame and the nomenclature to be used in the following analysis: is the azimuthal angle that indicates the position of a ball within the bearing; c1 is the contact direction between the upper raceway of the inner ring and the lower raceway of the outer ring; c2 is the contact direction between the lower raceway of the inner ring and the Wind Energ. (2012) \u00a9 2012 John Wiley & Sons, Ltd. DOI: 10.1002/we upper raceway of the outer ring; dw and dpw are, respectively, the ball diameter and ball centre diameter; rc is the raceway radius, identical for the four raceways"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002223_s1560354717030042-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002223_s1560354717030042-Figure2-1.png",
        "caption": "Fig. 2. Roller racer on a plane.",
        "texts": [
            " We also note that the analysis of the system (which involves the search for tensor invariants) agrees with the general scheme of the hierarchy of dynamical behavior of nonholonomic systems, which is discussed and illustrated in [2, 3] by the rolling motion of a rigid body on a plane and a sphere. 2. EQUATIONS OF MOTION Consider the problem of the motion of the simplest wheeled vehicle, the roller racer, on a plane. The roller racer consists of two coupled platforms which are rigid bodies and can freely rotate in a horizontal plane independently of each other (see Fig. 2). Each platform has a rigidly attached wheeled pair consisting of two wheels lying on the same axis. We define three coordinate systems: \u2014 an inertial coordinate system Oxy; \u2014 a noninertial coordinate system C1x1y1 attached to the first platform, with origin C1 at the center of mass of the wheeled pair. We assume that the axes C1x1 and C1y1 are directed, respectively, along a tangent and a normal to the plane of the wheels; \u2014 a noninertial coordinate system C2x2y2 attached to the second platform, with origin C2 at the center of mass of the wheeled pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure7.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure7.3-1.png",
        "caption": "Fig. 7.3 Diagram of gyroscope eccentric rotation by a sinusoidal law",
        "texts": [
            " The spinning top is constantly being displaced and moved by these asymmetric forces. The eccentric rotating mass of the top represents harmonic nutation, which means that the top is forced to nutate at the frequency of excitation. A plot using the nutation amplitude along one axis and the forcing frequency along the other axis is then described as a performance or response curve for the system. The eccentric rotation of the mass at about the top axis is modelled as a sinusoidal wave, as shown in Fig. 7.3. Here, the function y = esin\u03b1 denotes the displacement of the eccentric mass that represents the excitation input, where e is the eccentricity of mass location. The frequency of this sine wave is also the frequency at which nutation occurs. The analysis of gyroscope motions and nutation is conducted using the example of a tilted top on the angle \u03b3 to the horizontal that is not well-balanced. The analysis of the top motions is conducted for its rotation around the support point O in the counterclockwise direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000733_0022-2569(71)90002-4-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000733_0022-2569(71)90002-4-Figure15-1.png",
        "caption": "Figure 15. Approximate single-cam mechanism with two rigidly connected oscillating roller followers.",
        "texts": [
            " Thus the forward motion of the follower determines already its return motion. The idea is nov,' to construct a pitch profile c according to (6.1) and then to combine it with a finite yoke AP,4. It is advisable to choose the lever length L and the central distance OP = lo f the pivot P so that 17 L 2 - l z = b 2, (6.2) to have exact coincidence in the symmetric middle positionAoPAo of the yoke. In other positions there is only approximate coincidence: A and ,,~ cannot belong to c at the same time, but the error is rather small. This is to be seen in Fig. 15 which illustrates an example constructed by means of the func t ion f ( r ) = e . cos r. In this case the working cam profile ~ is a curve parallel to a Pascal snail c: r = e\" cos r + b . (6.3) The pitch profile c (6.3) is convex ifb >= 2e > 0. A numerical investigation of the errors occurring would be desirable. A new kind of single-cam mechanism was recently proposed by Jackowski and Dubil[5]: Two oscillating followers PA and QB of equal length L and with equal end rollers (centers A and B, common radius a) are operated by a cam disk c whose center O is the mid-point of the segment PQ = 2ljoining the follower pivots P and Q"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002975_tvt.2019.2943414-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002975_tvt.2019.2943414-Figure1-1.png",
        "caption": "Fig. 1. Structure of the liquid-cooled PMR. Fig. 2. Structure of the water channel.",
        "texts": [
            " The permeability distribution curve of the retarder stator is obtained by a simple permeability measuring instrument to evaluate the skin effect on the permeability. Thus, the effective permeability function of the stator is obtained at different rotational speeds, and the transient air-gap magnetic field model is optimized by using the effective permeability function. The simulation results showed that the optimized transient air-gap magnetic field computational model is in good agreement with the FEM. Finally, the calculation model of the eddy current braking torque was verified by the bench test. II. STRUCTURE AND WORKING PRINCIPLES Fig. 1 shows the structure of the liquid-cooled PMR. Sixteen PMs are evenly distributed on the mechanical support in a circular arrangement, with opposite polarity for the adjacent PMs. The rotor and PMs rotate at the angular velocity \u03c9. When the PMR is operating, the stator is pushed to a position by the cylinder and cuts the magnetic lines generated by the PMs, inducing the eddy currents and the braking torque according to Lenz\u2019s law. Then, the kinetic energy of the vehicle is converted to heat on the stator, leading to a sharp increase in the temperature of the stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000448_j.jsv.2008.09.050-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000448_j.jsv.2008.09.050-Figure6-1.png",
        "caption": "Fig. 6. Model of an eccentric gear pair.",
        "texts": [
            " 3 shows a repeating, small amplitude disconnection of the two gears, whereas Fig. 5 shows a large amplitude repeating pattern where the drive gear tooth actually completely traverses the freeplay region and impacts the opposing driven gear tooth, so that torque transfer is reversed. Fig. 4 shows a gear trajectory that displays non-repeating disconnection amplitudes. To check that this non-repeating behaviour is not due to transients, a test over 660 s was conducted, which showed that no significant changes occur in the response. Fig. 6 shows the important geometrical features of a gear pair incorporating eccentricity (grossly exaggerated for clarity). Subscript 1 denotes a drive gear or shaft while subscript 2 denotes driven gear or shaft. y1 and y2 are the angular motions about the shaft centres, y1 being measured in an anticlockwise direction and y2 being measured in a clockwise direction. rb is the base circle radius of each gear and x is the pressure angle. Line CC is the common pitch circle tangent, while length N is the length of the line of action to the pitch point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002786_s12206-018-1216-3-Figure25-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002786_s12206-018-1216-3-Figure25-1.png",
        "caption": "Fig. 25. Diagnosis results of the experiment signal 1: (a) TEERgram; (b) ES of the signal corresponding to node (4, 4) in (a).",
        "texts": [
            " As seen, the ORFF fo and its doubling frequency 2fo - 4fo are identified productively whereas the IRFF fi cannot be extracted. The experiment fault signal is processed by E-Kurtogram method. Fig. 24(a) displays that the node (3, 3) has the maximum kurtosis value. Fig. 24(b) illustrates the ES of the frequency band signal corresponding to node (3, 3). As seen, the ORFF fo and its doubling frequency 2fo - 4fo are identified productively whereas the IRFF fi cannot be extracted. The experiment fault signal is processed by the TEERgram method. Fig. 25(a) displays that the node (4, 4) has the maximum kurtosis value. Fig. 25(b) illustrates the ES of the frequency band signal corresponding to node (4, 4). As seen, the ORFF fo and its doubling frequency 2fo - 3fo are identified productively whereas the IRFF fi cannot be extracted. The experiment fault signal is processed by FERgram method. Fig. 26(a) displays the FERgram of outer ring fault. As shown, the maximum FER value is marked by the red rectangle and is at node (3, 2). That is to say, the frequency band signal corresponding to node (3, 2) contained the most outer ring fault information and its ES is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003285_17452759.2020.1823093-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003285_17452759.2020.1823093-Figure3-1.png",
        "caption": "Figure 3. (a) A photo shows the as-built short fluid channels which are used for profile and surface roughness measurements; (b) a schematic of the downskin part in SLM processing.",
        "texts": [
            " There are three plugs A, B, and C in each fluid channel shown in Figure 2(a), which are used to connect to pressure sensors. The building direction is shown in Figure 2(b). Default process parameters, which are the recommended parameters given in the SLM system, are used to build those samples. Short channel samples (8 mm in length), which are used for surface roughness and profile measuring, were also built using the same diameters and external support structures as the 235 mm fluid channel samples do, which are shown in Figure 3(a). The wall thickness tw of those measuring samples was calculated according to Equation. (1). tw = pfd 2[s] (1) where pf is the fluid pressure, d is the diameter of the fluid channels, [\u03c3] is the permissible tensile stress. [\u03c3] is calculated by \u03c3s/n, where n is ranged from 1.5\u20132 and \u03c3s is the yield strength of 316L stainless steel. By considering material strength, manufacturability, and fabrication quality, the wall thickness of the short fluid channels with various diameters is listed in Table 3",
            " It is noted that the wall thickness is different between the long fluid channel samples (the 235 mm channels for friction factor testing) and the short fluid channel samples (the 8 mm channels for surface roughness and profile measuring). The difference in the wall thickness may cause some discrepancy in the surface roughness and geometric tolerance. However, the difference is relatively small because the channel diameters are much greater than the layer thickness (50 \u03bcm). In the actual application (hydraulic manifolds or valves), a thin wall is desirable for lightweight design. The default process parameters, including the volume and downskin parts (as indicated in Figure 3(b)), were used which are listed in Table 4. It should be noted that the scanning strategy of all the experiments in this paper is \u2018stripes\u2019 to keep the same as fabricating Figure 2. (a) A schematic of a fluid channel sample with three pressure sensor plugs A, B, and C; (b) a photo of the as-built long fluid channel samples which are used for friction factor tests. the manifold. In the Renishaw system, the downskin part appears when the length of a cantilever is over 0.05 mm compared to the previous layer as shown in Figure 3(b). Since the standard layer thickness is 0.05 mm, the critical angle for downskin is 45\u00b0. Experiments of improving the fluid channel quality were also conducted on the 6-, 8-, and 10-mm-diameter channels by considering both geometric tolerance and surface roughness. It should be noted that only these three diameter fluid channels have been tested for improved parameters since they are widely used in the hydraulic industry. A compensation model presented by Kamat and Pei (Kamat and Pei 2019) was used to improve the geometric tolerance, which is based on the Euler-Bernoulli beam theory",
            " The cooling and solidification time on the downskin part significantly extends due to the very low thermal conductivity of the powders. The resultant sinking accumulates layer by layer leading to a reduced hydraulic diameter. The absolute difference in diameter between the design and the fabricated channels does not vary much. The relative discrepancy between the design diameters and measured hydraulic diameters indicates that the profile accuracy increases with increased channel diameters. Sinking becomes severer with increased diameter since the length of the cantilever increases as shown in Figure 3(b). However, the increasing rate of the cantilever is significantly lower (in micro metre) than the increasing rate of the channel diameter. Therefore, the relative discrepancy decreases with increased diameter. The surface roughness of the four locations, top, right, left, and bottom, in each fluid channel is shown in Figure 7(b). The roughness on the top part is extremely high, from approximately 50\u201380 \u03bcm. The surface roughness of the rest, right, left, and bottom, are approximately 10 \u03bcm with slight variations, which does not show dependency on the channel diameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001797_j.wear.2016.01.021-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001797_j.wear.2016.01.021-Figure2-1.png",
        "caption": "Fig. 2. (Left) schematic surface roughness instrument in situ, (right) schematic on gear tooth measurement.",
        "texts": [
            " The possibility of measuring roughness in situ is a fundamental property of this study. It enables the user to avoiding reassembling errors which may cause misalignments and loss of system compliance which would change the run-in behavior. The same measurement method and equipment as described by the authors [18] are used for measuring the surface profile during these tests. Roughness is measured on the gear wheel flanks by a Form Talysurf Series 50 mm Intra 2, and placed on the test gearbox as shown in Fig. 2. The stylus has a 2 \u03bcm tip and is small enough to reach the tooth root. A positioning stage was placed below the surface roughness measuring device which allowed several profiles to be measured by successive profile traces side-by-side in lead direction. It is important to note that the surface roughness measurements are performed with a contact profilometer without a skid (having as reference the profilometer's datum), enabling the extraction of form, waviness and roughness. To reposition the profilometer, specific fixtures are used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure8.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure8.4-1.png",
        "caption": "Figure 8.4. A twoparticlesystemmodelof moving antennacoils.",
        "texts": [
            " In addition , however, we must bear in mind in applications that the moment of momentum about C may be referred to a moving frame cp having an angular velocity W f relat ive to the inertial frame <1> . In this case (see (4.11) in Volume I) hc = hrc is a vector referred to a moving reference frame, and (8.45) is written as 8hdfJ, t) MdfJ, t) = 8t +W f x hdfJ, t ). (8.47) Two examples that illustrate use of the results (8.22) , (8.45) , and (8.47) follow. Example 8.3. A communications van has an antenna system modeled in Fig. 8.4 as two coils of equal mass m that move radially along a rigid control shaft that rotates with angular speed co about the vertical antenna axis. At an instant of interest, each coil is at a distance d from the center C and is moving with center directed variable speed v relative to the shaft frame cp = {C;id . The van moves with speed Vo in the ground frame <I> = {F;Ik } . (i) What is the total momentum of the system? (ii) What is the moment of momentum of the system relative to the Dynamicsof a Systemof Particles 315 center of mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002560_1350650118779174-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002560_1350650118779174-Figure9-1.png",
        "caption": "Figure 9. Schematics of a cylindrical thrust roller bearing.",
        "texts": [
            " A friction coefficient on the surface also increases the stresses at the subsurface according to Johnson.33 Many authors have shown that in a lubricated contact, even under lubricating boundary conditions the friction coefficient15 does not usually go higher than say bl \u00bc \u00bc0.11, this value will hardly modify the subsurface stresses. But it is better to see this with an example. Table 6 summarises the main parameters of a loaded cylindrical thrust roller bearing with the standard ISO designation 81212 schematics shown in Figure 9. The load represented in Table 6 is equivalent to C/P\u00bc 2, typical of endurance testing. With the data of Table 2, stress and fatigue calculation can be performed, for example using the fatigue Dang Van criterion, similarly as in Morales-Espejel and Brizmer.15 The full modelling scheme is represented in the flowchart of Figure 10 where the possibility to also apply wear is included. However, in the current example, zero wear is applied. The model shown in Figure 10 represents a simple RCF model used here for illustration purposes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000205_978-1-4615-9882-4_40-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000205_978-1-4615-9882-4_40-Figure10-1.png",
        "caption": "Figure 10 Response of WL-IOR in forward walking",
        "texts": [
            " Six types of preset walking patterns, forward, backward, rightway, leftway walking, CCW and CW turning, were designed according to the control laws aided by a simulation program named Walk Master having two-dimensional graphic output function. Forward walking, leftway walking and CW turning produced with Walk Master are shown in Figures 7 - 9. As a result of walking experiments with these patterns, smooth and stable quasi-dynamic forward walking is achieved, and stable static walkings are realized in other types of walking. Based on the experimental results, the response of machine model in forward walking is shown in Figure 10 by using graphical output function of Walk Master, and the trajectory in change over phase is shown in Figure 11. The walking time in each walking is shown in Table 1. Smooth and stable quasi-dynamic forward walking was achieved. The walking time was about 4.8s per step with a 45cm per step stride. Stable static backward, left way, rightway walking, CCW and CW turning, which are fundamental patterns of plane walking, were realized. As a result, the validity of newly proposed quasi dynamic walking and plane-walking control methods were experimentally sup ported"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure11.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure11.4-1.png",
        "caption": "Figure 11.4. Torque driven rotation of a rigid body-a nonconservative holonomic dynamical system.",
        "texts": [
            " , n,d (aT) st dt ai]r - aqr = Qr, for every nonconservative , holonomic dynamical system of n degrees of freedom . These equations, while the same as (11.15), are now applicable to every nonconservative, holonomic dynamical system. Writing Qr(i]r , qr, t) = -aV(qr)/aqr + Q~ (qr, qr, t) in terms of its conservative and nonconservative parts, we deduce from (11.73) the generalized form of Lagrange's equations (11.38) for nonconservative, holonomic dynamical systems . Example 11.10. A rigid body shown in Fig. 11.4 is driven by a torque J.L(t) about a fixed, principal body axis k in a smooth bearing at H . (i) Apply (11.73) to Introduction to AdvancedDynamics 533 derive the equationof motionfor the body.(ii) Repeatthe derivation from (11.38). Show that the result has the familiar form of the equation of motion of a driven pendulum. (iii) ApplyEuler's law to obtain the equation of motion. Solution of (i).Thesystemisholonomicwithonedegreeoffreedomdescribed by q\\ = 1/1; hence, (11.73) yields :, G:) -:: ~ Q. (1174"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003167_pi-c.1959.0034-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003167_pi-c.1959.0034-Figure5-1.png",
        "caption": "Fig. 5.\u2014Deviation of equipotential line from true circle.",
        "texts": [
            " 4 shows the relation between Djd and 7sTw for n = 2, 3 and 4 respectively. 0-3 0-1 \\ \\ \\ \\ \\ \\ \\ \\ n=4 \" n = 2 8 10 12 14 . 16 18 20 O/d Fig. 4.\u2014Relationship between Kn and Did. 22 To determine the electric field around bundle conductors with a known ratio of Did, it is necessary to find the corresponding value of Kn in order to locate the position of equivalent conductors. Kn can be calculated by eqn. (4) or read directly from Fig. 4. (3.2) Deviation of Equipotential Lines from True Circles Consider one of the bundle conductors in Fig. 5 and compare the equipotential passing through P and Q and the circle passing through the same points. The circle, which is the actual conductor periphery, has radius r and centre A as shown in Fig. 5. Let (p, 6) be the polar co-ordinates of the equipotential with the origin at A, and let e be the deviation of p from r per unit of r. Thus p = (1 \u2014 e)r. Section 9.2 gives the derivation of e in terms of 6 for n = 4. For other values of n the same procedure can be followed: (a) n=2. e = -kp]$in2d 2{2 + K2 cos 0 - [1 - c o s (b) n = 3. A5r 5 A2r 2 + Axr + A S ~ 6r6 + 5/f5r 5 + 4A4r 4 + 3A3r 3 + 2A2r 2 where A5 = 6R cos 6 A4 = 3R2(4 cos2 0 + 1) A3 = 6(2R3 + jR$ cos 0 - 8(Ug - R3) cos3 0 A2 = 3R(R3 +Rl)- 12(R% - R3)R cos2 0 Ax = - 6CR3, - i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002606_tia.2018.2888804-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002606_tia.2018.2888804-Figure1-1.png",
        "caption": "Fig. 1. Cross sections and winding configurations (The rotor pole is aligned with phase A, i.e., \u03b8e = 0 \u030a). (a) 6/4 VFRM. (b) 6/7 VFRM.",
        "texts": [
            " The derived torque equation and torque ripple reduction method can also be used for other VFRMs with an odd rotor pole number. This paper is organized as follows: the differences between 6/4 and 6/7 VFRMs are described in terms of winding configuration and inductance in Section II. In Section III, the instantaneous torque equation of 6/7 VFRM is derived by using harmonic analysis. Then, the harmonic current injection method is implemented into the field winding for torque ripple reduction in Section IV. Finally, the experimental verification is presented in Section V. Fig. 1 shows the cross section and winding configurations of 6/4 and 6/7 VFRMs. In VFRMs, the rotor pole number is equivalent to the number of pole pairs of a conventional AC machine. VFRMs have a doubly fed doubly salient configuration, which enables a simple and robust rotor structure. In both 6/4 and 6/7 VFRMs, the winding polarity is defined in Fig. 1, in which the field windings are connected in series with the same polarity. From the stator winding point of view, it shows alternating polarity as one stator winding moves clockwise or counterclockwise. In contrast, the armature winding configuration is different. Each armature winding is composed of two coils in the series connection, e.g., coils A1 and A2 for phase A. The phase coils of the 6/4 VFRM have a different polarity, whereas those of the 6/7 VFRM have the same polarity. It leads to bipolar phase flux-linkage waveforms because the dc component is cancelled out between two armature coils in each phase [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000305_20080706-5-kr-1001.01448-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000305_20080706-5-kr-1001.01448-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor helicopter scheme.",
        "texts": [
            " Moreover, the helicopter structure is assumed to be symmetric, which results in a diagonal inertia matrix. The helicopter as a rigid body is characterized by a frame linked to it. Let B = {Bb 1,B b 2,B b 3} be the body fixed frame, where the Bb 1 axis is the helicopter normal flight direction, Bb 2 is orthogonal to Bb 1 and positive to starboard in the horizontal plane, whereas Bb 3 is oriented in ascendant sense and orthogonal to the plane Bb 1OBb 2. The inertial frame I = {Ex,Ey,Ez} is considered fixed with respect to the earth (see Fig. 1). The vector \u03be = {x,y,z} represents the position of the helicopter mass center expressed in the inertial frame I . The vehicle orientation is given by a rotation matrix RI : B \u2192 I , where RI \u2208 SO(3) is an orthonormal rotation matrix [Fantoni and Lozano, 1995]. The rotation matrix is obtained through three successive rotations around the axes of the body fixed frame. The first one is given by a rotation around the Ex axis by roll angle, (\u2212\u03c0 < \u03c6 < \u03c0), followed by a rotation of pitch angle, (\u2212\u03c0/2 < \u03b8 < \u03c0/2), around the Ey axis from the new axis Bb 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001849_10402004.2016.1163759-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001849_10402004.2016.1163759-Figure2-1.png",
        "caption": "Figure. 2Displacement of inner ring centre relative to Outer ring centre cause by the radial load",
        "texts": [
            "5 for j = (0,\u041f)=1 for j \u2260 (0,\u041f) = Applied radial load, Va= Axial load Substituting equation of Wj in above equation we get, [7] Thrust load Equilibrium: Where, ACCEPTED MANUSCRIPT 12 = Total roller race way loading for length (l) for jth roller in axial direction At each roller location the thrust couple is balanced by a radial load couple. Therefore, [8] Where, h = roller thrust couple moment arm Therefore, equation [8] become as, [9] Where, is the eccentricity of the loading for jth roller and given by, Substitute the Wj and ejin Equation [9], ACCEPTED MANUSCRIPT 13 [10] Equilibrium of deflection The deformation of the inner-ring centre relative to the outer-ring centre owing to radial loading as shown in Figure 2.Sum of the radial deflection due to radial loading and radial interference caused by the axial deflection due to thrust loading minus the radial clearance is equal to the sum of the inner and outer raceway maximum contact deformations. \u2212 \u2013 2 = 0 [11] Four nonlinear simultaneous equations with four unknowns ( are obtained as below. 1. Equilibrium of deflection and deformation: u1 =0 [12] 2. Total roller loading: ACCEPTED MANUSCRIPT 14 2 [13] 3. Equilibrium condition for applied radial load: u3 [14] 4",
            " The load\u2013deflection factor S depends on the contact geometry. Local defect is one of the sources for excitation force and which is responsible for nonlinear vibration in shaft rotor bearing system. ACCEPTED MANUSCRIPT 16 Where \u03a3\u03c1 is the curvature sum which is calculated using the radii of curvature in a pair of principal planes passing through the line contact \u03b4 * is the dimensionless contact deformation obtained using curvature difference. The schematic diagram for determining the radial deflection is as per shown in figure2. If x and y are the deflections along X- and Y-axis and is the internal radial clearance, the radial deflection at the ith roller, at any angle \u2126i is given by [(x cos \u2126i +y sin \u2126i) - ]. So the E = S (\u03b4r)n , can be rewritten as E = ([( ) - )1.11 Since the Hertzian forces arise only when there is contact deformation, the springs are required to act only in compression. In other words the respective spring force comes into play when the instantaneous spring length is shorter than its unstressed length, otherwise the separation between roller and race takes place and the resulting force is set to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001518_j.mechmachtheory.2014.01.005-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001518_j.mechmachtheory.2014.01.005-Figure4-1.png",
        "caption": "Fig. 4. Origin of the face width direction.",
        "texts": [
            " The asperities friction coefficient, fc, is reported in the literature to be in the range of 0.1 to 0.13 [14]. Masjedi and Khonsari [18] have conducted experiments on a pair of steel rollers operating under high load and very low speeds to mimic the boundary lubrication regime. Themeasured friction coefficient varies in the same range. It is worthwhile to note that in all three dimensional plots in this paper, the origin of the coordinate of face width direction is on the toe of the bevel gear as shown in Fig. 4. Fig. 5 shows the load distribution in the bevel gear teeth. There is a jump along the LoA which resulted from the change in the number of gear pairs in contact. The load change along the face width is also considered as discussed before. Film thickness is a function of different parameters such as load, speed, viscosity, geometry, and elastic modulus. In this research, isothermal condition is assumed and viscosity variation as a function of only pressure has been considered using Roelands' formula"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003033_tie.2020.2982102-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003033_tie.2020.2982102-Figure9-1.png",
        "caption": "Fig. 9. Stator winding arrangements for the LSVPM machine with different poles. (a) Arrangements for one-pole-pair winding. (b) Arrangements for two-pole-pair stator winding. (c) Arrangements for four-polepair stator winding.",
        "texts": [
            " However, for regular LSPM machine, the slot number Z is much larger than steady pole-pair number Pe, so the effects of leakage inductance changing are almost negligible. The stator winding harmonic leakage inductance changing makes the difference between the proposed LSVPM machine and regular LSPM machine for pole-changing. Considering the starting performance, the proper rotor starting winding pole-pair should satisfy (2). In order to validate the earlier analysis, the starting average torque of LSVPM machines with different rotor winding polepair are compared. The stator winding arrangements are shown in Fig. 9. The corresponding 1/2 and 1/4 pole-changing circuit is shown in Figs. 2 and 10, respectively. It is shown that during starting process, switches are connected to point \u201ca\u201d; when the motor operates in steady state, the switches are connected to the point \u201cb.\u201d Fig. 11 shows the PM braking toque variation with rotor speed. When rotor winding pole-pair is 5, the pole-changing is not needed, and the PM braking torque maximum is 25 N\u00b7m approximately when speed is 60 r/min. When rotor winding pole-pair is 2 and 4, the pole-changing method is adopted, and the PM braking torque is eliminated as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001645_1464419317727197-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001645_1464419317727197-Figure5-1.png",
        "caption": "Figure 5. Cage unbalance mass set: (a) initial, (b) 1.6 g, (c) 3.5 g, and (d) 6.8 g.",
        "texts": [
            " Two probes (yc, zc) are installed in the bearing house at 90 apart and another two probes (xc1, xc2) are fixed on a subpanel at 180 apart as shown in Figure 4(b). In addition, a data capture system is used to obtain the data and its sampling frequency is 4000 Hz. The cage is designed with four screwed holes symmetrically in circumference and the various cage unbalance conditions are realized by fixing different mass nuts on the screwed holes. The initial without additional mass and the cage unbalance masses of 1.6 g, 3.5 g, 6.8 g are shown in Figure 5. The experiments are performed on the above test rig at different operating conditions as listed in Table 3 and the external loads correspond to the simulation. Measured center trajectories of the cage. The trajectories of the cage center in radial plane under different operating conditions are measured and listed in Table 7. From Table 7, it can be observed that the rotating speeds and the cage unbalances greatly influence the trajectories of the cage center. At the initial state, there is no cage whirl, but rather the cage is in an erratic motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000472_s11249-009-9461-3-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000472_s11249-009-9461-3-Figure1-1.png",
        "caption": "Fig. 1 Diagrams of apparatus. a Photograph. b Schematic",
        "texts": [
            " There are many other methods that have been applied in important studies of the rheology of lubricants at high pressure and shear; a review of which is given by Spikes et al. [3]. Notable examples are those using high pressure viscometry to look a shearing [15], and high pressure compression apparatus to look at compression effects [16]. 2 Temperature Mapping 2.1 Measurement Apparatus A lubricated contact is produced using a conventional optical interferometric ball on disc test rig (PCS Instruments Ltd., Acton, UK), where a steel ball is loaded against a sapphire disc, as shown in Fig. 1. Both ball and disc can be rotated independently to give a range of slide-roll-ratios if required. Alternatively, a shaft-less ball can be used which rotates freely and is driven by the disc. The lubricant is held in a temperature-controlled bath (\u00b10.5 C) and the ball is half immersed in lubricant to ensure fully flooded conditions. An infrared (IR) camera/microscope is positioned above the sapphire disc and focuses through the sapphire into the contact in order to measure IR radiation from the contact region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001523_tmag.2014.2364264-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001523_tmag.2014.2364264-Figure9-1.png",
        "caption": "Fig. 9. Open-circuit equipotential and flux distributions of single- and multitooth VFRMs, pf=15W.",
        "texts": [
            " In the following subsections, in order to further analyse the influence of Ns, Nr and n, the electromagnetic performance of single- and 4-tooth VFRMs with Nr=nNs+1 are selected for comparison since the 6/7 stator/rotor pole VFRM exhibits the highest average torque among the 6-stator pole single-tooth VFRMs as shown in Fig. 8 [20]. All the machines are globally optimized with maximum average torque under the same rated copper loss and stator outer radius. Their main parameters are detailed in Table I. For all the combinations, the winding configurations can be obtained based on the method mentioned in section II. (The winding configuration of 6/25 stator/rotor pole 4-tooth VFRM is same as that of 6/7 stator/rotor pole single-tooth VFRM which shown in Fig. 2(b)) B. Open-Circuit Field Distribution Fig. 9 shows the open circuit equipotential and flux density distributions of single- and 4-tooth VFRMs at the aligned position under the rated DC field current (pf = 15W for both machines). It can be seen that when stator and rotor pole combination is determined by Nr=nNs+1, both machines have short flux path and the coils belong to the same phase have completely independent flux loop. The open-circuit air-gap flux density waveforms of two VFRMs at the aligned position are shown in Fig. 10. It can be seen that the peak number of air-gap flux density under each coil depends on the number of small teeth per stator pole n, such as 4 peaks in multi-tooth VFRM with n=4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000280_s0076-6879(76)44043-0-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000280_s0076-6879(76)44043-0-Figure6-1.png",
        "caption": "FIG. 6. Silicone rubber pads of 6 mm width (lower left) are cut from a 125 mm strip (upper right).",
        "texts": [
            " There is no need for the cumbersome, time-consuming preparation of reagents when performing an analysis, since essentially all the reagents for a quantitative assay are already present on the pad. If samples are hard to obtain, the pad method could be another great advantage, since only 3-25 ~1 of sample are required. Silicone rubber (Dow-Corning Glass and Ceramic Adhesive, DowComing, Midland, Michigan) pads were prepared by pressing uncured silicone rubber between a glass plate and a stainless steel mold {Fig. 6), both of which were lined by a piece of glassine paper (Eli Lilly and Co.). The surfaces contacted with the silicone rubber were prelubricated with a thin layer of Dow-Corning silicone stopcock grease (Dow-Corning Co., Midland, Michigan). The silicone rubber was kept in the mold at room temperature for 2 days to cure. The cured strips were then removed, wiped, and washed briefly with concentrated KOH solution to remove the grease. Next the pads were washed with H20 and dried at 80 \u00b0 for 1 hr. The strips were cut to individual pads 6 mm in width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000599_s0263574708004633-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000599_s0263574708004633-Figure5-1.png",
        "caption": "Fig. 5. The HANA parallel manipulator introduced in ref. [15].",
        "texts": [
            " If the kinematics chain for the manipulator shown in Fig. 2(a) is denoted as (2-PRU)PRC, it will be (PRR)2R-PRC for the two designs shown in Fig. 4. This modification, which has no negative influence on the kinematics and rotational capability of the manipulator, can be also extended to the HALF* parallel manipulator with revolute actuators shown in Fig. 2(b). It is noteworthy that in the HALF* parallel manipulators the universal joints connected to the mobile platform can be replaced by spherical joints. Figure 5 shows the HANA parallel manipulator introduced in ref. [15], which is also one member of the family presented in ref. [13]. In the HANA manipulator, two legs (the first and second legs) consist of parallelogram. The kinematic chain of each of the two legs is the same as that of the third leg in the HALF parallel manipulator shown in Fig. 1. Therefore, the two legs can be also replaced by the PRC chain. The new version of the HANA parallel manipulator is illustrated in Fig. 6(a), which is referred to as the HANA* parallel manipulator where the P joints are actuated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001402_1464419313514572-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001402_1464419313514572-Figure3-1.png",
        "caption": "Figure 3. FE model: (a) outer race and partial housing, and (b) housing.",
        "texts": [
            " In this study, a 6308-type deep groove ball bearing is studied. The parameters of the bearing are listed in Table 3 and the schematic model is given in Figure 2(a). In addition, the size of the housing is shown in Figure 2(b) and its thickness is equal to 23mm along the Z-direction. In order to ignore the effect of the housing stiffness on the contact deformation between the outer race and housing, a substructure FE model including the outer race and the housing with a partial part (the thickness is 4mm) is studied, as shown in Figure 3(a). The clearance between the outer race and the housing is chosen to be zero in this study. The FE model is developed by a commercial software program.46 The outer race and the housing are meshed using three-dimensional solid elements, which is namely an eight-node tetrahedron solid element type having three DOF at each node, which is typically used for 3D modeling of solid structures.46 The Coulomb friction law with a constant friction Materials Density (kg/m3) Elastic modulus (GPa) Poisson\u2019s ratio GCr15 7830 219 0.3 42CrMoA 7850 206 0.28 QT400-18AL 7050 147 0.25 ZL102 2670 68 0.35 at KAI NAN UNIV on March 17, 2015pik.sagepub.comDownloaded from coefficient 0.1 is used for describing the contact between the outer race and the housing. The partial FE model including the outer race and the partial housing has 81,792 elements and 99,401 nodes. Moreover, in order to calculate the housing stiffness, the whole housing structure is also meshed using 3D solid element. As shown in Figure 3(b), the whole FE model of the housing has 76,560 elements and 83,150 nodes. In order to verify the FE method used in this study, the Hertzian contact theory47 is utilized. The size of the two cylinders is as follows: R1\u00bc 10mm, R2\u00bc 20mm, L1\u00bcL2\u00bc 40mm. The center line of the bigger cylinder is restricted. The radial load is applied to the center line of the smaller one. The load is equal to 500, 1000, and 1500N, respectively. The contact deformation of the two cylinders is calculated using FE method and the results are plotted in Table 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure10-1.png",
        "caption": "Fig. 10. (a) Collision-potent arrangement of two solid-angle zones. (b) Collision beginning between two solid-angle zones.",
        "texts": [
            " 9(c) illustrates the geometrical condition \u03bb\u2032 j \u2212 \u03b1j > \u03bb\u2032 i + \u03b2i (18) where for any value of \u03c8\u2032 i and \u03c8\u2032 j , there is no interference between the solid angles. In such configuration of the solid angles, a virtual hemisphere centered at P with an arbitrary radius r can be considered. In such hemisphere, two horizontal circles of i\u2032 and j corresponding to angles \u03bb\u2032 j \u2212 \u03b1j and \u03bb\u2032 i + \u03b2i can be considered, where as long as radius of circle j is greater than that of circle i\u2032, for any values of \u03c8\u2032 i and \u03c8\u2032 j , there is no interference between the solid angles of UAV j and i. In spite of Fig. 9(c), Fig. 10(a) shows a configuration where for some values of\u03c8\u2032 i and\u03c8\u2032 j collision between the solid-angle zones is possible. In the arrangement of Fig. 10(a), we have \u03bb\u2032 j \u2212 \u03b1j \u2264 \u03bb\u2032 i + \u03b2i, \u03bb \u2032 i + \u03b2i \u2264 \u03bb\u2032 j + \u03b2j (19) where \u03bb\u2032 i + \u03b2i is considered as the angle of collision between the solid angles, where its corresponding horizontal circle is denoted by circle Authorized licensed use limited to: University of Canberra. Downloaded on June 24,2020 at 16:03:50 UTC from IEEE Xplore. Restrictions apply. i\u2032. Accordingly, by having (19), interference between the solid angles of i and j is possible. In order to find the relation between \u03c8\u2032 i and \u03c8\u2032 j to prevent interference between their solid angles, the collision of the solid angles is considered as illustrated in Fig. 10(b). As this figure shows, the collision points of the solid angles i and j are denoted by Fi and Fj , where in order to prevent collision, we need to have |\u03c8\u2032 i \u2212 \u03c8\u2032 j | > \u03bai + \u03baj , where \u03bai and \u03baj denote the projections of \u03b6i and \u03b6j on the x\u2212 y plane, which are obtained as \u03bai = sin\u22121 ( GiFi PFi ) , \u03baj = sin\u22121 ( GjFj PFj ) . (20) Based on the dimension of solid-angle borders in Fig. 10(a), we have PFi = PFj = r cos(\u03bbi + \u03b2i), GiFi = r sin(\u03b6i), GjFj = r sin(\u03b6j). (21) Accordingly, \u03bai and \u03baj are simplified to \u03bai = sin\u22121 ( sin(\u03b6i) cos(\u03bbi + \u03b2i) ) , \u03baj = sin\u22121 ( sin(\u03b6j) cos(\u03bbi + \u03b2i) ) . (22) Based on the presented approach, all collision-free arrangements of the UAVs are obtained. To summarize such results, the set of all collision-free combinations of \u03c8\u2032 is and \u03bb\u2032 is in the determined position p is denoted by \u039bp, which is used to form an optimization problem in the following section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.92-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.92-1.png",
        "caption": "Fig. 2.92 Rear ICE, M-M clutch, MT and live-axle M-M transmission arrangement for the M-M DBW 2WD propulsion mechatronic control system [NEWTON ET AL. 1989].",
        "texts": [
            " Disadvantages of all rear ECE or ICE arrangements incorporate the lengths of the mechatronic control runs from the driving position and the reality that the driver may not be experienced enough to perceive the sound of the ECE or ICE and estimate its angular velocity, to change gear, if automatic transmission is used. Transverse rear ECE or ICE engine M-M transmission arrangements evidently necessitate an angle drive, and some manufacturers produce such a unit. It normally comprises a bevel gear pair in a casing that can be fastened onto the MT or ECE/ICE and M-M clutch or torque converter (TC) assembly. In Figure 2.92, a retarder \u2013 transmission brake \u2013 is built-in the MT (gearbox) that is fastened to the angle-drive casing [NEWTON ET AL. 1989]. A coupling joins the angle drive shaft to the ECE or ICE and M-M clutch assembly in this arrangement. 2.4 M-M Transmission Arrangement Requirements 259 An advantage of the dead-axle M-M transmission arrangement is a substantial attenuation in the unsprung mass that gives both better driving and road holding. Parenthetically, the insinuation that an everlasting inflexible axle restrains its wheels at a \u03c0/2 rad angle to the road is evidently a fantasy: the result of a bump under one wheel is to predispose both wheels uniformly in relation to the on and/or off-road"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure2-1.png",
        "caption": "Fig. 2. Design of tooth profiles based on path of contact.",
        "texts": [
            " 1 , for the same path of contact of the engaged tooth profiles, there may be two types of shape forms for virtual rack cutter, which are used to generate the driving tooth profiles and the driven one, respectively. Firstly, it is assumed that the shape form of virtual rack cutter is like Fig. 1 a. In order to establish the mathematical models of the conjugate tooth profiles, four coordinate systems S 1 ( o 1 \u00d71 y 1 ), S 2 ( o 2 \u00d72 y 2 ), S 3 ( o 3 \u00d73 y 3 ) and S ( oxy ) are set up as displayed in Fig. 2 . S ( oxy ) is a fixed coordinate system whose origin o coincides with the pitch point P , while S 1 ( o 1 \u00d71 y 1 ) and S 2 ( o 2 \u00d72 y 2 ) are rotating coordinate systems attached to the centers of the driving gear and the driven gear, respectively. S 3 ( o 3 \u00d73 y 3 ) is a moving coordinate system attached to the virtual rack cutter, which coincides with S at the start position. 1 , 2 and 3 represent the engaged tooth profiles for the driving gear, the driven gear and the rack cutter, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000833_s00170-010-3142-0-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000833_s00170-010-3142-0-Figure7-1.png",
        "caption": "Fig. 7 The temperature field distribution with the radius of 1 mm; a global and b local",
        "texts": [],
        "surrounding_texts": [
            "Through preliminary experiments, the basic process parameters were optimized with the use of 6 mm/s scanning speed and 250 W laser power. The laser energy transfer efficiency is set to 0.35 [19]. The substrate material utilized was also 316LSS. The molten pool temperature distributions were calculated with different layer numbers of thin wall and different Fig. 9 The relationship between temperature distribution and radius radiuses of thin-walled rings, respectively. Because of the fluctuation of molten pool temperature in each layer, the mean temperature of each layer is considered as the temperature of the deposition layer. 3.1 The influence of accumulating layer number on the molten pool temperature The model dimension along x-, y-, and z-axes direction of thin wall is 60\u00d70.5\u00d73 mm3. The calculation is performed for the deposition from the first layer to the last layer (the 15th layer). Figures 3, 4, and 5 show the typical temperature field distributions of the fabricated thin wall with different layer numbers. The calibrated model was then used to simulate the entire 15-layer LDMD process. The temperature distributions with layer number were shown in Fig. 6a under constant laser power condition. Based on the 1,570\u00b0C produced by temperature field computation of the first deposited layer, the trend of laser power changing could be obtained with layer by layer by keeping a constant molten pool temperature, as shown in Fig. 6b. It is observed from Fig. 6a that the calculated temperature increases with the layer number. Because the substrate is cold during deposition of the first few layers, and as more layers are deposited, they act as a barrier to heat conduction to the substrate, the part becomes hotter and the temperature increases with the layer number. In order to achieve a steady temperature distribution surrounding the molten pool, the laser power must be adjusted for each layer. Figure 6b shows the laser power applied for each layer when keeping the molten pool temperature stable. Provided that the laser power of the first deposition layer is denoted by P. The declined percentages of laser power are denoted by \u03b1 with the increasing layer number when the temperature of each layer is consistent with the temperature of the first layer. Then the laser power of any layer can be calculated by P\u00d7\u03b1 under keeping the molten pool temperature of each layer stable. It is observed that the laser power decreases with the layer number. 3.2 The influence of curvature change of thin-walled rings on the molten pool temperature The thin-walled rings with different curvatures can be handled by defining different radiuses. To investigate the Element Wt.% influence of different thin-walled rings\u2019 radiuses on the molten pool temperature, the molten pool temperature distribution is studied with the radius of R=1, 2, 3, 4, 5, 6, 8, 10, and 15 mm when depositing the first layer. Figures 7 and 8 show the typical temperature field distributions of the thin-walled rings with the radius of 1 and 4 mm, respectively. The relationship between temperature distribution and radius was shown in Fig. 9. As can be seen from Fig. 9, the molten pool temperature decreases with the radius, namely, the molten pool temperature increases with the curvature. It is also observed that the molten pool temperature tends to be gentle when the radius is more than 4 mm. This indicates that the influence of the radius on the molten pool temperature is weak when the radius is more than 4 mm. In order to keep the molten pool temperature stable for different radiuses, the trend of laser power changing can be obtained based on the 1,570\u00b0C produced by temperature field computation of the thin wall\u2019s first layer. And the relationship between laser power and radius was shown in Fig. 10. According to section 3.1, the laser power of any layer can be calculated by P\u00d7\u03b1 under keeping the molten pool temperature of each layer stable. To keep the temperature distributions of the thin-walled rings with different curvatures consistent with the thin wall, the decline percentages of laser power are denoted by \u03b2 with the increasing curvature. Combining Fig. 6b and 10, the trend of laser power changing with layer number and curvature can be obtained under keeping melt pool temperature stable. The laser power of the first deposition layer used is denoted by P. The declined percentages of laser power are denoted by \u03b1 with the layer number and \u03b2 with the curvature. Then the laser power of any layer and any curvature can be calculated by P\u00d7\u03b1\u00d7\u03b2."
        ]
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure5-1.png",
        "caption": "Figure 5. Piston mesh for HT modelling (cooling gallery in blue)",
        "texts": [
            "5 l\\min has been chosen as boundary conditions at the inlet of the cooling gallery along with a constant value of heat transfer coefficient of 3,000 W/m2K. Inside the cooling gallery, k-\u03b5 turbulence model has been selected. For the external piston geometry, heat transfer coefficients shown on Table 1 have been used as boundary conditions. Meanwhile a temperature level of 1,000\u00b0C and 120 bar were chosen as combustion gas conditions at the piston crown. A normal force of 70 kN was considered at piston pin bore for later FEA analysis. Finally a mesh with a base size of 3mm has been selected for the HT modelling, used mesh can be observed on Figure 5 and on Table 2 where the number of cells is provided. In order to analyze the influence of introducing a cooling gallery near the top land in a gasoline engine piston, a heat transfer analysis has been repeated for the same piston model with and without the insert of a cooling gallery. Heat transfer study results have been analyzed in terms of temperature and heat flux ratios at each of the piston regions. In order to simplify the results analysis, both parameters have been integrated across the studied surfaces and compared with results from previous works [9, 11, 12, 13, 14, 15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure6.31-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure6.31-1.png",
        "caption": "Figure 6.31. The Coriolis effect on the trajectory relative to the Earth of Foucault's pendulum viewed from its point of support at a place in the northern hemisphere where its apparent rotation is clockwise .",
        "texts": [
            "113t) shows that the initial position vector Xo = xoi, viewed from the point of support, has been rotated through an angle \u00abrr , which is clockwise when co > aand counterclockwise when to < O. The second relation in (6.113f) shows that w > a in the northern hemisphere, to < a in the southern hemisphere, and co =aat the equator where the motion is always simple harmonic. Therefore, as first demonstrated by Foucault, relative to the Earth. the plane of oscillation ofa pendulum has an apparent clockwise rotation in the northern hemisphere, a counterclockwise rotation in the southern hemisphere, and no rotation at the equator. The motion is illustrated in Fig. 6.31 for the northern hemisphere. The pendulum starts from a southward displaced position of rest at a small distance Xo from the plumb line. As the bob moves on its outward swing, it experiences a Coriolis force directed eastward; but on its return swing, the Corio lis force is Dynamics of a Particle 189 directed westward . The deflection always is toward the right of the direction of the swing in the northern hemisphere. This is shown in Fig. 6.31a. Hence, the bob, after one period, has undergone a net displacement westward to the position x(r) = xo(coswri - sin wrj), the same distance from the origin, but rotated clockwise through a small angle wr from xo, as shown in Fig. 6.3 lb. At each time T(n) = nr /2, the same thing is repeated over and over, so the bob traces the star shaped trajectory described by (6.1130) and illustrated in Fig. 6.31. The apparent motion in the southern hemisphere for which 'A < 0 is counterclockwise. The vertical plane of the pendulum's oscillations thus rotates relative to the Earth with Foucault's angular speed co = Q sin 'A, as indicated in (6.113t). The number of days rd('A) required to complete one full revolution of the plane of oscillation of the pendulum is thus given by rd('A) = 1/ sin 'A. Consequently, Foucault 's pendulum takes I day to complete its apparent turn at the poles where 'A =\u00b1n / 2, and this cyclic time increases as the latitude 'A decreases toward the equator where the effect disapp ears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000188_s00170-008-1785-x-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000188_s00170-008-1785-x-Figure2-1.png",
        "caption": "Fig. 2 Laser-repaired sample",
        "texts": [
            " The thermal boundaries are all described: k @T @n \u00bc hq \u00fe hc T T1\u00f0 \u00de \u00f016\u00de where hq is laser heat flux density and hc is a combined transfer coefficient for the radiative and convective boundary conditions and given by Goldak: hc \u00bc 24:1 10 4\"T1:61: \u00f017\u00de Initial condition: T t\u00bc0j \u00bc T0, T0 is room temperature. At the bottom of the substrate, the adiabatic boundary condition is assumed. A laser-repairing case has been chosen to be an applied model adopting the method discussed above and using the commercial finite element tool ABAQUS, as shown in Fig. 2; the part is as substrate and represented by green colour. The dimensions of the base of the part are 36\u00d74.8\u00d7 6.00 mm, dimensions of the superstructure of the part are 30\u00d72.4\u00d76.00 mm and the repaired two layers are represented by brown colour. The cross-section of each layer is 30\u00d72.4 mm; the deposited thickness is 0.4 mm; grids of the substrate are 0.6\u00d70.6\u00d70.6 mm; grids of the repairing layers are 0.6\u00d70.3\u00d70.2 mm. Scanning paths are set to linear paths. Each layer possesses different scanning order, as described in Fig",
            " Laser-processing parameters are set: laser power is 800 W; scanning velocity is 300 mm/min; laser beam diameter is 0.6 mm; spectral absorptivity of nickel is 0.15\u20130.35. In this study, 0.25 is adopted. 4.1 Temperature profiles It is seen from Fig. 5 that only the laser-passed elements are activated to the repaired layers. At the same time, the gap elements are endued with corresponding thermal conductivity, and the heat transfer diffuses in the big substrate. In the laser-applied neighbouring region, a great temperature gradient is formed. The temperature history of node A in layer 1 (shown in Fig. 2) is illustrated in Fig. 6; there are a total of eight peak values. The maximum value appears at the location where the laser is just applied. The second peak value appears at the time where the laser passes the neighbourhood second line path, and the temperature decrease is much more compared with the first peak. The third peak value appears where the laser passes the neighbourhood third line path, and the time interval between the neighbourhood second line and the neighbourhood third line is very short, as shown in Fig. 7. When the laser enters the second layer, the peak value temperature increases a little due to the increase in the whole temperature of the sample. However, with the location approaching node A from the second layer, the peak value temperature increases gradually, but is definitely lower than the first peak value where the laser is applied directly. The temperature history of node B in the substrate (shown in Fig. 2) is illustrated in Fig. 8. There are also eight peak values; obviously, the reason is the same as with node A in layer 1, but there is a big difference. The heat transfer of substrate to node B is very rapid and exhibits an incremental trend in temperature. The result is close to the experimental result; as the laser builds more and more powder, the substrate becomes hotter and hotter. In addition, node B is located in the middle of substrate along the X direction, so the interval of peak values appears more uniform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002053_j.ijnonlinmec.2014.11.015-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002053_j.ijnonlinmec.2014.11.015-Figure5-1.png",
        "caption": "Fig. 5. Finite element model for radial ball bearing stiffness.",
        "texts": [
            " The time varying radial stiffness can be approximately calculated analytically or more precise by experimental measuring of ball bearing displacement in terms of predefined external loads [20,21]. The more comfortable but on same time equally accurate procedure for ball bearing stiffness calculation is by time dependent finite element analysis for one time varying period of one ball passing along the contact period (period during one ball is continuously in contact). The finite element model developed for calculation of the radial ball bearing stiffness is given in Fig. 5. The node for displacement reading is chosen in accordance with the definition of ball bearing stiffness and is placed near the contact between the inner ball bearing ring and shaft.Fig. 3. Physical model of mechanical system with rolling element bearing [19]. Please cite this article as: I. Atanasovska, The mathematical phenomenological mapping in non-linear dynamics of spur gear pair and radial ball bearing due to the..., International Journal of Non-Linear Mechanics (2014), http://dx.doi.org/10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002343_icpe.2015.7167845-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002343_icpe.2015.7167845-Figure1-1.png",
        "caption": "Fig. 1. Principle of vibration generation in SRM",
        "texts": [
            " In this paper, a relationship between a variation of the input voltage and generated acceleration of vibration is firstly described considering all of the resonance vibration due to switching excitation. Then the method to produce the voltage waveform which includes finite frequency is proposed realized by the Pulse Width Modulation (PWM). In the proposed method the voltage waveform is changed only when the turned off timing, the voltage does not excite the vibration of the natural frequency. The effectiveness is verified by experimental results compared with the result by the conventional single pulse operation. Principle of a rotating mechanism for SR motors is shown in Fig. 1. The electromagnetic force is on track to the path of the flux linkage from the stator teeth to the salient-pole of rotor. The electromagnetic force is divided into two force vectors, one is a force named the radial force aligned in a radial direction and the other is the tangential force aligned in a circumferential direction. Since this radial force is usually over ten times larger than the tangential force, the radial force of SR motor is a main cause of generating vibration in SR motors. Vibration Reduction Method in SRM with a Smoothing Voltage Commutation by PWM Akiko Tanabe and Kan Akatsu Shibaura Institute of Technology, Japan 9th International Conference on Power Electronics-ECCE Asia June 1 - 5, 2015 / 63 Convention Center, Seoul, Korea 2015 KIPE The amplitude of the radial force becomes largest at the position of the rotor and stator is aligned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure10-1.png",
        "caption": "Fig. 10 Thermal FE analysis results for all rollers heated equally to produce a 130.5 C average cup temperature (heating scenario 13 in Table 2)",
        "texts": [
            "5 C bearing cup temperature is well below the HBD threshold for an ambient temperature of 25 C and, therefore, this bearing will most likely continue to operate abnormally while undetected by conventional wayside bearing health monitoring equipment. Simulations 9 and 10 in Table 2 are two other hypothetical heating scenarios that demonstrate how certain rollers can reach unsafe operating temperatures without heating the bearing cup anywhere close to the hot-box alarm threshold. Finally, simulation 13 in Table 2, shown in Fig. 10, provides an insight into the operating conditions that would lead to a bearing cup temperature of 130.5 C, which would trigger the HBD alarm. The results reveal that all 46 rollers within the bearing have to reach an operating temperature of 149.5 C, generating a total heat input of 2208 W, in order for the bearing cup to reach 130.5 C. This heating scenario demonstrates the extreme operating conditions that must occur before conventional wayside detectors tag that bearing for removal from service"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001470_0016-0032(65)90310-8-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001470_0016-0032(65)90310-8-Figure2-1.png",
        "caption": "FIG. 2. FIG. 3. FIG. 4.",
        "texts": [],
        "surrounding_texts": [
            "where ~,,~. and ~.~ are un i t vec tors d i rec ted along the j and k axes and\nl~j = l~ cos ~f,t (ij) = (12), (23), (31) (3) li~ = l~ sin ~]~t (ik) = (13), (21), (32).\nThe velocities and accelera t ions of the points L~ wi th respec t to the veh icu la r coord ina te sys t em are\ndt / v = ~/~l~k~j -4- ~i~l~j~ok ( i jk) = (1..3), (231), (312). (4)\n=\ndt ~ / r - ~ $ 1 ~ -- ~ $ l ~\nSubs t i tu t ing Eq. 4 in to Eq. 1, the componen t s of accelera t ion of the points L~ along the vehicu lar axes are\n= ~ [ - A ~ -4- (5~1~ -- ~ l~ - ) -4- 2 ~ ( ~ l ~ . + ~ l ~ ) -4- t2~(~,.l~. -4- 9\u00a2~1~)~ + ~ ,\u00a2[A~ - o,z?l~\u00a2 - ~,~l~, - 2,~zi~o~l~\u00a2 + ~,\u00a2~**l~ - l~(9\u00a2? + ~ ) ~\n+ ~ [ A ~ - - ~f$1~ + f i~ l~ - 2 ~ , ~ 1 ~ + ~ l ~ -- 1~(9\u00a2$ + ft~2)~ ( i jk) = (123), (231), (312). (5)\nThe sensi t ive axes of the acce le rometers are al igned in such a way t h a t the accelerometers A~( i = 1, 2, 3) measure the componen t s along ~i of Eq. 5. i.e.,\nA~ = A~ -4- (~vjl~k -- ft~l~j) + 2~dP~flo ' A- ~kl~k) -4- 9~(9\u00a2~.1~j A- 9~kl~k)\n( i jk) = (123), (231), (312) (6) where lis and l~k are given by Eq. 3.\nBy a p roper choice of t ime t, lo\" or l~k can be made equal to \u00b1 l i as follows :\nf li t - 2n~r OJ f i lij ---- --l~ t (2n + 1)~\"\n(ij) = (12), (23), (31) li t - (4n + 1)Tr\n20~ f i\nli~ ---- (4n + 3)~ - l l t -\n20~ f i\n(ik) = (13), (21), (32)\n= o , 1, 2 . . . . ( 7 )\nSubs t i tu t ing Eq. 7 in to Eq. 6, and uti l izing the fac t t h a t w h e n lii = ~ li, lik = 0 and vice versa, the following m a y be wr i t t en :\nvo,. 28o, ~o. 4, O~tobe~ 196s 3 0 9",
            "A i l = Avi - (~kli + 2o~]~9,~l~ + ~2,i~jli\nA ~ = A ~ + (~kl~ - - 2 o o f i ~ f l i - - 9~t2,jli\nA~x, = A~i + (Lfl , + 2o~fSLkl~ + ~ k l ~ A iv = A,~ - (L, j l l - 2\u00a2of,:ft,,kli -- ~,~2~l~ (8)\nwhere Ai~, A~,2, A i r , Ae2, are defined as\nA ~ = A~(l~i = l~)\nA ~ = A~(l~i = - l~)\nA~v = A~( l~ = l~) A,2, = A , ( l , , = - l~). (9)\nBy forming the sums and differences of Ai~-A~,2 and A ~ v - A ~ , Eq. 10 is obtained\nTo utilize Eqs. 10 successfully some valid assumptions for the particular type of application are made. The s teady angular velocity of the vehicle with respect to the inertial system may be estimated as not less than 0.4 min per second, and the maximum angular velocity need not exceed 30 rain per second. The other assumptions are: wi~ = wf i -- 1, 2, 3;\nThere are no sudden changes in angular velocity; xf is sufficiently high such tha t ~ + ~2 << ~f~2;\nThe time constant of the accelerometer is low compared to the time taken for one revolution of the disc.\nAssuming the above, Eq. 10 can be rewritten as\n\u00bd ( A ~ I - A i 2 ) = V a t = li2~of~vj \u00bd(A~I, + A~v) = a t ' = A~ \u00bd(A~I, -- A~v) = \"\u00a2\u00a2; = 1,2~o/12vk ( i jk) = (123), (231), (312). (11)\n3 1 0 Journal of The Franklin I n s t i t u t e",
            "V \" f I +..k [ ...r..-~,, \u00b1\nA, - - - AI . 2 i s\n~ ~ , ~ , I -~'-~-~--~'-\nI 2'~f I ~ _ ,\nI 2 ~ - , I \u00f7 '\nFio. 5. Mechan iza t ion of aeeelerometer equa t ions .\n\u2022 A v I\n2mr\n)-~ Av z\n) ~ v z\n~ A v 5\nBy properly averaging the terms in Eqs. 11 and 12 both the components of linear acceleration and angular velocity, are obtained,\n~( ~ -t- a~') = Avi i = 1, 2, 3\nz~50f ~ lj -~--~k ~--- ~ (ijk) = (123), (231), (312). (12)\nEquations 8-12 are mechanized in Fig. 5.\nError Analyses\nThe following misalignments will cause an error in the accelerations and angular velocities obtained by using the mechanization diagram of Fig. 5 :\nThe center of rotation of the discs does not coincide with the origin of the vehicular system ; The rotat ion axes of the discs are not aligned with the vehicular axes; The sensitive axes of the accelerometers are not aligned with the respective vehicular axes; Sampling errors exist.\nVo]. 280, No. 4, October 1965 311"
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.11-1.png",
        "caption": "Figure 10.11. Spatial motion of a rigid rod hinged to a rotating shaft.",
        "texts": [
            "mw \u00a3 a The dynamic bearing reactions are then determined by their equations in (10.79h). o Exercise 10.7. Describe in analytical terms how you would go about correcting for the dynamic imbalance of the plate. Hint: Derive a system of equations of the type (lO.76b) and recall results of Exercise 10.6, page 445 . 0 10.12.5. Bearing Reaction Torque and Stability of Relative Equilibrium Example 10.10. A homogeneous thin rod of mass m and length \u00a3 is connected to a vertical shaft S by a smooth hinge bearing at Q. The shaft rotates with a constant angular velocity n, as shown in Fig. 10.11. (i) Derive the equation of motion of the rod. (ii) Determine as a function of e the hinge bearing reaction torque exerted on the rod at Q, for the initial data 8(0) = 0 at e(O) = eo. (iii) Analyze the infinitesimal stability of the relative equilibrium states of the rod. 448 Chapter 10 Solution of (i). The centra l point Q at the hinge being fixed in the inertial (machine) frame 0 = {F ; I k } , the equation of motion for the rod is obtained from Euler 's law (l0.66) in the principal body frame 2 = {Q; id ",
            " Then (l0.801) requires {J} = pZ _ [22 > O. Hence, the relative equilibrium state 8s = 0 is infinitesimally stable if and only if n < p = nc , the critical angular speed of the vertical shaft: nc = p = !\u00a5e, which is independent of the mass of the rod. In this case, the small amplitude circular frequency of the rod oscillations about the vertical state tis = 0 is Wv= (pz _ nZ)I /Z. Of course, the inverted vertical configuration of the rod 8s = x is impractical in respect of the suggested design in Fig. 10.11. Even so, (10.801) fails for 8s = n , and hence the inverted relative equilibrium state of the rod is inherently unstable for all angular speeds of the vertical shaft. 450 Chapter 10 Notice that when Q = Qc = p , u} :s 0 for all position s (l0.80j ). Hence, no infinite simally stable relative equilibrium states of the rod exist at the critical angular speed Q = Q c. Finall y, consider the case cosOs = p2/ Q2. This requires p/ Q < I ; hence (10.801)is satisfied, and the relative equi librium state Os = COS- I(p2/ Q2), regard - less of the mass of the rod, is infinite simally stable if and only if Q > P = Q c",
            " (1 - cos 80), and the last result then agrees with (10.122d) . 0 472 Chapter 10 Exercise 10.12. A uniform wheel of mass m and radius R rolls without slipping down a hill that resembles a cosine curve on [0, JT] . The center of the wheel has an initial speed vii at the top of the hill. Find the speed of the center of the wheel after it has dropped through a vertical height h from its initial position. 0 Example 10.16. Apply the energy method to derive the first integral of the equation of motion of the rod described in Fig. 10.11, page 447. Solution. The resultant force R exerted on the rod by the smooth hinge bearing is workless, and the gravitational force on the rod is conservative with total potential energy V = !mg\u00a3(I - cos B).The body frame 2 = {Q;i , j, k} is a principal reference frame at Q. Therefore, with the aid of (I 0.80a) and (I 0.80c) in (10.102), the total kinetic energy of the rod relative to Qis K = KrQ = ~m\u00a32(e 2 + Q2 sirr' B). The smooth hinge bearing exerts no torque about the hinge axis , the k direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001420_s11431-013-5433-9-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001420_s11431-013-5433-9-Figure10-1.png",
        "caption": "Figure 10 Three configurations of the R1R1R1R2-3R2P reconfigurable limb.",
        "texts": [],
        "surrounding_texts": [
            "Four planar five-bar metamorphic linkages and sixteen LFC chains are obtained in the previous sections. Reconfigurable limbs and parallel mechanisms are constructed in this section."
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.14-1.png",
        "caption": "Figure 10.14. Slipping motion of a billiard ball.",
        "texts": [
            " For a nontrivial rotation of a general rigid body under zero torque about a fixed point, the solution is more complicated, somewhat algebraically tedious , with results for the angular velocity components given in terms of Jacobian elliptic functions. Details may be found among resources listed in the reference s. A simpler example is provided in Problem 10.44, and an important special case is investigated later on. 10.15. Motion of a Billiard Ball As a final example in this series of applications of Euler's laws for a rigid body, we study the general motion of a billiard ball of radius R and mass m, initially at rest and struck horizontally by a cue, as shown in Fig. 10.14. Subsequent to the impulse , the ball acquires an instantaneous center of mass velocity Voand an angular velocity Wo in the inertial frame <1> = {o ; I, J, K}. Nothing is specified about the location of the impact, so these initial values shall remain arbitrary. The ball subsequently slips and rolls on the horizont al surface. The objective is to describe the motion of the ball on both an ideally smooth and on a rough horizontal surface, and in the latter case to (i) determine the slip speed of the contact point of the ball at 0, (ii) find the time T required for slipping to end, (iii) describe the Dynamics of a Rigid Body 457 motion of the center of mass during slip, and (iv) determine the angular velocity of the ball both during and after the slipping phase",
            " Thus, without friction , the ball spins steadily about its initial axis of rotation and its center moves with constant velocity along a straight path in <1>. 10.15.2. Motion on a Rough Surface Now suppose that the surface is rough with coefficient of dynamic friction v, and at time t the center of mass has a horizontal velocity v* and the ball is rotating with angular velocity w. These vectors are unknown; in all there are five unknown scalar components. As before, N +W = 0, and for a sphere w x lew = w x lew =O. Then, with reference to Fig. 10.14, Euler's laws (10.26) 458 and (10.65) in the inertial frame <1> require Chapter 10 mv\" = f, lew = Me = - RK x f. (l0.89a) Solution of (i), We first find the slip speed of the contact point at O.We shall assume that the tangential frictional force f at the contact point 0, so long as slip occurs, is determined by Coulomb's law of friction . This force acts in a direction opposite to the slip velocity Vs of the particle of the ball at 0, (l0.89b) where Vs = lv. I. The constraint equation for the absolute tangential slip velocity Vs of the body point in contact with the plane at 0 is Vs = v'+ w x ( - RK) in <1>, and hence Vs = v'-Rw x K",
            " (a) Show that three steady (constant) rotations with total angular velocity vectors w = (a , 0, 0) , (0, fl,0) , (0, 0, y) referred to principal axes ljr = (C ; ikl at the center of mass are exact solutions of the equat ions of mot ion. (b) The principal values of the inertia tensor referred to ljr are ordered so that I) > 12 > h Show that the steady rotations about the axes of greatest and least principal values of Ie are infinitesimally stable, while the rotation about the axis of the intermediate value of Ie is not. 10.46. Consider a homogeneous billiard ball shown in Fig. 10.14, page 457 and suppose that the horizontal impulsive action ,cT* occurs in the vertical plane through the center of mass, i.e , without \"English.\" Assume that.cr' is known . (a) Show that the height d above the mass center C at which the cue must hit the ball to produce pure rolling on the horizontal surface is given by d = 2R /5 . How does this result compare with the solution of Exerci se 10.9, page 460? Dynamics of a Rigid Body Problem 10.45. 0, k ' Inertial Frame 491 (b) Consider a ball struck high at h > d from C and struck low at h < d from C, and account for slipping on a rough surface with coefficient of friction v"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003153_b978-0-12-816634-5.00002-9-Figure2.9-1.png",
        "caption": "Figure 2.9 Bound metal deposition (BMD) extruder. Courtesy: Desktop Metals, Animesh Bose [28].",
        "texts": [
            " The advantages of BMD include that it does not use any heat source during printing process and therefore no residual stresses are generated. Printing is followed by sintering in a furnace involving slow uniform heating and minimal stress generation. Also, support structure removal is very easy and does not require machining. BMD is a faster process as compared to BJ. On the flip side the process does not yield full-density parts and requires a postprocess sintering to improve strength. BMD is being commercialized by Desktop Metal [28] (Fig. 2.9). Magnet-o-jet technology is based on magneto hydro dynamics (MHD) or more simply, the manipulation of liquid metal through magnetism [29]. It works by depositing aluminum wire into a 1200\u00b0C ceramic chamber where it melts. This molten medium is then electromagnetically pulsed\u2014 causing a droplet to form and eject with precision from a ceramic nozzle. The system delivers 1000 droplets per second with micron-level accuracy. Magnet-o-jet allows for the use of many alloys including 4043, 4047, and 1100 aluminum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000608_978-0-387-75591-5-Figure6.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000608_978-0-387-75591-5-Figure6.1-1.png",
        "caption": "FIGURE 6.1. A typical three-layered sandwich cylindrical structure with visco-elastic middle layer.",
        "texts": [
            " Hamidzadeh and Jaing (1995) and Hamidzadeh (2009) employed Hamidzadeh and Sawaya (1995) analytical method and developed a technique to consider the effect of different material loss-factors and thicknesses for constrained layer, as well as different ratios of shear modulus for visco-elastic layer to the elastic one. 6.2 Scope of the Chapter The constrained layer damping treatment with a visco-elastic core layer for a thick cylindrical structure is considered. An analytical procedure based on the solution that was developed in chapter 5 is employed for the threelayer configuration, which is depicted in Figure 6.1. In connection with the presented analytical method, the modal damping and natural frequencies for long composite circular structures are computed. The effects of geometry on the natural frequencies and loss-factors for different modes of a threelayer sandwiched thick infinitely long cylinder are discussed and presented. 6.3 Natural Frequencies and Modal Loss-Factors The determinant of the 3\u00d73 coefficient matrix presented by equation (5.38) can provide the natural frequencies of the composite cylinders"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure12-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure12-1.png",
        "caption": "Fig. 12. The 3T + 1-DOF parallel manipulator: (a) configuration 1 (b) configuration 2.",
        "texts": [
            ", intersecting and parallel working modes. It should be mentioned that the intersecting point is moving relative to the platform. To realize the symmetrical structure of the manipulator as much as possible, three limbs are connected to the end moving platform. Three L 0 F 1 C -limbs are utilized to construct the 3T + 1-DOF parallel manipulator. The constraint-couples are linearly independent. The manipulator can output a 3T bottom motion and a 1-DOF internal motion within the configurable platform, as drawn in Fig. 12 . When the moving platforms are viewed as rigid bodies, 5-DOF parallel manipulators with configurable platforms degen- erate into 4-DOF bottom manipulators. For 3T1R parallel mechanisms, the wrench system consists of two constraint-couples. According to the constraint synthesis method, the limbs used to form two constraint-couples can be synthesized. The pos- sible combinations are the L -limb and L -limb, L -limb and L -limb, L -limb and L -limb, L -limb and 0 F 2 C 0 F 0 C 0 F 2 C 0 F 1 C 0 F 2 C 0 F 2 C 0 F 1 C L 0 F 1 C -limb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000981_ecc.2013.6669816-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000981_ecc.2013.6669816-Figure2-1.png",
        "caption": "Fig. 2. The Quad-TiltRotor\u2019s operating principles",
        "texts": [
            " The article is structured as follows: In Section II the QuadTiltRotor\u2019s nonlinear model is described. In Section III the system modeling for control purposes is presented, and in Section IV the implemented control scheme is analyzed. In Section V a series of simulation studies of the proposed scheme are presented. The article is concluded in Section VI. 978-3-033-03962-9/\u00a92013 EUCA 1793 The Quad-TiltRotor\u2019s operating principles in the helicopter-like hovering mode, the fixed-wing longitudinal flight mode and the intermediate flight mode conversion phase are depicted in Figure 2. The Body-Fixed coordinates Frame (BFF) B = {Bx, By, Bz} and the North-East-Down (NED) [3] Local Tangential coordinates Plane (LTP) E = {N, E, D} are shown in Figure 1. Let \u2126 = {p, q, r} be the BFF rotational rates vector and \u0398 = {\u03c6 , \u03b8 , \u03c8} the LTP rotation angles vector. Also let U = {u, v, w} be the BFF velocity vector and XW = {xW , yW , zW} the LTP position vector. Via the Newton-Euler formulation the system\u2019s nonlinear dynamics are modeled as: FB = mU\u0307+\u2126\u00d7 (mU) MB = I\u2126\u0307+\u2126\u00d7 (I\u2126) X\u0307W = RB\u2192W U \u0398\u0307 = JB\u2192W \u2126 , (1) where FB = {Fx, Fy, Fz} the BFF total Force vector, MB = {Mx, My, Mz} the BFF total Moment vector, m the mass and I the moment of inertia matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001365_wcica.2014.7052991-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001365_wcica.2014.7052991-Figure1-1.png",
        "caption": "Fig. 1. The inertial frame {W } and the body-fixed frame {B} for a quadrotor balancing a pendulum.",
        "texts": [
            "ndex Terms\u2014 Aerial robotics, quadrotor control, inverted pendulum, approximate value iteration, reinforcement learning. I. INTRODUCTION A pendulum on top of a quadrotor, Fig. 1, requires controls to balance the pendulum and to stabilize the aerial vehicle. Solving this complex problem offers insight into advanced control strategies that can be considered for similar aerial manipulation tasks. The flying inverted pendulum was first introduced in [2] where it was solved designing linear controllers for stabilization. However, the results indicated that a learning approach could improve the system performance [2]. Reinforcement learning (RL) has grown as an effective framework for control applications in recent years, due to its ability to learn from available data rather than fully-understood system models",
            " Further the resulting action does not depend on the samples available and the policy gives consistent results. For these reasons, the convex sum policy is a good candidate for the flying inverted pendulum problem. The model presented here is used for simulations and for next state evaluation during the convex policy. We assume that the the pendulum mass is small compared to the quadrotor mass, so the reactive forces of the pendulum on the quadrotor are negligible. [2]. The world coordinate frame {W } and the body-fixed frame {B} are shown in Fig. 1. {B} is attached to the center of mass of the quadrotor. The rigid body equations of motion of the quadrotor are [11] m x\u0308y\u0308 z\u0308  = \u2212  0 0 mg + R 00 T  , (5) R\u0307 = R\u2126\u00d7, (6) I\u2126\u0307 = \u2212\u2126\u00d7 I\u2126 + \u03c4 , (7) where m \u2208 R is the mass of the quadrotor, [x y z] T \u2208 R3 is the position of the quadrotor center of mass respect to {W }, g \u2208 R is the constant gravitational acceleration, R \u2208 SO(3) is the rotational matrix of {B} with respect to {W }, T \u2208 R is the total upward thrust, \u2126 \u2208 R3 is the angular velocity of {B} with respect to {W }, I \u2208 R3\u00d73 is the constant inertia matrix expressed in {B}, \u03c4 \u2208 R3 is the moment applied to the quadrotor by the aerodynamics of the rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001144_20110828-6-it-1002.03266-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001144_20110828-6-it-1002.03266-Figure4-1.png",
        "caption": "Fig. 4. Schematic of VTOL aerial vehicle with dual-axis OAT mechanism.",
        "texts": [],
        "surrounding_texts": [
            "Single-Axis Oblique Active Tilting (sOAT): In the simplest method, called single-axis OAT or sOAT, the fans or propellers tilt about a fixed and oblique horizontal axis, and the corresponding tilt path lies along a vertical plane oriented at a fixed angle \u03b1 from the longitudinal direction Fig. 5. The tilt angle \u03b2 is measured along the tilt-path plane, and is zero when the propeller spin axis is vertical. sOAT provides full, helicopter-like pitch control of the vehicle. Moreover, it also improves stability and control in yaw and roll either by reducing their high degree of coupling intuitively associated with dual-fan rotorcrafts or by taking advantage of that coupling. This distinct superiority, together with its simplicity, makes sOAT an exceptional choice of control method for small UAVs. Dual-Axis Oblique Active Tilting (dOAT): There is much more to be gained by taking full advantage of the dual-axis OAT capability including the potential for better control response for independent 6-axis control, vertical takeoffs and landings from severely sloped terrain, remaining perfectly level in hover, remaining stationary while pitching and yawing to track a target, and extreme maneuvering in three dimensional space, see Gress (2003). The capabilities of dOAT are still an open area of research and exploration. To investigate these capabilities and verify the characteristics of this control mechanism, in this paper a full model of the dual-fan VTOL aerial vehicle with lateral and longitudinal tilting rotors is derived in this paper which represents a general dynamic model for this kind of vehicle and can be used to explore the features of both sOAT and dOAT."
        ]
    },
    {
        "image_filename": "designv10_12_0001547_iros.2013.6696825-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001547_iros.2013.6696825-Figure13-1.png",
        "caption": "Figure 13. Image of the head section passing through an elbow.",
        "texts": [
            " Therefore, friction between the robot and the pipe occurs and, as the surface of the robot is rubber, friction between the robot and the pipe is high. In addition, the steps between a unit and a joint of the robot constitute an obstruction to traveling. To solve this problem, we need to reduce the friction of the robot. Second, we explain problem (2). Figure 12(a) shows the elbow (JIS K 6775, Rc = 1.0 ID) of a gas pipe from Sekisui Chemical Company. This pipe is commonly used for buried 1-inch gas pipes. Figure 12(b) shows two types of elbows, both having a narrow width. Figure 13(a) shows the state when the head section of the robot is passing through a narrow elbow. As mentioned, the head section comprises a hemispherical ABS resin section and a rubber tube. As seen in Figure. 13(a), the rubber tube buckles, and the head unit eventually smash into the elbow. The approach angle of the robot into a narrow elbow is obviously smaller than for a wide elbow, as shown in Figure. 13(b), and thus the head unit collides with a narrow elbow more than it would with a wide elbow. Therefore, the robot cannot pass through a narrow elbow while it can pass through a wide elbow. To solve this problem, we need to alter the head section. Thus, to restate the above, for a robot to be able to pass through continuous elbows that are found in real-life environments, we need to reduce the friction of the robot and alter the head section. (a) Extension. (b) Contraction. \u2026 Wavelength Propagation speed Direction Endoscope Natural rubber tube ABS resin DirectionAcrylic pipe Push-pull scale GuideFixed part Figure 14 shows an image of a low-friction robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001958_tmag.2018.2841874-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001958_tmag.2018.2841874-Figure1-1.png",
        "caption": "Fig. 1. Stator model. (a) TP-SL winding. (b) TP-DL winding. (c) DTP-DL winding. (d) TP-FL winding. (e) DTP-FL winding.",
        "texts": [
            " Finally, an axial flux integrated-starter generator (ISG) with dual three-phase fourlayer (DTP-FL) winding and radial segmented PM experiment platform is established for validating the proposed method. In this section, a 12-slots/10-poles SPMSM with different winding layouts and axial segmentation number is introduced. MMF of different winding layouts is analyzed. Stator winding layout of 12-slots/10-poles SPMSM is generally classified into the following several categories: TP single-layer (TP-SL) winding layout in Fig. 1(a); TP doublelayer (TP-DL) winding layout in Fig. 1(b); DTP-DL winding layout in Fig. 1(c); TP-FL winding layout in Fig. 1(d); and DTP-FL winding layout in Fig. 1(e). Rotor model adopts surface-mounted PM considering different axial segmentation numbers as shown in Fig. 2, and the conductivity of PM is 6.67e5 (Simens/m). 0018-9464 \u00a9 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Main parameters of a 24-kW SPMSM are given in Table I. Current source is applied to stator winding, thus the normalized winding MMF is obtained by finite element method (FEM), which neglects the effect of flux leakage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure5.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure5.3-1.png",
        "caption": "Fig. 5.3 A double pendulum consists of an upper arm and a lower arm joined end to end. The combination provides a good model of the upper and lower arm or the upper and lower parts of the leg. It also provides a good model to analyze the swing of a bat. The two arms start out at right angles when pitching a ball or swinging a bat or a golf club, as shown here, then straighten out just before throwing or impacting the ball",
        "texts": [
            " If you then swing another rod at the bottom end of the top rod you will have a model of the upper arm at the top and a forearm at the bottom, with an elbow joint joining the two rods and a shoulder joint at the top. The easiest way to make the elbow joint is to drill holes through the two rods and join them with a loose-fitting bolt or a short loop of string. A neat experiment is to make a double pendulum and then pull it aside so that the upper arm is horizontal and the lower arm is almost vertical and above the horizontal, as shown in Fig. 5.3. If you then release the pendulum, the lower arm starts to fall vertically and pushes down on the upper arm, causing the upper arm to rotate faster than it would if it was a single pendulum. Both arms swing around until both reach the bottom of their circular path, at which time the upper arm has slowed down considerably and the lower arm is rotating rapidly. This happens naturally without any force acting on the system other than the force of gravity. The resulting motion 5.4 Double Pendulum 83 is very similar to that of the arm actions when throwing a ball or swinging a bat or when swinging a golf club or a tennis racquet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001271_j.jtbi.2014.09.008-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001271_j.jtbi.2014.09.008-Figure2-1.png",
        "caption": "Fig. 2. The illustration of actuated SLIP. (a) the actuated SLIP model. Here m, k, c, l0 \u03b2 are body mass, leg stiffness, linear leg damping, leg original length and landing angle respectively. During stance, the leg swings forward under the actuation of hip torque and lifts off when the reaction force between the foot and the ground becomes zero. Similar to SLIP, during flight, the leg is quickly reset to a constant landing angle \u03b2 with an un-stretched leg. (b) human running motion. The dashed line stands for the virtual spring leg.",
        "texts": [
            " Previous research about SLIP has shown that there exists a certain relationship between relative stiffness and leg landing angle for periodic solutions (Seyfarth et al., 2002). However, SLIP is energy conserving and cannot predict net energetic cost of locomotion. We therefore extended it to include a mathematically simple actuation and damping so that energetic cost predictions can be made. The governing equations of the model are derived and nondimensionalized to simplify analysis and comparison across many species of legged animals. As shown in Fig. 2, an established physics-based model of locomotion is used for this study, based upon the canonical Spring-Loaded-Inverted-Pendulum model (Shen and Seipel, 2012). It includes actuation which is capable of representing the combined effects of both hip and ankle torque during locomotion, and the effective action of the knee is represented as a spring along the leg in order to agree with the established spring-mass modeling framework that has been used to analyze and compare experimental data collected from species across the animal kingdom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003437_j.ymssp.2020.107158-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003437_j.ymssp.2020.107158-Figure4-1.png",
        "caption": "Fig. 4. Variations of Mii and Mij in the workspace. (a) M11, (b) M22, (c) M33, (d) M12, (e) M13, (f) M23.",
        "texts": [
            " For the studied industrial-grade parallel tool head, besides the geometrical and dynamic parameters, the inertia matrixM and gravity term G are only determined by a and b. In other words, the dynamic characteristics of the parallel tool head are affected by the orientation of the moving platform [38]. Then, M and G can be further expressed as: M \u00bc M11 M12 M13 M21 M22 M23 M31 M32 M33 2 64 3 75 \u00f014\u00de G \u00bc G1 G2 G3 2 64 3 75 \u00f015\u00de where Mij and Gi are the elements of M and G, respectively, and i j\u00f0 \u00de \u00bc 1;2;3. Inertia is the important parameter of dynamic model, and Fig. 4 describes the variations of the elements of inertia matrix M. Because M is a symmetric matrix, only half elements of M are considered (i.e. M11, M22, M33, M12, M13, and M23). On the other hand, because the dynamic characteristics of the parallel tool head are affected by the orientation of the moving platform, only a and b need to be considered. All used geometrical and dynamic parameters are given in Appendix B, and the selected workspace is a b\u00f0 \u00de 2 p=6 p=6\u00bd rad. The results shown in Fig. 4 indicate that: 1) the non-diagonal elements (i.e. Mij) are much smaller than the diagonal elements (i.e.Mii); 2) althoughMii will change in the workspace, the variation range is very small (less than 0:0015kg m2), thus, the diagonal elements can be considered as a constant. Based on these two characteristics, the coupling relation between different driving shafts can be neglected, and the load inertia of each driving shaft can be regarded as a constant, which provide base for control system modeling",
            " (28) and (32), epi can be written as: epi \u00bc JiTvi KppiKpviKt q v ri \u00fe Tvi Kppi \u20acqri \u00fe 1 Kppi _qri \u00fe Tvi NKppiKpviKt _sdi \u00f033\u00de Next, the tracking error prediction result is compared with the actual value under the typical motion condition, and Kpp1 is set as 50 s 1. Based on the result shown in Fig. 11, the prediction result is very close to the actual value, which verifies the effectiveness of Eq. (33). Moreover, it can be seen that the tracking error is determined by the load inertia when the motion parameters and the control parameters are determined, and based on Fig. 4, Mii is nearly constant in the workspace, this is the reason why the tracking error is almost the same with different orientations in Fig. 10. Furthermore, how to decrease tracking error to improve tracking performance through a simple and effective method is another main task in industry. Based on Eq. (33), because Ji and Tvi are much less than 1, it can be seen clearly that the coefficient of the velocity term is much larger than other coefficients, which indicates that the tracking error is mainly affected by the desired velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-Figure8.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-Figure8.2-1.png",
        "caption": "Fig. 8.2 Scheme of the gyroscope\u2019s stand with the counterweight",
        "texts": [
            "3) where b is the mass of the centre beam; f is the coefficient of friction of sliding supports; d is the diameter of the supports B and D; \u03b4 = 45\u00b0 is the angle of the conical surface of the sliding bearing; other parameters are as specified above. The rotation of the gyroscope around axis generates the centrifugal forces produced by the centre mass, and hence, the frictional torque acting on the sliding supports B and D is expressed by the following equation: Tfm = mrlm f d 2 cos \u03b4 \u03c92 x (8.4) where mr is resulting load mass: lm is the location of resulting load mass (Table 8.1; Fig. 8.2); other parameters are as specified above. The load torque T produces the resistance torques of the centrifugal T ct and Coriolis T cr forces acting around axis ox and precession torques of the common inertial forces T in, and the change in the angular momentum T am around axis oy. The precession torques produce the additional load on the supports B and D. Then, the frictional torque generated by the precession torque is represented by the following equation: Tfp\u00b7x = Tam\u00b7x = f d cos(\u03b4 \u2212 \u03c4) 2h cos \u03b4 J\u03c9\u03c9x (8.5) where T p\u00b7x is the precession torque (Table 3.1, Chap. 3); h is the distance from the centre mass of the gyroscope to the centre of the spherical journal of the centre beam with supports B and D; \u03c4 is the constructive angle (Fig. 8.2); other parameters are as specified above. The total frictional torque acting on supports of the gyroscope stand is represented by the following equations: Tfx = TfA + Tfm + Tfpx = Ag f d 2 cos \u03b4 + mrlm f d 2 cos \u03b4 \u03c92 x + f d cos(\u03b4 \u2212 \u03c4) 2h cos \u03b4 J\u03c9\u03c9x (8.6) where all parameters are as specified above. Substituting defined equations for the external and inertial torques of the gyroscope (Eqs. 8.2\u20138.6) into Eq. (8.1) yields the following differential equation: Jx d\u03c9x dt = ( Ml \u2212 s a 2 \u2212 Ga ) g cos \u03b3 \u2212 [ (Ag + mrlm\u03c92 x ) f d 2 cos \u03b4 + f d cos(\u03b4 \u2212 \u03c4) 2h cos \u03b4 J\u03c9\u03c9x ] \u2212 ( 2\u03c02 + 8 9 ) J\u03c9\u03c9x (8",
            "8) represents the mathematical model of the gyroscope motion with the spinning rotor when its motion around axis oy is blocked. The case study and first practical tests were conducted for the condition of the gyroscope turn on the angle \u03b3 = 91.57\u00b0, which calculated by the geometrical parameters of the stand. At the starting condition, the gyroscope counterweight has contacted with the surface of the platform.At the end of the turn, the spherical frame of the gyroscope has contacted the platform (Fig. 8.2). The surfaces of sliding support of the arm and spherical ball of the beam polished and handbooks give the value of the dry frictional coefficient, f = 0.15\u20130.18, [16\u201318]. The parameter l = 35.5 mm (Fig. 8.2), the angular velocity of the spinning rotor is \u03c9 = 10,000 rpm, other parameters represented in Table 8.1 and Fig. 8.2. Substituting defined data into Eq. (8.8) and transformation yields the following expression: 4.780082 \u00d7 10\u22124 d\u03c9x dt = (0.146 \u00d7 0.0355 \u2212 0.005 \u00d7 0.025 \u2212 0.098 \u00d7 0.05) \u00d7 9.81 cos \u03b3 \u2212 0.277 \u00d7 9.81 \u00d7 0.16 \u00d7 0.00424 2 cos 45\u25e6 \u2212 0.043 \u00d7 0.03674418 \u00d7 ( 0.16 \u00d7 0.00424 2 cos 45\u25e6 ) \u03c92 x \u2212 [ 0.16 \u00d7 0.00424 \u00d7 cos(45\u25e6 \u2212 38.581266\u25e6) 2 \u00d7 0.0569254 cos 45\u25e6 ] \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10.000 \u00d7 ( 2\u03c0 60 ) \u03c9x (8.10) Simplification and transformation of Eq. (8.10) give the following expression: 4.780082 \u00d7 10\u22124 \u00d7 d\u03c9x dt = 1",
            "28) Substituting defined parameters above into Eq. (8.28) and solving yield the following result t = \u221a 2\u03b3 \u03b5x = \u221a 2 \u00d7 91.57\u25e6 \u00d7 \u03c0 180\u25e6 \u00d7 1.333736781 = 1.54 s (8.29) The final computing is conducted for Eq. (8.7) to define the time of the gyroscope motion around axis ox with the hypothetical action of the resistance inertial torques. The comparative analysis of the results of practical tests and the analyticalmodel validate the deactivation of the inertial torques. Substituting definedparameters presented in Table 8.1 and Fig. 8.2 into Eq. (8.7), transformation and simplification yield the following equation: 4.780082 \u00d7 10\u22124 \u00d7 d\u03c9x dt = (0.146 \u00d7 0.0355 \u2212 0.005 \u00d7 0.025 \u2212 0.098 \u00d7 0.05) \u00d7 9.81 \u00d7 cos \u03b3 \u2212 0.277 \u00d7 9.81 \u00d7 0.16 \u00d7 0.00424 2 cos 45\u25e6 \u2212 [ 2 (\u03c0 3 )2 + 1 ] \u00d7 0.16 \u00d7 0.00424 2 \u00d7 0.056925 \u00d7 cos(45\u25e6 \u2212 38.581\u25e6) \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10.000 \u00d7 2\u03c0 60 \u03c9x \u2212 [ 2 (\u03c0 3 )2 + 8 9 ] \u00d7 0.5726674 \u00d7 10\u22124 \u00d7 10.000 \u00d7 2\u03c0 60 \u03c9x (8.30) Simplification of Eq. (8.30) brings the following expression: 4.780082 \u00d7 10\u22124 \u00d7 d\u03c9x dt = 1.54998 \u00d7 10\u22123 cos \u03b3 \u2212 1",
            " The bar of the gimbal is contacted with the angular rocker that presses the platform of the digital scale of Model TS-SF 400A with division one gr. The digital scale has demonstrated the value of the force generated by the precession torque. The practical result is compared with the theoretical value of the force of the precession torque computed for the horizontal location of the running gyroscope. The torque and forces acting on the gyroscope stand are represented in Fig. 8.5. The basic geometrical parameters of the stand are represented in Table 8.1, Fig. 8.2 and in Sect. 8.1. The value of the velocity is changed with the change in the angle of the gyroscope turn and time of motion. The force of the precession torque is varied with the change of the angular velocity and the time of the motion of the gyroscope. The expression of the precession torque for the horizontal location (\u03b3 = 0\u00b0) of the gyroscope is represented by substituting \u03c9x (Eq. 6) into T am = J\u03c9\u03c9x: Tam = J\u03c9 \u00d7 (3.086464199 cos 0\u25e6 \u2212 2.595701613) ( 1 \u2212 e\u22121.050580906t) = 0.490762586J\u03c9 ( 1 \u2212 e\u22121"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000434_1077546307081325-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000434_1077546307081325-Figure1-1.png",
        "caption": "Figure 1. (a) Cross-section of the translational guide, (b) Detailed view of ball bearing contact.",
        "texts": [
            " Finally, the evaluated describing functions are compared in the frequency domain within the frequency range of interest. The effect of these nonlinearities in the joints on overall machine performance is beyond the scope of this paper, but is described separately in Dhupia et al. (2007). ANALYSIS Translational guides were chosen for experimental evaluation as they are among the most common joints in machine tools. The translational guide chosen for the experiment was a Bosch-Rexroth linear guide system: R1621, size 30. The cross-section of the translational guide used for the experiment is shown in Figure 1. The joint consists of two components, the rail and the runner block and the contact is made through the preloaded ball bearings. A model for joint stiffness under normal load P is developed using Hertzian mechanics in this at Queen Mary, University of London on June 20, 2014jvc.sagepub.comDownloaded from section. The model accounts for joint stiffness as a property based on material properties, geometry and preload, but can be directly estimated from experiments. The model is derived based on the assumption that the runner block and the rail are rigid and all compliance in the system may be attributed to the ball bearings. The ball bearings are located in four tracks as shown in Figure 1. The lower track bearings are denoted with subscript L and the upper track by subscript U. The objective of the model is to describe the relationship between external load P and relative displacement z, taking into account the stiffness relationship at the ball bearings: P f z or , z f 1 P (1) where, z z1 z2 at Queen Mary, University of London on June 20, 2014jvc.sagepub.comDownloaded from The contact deformation of the single ball within two grooves can be found by Hertzian analysis as dependent on the normal load Pball as (Rivin, 1999)",
            " ball in contact with flat surface), then n 1 Or, the deformation-load relationship in equation (2) may be defined simply by the model dball P2 3 ball (3) where, depends upon material and geometrical properties of the joint. Since the bearings are preloaded, a nominal deformation d0 is present even when no external load P is applied. When load P is applied, the lower set of bearings experience deformation dL and the above set of bearings experience deformation dU . When, the balls in all tracks are in contact with the grooves, the amount of compression the balls in the lower tracks experience must be equal to the amount of decompression the balls in upper tracks experience (see Figure 1) and they can be related to the relative displacement z through the following equation: dL d0 sin d0 dU sin z (4) Let PL be the normal load experienced by the balls in the lower track and PU be the load experienced by the balls in the upper track. Then, the relationship between the joint deflection and the normal loads developed at the ball bearing may be obtained by using equation (3) and equation (4): z P2 3 L P2 3 0 sin P2 3 0 P2 3 U sin (5) Finally, to relate normal loads at the ball bearing (PL and PU ) to external load P, we consider the free body diagram of the runner block and equate the forces in the vertical direction to get the relationship: P 2PU sin 2PL sin (6) at Queen Mary, University of London on June 20, 2014jvc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001645_1464419317727197-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001645_1464419317727197-Figure7-1.png",
        "caption": "Figure 7. Wear in the region B at different cage unbalance masses: (a) mec\u00bc 1.6 g, (b) mec\u00bc 3.5 g, and (c) mec\u00bc 6.8 g.",
        "texts": [
            " The wear sizes are used to evaluate the wear extent of the cage guiding surface. It can been seen that the wear size of the guiding surface gradually increases from 0 position of the unbalance to 180 . In other words, the wear in the region B of 180 is more serious than the wear in the region A of 0 as shown in Figure 6, which indicates that the interaction of cage\u2013inner ring mainly takes place in the region opposite to the unbalance if the cage is guided by the inner ring. The wear in the region B at different cage unbalance masses under the same conditions are shown in Figure 7. It is observed that wear sizes in the region B of the cage guiding surface are extended and aggravated as increasing the cage unbalance masses, which is in accordance with the predicted wear rate of cage guiding surface as shown in Figure 3(a). It is revealed that the cage unbalances intensify the wear of the cage guiding surface and then might shorten the service life of cage and bearing. Figure 8 depicts the different wear of the cage pocket due to cage unbalances. The wear of the cage pocket is observed, but the wear extent of cage at different cage unbalances are approximated and not aggrandized, which agree with the emulation results shown in Figure 3(b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure3.3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure3.3-1.png",
        "caption": "Fig. 3.3 (a) A ball traveling to the left and spinning clockwise when viewed from above, curves to the right. (b) Air flowing past a spinning ball at rest is deflected downward in this diagram, with the result that the air exerts an upward force on the ball known as the Magnus force",
        "texts": [
            " There is the usual force of gravity pulling it toward the earth, there is the usual backward force due to air resistance, and there is an additional force that deflects the ball in a direction at right angles to its path. The additional force is known as the Magnus force, named after one of the early scientists who discovered its existence. Some simple demonstrations of the Magnus force are described in Project 2. The Magnus force does not alter the speed of the ball but it acts at right angles to the path of the ball and at right angles to the spin axis. For example, consider the situation shown in Fig. 3.3a where a ball is pitched in a horizontal direction, is traveling right to left, and is spinning about a vertical axis in a clockwise direction when viewed from above. In that case, the Magnus force acts in a horizontal direction, causing the ball to curve to the right when viewed by the pitcher (or to the left when viewed by the batter). If the ball was spinning counter-clockwise, it would curve in the opposite direction. The origin of the Magnus force can be explained by imagining that the ball spins clockwise about a fixed axis, and that the air is flowing past the ball, as shown in Fig. 3.3b. The air is deflected downward by the ball since it is dragged in a clockwise direction by friction between the ball and the air, with the result that there is an equal and opposite force exerted by the air on the ball. The effect of the Magnus force is to change the curvature of the trajectory. The trajectory of a ball curves downward due to the downward gravitational pull of the 3.6 Effects of Spin on the Trajectory 45 earth, but the Magnus force can increase or decrease that curvature depending on the direction of the Magnus force",
            " The ball, therefore, lands at time t D 2tm after traveling a horizontal distance R given by R D 2vxotm D 2xoyo 9:8 D v2sin.2 / 9:8 ; Appendix 3.2 Measurement of Drag Force 53 where sin.2 / D 2sin cos . R is commonly known as the range of the ball. If it is launched at y D 0 and lands at y D 0 then R is a maximum when sin.2 / D 1 or when D 45\u0131. In that case, R D v2=9:8. Appendix 3.2 Measurement of Drag Force It is difficult to measure CD accurately for baseballs and softballs using flight time information since air drag has a relatively small effect on the flight of these balls, at least over small distances. Figure 3.3 shows a much bigger effect over large distances since the drag force then acts for a relatively long time and slows the ball considerably. By way of example, consider a baseball pitched at a horizontal speed of 80 mph (117.4 ft s 1) over the 60 ft horizontal distance from the pitcher to the batter. In the absence of air resistance, the ball would travel at 117.4 ft s 1 the whole way, taking 60/117.4 D 0.51 s to arrive. The effect of air resistance can be estimated from (3.1), giving mdv=dt D F D 1 2 CD v2A D 0:0026CDv2 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002160_icra.2016.7487629-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002160_icra.2016.7487629-Figure1-1.png",
        "caption": "Figure 1. Reference frames of the IRB 120 robot.",
        "texts": [
            " Then, the experimental setup is described and the new measuring device and the automated measuring process are detailed. Next, we present a random configuration generation algorithm, and assess the effector of the measuring noise. Finally, we present a real calibration with the new measuring device, and validate the results with a laser tracker. The following section presents the nominal kinematic model of the robot, and details the kinematic and nonkinematic errors that were selected for identification. A. Kinematic Model The calibration process is applied to the ABB IRB 120 (Fig. 1), a six-degrees-of-freedom (6-DOF) small serial industrial robot. This robot is comprised of six revolute joints, and its kinematic model is developed according to the Modified Denavit-Hartenberg (MDH) approach, as presented in [21]. This model involves nine reference frames: the world frame {W}, the base frame {0}, the tool frame {tool}, and the six link frames {1}, {2}, \u2026, {6}. The origin of the frame {W} is located at the center of precision ball 1. As shown in Fig. 1, its x axis points toward the center of ball 2, and its y axis is in the plane formed by the centers of balls 1, 2 and 3. These are the balls that will be probed with our device. The x, y and z axes of {tool} are defined as aligning with the axes of the stems of the three digital indicators. Given the vector of the joint variables, [ ]1 2 6 T= \u03b8 ,\u03b8 ,...,\u03b8q , (1) the end-effector\u2019s pose {tool} with respect to (w.r.t.) {W} is 0 6 0 6 ( )( )W W tooltool = qT q T T T , (2) where i jT is the homogeneous matrix representing the pose of frame {i} w"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001526_j.oceaneng.2013.05.003-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001526_j.oceaneng.2013.05.003-Figure1-1.png",
        "caption": "Fig. 1. Coordinate system.",
        "texts": [
            " The controllers' performance is evaluated via execution of some simulations. The rest of the paper is as follows. In Section 2, the dynamic of a warship is studied and the perturbed model of the fin-roll dynamics is extracted. Fixed gain and adaptive sliding mode control are designed in Section 3. In Section 4, simulation results are demonstrated and finally a conclusion is made in Section 5. In this section, the mathematical model for the ship dynamic is presented for a naval vessel with 4-degree of freedom. The ship model and the coordinate systems are depicted in Fig. 1. The translation motion of the ship in three directions are surge, sway, and heave; the rotation motion about three axes of x0, y0, z0 are roll, pitch, and yaw, respectively. Motion in pitch and heave can generally be neglected. The dynamic equation of the motion in the body fixed frame is given by Perez (2005) in a vector form: MRB _\u03c5\u00bc \u03c4\u00f0_\u03c5; \u03c5; \u03b7\u00de\u2212CRB\u00f0\u03c5\u00de\u03c5 _\u03b7\u00bc J\u00f0\u03b7\u00de\u03c5 \u00f01\u00de where MRB is the mass and inertia matrix due to the rigid body dynamic, CRB\u00f0\u03c5\u00de\u03c5 includes the coriolis and centripetal forces and moments, and J\u00f0\u03b7\u00de is the transformation matrix",
            " The hydrodynamic models Xhyd;Yhyd;Khyd;Nhyd in the vessel are given as follows: Xhyd \u00bc X _u _u\u00fe Xujujujuj \u00fe Xvrvr \u00fe Ta Yhyd \u00bc Y _v _v\u00fe Y _r _r \u00fe Y _p _p\u00fe Y jujvjujv\u00fe Yurur \u00fe Yvjvjvjvj \u00fe Yvjrjvjrj \u00feYrjvjrjvj \u00fe Y\u03d5juvj\u03d5juvj \u00fe Y\u03d5jurj\u03d5jurj \u00fe Y\u03d5uu\u03d5u2 Khyd \u00bc K _v _v\u00fe K _p _p\u00fe K jujvjujv\u00fe Kurur \u00fe Kvjvjvjvj \u00feKvjrjvjrj \u00fe Krjvjrjvj \u00fe K\u03d5juvj\u03d5juvj \u00fe K\u03d5jurj\u03d5jurj \u00feK\u03d5uu\u03d5u2 \u00fe K jujpjujp\u00fe Kpjpjpjpj \u00fe Kpp\u00fe K\u03d5\u03d5\u03d5\u03d5 3\u2212\u03c1g\u2207Gz\u00f0\u03d5\u00de Nhyd \u00bcN _v _v\u00fe N_r _r \u00fe Njujvjujv\u00fe Njujrjujr \u00fe Nrjrjrjrj \u00fe Nrjvjrjvj \u00feN\u03d5juvj\u03d5juvj \u00fe N\u03d5ujrj\u03d5ujrj \u00fe N\u03d5ujuj\u03d5ujuj \u00f03\u00de where \u03c1 is the mass density of water, g is the gravity constant, Gz\u00f0\u03d5\u00de is the buoyancy, and \u2207 is the ship displacement. The rudder equation is added to the system when simulation is done and its dynamic is not considered in this paper. The position of the fin on the ship is shown in Fig. 1. The hydrodynamic forces acting on fins can be written as follows (Perez, 2005; Surendran et al., 2007): Xf in Yf in Kf in Nf in 2 66664 3 77775\u00bc \u2212T \u2212N sin \u00f0\u03b2\u00de 2Nrf LGN sin \u00f0\u03b2\u00de 2 66664 3 77775 \u00f04\u00de where \u03b2 is the fin tilt angle, LG is the longitudinal distance from the center of pressure of the fin to the center of gravity. T and N are computed as follows: where L and D are lift and drag forces. \u03b1e is the effective angle of attack computed by \u03b1e \u00bc\u2212\u03b1f\u2212\u03b1; \u03b1f \u00bc tan \u22121 rf p u \u00f06\u00de where \u03b1f is the flow angle, and \u03b1 is the mechanical angle of the fin"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000039_nme.1990-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000039_nme.1990-Figure5-1.png",
        "caption": "Figure 5. Rectangular membrane subjected to in-plane bending moment: (a) analytical model and (b) finite element model.",
        "texts": [
            " In this section, we present some numerical examples for verification and validation of the proposed method. Newton\u2013Raphson iterations are performed in order to search the equilibrated state. We adopt the following condition as the convergence criterion: |R(i)|/|R(1)| (99) where R(i) is the residual forces at the i th iteration step and is a threshold value. Consider a rectangular membrane subjected to normal stress 0 in the y-direction, axial load P = 0th in the x-direction and in-plane bending moment M on the both sides as shown in Figure 5(a). Note that h is the length of the sides and t is the thickness of the membrane. With increasing moment M , the bandwidth b of vertical wrinkles grows from the lower part of the membrane. This simple problem has served as a benchmark for various numerical approaches in the analysis of partly wrinkled membranes. An analytical solution of the problem is presented in Reference [31]. It is shown in the reference that the bandwidth of wrinkled region is given by b h = \u23a7\u23a8\u23a90, M/(Ph)< 1 6 3M/(Ph) \u2212 1 2 , 1 6 M/(Ph)< 1 2 (100) The normal stress x in the x-direction of the membrane is expressed as x 0 = \u23a7\u23aa\u23a8\u23aa\u23a9 2(y/h \u2212 b/h) (1 \u2212 b/h)2 , b/h<y/h 1 0, 0 y/h b/h (101) Copyright q 2007 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 71:1231\u20131259 DOI: 10.1002/nme The relation between the overall curvature of the membrane and the moment M is determined by 2M Ph = \u23a7\u23aa\u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23aa\u23a9 1 3 Eth2 2P , Eth2 2P 1 1 \u2212 2 3 \u221a 2P Eth2 1 , Eth2 2P >1 (102) A finite element model of the rectangular membrane is shown in Figure 5(b). Only the right half of the membrane is modelled by symmetry. The model consists of 55 isoparametric ninenode membrane elements. All nodes along the left edge are fixed in the x-direction, and are free to move in the y-direction except for the central node. The axial load P and the moment M are replaced by two equivalent nodal forces. In this problem, we adopt the threshold value of = 10\u22128. Figure 6 shows a comparison of numerical and analytical results for the moment\u2013curvature relation. The curvatures corresponding to numerical results are obtained from the nodal displacements by assuming that the y displacements are described by a quadratic function of x "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002605_01691864.2018.1556116-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002605_01691864.2018.1556116-Figure3-1.png",
        "caption": "Figure 3. Configuration shows how the motors produce the moments about the x-axis in any direction. The directions in this figure are for the thrust forces and for the drag moments which are in the opposite direction of the rotating speed.",
        "texts": [
            " Hence, replacing the fixed dihedral angle with a varying one will add potential to the quadrotor to perfectly face more stability problems as recommended in the future work of the aforementioned work (see Figure 2). Thus, considering different tilting axes with changeable values is to trend the designmodification to servemore than one idea, i.e. increasing the DOFs and improving the hover. Furthermore, this thrust vectoring may be subjected to transform the quadrotor to a hybrid vehicle which can move onto surfaces using horizontal thrust force components (see Figure 3). For the proposed design, it is needed to make a slight change in the conventional configuration which maintains the moment balanced. This different configuration is to make the front and left propellers rotate clockwise while back and right ones rotate counterclockwise as in Figure 1(c). The purpose of this change is tomake the horizontal and vertical components of the thrust forces and dragmoments cooperate or eliminate each other while tilting the propellers that will be discussed in detail in Section 3",
            " And the other case is to achieve horizontal motion in the y-axis without any inclination in the quadrotor body about the x-axis. Case (1):This case discusses hoveringwith a roll angle. The following procedure explains how to implement this case: \u2022 The rotors-1, 2 will be used to produce a torque that controls the roll angle, their tilt angles will be equal in their values but have different signs, and are produced by the controller. According to the direction of the tilting, the direction of themoment will be determined as in Figure 3. \u2022 The other two rotor tilt angles should have the same value which is varying according to the relation in Equation (18) to prevent the quadrotor moving in the y-direction as the horizontal components of the forces Figure 4. Free body diagram for the tilted hovering mode with roll angle, the x-axis is perpendicular to the paper and inward. will be balanced as shown in Figure 4 (\u03b13 = \u03b14 = \u03b134). \u2022 To prevent the craft from making a yaw angle about the z-axis it is needed tomaintain the rotational speeds of all rotors the same (\u03c91 = \u03c92 = \u03c93 = \u03c94 = \u03c9)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003174_s11012-019-01115-y-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003174_s11012-019-01115-y-Figure4-1.png",
        "caption": "Fig. 4 Structure of the planetary gear set",
        "texts": [
            "3 TVMS calculation of a gear pair For a gear pair with gear ratio ranging from 1 to 2, there are single and double pairs of gear teeth meshing alternatively. The TVMS of the ith pair of gear teeth can be written as follows: 1 kti \u00bc 1 khi \u00fe X2 j\u00bc1 1 kaji \u00fe 1 kbji \u00fe 1 ksji \u00fe 1 kfji \u00f020\u00de where subscript j describes the jth gear tooth. For the double pairs of gear teeth, the TVMS can be given as follows: k \u00bc X2 i\u00bc1 kti \u00f021\u00de where i \u00bc 1; 2 denote the first and second pair of the gear teeth, respectively. 2.4 TVMS of a planetary gear set The structure of a planetary gear set is shown in Fig. 4. It is composed of a sun gear (s), a ring gear (r) and N planet gears (p) which are held by one carrier (c). The relative phasing relationships of N sun-planet and ring-planet gear pairs can be calculated as follows [38]: csi \u00bc Zswi 2p cri \u00bc Zrwi 2p \u00f022\u00de Based on the relative phasing relationships, the expressions of the TVMS for the ith sun-planet and ring-planet gear pairs can be written as follows: Kspi \u00bc Ksp1\u00f0t csiTm\u00de Krpi \u00bc Krp1\u00f0t criTm crsTm\u00de \u00f023\u00de Spalling defect is one of the typical tooth failures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001668_s40194-017-0533-y-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001668_s40194-017-0533-y-Figure4-1.png",
        "caption": "Fig. 4 a Distribution of current density (A/m2). b Thermal distribution (\u00b0C) during the deposition",
        "texts": [
            " The thermal losses\u2014radiation, convection, and conduction\u2014in the substrate and the wire are included in the numerical model which used a two-step algorithm (Fig. 3). The results on the temperature field (T(x,y,z)) shown are in steady state. They are obtained by following a few steps: (1) a frequency study is made at the beginning to model the electromagnetic field (HPV(x,y,z)) created by the circulation of current in the coil of the inductor system. This magnetic field is also used\u2014in the same step\u2014to obtain the current density in the different components\u2014wire and substrate (Fig. 4a). It is this density of current which is used for the second step. (2) A stationary thermal study is made using the first step\u2019s results (Fig. 4b). The current density obtained is reused to be assimilated as a heating source in the study. A movement of the substrate and the wire is made virtually\u2014to simulate the evolution of the deposition rate\u2014by associated an extremity of the wire\u2014respectively of the substrate\u2014with an ambient temperature and add a movement of this temperature field at the speed of the wire feeding\u2014respectively at the travel speed. So, the results shown are in Eulerian point of view. Three parameters are temperature-dependent: the electrical conductivity, \u03b3(T); the thermal conductivity, \u03bb(T); and the specific density, \u03c1c(T)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000029_s00170-006-0851-5-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000029_s00170-006-0851-5-Figure3-1.png",
        "caption": "Fig. 3 A limb with its infinitesimal screws",
        "texts": [
            " The mechanism under study is a spatial mechanism; thus, the Lie algebra involved requires that dime(3)=6. In order to satisfy the dimension of the subspace spanned by the screw system for each limb, the 3-RPS parallel manipulator can be modelled as a 3-R*RPS parallel manipulator, see Huang [11], in which the revolute joints R* are fictitious kinematic pairs where the corresponding joint rates are all equal to zero. Let \u03c9=(\u03c9X, \u03c9Y, \u03c9Z) the angular velocity of the moving platform, w.r.t. fixed platform, and vO=(vOX, vOY, vOZ) the translational velocity of the point O, see Fig. 3, where both three-dimensional vectors are expressed in the reference frame XYZ, see Fig. 3. Then, the velocity state VO=(\u03c9, vO), also known as the twist about a screw, of the moving platform w.r.t. fixed platform, can be written, see Sugimoto [15], through each one of the limbs as follows 0w i0 1 $ 1 i \u00fe1 w i1 2 $ 2 i \u00fe2 w i2 3 $ 3 i \u00fe4 w i4 5 $ 5 i \u00fe5 w i5 6 $ 6 i \u00bc VO i 2 1; 2; 3f g (21) where, in particular, 1wi 2 \u00bc q : i is the joint rate velocity of the i-th actuated prismatic joint, while 0wi 1 \u00bc 0 is the joint rate velocity of the i-th imaginary revolute joint, in the same limb",
            " Finally, once the angular velocity of the moving platform and the translational velocity of the point O fixed at it are calculated, the translational velocity of the center of the moving platform, vC, is calculated using classical kinematics. Indeed vC \u00bc vO \u00fe \u03c9 rC=O \u00f027\u00de In this section the acceleration analysis of the parallel manipulator is carried out by means of the theory of screws. Let w : \u00bc w : X ;w : Y ;w : Z\u00f0 \u00de the angular acceleration of the moving platform, w.r.t. fixed platform, and aO \u00bc aOX ; aOY ; aOZ\u00f0 \u00de the translational acceleration of the point O, where both three-dimensional vectors are expressed in the reference frame XYZ, see Fig. 3. The reduced acceleration state AO \u00bc w : ; aO w vO\u00f0 \u00de, or accelerator for brevity, of the moving platform w.r.t. fixed platform can be written, for details see Rico and Duffy [16], through each one of the limbs as follows A0 \u00bc0 w : 0 1$ 1 \u00fe1 w : 1 2$ 2 \u00fe2 w : 2 3$ 3 \u00fe3 w : 3 4$ 4 \u00fe4 w : 4 5$ 5 \u00fe5 w : 5 6$ 6 \u00fe $Liei i 2 1; 2; 3f g \u00f028\u00de where $Liei is the i-thLie screw, which is calculated as follows $Liei \u00bc 0\u03c9 0 1$ 1 1\u03c9 1 2$ 2 \u00fe :::\u00fe5 \u03c9 5 6$ 6 \u00fe 1\u03c9 1 2$ 2 2\u03c9 2 3$ 3 \u00fe ::: \u00fe5 \u03c9 5 6$ 6 \u00fe ::: \u00fe 4\u03c9 4 5$ 5 5\u03c9 5 6$ 6 and the brackets \u00bd denote the Lie product"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.7-1.png",
        "caption": "Fig. B.7 Car\u2019s wheels following a circular path",
        "texts": [
            " The rolling disc of the vertical positiondoes notmanifest gyroscopic effects anddemonstrates the rectilinearmotion. B.7 Gyroscopic Torques Acting on a Car Wheels Rounding a Curve The car of the mass of 2500 kg with its centre of mass at 0.5 m in above the road and its four the disc-type wheels have 0.4 m radius and 50 kg weight each. For simplicity, two wheels are connected by a straight axle with a length of 2.0 m. The car is moving on a road with a velocity 40 km/hr by a circular path of radius 10 m with the centre of the axle as shown in Fig. B.7. Find the gyroscopic torques, exerted on the car. Solution The moving wheel manifests gyroscopic effects as the action of the inertial torques generated by its rotating mass. The equations of inertial torques are represented in Table 3.1 of Chap. 3, whose components are as follows: \u2022 The resistance torques generated by the centrifugal Tct = 2\u03c02 9 J\u03c9\u03c9y and Coriolis Tcr = 8 9 J\u03c9\u03c9yforces of the spinning disc acting around axis oy. Appendix B: Applications of Gyroscopic Effects in Engineering 257 \u2022 The precession torques generated by the change in the angular momentum Tam = J\u03c9\u03c9yof the disc and the common inertial forces Tin = 2\u03c02 9 J\u03c9\u03c9y acting around axis ox"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001058_s11432-013-4787-8-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001058_s11432-013-4787-8-Figure1-1.png",
        "caption": "Figure 1 The coordinate systems.",
        "texts": [
            " The cargo movies along the rail system on the cargo deck, which coincides with the airplane longitudinal body axis. 4) The relative movement between the aircraft and the cargo is translational. 5) The weight and the inflation dynamics of the extraction parachute are ignored, and thus the extrac- tion force is assumed to be constant. Assumptions 1) and 2) are widely-adopted simplifications for aircraft modeling, and assumptions 3)\u20135) are related to the heavy cargo operation. Three coordinate systems for the aircraft modeling during airdrop are illustrated in Figure 1. 1) The earth frame Ogxgygzg: the origin Og is chosen on the ground surface; Ogxg points to certain chosen direction; Ogzg points vertically downward; Ogyg is perpendicular to the Ogxgzg plane, and satisfies the RH rule with respect to Ogxg and Ogzg. 2) The body-fixed frame Oxbybzb: the origin O is chosen at the center of gravity; Oxb points through the nose of the craft, parallel to the fuselage reference line; Ozb points downward in the symmetry plane of the vehicle, perpendicular to Oxb; Oyb is perpendicular to the symmetry plane of the vehicle and points out the right wing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003097_j.rcim.2020.102053-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003097_j.rcim.2020.102053-Figure4-1.png",
        "caption": "Fig. 4. Screenshot of the CoCo Graphical User Interface (GUI)",
        "texts": [
            " For the 3D-visualization of the scene, stereolithography (STL) objects are loaded and displayed with Helix Toolkit [31] a higher level Application Programming Interface (API) for working with 3-D in Windows Presentation Foundation (WPF). The collision detection between the objects is realized with BEPUphysics [32]. Since many collision checks are necessary for path planning, convex hulls are internally used to represent objects like robots, the linear track and the pick-up table. The tool shape in the production scenario is internally represented as a mesh structure, since it is intended to be used for lay-up. Fig. 4 shows a screenshot of the CoCo planning system. On the left side the actual scene in rendered and the found path is drawn with blue points and red lines. On the right side the user can select different planers and change their settings. EA are population-based search technique which imitate biological behavior to find solutions for otherwise unsolvable mathematical problems [33, p.253]. The EA are based on a theory by Charles Darwin (1809\u20131882) which he published in his book On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life [34]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.31-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.31-1.png",
        "caption": "Fig. 17.31 Ideal turning angles \u03b1 and \u03b2 of the front axes of a car during a turn",
        "texts": [
            " This yields an equation of the same type: \u2212 r1 sin\u03d52 + r2 i2 sin\u03c82 = r1r2 ( 1\u2212 1 i2 ) sin(\u03d52 \u2212 \u03c82) . (17.131) This is the second Eq.(17.122). The further steps of solution are as before. The method of solution for five parameters (see (17.123), (17.124)) remains the same if one or two of the Eqs.(17.124) are replaced by the requirement that the transmission ratio is prescribed for one or two of the remaining pairs of angles. 614 17 Planar Four-Bar Mechanism In an automobile the steering mechanism causes the axes of the front wheels to turn about points A0 and B0 fixed in the car body. In Fig. 17.31 the axes are shown in a vertical projection during a left turn. With an ideal steering mechanism the turning angles \u03b1 and \u03b2 are coordinated such that the two front axes and the rear axis of the car have, independent of the radius R of the curve, a common intersection point. The lengths and h are constant parameters. From triangles the equations are obtained: h = (R\u2212 /2) tan\u03b1 , h = (R+ /2) tan\u03b2 . Elimination of the variable R results in cot\u03b2 \u2212 cot\u03b1 = h . (17.132) This equation defines the function \u03b2(\u03b1) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.11-1.png",
        "caption": "Figure 2.11. CAD model of a reactionless spatial 3-dof mechanism",
        "texts": [
            " Although the reaction forces and moments on the base of each leg may not be zero in the real system with the solid platform because of the distribution of the internal forces, the net reactions on the base will be equal to zero. A reactionless planar 3-dof mechanism is shown in Figure 2.10. The mechanism has been obtained using the synthesis approach described above and each of the 2- dof legs has been optimised (including a point mass) using the approach presented in the preceding section. Similarly, a reactionless spatial 3-dof mechanism is shown in Figure 2.11. In this case the three 2-dof legs are mounted in different planes and attached to a common platform through spherical joints. The platform, therefore, has three degrees of freedom in space. In both of the above cases, dynamic simulations were performed and the results obtained confirmed the reactionless property. A very thin platform was used in the spatial case, which may not be feasible in practice. Spatial reactionless parallel 6-dof mechanisms were also synthesised in [2.19]. Although the mechanisms synthesised are reactionless, it is conjectured that the designs obtained may represent only a fraction of the possible architectures because of the mathematical modelling used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure14.15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure14.15-1.png",
        "caption": "Fig. 14.15 Reflection point Q\u2032 and circle points at infinity. Center Q0 on circumcircle of pole triangle",
        "texts": [
            " Since these reflected circles are concurrent in S , the line Q1Q2Q3 passes through S . 14.4 Relationships Between Three Positions 429 Infinitely Distant Circle Points The interchangeability of center point Q0 and reflection point Q\u2032 has the consequence: If Q0 is an arbitrarily prescribed point on the circumcircle of the pole triangle, the corresponding reflection point Q\u2032 and the corresponding circle points Q1 , Q2 , Q3 are at infinity. The direction toward the reflection point Q\u2032 is determined by the angle \u03b2 against the triangle side P23P31 (Fig. 14.15). Proposition: The direction toward the circle point Qi (i = 1, 2, 3) is normal to the line Q0S i . The proof is given for the case i = 3 : The lines leading from P23 toward Q\u2032 and Q3 , respectively, must be symmetric with respect to the line P23P31 . This is, indeed, the case since not only the two angles \u03b2 are equal, but also the two angles denoted \u03b1 are equal. The reason is that \u03b3 = 90\u25e6 \u2212 \u03b1 is the angle subtended by the chord S3P23 . End of proof. Sense of Triangle of Circle Points In Fig. 14",
            " Following Fig. 14.13 special cases (a) and (b) were explained when a pole is chosen either as center point or as circle point. Figure 14.14 explains how to determine solutions with a center point Q0 at infinity and with circle points Q1, Q2, Q3 along a straight line. The straight line is passing through the orthocenter S of the pole triangle. If the line is prescribed, the circle points are determined, and if a single circle point is prescribed, the line and the other two circle points are determined. Figure 14.15 explains how to determine solutions with circle points lying at infinity. As center point Q0 an arbitrary point on the circumcircle of the pole triangle can be chosen. The chosen point determines the directions Q0Qi (i = 1, 2, 3) in the three positions. They are the normals to the lines Q0S i . Instead of Q0 the direction towards a single infinitely distant circle point, say Q3 , can be chosen. It determines the line Q0S 3 and, consequently, Q0 and the other two directions. Four prescribed positions of the coupler plane determine six poles, four pole triangles, three pole quadrilaterals and the associated pole curve p (see Figs",
            " Hence Q3 is the point of intersection of these two lines. There is only a single solution with a center point Q0 at infinity and with circle points Q1, Q2, Q3, Q4 along a straight line. The center point Q0 is the infinitely distant point on the asymptote of the pole curve. The straight line is orthogonal to the asymptote. Since it is passing through the orthocenters, of all four pole triangles (see Fig. 14.14) collinearity of these orthocenters is proved. Likewise, there is only a single solution with circle points Q1, Q2, Q3, Q4 at infinity. From Fig.14.15 it is known that the center point Q0 is located on the circumcircles of all four pole triangles. These circles have a single point of intersection U (Fig. 14.22). As in the case of three positions, the directions Q0Qi (i = 1, 2, 3, 4) toward the infinitely distant circle points are determined from pole triangles (Fig. 14.15). A center point Q0 on p close to U is associated with a very long crank with very distant circle points. Circle point curves: The geometric locus of the circle point Qi is called circle point curve ki ( i = 1, 2, 3, 4 ). If a single circle point curve, say k1 , is known, the other three curves are obtained by rotating k1 about poles. From Fig. 14.13 and Eq.(14.50) it is known that Q1 and Q0 switch roles if 17.14 Four-Bars Producing Prescribed Positions of the CouplerPlane.BurmesterTheory 631 632 17 Planar Four-Bar Mechanism the angles \u03d512 and \u03d513 are replaced by \u2212\u03d512 and \u2212\u03d513 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000741_s11668-010-9395-y-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000741_s11668-010-9395-y-Figure8-1.png",
        "caption": "Fig. 8 Geometric features of the crack",
        "texts": [
            " Mathematically, the crack propagation angle estimated by the method of Paris\u2013Erdogan can be written as h \u00bc 2 tan 1 1 4 KI KII ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KI KII 2 \u00fe8 s 0 @ 1 A 2 4 3 5 \u00f0Eq 7\u00de The principle of automatic construction of the toothed gear meshing is clear as can be seen in Fig. 6. The gear have 14 teeth with a crack in the foot tooth (Fig. 7). It is worth noting, on the one hand, that the computing only takes place in three successive teeth to reduce the resolution time. On the other hand, the finite Fig. 7 Meshing of gear within crack element used at the neighborhood of the crack, are special types (used extensively in the literature). Figure 8 presents the geometrical parameters of the crack (a, w, and h). The analysis used 8-nodes, plane stress, and quadrilateral finite elements. The material used was steel. For boundary conditions, four hub nodes were fixed. To calculate the stress intensity factors, a parametric study is carried out according to the crack geometry (Fig. 8). We are going to calculate KI and KII factors using the displacement correlation method, using a quasi-static study led by ANSYS finite element code. As shown in Fig. 9, crack initiation is localized in the tooth foot for w = 35 , on the fillet which is the position of the greatest tensile stress for the solid gear (Fig. 9). Variation of KI and KII According to the Crack Depth According to Fig. 10, the KI variation is more important than the KII one, which is nearly constant according to the crack depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001100_0954406211415321-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001100_0954406211415321-Figure6-1.png",
        "caption": "Fig. 6 Planar three-link serial manipulator",
        "texts": [
            "comDownloaded from Comparing the results of the proposed method with past works show that the results of the proposed method are in good agreement with past work, which confirms the accuracy and ability of the proposed method. In addition, solving the singular cases is the same as solving non-singular ones, and this method has no sensitivity to singularity. Proc. IMechE Vol. 226 Part C: J. Mechanical Engineering Science at The University of Edinburgh on November 24, 2014pic.sagepub.comDownloaded from The time-optimal point-to-point motion of a simple redundant manipulator, as shown in Fig. 6, is studied to investigate the effect of changing the point-topoint motion to straight-line motion. The time-optimal trajectory planning of this manipulator along a straight-line path has been studied in [10], and the physical parameters, as well as the initial condition and the final point, are taken from this reference. The initial states are as follows X t0\u00f0 \u00de \u00bc =6 2 =3 2 =3 0 0 0 T \u00f035\u00de The final posture of arm is so that the end-effector should be at the final point while the joints are in inaction status"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003437_j.ymssp.2020.107158-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003437_j.ymssp.2020.107158-Figure7-1.png",
        "caption": "Fig. 7. (a) The prototype of the parallel tool head. (b) A 5-DOF hybrid machine tool based on the parallel tool head.",
        "texts": [
            " The relation between si and epi can be further obtained as: si \u00bc GpciGvciKtN GpiGvciKt \u00fe 1 epi \u00fe GpiGvciKt GpiGvciKt \u00fe 1 sdi \u00f023\u00de Up to now, the physics-based mechatronics modeling of the parallel tool head has been completed. Next, related simulations in different positions of the workspace can be performed under certain motion conditions to obtain the key state variables (i.e. tracking error and driving torque), instead of experiments. Meanwhile, compared with the system identification, the modeling process has clear physical meaning, which is beneficial to carry out further applications. The prototype of the industrial-grade parallel tool head is shown in Fig. 7, and its nominal geometrical and dynamic parameters are the same as the values given in Appendix B. In this section, an experiment will be firstly performed to identify the friction torque of each driving shaft; then, the comparisons between simulations and experiments will be given to verify the effectiveness of the mechatronics modeling. In order to identify the friction torque of each driving shaft, a reciprocating feed motion along OZ-axis is designed with different orientations, and the motion conditions determined by typical machining requirement are given as: L \u00bc 40mm amax \u00bc 1m=s2 v \u00bc 50mm=s Tt \u00bc 10s 8>>< >>: \u00f024\u00de where L is the motion stroke; amax is the maximum acceleration of the acceleration and deceleration phases; v is the velocity during the constant velocity phase; and Tt is the total motion time; the motion rules of velocity and acceleration are S-curve and modified trapezoid, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001994_j.matdes.2018.11.008-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001994_j.matdes.2018.11.008-Figure1-1.png",
        "caption": "Fig. 1. Synchronous induction assisted laser deposition p",
        "texts": [
            " In this study, with introduction of synchronous induction, some Ti-6Al-4 V titanium depositions were carried out, the microstructure characteristic and thermal behavior were investigated, and the influence mechanism of the thermal behavior caused by two thermal heat source onmicrostructure formation were discussed. Some single-pass deposition experiments were completed on the self-made synchronous induction assisted laser deposition system which is consisted of four subsystems: 3 kW fiber laser, 50 kWhigh frequency induction heater (15\u201335 kHz), powder feed system involve a side-injection nozzle tip and 3-axis working table. Fig. 1 shows the process of the synchronous induction assisted laser deposition. A plate 140 mm long, 6 mm wide, 50 mm high serves as the substrate, laser and inductive coil were set coaxially and heat the surface of substrate synchronously in the deposition experiment shown in Fig. 1(a). Fig. 1 (b) presents more details about the formation of deposited layer, the laser beam and the coil keep stationary while the substrate moving with the working table and the powder flow from the side-injection nozzle was injected into the molten pool formed by the heating of the two heat sources. The coil with an inner diameter of 10 mm and an outer diameter of 25 mm was placed about 2 mm from the surface of the substrate and parallel to it during the whole deposition process. The triple helix coil was coiled by a copper tube with a diameter of 5 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure10-1.png",
        "caption": "Fig. 10. The prototype after sticking the strain gauges.",
        "texts": [
            " the force mapping analysis and Saint Venant principle, the middle part of the measuring unit along the axial direction is less affected by the tangential force, bending moment or torque, so this part is the best place to stick the strain gauge. When the measuring branches are pulled/pressured, the corresponding resistance values Table 5 Measurement range of the prototype. Force/Torque Fx/kN Fy/kN Fz /kN Mx/N\u2219m My/N\u2219m Mz/N\u2219m Range \u00b115 \u00b115 \u00b15 \u00b1100 \u00b1100 \u00b1150 Fig. 11. The calibration sys of the strain gauges change and are connected to the external circuit through the transmission lines, which are converted into voltage output. The prototype after sticking the strain gauges is shown in Fig. 10. The measurement range of the force sensing mechanism is shown in Table 5. The calibration system of the prototype, as shown in Fig. 11, which is mainly composed of the calibration hardware and software. The calibration hardware includes a loading platform, weights, a signal acquisition instrument, a computer, etc. The software is mainly written in the LabVIEW environment software system for signal processing and data conversion. By using the collected data corresponding to the loading of Fy, the curves depicting the relationship between voltage outputs of each branch and the standard loading are obtained as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001699_jas.2014.7004623-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001699_jas.2014.7004623-Figure1-1.png",
        "caption": "Fig. 1. Figure showing the inertial earth-fixed frame and the body-fixed frame for a vessel.",
        "texts": [
            " Vessel Dynamics Consider a group of N fully actuated vessels, and the multiple-input-multiple-output (MIMO) dynamics of the 3 degrees-of-freedom (3DOF) vessel i is \u03b7\u0307i = Ri(\u03b7i)\u03bdi, nnum (1) Mi\u03bd\u0307i = \u03c4i \u2212 Ci(\u03bdi)\u03bdi \u2212 Di(\u03bdi)\u03bdi + Ri(\u03b7i)Tdi, (2) where \u03b7i = [xi, yi, \u03c8i]T \u2208 R3, i = 1, 2, \u00b7 \u00b7 \u00b7 , N , is the vector representing the inertial earth-fixed frame position and heading, respectively; \u03bdi = [ui, vi, ri]T \u2208 R3 is the vector representing the vessel surge, sway, and yaw velocities, respectively as shown in Fig. 1; di = [di1, di2, di3]T \u2208 R3 is the vector representing the unknown disturbance from the environment, and/or unmodeled dynamics, among others; and \u03c4i \u2208 R3 is the vector of input signals. The matrices Ri(\u03b7i), Mi, Ci(\u03bdi), and Di(\u03bdi) are given as below: Ri(\u03b7i) = \u23a1 \u23a3 cos \u03c8i \u2212 sin \u03c8i 0 sin \u03c8i cos \u03c8i 0 0 0 1 \u23a4 \u23a6 , Mi = \u23a1 \u23a3 mi11 0 0 0 mi22 mi23 0 mi32 mi33 \u23a4 \u23a6 , Ci(\u03bdi) = \u23a1 \u23a3 0 0 ci13 0 0 ci23 \u2212ci13 \u2212ci23 0 \u23a4 \u23a6 , Di(\u03bdi) = \u23a1 \u23a3 di11 0 0 0 di22 di23 0 di32 di33 \u23a4 \u23a6 , with mi11 = mi \u2212 Xiu\u0307, mi22 = mi \u2212 Yiv\u0307, nnum mi23 = mixig \u2212 Yir\u0307, mi32 = mixig \u2212 Niv\u0307, nnum mi33 = Iiz \u2212 Nir\u0307, nnum ci13 = \u2212mi22vi \u2212 mi23ri, ci23 = mi11ui, nnum di11 = \u2212Xiu \u2212 Xiu|u||ui| \u2212 Xiuuuu2 i , nnum di22 = \u2212Yiv \u2212 Yi|v|v|vi| \u2212 Yi|r|v|ri|, nnum di23 = \u2212Yir \u2212 Yi|v|r|vi| \u2212 Yi|r|r|ri|, nnum di32 = \u2212Niv \u2212 Ni|v|v|vi| \u2212 Ni|r|v|ri|, nnum di33 = \u2212Nir \u2212 Ni|v|r|vi| \u2212 Ni|r|r|ri|nnum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure10.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure10.1-1.png",
        "caption": "Fig. 10.1 Radial flux switched reluctance machine examples, showing a Nph = 3 phase machine with a 6/4 stator/rotor configuration. (a) Unaligned position (phase A). (b) Aligned position (phase A)",
        "texts": [
            " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Fig. 9.33 Simulation of an induction machine drive with rotor flux oriented UFO controller and field weakening controller . . . . . . . . . . 333 Fig. 9.34 Simulation results for induction machine drive with rotor flux oriented UFO controller and field weakening controller . . . . . 334 Fig. 9.35 Simulation results for induction machine drive with rotor flux oriented UFO controller and field weakening controller . . . . . 336 Fig. 10.1 Radial flux switched reluctance machine examples, showing a Nph = 3 phase machine with a 6/4 stator/rotor configuration. (a) Unaligned position (phase A). (b) Aligned position (phase A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Fig. 10.2 2/2 single-phase switched reluctance motor . . . . . . . . . . . . . . . . . . . . . . 343 Fig. 10.3 Single-phase equivalent circuit of a switched reluctance machine . . . . . . . . . . . . . . . . . . . . . . . . . . ",
            " Its inherently low cost construction benefit has been used to advantage in hand-held power tools [20], household appliances (mixer/kneading machines, vacuum cleaners with power range 0.5\u2013 2 kW), sliding doors, and electrical vehicles (traction drives for cars 50 kW range and scooters [10, 21]). Its benefit in terms of robustness has led to applications in 10.1 Basic Machine Concepts 341 aerospace other than the one indicated above and in the mining industry (e.g., in high-performance explosion proof drives with power levels up to 400 kW). The machine is characterized by discrete stator and rotor poles, which is commonly referred to as a doubly salient structure [2, 12, 13]. Figure 10.1 shows a typical machine configuration. The example three-phase machine (Nph = 3) has six stator teeth Ns = 6 and four rotor teeth Nr = 4, a configuration which is known as a 6/4 structure. The windings are typically positioned around each stator pole, which is why this winding arrangement is referred to as concentrated or short pitched. From a magnetic perspective, each phase of the 6/4 machine has two magnetic poles per phase, i.e., one pole pair (p = 1), given that diametrically opposed coils are electrically connected in series or in parallel. For example, phase A is made up of the coils located on teeth A and A\u2019. If this phase is excited, a magnetic flux path is formed by the two stator teeth A\u2013A\u2019, the rotor and stator yoke (see Fig. 10.1b). Observing one phase of Fig. 10.1, it can be seen that two equilibrium positions of the rotor exist. The rotor position shown in Fig. 10.1a is called the unaligned position with respect to phase A\u2013A\u2019. The rotor angle at this position \u03b8 is defined as \u03b8u. The position of smallest magnetic reluctance is called the aligned position \u03b8a, as is shown in Fig. 10.1b. The width of the rotor and stator poles are defined as \u03b2s and \u03b2r. The interpolar arcs of stator and rotor (\u03c4sp and \u03c4rp), which represent the angle between two adjacent rotor or stator teeth, shown in Fig. 10.1b, are determined by \u03c4sp = 2\u03c0 rad Ns , \u03c4rp = 2\u03c0 rad Nr . (10.1) 342 10 Switched Reluctance Drive Systems Definition of Electrical Angle The position of the rotor is directly correlated with the mechanical angle \u03b8m. One period describes one revolution of the rotor. To become independent of the machine configuration it is reasonable to specify the rotor position of switched reluctance machines in electrical degrees. The electrical angle is defined by the periodicity of the machine. For example, in Fig. 10.1 the rotor repeats every 90\u25e6 mechanical (\u03c4rp). Hence, this is defined as one electrical period of 360\u25e6. The relationship between electrical and mechanical angle is given in Eq. (10.2). \u03b8e = Nr\u03b8m. (10.2) Note that the switched reluctance machine illustrated in Fig. 10.1 is radial flux oriented, given that the flux which crosses the air-gap is predominantly in the radial direction. Most machines in use are of this type, given the fact that this approach allows the machine to be manufactured by stacked laminations, as used in, for example, induction and synchronous machines. Possible Machine Configurations The relationship between the number of stator teeth Ns, magnetic pole pair number p, and number of electrical phases Nph for switched reluctance machines may be written as Ns = 2pNph"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure1.54-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure1.54-1.png",
        "caption": "Fig. 1.54 Principle layouts of three different independent-sprung, planetary gearless, SM&GWs with rotary DC-AC/AC-DC macrocommutator (unwound outer rotor and wound inner stator) in-wheel-hub E-M/M-E motors/generators and tubular linear DC-DC macrocommutator drum-, disc- or ring-brake actuator E-M motors [FIJALKOWSKI 1997].",
        "texts": [
            " An advantage of series hybrid-electric DBW 4WD propulsion mechatronic control system may be that a novel form of ICE can be used, designed specifically for high efficiency constant reciprocating velocity and power operation and minimum emission. Other longer-term options include future hydrogen-fuelled ICEs and fuel cells, with the prospect of the virtually zero emission vehicles (ZEV). The DBW 4WD propulsion mechatronic control system using SM&GWs with the DC-AC/AC-DC macrocommutator magnetoelectrically-excited in-wheel- hub motors/generators may eliminate the necessity of axles and drive shafts, which may allow a separate suspension of each independent-sprung SM&GW (Fig. 1.54) [FIJALKOWSKI 1997]. 1.14 Purpose of RBW 105 The rotating housing is made in the form of a wheel hub, designed to fit the standard rim sizes on the automotive market. The DC-AC macrocommutator magnetoelectrically-excited in-wheel-hubmotors\u2019 transmission offers complete freedom in the design of the intelligent vehicle. While the basic principles of hybrid-electric DBW 4WD intelligent vehicles remain the same for virtually all classes of intelligent vehicles, the actual arrangements vary -- for instance, some may have 2WD that is either FWD or RWD, and others 4WD"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003167_pi-c.1959.0034-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003167_pi-c.1959.0034-Figure2-1.png",
        "caption": "Fig. 2.\u2014Equipotential lines surrounding a bundle of conductors. (a) Two conductors. (b) Threa conductors.",
        "texts": [],
        "surrounding_texts": [
            "The electric field surrounding bundle conductors can be determined by replacing each conductor of the bundle by one of negligible radius displaced slightly from the centre of the original conductor. This is based on the feet that equipotential surfaces near such a thin conductor are nearly cylindrical, so that an actual conductor may be so placed as to take up the position of one of the equipotentials. The accuracy of the method depends on the ratio, Did, between the diameter of the bundle circle and that of each conductor; the greater the ratio, the more accurate is the method. With the ratios usually found in highvoltage transmission lines, the deviation of the equipotential surface from a true cylinder is small, and it can be arranged that the deviation is zero at the point of maximum surface gradient. Maximum deviation from the surface of a cylinder occurs somewhere between points of maximum and minimum gradients. For example, with a bundle of two conductors and Did =10 , this maximum deviation does not exceed 0-5%; with Did = 20 it is about 0-1 %. The analysis deals with single-phase lines with a bundle of 2, 3 or 4 conductors, but it can be extended to cover any number of conductors in a bundle. For 3-phase lines the resultant field can be found by the principle of superposition when the fields due to the two other phases are taken into consideration. In the latter case, the electric charge per metre of each phase is to be determined with all the three phases and their images involved. Formulae giving the potential gradient at any point on a conductor surface are developed and compared with those given by Cahen.1 The method is checked by experimental field mapping using a circular double-layer electrolytic tank."
        ]
    },
    {
        "image_filename": "designv10_12_0002609_b978-0-12-814130-4.00007-5-Figure7.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002609_b978-0-12-814130-4.00007-5-Figure7.7-1.png",
        "caption": "Figure 7.7 Nanoparticle-functionalized multijunction biosensor system; (A) 3-D printed multiplexing circuit module and sensing platform, (B) Assembled multi-junction sensor chip, (C) Changes in current with respect to food pathogen concentrations, (D and E) Food pathogen quantification at the circuit junctions (Yamada et al., 2016).",
        "texts": [
            " A disposable sensor chip was fabricated with a layer of single walled carbon nano tubes (SWCNTs) network on printed circuit board. Polyclonal antibodies specific toward E. coli and S. aureus were immobilized on the sensor surface through streptavidinebiotin linkages. The biorecognition between the bacterium and antibody was converted into electrical signals in the circuit and measured amperometrically. Fabricated sensor has the advantages of portability, accuracy, simplicity, and multiple analyte detection (Yamada et al., 2016) (Fig. 7.7). Fullerenes are an allotrope of carbon in the form of hollow structures. The size and geometry depends on the number of carbon atoms present in it. Fullerenes are known for their superlative electrical conductivity, which finds application in the fabrication of electrochemical sensors as electrode surface modifier. In an interesting study, fullerenes (F60 and F70) and carbon nanotubes (SWCNTs and MWCNTs) were used as an electrode surface modifier and it was found that CNTs were better at enhancing the graphite electrode sensitivity toward ascorbic acid than fullerenes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000844_icra.2011.5980144-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000844_icra.2011.5980144-Figure2-1.png",
        "caption": "Fig. 2. Simulation model and an example of the leg trajectory(left)",
        "texts": [
            " To derive specific resistance, we develop a simplified numerical simulator. In this section, we explain a kinematic model and method of numerical analysis. There is an infinite of possibilities for the leg trajectory within leg\u2019s workspace to produce propulsive motion in wheeled mode. To simplify the problem, we assume that; 1) all legs are in support phase, 2) all legs are massless and center of gravity of the robot is located at the middle of the body, 3) left-and-right legs move symmetric and periodic. Fig.2 shows a coordinate system for a numerical analysis. The axis of the passive wheel is fixed to the leg at a right angle and its camber angle is also kept at a right angle. We assume a symmetric leg trajectory as follows: d(t) = do f f set + d0 ( sin(\u03c9t + 3\u03c0/2)+ 1 ) , (1) \u03b8 (t) = \u2212\u03b80 sin(\u03c9t + 3\u03c0/2 + \u03c6). (2) d0 and \u03b80 are amplitudes of sinusoidal oscillation in the normal and tangential directions of the passive wheel, respectively. \u03c9 determines an angular velocity of the oscillation. \u03c6 is a phase difference between the oscillations in the normal and tangential direction. (Here, we introduce appropriate offsets considering initial posture and leg\u2019s workspace of the hardware prototype.) There are four control parameters, d0,\u03b80,\u03c9 ,\u03c6 , to modulate the leg trajectory in Eqn.(1),(2). An example of the leg trajectory is illustrated in Fig. 2. We assume Coulomb friction at a contact point of the passive wheel on the ground, and thus the resulting tangential force Ft(t) and normal force Fn(t) due to the periodic leg motion can be expressed as follows: Ft(t) = \u2212sgn ( V cos\u03b8 (t)+ d(t)\u03b8\u0307(t) ) \u00b7\u03bct \u00b7mg/4, (3) Fn(t) = \u2212sgn ( V sin\u03b8 (t)+ d\u0307(t) ) \u00b7\u03bcn \u00b7mg/4. (4) Here, sgn(\u2217) is signum function and V is propulsive velocity. \u03bct ,\u03bcn are Coulomb friction coefficients in the tangential and normal direction, respectively. m is a total mass of the robot and g is gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure13-1.png",
        "caption": "Fig. 13. The 3T1R + 1-DOF parallel manipulators: (a) type 1 (b) type 2.",
        "texts": [
            " As a result, the manipulator with two L 0 F 2 C -limbs is constructed. The plane determined by two constraint-couples in one limb is parallel to that in the other limb. Namely, the constraint-couples are linearly independent. Besides, two par- allel revolute joints are arranged on the configurable platform to perform sizeable rotational output [14] . Then the 3T1R parallel manipulator with large orientation-workspace in one direction is obtained. Two 3T1R + 1-DOF parallel manipulators with the Bennett platform are depicted in Fig. 13 . The constraint system of 2T2R parallel mechanisms has one constraint-force and one constraint-couple. Then all probable structures of limbs to form the constraint system can be obtained. They are the L 1 F 1 C -limb and L 0 F 0 C -limb, L 1 F 1 C -limb and L 0 F 1 C -limb, L 1 F 1 C -limb and L 1 F 0 C -limb, L 1 F 0 C -limb and L 1 F 0 C -limb, L 1 F 0 C -limb and L 0 F 1 C -limb. With the topological arrangements in Figs. 8 (d), the L 0 F 1 C -limb and the L 1 F 1 C -limb are synthesized. The constraint-couple of the L 0 F 1 C -limb is parallel to the constraint-couple of the L 1 F 1 C -limb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure17-1.png",
        "caption": "Fig. 17. Two different coordinate systems in PAM-stamp and ABAQUS.",
        "texts": [
            " The residual stresses of point A are acquired from the stress contour (Fig. 5) as rx \u00bc 135:057 MPa and ry \u00bc 131:152 MPa. Considering the reduction of the residual stress from the natural aging, the residual stress are recalculated as r0 x \u00bc 121:551 MPa and r0 y \u00bc 118:037 MPa with the subtractive ratio of 10%. The angle between the Y-axis and the line connecting the bolt hole center and point A is 22.5 deg. The coordinate system in point A is x0oy0 while it is xoy in ABAQUS software, and the angle between x-axis and x0-axis is 22.5 deg (a \u00bc 22:5 ), as shown in Fig. 17. Therefore, the residual stress in the coordinate system of point A needs to be transformed into the coordinate system of the ABAQUS software using following equations [11]: s0 \u00bc rx ry 2 sin 2a\u00fe sxy cos 2a r0 x \u00bc rx\u00fery 2 \u00fe rx ry 2 cos 2a sxy sin 2a r0 y \u00bc rx\u00fery 2 rx ry 2 cos 2a\u00fe sxy sin 2a 8>< >: \u00f017\u00de The stresses of point A are calculated after introducing the residual stresses, and the third invariant of the stress deviator is used to judge the deformation state of the point. A stress comparison in one cycle before and after introducing the residual stress is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001268_j.bios.2014.06.054-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001268_j.bios.2014.06.054-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of the hybrid microfluidic fuel cell components.",
        "texts": [
            "0028 mS cm 1), and all the tests are performed at 2572 \u00b0C; the external resistance is of 50 \u03a9. The microfluidic fuel cell is built using a PVC chip employing adhesive aluminium as electrode collectors and several sheets of polymeric materials (Gonzalez-Guerrero et al., 2013). First, 188 mm thick cyclo-olefin polymer (COP) Zeonerfilms layer (ZF16-188) and four layers of 80 mm thick PET-double-side adhesive layers (ARcares 8725) were cut in a Silhouette Portrait plotter and aligned to form the chip frame (25 50 mm2) with a window of 20 20 mm2 (Fig. 1a). Next, a 500 mm PVC chip containing adhesive aluminium electrode collectors is assembled inside the window (Fig. 1b). Then, the channel cut made of Silastics was 3 mm wide, 5 mm high and 20 mm long (Fig. 1c). Finally, the top portion is constructed of two COP layer (ZF16-188) and 80 mm PETdouble-side adhesive (AR8725) layer (Fig. 1d). Prior assembling the microfluidic fuel cell, the anodic and biocathodic catalysts were deposited on the adhesive aluminium electrode collectors by a spray method (allowing an effective geometrical area of 0.05 cm2 per compartment). An alkaline solution of 5 mM glucose in 0.3 M KOH previously saturated with nitrogen was passed through the anode compartment at 25 mL min 1 of flow rate (equivalent to an organic loading rate (OLR) of 46.8 mg day 1). The cathodic compartment was fed with PBS (pH 5) previously saturated with oxygen at the same flow rate (Fig. 1e). The polarisation curves are obtained at 0.02 V s 1 of scan rate keeping the microfluidic fuel cell at 2572 \u00b0C. The power density (P in mW cm 2) is calculated by the product of potential in V and the current density J (current in mA, previously divided by the electrode surface area in cm2) in each point of the graph (P\u00bcVJ). The FTIR spectra for Lac-ABTS/C composite are shown in Fig. 2. For Vulcan carbon, the C\u2013C and C\u2013O vibrations were observed indicating the presence of acid groups which favours the ABTS or enzyme adsorption on the support"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003366_0954406220920692-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003366_0954406220920692-Figure2-1.png",
        "caption": "Figure 2. Photographs of WAAM SS316 shield plate piece: (a) first layer; (b) semi-finished part.",
        "texts": [
            " The CAD file of the shield plate piece was sliced into layers, and the WAAM began from the XOY plane to the OZ direction. The traveling path was back and forth, leaving two adjacent tracks was opposite. This layer-by-layer process was repeated until the piece was completed. The average layerthickness was approximately 3mm. Then followed by a heat treatment, this piece was annealed at 1100 C for 3 h with cooling in the furnace until 120 C before being taken out. The photographs of manufacturing process and semi-finished SS316 shield plate part are shown in Figure 2. The OX axis was the traveling path direction, OY axis was perpendicular to the traveling path direction, and OZ axis was the depositing direction. The stainless steel 316 wires with a diameter of 1.2mm were employed as the starting material, and the required chemical composition (wt%) of the stainless steel 316 wires are shown in Table 1. The chemical composition (wt%) of WAAM SS316 shield plate piece product was measured and is listed in Table 1. In order to obtain the requirement on the accuracy and surface quality of the WAAM SS316 shield plate component, the follow-up of machining and accurate measurement was adopted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001237_iros.2011.6095061-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001237_iros.2011.6095061-Figure11-1.png",
        "caption": "Fig. 11. Walking balance controller block diagram",
        "texts": [],
        "surrounding_texts": [
            "A. Stability Analysis To analyze the dynamic stability of a gait pattern generated based on the coupled oscillator model, we calculated ZMP by (4) and (5). We used the physical property of DARwIn-OP as in Table I for the simulation. \u2211 *( \u0308 )  \u0308 + \u2211 ( \u0308 ) ( ) \u2211 *( \u0308 )  \u0308 + \u2211 ( \u0308 ) ( ) The purpose of the simulation is to verify the correlation of oscillator parameter with dynamic stability of walking. Generally, as and are given by a high level task such as a foot step generator or path planner, we can adjust for attaining dynamic stability. Considering the DSP ratio of human, we assumed that was 0.25, and other parameters were set to the same value used in the previous section. The simulation results are shown in Fig. 8. The outer rectangle presents the footstep, and inner rectangle means the stable margin for ZMP analysis. The discontinuity of the ZMP trajectory comes from the lifting and landing motion of the foot, which presents a phase changing between DSP and SSP. Fig. 8(a) shows that the ZMP trajectory almost escapes from the inner rectangle, which means the unstable state of walking is caused by low . Because the ZMP trajectory lies on outside of the stable margin during changing phase as in Fig. 8(c) due to low , the dynamic stability is not guaranteed. We can find the proper and for a stable walking in Fig. 8(b) which illustrates that the ZMP trajectory is always in the support polygon. variant from 0.1 to 0.55 in Fig. 10. As is increased, the ZMP trajectory diverges from the COM trajectory. The adjustment of the ZMP trajectory can be also achieved by the modification of , we use for tuning the velocity of the COM. Finally, we tested the ZMP trajectory with variant from 0.8 to 1.4 in Fig. 9. The result shows that the large makes the ZMP trajectory to converge on the COM trajectory. B. Balance Controller Through the ZMP simulation, we can find appropriate parameters for stable walking. However, because there is the model error of a humanoid, it is hard to apply the parameters on a real robot without any compensation method. In addition, in a small size humanoid, the low accuracy of actuators can be a problem which makes it difficult for a robot to keep up with the desired trajectory. Therefore, based on the analyzed relation between oscillator parameters and dynamic stability in previous section, we propose the balance controller correlating with oscillator parameters and sensor data. We assume the dynamic model of a humanoid to be an inverted pendulum model. From its dynamic formula in (6), we designed the feedback controller generating the cancelation torque required to sustain dynamic stability as in (7).  \u0308 ( )  \u0307 ( ) means an angle error of a robot between the sensed trajectory and desired trajectory. is the height of COM, and is the mass of the COM. The computed compensation torque is provided to the balance oscillator parameter . Although the physical meaning of is not torque but angular position and because the actuators of DARwIn-OP support only position control and speed control, we assume that operates as a torque generator. Then, In this section, we proved the correlation between oscillator parameters and dynamic stability based on the ZMP simulation and showed how to decide the appropriate parameters. We also proposed the balance controller compensating not only model error but also the low accuracy of the actuator in a small size humanoid for stable walking."
        ]
    },
    {
        "image_filename": "designv10_12_0003456_j.actamat.2020.09.071-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003456_j.actamat.2020.09.071-Figure1-1.png",
        "caption": "Fig. 1. The dual-laser experimental set-up.",
        "texts": [
            " In addition to the lateral spatial offset between the two molten ools, we include a temporal offset between the two lasers, which ffectively produces an in-line spatial offset. The introduction of he temporal offset allows us to further investigate how two lose pools interact with each other within this broader parameter pace. We find a new regime where periodic structures are prouced at certain spatial offsets at each of the different laser powrs tested. Additionally, adjusting spatial offsets within this regime hanges the wavelengths of the periodic structures. . Experimental system Fig. 1 shows the set-up for the dual-laser experiments. In this et-up, two 1070 nm wavelength lasers with Gaussian-shaped eams operating in continuous-wave (CW) mode are used as the aser sources. The laser beams, after being narrowed by focusing elescopes, pass through 3D scanning systems consisting of beam xpanders, 2D scanners and F- \u03b8 lenses. Each of the scanning sysems has a scan field of 178 \u00d7 178 mm 2 . By putting two scan- ers side-by-side, an overlapping scan area of 20 \u00d7 178 mm 2 is reated. Both lasers and scanners are controlled by control cards nstalled in a PC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure4.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure4.17-1.png",
        "caption": "Fig. 4.17 Dynamic model of a two-mass drive train",
        "texts": [
            " The result shows that the load inertia J2 appears as an equivalent inertia Je on the drive side of the transmission, which is computed according to Jeq = ( r1 r2 )2 J2. (4.27) Hence, the inertia Jeq seen at the machine side of the transmission will be greater than the actual load inertia J2 in case r1 > r2, which is the case shown in Fig. 4.16. Note that Eq. (4.26) can be derived easily by considering the change of kinetic energy stored in the system. 4.3 Drive Dynamics 113 The process of transmitting power from the electrical machine to the load is considered in this subsection with the aid of Fig. 4.17. Shown in Fig. 4.17 are two rotating masses with inertia J1 and J2, which are assigned to the rotor of the electrical machine and load, respectively. A coupling of some type, which may simply be a shaft, is used to link the two masses. If the coupling is sufficiently stiff, the two inertias may be simply represented by the sum of the two inertias Jtotal. In this case, Newton\u2019s second law for the drive train is given as Te \u2212 Tl = Jtotal d\u03c9m dt (4.28) with Jtotal = J1 +J2 and \u03c9m = \u03c9m 1 = \u03c9m 2. Furthermore, the relationship between angular frequency and shaft angle is reduced to \u03c9m = d\u03b8/dt, with \u03b8m 1 = \u03b8m = \u03b8m 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003517_tie.2021.3050369-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003517_tie.2021.3050369-Figure1-1.png",
        "caption": "Fig. 1. Axial-flux PM eddy-current coupling.",
        "texts": [
            " The effects of PM and air gap thicknesses, and the torque contribution from the overhangs of conductor back iron, are all taken into considered in the proposed analytical model. II. GENERIC 3-D ANALYTICAL MODEL A. Problem Descriptions A typical axial-flux PM eddy current coupling is conventionally composed of the PM rotor, where the PMs are normally mounted on the surface of its back iron, and the conductor rotor constituted by the plain conductor layer and its back iron, as depicted schematically in Fig. 1. To simplify the analytical solution to the 3-D motional eddy current problem containing both the ferromagnetic and PM regions, the following assumptions are made: 1) The conductor and its back iron are \u201cstationary\u201d, while the magnet blocks and the corresponding back iron are \u201cmoving\u201d with the slip velocity v . 2) The magnetic permeability of conductor back iron is represented as an equivalent mean permeability eq to take P Authorized licensed use limited to: Cornell University Library. Downloaded on May 24,2021 at 10:41:33 UTC from IEEE Xplore",
            " 3) All field quantities are periodic symmetric in the direction parallel to the direction of motion. By assuming the same mean radius for the cylindrical conductor and PM rotors and the equivalent cuboid for the PMs of various shapes, a 3-D four-region field model illustrated in Fig. 2 can be created, where S1, S12, S23, S34, and S4 are either the interfaces between the adjacent regions or the boundary interfaces. The three spatial axes x, y, and z in Fig. 2 are respectively corresponding to the circumferential, axial, and radial directions of the coupling depicted in Fig. 1, and the x-y plane goes through the center line of conductor layer. B. Basic Governing Equations Based on the above assumptions, the motional conductor eddy current problem involving the nonlinear iron regions is simplified to a linear problem. For the field domain containing PMs, the basic governing equation can be described as   0 e     A H M . (1) According to Ampere\u2019s law, there is  H J (2) where the eddy current term t          A J v A . (3) Since the conducting regions including both the conductor layer and its back iron are all homogenous, the conductivity of each region is the same everywhere",
            " (48) The electromagnetic torque is equal to the transmitted torque owing to the fact that there are no mechanical losses in an eddy current coupling. According to the 3-D model shown in Fig. 2, the torque is expressed as c bT T T  (49) where 23 34 22 2 22 2 2 1,3 1,32 c p c p w ypc s c zknw y k n c p T k n A dxdydz w                            (50) 34 4 22 2 22 2 2 1,3 1,32 c p c p w ypb s b zknw y k n c p T k n A dxdydz w                            . (51) Back Iron In the 3-D four-region field model depicted in Fig. 2, the overhangs of conductor back iron (see Fig. 1) are omitted, which will result in a smaller torque calculation result than the actual value. In fact, the motion-induced eddy currents exist everywhere in the conductor back iron, while the resultant eddy current loss is directly associated with the volume of back iron, V , according to 2 VeP dV  J . (52) Furthermore, in the light of the correlation between the torque and the eddy current loss Authorized licensed use limited to: Cornell University Library. Downloaded on May 24,2021 at 10:41:33 UTC from IEEE Xplore"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001491_s12540-014-5011-0-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001491_s12540-014-5011-0-Figure3-1.png",
        "caption": "Fig. 3. Scanning strategy used on SLM experiments (a) and building platform with single tracks divided in scanning speed families (b). Based from [15].",
        "texts": [
            " During experimentation, the minimum diameter of the laser was used exclusively. In the experimental set-up, the powder layer deposition was performed by adding the CoCrMo powder manually into the variable depth building platform made of steel grade AISI 1045 with dimensions of 250\u00d7250\u00d730 mm. The variable thickness of the powder, which ranged from 40 to 500 \u00b5m, was achieved by an inclined plane ground over the steel platform. To simplify interpretation, samples were built using a straight laser scanning trajectory parallel to the layer thickness growth (Fig. 3). The summary of the factorial design of experiments (DOE) used on the deposition are listed in Table 2. The DOE was a factorial plan with no replicas, where 80 tracks had been designed from the combination of 4 levels of scanning speed with 20 different laser power values, and powder layer thickness varied from 40 to 500 mm along each single track (also shown in Fig. 3). The forming process was performed without a controlled atmosphere as the present experiment was achieved in a prototype machine where shielding was not feasible. Power and scan speed were kept constant in each single track. However, layer thickness was calculated by translating the length of continuous track by using the following Eq. (1). (1) where LTmin is the minimum layer thickness at the original powder bed (40 \u03bcm), x is the position along the scan vector (from 0 to 230 mm), and \u03b1 is the slope angle (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.169-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.169-1.png",
        "caption": "Fig. 2.169 Principle layout of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and high-pressure gaseous hydrogen tank [DaimlerChrysler NECAR 4; LARSON 2003].",
        "texts": [],
        "surrounding_texts": [
            "As was previously mentioned, in principle the FC is an exceptionally uncontaminated energy conversion CH-E generator that may generate electrical energy using hydrogen and oxygen for fuel and create water as its exhaust gas emission. On the other hand, when functional applications, predominantly automotive ones, are estimated, the dilemma occurs of how to keep the necessary hydrogen onboard a HEV. Two categories of FC HE transmission arrangements have been built-up for the HE 2BW DBW propulsion mechatronic control system. The first category keeps hydrogen directly onboard, while the second category reforms hydrocarbon fuel onboard the HEV. A principle layout of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and onboard hydrogen storage device is shown in Figure 2.163 [KAWATSU 2000]. A principle layout of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and on-board methanol reformer is shown in Figure 2.164 [KAWATSU 2000]. A particular attribute of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and onboard methanol reformer is that it is a hybrid system that acts as a PES, that is, the electrical energy source (EES) forms a junction with 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 365 a secondary CH-E/E-CH storage battery (for example, NiMH) that acts as a SES (an electrical energy shock absorber). This lets the FC HE transmission arrangement have continuous accurate mechatronic control over the sharing of electrical energy. It additionally allows the possibility to continuously operate the FC in the high-efficiency functional range. The methanol reformer is a small-scale chemical plant mounted in the HEV. It has been greatly compacted by connecting into a separate component, the discrete parts that develop the methanol reformer, incorporating the fuel vaporisation part, the reforming reaction part, and the CO2 reduction part. It has also become feasible to get a better starting ability and responsiveness by reducing the thermal energy (heat) capacity of the methanol reformer. Start-up time has been reduced to under 3 min, and response time has been enhanced to less than 10 s. Besides, the reforming efficiency has been enhanced by using a catalyst. Principle layouts of the FC HE transmission with the 4 \u00d7 2 or 4 \u00d7 4 wheel arrangements and high-pressure gaseous hydrogen tanks are shown in Figures 2.165 \u2013 2.170. Automotive Mechatronics 366 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 367 In the FCEV shown in Figures 2.165, the FC stack, the power control unit, and the E-M motor are mounted at the front of the HEV, while the four highpressure gaseous hydrogen tanks are installed under the floor at the rear. The CH-E/E-CH storage battery is kept under the floor or in the luggage compartment [KAWATSU 2000]. Automotive Mechatronics 368 The FCEV \u2018Hy-Wire\u2019 has shown in Figure 2.170 uses HE DBW 4WD propulsion technology to provide mechatronic control over operations. It is powered by a FC that, together with the drivetrain, is stored on a skateboard chassis. This HE transmission arrangement lets the vehicle designers create a number of different body forms while still maintaining roomy interiors [HAMILTON 2002]. Moreover, the 2WD or DBW 4WD propulsion mechatronic control system (for example, with the following major components: PEFC; traction brushless DC-AC/ AC-DC macrocommutator IPM magnetoelectrically-excited synchronous motor/ generator, high-pressure hydrogen storage tank and NiMH storage battery), a rackand-pinion SBW 2WS or 4WS conversion mechatronic control system and a heat pump air conditioning system that uses CO2 refrigerant are also included. For the reason that the FCEV uses a radiator for cooling, the total area of the openings is about 2.5 times that of a normal automotive vehicle, and the front grill has a double frame construction too, that both undergoes high-quality cooling performance and permits the HEV\u2019s outer shell to articulate its innovative sight [KAWATSU 2000]. Of course, the FC HE transmission arrangement for the HE DBW 2WD propulsion mechatronic control system is intended to improve fuel economy and goals for excessive responsiveness when the HEV is in transitional circumstances. The electrical energy source (EES) is an HE configuration of the FCs, i.e., the PES and a CH-E/E-CH storage battery, i.e., SES. The output electrical energy from the FCs and the charging and discharging of the storage battery are mechatronically controlled in relation to the functioning circumstances of the HEV. 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 369 A NiMH storage battery with greater energy and power density is used for the storage battery so as to make it possible to run the HEV as an AEV only using the storage battery, thus getting a better fuel economy under low-load circumstances. For instance, as shown in Figure 2.171, the FCs and the traction brushless DC-AC/ AC-DC macrocommutator IPM synchronous motor/generator are linked in series so as to obtain better efficiency in the steady circumstances that generally take place during HEV manoeuvres [KAWATSU 2000]. The CH-E/E-CH storage battery, with its low power ratio, is arranged in parallel with the FCs through a DC-DC macrocommutator acting as a DC-DC converter and supplies electrical energy assistance when the FC response is postponed or when the HEV is driven under high loads. The CH-E/E-CH storage battery also absorbs the electrical energy recovered by regenerative braking and acts as the electrical energy source (EES) for AEV function under low loads. The hybrid control (electric energy control) of the FCs and the CH-E/E-CH storage battery is achieved by controlling the output voltage from the DC-DC converter. The FC H-E transmission arrangement for the HE DBW 2WD propulsion mechatronic control system is shown in Figure 2.172 [KAWATSU 2000]. This mechatronic control system is separated into two operational discrete systems. Automotive Mechatronics 370 The FC system is the electrical energy source (EES) that supplies the HEV\u2019s propulsion power, while the hybrid system uses the output power from the FC system with great efficiency. The FC system is composed of the FCs themselves, fuel supply system parts, and cooling system parts. Hydrogen is delivered to the FCs from the high-pressure storage tanks by means of a regulator. Any residual hydrogen remaining after the FC reaction is restored to the source area of the FCs by an exchange E-M-F pump. Air is pressurised by an E-M-P compressor, after that it is pumped to the FCs through a humidifier. The latter gets water vapour from the exhaust air of the FCs and uses it to humidify the inward compressed air. An E-M-F pump may flow coolant between the FCs and the radiator. In addition, mechatronic control of the supplementary parts, for example, the E-M-P compressor, and so on, is optimised in relation to the FC output, consequently the FCs function with a minimum of loss thanks to the supplementary implements. The hybrid system consists of a FC system, a CH-E/E-CH storage battery, a DC-DC macrocommutator acting as a DC-DC converter, and a traction brushless DC-AC/AC-DC macrocommutator IPM magnetoelectrically excited synchronous motor/generator. The core of the HEV\u2019s propulsion power is the output power from the FCs, but when their output power is not enough, as in fast acceleration, hill climbing, and high-speed passing transitions and high-load manoeuvring, electrical energy assistance is supplied by the storage battery. In addition, in low-load manoeuvring, the FC supplementary implements are turned off and the HEV is in motion as an AEV using the electrical energy from the storage battery and nothing else. Currently, HEVs have been developed for significantly cleaner and more efficient automotive vehicles. FCEVs, such as, the Honda Insight and Toyota Prius, particularly, were tested by the U.S. Department of Energy (DoE) to evaluate the liquid fuel saving [KELLY AND RAJAGOPALAN 2001]. Obviously, the FC has been developed to become the main energy source in various applications. The FC transit bus that has been designed and developed by the DoE has been acknowledged as a zero emission vehicle (ZEV). Its only exhaust emission is in fact water vapour [DOE 2003]. One of the main weak points of the FC is its slow dynamics [GOPINATH ET AL. 2002; NERGAARD ET AL. 2002; LEE ET AL. 2003]. Indeed, the dynamics of the FC is restricted by the hydrogen delivery system that contains M-F pumps and fluidic valves and, in some cases, a reforming process. Above all, a step electrical energy load may involve enormous variation of the voltage of the automotive 42 VDC EED bus, because the main energy source has a slow dynamic response. Besides, the FCEV has a problem when starting the E-M motor that demands high energy in a short time. 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 371 To solve these problems, the FCEV must have an auxiliary energy source to supply high transient energy. High-current ultracapacitor technology has been developed for this purpose [ORT\u00daZAR ET AL. 2003]. Subsequently, the very quick power response of ultracapacitors may be used to add to the slower power output of the FC to create the compatibility and performance characteristics necessary for FCEVs as shown in Figure 2.173 [THOUNTHONG ET AL. 2005]. Relative to CH-E/E-CH storage batteries, ultracapacitors have one or two orders of magnitude higher specific power, and much longer lifetimes. Because they are capable of millions of cycles, they are virtually free of maintenance. Their enormous, rated currents enable quick discharges and quick charges as well. Their quite low specific energy, relative to CH-E/E-CH storage batteries, is in most circumstances the factor that determines the feasibility of their employment in a particular high-power application [DESTRAZ ET AL. 2004]. In Figure 2.173 a FC HE transmission arrangement is shown having a FC as the main energy source and ultracapacitors as the auxiliary energy source. It particularly specifies the mechatronic control algorithm for ultracapacitors\u2019 DC-DC macrocommutator (converter). Experimental results show that ultracapacitor technology is suitable for providing electrical energy in automotive EED systems. In Figure 2.174 a Chevrolet Sequel, which is about the size of a Cadillac SRX, is shown. It is the first FCEV to achieve 0 \u2013 96 km/h (0 - 60 mph) in under 10 s and has a 480 km (300 mile) range. Automotive Mechatronics 372 It has unequalled handling on snow and ice, or uneven terrains. 42% more torque for unparalleled acceleration, and shorter braking distance than an equal size conventional vehicle. The Chevrolet Sequel\u2019s sophisticated RBW or XBW integrated chassis mechatronic control hypersystem replaces the mechanical and fluidical linkages of conventional vehicles with electrical wires and actuators. This means fewer parts to wear out, and because RBW or XBW integrated chassis mechatronic control hypersystems work like a fast computer, the Chevrolet Sequel has enhanced acceleration, braking, and overall handling."
        ]
    },
    {
        "image_filename": "designv10_12_0001866_s00170-017-9988-7-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001866_s00170-017-9988-7-Figure1-1.png",
        "caption": "Fig. 1 Definitions of skiving coordinate systems",
        "texts": [
            " Then, the influences on the helix deviations and the profile deviations of the tool eccentricity error are discussed. The contributing factors of the waves, generally appearing on the tooth flanks in skiving, are investigated, and the wave-form of the waves and the influences on skiving accuracy are analyzed. * Shi-Min Mao maosm@mail.xjtu.edu.cn 1 State Key Laboratory for Manufacturing System Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China 2 Qinchuan Machine Tool & Tool Corporation, Baoji 721008, China As shown in Fig. 1, several coordinate systems are defined in the calculations of gear helix deviation and profile deviation. S1(x1, y1, z1) is the fixed coordinate system of workpiece that rotates around and moves along axis of z1. Coordinate system Sw(xw, yw, zw) is rigidly attached to the workpiece, and its original position is identical with S1. S2(x2, y2, z2) is the fixed coordinate system of the cutter that rotates around the axis of z2. Coordinate system Sc(xc, yc, zc) is rigidly attached to the cutter, whose original position is identical with S2, and S 0 c x 0 c; y 0 c; z 0 c is the coordinate system attached to the cutter which has an eccentricity error e",
            " \u00fe arccos rbffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x02 w \u00fe y02 w q 0 B@ 1 CA \u00f021\u00de The coordinates of point A can be obtained by using the angle Q and the involute tooth profile equations [21], then the tooth profile deviation can be expressed as the distance between the point A\u2032 and the point A: d \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x0 w\u2212xw 2 \u00fe y0 w\u2212yw 2q \u00f022\u00de A numerical example of tooth profile deviation calculation is carried out, which is aimed at analyzing the influences on the gear tooth profile deviation of the tool position and orientation errors. The basic parameters of the cutter and the internal gear are shown in Table 1. The calculation results of tooth profile deviation are shown in Section 2, in which the vertical axis represents the rolling length of the standard involute tooth profile. The curves on the left side of the vertical axis represent the tooth profile deviations of the flanks skived by the approach edges \u201cA\u201d which is the earliest side edge of a cutter tooth that cuts into the workpiece as shown in View P in Fig. 1. The curves on the right side of the vertical axis represent the tooth profile deviations of the flanks skived by the recess edges \u201cR\u201d which is the last side edge of a cutter tooth that separates from the workpiece. The horizontal axis represents the tooth profile deviations of the both sides of the tooth space, which is similar to the tooth profile measurement report by gear measuring machine. The tooth profile deviations of the gears on pitch circle are zero, and the deviations are positive if the curves extend to the middle range of the horizontal axis and vice versa",
            " 4b, c, when the tool eccentricity error e is about 20 \u03bcm, sharp waves appear on the tooth flanks of the workpiece, while the waves are weakened when the eccentricity error e is reduced to 10 \u03bcm by improving the tool setting accuracy. In addition, about seven waves, with wavelength close to 2 mm, appear on the tooth flanks of both the workpieces. The tool eccentricity error has influences on the cutting depths of the cutter teeth in skiving. The eccentricity error of the cutter can be expressed in Sc as: e \u00bc e 0 0\u00bd \u00f023\u00de When the eccentricity error e is zero, the position coordinates of a cutting point on the side edge of the cutter tooth \u201ci\u201d, as shown in view P in Fig. 1, can be expressed by the variable parameters u and i in Sc as: rci u; i\u00f0 \u00de \u00bc M2c i\u22c5\u03c6cp \u22c5rc u\u00f0 \u00de \u00f024\u00de where \u03c6cp is the pitch angle of the cutter and can be expressed as \u03c6cp \u00bc 2\u03c0 . Zc \u00f025\u00de When e is not zero, the position coordinates of a cutting point on the side edge of the cutter tooth \u201ci\u201d can be expressed in Sc as: r*ci u; i\u00f0 \u00de \u00bc rci \u00fe e \u00f026\u00de In the fixed coordinate system of workpiece S1, r*ci and rci can be separately expressed as: r 1\u00f0 \u00de ci u; i\u00f0 \u00de \u00bc M\u22121 21 \u22c5M2c \u2212i\u22c5\u03c6cp \u22c5rci \u00f027\u00de r* 1\u00f0 \u00de ci u; i\u00f0 \u00de \u00bc M\u22121 21 \u22c5M2c \u2212i\u22c5\u03c6cp \u22c5r*ci \u00f028\u00de The cutting depth variation \u0394d, difference between the actual cutting depth and the theoretical cutting depth, can be expressed as: \u0394d \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 1\u00f0 \u00de ci 2 \u00fe y 1\u00f0 \u00de ci 2r \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x* 1\u00f0 \u00de ci 2 \u00fe y* 1\u00f0 \u00de ci 2r \u00f029\u00de By applying the Eq",
            "16 mm, and if the face width of the workpiece is 15 mm, there will be 7 waves on each tooth flank approximately, which corresponded to the experiment results shown in Fig. 4. While, when the number of teeth of the cutter Zc is reduced to 32 or 24, the wavelength Lwave of the helix deviation will be decreased, and the fluctuation of the wave is more obvious when Zc is 32. There will be a new cutter mark on the tooth flank of the workpiece for each cut of a cutter tooth, so each cutter mark on the tooth flanks corresponds with a cutter tooth. The angle\u03b8 as shown in view P in Fig. 1, positively related with the waviness of the tooth flanks of the workpiece, is the included angle between the cutter teeth iand j that correspond with two adjacent cutter marks on the tooth flank. If \u03b8 is small, the cutter tip circle deviations h i and h j, as shown in view P in Fig. 1 are approximated and the difference between the depths of the two adjacent cutter marks is small, so the tooth flanks of the workpiece will be smooth and vice versa. The angle \u03b8 can be affected by the cutter number of teeth Zc, and the relationship between \u03b8 and Zc is shown in Fig. 7b. When Zc is close to Zw/n (n is an integer), \u03b8 is small, so the difference between the depths of the two adjacent cutter marks is inconspicuous, then the tooth flanks of the workpiece will be smooth, which corresponded to the numerical example shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure5-1.png",
        "caption": "Fig. 5. (a) The Bennett platform (b) The Bricard platform.",
        "texts": [
            " Taking the classic four-bar Bennett linkage as an example, the directions of every two alternative revolute joints of the linkage intersect at two points. After establishing a suitable reference coordinate at one of the common points, the wrench system of the limb consists of three screw constraints [ 30 , 31 ]. Similarly, the 1-DOF Bricard linkage with every two spaced revolute joints intersecting at two moving points can be obtained. The detailed analysis progress has been introduced in reference [32] . The diagrams of the Bennett platform and Bricard platform are depicted in Fig. 5 . The above planar parallelogram linkage, 4 R spherical linkage, Bennett linkage, Bricard linkage and the six-bar meta- morphic linkage are adopted to form configurable platforms with integrated end-effectors. Resulting from the distinctive geometric characteristic of the revolute joints, the platform can switch between two working phrases. The integrated end- effectors which are mounted on the top of revolute joints can cooperate with each other to perform parallel or intersecting motions. Besides, the 1-DOF single-loop configurable platforms can be further extended to multi-DOF platforms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002856_ab3c3a-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002856_ab3c3a-Figure11-1.png",
        "caption": "Fig. 11. Vibration measurement results of the bonded-type piezoelectric transducer. (a) Amplitude-frequency curves of the two operating vibration modes. (b) Vibration shape of the symmetric mode. (c) Vibration shape of the anti-symmetric mode.",
        "texts": [
            " 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M a u cr ip t 12 Measuring points ClampTransducer Laser scanning head Fig. 10. Experimental setup for measuring the vibration characteristics of the prototype of the proposed piezoelectric transducer. The amplitude-frequency curves and vibration shapes of the two operating vibration modes are obtained, as shown in Fig. 11. In Fig. 11(a), the resonant frequencies of the anti-symmetric and symmetric vibration modes are 68.592 kHz and 69 kHz, respectively, leading a resonant frequency difference of 408 Hz. This difference, which mainly caused by machining errors, is acceptable. Fig. 11(b) shows that the two parallel beams of the piezoelectric transducer simultaneously contracted or extended, indicating that the symmetric vibration mode was excited. Fig. 11(c) illustrates that one beam contracted and the other beam extended at the same time, indicating that the antisymmetric vibration mode was stimulated. These vibration measurement results are in good agreement with the results of FEM modal analysis. (a) Vibration direction& (b) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A cc ep te d M an us cr ip t 13 The motion trajectories of points P and Q were tested by a three-dimensional laser Doppler vibrometer (PSV-500-3D-M, Polytec, Germany), as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002288_042020-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002288_042020-Figure2-1.png",
        "caption": "Figure 2. Main bearing arrangements",
        "texts": [
            " Palliatives like flexible couplings and mechanical load equalization can reduce non-torque load effects, and ease the analysis task by shifting interfaces and allowing decoupled analyses. It is thus tempting to pose the rhetorical question if modelling and simulation options, and the challenge of treating structural flexibility in a consistent manner, ultimately influences design choices. Main bearings have a difficult place in that they are implicitly considered a part of the drivetrain unless dissociated by decoupling devices or simply gearless designs; then they seem somewhat ignored, a point well illustrated in Van Kuik et. al [28]. Figure 2 shows an array of drivetrain arrangements found in modern turbines, the one on the far left representing the most traditional variant. The relatively slender shaft can be supported by bearings able to accommodate some bending. Combined with a overhung gearbox, or direct drive generator, with resilient torque reaction support, this type of arrangement can be less affected by non-torque loads than a three-point support. Moving right in the figure, the arrangements represent compacting by the use of larger-diameter multi-row cylindrical roller bearings - or more commonly - opposing tapered roller bearings, ultimately the double-row tapered roller bearing in an inverted configuration, and to the far right an inverted design where the hub rotates around a spindle. Figure 2 helps illustrate that these drivetrains are not readily represented by the same model, simply by adjusting parameters. It is obvious that the arrangement on the far left is a good candidate for exchangig forces and moments for displacements in 6 DOF at the shaft ends. Cost models encourage increasing turbine size in order to harvest wind energy at greater heights and give fewer unit operations and access points. Inctreased structural flexibility and lowered natural frequencies however pose significant design challenges, as cited by the UPWIND project [5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000568_j.polymertesting.2010.12.005-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000568_j.polymertesting.2010.12.005-Figure8-1.png",
        "caption": "Fig. 8. Meshed PP honeycomb core using ANSYS code.",
        "texts": [
            " The values of the angle and geometry of the honeycomb structure were obtained, averaging the measurements carried out in different cells. These values correspond to: t \u00bc 0.25 mm, Es \u00bc 1.5 GPa, Gs \u00bc 564 MPa, b \u00bc 15 mm, l \u00bc h \u00bc 5.4 mm and q \u00bc 30 .The values obtained by this method, replacing previous data in Eqs. (15)\u2013(19), were: Ez \u00bc 106 MPa Gxz \u00bc 23:3 MPa Gyz \u00bc 15:1 MPa ANSYS was used for FEM calculation. The model was based on shell elements that copied the shape of the inner structure ina repetitiveway, as showninFig. 8. Thegeometric parameterswere the sameas thevaluesused in the analytical approach, and possible geometry defects were not considered. The double thickness was characterized using two shells perfectly bonded. The elastic moduli of PP core and aluminium skin were assumed to be 1.5 GPa and 70 GPa, respectively.The values obtained by this method were: Ez \u00bc 104 MPa Gxz \u00bc 20:7 MPa Gyz \u00bc 14:2 MPa Comparison between different methods is summarized in Table 3. On the one hand, the agreement between the elastic modulus in the z direction Ez is rather good; the maximum variation being lesser than 8% for the 4 methods analysed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure4-1.png",
        "caption": "Fig. 4. FBD of bottom cables with variable length.",
        "texts": [
            " In the reviewed wrench feasibility analysis of [14], the effects of cables weight have been ignored, where in ACTRs with land-fixed winches, length variation of the bottom cables and limitation of UAVs maximum thrust force, make it more realistic to consider the weight effects of varying-length cables in the presented wrench feasibility analysis. Similarly, because of having a short length and consequently a small constant mass, the weight effects of the UAV-connected cables are assumed to be negligible. In order to consider the cable weight effects, \u03b7i is considered as the length density of the cables, where FBD of bottom cable i is shown in Fig. 4(c). In order to simplify such effects, the effects of cable sagging on deformation of the cable profile are assumed to be negligible and the cable is approximated by a straight line, as illustrated in Fig. 4(a)\u2013(c). Accordingly, the tension along the connecting line between any winch and the platform is \u03c4i and the weight of cable is considered as an evenly distributed force \u03b7ig along the cable length, where two concentric vertical force with magnitudes 1 2 \u03b7igli are applied on the cable\u2019s end points to satisfy the static equilibrium conditions. Accordingly, the free-body diagram (FBD) of the platform is considered as illustrated in Fig. 3(b), where in addition to \u03c4is and the platform\u2019s weight, the weight effect of winch-connected cables 1 2 \u2211n i=1 \u03b7ilig is also applied on it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000347_tmech.2007.915058-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000347_tmech.2007.915058-Figure4-1.png",
        "caption": "Fig. 4. Fish cutting machine.",
        "texts": [
            " In this stage, the designer may need to develop computer programs and use available simulation tools for the design tasks. The analysis in this stage should be as accurate as possible. It is not a critical problem if the runtime of the simulations is high because it is not repeated many times. 10) Aggregate the partial scores by using the Choquet integral to determine the global score of each elite design. The design with the highest global score is considered the optimum design. Detailed design of the manipulator of an industrial fish cutting machine (Fig. 4) is presented here. This machine is used in industry to automatically cut the head of fish with minimum meat wastage. In this machine, as a fish is moved to the cutting zone by a conveyer system, a camera takes an image of the fish. The location of the gill, the best reference location for the cutting, is identified by an image-processing routine, and the corresponding coordinates are sent to the controller. At this point, the operation of the manipulator begins. Its function is to accurately move the cutting blade to the desired cutting location"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000316_1.29112-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000316_1.29112-Figure1-1.png",
        "caption": "Fig. 1 X-35B engine layout.",
        "texts": [
            " Section IV provides the results of the digital simulations. Conclusions are presented in Sec. V. A. Model of the V-1 Aircraft First, we present the model of the V-1 aircraft, which is equipped with an engine layout similar to the X-35B. The X-35B JSF fighter has a JSF119-611 engine that has a three bearing swivel duct (3BSD) providing the aft post with axial thrust and vectored-thrust capability in pitch and yaw. The lift fan provides augmented thrust on the forward post. A set of roll ducts is used for lateral control. As shown in Fig. 1, the 3BSD nozzle can turn from 0 to 95 deg on the pitch axis, as well as from 12 to 12 deg on the yaw axis; the lift-fan nozzle can turn from 34 to 95 deg on the pitch axis [19]. The control inputs of the aircraft include vT , vq, vr, fT , f, Tl, Tr, a, r, c, and e. All the actuator dynamics are second order with position and rate saturation constraints. The actuator characteristics are described in Table 1 in which is the damping ratio and !n is the natural frequency. Only a longitudinal model of the V-1 aircraft is presented in the paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000007_978-1-4613-2811-7_7-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000007_978-1-4613-2811-7_7-Figure4-1.png",
        "caption": "Figure 4. Example of semipart cell.",
        "texts": [],
        "surrounding_texts": [
            "boundary, constructive solid geometry (CSG) and cell decomposition represen- tation schemes and concludes that all could be used during the derivation of ac ceptable cutting strategies [Armstrong 1982]. Decisions in manufacturing planning often involve consideration of local geometries. If so me spatial order ing is imposed upon the representations by deriving a decomposition of cells, each of which holds either a boundary or CSG representation of the material in the cell, then local regions of interest will be readily accessible. These cells may also hold local representations of fixtures and the final part which is to be produced. Spatially Ordered Representation Scheme-This approach uses a decomposi tion imposed by a lattice work of planes parallel to the major axes. It is advan tageous to keep the internal details of the resulting cells simple; the positioning of the lattice planes has been implemented to achieve this. The cells are derived from the boundary representation of the part. Infinite planes are then posi tioned coincident with each plan ar face and tangential to each cylindrical half space. This particular method is appropriate to the PADL-l domain. In a larger geometrie domain it is likely that each plane would be positioned to pass through each vertex and line of tangency of the component. The lattice planes for a simple part are illustrated in Figure 2. Slices through the resulting decom position, normal to the vertieal axis, are shown in Figure 3. ReJerences pp. J 5 3- J 54 For the present implementation, the stock is assumed to be a rectilinear block, so each resulting cell is represented as one of the following: \u2022 Stock cello The cell contains only stock material, all of which must be re moved. Any of the six cell boundary faces may be of type stock when it lies on the face of the stock, part when it lies on the face of the part and internal when it does not correspond to any real surface. \u2022 Part cello The cell contains only finished part material, none of which must be removed. \u2022 Semipart cello The cell contains both part material and stock material. Fundamental Algorithms-Having obtained a cell decomposition, various low-level routines are provided which, given a cell and a tool path positioned relative to that cell, indicate whether that tool path is permissible within the cell, and, if not, what subset (if any) of the path is permissible. This is deduced by first identifying other cells through wh ich the path passes, and then checking for a collision with internal cell faces within these cells. Application Modules-The setup derivation, roughing, and finishing modules make use of the fundamental algorithms by testing required paths against cells in a given order. For example, where a path is not permissible within acelI, then all the cells below it in the search sequence can be marked as unmachina ble in that setup."
        ]
    },
    {
        "image_filename": "designv10_12_0002181_j.ijfatigue.2016.08.020-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002181_j.ijfatigue.2016.08.020-Figure14-1.png",
        "caption": "Fig. 14. Stress results around the bolt hole.",
        "texts": [
            " But in the cornering fatigue test, the steel wheel is fixed while the load rotates with the speed of 1200 rpm (far below the rotational speed corresponding to the first natural frequency), thus the dynamic rotational loading process can be converted into a static problem. To simulate the cornering fatigue test, the load is respectively applied on the end of the moment arm at every 22.5 deg. The stress distribution of the wheel under the load applied at 0-deg position is shown in Fig. 12. There are large operating stresses around the area (dangerous position) between the bolt hole and the bump ring (shown in Fig. 14). Each point of the wheel is in different deformation conditions, which can be determined by the third invariant of the stress deviator [14], as shown in Fig. 13. One dangerous point is selected and defined as point A in Fig. 14 to research its stress state in the following investigation. Fig. 15 is a stress curve from the data of the cornering stress of point A (Fig. 14) obtained in 16 simulations. This point suffers the tension/compression stress states for 16 different load positions, eventually leading to fatigue crack after certain cycles because of the high stress amplitude. The residual stresses in two directions on the surface are measured by X-ray diffraction method in Section 2.2, while the residual stress along the thickness direction cannot be detected. But the operating stresses of each point in six directions (three normal stresses and three shear stresses) can be obtained by the simulation of the cornering fatigue test",
            " The experiment is conducted based on GB/ T5334-2005, and four same tests are conducted to ensure the accuracy of the experiment. The average value of the experimental fatigue life is 137,438 revolutions and the fixing torque of the bolt of 120 Nm. The cracking position is generated in the area between the bolt hole and the bump ring and extended along the circumferential direction [16]. The results of four experiments show that the cracking positions of the wheel disc are all at the corner between the bolt hole and the bump ring (Fig. 16), which are consistent with the simulation results (shown in Fig. 14). Stresses of point A without considering the residual stress are recorded including its maximum stress, minimum stress, average stress and alternating stress amplitude based on ABAQUS simulation results, as shown in Table 6. Considering the influence of the average stress, the alternating stress is converted into the symmetrical cyclic stress by Gerber equation: ra rR\u00f0 1\u00de \u00fe rm rb 2 \u00bc 1 \u00f015\u00de where rm is the average stress, ra is the alternating stress amplitude, rR\u00f0 1\u00de is the symmetrical cyclic stress amplitude and rb is the tensile strength of the material, as shown in Table 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002124_tmag.2015.2481934-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002124_tmag.2015.2481934-Figure5-1.png",
        "caption": "Fig. 5. Quarter of the machine cross section.",
        "texts": [
            " To further evaluate the accuracy of the proposed methods, time-stepping analysis was performed on two slightly different four-pole permanent magnet (PM) machines rotating at 15 000 r/min, one with open and the other with semiclosed slots. Five electrical periods after synchronization at 0 s were simulated with 400 steps per period. The main dimensions of the machines can be found in Table I. The machine with semiclosed slots has a slightly larger stator radius, but otherwise the dimensions are equal. The machines have a single-layer winding with three effective turns per slot, and 16 strands in parallel in each phase. A quarter of the machine cross section is presented in Fig. 5. Phases and turns are emphasized with different colors and shadings, respectively. The open-slotted machine was analyzed first. Fig. 6(a) and (b) shows the mesh over one slot pitch used with the brute-force and proposed methods, respectively. Fig. 7 shows the circulating current losses as a function of time [1]. The blue line denotes the results obtained with the brute-force method, while the two proposed methods are displayed with red and black lines. It can be seen that the two proposed methods gave almost equal results, both \u223c20% larger than the brute-force method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002948_s12206-019-0501-0-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002948_s12206-019-0501-0-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of defect on inner raceway and outer raceway.",
        "texts": [],
        "surrounding_texts": [
            "theory. Nakhaeinejad and Bryant [11] proposed a dynamic model of faulty rolling element bearing utilizing vector bond graphs in which the surface profile changes represent the defects on raceways. Kulkarni and Sahasrabudhe [12] developed a dynamic model of ball bearing using cubic Hermite spline to simulate the process when the ball strikes the defects on outer race. Recent work done by Govardhan et al. [13] investigated the excitations caused by bearing defect under dynamic radial load which was considered to be composed of a static and a harmonic components. Liu et al. [14] investigated the effect of the defect depth on bearing vibration considering the timevarying displacement and contact stiffness for the first time. Moreover, Sassi [15], Arslan [16], and Patel [17] also had done some works on the vibration of bearing with surface defects. In these researches, bearing with single and multiple defects were investigated, and the characteristic frequencies can be found in the spectrums. Besides the localized and distributed defects above, some researchers also paid attention to the vibration induced by the bearing material defects, e.g. material inclusions [18], which would also make the motion of the system more complicated.\nIt can be found that most studies focus on the waviness [19- 22] or the defect on raceways. For localized defects, only a few researchers have investigated the effect of one or two defects on inner or outer race by means of numerical method. However, it is inevitable to produce even more defects on races, and the distribution of defects may be uniform or random. Moreover, surface defects coupled interface friction or the eccentricity of the bearing-rotor system is barely investigated until now.\nIn this paper, a model has been established to systematically investigate the influence of size of defect, number of defects, defect location, distribution of defects, and defect coupled interface friction or the eccentricity of the bearing-rotor system. In the present model, the contact force between balls and raceways is calculated based on the Hertz contact theory. The kinematic relationship between balls and races is established with raceway control hypothesis. The contact deformation is figured out considering the defect. The set of nonlinear differential equations of motion is solved based on the fourth order Runge-Kutta method. After the proposed model is validated by the existent model, the effect of size, number, and distribution of defect, etc is explored finally.\n2. Theoretical model\n2.1 Dynamic model of deep groove ball bearing\nIn order to establish the kinematic equations, following hypotheses are made:\n(1) \u201cRigid ring hypothesis\u201d is adopted, namely, only the local elastic contact deformation between balls and raceways is considered, and the elastic-plastic deformation of the whole bearing rings is ignored.\n(2) The balls are in pure rolling on the bearing raceways. For deep groove ball bearing, the orbital angular velocity of\nsteel balls is\ni c i\ni e\nD D D w w= \u00d7 +\n(1)\nwhere \u03c9i is the angular velocity of inner ring, Di and De are the groove bottom diameters of inner raceway and outer raceway, respectively.\nWithout loss of generality, it is assumed that the outer ring of the bearing is rigid and fixed. As shown in Fig. 1, due to the radial force Fr, the center of inner ring has the displacements in both x and y directions. At any instant t, the displacement of inner race groove bottom at the azimuth angle \u03c6j can be written as\ncos sinj j jd x yj j= + (2)\nwhere \u03c6j is the azimuth angle of jth ball. Assuming that the bearing has a total of Z balls, \u03c6j can be written as\n( )2 1 / .j cj Z tj p w= - + \u00d7 (3)\nAssume that the radial clearance of the bearing is u; then the elastic deformation between the jth ball and raceways at the azimuth angle \u03c6j is\n.j jd ud = - (4)\nBased on the Hertz contact theory, the contact force Qj be-\ntween the jth ball and the races can be obtained as follows:\n1.5 0 00 jj j j K Q dd d \u00ec \" \u00b3\u00ef= \u00ed \" <\u00ef\u00ee (5)\nwhere K is the load-displacement coefficient which can be obtained from the following formula [23]:\n1/ 1/ 1 . (1 ) (1 )\nn\nn n i e\nK K K \u00e9 \u00f9 = \u00ea \u00fa+ + +\u00eb \u00fb\n(6)",
            "For point contact, the index n is 1.5 and 1.11 for the line contact. Ki and Ke are the load-displacement coefficients for the contacts between ball and inner raceway or outer raceway, respectively, which are evaluated by following equations\n1/2 * 4 2 ' 1 3( )\nn\ni i i\nEK r d \u00e6 \u00f6 = \u00e7 \u00f7\u00e7 \u00f7 \u00e8 \u00f8\u00e5 (7)\n1/2 * 4 2 ' 1 3( )\nn\ne e e\nEK r d \u00e6 \u00f6 = \u00e7 \u00f7\u00e7 \u00f7 \u00e8 \u00f8\u00e5 (8)\nwhere \u2211\u03c1 is the curvature sum of the contact point, E\u2019 is the equivalent elastic modulus which can be calculated as follows:\n2 2 1 2\n1 2\n1 1 1 'E E E n n- - = + (9)\nwhere E1, E2 are the Young\u2019s modulus, and \u03bd1 \u03bd2 are the Poisson\u2019s ratio, respectively. \u03b4* in Eqs. (7) and (8) is the dimensionless contact coefficient which can be evaluated by following formula:\n1/3\n1 2\n2\n2 ( )* 2 ( ) L L k pd p k k \u00e6 \u00f6 = \u00e7 \u00f7 \u00e8 \u00f8 (10)\nwhere L1(\u03ba), L2(\u03ba) are the first and second kind of complete elliptic integrals with \u03ba is the ellipticity of the contact area, they are calculated by the following equations:\n1/2 /2 2\n1 20\n1/2 /2 2\n2 20\n1( ) 1 1 sin\n1( ) 1 1 sin .\nL d\nL d\np\np\nk q q k\nk q q k\n-\u00ec \u00e9 \u00f9\u00e6 \u00f6\u00ef = - -\u00ea \u00fa\u00e7 \u00f7\u00ef \u00e8 \u00f8\u00eb \u00fb \u00ed \u00e9 \u00f9\u00ef \u00e6 \u00f6= - -\u00ea \u00fa\u00ef \u00e7 \u00f7 \u00e8 \u00f8\u00eb \u00fb\u00ee \u00f2 \u00f2 (11)\nThe contact forces applied on inner race by all the balls can be divided into the components in x and y directions and expressed as\n1\ncos . sin Z jx\nj jy j\nQ Q Q j\nj=\n\u00e9 \u00f9\u00e9 \u00f9 = \u00ea \u00fa\u00ea \u00fa\n\u00ea \u00fa \u00ea \u00fa\u00eb \u00fb \u00eb \u00fb \u00e5 (12)\nFinally, the differential equations of motion for the bearing-\nrotor system can be established as follows,\n2\n2 cos sin x r i i y i i Mx Cx Q F Me t My Cy Q Me t w w w w \u00ec + + = +\u00ef \u00ed + + =\u00ef\u00ee && & && &\n(13)\nwhere M is the total mass of shaft and inner ring, C is the damping coefficient, e is the eccentricity of the unbalanced mass of the bearing-rotor system. If the system is well balanced, the eccentricity e = 0.\nEq. (13) is the second order nonlinear differential equation, which can be rewritten as the following set of the first order differential equations:\n1 2\n2\n2 2\n3 4\n2\n4 4\ncos\nsin\nr i i x\nyi i\nz z F Me t C Qz z M M M z z\nQMe t Cz z M M M\nw w\nw w\n=\u00ec \u00ef +\u00ef = - -\u00ef \u00ed =\u00ef \u00ef \u00ef = - - \u00ee & & & &\n(14)\nwhere 1z x= , 2z x= & , 3z y= , 4 .z y= &\n2.2 Surface defect model\nFigs. 2(a) and (b) schematically show the defect appeared on outer raceway and inner raceway, respectively. When the ball rolls over the defect, the additional displacement \u0394 of the ball center can be obtained as follows,\n= (1 cos ) 2 D W D D - (15)\nwhere W is the width of the defect, D is the ball diameter. Since the width of the defect is much smaller relative to the ball diameter, the additional displacement \u0394 is tiny when the",
            "ball is riding over the defect. It can be assumed that the depth d of the defect is greater than the additional displacement \u0394, then the influence of the depth of the defect is not taken into account. Here, the rectangular defect is assumed as an example, the defect with other shapes can be considered through the similar way; however, in present two degrees of free-dom for deep-groove ball bearing, the defect shapes have negligible effect as shown in Appendix A.\nFig. 3 shows the schematic diagram of bearing with surface defects. As the outer ring is fixed, the azimuth angle of outer raceway defect always keeps unchanged as:\n( 1)j j e e eW Dz a= + - , j = 1,2 (16)\nwhere \u03b1e is the azimuth angle of the outer race defect center. When multiple defects are distributed on the outer raceway, assuming the difference between the azimuth angle of nth defect and the azimuth angle of the first defect is \u03b8e\nn, then the azimuth angle range of nth defect is\ne e nj j n ez z q= + , j = 1,2. (17) The inner raceway defect moves with the inner ring at an angular velocity \u03c9i, the azimuth angle of the defect at the moment t can be expressed as\ni i i( 1)j jt W Dz w= + - , j = 1,2. (18)\nSimilarly, when there are multiple defects on inner race, the\nazimuth angle range of the nth defect is\ni i i nj j nz z q= + , j = 1,2. (19)\nThe relative position between ball and defects can be judged from the azimuth angle of ball (Eq. (3)) and the azimuth angle range of surface defects (Eqs. (16)-(19)). \u03b2 is used to represent the relative position between ball and the defect.\n\u03b2 = 1 means the ball is right falling into the defect, and \u03b2 = 0 means the ball is not in the defect which can be expressed as follows\n1 2 1 2 i i i i\ni 1 or 0 other cases n n j jz j z z j z b \u00ec \u00a3 \u00a3 \u00a3 \u00a3\u00ef= \u00ed \u00ef\u00ee \uff0c (20)\n1 2 1 2 e e e e\ne 1 or 0 other cases . n n j jz j z z j z b \u00ec \u00a3 \u00a3 \u00a3 \u00a3\u00ef= \u00ed \u00ef\u00ee \uff0c (21)\nAfter considering the local defects, at the azimuth angle \u03c6j, the elastic deformation between ball and raceways will be changed from Eq. (4) to the following equation:\ni i e ecos sinj j jx y ud j j b b= + - - D - D (22)\nwhere \u0394 is the additional displacement of the ball center induced by a defect as given by Eq. (15).\nSubstituting Eq. (22) into Eq. (5), we can establish the motion differential equations of the bearing-rotor system considering the surface defects.\n3. Numerical approaches\nIn present study, the fourth order Runge-Kutta method is used to solve the nonlinear differential equations (Eq. (14)). Eq. (14) can be written as\n( ) ( , ( )) .z t f t z t=& (23)\nThen, following the fourth order Runge-Kutta method,\n1 1 2 3 4( 2 2 ) 6n n\nhz z K K K K+ = + + + + (24)\nwhere h is the step length in the program, zn = z(tn) and\n1\n2 1\n3 2\n4 3\n( , )\n( , ) 2 2\n( , ) 2 2 ( , ) .\nn n\nn n\nn n\nn n\nK f t z h hK f t z K\nh hK f t z K\nK f t h z hK =\u00ec \u00ef \u00ef = + + \u00ef \u00ed \u00ef = + + \u00ef \u00ef = + +\u00ee\n(25)\nThe solving process is detailed as shown in Fig. 4.\n4. Model validation\nIn order to verify the developed model, we compared the results from the present model with that in Ref. [9]. The same bearing, working conditions and defect parameters as in Ref. [9] were used.\nWhen one single defect is located on the outer raceway, the"
        ]
    },
    {
        "image_filename": "designv10_12_0000670_tbme.1972.324103-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000670_tbme.1972.324103-Figure10-1.png",
        "caption": "Fig. 10.",
        "texts": [
            "562 J [10(f/200) - f8/20 - f13/20] di f8/20 - 0.25[p7/20 -0.1(p8/2)] rt p8/2 0.903 J [fs/20 - 10(f9/200)] dt f9/20 = 10(p8/2 - p9/2) PO = 0.75f [f/920 -Jfo20 + 2.5(f12/50) + f,3/20] da fio/20 = 10(p9/2 - P1o/2) rt pl/2= 1.5f [flo/20- 10(f1/200)ldt fls/20 =p6/20 - 0.2(pll/4) p11/4 1.875 JR (fss20- f112/20) dt f12/20 0.1[2(pil/4) -p/2] /f3/20 0.25[p7/20 - 0.1(pg/2)]. (19) (20) (221) (22) (23) (24) (25) (26) (27) (28) (29) The reciprocal compliance curves for the left and right ventricles followed the curves shown in Fig. 10, in which a half-sinusoid is used (solid curve) for -a 106 (4) RIDEOUT: CARDIOVASCULAR SIMULATION IN EDUCATION systolic period r8 = 0. 314 s and a normal diastolic period 'rd=0.5 s. For the right ventricle the scaled quantity required, 1/200CO, had a=2.5, p3=0.066, while for the left ventricle 1/1332C4 had a=9.5, ,B=0.1. A better shape for the reciprocal compliance sometimes used is the semitriangular curve (shown dotted in Fig. 10). Initialization of the system requires initial conditions on q and p corresponding to the desired total volume (see Table I). ACKNOWLEDGMENT The author has had the advantage of being able to discuss problems of modeling with Dr. Jan E. W. Beneken and others in his group at the Institute of Medical Physics TNO, Utrecht, The Netherlands. Particular thanks go to the students who participated in the first trial runs of the course described, to the staff of the Hybrid Computer Laboratory at Wisconsin, and to many staff members in the Medical School of the University of Wisconsin for their assistance and en- couragement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001357_bi3017119-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001357_bi3017119-Figure1-1.png",
        "caption": "Figure 1. Reaction coordinate profiles for nonenzymatic (top profile) and enzymatic (bottom profile) heterolytic bond cleavage at a reactant R to give a high-energy reactive intermediate I. The activation barrier for formation of the intermediate, \u0394G\u29e7 f, is equal to the sum of the large thermodynamic barrier to formation of the reactive intermediate, \u0394Go, and the small barrier for the reaction in the reverse direction, \u0394G\u29e7 r. If \u0394G\u29e7 r is not changed when the process proceeds to the enzymatic reaction, then the stabilization of the intermediate at the active site of an enzyme catalyst (E\u00b7I) by an amount \u0394\u0394Go will result in a corresponding reduction in the activation barrier for formation of the intermediate, such that \u0394\u0394G\u29e7 f = \u0394\u0394Go.",
        "texts": [
            "1021/bi3017119 | Biochemistry XXXX, XXX, XXX\u2212XXX enolates, respectively. They were among the most intensively studied protein catalysts between 1960 and 1980, in work that was guided by the notion that comparisons of the reaction coordinate profiles for the nonenzymatic and enzyme-catalyzed processes can provide important insight into the origin of the enzymatic rate enhancement. The activation barrier for a nonenzymatic reaction that proceeds through an unstable intermediate is composed mainly of the thermodynamic barrier to formation of the intermediate, \u0394Go (Figure 1). The direct route toward lowering this barrier is to stabilize the enzymebound intermediate relative to the enzyme-bound substrate, \u0394\u0394Go (Figure 1). This is in accord with Pauling\u2019s proposal that the large rate enhancements for enzymes are due to the high specificity of the protein catalyst for binding the reaction transition state,3 which according to Hammond closely resembles the reactive intermediate.4 The ligand binding energy required to account for the rate enhancement of such enzymes is generally so large that it cannot be expressed entirely at the ground state Michaelis complex, because this would result in effectively irreversible ligand binding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000789_978-1-4419-8113-4-Figure16.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000789_978-1-4419-8113-4-Figure16.2-1.png",
        "caption": "Fig. 16.2 Bounce of a spinning ball dropped onto an inclined surface. If the surface is tilted to the right, the ball bounces almost vertically. If the surface is tilted to the left, the ball bounces a long way to the left",
        "texts": [
            "4 Bounce Off an Inclined Surface 265 But if you try to rotate the ball around a vertical axis then the ball doesn\u2019t grip as well. The reason is that you can exert a torque by hand, on the edge of the ball, that is much larger than the torque exerted by the friction force near the axis. It is like loosening a nut with a long wrench, which is much easier than loosening the nut by hand. An important bounce event in baseball and softball, as well as in tennis and golf, is the bounce of a spinning ball off an inclined surface, as shown in Fig. 16.2. In tennis, a player can tilt the racquet head to vary both the rebound angle and spin of the ball. In fact, the modern game of tennis is dominated by the amount of spin that players impart to the ball. Players launch themselves off the court by belting the ball as hard as they can to spin the ball as fast as they can. Their opponent does the same, so the ball returns spinning furiously. If the player just taps or pushes the ball back at low speed, the ball will bounce off the strings at a strange angle",
            " In baseball and softball, the pitcher usually spins the ball rapidly so that it follows a strongly curved path through the air. The batter\u2019s main task is simply to connect with the ball, but if he is very good or just lucky, he can strike the ball above or below the axis to put even more spin on the ball. The ball impacts on the curved surface of the bat but the effect is the same as an impact on an inclined surface. The result is that the ball deflects skyward if the ball strikes above the long axis of the bat or it deflects down toward the ground if the ball strikes below the axis. In Fig. 16.2, the ball on the left is incident with backspin, while the ball on the right is incident with topspin. The direction of the spin is the same in both cases, but the ball on the left is incident from left to right relative to the surface, and the ball on the right is incident from right to left. If the ball was incident without any spin then it would bounce to the right off the left hand surface and to the left off 266 16 Ball Bounce and Spin the right hand surface. The effect of the counter-clockwise spin, on its own, is to deflect the ball to the left"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002006_j.aej.2018.12.010-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002006_j.aej.2018.12.010-Figure3-1.png",
        "caption": "Fig. 3 Material phase distribution during the deposition of the second layer.",
        "texts": [
            " In order to simulate the deposition process, the element birth technique was used to activate elements when they are subjected to the flux induced by the laser beam. Temperature-dependent thermal and mechanical properties were used, as obtained from [9]. The powder thermal conductivity and density were set to 0.2 W/m K and 3930 kg/m3, respectively [17]. The subroutine USDFLD was used to model phase change from powder to solid state. Material phase distribution during the deposition of the second layer is shown in Fig. 3, as an example. The simulated laser beam was assumed to have a circular cross-sectional area, and was perpendicular to the scanned powder surface, having a uniform and constant power density. Accordingly, the surface heat flux (I) was assumed to be uniform, as given by Eq. (4), where P refers to the laser power, r is the laser beam radius (1.25 mm in the current case), and g represents the absorption coefficient that was found to be 0.4 for the current conditions based on the experimental results of Liu [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003706_j.wear.2021.203687-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003706_j.wear.2021.203687-Figure1-1.png",
        "caption": "Fig. 1. 3D drawings of worm gear test rig.",
        "texts": [],
        "surrounding_texts": [
            "For several decades, grease has been used in the lubrication of rolling element bearings. For the lubrication of gears, especially worm gears, oil still plays a vital role to this day. However, from recent developments, the advantages of grease over oil in certain gearing applications has become more attractive, especially for the \u2018filled for life\u2019 small size gearboxes at slow speed and light load applications. This is leading to a greater adoption of grease within gearbox lubrication systems. In a paper reported by Fukuyama [1], he stated that over the last few decades, electrical machines such as geared motors have changed from oil to grease lubricant throughout Japan. Hence, small size and slow speed worm gears have become increasingly important in power transmission and gear applications due to the ever more rigorous requirements regarding, for example, performance and weight constraints. Often these slow speed, small size worm gear applications are grease lubricated. Compared to oil lubrication, grease shows a lower load carrying capacity, and less heat removal due to the limited cooling power. Conversely, less effort is expended for the housing seal of grease. In addition to the above, grease lubrication is a better choice to avoid leakage and contamination of finished products, such as required within the food industry. Therefore, gears running at slow speeds are increasingly adopting grease lubrication. Recently, the ISO (ISO 14635-3) published a standard method to investigate the wear behavior of grease lubricated gears in a FZG back to back gear setup. In conjunction to ISO 14635-3, there were a few papers which conducted experimental work on the load carrying capacity of grease lubricated gear utilization using the FZG gear test rig [2\u20134]. To date, there has not been a paper dedicated to the systematic analysis of the wear products, focusing on worn surfaces and wear particle analysis from grease lubricated worm gears. The capture and subsequent analysis of wear particle as a means of assessing the wear state of critical machinery element, whether the system is healthy or deteriorating condition, such as oil lubricated bearings and gears as parts of vital machinery in industrial plants has been reported over the past few decades [5\u20139]. From determinations of wear particle quantity or concentration to evaluate a severity of machinery condition to morphological assessment i.e. overall shape, surface texture, color, edge detail, thickness ratio, aspect ratio for diagnosis of the governing wear mechanisms [10and11]. In addition, a number of research works have reported on the combination use of predictive E-mail address: surapol.r@eng.kmutnb.ac.th. Contents lists available at ScienceDirect Wear journal homepage: http://www.elsevier.com/locate/wear https://doi.org/10.1016/j.wear.2021.203687 Received 17 August 2020; Received in revised form 6 December 2020; Accepted 13 December 2020 Wear xxx (xxxx) xxx maintenance techniques such as vibration in conjunction with wear particle analysis of oil lubricated worm gears [12\u201316]. Even with the abundant amount of research works that have been published in the field of wear particle tribology in the last few decades, there still lacks research work concentrating on the analysis of wear and wear product assessment of grease lubricated worm gear prediction and/or diagnostic in particular. Thus, a series of investigations were recently carried out at the author\u2019s laboratory with the aim of investigating the fundamentals of wear, studying grease lubricated worm gear pair tribosystem. All experiments were performed under controlled test conditions. In this paper, four different worm gear wear mechanisms, namely normal adhesive wear, three body abrasive wear, moisture corrosion wear and S. Raadnui Wear xxx (xxxx) xxx acid attacked wear are assessed utilizing the full factorial Design of Experiments (DOE). The effects of main worm gear wear variables and interaction between wear variables are assessed. The results of wear product analysis were also analyzed with utilization of optical and SEM micrographs."
        ]
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.9-1.png",
        "caption": "Figure 2.9. CAD model of a reactionless planar 2-dof mechanism",
        "texts": [
            " In this case, the distal four-bar linkage is first balanced and then, its mass and inertia are added to the link on which it is attached to perform the balancing of the proximal four-bar linkage. By repeating this procedure, a multi-dof planar mechanism can be obtained simply by stacking the four-bar linkages on each other. An example of a 2- dof mechanism obtained with this approach is shown schematically in Figure 2.8 where the first index of the subscript stands for the number of the link, while the second index stands for the number of the mechanism. Figure 2.9 shows the mechanism synthesised after performing an optimisation of the distribution of the mass. The 2-dof mechanism introduced in the preceding subsection can also be used to synthesise reactionless parallel 3-dof mechanisms. This can be achieved by using the 2-dof mechanism as a leg for the 3-dof mechanism. By connecting three such legs from a fixed base to a common platform, a 3-dof reactionless mechanism can be obtained. However, the mass and inertia of the moving platform also need to be considered in the balancing equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001602_icamimia.2015.7508004-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001602_icamimia.2015.7508004-Figure1-1.png",
        "caption": "Fig. 1. The Parrot AR.Drone2 body reference frame: (\u03c6, \u03b8, \u03c8) denotes the rotation along x, y, z axis, respectively. To ensure a stable flight control system, the system relies on accurate velocity estimation and optical flow reading. In our flight test facility, we have embedded our Vicon motion tracking system with the navigation system of the Parrot AR.Drone, acting as a fake indoor Global Positioning System (GPS).",
        "texts": [],
        "surrounding_texts": [
            "Keywords\u2014Self-tuning Autopilot, Quadcopter Drone, Trajectory Tracking, Fuzzy Inference System.\nI. INTRODUCTION\nROBOTIC aircraft, technically known as Unmanned Aerial Vehicle (UAV), or colloquially as \u201cdrone,\u201d has been widely implemented in various aspects of modern people\u2019s lives in both civilian and military domains, starting from surveillance, law enforcement, wildlife monitoring, industrial diagnostics and inspections (e.g., power line, crack detection on high-rise building and bridge) as well as aerial photography and mapping, to name a few [1], [2]. Unlike helicopters, quadcopter drones can offer many advantages. Firstly, it offers much simplicity in the design and maintenance in the absence of a large propeller and swash plate to adjust the blade during rotation, since it employs a fixed-pitch blade configuration. Secondly, the system is also reasonably safer for human interaction, due to a significant reduction in the diameter of the blade to produce the same amount of thrust [3].\nConsidering its autopilot system, we have implemented a PID control law in our Parrot AR.Drone2 quadcopter drone due to its simplicity [4]. The availability of powerful tuning algorithms (e.g., Ziegler Nichlos, root locus, and pole placement) has made the design process a rather easy task. However, in certain applications, we feel that it is still necessary to further optimise the performance of our fixed-gain PID autopilot (i.e., to minimise the overshoots while achieving shorter settling time) beyond conventional means. In doing so, we are indeed faced by multiple control strategies. Driven by the fact that most UAV researchers have heavily focused on the development of model-based control systems in designing their autopilot systems (e.g., robust and optimal controls (i.e.,\nH2 and H\u221e [5], Linear Quadratic Gaussian (LQG), Linear Quadratic Regulators (LQR) [6] as well as \u03bc-synthesis robust autopilots [7]), we would like to consider a slightly different avenue by proposing an adaptive autopilot by means of fuzzy inference system whose benefits can be depicted as follows.\nFirstly, the design process is based on the intuitive knowledge, which can be a lot more convenient for user-interface due to easy interpretation of the rules, especially from the point-of-view of lay persons (e.g., operators). Fuzzy logic control also offers computational simplicity compared to other model-based autopilots, (e.g., model reference adaptive system (MRAS) [8], [9], or adaptive control based on the MIT rule [10]) which are considered highly-mathematical. Furthermore, its rule-base nature offers simplicity when it comes to checking and validating the consistency and completeness of the system. Fuzzy logic controls can also be regarded as a language of uncertainty due to its ambitiousness, making it suitable to deal with many engineering applications, where the presence of uncertainty is indispensable [11].\nOn the other hand, while model-based control systems may lead to a reasonably good control performance, they may be expensive in terms of computational expense. Also, the requirement of possessing a certain level of mathematical knowledge for UAV operators or practitioners in order to be able to fine-tune and comprehend the performance of the autopilots could limit the practical usefulness of the proposed systems; as for some people, simplicity and practicality matter the most. Furthermore, while some scholars have considered the use of fuzzy logic control (FLC) for controlling quadcopter drones [12]; the implementation of fuzzy self-tuning autopilot",
            "for a Parrot AR.Drone quadcopter has not yet been discussed in the literature.\nHence, our contribution in this paper, addressing current research gaps, can be elaborated as follows. Based on the AR.Drone2 transfer function models derived in [4], as an initial thrust of this research, we design three PD autopilots for controlling both lateral and longitudinal motions of the system. We further optimise the performance of our control systems by implementing a self-tuning autopilots by means of the fuzzy logic system. We also perform a comparative study on the performance of our adaptive autopilot with respect to a fixedgain controller and a fuzzy logic counterpart. This research serves as a preliminary study on the feasibility of our proposed autopilot, before implementing it in practice.\nThe organisation of our paper can be elaborated as follows. In Section 2, we depict the mathematical models of our system in terms of its multi-input multi-output (MIMO) transfer function obtained from experiment-based modelling or system identification technique due to [4]. In Section 3, we depict the framework of our self-tuning autopilots. Furthermore, in Section 4, we investigate the performance of our proposed systems by means of extensive computer simulations. To highlight its benefits, we present a comparative study with respect to the performance of a fixed-gain PD autopilot and a fuzzy logic controller. Finally, Section 5 concludes this paper.\nIn this section, we shall recall the MIMO transfer funtions of Parrot AR.Drone2 derived in [4]. Within our research group, the author in [4] employed a system identification technique to derive the MIMO transfer function model. Being an underactuated system, accompanied with severe cross-coupling and highly non-linear rigid-body dynamics; modelling and control of the quadcopter drones are indeed challenging tasks. The non-linear rigid-body dynamics of the quadcopter drone, derived from first principles, can be found in [4]. It should be pointed out that the linearised models near hover is sufficiently accurate for attitudes less than 30\u25e6 with an accuracy around 90% [4].\nThe block diagram of the control loops of Parrot AR.Drone2 is given in Fig. 2. The motion of the system\ncan be represented by the following state variables x =\n[px p\u0307x py p\u0307y pz p\u0307z \u03c6 \u03c6\u0307 \u03b8 \u03b8\u0307 \u03c8 \u03c8\u0307]T , where (px, py, pz) indicates the coordinate position of the drone (x\u0307, y\u0307, z\u0307) points out linear velocity across (x, y, z) axis, while (\u03c6, \u03b8, \u03c8) indicates the rotational movements (i.e., roll, pitch, and yaw), respectively; and (\u03c6\u0307 \u03b8\u0307 \u03c8\u0307) denotes the angular velocity of the drone.\nThe inner control loop consists of an attitude loop whose control input is given by u = [\u03c9\u0394h \u03c9\u0394\u03c6 \u03c9\u0394\u03b8 \u03c9\u0394\u03c8]. The relations between the input variables and the angular speed of the rotors are given as follows.\n\u0394\u03c9F + \u03c9h = 1/4(\u03c91 + \u03c92 + \u03c93 + \u03c94)\n\u0394\u03c9\u03c6 = 1/2(\u03c92 \u2212 \u03c94) \u0394\u03c9\u03b8 = 1/2(\u03c93 + \u03c91)\n\u0394\u03c9\u03c8 = 1/4(\u03c91 \u2212 \u03c92 + \u03c93 \u2212 \u03c94),\nwhere \u03c9i, i = 1, 2, 3, 4 corresponds to the individual motor of the drone, \u0394\u03c9h denotes the angular speed to maintain hover, while \u0394\u03c9F is the rotation due to vertical movement, \u0394\u03c9\u03c6,\u03b8,\u03c8 denotes motor rotations causing roll, pitch and yaw, respectively. The autopilot for the attitude loop has been carefully designed by the manufacturer. For safety reasons, it is not made adjustable from the end user\u2019s point-of-view. However, we can easily reprogram the outer loop autopilot which runs under the Robotic Operating System (ROS).\nFor 3D position control, we can represent the dynamics of our quadcopter drone with a 3-input, 3-output MIMO transfer function [4]. Firstly, the transfer function of the horizontal velocity vx with respect to \u03b8in is given by:\nvx(s) \u03b8in(s) =\n0.7955\ns2 + 4.1881s+ 7.1429 . (1)\nThe transfer function in (1) has a pair of complex conjugate poles at: s1,2 = \u22122.0941 \u00b1 1.6607i with damping factors of \u03b61,2 = 0.784, natural frequencies of \u03c91,2 = 2.67 rad/s. Secondly, the transfer function of the horizontal velocity vy with respect to \u03c6i is given by:\nvy(s)\n\u03c6in(s) =\n116.24s+ 67.2488\n1000s2 + 982.664s+ 301.338 . (2)\nThe transfer function in (2) has a pair of complex conjugate poles located at s1,2 = \u22120.491\u00b10.245i with \u03b61,2 = 0.895, and \u03c91,2 = 0.549rad/s. Subsequently, the transfer function of the vertical velocity vz with respect to altitude input commands is given by:\nvz(s)\nvzin(s) =\n17.6902s2 + 37.7142s+ 422.62\ns4 + 11.6091s3 + 68.3946s2 + 257.045s+ 688.244 .\n(3)\nThe transfer function in (3) has two pairs of complex conjugate poles located at s1,2 = \u22125.10 \u00b1 2.73i and s3,4 = \u22120.705 \u00b1 4.48i with \u03b61,2 = 0.882 and \u03b63,4 = 0.155 with \u03c91,2 = 5.78, \u03c93,4 = 4.54, respectively.\nIt should be noted that the secondary effects of control in our system is significant. As the AR.Drone pitches, the thrust component in the vertical direction will decrease too, causing the drone to lose its altitude. This loss is significant since it is not compensated by the system. i.e., by increasing all rotor"
        ]
    },
    {
        "image_filename": "designv10_12_0000218_j.cirp.2007.05.069-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000218_j.cirp.2007.05.069-Figure1-1.png",
        "caption": "Figure 1: Schematic representation of simulation testing machine for hot rolling",
        "texts": [
            " In order to measure the coefficient of friction, a new simulation testing machine in the laboratory must be developed instead of the small-scale hot rolling mill, the two disks testing machine and so on. In this paper, the simulation testing machine in the laboratory for measuring the coefficient of friction in hot sheet rolling is developed and the coefficients of friction are measured. Form these coefficients of friction, the lubrication behavior at the interface between roll and workpiece is evaluated and the lubrication mechanism is proposed. Figure 1 shows the schematic representation of the simulation testing machine for the evaluation of the lubrication behavior in hot sheet rolling. This testing machine consists of a main stand, a sub stand, a furnace and a tension device. An infrared image furnace is set between the main and the sub stands. The specification of the simulation testing machine is summarized in Table 1. The rolling speed of the main stand can be continuously changed up to 207m/min using 37kW DC motor, the timing belt and the electrical genetically operated friction clutch",
            " The coefficient of friction can be calculated from P and G using the following equation, = G/(PR) where R is the roll radius. The coefficient of friction is used in order to understand the lubrication behavior at the interface between roll and workpiece. The workpiece material used is SPHC(0.15C-0.6Mn steel). The strips with the dimensions of a thickness of 9mm, a width of 22mm and a long of 2750mm are used. The roll material of the upper roll of the main stand is SKD61 and the diameter is 100mm. The surface roughness of the roll is Ra0.2 m. The strip is set on the table as shows in figure 1. The strip edge is clumped with the chuck part of the tension device and the strip is compressed by the rolls of the sub stand. The strip is heated up to a high temperature using the infrared image furnace. The atmosphere in the infrared image furnace is controlled with Ar gas. The slip rolling simulation test is carried out during a distance of 400mm at a certain rolling reduction ts in the main stand. In the infrared image furnace, 48 infrared image lamps are installed. The temperature in the furnace is controlled by the ES100P digital controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003287_s00170-020-06104-0-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003287_s00170-020-06104-0-Figure2-1.png",
        "caption": "Fig. 2. Three-dimensional finite element model and meshing",
        "texts": [
            " The equivalent volumetric heat source is calculated according to the process parameters: Q \u00bc mL AP DHLt \u00f06\u00de where mL is the heat source coefficient, which is utilized to ensure the correct amount of heat input and is determined through the experiment; A is the laser energy absorptivity of Ti\u20136Al\u20134V alloy, and a value of 0.3 is utilized [10]; P is the laser power (W); D is the laser spot diameter (\u03bcm); H is the hatch spacing (\u03bcm); and Lt is the powder layer thickness (\u03bcm). The interaction time between the heat source and powder material is defined by D/v [24], and then a cooling process between powder layers with a 20 s is carried out according to the actual process. The three-dimensional finite element model and meshing are displayed in Fig. 2. The metal substrate of Ti\u20136Al\u20134V alloy with a dimension of 500 \u00d7 200 \u00d7 25 mm3 was utilized. The dimension of the thin-walled parts is listed in Table 1, comprising length, thickness, and height of the part. The process parameters with the 300 W laser power, 1000 mm/s scanning speed, 0.1 mm hatch spacing, 0.04 mm powder thickness, and 150 \u03bcm spot diameter were utilized in the simulation since they have been proven to manufacture the full-dense Ti\u20136Al\u20134V parts [31]. Both the thin-walled parts and the substrate were fine meshed with the tetrahedral elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000241_j.ijfatigue.2007.02.003-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000241_j.ijfatigue.2007.02.003-Figure5-1.png",
        "caption": "Fig. 5. Finite element model of the contact between raceway and rolling element.",
        "texts": [
            " (15) (Lemaitre [15], Chaboche [18]), which takes into account the proportional impact of the effective plastic deformation p on damage change. The evolution equation to record the damage is given as follows: _D\u00bc r2 eq 2 3 \u00f01\u00fe m\u00de\u00fe3\u00f01 2m\u00de rkk 3req 2 2 S E\u00f01 D\u00de2 _p a\u00f0p\u00de; a\u00f0p\u00de\u00bc 1; if p P pD 0; if p< pD \u00f015\u00de where the effective plastic deformation growth is defined by: _p \u00bc _k 1 D \u00f016\u00de and the initial damage threshold pD is defined by the size of accumulated plastic deformation p, pD = max(p(D = 0)). The numerical model of the rolling contact between the bearing ring raceway and a rolling rotational element (Fig. 5) is designed with the newly developed finite element. On the basis of constitutive equations, the finite element code is generated by means of the AceGen software package and applied (Korelc [23]) in the ELFEN commercial software environment. It enables us to monitor the actual low cycle development of the strain deformation or hardening/softening and material damage growth. The numerical model of the rolling contact comprises the measured geometric and material values of the test bearing ring (Kunc [13])",
            " After having measured the changes in hardness along the cross-section of bearing raceways, we entered the monotonic (E, ry and m), isotropic and kinematic (b, R1, and c\u00f0n\u00de;X \u00f0n\u00de1 ;mn) and damage (S, pD and Dc) material parameters into the damage model (Table 1). These parameters were derived from the results obtained in one-axis monotone and cyclic tests (Kunc [12]). In the discrete-valued model of contact between a raceway model and a rolling element the influence of rolling was not considered (friction in the contact is neglected). To reduce the rolling contact model, geometrical symmetry was taken into account (Fig. 5). In loading the raceway, the oscillating load of the rolling element equals the maximum contact force Fmax = 15.88 kN, which is 2.7 times higher than the actual allowed load according to the criterion of maximum sub-surface stress. As regards the actual thickness of the quenched layer, the rolling contact load is 15 times higher than the allowed value Fdop = 1.04 kN (Kunc [13]) due to insufficient thickness of the hardened layer (only 0.6 mm). The actual rolling contact load is determined for the initial non-plastic state of the bearing raceway and thus the numerical model does not consider the reduction in maximum contact force at the most heavily loaded rolling element occurring as a result of changes or permanent deformation in the bearing raceway"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003247_978-981-15-6475-8-FigureB.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003247_978-981-15-6475-8-FigureB.2-1.png",
        "caption": "Fig. B.2 Motorcycle running by the circular track",
        "texts": [
            " The wheels are of 650 mm diameter and have the property of the disc. A moment of inertia of the wheel is 0.5 kg m2. The moment of inertia of the rotating parts of the engine is 0.1 kg m2. The axis of rotation of the engine crankshaft is parallel to that of the road wheels and the same sense. The gear ratio is 5 to 1. Determine the moment applied to the steering bar by the rider and the angle of heel necessary when the motorcycle is taking a turn over a track of 30.0 m radius at a speed of 60.0 km/h (Fig. B.2). Solution The presented data enable to calculate the torque generated by the centrifugal, Coriolis and common inertial forces and the change in angular momentum of the two wheels and an engine. The components of these equations are the mass moment of inertia, angular velocity and angular precession of the wheels (Table 3.1 of Chap. 3). Appendix B: Applications of Gyroscopic Effects in Engineering 241 The angular velocity of the wheel is \u03c9 = V r = 60000m 3600 s \u00d7 0.65/2m = 51.282 rad/s (B.2.1) where V is the linear velocity of the motorcycle, r is the radius of the wheel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.1-1.png",
        "caption": "Fig. 17.1 Planar four-bar in the two positions existing for a given input angle \u03d5",
        "texts": [
            " The link of length 1 in four-bar 1 is the fixed link. On this link the x, y reference system is fixed. The kinematics is analyzed as follows. The links of lengths 4 and a4 are eliminated and thereby the constraints on the x, y-coordinates of the endpoints P1, P2, P3, P4 : (x2\u2212x1) 2+(y2\u2212 y1) 2\u2212 24 = 0 , (x4\u2212x3) 2+(y4\u2212 y3) 2\u2212a24 = 0 . (4.8) The resulting system of four-bars 1 , 2 , 3 has the degree of freedom three. As independent variables the input angles \u03d51 , \u03d52 , \u03d53 of these four-bars are chosen. Figure 17.1 shows that a four-bar with input angle \u03d5i can assume two positions with output angles \u03c8i1 and \u03c8i2 . Their sines and cosines are determined by (17.12) and (17.11). For four-bar 1 the equations are cos\u03c81k = AC + (\u22121)kB \u221a A2 +B2 \u2212 C2 A2 +B2 , sin\u03c81k = BC \u2212 (\u22121)kA \u221a A2 +B2 \u2212 C2 A2 +B2 \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (k = 1, 2) , (4.9) 4.2 Illustrative Examples 145 A = 2r2( 1 \u2212 r1 cos\u03d51) , B = \u22122r1r2 sin\u03d51 , C = 2r1 1 cos\u03d51 \u2212 (r21 + 21 + r22 \u2212 a21) . } (4.10) The x, y-coordinates of the points A and B in these two positions are expressed in terms of 1 , r2 , cos\u03c81k , sin\u03c81k and of parameters specifying body 1 ",
            " Geometrische Grundlagen, Profilverschiebungen, Toleranzen, Festigkeit. 2nd ed. Springer Berlin, Hei- delberg, New York 16. Roth K (1998) Zahnradtechnik. Evolventenverzahnungen zur Getriebeverbesserung. Evoloid-, Komplement-, Keilschra\u0308g-, konische-, Konus-, Kronenrad-, Torus-, Wa\u0308lzkolbenverzahnungen, Zahnrad-Erzeugungsverfahren. Springer Berlin, Heidelberg 17. Schoenflies A, Gru\u0308bler M (1908) Kinematik. In: [11]:190\u2013278 18. Townsend D P (Ed.) (1992) Dudley\u2019s Gear Handbook. McGraw-Hill, New York Chapter 17 Planar Four-Bar Mechanism The solid lines in Fig. 17.1 are the links of a planar four-bar mechanism or briefly planar four-bar. The link lengths (base or fixed link), r1 (input link), r2 (output link) and a (coupler) are free parameters. They determine, whether individual links can rotate relative to others full cycle (i.e., unlimited) or through an angle smaller than 2\u03c0 . The link lengths also determine the so-called transfer function relating the output angle \u03c8 to the input angle \u03d5 . The time derivative of this function yields the transmission ratio i = \u03d5\u0307/\u03c8\u0307 as function of \u03d5 ",
            " The combination of the four-bar A0ABB0 with the crank mechanism MDB results in a machine in which C is moving periodically back and forth the straight section when the crank is rotating. Point C can be used as guide for the piston of the pump at an oil-well. In this section answers are given to the following questions. Through which angle can two neighboring links of a four-bar rotate relative to each other? Under which condition is this angle unlimited? In this case, one link is said to be fully rotating relative to the other. For every possible angle \u03d5 between two neighboring links there exist two positions of the four-bar (see Fig. 17.1). In some four-bars the transition from one of these positions into the other can be achieved by a continuous motion. In others the transition is possible only by disconnecting and reassembling the four-bar. Under which conditions is disconnection and reassembly necessary? The properties addressed by these questions do not depend on which link is chosen as fixed link and which as input link. Arbitrarily, the angle \u03d5 of the link of length r1 against the 17.1 Grashof Condition 569 link of length is investigated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003388_tpel.2020.2998188-Figure16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003388_tpel.2020.2998188-Figure16-1.png",
        "caption": "Fig. 16. Prototype and parts of MFM-BDRM.",
        "texts": [
            " 0885-8993 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. greatly, and the electromagnetic torque decreases slightly, and the PMs have no demagnetization risk. Therefore, the current phasor can be selected in this range in practical control. To verify the validity of the above analysis, a prototype of MFM-BDRM is designed and manufactured, as shown in Fig. 16. The pole pairs of stator and PM rotor are 4 and 17, respectively, and the number of magnetic blocks is 21. The structure of PM rotor and stator is similar to that of traditional PM machine. It is special to manufacture the modulating ring rotor. A magnetic block holder with zirconium dioxide material is adopted and manufactured to keep enough mechanical strength and to reduce harmonic loss at the same time. The main parameters of MFM-BDRM prototype are listed in Table III. The tested d/q-axis inductances versus currents are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001182_1.4005846-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001182_1.4005846-Figure1-1.png",
        "caption": "Fig. 1 (a) Location of the sensors on the shaft where 1 and 2 stand for first and second sensor, respectively [11]. (b) 3D schematic view of a gear system.",
        "texts": [
            " For example, DET in a periodic system (long diagonal lines and few single points) takes a higher value than in a stochastic system (only single points). Note that the correct results of the RQA depend on proper choice of the embedding parameters (embedding dimension and embedding time delay). Furthermore, a subspace of all measured coordinates can be used. We have tested single-stage transmission gears with angular teeth. The scheme of the gears and the location of the acceleration sensors are shown in Fig. 1. The gears were dismounted and examined carefully after being in operation for a long time. It appeared that the gear system had been damaged; therefore the transmission system was replaced by a new (healthy) one and run again. We have recorded the vibration of acceleration in three directions (x, y, z) with a sampling frequency of 40 kHz for both damaged and healthy systems. The damage to the transmission occurred after 3 h and 15 min of the gear system work. The stop signal was due to the presence of a chips sensor",
            " 134 / 041006-3 Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use differences between the healthy and faulty transmission gears. In the present approach, instead of using a filtering algorithm, we propose to use the simultaneously recorded data from three directions. The obtained data form vectors of the phase space. Thus we focus on comparison of the two different time series for faulty and healthy gears, recorded with a single 3D sensor (1 in Fig. 1). As expected, sensor 2 (Fig. 1) gave similar results (see Table 1). The corresponding time series for the healthy and damaged gears are presented in Fig. 2. Note that the wider distribution of measured points is clearly visible for the faulty gear pair (Fig. 2(b)). In Table 1 one can compare basic statistical parameters including mean values, standard deviation, and kurtosis used for all three directions, i.e., x, y, and z are compared in Table 1. Comparing the statistics obtained, higher mean values for acceleration of healthy gears in y and z direction (H1) can be noted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure7-1.png",
        "caption": "Fig. 7. Force diagram of the force sensing mechanism.",
        "texts": [
            " According to the force characteristics of the flexible spherical joint, it can be deduced that the deformation on the measuring unit caused by the pull/pressure in the axial direction is much larger than the tangential force, bending moment or torque when both ends of the measuring unit are subjected to stress. It can be considered that the deformation of the measuring unit in the axial direction is mainly caused by the pull/pressure in the axial direction. The six-component external force on the moving platform and the axial force of each measuring unit are shown in Fig. 7. The relation between the six-component external force on the moving platform and its six-component displacement can be expressed as follow: F \u00bc KX \u00f018\u00de If the stiffness matrix K is reversible, then X \u00bc CF \u00f019\u00de where K is the overall stiffness matrix of the force sensing mechanism which has been calculated, C \u00bc K 1 is the overall flexibility matrix of the force sensing mechanismwhich is the converse matrix of K . Table 2 Basic structure parameters of the force sensing mechanism. d D a b h rs t b 38 78 p/18 p/12 p/12 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002826_j.mechmachtheory.2019.05.022-Figure11-1.png",
        "caption": "Fig. 11. Velocity of meshing point M .",
        "texts": [
            " Thus \u03c3 = ( cos \u03b1 / cos \u03b1 ) \u03c3 = 1 . 0421 \u03c3 . The F F i Fc Fc Fc F i F i F i maximum root bending stress of the CRC gear is higher by about 4%. The result shows that the CRC gear can remain about the same bending strength as the involute gear. 4.3. Sliding coefficient The relative sliding between tooth profiles can induce wear or even scoring on tooth surfaces, which affects the stability and accuracy of transmission. Usually, sliding coefficient is used to measure the wear between tooth profiles. As depicted in Fig. 11 , one pair of engaged tooth profiles, 1 and 2 mesh at point M at some instant. o 1 and o 2 are centers of gear 1 and gear 2, respectively. Point P is the pitch point. c is the path of contact, whose curvature center at point M is H . The coordinate system S 1 ( o 1 \u00d71 y 1 ), S 2 ( o 2 \u00d72 y 2 ) and S ( oxy ) are the same as the foregoing. \u03c3 1 is the sliding coefficient at point M for 1 , which can be defined as \u03c31 = \u2223\u2223\u2223 d 1 r I d t \u2223\u2223\u2223 \u2212 \u2223\u2223\u2223 d 2 r d t \u2223\u2223\u2223\u2223\u2223 d 1 r I d t \u2223\u2223 (49) Where r I and r \u220f are the vectors of meshing point M relative to the respective centers of gear 1 and gear 2; d 1 r I d t and d 1 r d t are the velocity of M with respect to the rotating coordinate system S 1 and S 2 , respectively",
            " The velocity of meshing point M relative to the fixed coordinate system S , are calculated follows, respectively d r I d t = \u03c9 I \u00d7 r I + d 1 r I d t (50) d r = \u03c9 \u00d7 r + d 2 r (51) d t d t Where d r I d t and d r d t are the velocity of M in S ; \u03c9 I and \u03c9 are the angular velocity vector of 1 and 2 , respectively; | \u03c9 I | = \u03c9 1 , | \u03c9 | = \u03c9 2 ; \u03c9 I \u00d7 r I and \u03c9 \u220f \u00d7 r \u220f are the convected velocity of M . Because the path of contact is just the motion trajectory of meshing point in the fixed coordinate system, d r I d t and d r d t must be tangential to c . The included angle between the line PM and d r I d t is \u03bc, and that between PM and \u03c9 I \u00d7 r I is \u03bb. From Fig. 11 , the magnitude of d r I d t can be obtained as \u2223\u2223\u2223\u2223d r I d t \u2223\u2223\u2223\u2223 = \u2223\u2223\u03c9 I \u00d7 r I \u2223\u2223 cos \u03bb cos \u03bc = \u03c9 1 r 1 cos \u03b1 cos \u03bc = \u03c9 1 r 1 \u2223\u2223\u2223\u2212\u2212\u2192 HM \u2223\u2223\u2223 | l | = \u03c9 2 r 2 HM l (52) As d r I d t is perpendicular to \u03c9 I and \u2212\u2212\u2192 HM , respectively, d r I d t can be viewed as the velocity of M revolving about H . Suppose the angular velocity for the revolving is \u03c9 H . When H is above the pitch point P , l > 0. Otherwise, l < 0. As displayed, \u03c9 H and \u03c9 I are opposite in direction when l > 0, and they have the same direction when l < 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.17-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.17-1.png",
        "caption": "Figure 7.17. Huygens's isochronal pendulum.",
        "texts": [
            " Huygens's Isochronous Clock The isochronous, cycloidal pendulum was invented in 1673 by the Dutch scientist and ingenious clockmaker, Christian Huygens (1629-1695). The idea was used in construction of a pendulum clock to assure that its period would not change with variation s in the amplitude of its swing . Huygens was able to produce a cycloidal motion of the bob by applying the property that the evolute of a cycloid is another cycloid of the same kind as the generating curve. The evolute of the cycloid is the path traced by the center of curvature of the generating cycloid. In Fig. 7.17, the evolute of the cycloid arc 0 S is the similar cycloid arc QS, both are generated by a circle of radius a. As P moves from S toward 0, the center of curvature T of the arc 0 S traces the arc from S to Q. In other words, if a string of length 4a is tied to a fixed point Q that forms the cusp of an inverted cycloidal curve in Fig . 7.17, and the string is pulled over the contour arc QS to point S where the bob is rele ased from rest, the bob will describe the same cycloidal path as as our sliding particle in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003447_s11665-020-05061-9-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003447_s11665-020-05061-9-Figure4-1.png",
        "caption": "Fig. 4 Schematic representation the arrangement of strain-gauge rosettes on part II of the sample",
        "texts": [
            " The relaxed deformations were acquired using a K-RY61-1.5/120R (HBM Italia S.r.l., Italy) Type B three-element rosette connected to a specialized amplifier. The surface of the specimen was manually prepared for the installation of the strain-gauge rosette using 200 and 400 grit SiC paper and wiped from contaminants and dust. The rosette was then bonded using Z70 cold curing superglue with the BCY01 (HBM Italia s.r.l., Italy) accelerator. The rosette cables were then blocked using an X60 (HBM Italia s.r.l., Italy) bicomponent cold curing glue. Figure 4(a) shows a schematic representation of the arrangement of strain-gauge rosettes on the specimen. Then, the sample was glued on a fixed platform and successively the end mill was aligned in the center of the strain-gauge rosette. In Fig. 5(a) and (b), a sample prior and during the measurement phase is illustrated. Incremental hole-drilling tests were carried out by executing a sequence of 24 steps each with a penetration depth of 50 lm; the relaxed deformation was acquired after each increment. The result of the drilling phase is visible in Fig. 5(c). The automatic RSM software (SINT Technology S.r.l, Italy) was used to acquire the deformation for each increment. The acquired deformations were then introduced into the EVAL software (SINT Technology S.r.l, Italy) in order to compute the residual stress profiles. The back-calculation was carried out in order to evaluate the stresses along specific directions. The selected directions (Fig. 4) correspond in detail Journal of Materials Engineering and Performance to the building direction (i.e., z-axis), and the normal to the plane in which the rosette was applied (i.e., x-axis). As the selected directions are not necessarily principal directions, the outputs of the stress computation consist of two normal stresses (acting parallel to the two selected directions, respectively) and a shear stress sxz (acting on the plane defined by the two selected directions). Vickers microhardness values were evaluated on the XZ cross section by means of a Leica VMHT indenter (UHL Technische Mikroskopie GmbH, Germany)",
            " Because of these reasons, the effect of the distance from the substrate on the residual stress trends will be reported only for C-0090-sample. The lower and more stable residual stress values of 0 -90 samples can be attributed to the repeatable track length. The 0 -60 strategy is in fact characterized by tracks having very different lengths and therefore different cooling conditions (Ref 32). Figure 11 depicts the residual stresses of the C-0090-AB sample measured at two different heights, which are located at z = 4 mm and z = 16 mm from the substrate, according to the scheme of Fig. 4. The components of rx recorded at different height are reported and compared in Fig. 11(a). In the upper position, near to the surface a tensile state occurred, in all the depth the stress ranges between 30 and 230 MPa and a slightly oscillatory trend is visible. At the lower height of the C0090-AB sample, near to the substrate, the stress exhibited a high positive value of about 640 MPa. Then, the stress abruptly decreases, and a compressive stress of 300 MPa was measured at a depth of about 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.19-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.19-1.png",
        "caption": "Fig. 3.19 Classic tractor ABS schematic [FHWA-MC 1998].",
        "texts": [
            " Benefits: Increases steering and vehicle stability during braking;reduces possibility of jacknifing and trailer swing; reduces wheel-tyre flat spotting; If the electrical/electronic system fails, the ABS is shut off, returning the vehicle to normal braking; on some systems, the ABS is only shut off at the affected wheels; An optional feature that controls excessive wheel spin during acceleration, reducing the possibility of power skids, spins or jacknifes; Built-in system that makes maintenance checks quick and easy; ABS are compatible with automotive industry standard hand-held and computer-based diagnostic tools; blink codes and other diagnostic schemes may also be used for troubleshooting, if other tools are not available; Informs the driver and technician that an ABS fault has occurred; the warning lamp may also transmit blink code information; it does not signal all possible faults. This section describes the design and operation of ABS components. When the readers complete this section, they should understand the purpose and function of all major ABS parts including the ECU, the modulator\u2019s fluidical valve, the wheel angular-velocity sensor, ABS malfunction/ indicator lamp, ABS diagnostic components, and traction control. Modern ABSs all feature the following major components, shown in Figure 3.19, for s classic anti-lock BBW AWB dispulsion mechatronic control system [FHWA-MC 1998]: Electronic control unit (ECU); Modulator fluidic valves; Wheel angular-velocity sensors (pickup and exciter); ABS malfunction indicator lamps; Diagnostics. 3.5 Anti-Lock EFMB 467 Electronic Control Unit (ECU) - The ECU processes all ABS information and signal functions. It receives and interprets voltage pulses generated by the sensor pickup as the exciter teeth pass by and uses this information to determine [FHWA-MC 1998]: Impending wheel lock-up; When/how to activate the ABS modulator\u2019s fluidic valves"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001151_00207179.2013.868610-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001151_00207179.2013.868610-Figure1-1.png",
        "caption": "Figure 1. Two-link robot manipulator model.",
        "texts": [
            " (25) Thus, it can be obviously found that the states can reach and thereafter stay on the manifold s = 0 under control law (8). Step 2. Stability analysis of pseudospectral method After reaching the manifold s = 0, the state equation (3) degenerates into Equation (9). According to the convergence of the Chebyshev pseudospectral method in Lemma 3.6 , we can obtain that the control law u\u0303 = C\u22121 1 h stabilises the control system (9). Thereby, the stability of system (3) after states reach the sliding manifold is proved. Figure 1 shows two-link rigid RMs, where q1 and q2 are angular positions, m1 and m2 are the two joint masses and r1 and r2 are the arm lengths. The dynamic equation of RM model in Figure 1 is given by [ a11(q2) a12(q2) a21(q2) a22(q2) ] [ q\u03081 q\u03082 ] + [\u2212b12(q2)q\u03072 1 \u2212 2b12(q2)q\u03071q\u03072 b12(q2)q\u03072 1 ] + [ c1(q1, q2)g c2(q1, q2)g ] = [ u1 u2 ] + [ d1 d2 ] , (26) where a11(q2) = (m1 + m2)r2 1 + m2r 2 2 + 2m2r1r2cosq2 + J1, a12(q2) = a21(q2) = m2r 2 2 + m2r1r2cosq2, a22(q2) = m2r 2 2 + J2, b12(q2) = m2r1r2sinq2, c1(q1, q2) = (m1 + m2)r1cosq2 + m2r2cos(q1 + q2), c2(q1, q2) = m2r2cos(q1 + q2). The physical parameters under consideration are listed as follows: r1 = 1m, r2 = 0.8m, J1 = 5kg m, J2 = 5kg m, m1 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000700_s11044-009-9145-7-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000700_s11044-009-9145-7-Figure3-1.png",
        "caption": "Fig. 3 A reachable workspace W1 of the 2(PS + HPS + CPS) serial\u2013parallel manipulator: (a) the isometric view, (b) the top view, (c) the upper view, (d) the front view",
        "texts": [
            " Thus, the active/constrained forces (Fai1,Ff i1) of the upper manipulator and the active/constrained forces (Fai,Ff i) of the lower manipulator can be solved from (20) and (28) as follows: \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 Fa11 Fa21 Fa31 Ff 11 Ff 21 Ff 31 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u2212( JT 1 )\u22121 JT R [ F 1 T 1 ] , \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 Fa1 Fa2 Fa3 Ff 1 Ff 2 Ff 3 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u2212( JT )\u22121 G [ F 1 T 1 ] . (28) A reachable workspace W1 of the 2(SP + SPR + SPU) manipulator is defined as all the positions that can be reached by the central point of the platform m1 [24]. When given the maximum extension rmax and the minimum extension rmin of active legs ri (i = 1,2,3) for the lower manipulator, and given the maximum extension rmax 1 and the minimum extension rmin 1 of active legs ri1 for the upper manipulator, W1 can be constructed by a simulation mechanism of this manipulator [13] (see Fig. 3). In fact, W1 is formed by 3 upper surfaces Sun (n = 1,2,3),15 side surfaces Scn1 (n1 = 1,2, . . . ,15), and 12 lower surfaces Sln2 (n2 = 1,2, . . . ,12). Set L = 120, Li1 = l = 80, li1 = 60, rmin = 110, rmax = 160, rmin 1 = 90, rmax 1 = 130, the increment of active leg \u03b4r = 5 cm, \u03b8 = 60\u25e6, n0 = (rmax \u2212 rmin)/\u03b4r, n01 = (rmax 1 \u2212 rmin 1)/\u03b4r . When given 4 of ri and ri1 the suitable limited values of (rmin, rmax, rmin 1, rmax 1), and varying the remaining 2 of ri from rmin to rmax and ri1 from rmin 1 to rmax 1, each of (Sun, Scn1, Sln2) can be constructed by processes (see Table 1)",
            " When given ri and ri1 (i = 1,2,3), the 4 groups of forward displacement solutions of the lower manipulator and the 4 groups of forward displacement solutions of the upper manipulator can be solved by using the above relevant analytic formulae. Then, the 4 \u00d7 4 = 16 forward displacement solutions of the 2(SP + SPR + SPU) serial\u2013parallel manipulator can be solved. 372 Y. Lu et al. In order to verify analytic solutions and determine the acceptable analytic solutions from multisolutions, the simulation mechanism of the 2(SP + SPR + SPU) manipulator (see Fig. 3(a)) is applied for solving the forward displacement solutions when given ri (i = 1,2,3) and ri1. By comparing, only one of the 16 groups of analytic solutions coincides with the simulation solution. Thus, the acceptable analytic solutions can be determined from multisolutions. In the inverse kinematic analysis, when given (Zo,\u03b1,\u03bb,c Zo1, c \u03b11, c \u03bb1), see Fig. 4(a)\u2013 (b), the extension, velocity, acceleration of active legs ri and ri1 (i = 1,2,3) are solved, see Fig. 4(c)\u2013(e). In the forward kinematic analysis, when given the extension, velocity of active legs ri and ri1 (i = 1,2,3), see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001690_j.mechmachtheory.2015.05.013-Figure2-1.png",
        "caption": "Fig. 2. Skew angle of imaginary crown gear.",
        "texts": [
            " \u03c1c and \u03c1s are the radii of curvatures of circular arcs in xz and xy planes, respectively. \u03c1c and \u03c1s have influence on \u0394c and \u0394s, respectively. The following equations yield considering the relations between \u03c1c, \u0394c, Mn, and \u03b1 in xz, and between \u03c1s, \u0394s, and b in xy planes, respectively [19]: \u03c1c \u00bc \u0394c2 \u00fe Mn . cos\u03b1 2 2\u0394c \u03c1s \u00bc \u0394s2 \u00fe b2 4 2\u0394s : \u00f02\u00de Since skew bevel gears have teeth that are straight and oblique, the skew bevel gears have the skew angle. Therefore, the imaginary crown gear also has the skew angle that is defined as \u03b2 as shown in Fig. 2. The tooth surface of the imaginary crown gear is expressed in O-xyz using \u03c1c and \u03c1s: X u; \u03b8\u00f0 \u00de \u00bc \u2212\u03c1c cos\u03b8\u2212 cos\u03b1\u00f0 \u00de\u2212\u03c1s 1\u2212 cosu\u00f0 \u00de \u00fe \u03c1s sinu tan\u03b2 \u03c1s sinu\u00fe Rm \u03c1c sin\u03b1\u2212 sin\u03b8\u00f0 \u00de 2 4 3 5 : \u00f03\u00de The unit normal of X is expressed by N. X expresses the equation of the tooth surface of the imaginary crown gear. The imaginary crown gear is rotated about the z axis by angle\u03c8 and generates the tooth surface of the skew bevel gear. This rotation angle,\u03c8, of the crown gear, is the generating angle.When the generating angle is \u03c8, X and N are rewritten as X\u03c8 and N\u03c8 in O-xsyszs assuming that the coordinate system O-xyz is rotated about the z axis by \u03c8 in the coordinate system O-xsyszs fixed in space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.109-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.109-1.png",
        "caption": "Fig. 2.109 Positioning of the BEV \u2013 EV1 chassis and propulsion systems [General Motors; CHESTNUT 2001].",
        "texts": [],
        "surrounding_texts": [
            "An E-M transmission arrangement has been used in almost every transportation application that ECE or ICE-powered automotive vehicles have used, including light cars and vans to large city buses. Most BEVs use the body and mechanical parts of commercially available ECE- or ICE-powered automotive vehicles (see Figs 2.108 and 2.109). The major BEV components are M-M transmission arrangement that consists of the M-M transmission, differential, power steering, etc.; E-M/M-E motor/generator, or alternatively SM&GWs with a brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator reluctance and/or IPM magneto-electrically-excited wheel-hub motors/generators; Automotive Mechatronics 290 The location of the major components depends upon the BEV type and construction. Several other E-M transmission arrangements, used by BEVs are currently available. BEV technology is being developed at a fast pace and several new types are currently being tested. In some BEVs, the major components identified in Figure 2.107 are combined. Some of the components, such as the protection system and auxiliary supply system, are similar to those used in standard ECE- and/or ICE-powered automotive vehicles. For instance, an alternative E-M transmission arrangement features two CH-E/E-CH storage battery modules for better mass distribution and two interior permanent magnet (IPM) E-M/M-E motors/generators that are mounted directly on the rear axle shafts, is shown in Figure 2.110 [STEPLER 1991]. 2.7 E-M DBW AWD Propulsion Mechatronic Control Systems 291 Powering the BEV\u2019s E-M motors are maintenance-free sodium-nickel chloride storage battery packs. Accounting for some 360 kg (800 lb) of the BEV\u2019s total mass of 1,500 kg (total weight of 3,349 lb), the CH-E/E-CH storage battery can be recharged in 12 h. An evacuated double-wall steel box provides thermal insulation for the storage battery\u2019s solid electrolytes and molten electrolyte of sodium aluminium chloride. The CH-E/E-CH storage battery operates at a temperature of 584 K (311 oC; 518 oF) to 670 K (397 oC; 662 oF). The BEV\u2019s interior may be heated by using CH-E/E-CH storage battery temperature [STEPLER 1991]"
        ]
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure15.43-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure15.43-1.png",
        "caption": "Fig. 15.43 Rectangle in a position \u03d5 with instantaneous center of rotation P and with P0 on the edge A\u2032B\u2032",
        "texts": [
            "42a shows that the curve E5(b) in phase 5 is the line y \u2261 b for x \u2265 0 . The curve E1(b) is the reflection of E5(b) in g . It is the line parallel to g1 at the distance b . Its equation is x sin\u03b1\u2212 y cos\u03b1\u2212 b = 0 (x cos\u03b1+ y sin\u03b1 \u2265 0) . (15.160) From this it follows that the domain \u03935 is the first quadrant of the x, y-plane, and that \u03931 is the reflection of \u03935 on g . Furthermore, the symmetry axis g is the boundary G15 between the domains \u0393 \u2032 1 and \u0393 \u2032 5 . Next, a parametric equation is given for the curve E3(b) in phase 3 of the motion. Figure 15.43 shows a rectangle of width b in phase 3 . The instantaneous center of rotation P (or pole P ) is the intersection of the 516 15 Plane Motion normals to g1 at A and to g2 at B . It has the coordinates xP = sin\u03d5/ sin\u03b1 and yP = cos\u03d5/ sin\u03b1 . Its distance from 0 is 1/ sin\u03b1 independent of \u03d5 . Thus, the pole is moving on the circle with radius 1/ sin\u03b1 about 0 . Let n(\u03d5) be the normal to AB through P . In the figure the quantities \u03d5 and b and the location of P0 are chosen such that the following conditions are satisfied: a) P0 lies on A\u2032B\u2032 b) P0 lies on n(\u03d5) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001568_0954410014558692-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001568_0954410014558692-Figure1-1.png",
        "caption": "Figure 1. Depiction of a quad-rotor.",
        "texts": [
            " The skew-symmetric matrix S\u00f0a\u00de 2 R 3 3 for any a \u00bc \u00bda1, a2, a3 T 2 R 3 is S\u00f0a\u00de \u00bc 0 a3 a2 a3 0 a1 a2 a1 0 2 64 3 75 It satisfies aTS\u00f0a\u00de \u00bc 0, and S\u00f0a\u00deb \u00bc S\u00f0b\u00dea, bTS\u00f0a\u00deb \u00bc 0 for any b 2 R 3. In denotes n n unit matrix. tanh\u00f0a\u00de \u00bc \u00bdtanh\u00f0a1\u00de, tanh\u00f0a2\u00de, tanh\u00f0a3\u00de T for any a 2 R 3, where the hyperbolic tangent function is tanh\u00f0ai\u00de \u00bc eai e ai eai\u00fee ai , \u00f0i \u00bc 1, 2, 3\u00de and it satisfies j tanh\u00f0ai\u00dej5 1, tanh\u00f0ai\u00de \u00bc 0 if and only if ai\u00bc 0. Two reference frames are adopted for mathematical modeling as shown in Figure 1. The earth reference frame F i: this frame is fixed to the earth, with the origin Oi locating at a fix point on the ground. The xi axis points to the north and the zi axis points upright. The yi axis completes a right hand orthogonal frame. The body reference frame F b: this frame is fixed to the quad-rotor body. The origin Ob locates at c.g. (center of gravity) of the quad-rotor body, with the xb axis pointing to the head of the quad-rotor. The zb axis is perpendicular to the xb axis and points upright"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003733_j.mechmachtheory.2021.104320-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003733_j.mechmachtheory.2021.104320-Figure13-1.png",
        "caption": "Fig. 13. Free body diagram of a gear considering a single teeth pair and the coordinate system (Positive moment from z to x = \u03be \u00b7 p bt ).",
        "texts": [
            " Nomenclature Quantity Description (Unit) \u03b1i A,E (\u03be , i ) partial lever arm (m) \u03b1 f minimum load ratio (contact line) \u03b1k minimum stiffness ratio (path of contact) \u03b1L minimum stiffness ratio (contact line) \u03b1n normal pressure angle (rad) \u03b2 helix angle (rad) \u03b2b base helix angle; \u2220 EE\u2019H , see Figure 1 (rad) \u03b4(\u03b7) normalised path of contact coordinate shift \u03b4b transmission error (path of contact) (m) i s (\u03be , i ) lever arm balance (m) i h A,E (\u03be , i ) lever arm balance (m) \u03b7 normalised coordinate along a contact line \u03b3 i A,E (\u03be , i ) fraction of the length of a contact line \u03bb normalised distance AC p bt , Figures 5 and 16 F i s,h (\u03be , i ) load sharing ratio with friction R load sharing ratio at \u03be = 0 \u03bc constant average gear friction coefficient T 1 A see Figure 13 (m) T 2 E see Figure 13 (m) T 1 , 2 L i (\u03be , i ) distance to contact line (m) T 1 , 2 L A,E i (\u03be , i ) distance to point of equivalent load (m) \u03c6i (\u03be , i ) normalised path of contact coordinate shift \u03c6i L (\u03be , i ) normalised contact line coordinate shift \u03c8 parameter related to the c f h factor A start point of meshing C pitch point E end point of meshing O 1 , 2 axis of rotation; centre of a circle T 1 , 2 contact point of tangent (mesh lines) at base circle \u03b81 , 2 angular displacement ( rad) \u03b5 total contact ratio, \u03b5 = \u03b5 \u03b1 + \u03b5 \u03b1 \u03b5 L normalised maximum contact line length \u03b5 \u03b1 transverse contact ratio, \u03b5 \u03b1 = AE p bt , see Figure 1 \u03b5 \u03b2 overlap ratio, \u03b5 \u03b2 = EH p bt , see Figure 1 \u03be normalised coordinate along the path of contact a centre distance (m) b facewidth (m) c \u2032 single stiffness, ISO 6336 method B ( N m \u22122 ) c f f normalised parabolic line load correction factor c f s,h stiffness correction factor CF i A,E (\u03be , i ) normalised position of load application centre f i (\u03be , \u03b7, i ) normalised parabolic line load distribution F i a A,E (\u03be , i ) friction force (N) F i a (\u03be , i ) friction force (N) F N s,h tooth normal force, transverse plane (N) F i N s,h (\u03be , i ) force normal to teeth pair i, transverse plane (N) F P i A,E (\u03be , i ) line load fraction H(",
            " ) Heaviside function i teeth pair shift (integer) k Heaviside function steepness k i h (\u03be , \u03b7, i ) normalised single teeth pair slice mesh stiffness k i L s,h (\u03be , \u03b7, i ) normalised line stiffness distribution k i s (\u03be , i ) normalised single teeth pair slice mesh stiffness K ISO max maximum single pair stiffness, equation (27) (N m \u22121 ) kl i s,h (\u03be , i ) normalised single teeth pair mesh stiffness Kl u s,h (\u03be , i ) unbounded normalised gear mesh stiffness Kl s,h (\u03be ) normalised gear mesh stiffness M i 1 , 2 (\u03be ) single teeth pair torque (N m) m n normal module (m) M 1 , 2 torque (N m) p bt transverse pitch on base cylinder (m) P V ZP s,h power loss along the path of contact (W) r a 1 , 2 tip radius, O 1 B , O 2 A , see Figure 13 (m) r b1 , 2 base radius, O 1 , 2 T 1 , 2 , see Figure 13 (m) S i f (\u03be , i ) switching function T V ZP s,h (\u03be ) gear friction torque (N m) T i V ZP s,h (\u03be , i ) total single teeth pair friction torque (N m) T l s,h (\u03be ) static trim function Ul i \u221e (\u03be , i ) normalised complementary contact line length Ul i m (\u03be , i ) normalised simplified contact line length Ul i \u03b3 (\u03be , i ) normalised contact line length in CEE\u2019C\u2019 UL i s,h (\u03be , i ) contact line length (m) Ul i s,h (\u03be , i ) normalised contact line length x 1 , 2 profile shift coefficient z 1 , 2 number of teeth Superscript \u02d9 time derivative \u2019 other face of the gear i teeth pair number (integer) Subscript 1 driving body 2 driving body \u03c6L related to \u03c6i L (\u03be , i ) A points in AA\u2019C\u2019C, see Figure 16 E points in CEE\u2019C\u2019, see Figure 16 f related to parabolic line load sharing h helical gear s spur gear the middle of the 20th century [19\u201325] ",
            " Assume that the transmission error due to gear mesh stiffness at the driven body translated to the path of contact is \u03b4b (\u03be ) , a deflection in the direction of \u03be . The gear mesh stiffness is then for a linear system, by definition, given by Eq. (36) . F N s,h is the total normal force supported by the meshing teeth in the direction of the intersection between the plane perpendicular to the axis of rotation and the plane of action, \u03be , Eq. (37) . In Eq. (37) , r b2 is the base radius of the driven body, ( r b2 = O 2 T 2 in Fig. 13 ), and M 2 is the torque imposed at the driven body. K ISO max \u00b7 Kl s,h (\u03be ) = F N s,h \u00b7 1 \u03b4b (36) F N s,h = M 2 r b2 (37) Considering the same deflection, \u03b4b (\u03be ) , for all the meshing teeth pairs in contact at a given \u03be and from the definition of stiffness, the total force supported by an individual meshing teeth pair along the path of contact, F i N s,h (\u03be , i ) , is given by Eq. (38) . In Eq. (38) , kl i s,h , is the normalised single teeth pair mesh stiffness, Eqs. (14) and (32) . F i N s,h (\u03be , i ) = \u03b4b \u00b7 K ISO max \u00b7 kl i s,h (38) Combining Eqs",
            " M i 2 (\u03be , i ) M 2 = F i N s,h \u00b7 r b2 floor ( \u03b5 ) \u2211 i = \u2212floor ( \u03b5 ) ( F i N s,h \u00b7 r b2 ) \u21d4 M i 2 (\u03be , i ) = M 2 \u00b7 F i N s,h floor ( \u03b5 ) \u2211 i = \u2212floor ( \u03b5 ) F i N s,h (41) The load supported by all the meshing teeth pairs in action must balance the driven torque, Eq. (42) . F N s,h = M 2 r b2 = floor ( \u03b5 ) \u2211 i = \u2212floor ( \u03b5 ) F i N s,h (42) Combining Eqs. (39) , (41) and (42) the fraction of the torque that is supported by each teeth pair can be calculated according to Eq. (43) . M i 2 (\u03be , i ) = M 2 \u00b7 kl i s,h Kl u s,h \u00b7 T l s,h (43) Fig. 13 is the free body diagram of a gear considering just a single meshing teeth pair. In order to understand the effect of the friction forces the driving and driven bodies must be separated. Fig. 14 a is the free body diagram of the driven body. From this diagram a load balance equation of the driven body can be established, Eq. (44) . M i 2 + F i a \u00b7 T 2 L i \u2212 F i N s \u00b7 r b2 = 0 (44) In Fig. 14 a, the friction force F i a is represented as if the meshing process was between A and C, see Fig. 13 . At the moment that the contact line passes through C, the friction force F i a reverses and remains like that between C and E. In order to account for the reversal of the friction force at the pitch line, CC\u2019, the switching function S i f (\u03be , i ) was introduced, Eq. (45) , see Fig. 15 . In S i f (\u03be , i ) , \u03bb is the normalised distance AC ( Figs. 5 and 13 ), as defined by Eq. (46) . S i f (\u03be , i ) = 1 \u2212 2 \u00b7 H ( \u03be \u2212 \u03bb \u2212 i ) (45) \u03bb = AC p bt (46) Assuming a constant average friction coefficient and a Coulomb friction model, where the friction coefficient is defined as the ratio between the friction and normal forces, the friction force F i a (\u03be , i ) accounting for the reversal of direction at CC\u2019 is written according to Eq",
            " (44) , the normal force, F i N s (\u03be , i ) , is obtained, Eq. (48) . F i N s (\u03be , i ) = M i 2 r b2 \u2212 \u03bc \u00b7 S i f \u00b7 T 2 L i (48) Consider Fig. 14 b, the free body diagram of the driving body. Since the friction, F i a (\u03be , i ) , and normal, F i N s (\u03be , i ) , forces result from the separation of the driving and driven bodies, Eqs. (47) and (48) can be substituted in the torque balance equation of the driving body, Eq. (49) . In Eq. (49) , rb 1 is the base radius of the driven body, r b1 = O 1 T 1 , see Fig. 13 . Simplifying, the driving torque considering friction forces is obtained, Eq. (50) . M i 1 + F i a \u00b7 T 1 L i \u2212 F i N s \u00b7 r b1 = 0 (49) M i 1 (\u03be , i ) = M i 2 \u00b7 r b1 \u2212 \u03bc \u00b7 S i f \u00b7 T 1 L i r b2 \u2212 \u03bc \u00b7 S i f \u00b7 T 2 L i (50) If the torque at the driven body is imposed, a common situation, the total torque at the driving body is the theoretical frictionless driving torque plus a friction term, T i V ZP s (\u03be , i ) , Eq. (51) . M i 1 (\u03be , i ) = M i 2 \u00b7 r b1 r b2 + T i V ZP s (51) Matching the right hand side of Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001513_tec.2014.2353133-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001513_tec.2014.2353133-Figure11-1.png",
        "caption": "Fig. 11. Electromagnetic finite-element model of an axial flux PMSM.",
        "texts": [
            " As would be expected, as v\u2217 decreases, magnet losses increase because the harmonic distortion of the current waveform increases. The increase in losses from v\u2217 = 0.8 to 0.5 is 32%. Apart from the loss in efficiency this is an important characterization for an electrical machine of this type as, assuming a linear thermal system, this would lead to a steady-state temperature rise increase of 32% in the magnets. IV. VALIDATION OF FEA In order to show the usefulness of the experimental method it has been used to validate a series of transient FEA, which have been used to gain a deeper understanding of magnet losses. Fig. 11 shows the finite-element model with components and main boundary conditions identified. The commercial code Ansoft Maxwell 14.0.2 has been used to perform the analyses. Ansoft uses the T-\u03a9 finite-element formulation to solve 3-D transient electromagnetic problems. A detailed description of this formulation is given in [17]. Magnet losses are calculated at each time step from q = 1 \u03c3 \u222b V J2dV (17) where q is the predicted magnet loss (W), \u03c3 is the conductivity of the magnet material (S/m), and J is the current density (A/m3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure6-1.png",
        "caption": "Fig. 6. Pressure distribution in the oil film for Dc = 0.125 mm sliding base setting change.",
        "texts": [
            " The influence of sliding base setting (c) on EHD lubrication characteristics is shown in Fig. 5. Several observations can be made: a small change in sliding base setting causes sharp increase in the maximum oil pressure and a moderate improvement of the EHD load carrying capacity. The change of the friction factor is quite opposite than that of the EHD load carrying capacity: with an increase in W the friction factor is reduced, and vise versa. Finally, the change in sliding base setting appears to have very little influence on maximum oil temperature. From Fig. 6, it can be seen that a sliding base setting change of Dc = 0.125 mm causes an increase in maximum oil pressure of 21% and 7% in EHD load carrying capacity, and also a reduction in friction factor of 4%. The influence of basic radial setting (e) is similar to that for sliding base setting (Figs. 7\u20139), but there is a significant drop in maximum oil pressure and EHD load carrying capacity for negative values of De, followed by a significant increase in power losses. Therefore, such a change of basic radial setting worsens the conditions of EHD lubrication and it should be avoided"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001514_s00034-013-9572-9-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001514_s00034-013-9572-9-Figure1-1.png",
        "caption": "Fig. 1 Configuration chart of X-33 [35]",
        "texts": [
            " 4, which shows its effectiveness in dealing with modeling uncertainties, external disturbances, and actuators faults. Simulation results are provided in Sect. 5 to demonstrate the superiorities of the method over some existing work. Finally, the paper is concluded in Sect. 6. 2 Modeling of Near Space Vehicles 2.1 Attitude Motion This section briefly describes the dynamic six degrees freedom of near space vehicles. In this paper, we consider six equations of the attitude angle \u03b3 and attitude angular rate \u03c9. In the work of [2] and [3], the dynamic equations of re-entry vehicles by X33 as shown in Fig. 1 are described. Attitude motion on re-entry launch vehicle is described as follows: { J \u03c9\u0307 = \u2212\u03a9J\u03c9 + u \u03b3\u0307 = R(\u00b7)\u03c9 (1) where J \u2208 R3\u00d73 is the symmetric, positive definite moment of inertia tensor, \u03c9 = [p,q, r]T is the angular rate (roll, pitch, and yaw rate, respectively) vector, u \u2208 R3\u00d71 is the control torque vector. The skew symmetric matrix \u03a9 is given by \u03a9 = \u239b \u239d 0 \u2212\u03c93 \u03c92 \u03c93 0 \u2212\u03c91 \u2212\u03c92 \u03c91 0 \u239e \u23a0 (2) The angle vector \u03b3 is defined for re-entry modes in the following. In the re-entry mode [12], R(\u00b7) is defined as follows: R(\u00b7) = \u239b \u239dcos\u03b1 0 sin\u03b1 sin\u03b1 0 \u2212 cos\u03b1 0 1 0 \u239e \u23a0 (3) \u03b3 = [\u03c6,\u03b2,\u03b1]T and \u03c6,\u03b2,\u03b1 are the bank, sideslip, and the attack angles, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003301_s11085-020-10005-8-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003301_s11085-020-10005-8-Figure10-1.png",
        "caption": "Fig. 10 SEM\u2013EDS analyzes and elementary mapping of SLM plate after exposure for 100\u00a0h at 900\u00a0\u00b0C in dry air",
        "texts": [
            " SEM\u2013EDS concentration profiles were carried out across the metal-oxide interface of the two samples in order to quantify the as-highlighted chromium depletion. They are presented in 1 3 Figs.\u00a09 and 10 and show that in the case of wrought samples (Fig.\u00a09), the Cr content at the outer part of the metal decreases below 12 wt% both under the continuous layer and the nodules. The value is even lower than 10 wt% in the first 3\u00a0 \u00b5m of depth. In contrast, the SLM plates exhibit small Cr depletion of the substrate in the region situated just below the oxide layer. As shown in Fig.\u00a010, Cr content in the substrate never drops below 12 wt%, regardless of the depth and the location under the layer. Figure\u00a011 shows the evolution of Vickers microhardness with the ageing temperature. The microhardness values corresponding to raw samples are equally indicated 541 1 3 Oxidation of Metals (2020) 94:527\u2013548 and show that SLM plates are harder (225 \u00b1 6 HV) than wrought samples (190 \u00b1 6 HV). Moreover, both raw samples have higher hardness than reference value of AISI 316L (155 HV [40]). Oxidation at temperatures between 700 and 900\u00a0\u00b0C leads to small decrease of hardness for wrought samples, but any change was not noticed for SLM plates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000774_bit.260170605-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000774_bit.260170605-Figure2-1.png",
        "caption": "Fig. 2. pH dependence curves for different Amberlite resins-invertase complexes. Sodium acetate buffer 0.01M; pH adjusted either with sodium hydroxide or with hydrochloric acid solutions; 22\u00b0C. Free invertme( 0). Invertase-resins complexes: IRA 93 (+), IRA 900 (A), IRA 45 (O), IRA 410 (m), 200 (O), IRA 50 (A), IRA 120 (0).",
        "texts": [
            " Then desorption of adsorbed invertase from macroreticular resins was measured as a function of the molarity and pH of washing solutions. Table I1 shows the enzymatic activities remaining after washing. The washing was continued until desorption ceased, as measured by adsorbance at 275 nm. These results show that protein desorption from an ionic support is significant. Similar observations were made by Lilly et al.12 However desorption seemed to be more dependent on salt concentration than on pH. pH dependence of the adsorbed invertase activity The results, indicated in Figure 2, show a shift of the optimum pH of the adsorbed enzyme in comparison to that of the free enzyme. TABLE I1 Invertase Desorption as a Function of Molarity and pH; Temperature 22\u00b0C- Resin Amberlite type IRA 93 IRA 900 200 Sodium acetate b d e r 0.1 1 0.1 1 0.1 1 molarity PH 3 5.9 2.4 6.3 3 5.9 2.4 6.3 3 5.8 2.4 6 .3 Activity remainmg 85 85 55 43 90 84 73 63 92 93 75 64 on the resin (%I a Conservation of activity is evaluated by comparison with activity measured before desorption. Similar results were already obtained by Kstchalski et al.13 and Suzuki et al.3 This shift may be due to a pH difference between the solution and the close proximity of the resins. Figure 2 also shows that optimum pH\u2019s of cationic resin-invertase complexes are shifted toward more basic pH\u2019s (0.5 to 1 unit) ; on the other hand, the pH optimum of anionic resin-invertase complexes is shifted towards a more acidic pH (0.5 to 1.5 units). Goldstein et al.I4 have shown that it is due to a different distribution of hydrogen and hydroxyl ions between the \u201cionic phase\u201d (on which the enzyme is immobilized) and This phenomenon is well known. the external solution. This phenomenon is also responsible for the modifications of the pH dependence curves"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.165-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.165-1.png",
        "caption": "Fig. 2.165 Principle layout of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and high-pressure gaseous hydrogen tank [Toyota\u2019s FCHV-4; KAWATSU 2000].",
        "texts": [],
        "surrounding_texts": [
            "As was previously mentioned, in principle the FC is an exceptionally uncontaminated energy conversion CH-E generator that may generate electrical energy using hydrogen and oxygen for fuel and create water as its exhaust gas emission. On the other hand, when functional applications, predominantly automotive ones, are estimated, the dilemma occurs of how to keep the necessary hydrogen onboard a HEV. Two categories of FC HE transmission arrangements have been built-up for the HE 2BW DBW propulsion mechatronic control system. The first category keeps hydrogen directly onboard, while the second category reforms hydrocarbon fuel onboard the HEV. A principle layout of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and onboard hydrogen storage device is shown in Figure 2.163 [KAWATSU 2000]. A principle layout of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and on-board methanol reformer is shown in Figure 2.164 [KAWATSU 2000]. A particular attribute of the FC HE transmission with a 4 \u00d7 2 wheel arrangement and onboard methanol reformer is that it is a hybrid system that acts as a PES, that is, the electrical energy source (EES) forms a junction with 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 365 a secondary CH-E/E-CH storage battery (for example, NiMH) that acts as a SES (an electrical energy shock absorber). This lets the FC HE transmission arrangement have continuous accurate mechatronic control over the sharing of electrical energy. It additionally allows the possibility to continuously operate the FC in the high-efficiency functional range. The methanol reformer is a small-scale chemical plant mounted in the HEV. It has been greatly compacted by connecting into a separate component, the discrete parts that develop the methanol reformer, incorporating the fuel vaporisation part, the reforming reaction part, and the CO2 reduction part. It has also become feasible to get a better starting ability and responsiveness by reducing the thermal energy (heat) capacity of the methanol reformer. Start-up time has been reduced to under 3 min, and response time has been enhanced to less than 10 s. Besides, the reforming efficiency has been enhanced by using a catalyst. Principle layouts of the FC HE transmission with the 4 \u00d7 2 or 4 \u00d7 4 wheel arrangements and high-pressure gaseous hydrogen tanks are shown in Figures 2.165 \u2013 2.170. Automotive Mechatronics 366 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 367 In the FCEV shown in Figures 2.165, the FC stack, the power control unit, and the E-M motor are mounted at the front of the HEV, while the four highpressure gaseous hydrogen tanks are installed under the floor at the rear. The CH-E/E-CH storage battery is kept under the floor or in the luggage compartment [KAWATSU 2000]. Automotive Mechatronics 368 The FCEV \u2018Hy-Wire\u2019 has shown in Figure 2.170 uses HE DBW 4WD propulsion technology to provide mechatronic control over operations. It is powered by a FC that, together with the drivetrain, is stored on a skateboard chassis. This HE transmission arrangement lets the vehicle designers create a number of different body forms while still maintaining roomy interiors [HAMILTON 2002]. Moreover, the 2WD or DBW 4WD propulsion mechatronic control system (for example, with the following major components: PEFC; traction brushless DC-AC/ AC-DC macrocommutator IPM magnetoelectrically-excited synchronous motor/ generator, high-pressure hydrogen storage tank and NiMH storage battery), a rackand-pinion SBW 2WS or 4WS conversion mechatronic control system and a heat pump air conditioning system that uses CO2 refrigerant are also included. For the reason that the FCEV uses a radiator for cooling, the total area of the openings is about 2.5 times that of a normal automotive vehicle, and the front grill has a double frame construction too, that both undergoes high-quality cooling performance and permits the HEV\u2019s outer shell to articulate its innovative sight [KAWATSU 2000]. Of course, the FC HE transmission arrangement for the HE DBW 2WD propulsion mechatronic control system is intended to improve fuel economy and goals for excessive responsiveness when the HEV is in transitional circumstances. The electrical energy source (EES) is an HE configuration of the FCs, i.e., the PES and a CH-E/E-CH storage battery, i.e., SES. The output electrical energy from the FCs and the charging and discharging of the storage battery are mechatronically controlled in relation to the functioning circumstances of the HEV. 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 369 A NiMH storage battery with greater energy and power density is used for the storage battery so as to make it possible to run the HEV as an AEV only using the storage battery, thus getting a better fuel economy under low-load circumstances. For instance, as shown in Figure 2.171, the FCs and the traction brushless DC-AC/ AC-DC macrocommutator IPM synchronous motor/generator are linked in series so as to obtain better efficiency in the steady circumstances that generally take place during HEV manoeuvres [KAWATSU 2000]. The CH-E/E-CH storage battery, with its low power ratio, is arranged in parallel with the FCs through a DC-DC macrocommutator acting as a DC-DC converter and supplies electrical energy assistance when the FC response is postponed or when the HEV is driven under high loads. The CH-E/E-CH storage battery also absorbs the electrical energy recovered by regenerative braking and acts as the electrical energy source (EES) for AEV function under low loads. The hybrid control (electric energy control) of the FCs and the CH-E/E-CH storage battery is achieved by controlling the output voltage from the DC-DC converter. The FC H-E transmission arrangement for the HE DBW 2WD propulsion mechatronic control system is shown in Figure 2.172 [KAWATSU 2000]. This mechatronic control system is separated into two operational discrete systems. Automotive Mechatronics 370 The FC system is the electrical energy source (EES) that supplies the HEV\u2019s propulsion power, while the hybrid system uses the output power from the FC system with great efficiency. The FC system is composed of the FCs themselves, fuel supply system parts, and cooling system parts. Hydrogen is delivered to the FCs from the high-pressure storage tanks by means of a regulator. Any residual hydrogen remaining after the FC reaction is restored to the source area of the FCs by an exchange E-M-F pump. Air is pressurised by an E-M-P compressor, after that it is pumped to the FCs through a humidifier. The latter gets water vapour from the exhaust air of the FCs and uses it to humidify the inward compressed air. An E-M-F pump may flow coolant between the FCs and the radiator. In addition, mechatronic control of the supplementary parts, for example, the E-M-P compressor, and so on, is optimised in relation to the FC output, consequently the FCs function with a minimum of loss thanks to the supplementary implements. The hybrid system consists of a FC system, a CH-E/E-CH storage battery, a DC-DC macrocommutator acting as a DC-DC converter, and a traction brushless DC-AC/AC-DC macrocommutator IPM magnetoelectrically excited synchronous motor/generator. The core of the HEV\u2019s propulsion power is the output power from the FCs, but when their output power is not enough, as in fast acceleration, hill climbing, and high-speed passing transitions and high-load manoeuvring, electrical energy assistance is supplied by the storage battery. In addition, in low-load manoeuvring, the FC supplementary implements are turned off and the HEV is in motion as an AEV using the electrical energy from the storage battery and nothing else. Currently, HEVs have been developed for significantly cleaner and more efficient automotive vehicles. FCEVs, such as, the Honda Insight and Toyota Prius, particularly, were tested by the U.S. Department of Energy (DoE) to evaluate the liquid fuel saving [KELLY AND RAJAGOPALAN 2001]. Obviously, the FC has been developed to become the main energy source in various applications. The FC transit bus that has been designed and developed by the DoE has been acknowledged as a zero emission vehicle (ZEV). Its only exhaust emission is in fact water vapour [DOE 2003]. One of the main weak points of the FC is its slow dynamics [GOPINATH ET AL. 2002; NERGAARD ET AL. 2002; LEE ET AL. 2003]. Indeed, the dynamics of the FC is restricted by the hydrogen delivery system that contains M-F pumps and fluidic valves and, in some cases, a reforming process. Above all, a step electrical energy load may involve enormous variation of the voltage of the automotive 42 VDC EED bus, because the main energy source has a slow dynamic response. Besides, the FCEV has a problem when starting the E-M motor that demands high energy in a short time. 2.9 HE DBW AWD Propulsion Mechatronic Control Systems 371 To solve these problems, the FCEV must have an auxiliary energy source to supply high transient energy. High-current ultracapacitor technology has been developed for this purpose [ORT\u00daZAR ET AL. 2003]. Subsequently, the very quick power response of ultracapacitors may be used to add to the slower power output of the FC to create the compatibility and performance characteristics necessary for FCEVs as shown in Figure 2.173 [THOUNTHONG ET AL. 2005]. Relative to CH-E/E-CH storage batteries, ultracapacitors have one or two orders of magnitude higher specific power, and much longer lifetimes. Because they are capable of millions of cycles, they are virtually free of maintenance. Their enormous, rated currents enable quick discharges and quick charges as well. Their quite low specific energy, relative to CH-E/E-CH storage batteries, is in most circumstances the factor that determines the feasibility of their employment in a particular high-power application [DESTRAZ ET AL. 2004]. In Figure 2.173 a FC HE transmission arrangement is shown having a FC as the main energy source and ultracapacitors as the auxiliary energy source. It particularly specifies the mechatronic control algorithm for ultracapacitors\u2019 DC-DC macrocommutator (converter). Experimental results show that ultracapacitor technology is suitable for providing electrical energy in automotive EED systems. In Figure 2.174 a Chevrolet Sequel, which is about the size of a Cadillac SRX, is shown. It is the first FCEV to achieve 0 \u2013 96 km/h (0 - 60 mph) in under 10 s and has a 480 km (300 mile) range. Automotive Mechatronics 372 It has unequalled handling on snow and ice, or uneven terrains. 42% more torque for unparalleled acceleration, and shorter braking distance than an equal size conventional vehicle. The Chevrolet Sequel\u2019s sophisticated RBW or XBW integrated chassis mechatronic control hypersystem replaces the mechanical and fluidical linkages of conventional vehicles with electrical wires and actuators. This means fewer parts to wear out, and because RBW or XBW integrated chassis mechatronic control hypersystems work like a fast computer, the Chevrolet Sequel has enhanced acceleration, braking, and overall handling."
        ]
    },
    {
        "image_filename": "designv10_12_0002467_j.conengprac.2017.02.009-Figure8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002467_j.conengprac.2017.02.009-Figure8-1.png",
        "caption": "Fig. 8. Disc and beam system.",
        "texts": [
            " Therefore, the disturbance \u03be t( ) can be estimated using the same results: a p t a p t a p t q t( ) + ( ) + ( ) = ( ),0 0 1 1 2 2 (37) with \u222b \u222bq t y t y t T y t T \u03ba u \u03c4 d\u03c4 d\u03c4 p t T p t tT T p t t T tT T ( ) = ( ) \u2212 2 ( \u2212 ) + ( \u2212 2 ) \u2212 ( ) ( ) = ( ) = \u2212 ( ) = \u2212 2 + . t T t \u03c4 T \u03c4 \u2212 \u2212 1 1 2 0 2 1 2 3 2 2 2 3 7 6 4 2 2 (38) Fig. 7 shows the experimental responses of the proposed strategy applied to the roto-magnet system. These experimental results are obtained using (36)\u2013(38) and setting T=0.01 for the algebraic estimation of \u03be t( ). The plots demonstrate the effectiveness in disturbance rejection and setpoint tracking of the proposed strategy. The disc and beam system (see Fig. 8) consists of a PWM full-bridge driver, a DC motor with a reduction gearbox, an ultra-sonic sensor, a four bar mechanical system and a sliding disc. This system is very similar to the conventional ball and beam system except that there is a sliding disc that moves along a beam instead of a rolling ball. The sliding disc is allowed to move with one degree of freedom along the length of the beam. A lever arm is attached to the beam at one end, and a DC geared motor at the another end. As the DC motor turns by an angle \u03b8 t( ), the lever changes the angle of the beam by an angle \u03b1 t( )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.5-1.png",
        "caption": "Figure 2.5. Alternative architecture of leg for the 6-dof parallel mechanism with revolute actuators",
        "texts": [
            ",,1,0 iDi (2.29) An example of balanced mechanism is represented schematically in Figure 2.4. As discussed above, gravity compensation can be obtained without necessarily imposing force balancing by using elastic components to store potential energy. To this end, Equation (2.7) can be used. As an example, the gravity compensation of a 6-dof parallel mechanism is now presented. In this architecture, each of the legs is mounted on a passive revolute joint having a vertical axis of rotation, as shown in Figure 2.5. The leg itself is a planar mechanism with a parallelogram ABCD, a distal link CPi and a spherical joint at point Pi. Additionally, a second parallelogram mechanism BEFC is introduced in the leg, as represented in Figure 2.5. The second parallelogram mechanism is used to actuate the link CP thereby improving the mechanical advantage. The link of length ri1 is the actuated link. The potential energy of the springs used in the mechanism can be written as 6 1 22 2 1 i iuiuilils ekekV (2.30) where iilililili dhdhe sin222 1 (2.31) iiuiuiuiui dhdhe sin222 2 (2.32) where i and i are the angles between links BC and BE and the coordinate axis xi, respectively. The gravitational potential energy of the whole mechanism consists of the gravitational potential energy of the moving platform and the links of the legs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000209_978-1-84800-147-3_2-Figure2.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000209_978-1-84800-147-3_2-Figure2.7-1.png",
        "caption": "Figure 2.7. Three families of reactionless four-bar linkages",
        "texts": [
            " l2 = d, l3 = l1 for Case II; l2 = l1, l3 = d for Case III). By re-deriving the force balancing conditions for the two cases and substituting these conditions into Equation (2.38) results in a new set of coefficients js,t,u. Finally, the dynamic balancing conditions (2.42) and (2.43) are obtained by forcing these coefficients js,t,u to be zero and in conjunction with the new force balancing conditions respectively for Cases II and III. The corresponding families of balanced planar four-bar linkages are shown in Figure 2.7. In each case, there are no separate counter-rotations and only counterweights are required for complete balancing. As indicated in the figure, mi and li are the mass and length of the ith bar and d is the distance between the two joints on the fixed base. Vector ri connects the corresponding revolute joint to the centre of mass of bar i which should be on the axis of the bar. For Case I, the balancing conditions are written as 321 ,,1 llld 23 322 3 12 11 22 ,1 lm lrm r lm rm lr 2 12222 2 m Irlrm k c 3 13333 3 m Irlrm k c (2",
            " These dimensional constraints make all three types of linkages foldable, i.e. all the bars can be aligned on the base. Therefore, these mechanisms are generally not suitable for machinery where the input link must be driven through full rotations. However, for multi-degree-of-freedom applications (e.g. robotic applications), the above linkages can be considered as one-dof components providing sufficient range of motion for most practical purposes. By inspection of the three families of reactionless four-bar linkages in Figure 2.7, it can be found that Cases I and III are, structurally speaking, completely the same. They are classified as two separate cases due to the difference in the mounting mode as well as the actuation (i.e. the first link as input link). Since the centre of mass of a reactionless mechanism remains fixed for any configuration, the position of the centre of mass of the mechanisms in Figure 2.7 can be determined by considering a folded configuration. Therefore, the centre of mass is on the base line P1P3 and located at a distance of r from joint P1. This distance can be obtained, for all three cases, as follows: for Case I, tm lmrmlm r 131112 (2.45) while for Cases II and III, tml lmrmlmd r 1 131112 (2.46) where mt = m1 + m2 + m3. The radius of gyration kt for the whole mechanism with respect to its centre of mass can be written as follows: t tdg t m rmII k 2 (2.47) where 2 33 2 22 2 11 kmkmkmI g 2 33 2 212 2 11 rdmrlmrmId (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001428_978-1-4471-4510-3-Figure7.15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001428_978-1-4471-4510-3-Figure7.15-1.png",
        "caption": "Fig. 7.15 Contact-aided flexure shown deflected on a circular contact profile",
        "texts": [],
        "surrounding_texts": [
            "Compliant mechanisms are well suited for application in biomedical applications because of their low wear, the ability to be fabricated of biocompatible materials, and their compactness. There are many possible research areas and applications, and one implant is described here as a illustrative example. The design objective of the spinal implant is to restore healthy physiologic biomechanics to the degenerated spinal segment. Because the healthy motion and the degree of mechanical dysfunction of the spine varies significantly from person to person [37, 39], the device is tailorable to the needs of the patient via surgeonselectable inserts. There may also be therapeutic benefits to intentional adjustment of the devices stiffness to induce and support remodeling of the surrounding tissue architecture [44]. This example discusses the design and validation of a spinal implant capable of nonlinear stiffness and adjustability, including analytical and numerical models, benchtop, and cadaveric testing results. Example Implant Design A compliant mechanism3 was designed as a spinal implant to share load with a damaged or diseased intervertebral spinal disc, as shown in Fig. 7.13. The baseline configuration of the spinal implant is based on the lamina emergent torsional (LET) joint [47]. The LET geometry offers advantages in terms of manufacturability and independently controlled flexibility in multiple directions [24, 25]. The device consists of a LET joint that has been split into two parts that are independently attached to the vertebral pedicles. The vertebra themselves act as semirigid connections between the two parts of the LET joint. The attachment to the vertebral pedicles is accomplished via pedicle screws. Each half of the baseline device 3This section is based on \u201cSpinal Implant Development, Modeling, and Testing to Achieve Customizable and Nonlinear Stiffness\u201d by E. Dodgen, E. Stratton, A.E. Bowden, L.L. Howell, in Journal of Medical Devices, vol. 6, doi:10.1115/1.4006543, 2012. Used with kind permission \u00a9 ASME. configuration is composed of two attachment posts, two flexures, and a central connecting beam. The two flexures and the central connecting beam form a C-shape. The bilateral components are positioned on either side of the two vertebral bodies to which they are attached. Optional inserts adjust the force-deflection response of the flexures to meet the target spinal kinetic response deemed appropriate for the individual patient. Figure 7.14 shows the baseline configuration deflected in the two modes of loading for which it was designed. The optional contact-aided insert design is configured as two parts which connect together and attach to the central connecting beams of the baseline device. The elliptical contact surfaces of the inserts are designed such that as the flexures of the baseline configuration deflect during spinal motion, they come into contact with the surfaces, altering the force deflection relationship in a controlled and specific manner, as shown in Figs. 7.15 and 7.16. Through alteration of the elliptical parameters for the contact surfaces, the insert can be modified to provide a wide range of variability in stiffness. The intended use is for clinicians to select the desired insert configurations appropriate to the patient pathology. If the response of the implant needs to be modified due to changes in the patient pathology, then the insert can be replaced without changes to the pedicular attachment sites. Figure 7.17 displays a prototype of the insert and how it attaches to Fig. 7.17 Contact-aided attachment for baseline configuration the baseline configuration of the implant. The dimensions of the baseline configuration and the semimajor a and semiminor b axes of the elliptic surfaces are shown in Fig. 7.18. The surfaces of the insert are positioned such that the flexures come into contact with them as the device is pulled in tension (i.e., during flexion and during contralateral bending) or compressed (i.e., during extension and during ipsi- lateral bending). The elliptical geometry of the insert used in conjunction with the flexures geometry defines the stiffness of the implant. The ideal design performance of the device was evaluated using analytical modeling, finite element modeling, and benchtop testing of prototypes."
        ]
    },
    {
        "image_filename": "designv10_12_0000972_978-3-642-22164-4_2-Figure2.6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000972_978-3-642-22164-4_2-Figure2.6-1.png",
        "caption": "Fig. 2.6 Chattering of the aircraft horizontal stabilizer: a switch from a linear control to a 3-sliding one",
        "texts": [
            " The actuator output has the physical meaning of the horizontal stabilizer angle, and its significant chattering is not acceptable. Following are unpublished simulation results (1994) revealing the chattering features of a linear dynamic control based on the H\u221e approach and a 3-sliding-mode control practically applied afterwards in the operational system (1997). In order to produce a Lipschitzian control, the 3-sliding-mode controller was constructed according to the described chattering attenuation procedure. The comparison of the performances is shown in Fig. 2.6. The control switches from the linear control to the 3-sliding-mode control at t = 31.5. The chattering is caused by the inevitably relatively large linear-control gain. Following is the 5th order differentiator: z\u03070 = v0,v0 =\u22128L1/6|z0 \u2212 f (t)|5/6sign(z0 \u2212 f (t))+ z1, z\u03071 = v1,v1 =\u22125L1/5|z1 \u2212 v0|4/5sign(z1 \u2212 v0)+ z2, z\u03072 = v2,v2 =\u22123L1/4|z2 \u2212 v1|4/5sign(z2 \u2212 v1)+ z3, z\u03073 = v3,v3 =\u22122L1/3|z3 \u2212 v2|4/5sign(z3 \u2212 v2)+ z4, z\u03074 = v4,v4 =\u22121L1/2|z4 \u2212 v3|4/5sign(z4 \u2212 v3)+ z5, z\u03075 =\u22121.1Lsign(z5 \u2212 v4); f (6) \u2264 L"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.144-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.144-1.png",
        "caption": "Fig. 2.144 HEV driving circumstances during stopping [DRIESEN 2006].",
        "texts": [
            "141 HEV driving circumstances are shown during acceleration when maximum power is required, the CH-E/E-CH storage battery may also supply power and boost the series/parallel HEV\u2019s performance. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 337 In Figure 2.142 HEV driving circumstances are shown during deceleration and braking the E-M motor is turned into a M-E generator to charge the highvoltage CH-E-CH storage battery. No liquid fuel consumption \u2013 no exhaust emissions. Automotive Mechatronics 338 In Figure 2.143 HEV driving circumstances are shown during charging when the CH-E/E-CH storage battery gets low and the ICE may automatically start to recharge it. In Figure 2.144 HEV driving circumstances are shown during stopping when the ICE automatically shuts off when the series/ parallel HEV is stopped. Further optimising of the ICE operating range is necessary so as to achieve optimum hybrid system energy efficiency. As a result, fuel economy during medium- and high-velocity constant running, in particular, could be improved. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 339 Figure 2.145 shows ICE braking and the fluidical brakes\u2019 braking allocation [THS II 2004]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001565_0954406214562632-Figure14-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001565_0954406214562632-Figure14-1.png",
        "caption": "Figure 14. The assembly drawing of spiral bevel gear.",
        "texts": [],
        "surrounding_texts": [
            "Make use of Matlab to program and calculate the machining adjustment parameters of gear and pinion, then put in the above parameters to get their tooth surface discrete points cloud, and output the points cloud data documents as shown in Figure 5. Sample 12,445 discrete points of gear and 24,644 of pinion, which is adequate for the precision of modeling and processing such gears with geometry specification. Based on the design parameters of gear set shown in Table 1, the adjustment parameters can be calculated through Matlab program. Tables 2 and 3 indicate the calculated adjustment parameters for gear and pinion, respectively. Ru, g, P!2, and ! are the cutter parameters for gear; Rp, p, and f are the cutter parameters for pinion; Sr2, q2, Em2, XB2, XD2, and m2 are the gear machine-tool settings; Sr1, q1, Em1, XB1, XD1, and m1 are the pinion machine-tool settings; m1c (m2c) is the ratio of instantaneous angular velocities of the pinion (gear) and the cradle; C and D are the modified roll coefficients for calculating rotation angle. Digital true tooth surface modeling The curved surface reconstructed in the 3D software (SolidWorks) via leading points cloud documents by means of reverse engineering, is not smooth but stitched by many small curved surfaces, as shown in Figures 6 to 12. A crack seems to be in the middle of the curved surface, which not only influences the visual effects, but also prevents contact analysis and xm1 ym1 zm1 ya1 oa1 za1 xa1 yb1 y1 o1 (ob1) x1 xb1 z1 (zb1) \u0394Em1 \u0394X B1 \u0394X D1 m 2 \u03a6 1 om1 \u03b3 Figure 4. Workpiece coordinate system for pinion. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from solution in FEA, and even contact setting. Therefore, it is necessary to adopt other methods or approaches to deal with the reconstruction. The uneven tooth surface is modeled via the function of \u2018\u2018Scan To 3D.\u2019\u2019 Points cloud can almost automatically form the curved surface in software only by simple operations, at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from in no need of many man-made operations. However, by use of \u2018\u2018Scan To 3D,\u2019\u2019 some points cannot be scanned and thus ignored. Moreover, as the sequence and path of scan cannot be controlled, the surfaces do not look smooth with numerous cracks. In order to solve these problems, the method of \u2018\u2018Lofted Surface\u2019\u2019 is adopted to create the surface. Firstly, all the points make up lines in order. Secondly, use the function of \u2018\u2018Lofted Surface\u2019\u2019 to select the lines in sequence. Thirdly, form the smooth surfaces. Finally, by means of \u2018\u2018Clipping,\u2019\u2019 \u2018\u2018Array,\u2019\u2019 and other operations, model smooth spiral bevel gear and pinion. The digitized and high-precision true tooth surfaces under the study of this paper are shown in Figures 13 and 14. Smooth tooth surface can also reduce model errors and lay a foundation for high precision machining and FEA. Gear cutting and contact pattern experiments To verify the technical advancement and practicability in engineering digitized true tooth surface of spiral bevel gear based on machining adjustment parameters, this study gets the NC codes via NC process simulation software from 3D model with machining adjustment parameters and then inputs the codes to five-axis NC machine tools to conduct gear cutting experiments. Figures 15 and 16 show the processing of gear cutting in YH606 CNC Curved Tooth Bevel Gear Generator made by Tianjin Jing Cheng Machine Co., Ltd of China. The gear and pinion after processing are as shown in Figures 17 and 18, which completely meet the required design precision. Figure 13. The smooth tooth surface. Figure 12. The uneven assembly drawing of spiral bevel gear. at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from To better illustrate the problem, other related experiments have also been conducted. The illustration of VHG is shown in Figure 19. H is the movement along the pinion axis, while G is the movement along the gear axis, and V is the offset of the gear set. When doing the experiments of contact pattern for spiral bevel gear set, keep the offset (V) at the value of 0, and the true backlash for the gear is set at 0.22mm. Each time, only change the value of H from 0.2 to \u00fe0.2. In this way, three experiments have been done, setting the value of H as \u00fe0.2, 0, and 0.2, respectively. The transmitted torque of contact patterns experiment was 20Nm according to at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from some standard; Figures 20 to 22 show the results of contact pattern experiments of three complete teeth in gear, without use of any correction in the tooth surfaces of pinion, from which it can be told that the contact pattern for the gear set is not bad, for it satisfies all the requirements of engineering. The gear cutting experiment can prove the validity of the precise modeling method of spiral bevel gear true tooth surface, which can be used in mechanical engineering, besides theoretical research. Breaking the blockade on Gleason technology, the spiral bevel gear true tooth modeling method, without any Gleason at UNIVERSITY OF WINDSOR on September 29, 2015pic.sagepub.comDownloaded from software, can calculate the machining adjustment parameters. General NC machine can also be used to process spiral bevel gear, needless of special purpose machine for Gleason spiral bevel gear and Gleason software. This is the contribution of this research, other method cannot processing spiral bevel gear in general NC machine, the special purpose machine of spiral bevel gear and Gleason software are needed. The gear contact pattern experiments are the test method for the rotating gear pair. From the contact spot, vibration and noise of gear pair can be assessed in the same case. The use of standard spherical involute 3D model has no meaning in engineering, for it fails to get good contact pattern. In fact, spiral bevel gear is not the standard spherical involute, but just a modified spherical involute. It is the value and the reason why to use machining adjustment parameters to get the true tooth surface precise modeling processed in NC machine."
        ]
    },
    {
        "image_filename": "designv10_12_0003329_j.mechmachtheory.2019.103753-FigureA.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003329_j.mechmachtheory.2019.103753-FigureA.2-1.png",
        "caption": "Fig. A.2.1. The coordinate systems of two adjacent links connected by revolute joints.",
        "texts": [
            " The transformation matrix is as follows [ T i (i +1) ] = \u23a1 \u23a2 \u23a2 \u23a3 cos \u03b8i \u2212 cos \u03b1i (i +1) sin \u03b8i sin \u03b1i (i +1) sin \u03b8i a i (i +1) cos \u03b8i sin \u03b8i cos \u03b1i (i +1) cos \u03b8i \u2212 sin \u03b1i (i +1) cos \u03b8i a i (i +1) sin \u03b8i 0 sin \u03b1i (i +1) cos \u03b1i (i +1) R i 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 (A.2.2) [ T (i +1) i ] = [ T i (i +1) ]\u22121 = \u23a1 \u23a2 \u23a2 \u23a3 cos \u03b8i sin \u03b8i 0 \u2212a i (i +1) \u2212 cos \u03b1i (i +1) sin \u03b8i cos \u03b1i (i +1) cos \u03b8i sin \u03b1i (i +1) R i sin \u03b8i sin \u03b1i (i +1) sin \u03b8i \u2212 sin \u03b1i (i +1) cos \u03b8i cos \u03b1i (i +1) \u2212R i cos \u03b8i 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 (A.2.3) The coordinate systems of two adjacent links connected by revolute joints are shown in Fig. A.2.1 : the line along the revolute axis of joint i is set as the coordinate axis z i ; the line along the common normal between joint axes z i \u22121 and z i is set as the coordinate axis x i . The D-H parameters are defined as follows: a i ( i + 1) is the length of link i ( i + 1), which is the common normal distance from z i to z i + 1 positively along the direction of x i + 1 ; \u03b1i ( i + 1) is the twist of link i ( i + 1), which is the rotation angle from z i to z i + 1 positively along the direction of x i + 1 ; R i is the offset of joint i , which is the common normal distance from x i to x i + 1 positively along the direction of z i ; \u03b8 i is the revolute variable of joint i , which is the rotation angle from x i to x i + 1 positively along the direction of z i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003451_itherm45881.2020.9190562-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003451_itherm45881.2020.9190562-Figure1-1.png",
        "caption": "Fig. 1 Considered computational domain for (a) electro-magnetics and (b) CFD simulation.",
        "texts": [
            " A 125 kW BMW i3 permanent magnet synchronous motor (PMSM), having a slot/pole ratio of 72/12, has been chosen for the coupled electro-magnetics and thermal simulation. The stator lamination diameter, stator bore, slot depth, shaft diameter, and axial lamination length are 240.90 mm, 179.76 mm, 21.5 mm, 60 mm, and 130 mm, respectively [16]. For the electro-magnetic simulation, fully assembled BMW i3 motor including shaft and end winding has been chosen as the computational domain, as depicted in Fig. 1(a). In the BMW i3 motor, the rotor is sliced into six segments along the motor axis and stacked in a skewed fashion to reduce the cogging torque. Therefore, the skewed flux linkage to the permanent magnet is calculated as follows [17]: \u03bbskew(\u03b8)= \u2211 kms\u03bbncos(n\ud835\udf03\ud835\udc5f+\u2205n) N n=1 (1) Where, \ud835\udc58\ud835\udc5a\ud835\udc60 is the skew factor and is a function of skew angle [16]: \ud835\udc58\ud835\udc5a\ud835\udc60 = \ud835\udc60\ud835\udc56\ud835\udc5b( \ud835\udc5b\ud835\udf0c 2\u2044 ) ( \ud835\udc5b\ud835\udf0c 2\u2044 ) (2) Where, \ud835\udf0c is the skew angle. By considering only the DC current, at a constant phase current, winding/copper loss is calculated using the following equation [18]: \ud835\udc43\ud835\udc50,\ud835\udc59 = 3\ud835\udc3c2\ud835\udc45\ud835\udc4e[1 + \ud835\udefc\ud835\udc47(\ud835\udc47\ud835\udc64 \u2212 \ud835\udc47\ud835\udc4e)] (3) Moreover, modified Steinmetz iron loss model has been utilized for the stator and rotor core loss calculations. N38UH is used as magnet material with a maximum allowable temperature of 180oC and M250-35A is used as stator and rotor lamination material. Two-dimensional finite element based EMag solver of Motor-CAD software has been utilized for the electro-magnetic simulation. Motor-CAD Lab module has been used for efficiency mapping of the motor over the full speed range. Figure 1(b) presents the schematic of the computational domain for the CFD/HT simulation. In order to reduce the computational cost, only 1/12th section in the radial plane utilizing radial symmetry has been considered as computational domain for the thermal modeling. Moreover, only 1/6th section along the motor length has been considered for the thermal modeling. Additionally, motor shaft and end winding have been neglected for the CFD/HT simulation. The considered domain consists of six winding slots, along with the corresponding liner of a thickness of 0.3 mm, two magnetic poles, and the air gap of a thickness of 0.5 mm between the stator and rotor lamination, as illustrated in the Fig. 1(b). Authorized licensed use limited to: UNIVERSITY OF ROCHESTER. Downloaded on September 20,2020 at 12:02:02 UTC from IEEE Xplore. Restrictions apply. By neglecting radiation heat transfer and considering uniform heat generation, steady state energy equation of the following form has been solved to compute the temperature distribution of the motor: 1 \ud835\udc5f \ud835\udf15 \ud835\udf15\ud835\udc5f (\ud835\udc5f \ud835\udf15\ud835\udc47 \ud835\udf15\ud835\udc5f ) + 1 \ud835\udc5f2 \ud835\udf152\ud835\udc47 \ud835\udf15\ud835\udf032 + \ud835\udf152\ud835\udc47 \ud835\udf15\ud835\udc672 + ?\u0307? \ud835\udc58 = 0 (4) Where \ud835\udc58 is the thermal conductivity of the material, and ?\u0307? is volumetric heat source. A radial symmetric boundary condition is applied on the two side walls of the stator and rotor lamination"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure2.127-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure2.127-1.png",
        "caption": "Fig. 2.127 Layout of the steered, motorised and/or generatorised wheel (SM&GW) - (A) and the physical model of the brushless DC-AC/ AC-DC macrocommutator reluctance and IPM magnetoelectrically-excited in-wheel-hub motor/generator - (B) [FIJALKOWSKI 1984; 1990].",
        "texts": [],
        "surrounding_texts": [
            "The high-performance, all-round energy-efficient, mechatronically-controlled trimode HEV, termed the \u2018Poly-Supercar\u2019, shown in Figure 2.125, may be an advanced ultra-light hybrid that means it will be electrically-powered by a highdensity mechanical energy-storing, high-angular-velocity M&GF pack that is backed up by primary energy sources (PES), a small hydrogen (metal-hydrate) combustion gas turbine-generator/motor (GT-G/M) that is based on the Fijalkowski turbine boosting (FTB) system, or the Fijalkowski enginegenerator/motor -(FE-G/M) and electrified highway or powered roadway designed to extend the HEV\u2019s range. On purely M&GF power, the HEV is expected to achieve a range up to 500 km. The PES, when used, will extend that range to 1,000 km, yet still allow the HEV to meet even CARB\u2019s requirements for zero-emission vehicles (ZEV). The road-powered HEV reflects the fact that it may derive most or all of its electrical energy from electric cables buried in conventional-looking roadways. Underneath the road surface, electric cables (conductors or even superconductors) may be threaded through metal road channels called core elements. The cables may carry an electric current that will create an electromagnetic field. The HEV termed the Poly-Supercar, travelling on the electrified highway or powered roadway, may extract electrical energy from this electromagnetic field through an inductive pickup mounted underneath the vehicle. The transfer of electrical energy between these two elements will occur contactlessly (without a physical power connection between the roadway and the HEV). 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 319 The electrical energy extracted from the roadway will be used to recharge a highdensity mechanical energy-storing high-angular-velocity M&GF in the HEV and to power the vehicle\u2019s traction in-wheel-hub motors/generators on each SM&GW for the HE DBW 4WD propulsion mechatronic control system and other AE functional systems. While travelling off the electrified highway or powered roadway, the HIV\u2019s onboard AGT-G/M or FE-G/M and M&GF provide electrical energy, just as in a conventional parallel HE transmission arrangement. While lighter in mass than in a conventional parallel HE transmission arrangement, this onboard M&GF may be crucial to the vehicle\u2019s DBW 4WD propulsion mechatronic control system design. By providing an electrical energy source (EES) in the absence of an electrified highway or powered roadway, this M&GF may minimise the number of lane-kilometres (lane-miles) that must be electrified or powered. It is estimated that if 2 or 3% of lane-kilometres in a region were electrified or powered, this would enable greater regional mobility. The electrified highway or powered road will operate at a high frequency of 21 kHz and will feed energy to the HEV. A high-frequency system is designed to eliminate the acoustic noise found in existing roadways operated at a frequency of 400 Hz. Triad Hybrid Power Systems - A generation change in triad (tri-mode) hybrid power systems (HPS) is taking place. For over 20 years, the author has been performing research-and-development (R&D) work, at the Automotive Mechatronics Institution, Cracow University of Technology, Poland, on novel very advanced crankless prime movers, that is the ECE, termed the automotive gas turbine-generator/motor (GT-G/M) that is based on the Fijalkowski turbine boosting (FTB) system, shown in Figure 2.126 (a), or the 2-, 4- or even 5-stroke thermo-dynamic cycle, twin-opposed-piston, crankless ICE, termed the Fijalkowski engine-generator/motor (FE-G/M), shown in Figures 2.126 (b) and (c) [FIJALKOWSKI 1985A; 1986]. The AGT-G/M that is based on the FTB system, was conceived in the 1980s and first presented and published in February, 1985 at the Autotechnologies \u201985: International Forum on New Automotive Technologies, in Monte Carlo, Monaco [FIJALKOWSKI 1985A]. The FE-G/M, was also conceived in the 1980\u2019s and first presented and published in October, 1986 at the Eighth Electric Vehicle Symposium in Washington, DC [FIJALKOWSKI 1986]. It has one or more moving parts, a three-shaft AGTG/M configuration, or a piston-rod assembly. For instance, the FE-G/M is constructed of one or more pairs of directly opposed pistons with respective cylinders and heads, and one or more interior permanent magnet (IPM) arrays fixed to the connecting rod between them, or driven by a double-ended cam mechanomechanical (M-M) camshaft, or a giant-electro-rheological fluid (GERF), or a nano-magneto-rheological fluid (NMRF) translational motion-to-rotary motion (TM-RM), or a rotary motion-to-translational motion (RM-TM) mechatronic commutator, that is a TM-RM/RM-TM fluido-mechanical (F-M) mechatronic commutator that replaced the conventional ICE M-M crankshaft [FIJALKOWSKI 1985A; 1986; 1994; 1998; 1999C; 2000C]. Automotive Mechatronics 320 For example, the piston-rod assembly shuttles back and forth in a straight line from compression-ignition to compression ignition in its opposing cylinders. Mechanical energy from combustion and expansion of the fuel mixture is concentrated in a straight line, and because the pistons are not experiencing angular loading in the cylinders (as seen in conventional crank engine configurations), friction is substantially reduced and this translates to greater mechanical energy output. Further, with the elimination of the M-M crankshaft, its friction and mass are substantially reduced resulting in even greater mechanical energy output. For instance, the new crankless prime mover, termed GT-G/M or FE-G/M may propel 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 321 the HEV cross-country at over 60 km/h and 160 km/h on good roads \u2013 certainly not a high-speed unit but adequate for its purposes [FIJALKOWSKI 1985A]. The author considered a novel mobility and steerability concept of HEVs with E-M differentials. The use of these novel triad hybrid mobility and triad hybrid steerability enhancing concept DBW AWD propulsion mechatronic control systems for HEV opens up wide possibilities for improving fossil and non-fossil fuel economy, cutting initial and whole-life DBW AWD propulsion costs, protecting the environment, and improving distribution of terrain thrust (gross tractive effort) as well as keeping both the net motion resistances of the DBW AWD propulsion and SM&GW sinkages (rut depth) low not only by increasing the velocity of travel but also decreasing the rolling resistances of all the SM&GWs. Automotive Mechatronics 322 The ability of the HEVs to retain a sufficient level of mobility may exist, even if they have lost single or more SM&GWs. Using differential torque and/or speed controls of the outer SM&GWs as well as current and/or voltage controls of the inner SM&GWs, can increase the lateral motion control effect, especially when recovering from braking with the inner SM&GWs acting as the AC-DC macrocommutator wheel-hub generators, because the front gravitational forces on the HEVs become greater than the respective rear ones. At the same creep, this leads to greater horizontal (longitudinal and lateral) forces. The experimental proof-ofconcept DBW AWD propulsion mechatronic control systems used on HEVs satisfy nearly all the same essential requirements as for the running gear systems used on conventional vehicles [FIJALKOWSKI, 1986; 1990, 1994], namely: To apply an E-M \u2018single-shaft\u2019 DBW AWD propulsion mechatronic control system to a complete number of SM&GWs; To allow the outer side of the curve a positive propelling (driving) torque and at the inner side, a negative dispelling (braking) torque, achieving their maximum value for pivot-skid steering; To occupy the minimum volume within the space envelope of the HEV; To distribute the mass of the HEV over relatively a spacious ground surface or soil area. The requirements of the first feature may contribute to a very good soft soil performance of HEVs. The third feature may tend to conflict with requirements of the first feature. Triad Hybrid Pivo-Skid Steering \u2013 Pivot-skid steering belongs to HEVs consisting of a body-unit of a single pivot point system in which the pivot is not positioned over the axle of either body-unit. In a HEV, steering is realized by bending the vehicle about a pivotal point, and in consequence, is often referred to as pivot-skid steering. It has been realistic to ask just why pivot-skid steering is successful when conventional steering is unsuccessful, but comparative experiments demonstrate that HEVs with pivot-skid steering are capable of extricating themselves from ruts, mud holes, and other obstructions. No particular increase in drawbar pull is perceptible with pivot-skid steering over a conventional vehicle on a straight pull. The advantage in the pivot-skid steered HEV appears to be its ability to \u2018step\u2019 or \u2018wiggle\u2019, and each time (full-time) the HEV is steered, an insignificant forward motion is gained. It is in this manoeuvre that the net tractive effort or drawbar-pull is sensed to somehow increase. Here drawbar-pull is regarded as the tractive effort developed by an HEV as a surplus of motion resistance (net tractive effort). Since the drawbar-pull is obviously increased (motion resistance reduced) during the steering manoeuvre, it may be concluded that there must be something anomalous to pivot-skid steering that creates this increase. It has been found that, when negotiating rutted circumstances, an HEV with pivot skid steering may move the front SM&GWs out of the rut into adjacent soil, whereas this cannot be done with the standard automotive steering system, termed Ackermann steering, that uses two pivot points (one at each front wheel), and this creates a more constant wheelbase than does pivot-skid steering. 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 323 A \u03c0/2 rad alteration in the sense of direction can be made without forward motion of the HEV. The setting of the steering trunnion near the centre of the vehicle also results in almost perfect tracking of the front and rear SM&GWs. This feature is imperative in avoiding obstructions and, at the same time, enables the HEV to be steered either forward or backward without difficulty, as the steering characteristic of it does not alter with the steering\u2019s sense of direction. This steering characteristic makes possible the ready use of dual controls that enable the driver to drive forward or backward with equal ease; and this significantly reduces the necessity of manoeuvring and turning in difficult terrain. One factor noted in experiments is that conventionally steered HEVs are exceptionally more unstable uphill than skid- steered HEVs. Triad hybrid pivot-skid steering is also especially realised through the creation of a differential velocity between the inner and outer SM&GWs by means of three E-M differentials, namely front-wheel drive (FWD), centre-wheel drive (CWD), and rear-wheel drive (RWD) E-M differentials. On HEVs, the SM&GWs on each side can be driven at various values of the wheel angular velocity in forward and reverse (all SM&GWs on a side are driven at the same rate). There is no explicit steering mechanism \u2013 as the name implies, steering is carried out by actuating each side at a different rate or in a different sense of steering direction, causing the SM&GWs to slip, or skid, on the ground. For instance, when the SM&GWs on the left side are driven forward and the SM&GWs on the right side are driven in reverse at the same rate, the result is a clockwise zero radius turn about the centre of the HEV. Skidding has some disadvantages including wheel wear but for a HEV there is no choice. The reduced friction of a non-paved surface helps to reduce wheel wear. Multiple-drive SM&GWs on each side give greatly increased traction, especially on rough terrain. The concept of triad hybrid pivot skid steering HEVs is an attractive one in that it opens up much of the capacity between the SM&GWs for things other than steering components, such as carrying cargo. On the other hand, in the case where a HEV is longer than its width (such as in this instance), conventional pivot-skid steering alone doesn\u2019t act. Knowing that the maximum value of the turning torque generated by the differential SM&GW torques being applied to the left and right sides, respectively, is a function of the lateral distance from the HEV centre-line to each SM&GW, and the wheel friction force, the resisting torque acting against this turning torque (torque resisting turn) is a function of the fore aft distance from the HEV centreline to each SM&GW and the wheel friction force. Since on average the distances are greater than the lateral distance from the HEV centreline to each SM&GW, then the torque resisting turn is greater than the maximum value of the turning torque, or reiterated, the torque resisting the turn is greater than the turning torque being generated. That is why; conventional pivot-skid steering doesn\u2019t work for HEVs that are longer than they are wide. The advantage of triad hybrid pivot-skid steering is that it permits the HEV to \u2018turn on a dime\u2019, and rapidly alter the steering sense of direction just by letting down the in-wheel-hub E-M motors. Automotive Mechatronics 324 The disadvantage is that it makes less efficient use of its in-wheel-hub E-M motors, and results in random odometry logs because the SM&GWs often slide along the ground surface. Since the steering sense of direction-finding system was tuned to those preceding conventional HEVs, it tended to anticipate that the vehicle would be able to turn very fast, even at high vehicle velocity, but disappointingly that is not the case. This is due predominantly to the pivot-skid steering concept, but perhaps also to the very loose soil. That\u2019s why the author would like to put into effect some hardware and software alterations that should enhance its mobility and steerability performance, by proving it down until it realises the recently commanded steering sense of direction. A very advanced series HE transmission arrangement for the HE DBW 4WD propulsion mechatronic control system is based on a novel E-M axleless progressively variable transmission (APVT), a mechanical energy store (MES) that I is a high-density, mechanical energy storing, high angular velocity motorised and/or generatorised flywheel (M&GF) with the brushless DC-AC/AC-DC macrocom-mutator twin composite-disc flywheel motor/generator and onboard electronic control instrument (ECI) that controls all automotive functional systems. These techniques may allow for low pollution and efficient manufacture and use of mechanical energy. The expected average improvements are: 60% of fossil-fuel savings and 75% of pollution reduction. Further changes that may be directly noticed by the driver are a more comfortable ride due to a shiftless and stepless fast acceleration from zero to maximum values of vehicle velocity. A full-time series HE DBW 4WD propulsion mechatronic control system may noticeably enhance both comfort and safety. The simplicity of the novel concept is visible when comparing the number and size of the propulsion mechatronic control system\u2019s components and their series HE transmission arrangement in a \u2018Standard\u2019 and a \u2018Novel Concept\u2019 HEV: Standard ECE or ICE; ECE or ICE starter; M-M clutches; MT (gearbox); M-M propeller shafts; M-M driveshafts; M-M differentials; F-M wheel-drum, -disc or -ring brakes. Novel Concept M-E/E-M generator/motor [an automotive gas turbine-generator/motor (AGT-G/M) or the Fijalkowski engine-generator/motor (FE-G/M)]; Steered, motorised and/or generatorised wheels (SM&GW); Motorised and/or generatorised flywheel (M&GF); Chemical energy-storing, very advanced CH-E/E-CH storage battery; Solar-cell panel; Inductive pickup; 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 325 ASIM macrocommutator and ASIC microcomputers; E-M wheel-drum, -disc or \u2013ring brakes. The ECE\u2019s or ICE\u2019s fluidic cooling system, fuel tank, onboard M-E generator, and SLI CH-E/E-CH storage battery are less than half of its present size. This results in mass reductions of approximately 300 kg for an automotive vehicle with a present curb mass of 1,200 kg .The components of this series HE transmission arrangement for the HE DBW 4WD propulsion mechatronic control system may be arranged with each other with a great degree of freedom, allowing the best space use and mass distribution. The best distribution of FWD and RWD loads (e.g. 50/50) and a reduced height of the barycentre (centre of gravity) can be easily achieved. This and the reduced unsprung mass of the SM&GWs leads to increased active safety and riding comfort. The functionality of the HEV may be increased without additional cost and mass due to the ease of controllability of the HE DBW 4WD propulsion mechatronic control system\u2019s components. An AGT-G/M that is based on the FTB system or the FE-G/M [FIJALKOWSKI, 1985, 1986], may charge the high-density mechanical energy-storing high angular velocity M&GF with stored mechanical energy. The ECE or ICE may be cut-off by the onboard central ECU when the M&GF is filled and provides the electrical machines (in-wheel-hub motors/generators) on each SM&GW with electrical energy in the form of an electrical current to accelerate and propel the HEV. During regenerative braking and/or cornering, the electrical machines become in-wheel-hub M-E generators and transmit the braking and/or cornering electrical energy back to the M&GF. The size of the in-wheel-hub M-E/M-E motors/generators is such that they can provide sufficient braking and/or cornering torques to lock the SM&GWs in all circumstances and very high torque to accelerate the HEV at all values of vehicle velocity. The easy torque and angular-velocity control of each SM&GW may lead to an efficient full-time DBW 4WD propulsion mechatronic control. The infinite adjustability of the in-wheel-hub E-M/M-E motors/generators on each SM&GW may be controlled by the ECI, giving the APVT a variety of additional functions, such as HE DBW 4WD propulsion, lockable FWD and RWD, as well as CWD E-M differentials, ABS and ARS, as well as ESP. The series HE transmission arrangement will allow additional features that may improve the functionality and use of mechanical energy further: constant and variable angular velocity auxiliary-drive propulsion mechatronic control systems for trade-off power units are needed (e.g. onboard M-E generator, M-F pumps) and comfort fluidics (e.g. park automatic and so on). The mass distribution for the Poly-Supercar is assumed to be 50/50 under static and 75/25 under maximum braking and/or cornering dynamic circumstances. The size of the in-wheel-hub E-M motors is based on the maximum torque requirements under dynamic conditions, i.e. braking and/or cornering under full load. One in-wheel-hub E-M motor at constant values of the vehicle velocity and low accelerations, and two in-wheelhub E-M motors at significant levels of acceleration, may propel the HEV PolySupercar. Automotive Mechatronics 326 The artificial intelligence (AI) ECI corrects the steering position needed to balance the off-centre thrust during SM&GWs are actuated during braking and/or cornering. A HE DBW 4WD propulsion function, with or without locked FWD and RWD as well as CWD E-M differentials, can be selected through the human- and/or telerobotic driver (H&TD). The DBW 4WD propulsion mechatronic control system\u2019s AI ECI automatically selects these modes if the SM&GWs are spinning during acceleration or locked during braking. The principle layout of an HE transmission arrangement for the aforementioned HE DBW 4WD propulsion mechatronic control system is shown in Figure 2.128. The core of the series HE transmission arrangement for the mechatronic control system can be not only the onboard, high-density mechanical energy-storing 2.8 ECE/ICE HE DBW AWD Propulsion Mechatronic Control Systems 327 super-high-angular-velocity M&GF with a brushless DC-AC/AC-DC macrocommutator twin composite-disc flywheel E-M/M-E motor/generator and highcapacity chemical energy-storing MgH with Ni catalyst, FeTiH, LiPolymer, LiIon, NiMH, NiCd, NaNiCl2, NaS, AgZn, NiC or PbAcid storage battery co-operating with the AGT-G/M that is based on the FTB system, or the FE-G/M and solar-cell panel as well as the electrified highway or powered roadway, but also four SM&GWs with brushless AC-AC or AC-DC-AC or DC-AC/AC-DC macrocommutator reluctance and/or IPM magneto-electrically-excited in-wheel-hub motors/ generators and in-wheel-disc electro-mechanical brakes (EMB) for each FWD and RWD, and single reciprocating E-M accelerator-pedal actuator, driven by the linear tubular DC-AC macrocommutator pedal-actuator motor, for the right-foot accelerator pedal. Starting and Acceleration - The driver turns the key to activate thee onboard central ECI. The ECI senses the position of the right-foot accelerator pedal and switches on/off the ASIM macrocommutator electrical valves and provides the in-wheel-hub E-M motors on each SM&GW with electrical energy. The ASIM macrocommutator at the in-wheel-hub E-M motors may be adjusted from zero to larger reference control signals to produce sufficient torques to accelerate the HEV. Increased pressure at the accelerator pedal creates greater reference control signals and faster acceleration. For low and medium acceleration, only one SM&GW may be activated. At high acceleration or tractive efforts, two or more SM&GWs will drive the HEV. The ECI may correct the steering to compensate for off-centre thrust of the wheels. The ECI senses the revolution of all wheels and calculates its correct values of the wheel angular velocities depending on the hand-steering-wheel position. If the values of the wheel angular velocities are too high, the SM&GW slips. The ECI may reduce the torques (reference control signals) to prevent this situation. Rolling - The HEV drives at a constant vehicle velocity if there is no difference between the position of the accelerator pedal and the vehicle velocity of the HEV. The number of wheels activated (driven) will depend on the tractive effort needed and may be selected by the AI ECI or by the driver through a push bottom. A smooth transition to a coasting mode can be reached by moving the reference control signals into zero or near-zero accelerator-pedal position."
        ]
    },
    {
        "image_filename": "designv10_12_0001818_978-3-319-19740-1_15-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001818_978-3-319-19740-1_15-Figure6-1.png",
        "caption": "Fig. 6 A contact model of a mating pinion and gear",
        "texts": [
            " The geometry of the tooth surfaces of a pair of mating pinion and gear can be generally represented by the position vector, unit normal and unit tangent in the coordinate systems S1 and S2 that are rigidly connected to the pinion and the gear, respectively, as follows, Pinion : r1 \u00bc r1\u00f0u1; h1;u1\u00de n1 \u00bc n1\u00f0u1; h1;u1\u00de t1 \u00bc t1\u00f0u1; h1;u1\u00de f1\u00f0u1; h1;u1\u00de \u00bc 0 8>>< >: ; \u00f013\u00de Generated gear : r2 \u00bc r2\u00f0u2; h2;u2\u00de n2 \u00bc n2\u00f0u2; h2;u2\u00de t2 \u00bc t2\u00f0u2; h2;u2\u00de f2\u00f0u2; h2;u2\u00de \u00bc 0 ; 8>< >: \u00f014\u00de Formate gear : r2 \u00bc r2\u00f0u2; h2\u00de n2 \u00bc n2\u00f0u2; h2\u00de t2 \u00bc t2\u00f0u2; h2\u00de 8< : : \u00f015\u00de Step 3: Assembly of the pinion and gear members in their running position, as shown in Fig. 6, and representing the tooth surfaces of both members in a global coordinate system Sf that is fixed to the frame, including the assembling parameters, nominal offset and displacement E0 \u00fe DE, gear axial displacement \u0394G, pinion axial displacement \u0394P, and nominal shaft angle and displacement R0 +\u0394 R, as shown in Fig. 7. Given the initial contact position on the gear flank, the assembling displacements are determined using the improved algorithm described in [4]. Default displacement values of DE, \u0394G, \u0394P, and \u0394 R are zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001851_gt2016-56084-Figure13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001851_gt2016-56084-Figure13-1.png",
        "caption": "Figure 13. Tomographic images of (a) the blade # V sections, (b) cross-sections, and (c) longitudinal sections (colors are inverted).",
        "texts": [
            " Since stress values are highly sensitive to mesh quality and concentrations, value range checked only after the TO and stress constraints were not applied. As a result of TO, design of a blade with reduced weight, satisfying strength (Fig. 11), and eigenfrequency requirements with the constant airfoil surface was obtained. its section in (b) radial and (c) transverse directions. Blade # V was \u201cprinted\u201d by SLM on a small scale using Mlab Cusing equipment (Fig. 12). The minimum wall thickness was 0.15 mm. A blade of this design would be very difficult to produce by casting. There are tomographic images of some blade sections shown in Fig. 13. Results show good geometrical correlation between the CAD-model and the blade produced by SLM. It should be noted that AM and TO together form the perfect technology symbiosis, and allow us to improve the design of parts such as rotor turbine blades. AM provides more options in design than conventional manufacturing methods, but it is also necessary to take into consideration its technological restrictions. One important task of AM is to develop support structures if there is any need. These support structures are necessary for the stabilization of the structure during manufactoring [12, 16, 17]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002577_s11665-018-3574-5-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002577_s11665-018-3574-5-Figure2-1.png",
        "caption": "Fig. 2 Computational domain with powder particles distribution used for simulation",
        "texts": [
            " x1 \u00bc x2 \u00fe r1 \u00fe r2\u00f0 \u00de sin\u00f0h\u00fe dh\u00de sin/ \u00f0Eq 1\u00de y1 \u00bc y2 \u00fe r1 \u00fe r2\u00f0 \u00de sin\u00f0h\u00fe dh\u00de cos/ \u00f0Eq 2\u00de z1 \u00bc z2 \u00fe r1 \u00fe r2\u00f0 \u00de cos\u00f0h\u00fe dh\u00de \u00f0Eq 3\u00de where r1 and r2 are the radius of spheres 1 and 2, respectively, and / is the azimuth angle. The above-mentioned algorithm has been applied to obtain random powder distribution which would represent the powderbed condition. In this study, powder size distribution from 15 to 40 lm has been considered and the particles are defined over the 90-lm solid Ti-6Al-4V substrate as shown in Fig. 2. Volume fraction in Fig. 2 differentiates two materials: Ti-6Al4Vand argon. Ti-6Al-4V is defined by volume fraction 1, while argon has volume fraction zero and the free surface has volume fraction in between 0 and 1 and therefore represented by green color. To properly capture the volume fraction, a hexahedral mesh is defined over the domain. Mesh size of 5 lm has been used. The powder particles generated by sequential addition algorithm were read through FLUENT user-defined function (UDF). Laser heat source has been modeled as the conical volumetric heat source which is represented in Eq 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000829_j.mechmachtheory.2010.04.004-Figure1-1.png",
        "caption": "Fig. 1. Generation process of a DTT worm.",
        "texts": [
            " Recently, a novel type of toroidal worm gearing with concave worm profiles has been developed by the authors of this paper. The worm helicoid can be ground by a grinding disk according to its formation mechanism. The used grinding wheel has two generating tori which are symmetrical about its mid-plane. The mating worm gear is enveloped by using a toroidal hob identical with the generated worm. Therefore, the proposed worm gearing may be named the dual tori double-enveloping toroidal worm drive (the DTT worm drive). Fig. 1 is the schematic drawing for the machining process of the DTT worm. Obviously, a DTT worm drive has very good manufacturability. The greatest strength of the DTT worm is that the worm can avoid the undercutting efficiently and its edge-tooth always has enough top thickness even under the condition of multiplethreaded worm and low drive ratio [11,12]. Furthermore, the preliminary research shows some valuable meshing properties, for example, the wider contact zone of the wheel tooth surface [13], the longer double-line working length of the worm and the more desirable lubrication characteristics [14,15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003544_j.jmapro.2021.02.002-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003544_j.jmapro.2021.02.002-Figure15-1.png",
        "caption": "Fig. 15. Distribution of stress \u03c3y under the temperature of 1050\u2103.",
        "texts": [
            " Therefore a thermal stress-strain analysis was carried out to obtain the stress history base on thermal elastic-plastic theory. It could be seen that the duration of the molten metal was only 0.2 s under the laser heating. During the short time the heat input was mainly applied to melt the weld metal. That might be the main reason why the width and height of the weld metal were both linear with the heat input increasing. The stress distribution in the weld metal under high temperature of 1050 \u2103 was shown in Fig. 15. It could be seen that near the gap between the foil pair there was a high stress existing under the temperature of 1050 \u2103. The stress evolution during the cooling stage near the gap was shown in Fig. 16(a). When the temperature was higher than 933 \u2103, the y axial \u03c3y was higher than \u03c3z. However when the temperature was lower than 933 \u2103 \u03c3y was greater than \u03c3z that was one of the main mechanical reasons why the crack did not propagate along only y or z axial. The final residual stress distribution in the joint was shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001176_robio.2012.6490977-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001176_robio.2012.6490977-Figure1-1.png",
        "caption": "Fig. 1. Swing leg models. (A) Conceptual double pendulum model with point masses at the segment ends. (B) More realistic swing leg model with human-like segment mass distribution and hip translational accelerations as external input.",
        "texts": [
            " We find that the identified control can achieve swing leg placement into a large range of target points, that this placement is robust to disturbances in initial conditions and to sudden changes in the target during swing, and that the resulting swing leg trajectories and joint torque patterns compare to those of human walking and running. Finally, we discuss these findings in section V and summarize our plans for future work. In human and humanoids, leg placement is largely achieved by the motion of the hip and knee while the ankle contribution can be neglected. To develop intuition about the control strategies for swing leg placement, we use the classic double pendulum with the thigh and shank represented as massless rods of lengths lt and ls with point masses mt and ms attached to their ends (Fig. 1A). The hip is connected to an immovable trunk at the origin of the world frame, and the joint angles \u03c6h and \u03c6k are measured as shown in figure 1A. The resulting equations of motion are ((mt +ms)lt \u2212mslscos\u03c6k)lt\u03c6\u0308h = \u03c4h + \u03c4k \u2212msltlscos\u03c6k\u03c6\u0308k +mslsltsin\u03c6k(\u03c6\u0307k \u2212 \u03c6\u0307h) 2 +(mt +ms)ltgsin\u03c6h (1) msl 2 s \u03c6\u0308k = \u03c4k +msls(ls \u2212 ltcos\u03c6k)\u03c6\u0308h +mslsltsin\u03c6k\u03c6\u03072 h \u2212mslsgsin(\u03c6k \u2212 \u03c6h) (2) for the hip and knee, respectively, where \u03c4h and \u03c4k are the applied hip and knee torques. In addition to the conceptual model, we test the performance of our control with a more realistic simulation model of human swing motions (Fig. 1B). In this second model, the segment inertial properties are based on anthropomorphic data obtained from scaling tables [22] for a human with a body weight and height of 80kg and 180cm (mt=7kg, ms=4.3kg, dt=21.7cm, ds=30.3cm, lt=43cm, ls=43cm). Moreover, the model includes a knee stop realized by a restoring torque [23] \u03c4 resk = \u23a7\u23aa\u23a8 \u23aa\u23a9 k\u03c6(\u03c6k \u2212 \u03c6max)(1 + \u03c6\u0307k/\u03c6\u0307max), \u03c6\u0307k > \u2212\u03c6\u0307max \u03c6k > \u03c6max 0, otherwise (3) (\u03c6max=175deg, \u03c6\u0307max=0.01rads\u22121, k\u03c6=17.2Nmrad\u22121) and accounts for hip translational accelerations (ax, ay) in later comparisons to human swing phases in steady walking and running (Sec",
            " Using equation 11 to substitute \u03c6\u0308k in equation 10, we get mtl 2 t \u03c6\u0308h = \u03c4h + 2\u03c4k for the hip equation, which shows that a compensation torque \u03c4h = \u22122\u03c4k cancels the effect of knee torque on the hip motion. The second functional component engages when the leg has slowed down to zero angular velocity \u03b1\u0307 = 0, upon which a deliberate extension component is added to the knee torque, \u03c4 iii \u2032 k = \u03c4 iiik + kext(l0 \u2212 l), (12) where kext is a proportional gain and l0 = lt + ls. This active knee extension ensures that the leg reaches down to the ground. The control developed in the previous section is based on the simple double pendulum as a conceptual model (Fig. 1A). However, to test the control performance, we use a swing leg model that considers human-like segment mass distribution and the effect of hip translational accelerations generated by the body (Fig. 1B). With this more realistic model, we first tune the control parameters to achieve robust leg placement into a realistic range of target angles assuming large variations in initial conditions. We then compare the predicted patterns of the foot point motion and the joint torques with those of human walking and running, and evaluate the quality of the leg placement generated by the local feedback control during sudden changes in swing leg targets as well as during horizontal pushes on the foot point that simulate obstacle encounters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002518_j.eng.2017.05.021-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002518_j.eng.2017.05.021-Figure4-1.png",
        "caption": "Fig. 4. Experimental and simulation results of powder spreading. (a) Simulations can guide the design and optimization of the (b) powder rake; (c) simulation and (d) experimental results of spreading a powder layer over previous layers.",
        "texts": [
            " Mechanical polishing is not feasible, since it may break the neck and change the microstructure. In the powder-melting procedure, a focused electron beam is used. The morphology of single tracks is observed under an optical microscope (OM). A good index to evaluate the performance of powder-spreading machinery is the relative packing density of the powder bed. A more compacted powder bed is usually beneficial to the fabrication quality, which can be demonstrated by the powder-melting model, as introduced in Section 2.3. The simulations (Fig. 4(a)) can guide the design and optimization of the powder rake (Fig. 4(b)), including the rake shape and its translational speed. The relative packing density over either a flat substrate or the fluctuating surface of previous layers can be predicted (Fig. 4(c)) and then compared with experiments (Fig. 4(d)). Some preliminary simulation results reveal the following phenomena: \u2022 If the translational speed is relatively low, the rake shape does not affect the packing density, and the resultant packing density is high. \u2022 The packing density decreases with the increase of the rake speed, as illustrated in Fig. 5. It should be noted that the effect of rake vibration is not incorporated into the current model; however, in experiments, the vibration is influenced by the rake speed, and then in turn influences the powder spreading [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002206_tsmc.2017.2663523-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002206_tsmc.2017.2663523-Figure5-1.png",
        "caption": "Fig. 5. VCM actuated servo gantry system.",
        "texts": [
            " 4 accord with Theorem 4, that control input (17) not only can design the time instant M\u03b81 = 5 (M\u03b82 = 2) after which y2(k) completely tracks h(k), but also can make |y2(k) \u2212 h(k)| decrease monotonically for all 0 \u2264 k \u2264 4 (0 \u2264 k \u2264 1). In the mean time, y1(k) is bounded for all k \u2265 0. Besides, as we discussed after the proof of Theorem 4, that when |y2(0)\u2212h(0)| > \u03b4, a larger \u03b4 will bring a smaller M\u03b8 and a faster convergence rate. For Theorem 5, we will use an experiment example to illustrate the effectiveness and practicability of control method (24). The experimental subject is the servo gantry in a VCM actuated servo gantry system, which is depicted in Fig. 5. The manufacturer of this device is H2W Technologies, Inc. and the product code is NCC10-15-023-1X. Example 3: The dynamic model of this servo gantry is \u23a7 \u23a8 \u23a9 y1(k + 1) = y1(k) + Ty2(k) y2(k + 1) = y2(k) \u2212 KT Mvcm y1(k) \u2212 T Mvcm Ff (k) + TKFKu Mvcm u(k) \u2212 T Mvcm Fint(k). (31) In system (31), m = 1 and n = 2; y1(k) (in \u03bcm) and y2(k) (in mm/s) represent the position and velocity of the VCM, respectively; T = 0.1 ms is the sampling period; u(k) (in V) is the control voltage; Ff (k) (in N) and Fint(k) (in N) are the frictional force and interference force, respectively, where Ff (k) = { Fc + (Fs \u2212 Fc) exp [ \u2212(y2(k)/Vs) 2 ] + Fvy2(k) } \u00d7 sgn(y2(k)) Fint(k) = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003164_1.3662578-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003164_1.3662578-Figure2-1.png",
        "caption": "Fig. 2 Angular velocity relationships for a ball in an angular contact bearing",
        "texts": [
            " Contributed by the Lubrication Division of T H E A M E R I C A N S O - CIETY OP M E C H A N I C A L E N G I N E E R S and presented at the A S L E - A S M E Lubrication Conference, New York, N. Y., October 20-22, 1959. NOTE: Statements and opinions advanced in papers are to be understood as individual expressions of their authors and not those of the Society. Manuscript received at ASME Headquarters, August 3, 1959. ASME Paper No. 59\u2014Lub-9. carrying ball bearing simple rolling motion cannot obtain. As can be seen from the vector diagram of Fig. 2, the ball must have a spinning velocity (aB/i with respect to the inner race. The condition of outer-race control is illustrated; i.e., pure rolling at the outer race contact, rolling plus spinning at the inner race. Depending upon the relative conformities, speed, and ball size, \u2022NomenclatureOii = ao T = CF = Ro = Ri = Wi = cCB = w Bli = inner-race contact angle outer-race contact angle thrust load on a bearing centrifugal force of a single ball normal force on a ball at outer- race contact normal force on a ball at inner- race contact angular velocity of inner race angular velocity of a ball angular velocity of inner race with respect to a ball ws = spinning component of relative F = velocity o)K = rolling component of relative velocity r = radius of curvature of a race / - conformity f = r/D Us = sliding-friction coefficient in a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001292_1.4006273-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001292_1.4006273-Figure6-1.png",
        "caption": "Fig. 6 Thermal FE analysis results for six welded rollers in one cone assembly (heating scenario 3 in Table 2)",
        "texts": [
            "5 W (for each of the 46 rollers), and a maximum average roller temperature of 55 C. Thus, under normal operating conditions, the temperature of the rollers is only about 5 C (9 F) hotter than the average cup temperature. Figure 5 shows the results of the simulation along with the temperature distribution. Note that the axle was suppressed from the visual results to provide a better temperature visualization of the bearing surface. In the heating scenario \u201csix welded rollers\u201d (simulation 3 in Table 2), the FE model simulation presented in Fig. 6 replicates the laboratory dynamic test in which six rollers in one cone assembly were welded to the steel cage bars causing them to slide on the cup raceway rather than rotate. The results indicate that the operating temperature of the welded rollers was about 76 C, which is 21 C ( 38 F) hotter than the temperature of a roller in normal operation, yet, the average cup temperature of the bearing with six welded rollers was only 9 C above that of a normally operating bearing. The latter provides initial proof that a number of rollers within a bearing may experience considerable heating events without affecting the average cup temperature significantly since the bearing cup averages all the roller temperatures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001616_s10846-017-0520-y-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001616_s10846-017-0520-y-Figure1-1.png",
        "caption": "Fig. 1 Scheme of forces produced by rotors, and torques generated in attitude (roll, pitch and yaw angles) acting on the quadrotor",
        "texts": [
            " This quadrotor is an attractive rotary-wing vertical take-off and landing (VTOL) Unmanned Aerial Vehicle (UAV) for both military and civilian usages. In this type of vehicles, vertical motion is created by collectively increasing and decreasing the speed of all four rotors; pitch or roll motion is achieved by the differential speed of the front-rear set or the left-right set of rotors, coupled with lateral motion; yaw motion is realized by the different reaction torques between the (1,3) and (2,4) rotors. The main thrust is the sum of the thrusts of each motor, as shown in Fig. 1. Let the inertial frame and the fixed to the rigid aircraft frame respectively as: I = iI , jI , kI B = iB, jB, kB The generalized coordinates vector q defined as: q = (x, y, z, \u03c6, \u03b8, \u03c8)T \u2208 R 6 = (\u03be, \u03b7)T describe the position and orientation of the flying machine, the model could be separated in two coordinate subsystems: translational and rotational. They are defined respectively by \u03be = (x, y, z)T \u2208 R 3: denotes the position of the vehicle\u2019s mass center relative to the inertial frame I and \u03b7 = (\u03c6, \u03b8, \u03c8)T \u2208 R 3: describe the attitude of the aerial vehicle, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001082_robionetics.2013.6743606-FigureI-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001082_robionetics.2013.6743606-FigureI-1.png",
        "caption": "Fig. I. Quadcopter axis",
        "texts": [
            " We use 12 states for this state-space model, its position in world frame is denoted as E 1 = [x y z 1 ' its roll, pitch, yaw angles denoted as E2 = [\u00a2 e 1jJ 1 ' its velocity due to x-axis, y-axis, z-axis denoted as E3 = [:i; if i 1 , and its angular velocity due to x-axis, y-axis, z axis denoted as E4 = [p q r] . The state variable and its system input is x = [ Er Er Er Er] T , [ 2 2 2 2] T H U = WI W2 W3 W4 . ence, X= [ Xl, ... , X12] T U = [Ul, ... , U4] T B. Translational and Rotational Analysis Based on Newton's second law of translational motion [6], we have this equation: F = mv + (w x mv) (1) where w = 104 and v = 103. From fig.I, we could get the forces which is worked on the quad copter F = Fg - Fthrust (2) Therefore, equation 2 can be expressed as where m is the mass of quadco\ufffdr, T is vertical thrust of quadcopter against gravity and RB is the rotation ma trix from body-frame to world-frame or inertial-frame. s\u00a2seC1jJ , - C\u00a2S1jJ c\u00a2sec?j) , + S\u00a2S1jJ 1 s\u00a2seS1jJ + C\u00a2C1jJ c\u00a2seS1jJ - S\u00a2C1jJ s\u00a2ce c\u00a2ce Assume p, q, r, x, y, i \ufffd 0 , then 1 x = --T(c\u00a2sec1j; + s\u00a2s1j;) rn 1 jj = --T(c\u00a2ses1j; - s\u00a2c1j;) m. 1 i = g - -T(c\u00a2ce) m U sing rigid body rotational law, we have r = Iw + (w x Iw) where, I is moment of inertia of quadcopter (3) (4) (5) (6) Then, equation 6 can be written as Iw= and Tx = db(w\ufffd -w\ufffd) Thus, we have these equations for angular acceleration of quadcopter "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003548_s10999-021-09538-w-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003548_s10999-021-09538-w-Figure1-1.png",
        "caption": "Fig. 1 a The undeformed and b the final deformed mesh of the slit annular plate problem",
        "texts": [
            " 2018; Kulikov and Plotnikova 2008) and other rotation-free elements (Guo et al. 2002; Flores and On\u0303ate 2011; Zhou and Sze 2012) which possess only translational dofs. As an illustration, the popular benchmark problem in which a slit annular plate with inner radius 6 and outer radius 10 (Sze et al. 2004) meshed into 6 9 30 elements is analyzed by using the four-node shell element models S4 and S4R as well as the 8-node solid-shell element model SC8R of ABAQUS. A line force is applied at the free end of the radial slit while the other end of the slit is fully clamped. Figure 1 shows the undeformed and the final deformed configurations at the maximum line force at 0.8 unit of force per unit length. The default time increment in ABAQUS is adopted, i.e., the initial, minimum, and largest time increment sizes are 1, 10\u20135, and 1, respectively. The default automatic time increment option, see the first paragraph in Sect. 5, is employed. The analyses were conducted in a laptop PC with Intel(R) Core(TM) i9-9880H CPU (8 cores, 2.30 GHz) and 64 GB RAM. The predictions of S4, S4R and SC8R are practically identical",
            " In the automatic time increment process, if the solution cannot converge within 16 iterations, the scheme abandons the increment and starts again with the time increment reduced to one- quarter of the present value. If the solution still fails to converge, the scheme reduces the increment again. If the time increment becomes smaller than the minimum or the solution fails after 5 reductions, the analysis will be aborted. On the other hand, the time increment increases by 50% if the last two converged solutions are both attained within 5 iterations. The computation is conducted in the same laptop PC, with Intel(R) Core(TM) i9-9880H CPU (8 cores, 2.30 GHz) and 64 GB RAM, used to produce the results in Fig. 1 and Table 1. In the description of the examples and the ABAQUS calculations, SI units are employed and would not be further specified. The properties of paperboard E = 3 9 109, m = 0.3 and h = 0.27 9 10\u20133 are adopted (Filipov et al. 2017; Schulgasser 1983). The fold stiffness per unit crease length is taken to be proportional to the bending rigidity, i.e., k = D/L* where L* is a length scaling factor (Lechenault et al. 2014). For paperboards, L* varies typically from 1.6 9 10\u20133 to 133 9 10\u20133 m, see Table 1 of reference (Filipov et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002700_j.jmapro.2019.12.016-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002700_j.jmapro.2019.12.016-Figure7-1.png",
        "caption": "Fig. 7. Principle of grinding the worm tooth profile: (a) influence of the change of the radius of the grinding rod on the worm tooth surface; (b) relationship between the grinding rod and the grinded worm tooth surface.",
        "texts": [
            " 6b shows the worn surface of the rod after the surface grinding. From that figure it can be seen that the top part of the rod was worn out, which verified the theoretical prediction that the contact lines should appear on the top part of the rod. Since the quality of the worm tooth surface is affected by both R and \u03c62, it is therefore hypothesized that the error caused by the reducing R can be compensated by adjusting \u03c62. As mentioned before, any changes in the angle \u03c62 will lead to changes in the amount of axial feed. Fig. 7 illustrates the principle of minimizing the error caused by \u0394R by introduction \u0394\u03c62. Their relationship can be described as \u0394R=Ra \u00d7 \u0394\u03c62 and \u0394Rx = Rx/Ra \u00d7 \u0394R (when the contact point Op changes) (8) Due to the correlation between \u03c62 (\u0394\u03c62) and the amount of axial feed, Eq. (8) reveals the relationship between \u0394R and axial feeding. The agreement between the machining of worms and the theoretical models has been minutely elaborated in [4]. It was found that in the grinding process, the worm tooth surface also changed as the rotation speed of the grinding rod changed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001565_0954406214562632-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001565_0954406214562632-Figure3-1.png",
        "caption": "Figure 3. Cradle coordinate system (RH) for pinion.",
        "texts": [],
        "surrounding_texts": [
            "Spiral bevel gear, machining adjustment parameters, digitized true tooth surface Date received: 31 March 2014; accepted: 10 November 2014"
        ]
    },
    {
        "image_filename": "designv10_12_0003129_tcst.2020.3035004-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003129_tcst.2020.3035004-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor UAV with a cable-suspended payload.",
        "texts": [
            " 3) Two antisway trajectory generation methods are developed: minimum snap trajectory and LQ-shaping. The minimum snap trajectory is generated according to waypoints with the desired reaching time. The trajectory can release the aggressive motion of the system. Then, the trajectory is shaped by the LQ-shaping method to suppress the swing in the transient response of the minimum snap trajectory, with minimally changing the settling time. Finally, the methods are implemented on a quadrotor UAV and verified by both numerical simulations and experimental results. Fig. 1 shows a multirotor UAV with a cable-suspended payload. The payload is suspended as a pendulum under the UAV at a constant distance l from a geometric center (GC) of the UAV. The inertial frame E is defined by the orthogonal unit vectors xE, yE, and zE. Similarly, the body-fixed frame B is located on the GC of the UAV, and P is on the pendulum pivot. The position of GC of the UAV, pU , is denoted as [xyz]T with respect to the frame E, and the position of the payload pL is denoted as [xL yL zL ]T with respect to the frame P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002147_lra.2016.2528293-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002147_lra.2016.2528293-Figure4-1.png",
        "caption": "Fig. 4. Experimental setup used to perform needle insertion experiments. The setup provides translational and rotational motions of needle. An ultrasound machine (SonixTouch, Ultrasonix, BC, Canada) is used to track the needle tip position.",
        "texts": [
            " An estimate of curvature can be obtained from previous insertion data and by adding some safety margin, especially when pre-insertions are undesirable. The proposed algorithm and the procedure for finding the corresponding parameters are shown in Fig. 3 In this section, the steering method introduced in this letter is implemented for needle insertion into phantom and biological tissue. The experimental setup used for conducting the experiments is a 2-DOF prismatic-revolute robotic system as shown in Fig. 4. The translational motion of the needle is performed using a carriage actuated by a DC motor through a belt and pulley mechanism. The needle base is attached to a second DC motor, which is assembled on the translational carriage and performs the needle axial rotations [5]. Using the feedback from motor encoders, the position of the motor shaft is controlled using a PID controller. In these experiments, the needle is inserted at a constant velocity [21]. Using the feedback from motor encoders, the position of the motor shaft is controlled using a PID controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000254_j.jmatprotec.2008.03.067-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000254_j.jmatprotec.2008.03.067-Figure3-1.png",
        "caption": "Fig. 3 \u2013 Micro-element at friction interface.",
        "texts": [
            " In the next surfacing phase, the temperature field retains its quasi-steady condition all through. So, the emphasis is laid on calculating the temperature field in the preheating phase. 3.1. Friction heat source model During the preheating phase, the heat is produced mainly through friction. Based on the assumption that force distribution remains constant, friction heat was worked out through the following steps. First, an annulus with a width of dr and an inner radius of r at the friction interface was produced as illustrated in Fig. 3. 1394 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e d The area magnitude of the shadow part is ds = 2 r dr (1) and the friction force acted on the annulus is df = pf ds = 2 pf r dr (2) where is the friction coefficient between the consumablerod and the substrate. The symbol pf connotes local press at the friciton interface (Yao, 2001): pf = 3F 2 R2 \u221a 1 \u2212 ( r R )2 (3) where R is the consumable-rod\u2019s radius. The friction torsion with regard to point O is dM = r df = 2 pf r2 dr (4) and the friction power at the annulus is dw = dM n 60 2 = n 30 2 pf r2 dr (5) Such that the heat stream density at the annulus is q(r) = dw ds = npf 30 r (6) Take Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001791_978-90-481-9707-1_87-Figure28.7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001791_978-90-481-9707-1_87-Figure28.7-1.png",
        "caption": "Fig. 28.7 UAV with partial structural damage",
        "texts": [
            " Developing adaptive fault-tolerant controllers with associated quantifiable metrics for performance and without requiring restrictive matching conditions is an open area of research. Alternatively, a modelbased approach can also be used for fault-tolerant control. An overview of one such approach is presented here. Fault-tolerant control technique presented here is applicable to aircraft with possible damage that lies approximately in the body x z plane of symmetry, in other words vertical tail damage as illustrated in Fig. 28.7. A linear model of aircraft dynamics was derived in chapter Linear Flight Control Techniques for Unmanned Aerial Vehicles in this book. In that model A represents the matrix containing aerodynamic derivatives and B represents the matrix containing the control effectiveness derivatives. The states of the model considered here are x.t/ D \u0152u; w; q; ; v; p; r; T and the input given by u.t/ D \u0152\u0131e; \u0131f; \u0131a; \u0131r T (see chapter Linear Flight Control Techniques for Unmanned Aerial Vehicles in this book for definitions of these variables; details of the corresponding A and B matrices can be found in Li and Liu 2012)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001518_j.mechmachtheory.2014.01.005-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001518_j.mechmachtheory.2014.01.005-Figure1-1.png",
        "caption": "Fig. 1. Replacing the layers of bevel gear faces width with virtual spur gears.",
        "texts": [
            " Following the procedure developed by Akbarzadeh and Khonsari [8] analysis, contact of the bevel gear teeth is replaced with a set of rollers at each point. Film thickness, friction coefficient and Hertzian pressure at each point along the line of action (LoA) and each layer along face width are calculated. A parametric analysis of the key factors that influence the gear performance is presented. According to the Tredgold approximation [10], the contact of bevel gear teeth can be replaced with a pair of spur gears in which their center line will be laid on the axes of bevel gears as shown in Fig. 1. The number of teeth of virtual spur gears and their equal diameter can be found from the following equations [11]: where zspur \u00bc zbevel cos\u03b3 \u00f01\u00de dspur \u00bc dbevel cos\u03b3 \u00f02\u00de : zspur Number of teeth in virtual spur gear zbevel Number of teeth in bevel gear dbevel Pitch diameter of bevel gear dspur Pitch diameter of virtual spur gear \u03b3 Pitch cone angle. In this study, for higher accuracy, the face width of each tooth of bevel gear is replaced with multiple pairs of spur gears as shown in Fig. 1. In other words, each layer along the face width is replaced with a pair of spur gears. The load distribution is not uniform along the face width and the load changes linearly so that the maximum load is applied on the heel and the minimum at the toe. Moreover, the number of contacting teeth will affect the load distribution for bevel gears. After replacing the bevel gear with multiple spur gears, the load acting on each layer of bevel gear is applied on its equivalent spur gear. Then, the contact of gears pair is replaced with their equivalent rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000281_978-3-540-88464-4_2-Figure2.8-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000281_978-3-540-88464-4_2-Figure2.8-1.png",
        "caption": "Fig. 2.8. Leg searching-movements of a stick insect walking on rough terrain. The experimental situation was such that a stick insect reached the edge of a bridge (front leg) or crossed a gap between two bridges (middle and hind leg). In case of lacking foothold at the end of protraction, the leg performed characteristic searching-movements that look different for each kind of leg. Average trajectories of the tibia-tarsus-joint (heel) are plotted in a body-fixed coordinate frame, centred on the \u03b1-joint of the respective leg. Only the horizontal component of the movement is shown (xy-projection). (Fig. 1 from [86])",
        "texts": [
            " This leads to more natural movements regarding the dynamics of the movement and especially allows for searching movements, as can be found in the insect: An important adaptation of a swing movement can be observed in the stick insect when it does not find ground at the normal end of the swing movement. When the animal then steps into the hole, the leg performs a kind of search movements that consist of more or less regularly oscillating movements (locust: [157]; cockroach: [74, 195]; stick insect: [131, 18, 80, 23]). In stick insects of the species Carausius morosus, searching movements were shown to be stereotypic in that the tarsus movements always follow characteristic trajectories [80]. Fig. 2.8 shows how these trajectories differ between front, middle and hind legs. In front legs, tarsus loops are superimposed by retraction of the thorax-coxa joint. In middle legs, this retraction component is missing, in hind legs it is reversed into a continued protraction. Thus, each leg appears to search progressively towards the body centre. Careful analysis of the leg kinematics revealed no sign of switching from swing movement to a searching movement. In fact, Du\u0308rr [80] showed that swing-net is able to model a swing movement with a terminal set of searching loops without the need of an additional controller (as it had been previously suggested, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure11-1.png",
        "caption": "Fig. 11. Pressure distribution in the oil film for Dg = 5.5 mm basic offset setting change.",
        "texts": [],
        "surrounding_texts": [
            "The pertinent equations governing the pressure and temperature distributions and the oil film shape are the Reynolds, elasticity, energy, and Laplace\u2019s equations. Point contact EHD lubrication analysis is applied because of the theoretical point contact of mismatched hypoid gear teeth. The following general Reynolds equation is used: o ox F2 op ox \u00fe o oy F2 op oy \u00bc o ox F3 F0 \u00f0U1 U2\u00de o oy F3 F0 \u00f0V1 V2\u00de \u00fe q \u00f0W1 W2\u00de: \u00f010\u00de The full energy equation is applied q cp u oT ox \u00fe v oT oy \u00few oT oz k0 o2T ox2 \u00fe o2T oy2 \u00fe o2T oz2 ! \u00bc aT T u op ox \u00fe v op oy \u00fe g ou oz 2 \u00fe ov oz 2 \" # : \u00f011\u00de The equation governing the heat transfer in the pinion and gear teeth is Laplace\u2019s equation: o2Tm ox2 \u00fe o2Tm oy2 \u00fe o2Tm oz2 \u00bc 0; \u00f012\u00de where m = 1 for the pinion tooth, m = 2 for the gear tooth. The composite normal elastic displacement of contacting surfaces in point (x,y), caused by the pressure distribution p(X,Y), is given by nd gear design data Table 2 Basic p Point ra Cutter Machin Basic ti Basic sw Basic cr Sliding Basic m Basic ra Basic o Ratio o Table 3 Lubrica Ambien Minimu Pinion\u2019s Pressur Supplie Temper d\u00f0x; y\u00de \u00bc Kd Z xmax xmin Z ymax ymin p\u00f0X;Y\u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x X\u00de2 \u00fe \u00f0y Y\u00de2 q dX dY; \u00f013\u00de where Kd \u00bc 1 p 1 l2 1 E1 \u00fe 1 l2 2 E2 . The oil film thickness is defined by the expression h\u00f0x; y\u00de \u00bc h0 \u00fe d\u00f0x; y\u00de \u00fe s\u00f0x; y\u00de: \u00f014\u00de The geometrical separation of contacting surfaces, s(x,y), is determined by the real shape of the pinion and gear teeth, generated by the method described in papers [43,44]. In the instantaneous contact point of tooth surfaces s(x,y) = 0. The minimum film thickness, h0, is the minimal clearance of the two tooth flanks caused by the geometry and the elastic deformations of the flanks. inion machine tool settings Concave Convex dius of the cutter (mm) 75.5 75.5 blade angle ( ) 10.0 31.0 e root angle ( ) 3.4404 3.0231 lt angle ( ) 21.2246 18.8172 ivel angle ( ) 34.1845 47.0239 adle angle ( ) 79.8130 73.2048 base setting (mm) 16.498 22.237 achine center (mm) 1.117 0.190 dial (mm) 72.426 69.924 ffset setting (mm) 23.411 22.336 f roll 3.5510 3.4808 nt characteristics and operating parameters t lubricant viscosity (Pa s) 0.19361 m oil film thickness (lm) 1.27 revolution per minute (rpm) 2000 e viscosity exponent (Pa 1) 0.14504 10 7 d oil temperature ( C) 60 ature viscosity exponent (K 1) 0.027 Fig. 3. Pressure distribution in the oil film for the basic values of machine tool setting parameters. The viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included: g \u00bc g0 eag p bg \u00f0T Tg0\u00de; q \u00bc q0 1\u00fe a1 p 1\u00fe b1 p : \u00f015\u00de It should be mentioned that the density is also temperature dependent, but the investigations have shown that in the EHD lubrication of hypoid gears it can be neglected. In the viscosity\u2013pressure relationship the exponent ag is constant in the case of Barus equation and it is pressure dependent in Roelands\u2019 expression [32]: ag \u00bc ln\u00f0c1 g0\u00de p 1\u00fe p c2 z 1 : \u00f016\u00de The EHD load carrying capacity of the oil film is calculated from the pressure by simple integration [41] W \u00bc Z xmax xmin Z ymax ymin p dx dy: \u00f017\u00de The frictional load is defined by the following equations: FT \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F2 Tx \u00fe F2 Ty q ; FTx \u00bc Z xmax xmin Z ymax ymin g ou ox z\u00bc0 dx dy; FTx \u00bc Z xmax xmin Z ymax ymin g ov ox z\u00bc0 dx dy: \u00f018\u00de The friction factor is defined by the ratio of the frictional force to the load and it can be written as fT \u00bc FT W : \u00f019\u00de The Reynolds, elasticity, energy, and Laplace\u2019s equations represent a highly nonlinear integrodifferential system. This system of equations is solved by using the finite difference method and numerical integration. The finite difference method is based on a three-dimensional grid mesh in the oil film and in the teeth. The intervals used to divide the coordinates along the oil film are irregular, they decrease gradually as they approach the pressure peak. The use of such a nonuniform mesh reduces considerably the computational time. Automatic mesh generation in the oil film and in the gear teeth is included. The systems of linear equations, obtained by using finite difference approximation of the Reynolds, elasticity, energy, and Laplace\u2019s equations, are solved by the successive-over-relaxation method. The details of the presented theoretical background are described in Ref. [9]."
        ]
    },
    {
        "image_filename": "designv10_12_0003572_10775463211013245-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003572_10775463211013245-Figure3-1.png",
        "caption": "Figure 3. Deformation diagram of porous material under the load.",
        "texts": [
            " The constitutive model of the metal rubber. Metal rubber is a porous material with many holes, which is a type of orthogonal material. When the gear pair is in the meshing process, the force on the metal rubber is consistent in all directions. Therefore, it is feasible to analyze the structure with porous material theory. The structure model of the porous material is a hollow cube. The length of the cube is l, the thickness of the bar is u, and the load on the middle part of the beam is F, as shown in Figure 3. The maximum bending deflection of the beam \u03b4 can be calculated by the deflection equation (Coussot, 2005) \u03b4 \u00bc Fl3 \u00f048EsIs\u00de (11) where F = \u03c3l2, Is = u4/12, \u03c3 is the stress, Is is the moment of inertia of the bar, and Es is the elastic modulus of the bar. Combined with the compression strain equation \u03b5 = 2\u03b4/l, equation (11) can be expressed as \u03c3 \u00bc 2Es u4\u03b5 l4 (12) where \u03c3 = F/S, \u03b5 = X/L, \u03c1kl 3 = 12\u03c1su 2l, S is the compression area, X is quantity of compression, L is the height of the metal rubber, \u03c1k is the density of the metal rubber, and \u03c1s is the density of the beam in the metal rubber"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001335_j.apm.2013.05.056-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001335_j.apm.2013.05.056-Figure1-1.png",
        "caption": "Fig. 1. General coordinate systems of the worm-shaped tool machining for screw rotors.",
        "texts": [
            " Consequently, in this study, a general mathematical model is established for the generating machining of screw rotors with the worm-shaped tool. In addition, the relative moving coordinate system between the rotor and worm tool is built. The influence of tool feeds in the axial, radial and tangential directions on the generated rotor surface is investigated, and the generated rotor surface error is presented to check the correctness of the developed model. These may be helpful in predicting the tooth surface shape of the machined rotor while the moving path or speed of the worm-shaped tool is changed. As shown in Fig. 1, a general coordinate system for continuous machining of the screw rotor is presented, wherein the coordinate system Sw is affixed to the worm-shaped tool, rotating around the zw axis with a rotation angle /w, coordinate system Sr is affixed to the screw rotor while rotating around the zr axis with a rotation angle /r . The theoretical center distance (E0) is defined as the minimum distance between the rotation axis of the worm-shaped tool and that of the rotor being machined. The minimum distance equals the sum of pitch radiuses, rpw for the tool and rp for the rotor, and is expressed as follows: E0 \u00bc rpw \u00fe rp;i; \u00f02:1\u00de rp;i \u00bc Cdnr;i=\u00f0nr;1 \u00fe nr;2\u00de; \u00f02:2\u00de where Cd is the center distance between rotor axes, n is the number of teeth of the rotor, the subscript i \u00bc 1 denotes the male rotor and i \u00bc 2 denotes the female rotor",
            " The relationships between the shaft angle, the worm-shaped tool helix angle bw, and the machined rotor helix angle br are as follows: the shaft angle is the sum of the lead angle of the worm-shaped tool and the helix angle of the machined rotor if the worm-shaped tool rotates backward toward the screw rotor; otherwise, the shaft angle is the difference between them. The shaft angle can be calculated as follows: w \u00bc \u00f0br \u00fe jwjrbw\u00de; \u00f02:4\u00de where the helix angle of the worm-shaped tool can be calculated from the lead angle of the worm-shaped tool as bw \u00bc 90 kw, jr denotes the rotor rotation direction (jr \u00bc 1 for right and jr \u00bc 1 for left), and jw denotes the worm tool rotation direction (jw \u00bc 1 for right and jw \u00bc 1 for left). As indicated in Fig. 1, during machining of the worm-shaped tool, the ratio of worm-shaped tool rotation angle /w to rotor rotation angle /r must be constant; additionally, the rotor must be rotate differentially with a synchronized revolution offset to ensure the meshing condition when the worm-shaped tool is taking the feed movement. The relationship between the rotation angles of the worm-shaped tool and the rotor can be expressed as: /r \u00bc jw nw/w nr \u00fe D/r; \u00f02:5\u00de where D/r is the offset angle of the rotor corrected with the tool feeds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000007_978-1-4613-2811-7_7-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000007_978-1-4613-2811-7_7-Figure6-1.png",
        "caption": "Figure 6. PADL-J drawing orMBB test piece.",
        "texts": [],
        "surrounding_texts": [
            "adding pointers so that future analysis will be based on up-to-date details of the workpiece. Derivation of Setups-The method adopted here works from a list of setups to be tried. Initially thls list contains all six of the setups assumed possible. These are with the 1001 axis aligned to the positive or negative X, Y, or Z axes of the PADL-I system. Each setup on the list is examined to find the volume of material which can be removed. This is done by analysing the smallest tool pos sible passing along each face in each cel\\. Each tao I is selected from a tool file which holds available tool diameters and their maximum cutting length. Once all the setups have been considered, the one in which the most stock can be machined away becomes the confirmed setup and is removed from the list. The cell representation is then updated to reflect the removal of material during the setup. This is repeated until all the stock material has been removed or no more setups remain on the list. This is shown in Figure 5. References pp. 153-154 Derivation of Roughing Cuts-A simple strategy consisting of a number of parallel paths running along the length or width of the workpiece has been im plemented. The user must choose to which axis the paths are to be parallel. He must also specify a single tool size since the algorithm has not been imple mented for multiple tools. Only those cells accessible by the tool are selected and as the cutter paths within a cell are derived they are concatenated to any previous path if no colli sion is detected. If a collision is detected, then paths are generated to lift the tool to a safe plane above the workpiece, to rapidly traverse to the next position directly above where material removal may continue, and then lower the tool into the workpiece. If a cell is marked as having had all material removed in a previous setup, the feed rate is changed to rapid within that cell (see Figures 6 and 7). Derivation of Finishing Cuts-The spatially ordered cells are scanned until a face is found that requires machining, then the continuation of the face in the neighbouring cell is found, in the direction that would cause climb milling.* The next linked face or boundary is found, and so on, until either the starting point is revisited or the workpiece boundary is encountered. At this stage, gen eration of the finishing path may proceed in the opposite direction, causing con ventional milling. All faces are flagged once they have been machined, to prevent repeated machining later (see Figure 8)."
        ]
    },
    {
        "image_filename": "designv10_12_0000230_j.jweia.2007.06.031-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000230_j.jweia.2007.06.031-Figure1-1.png",
        "caption": "Fig. 1. Flow geometry and coordinate system.",
        "texts": [
            " Okamoto (1980) investigated the flow field of a sphere in contact with a plane and observed the wake structure and the aerodynamic force on the sphere. In the heat transfer field, a sphere was available for the heat transfer enhancement. Seban and Caldwell (1968) presented the effect of a spherical protuberance on local heat transfer on a plane. The present paper describes an experimental study of the flow field and the aerodynamic force on a sphere above a plane for various values of the height above the plane and of the turbulent boundary layer thickness. Fig. 1 shows the sphere-centered coordinate system used in the present study. Experiments were conducted in a low-speed wind tunnel with a working section of 400mm in height, 300mm in width and 1000mm in length. A sphere of diameter d \u00bc 57mm was positioned with a gap S above a plane. The gap S was varied from 0 to 30mm. For the free-stream velocity U \u00bc 22m/s, the Reynolds number based on d was Re \u00bc 8.3 104. The turbulent boundary layer was transformed by a tripping wire (TW) of diameter dt \u00bc 0, 5 or 12mm placed 700mm upstream from the center of the sphere"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003155_978-3-030-48977-9-Figure6.1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003155_978-3-030-48977-9-Figure6.1-1.png",
        "caption": "Fig. 6.1 Non-salient four-pole PM synchronous machine, showing a two-layer, three-phase stator winding and surface magnets on the rotor",
        "texts": [
            " In a synchronous machine, the excitation may be provided by permanent magnets or by a rotor based excitation winding which carries a field current if. In both cases, the flux density distribution due to the excitation is assumed to be sinusoidal. Furthermore, it is assumed that the magnetizing inductance is equal along both axes \u00a9 Springer Nature Switzerland AG 2020 R. W. De Doncker et al., Advanced Electrical Drives, Power Systems, https://doi.org/10.1007/978-3-030-48977-9_6 153 154 6 Synchronous Machine Modeling Concepts of the xy plane that is linked to the rotor. A cross-sectional view of a four-pole PM non-salient machine is given in Fig. 6.1. It shows the stator and the rotor with a set of surface mount magnets. Note the presence of a dual set of xy axes, because a four-pole machine is shown in Fig. 6.1. The machine does not carry any damper windings given that these are normally not found in inverter fed servo drive applications (to avoid losses) which are predominantly considered in this book. The machine can be described by an IRTF based model as shown in Fig. 6.2. The model was derived from the elementary model introduced in Sect. 4.2.1 by accommodating the stator resistance Rs and the stator leakage inductance L\u03c3s. The magnetizing inductance Lm is shown on the rotor side of the machine. In general, inductances of non-salient machines may be placed on either side of the IRTF module"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002127_cjme.2015.0710.091-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002127_cjme.2015.0710.091-Figure5-1.png",
        "caption": "Fig. 5. Hook-thread mechanism of a sewing machine",
        "texts": [
            " The corresponding screw system is as follows: ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 3 1 4 2 4 0 0 0; 1 0 0 , 0 0 1; 0 0 , 0 0 1; 0 0 , 1 0 0; 0 0 , 0 0 0; 1 0 0 , 1 0 0; 0 0 , CF CF F G G D e e f f = = = = = = $ $ $ $ $ $ (18) where screws CF1, CF2 and G1 are virtual pairs. As the virtual loop has six screws and their rank is only four, which indicates there are two over-constraints, 2 2 = . The whole mechanism has five links, and six pairs with eleven motilities, and the total over-constraints are 1 2 2  = + = , then we have ( ) ( )6 1 6 5 6 1 11 2 1.iM n g f = - - + + = - - + + =\u00e5 (19) The virtual loop way is simpler than the former. Fig. 5(a) shows a hook-thread mechanism for a sewing machine. The crank AB drives the rocker CDH via a link rod BC involving two spherical pairs. When connecting points G and H are also two spherical pairs, the output point I in link FG will be driven to achieve a desired trajectory. Firstly, the analysis of the over-constraint is needed before calculating the mobility of this mechanism. This mechanism is a complex multi-loop spatial one. To obtain the over-constraint, such complex problem should be simplified and separated into some sub-parts as far as possible based on the existent knowledge. For this mechanism, it can be considered to have three sub-mechanisms: A four-bar linkage ABCD with double spherical pairs, a spatial guide-bar mechanism AEFI, and also another four-bar linkage FGHD composed with two links DH and FG which are also connected by two spherical pairs G and H. Therefore, the complex mechanism could be decomposed into three separate sub-mechanisms, as shown in Fig. 5(b). The process will be broke down into four steps. (1) Estimate the over-constraint of ABCDA. According to the analysis above, the four-bar linkage mechanism ABCDA with double spherical pairs has no over- constraint, 1 0 = , and has one DOF besides a local DOF. (2) Estimate the over-constraint of AEFIA. The spatial guide-bar mechanism AEFIA consists of crank AE, a guide link EF and a spherical link FG. It is a single-loop mechanism with four links and four kinematic pairs. For the second loop since the crank passes through the axis A and identical with that of the first loop, there is no any kinematic couple between the two loops and the mobility formula can be applied directly",
            " Based on the screw theory, the screw system of the sub-loop is as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 3 3 2 3 3 3 4 6 6 5 7 7 0 1 0; 0 0 0 , 0 1 0; 0 , 1 0 0; 0 , 0 0 0; 1 0 0 , 1 0 0; 0 , 0 1 0; 0 , 0 0 1; 0 . A E F F F F F d f e f e f d f d e = = = = = = = $ $ $ $ $ $ $ (20) The seven screws are linearly dependent and only five of them are independent. They have one reciprocal screw, and CHINESE JOURNAL OF MECHANICAL ENGINEERING \u00b77\u00b7 the reciprocal screw is ( )3 70 1 0; 0 .r e e= - -$ (21) It is a constraint force parallel to Y-axis and passing through point F. It is denoted by a vector arrow in Fig. 5. Since the sub-mechanism AEF is a single loop one, the number of reciprocal screw is just its over-constraint, that is 2 1 = . (3) Sub-mechanism FGHDF. The FGHDF has four links. There are three spherical pairs(F, G and H) and one revolute pair D in the sub-mechanism. However, in fact, as link EF passes through the sphere center F and limits its two rotational freedoms, only one rotation freedom is left. That is to say, the four-bar linkage FGHDF can also be considered as a mechanism with only two spherical pairs like the mechanism ABCDA",
            " Then under the unified-mobility criterion, it is summed as ( ) ( )6 1 6 7 9 1 20 1 3.iM n g f = - - + + = - - + + =\u00e5 (22) There are three DOFs in the mechanism including two local DOFs, where links BC and GH can rotate freely. Note that for a complicated mechanism, it should be simplified firstly to break down the difficult problems into some easier ones, which is a common and nice choice. From this example it is found that although the linkage has three loops, there is no any motion couple among them and this property has been expressed in three-loop graph, as shown in Fig 5(b). Therefore, for kinematic analysis the loop graph should be considered and analyzed. For the example of Altmann No. 35[18], how to analyze the mobility of the strong coupling multi-loop spatial mechanism is shown hereby. The structure diagram and several parts of this mechanism are shown in Fig. 6(a). Fig. 6(b) is its kinematic diagram. Two cubic blocks c1 and c2 are installed on the input and output shafts b1 and b2 by two revolute pairs, respectively, Fig. 6(a) and Fig. 6(b), and meanwhile c1 connects with c2 by a planar kinematic pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.13-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.13-1.png",
        "caption": "Fig. 17.13 Four-bar in a position with stationary value of 1/i . The coupler point C momentarily coinciding with P12 has coordinates x and \u03b7",
        "texts": [
            "53) The corresponding angle \u03d5 is determined by the cosine law: cos\u03d5 = x2 + r21 \u2212 \u03b72 2r1x . (17.54) In Sect. 17.8.4 it is pointed out that not every real root x of (17.53) represents an intersection point of the coupler-curve with the x -axis. A root represents a singular point without kinematical significance if it is associated with values | cos\u03d5| > 1 . In what follows, only those roots are of interest which yield values | cos\u03d5| \u2264 1 . Let now C be the coupler-fixed point which coincides with P12 when the four-bar is in a position with a stationary value of 1/i . In Fig. 17.13 this situation is shown. The coordinate \u03b7 of this point is associated with a solution x of (17.53) which is equal to the stationary value of the coordinate x12 of the center P12 . Although x12 and x have different definitions, x as function of \u03b7 has the same stationary value. From this it follows that the implicit derivative of (17.53) with respect to \u03b7 is valid with dx/d\u03b7 = 0 . This is the equation (x\u2212 )(x2 + \u03b72 \u2212 r21)\u2212 x[(x\u2212 )2 + (\u03b7\u2212 a)2 \u2212 r22]\u2212 2 \u03b7(\u03b7\u2212 a) = 0 . (17.55) This equation and (17.53) together determine the unknowns x and \u03b7 ",
            " Yet, the coupler curve does not intersect the x -axis. In Fig. 17.38 the branch of this curve above the x -axis is shown. The three real roots are marked B0 , P1 and P2 . They represent singular points of the coupler curve. In order to understand this phenomenon (17.80) and (17.81) must be formulated for the special case b1 = \u03b7 , b2 = \u03b7 \u2212 a , \u03b2 = 0 , y = 0 : x2 + \u03b72 \u2212 2x\u03b7 sin\u03b1 = r21 , (x\u2212 )2 +(\u03b7\u2212 a)2 \u2212 2(x\u2212 )(\u03b7\u2212 a) sin\u03b1 = r22 . (17.101) Each equation expresses the cosine law for one of the triangles of Fig. 17.13 . The elimination of sin\u03b1 is possible without imposing the constraint equation cos2 \u03b1 + sin2 \u03b1 = 1 . Simple linear combination of the equations results in (17.100). Only those real solutions of this equation are admissible solutions for which Eqs.(17.101) yield | sin\u03b1| \u2264 1 . Symmetrical coupler curves of a different nature are generated if the fourbar and the coupler triangle satisfy the symmetry conditions r1 = r2 = r and b1 = b2 = b , respectively. Fig. 17.26 shows the system in its symmetrical trapezoidal position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001204_j.mechmachtheory.2013.04.002-Figure3-1.png",
        "caption": "Fig. 3. Parabolic curve at the third quadrant.",
        "texts": [
            " (19) and (20), the equations of the tooth profiles of the driving gear and the driven gear can be expressed respectively as x1 \u00bc a 1\u00fe i sin\u03c61 \u03b8\u00f0 \u00de \u00fe p1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin\u03b8 1\u2212 sin\u03b8 r cos\u03c61 \u03b8\u00f0 \u00de \u00fe p1 sin\u03b8 2 1\u2212 sin\u03b8\u00f0 \u00de sin\u03c61 \u03b8\u00f0 \u00de y1 \u00bc a 1\u00fe i cos\u03c61 \u03b8\u00f0 \u00de\u2212p1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin\u03b8 1\u2212 sin\u03b8 r sin\u03c61 \u03b8\u00f0 \u00de \u00fe p1 sin\u03b8 2 1\u2212 sin\u03b8\u00f0 \u00de cos\u03c61 \u03b8\u00f0 \u00de 8>>< >>: \u00f038\u00de x2 \u00bc ai 1\u00fe i sin \u03c61 u\u00f0 \u00de i \u00fe p1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin\u03b8 1\u2212 sin\u03b8 r cos \u03c61 u\u00f0 \u00de i \u2212 p1 sin\u03b8 2 1\u2212 sin\u03b8\u00f0 \u00de sin \u03c61 u\u00f0 \u00de i y2 \u00bc \u2212 ai 1\u00fe i cos \u03c61 u\u00f0 \u00de i \u00fe p1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin\u03b8 1\u2212 sin\u03b8 r sin \u03c61 u\u00f0 \u00de i \u00fe p1 sin\u03b8 2 1\u2212 sin\u03b8\u00f0 \u00de cos \u03c61 u\u00f0 \u00de i : 8>>< >>: \u00f039\u00de As the gears turn and the contact point moves to the third quadrant, we now study the driven gear and another parabola. Similarly, as shown in Fig. 3, supposing that the vertex of the parabola is located at (0, 0) and its focus at (0,\u2212p2/2), the equation of the parabolic curve in the third quadrant can be expressed as x0 \u00bc \u2212p2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin\u03b8 1\u2212 sin\u03b8 r y0 \u00bc \u2212 p2 sin\u03b8 2 1\u2212 sin\u03b8\u00f0 \u00de : 8>< >: \u00f040\u00de Supposing that the parameter r\u2033 is a non-dimensional parameter, which can be described as r\u2033 \u00bc p2 2 \u00bc k2r1, we then have the following equation. k2 \u00bc p2 2r1 \u00f041\u00de k2 is the ratio of r\u2033 to r1, r1 is the radius of the pitch circle of the driven gear",
            " (49) yields \u03b2 \u00bc sin\u22121 1\u22122k1\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k1 1\u2212k1\u00f0 \u00dep 2k1 1\u2212k1\u00f0 \u00de : \u00f051\u00de Substituting Eq. (51) into Eq. (48), the range of the parameter k1 without undercutting and interference can be yield. sin \u03c0 2z2 b 1\u22122k1\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k1 1\u2212k1\u00f0 \u00dep 2k1 1\u2212k1\u00f0 \u00de \u22641\u22122k1 1\u2212k1 : \u00f052\u00de Similarly, substituting Eq. (39) into Eq. (22), the critical condition of the undercutting of tooth profile of the driving gear can be obtained as follows: \u03b8 \u00bc sin\u22121 1\u22122k2 1\u2212k2 : \u00f053\u00de When the contact point is in the third quadrant as shown in Fig. 3, the angle \u03b3 should be greater than the angle corresponding to a quarter of a tooth of the driving gear. By using the same method, the range of the parameter k2 without undercutting and interference is given as sin \u03c0 2z1 b 1\u22122k2\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2 1\u2212k2\u00f0 \u00dep 2k2 1\u2212k2\u00f0 \u00de \u22641\u22122k2 1\u2212k2 : \u00f054\u00de Based on the analysis above, a design for an example gear drive with a variation of the parabolic parameters is taken to illustrate the proposedmethod and study the impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000427_elt.2008.104-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000427_elt.2008.104-Figure5-1.png",
        "caption": "Figure 5. Analysis of the phase inductance and the phase current.",
        "texts": [
            " The starting excitation control, the excitation commutating control, the constant-power output control, the over speed protection, the over voltage protection, the over current protection, the under voltage protection and also the displaying of some information are all implemented in the controller, which are based on the digital hardware and software. 978-1-4244-1833-6/08/$25.00 \u00a92008 IEEE 2 III. OPERATIONAL PRINCIPLES If the leakage flux of the switched reluctance generator is neglected, the phase inductance L(\u03b8 ) has the form shown in Fig.5, where Lmin is the minimum value of the phase inductance, Lmax is the maximum value of the phase inductance, \u03b8 r is one rotor period, \u03b8 m is the maximum phase inductance rotor position, \u03b8 a and \u03b8 b are related to the stator and the rotor pole-face factor. If the resistance of the phase windings, the voltage drop of the main switches and the on-state voltage drop of the flywheel diodes are neglected, the transient phase current of the switched reluctance generator shown in Fig.5 could be expressed as follows, )]([ )( min 1 a L L U i \u03b8\u03b8 \u03b8 \u03c9 \u03b8\u03b8 \u2212 \u2202 \u2202+ \u2212 = , )( 1 m\u03b8\u03b8\u03b8 \u2264\u2264 max 1)( L U i \u03c9 \u03b8\u03b8 \u2212 = , )( m\u03b8\u03b8 = )]([ )( max 1 m L L U i \u03b8\u03b8 \u03b8 \u03c9 \u03b8\u03b8 \u2212 \u2202 \u2202+ \u2212 = , )( 2\u03b8\u03b8\u03b8 \u2264\u2264m (1) )]([ )()( max 2212 m L L UU i \u03b8\u03b8 \u03b8 \u03c9 \u03b8\u03b8\u03b8\u03b8 \u2212 \u2202 \u2202+ \u2212\u2212\u2212 = , )( 2 b\u03b8\u03b8\u03b8 \u2264< min 2212 )()( L UU i \u03c9 \u03b8\u03b8\u03b8\u03b8 \u2212\u2212\u2212= , )( 3\u03b8\u03b8\u03b8 \u2264\u2264b where U is the phase excitation voltage, U2 is the output voltage of the generator, \u03c9 is the rotor angular speed, the main switches of the excitation power converter are turned on at the turn-on angle, \u03b8 1, turned off at the turn-off angle, \u03b8 2 , and the commutation is finished at commutation angle, \u03b8 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002576_j.promfg.2018.07.118-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002576_j.promfg.2018.07.118-Figure4-1.png",
        "caption": "Fig. 4. Tensile test specimen dimensions in mm.",
        "texts": [
            " The locations of interest were chosen using a sampling method used to maximize data point dispersion when projected onto any in-plane axis. The locations are shown on a thermal image of the wall in Fig. 2. 4 Author name / Procedia Manufacturing 00 (2018) 000\u2013000 Miniaturized ASTM E8 pin-loaded tensile specimens in the vertical (build) orientation were cut from a slice of the thin wall using wire EDM such that the gage section of the specimens coincided with the location of interest. The nominal dimensions of the gage section were 0.8 mm thick by 1.2 mm wide by 2.5 mm long as, shown in Fig. 4. Fig. 4. Tensile test specimen dimensions in mm. The miniature tension coupons were surface treated post-machining to remove any effects from the machining process with a 1.5 hour immersion in Kalling\u2019s Etchant to remove about 0.05 mm from the surface; etch resist was applied to the non-gage portions of the coupon. These cleaned specimens were tested under displacement control using a custom-built, miniature screw-actuated load frame. The tests were conducted under quasi-static, pure tension loading at a nominal (crosshead) strain rate of 5e-4/sec",
            " The locations of interest were chosen using a sampling method used to maximize data point dispersion when projected onto any in-plane axis. The locations are shown on a thermal image of the wall in Fig. 2. 4 Author name / Procedia Manufacturing 00 (2018) 000\u2013000 Miniaturized ASTM E8 pin-loaded tensile specimens in the vertical (build) orientation were cut from a slice of the thin wall using wire EDM such that the gage section of the specimens coincided with the location of interest. The nominal dimensions of the gage section were 0.8 mm thick by 1.2 mm wide by 2.5 mm long as, shown in Fig. 4. The miniature tension coupons were surface treated post-machining to remove any effects from the machining process with a 1.5 hour immersion in Kalling\u2019s Etchant to remove about 0.05 mm from the surface; etch resist was applied to the non-gage portions of the coupon. These cleaned specimens were tested under displacement control using a custom-built, miniature screw-actuated load frame. The tests were conducted under quasi-static, pure tension loading at a nominal (crosshead) strain rate of 5e-4/sec"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000900_s12283-011-0062-7-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000900_s12283-011-0062-7-Figure10-1.png",
        "caption": "Fig. 10 A diagrammatic summary of a typical male and female tennis shot",
        "texts": [
            " For clarity only fore-hand shots have been included. The impact angles shown vary between 14 and 33 from the perpendicular, this is shown diagrammatically alongside the plot. Male players had an average impact angle of 21.9 with a standard deviation of 4.6 . Female players had an average impact angle of 21.2 with a standard deviation of 3.9 . For further clarity the post-impact ball angle to the horizontal has also been included in Table 1. The data presented above are summarised diagrammatically in Fig. 10, the racket velocity at impact is very similar to a value at impact quoted by [19]. As a whole these data represent the first detailed collection of racket shot characteristics obtained during realistic play. Prior to impact, the ball approaches both male and female players with very similar velocities and spin. Each player\u2019s coach or practice partner delivered the ball very consistently. Both sexes struck the ball with very similar impact angles, male players were able to swing the racket with a higher speed on average"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003036_j.eml.2020.100731-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003036_j.eml.2020.100731-Figure6-1.png",
        "caption": "Fig. 6. (a) The experimental setup for the jumping tests. (b) Design principle of the underwater jumper that is designed by the reported TDM. (c) Jumping process of the underwater jumper, including the combustion, membrane oscillation and jumping out processes.",
        "texts": [
            " Taking the advantages of the extreme reaction-soft material interaction, the TDM provides a suitable selection to solve instantaneous rapid starting problems. The drawback of the TDM in the literature, however, is the relatively lower control accuracy due to the over-transient driving time [7,10\u201313,30\u201336]. The combustion-driven soft actuators reported in this study can be a potential solution to address the issue in the TDM by offering well controllability. Here, we develop the underwater jumpers designed by the TDM, which can jump out of water and back to land actively after completing, for example, the tasks of underwater observation. Fig. 6(a) shows the experimental setup for the jumping out test. The underwater jumpers are placed at the bottom of the water tank containing 0.5 m of water in depth. Fig. 6(b) shows the basic design principle of the untethered underwater jumpers. The jumpers consist of the body and reported soft actuator, which are modularly grouped by the assembly unit. The soft actuators are assembled upside down to the body such that to ensure the response unit heading to the seabed to generate an upward thrust force. The combustible gas is preset into the reaction unit, which is adequate to generate 1 to 2 times of out-of-water jumping. Fig. 6(c) shows the jump process captured by the high-speed camera, and the entire process are divided into three processes, including the combustion process, the membrane oscillation process and the jumping-out process (see Supplemental Video S2). During 0\u20138.9 ms when the combustion process was in progress, the response unit of the soft actuator generated an upward thrust force for the jumper by expanding the soft membrane against on the bottom of the tank. Prior to 150 ms, the robot swam to water surface with a membrane oscillation phenomenon which was consistent with the reported experimental results of the actuator test"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003174_s11012-019-01115-y-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003174_s11012-019-01115-y-Figure7-1.png",
        "caption": "Fig. 7 Spalled external gear tooth when the tooth number is greater than 41: a approach process and b recess process",
        "texts": [
            " Approach process: 1 kb \u00bc 1\u00fe h1 h2 Rr=Rb\u00f0 \u00de cos a3\u00bd 3 1\u00fe h1 h2 cos a2\u00bd 3 2ELh2sin 3a2 \u00fe Z a2 a1 3 1\u00fe h1 \u00fe h2 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3L hs= 2Rb\u00f0 \u00de\u00bd 3ls n oda 1 ks \u00bc 1:2 1\u00fe m\u00f0 \u00deh22 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd EL sin a2 \u00fe Z a2 a1 1:2 1\u00fe m\u00f0 \u00deh22 a2 a\u00f0 \u00de cos a E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda 1 ka \u00bc h23 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd 2EL sin a2 \u00fe Z a2 a1 h23 a2 a\u00f0 \u00de cos a 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda \u00f025\u00de Recess process: 1 kb \u00bc 1 h1 h4 Rr=Rb\u00f0 \u00de cos a3\u00bd 3 1 h1 h4 cos a2\u00bd 3 2ELh4sin 3a2 \u00fe Z a2 a1 3 1 h1 h4 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3L hs= 2Rb\u00f0 \u00de\u00bd 3ls n oda 1 ks \u00bc 1:2 1\u00fe m\u00f0 \u00deh24 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd EL sin a2 \u00fe Z a2 a1 1:2 1\u00fe m\u00f0 \u00deh24 a2 a\u00f0 \u00de cos a E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda 1 ka \u00bc h25 cos a2 Rr=Rb\u00f0 \u00de cos a3\u00bd 2EL sin a2 \u00fe Z a2 a1 h25 a2 a\u00f0 \u00de cos a 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda \u00f026\u00de Hertzian stiffness depends on the length of contact. When the spalling defect occurs, the modified expression of Hertzian stiffness can be obtained as follows: 1 khi \u00bc 1:275 L ls\u00f0 \u00de0:8F0:1 i E0:9 \u00f027\u00de When the tooth number is greater than 41, as illustrated in Fig. 7, the TVMS of the external gear tooth with the spalling defect under sliding friction can be obtained for approach process and recess process. Meanwhile, Hertzian stiffness is calculated by using Eq. (27). Approach process: 1 kb \u00bc Z a5 a1 3 1\u00fe h1 \u00fe h2 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3L hs= 2Rb\u00f0 \u00de\u00bd 3ls n oda 1 ks \u00bc Z a5 a1 1:2 1\u00fe m\u00f0 \u00deh22 a2 a\u00f0 \u00de cos a E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda 1 ka \u00bc Z a5 a1 h23 a2 a\u00f0 \u00de cos a 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda \u00f028\u00de Recess process: 1 kb \u00bc Z a5 a1 3 1 h1 h4 a2 a\u00f0 \u00de sin a cos a\u00bd f g2 a2 a\u00f0 \u00de cos a ( ) 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd 3L hs= 2Rb\u00f0 \u00de\u00bd 3ls n oda 1 ks \u00bc Z a5 a1 1:2 1\u00fe m\u00f0 \u00deh24 a2 a\u00f0 \u00de cos a E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda 1 ka \u00bc Z a5 a1 h25 a2 a\u00f0 \u00de cos a 2E a2 a\u00f0 \u00de cos a\u00fe sin a\u00bd L hsls= 2Rb\u00f0 \u00de\u00bd f gda \u00f029\u00de 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002975_tvt.2019.2943414-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002975_tvt.2019.2943414-Figure9-1.png",
        "caption": "Fig. 9. Transient magnetic field distribution in the stator obtained by FEM.",
        "texts": [
            " The effective reaction flux lines can be given in Fig. 7(a). The FEM shows that the sinusoidal eddy current of the stator is concentrated in a certain depth region under the alternating magnetic field, as shown in Fig. 8. Hence, as shown in Fig. 7(b), the MMF generated in the region of the eddy current based on Ampere\u2019s law [14] can be obtained by 2 s 1 s + i (A) ( , ) r c r F Hdl J r rdrd          (19) where, C is the integral circuit of the magnetic field intensity, as shown in Fig. 7(b), and rs is the internal radius of the stator. Fig. 9 shows that the magnetic field is concentrated at skin depth. The skin depth \u2206 can be obtained by 2    (20) where  is the effective permeability of the stator in the transient state. The permeability of the stator and the rotor iron part is much larger than those of the air-gap and the PM. Therefore, the MMF drops across the stator, and the rotor iron part is neglected [17], [18]. Hence, formula (19) can be replaced by: 2 s 1 s + 2 m 0 \u03b42( + ) ( ) / ( ) r i r h B r B drd             (21) Bring formula (17) into formula (21), the following expression can be obtained: 2 1 i 0[ ( )+ ( )]iB u B B d       (22) 3 3 0 s s m (( ) ) 6( ) r r u h        (23) Differentiating formula (22) with respect to  yields a differential equation as follows\uff1a i i 0( ) / ( ) ( )dB d uB uB     (24) According to formula (15) and (23), the air-gap flux density of the armature reaction can be obtained by 2 1 1 m i1 1 1 1 2 2 2 11 m i2 2 1 1 m2 2 i 2 ( 4 ) \u03c0(1+ )2 \u03c0 e - -( )2 - - - - 2 2 44 2 ( 4 ) \u03c02 \u03c0(1+ ) e + +( )2 + - - - 2 4 24 ( ) u u m m m m u pp u B k up p pu up p u u p B k B up p pu up BB                                       i3 3 m 2 11 i4 4 1 1 m2 2 \u03c0 \u03c0 e - - 2 2 2 ( 4 ) \u03c02 \u03c0(1+ e + +( )2 - 2 24 u m m u m m m m k B p p p u u p B k B up pu up                              m 2 1 1 m i5 5 1 1 2 2 ) 4 2 ( 4 ) \u03c0(1+ )2 \u03c0 e - -( )2 - - 2 4 24 u p u pp u B k up p pu up                              (25) where the coefficients k1, k2, k3, k4, and k5 are given in the Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002873_j.mechmachtheory.2019.103669-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002873_j.mechmachtheory.2019.103669-Figure2-1.png",
        "caption": "Fig. 2. The sliding and pivoting speeds on the contact ellipse.",
        "texts": [
            " The methodology to determine the two rolling lines locations on contact ellipse have been developed by Houpert [19] according to the ball\u2019s equilibrium of the forces and moments. This methodology is applied to the 7205B M-ACBB operating at low speed and low axial load for various constant friction coefficients in ball-races contacts. For an ACBB with the inner race stationary and the outer race rotating at a low rotational speed no, the race-ball sliding speeds (in the rolling direction) vsi and vso on the inner and outer ball-race contact ellipses respectively are determined in any slice located at distance y (Fig. 2), using the following formula [1]: vsi,o(y, no,\u03c9c,\u03c9b) = vi,o(y, no,\u03c9c) \u2212 vbi,o(y,\u03c9b) (5) where the angular speed of the ball \u03c9b and the orbital speed of the ball \u03c9c are considered the two unknown kinematic parameters. At a distance y from the centre of inner and outer contact ellipse, the tangential speeds vi and vo in the rolling direction can be expressed using Harris\u2019s equations [1]: vi(y, no,\u03c9c) = \u2212 [ dm 2 \u2212 Ai(y) \u00b7 cos (\u03b1) ] \u00b7 \u03c9i(no,\u03c9c) (6) vo(y, no,\u03c9c) = [ dm 2 + Ao(y) \u00b7 cos (\u03b1) ] \u00b7 \u03c9o(no,\u03c9c) (7) The relative rotational speeds \u03c9i and \u03c9o, as well as the ball rotational speed \u03c9b are presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002019_978-3-662-48487-6-Figure17.37-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002019_978-3-662-48487-6-Figure17.37-1.png",
        "caption": "Fig. 17.37 Measures of quality L/ and |B/L| of Tschebychev\u2019s straight-line approximations as functions of = r/",
        "texts": [
            "168) yield for the location y0 of the straight line and for the measure of quality B/ the formulas y0 = \u221a 2(1\u2212 ) + 1 8 (5\u2212 3 ) \u221a (5\u2212 3 )(1 + ) , (17.173) B = 2 \u221a 2(1\u2212 )\u2212 1 4 (5\u2212 3 ) \u221a (5\u2212 3 )(1 + ) . (17.174) For the ratio L/ Eqs.(17.143) yield y4 = 1 2 cot\u03b14[(3 \u2212 r)2 sin2 \u03b14 + 2 \u2212 r2] = 4 (5\u2212 3 ) \u221a (5\u2212 3 )(1 + ) , (17.175) L = 2x4 = 2 \u221a (3 \u2212 r)2 cos2 \u03b14 \u2212 y24 = 1 2 \u221a 3(5\u2212 3 )(1 + )(3\u2212 )(3 \u2212 1) . (17.176) From L/ and B/ the second measure of quality B/L is calculated. L > 0 requires that > 1/3 . The diagram in Fig. 17.37 shows as functions of the ratios L/ and |B/L| characterizing the quality of the straight-line approximation. The former should be large and the latter very small. These goals are achieved with values of close to 1/3 . Example: With = r/ = .4 (17.171), (17.173), (17.176) and (17.174), determine the coupler length a = 1.3 , the length y0 \u2248 2.19 and the measures of quality L/ \u2248 1.44 and |B/L| \u2248 .00020 . This is an excellent straight-line approximation. The entire coupler curve is shown in Fig. 17.38 . The four-bar is drawn in solid lines. Dashed lines show the cognate fourbar generating the same coupler curve. For the significance of the points B0 , P1 and P2 see the comment following (17.100). For comparison: The straight-line approximations by Watt / Evans (Fig. 17.34a,b ) and by Roberts (Fig. 17.35) are not nearly as good. The measures of quality for Roberts\u2019 approximation are L/ \u2248 1 and |B/L| \u2248 .0068 . From Fig. 17.37 it is seen that with increasing the measure of quality L/ improves while the essential measure of quality |B/L| deteriorates. For = r/ = .5 , for example, the measures are L/ \u2248 2.22 and |B/L| \u2248 .0022 . This is still a very good straight-line approximation. End of example. 626 17 Planar Four-Bar Mechanism Until after Tschebychev\u2019s work on straight-line approximations it was taken for granted that no plane mechanism consisting of rigid links with rotary joints could possibly generate an exact straight line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000845_tr.2010.2104017-Figure11-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000845_tr.2010.2104017-Figure11-1.png",
        "caption": "Fig. 11. Gearbox experimental setup.",
        "texts": [
            "0401, relatively slowly. But when the crack reaches the tooth central line (50% crack), and approaches to 80% crack, the ratio increases almost exponentially. In particular, for the crack level from 70% to 80%, the ratio increases from 0.0539 to 0.1955, very rapidly. When the crack becomes severe (e.g. 80% crack), the ratio change becomes very significant, more than 5 times what it was when the pinion was perfect and slightly damaged. Generally speaking, the ratio has the potential to assess the gear crack progress. Fig. 11 shows the gearbox experimental setup. The gearbox was a single stage reducer composed of a pinion with 20 teeth, and a gear with 21 teeth. The drive pinion speed was 1000 rpm (approximately 16.667 Hz), the driven gear speed was 15.873 Hz, and the meshing frequency was 333.333 Hz. During the experiment, the gearbox was kept running continuously for 12 days, until the pinion deteriorated to an abnormal state. Table III lists the gearbox status with the passage of time. An accelerometer was fixed on the bearing housing that supported the pinion shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems of hourglass worm drive.",
        "texts": [
            " In this study, the mathematical model of this novel hourglass worm drive is established based on the differential geometry theory and the spatial meshing principle. Computerized meshing simulations are carried out to examine the meshing performance. The contact area, transmission error and the capability of backlash-adjustable of this new type hourglass worm drive are checked by the performance test on the prototype. In order to explain the meshing principle of this novel hourglass worm drive, the coordinate systems are setup as shown in Fig. 1 . The coordinate system \u03c3 m ( o m : x m , y m , z m ) is fixed at the original position of the IHB gear and medium gear. The rotatable coordinate system \u03c3 1 ( o 1 : x 1 , y 1 , z 1 ) is rigidly connected to the IHB gear and medium gear, and rotates about axes z 1 with the angular velocity vectors \u03c9 1 . Similarly, the OPE hourglass worm and the relational fixed coordinate system \u03c3 n ( o n : x n , y n , z n ) are given. The rotatable coordinate system \u03c3 2 ( o 2 : x 2 , y 2 , z 2 ) is rigidly connected to the OPE hourglass worm, as well as rotates about axes z 2 with the angular velocity vectors \u03c9 2 ",
            " In the fixed coordinate system \u03c3 m , the equation of right flank tooth surface r 1 R can be represented as follows: r 1 R ( u , \u03b8 ) = [ x R 1 y R 1 z R 1 ] = [ r b cos ( \u03b4\u2212\u03b8\u2212u ) \u2212r b u sin ( \u03b4\u2212\u03b8\u2212u ) \u2212r b sin ( \u03b4\u2212\u03b8\u2212u ) \u2212r b u cos ( \u03b4\u2212\u03b8\u2212u ) r b cos \u03b1 tan \u03b2R \u03b8 ] (1) Similarly, the equation of left flank tooth surface r 1 L is expressed as follows: r 1 L ( u , \u03b8 ) = [ x L 1 y L 1 z L 1 ] = [ r b cos ( \u03b4 + \u03b8\u2212u ) \u2212r b u sin ( \u03b4 + \u03b8\u2212u ) r b sin ( \u03b4 + \u03b8\u2212u )+ r b u cos ( \u03b4 + \u03b8\u2212u ) r b cos \u03b1 tan \u03b2L \u03b8 ] (2) where, u and \u03b8 represent the surface parameters of 1 , \u03b4 is the half of the angular tooth thickness on the base circle, and \u03b1 is the pressure angle of reference circle. As shown in Fig. 1 , the helical angles of two flanks on the IHB gear should be satisfied the following condition: \u03b2L > \u03b2R (3) The tooth surface g of medium gear is actually an oblique plane that is in line contact with the IHB gear tooth surface. The inclination angles on both sides of the tooth surface are also different. The tooth surface of oblique planar gear can be formed as shown in Fig. 3 . In the fixed coordinate system \u03c3 m , the equation of right flank tooth surface r g R of the medium gear is expressed as follows: r g R (v , t) = [ x gR 1 y gR 1 z gR 1 ] = [ v \u2212 r g b + t sin \u03b2bR t cos \u03b2bR ] (4) Similarly, the equation of left flank tooth surface r g L can be expressed as follows: r g L (v , t) = [ x gL 1 y gL 1 z gL 1 ] = [ v r g b \u2212 t sin \u03b2bL \u2212 t cos \u03b2bL ] (5) Here, v and t represent the planar parameters of tooth surface g "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001738_s11249-014-0426-9-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001738_s11249-014-0426-9-Figure1-1.png",
        "caption": "Fig. 1 A ball-on-disc device and schematic of the film measuring system",
        "texts": [
            " In this article, a new test rig for high speeds was developed with the ability to achieve measurement of the traction force at high speeds up to 100 m/s and the lubrication film thickness at speeds up to 42 m/s using ROII technology. The lubrication behavior of starved EHL contacts at high speeds up to 30 m/s was the focus. The influence of centrifugal forces on the asymmetric shape of the oil reservoir and the reduction of film thickness were studied. Results under starved conditions are compared with those under fully flooded conditions. 2.1 Ball-on-Disc Test Rig A ball-on-disc test rig with the ability to measure traction force and obtain clear interference images is used in this test, as shown in Fig. 1. Balls and discs of different materials (such as steel, glass and ceramic) and diameters are used for the tests. The maximum speed of the highspeed spindles for driving the ball and disc are 75,000 and 60,000 rpm, respectively. The maximum linear speed can be up to 100 m/s under pure rolling conditions. In the test, a 22.225-mm-diameter steel ball and 90-mmdiameter glass disc (coated with a semireflective layer of chromium) are independently driven by high-speed spindles so that the overall entrainment speed can be controlled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000739_iros.2010.5651324-Figure10-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000739_iros.2010.5651324-Figure10-1.png",
        "caption": "Fig. 10. New contact point of first leg to get over obstacle",
        "texts": [
            " The new contact point enters the control area of the first leg at some time when the robot moves forward. By a new contact point allocated according to the desired moving direction and on an obstacle, the robot can change the moving direction and climb over the obstacle, respectively. In this paper, as for change of the moving direction, the positions of new contact points are derived empirically as shown in Fig. 9. In addition, when an obstacle exists ahead of the robot, the new contact point is made on the obstacle as shown in Fig.10. An operator gives the robot three commands of moving direction, going forward, turning right and turning left. When moving forward, a new contact point is allocated on the same line of the target point Ptarget with some distance ahead from the front edge of the control area. When turning left (right), a new contact point is allocated on the left (right) side of the control area. As the result, the segment gets a rotational torque for turning. The stroke length of the leg motion depends on the position of a new contact point Pnew1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000249_tac.1982.1103108-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000249_tac.1982.1103108-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [
            " B is nonsingular and Lemma 1 may again be applied to deduce that the feedback control u = - X ( x ) = - a 2 1 1 x ( p - % ; p > f . a t 0 globally asymptotically stabilizes the system and minimizes the cost functional x 2 1 - -controlled response kee response _ _ _ - _ x1 \u20181 \\ \\ \\ -1 As p decreases towards its lower bound, small values of state norm are penalized progressively more heavily in (9), whereas the converse is true for large values of state norm. The effects of such state penalization are clearly evident in Fig. 3. which depicts the time response of state norm, from an initial value of llxoll = 4, for the following three cases: a) p = i ; cr=d2; h r ( x ) = a l x l l x ; b ) p = l ; u = d 2 : N ( x ) = 2 x ( l i n e a r c a s e ) ; c) p = : : a = d 2 : N(x)=211x11-?x. Case a) yields a \u201cquadratic\u201d feedback with efficient regulation characteristics for large values of state norm. Case b) yields a linear feedback design with consequent exponential response. Case c) yields a \u201csquareroot\u201d feedback nith efficient regulation characteristics for small values of state norm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001136_1.4005462-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001136_1.4005462-Figure6-1.png",
        "caption": "Fig. 6 The 3D foot placement estimator searches for a foot placement location for an unstable body (a) that causes the body to enter the third region of stability (b) and not exit (c).",
        "texts": [
            " (42), (A3), (A7) and (A16). The 2D projection of Eq. (42) (achieved by setting \u20ach \u00bc _h \u00bc \u20acb \u00bc _b \u00bc 0) matches Wight et al.\u2019s Eq. (60). Now that it has been shown that foot placement can be used to stabilize a 3D inverted pendulum with a foot (in certain regions of its state-space) we will concentrate on deriving a method to find a desirable foot placement location given the state of the pendulum. The 3DFPE is an estimate of a good location to place a point contact foot to cause a 3D inverted pendulum with a rigid leg (Fig. 6) to transition from a dynamic state to a static standing pose. We assume that the plant to which the 3DFPE is being applied can maintain its balance once the ground projection of the COM is within the convex hull of its foot\u2014as is the case for the Euler pendulum (Fig. 5). The assumptions of the 3DFPE are very similar to those of the Euler pendulum: mass, inertia, and leg length are constant; the foot sticks and does not slip; and the contact is momentum-conserving. In addition, the 3DFPE assumes that a foot placement location that satisfies Eqs",
            " If the pendulum can enter the third region of stability, the direction of ~HGP and ~Hp1 will be parallel before and after contact and have matching u\u0302 vectors. ux uy 0 0 B@ 1 CA \u00bc 1 j~HGP \u00f0\u0302i\u00fe j\u0302\u00dej ~HGP j\u0302 ~HGP i\u0302 0 0 B@ 1 CA (43) If it is not possible to satisfy Eqs. (28) and (29) exactly, a measure of the error, e, associated with a particular choice of ux and uy can be calculated by computing the normalized angular momentum component that is parallel to ~g and ~r (where ~r is the leg vector as in Fig. 6 and is equivalent to~rp=q of the Euler pendulum). e \u00bc 1 ~Hp1 j~Hp1j ux uy 0 0 @ 1 A (44) As e approaches zero, the assumption that the plant rotates in a vertical plane after contact becomes better, making it possible to transition the biped into the third region of stability. Exactly how small e needs to be for the 3DFPE to be accurate remains an open question. The answer will likely be system-dependent and highly influenced by the ratio of the length of the leg to the size of the foot. We assume that steps taken along the line where the plane intersects the ground cause the pendulum to rotate in a vertical plane with a trajectory that leads the COM over the plant foot (satisfying Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.64-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.64-1.png",
        "caption": "Fig. 3.64 Outlook of the EMB (a) as well as comparison between the innovative EMB and the conventional EFMB systems (b) [CONTINENTAL TEVES INC. 2004].",
        "texts": [
            "9 Electro-Mechanical Friction Disc, Ring and Drum Brakes 539 With the EMB researchers are getting involved in pure EMB BBW AWB dispulsion technology that eliminates brake fluids and fluidic lines entirely. The braking force is generated directly at each wheel by high performance E-M motors; which are controlled by an ECU and actuated by signals from an EMB pedal module. The EMB includes all brake and stability functions. It is virtually noiseless, even in ABS mode. A comparison between the innovative EMB and the conventional EFMB systems is presented in Figure 3.64 [CONTINENTAL TEVES INC. 2004]. Advantages of the EMB are as follows: More precise mechatronic control; Reduced mass; Improved automotive vehicle dispatch rates; Higher reliability; Shorter stopping distances and optimised stability; More comfort and safety due to adjustable brake pedals; No brake pedal vibration in ABS mode; Virtually silent; Environmentally friendly no brake oily-fluid or air (gas); Improved crash worthiness; Space saving, using fewer parts; Easier assembly; Capable of analysing all required braking and stability functions; May be easily networked with future traffic management systems; Additional functions such as an electric parking brake (EPB) may be integrated easily; Improved maintenance through information digital monitoring of brake wear and other key characteristics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000691_978-94-007-0409-1-Figure3.58-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000691_978-94-007-0409-1-Figure3.58-1.png",
        "caption": "Fig. 3.58 Cross-section diagrams of a friction (a) disc EMB with a conventional rotary brushed DC-AC mechanocommutator brake-force-actuator motor, designed by ITT Automotive as well as (b) disc EMB and (c) ring EMB with the short-stroke linear tubular brushless DC-AC macrocommuator IPM brake-force-actuator motor, conceived and developed by the Cracow University of Technology\u2019s Automotive Mechatronics Institution, Poland [BALZ ET AL. 1996] -- (a); [FIJALKOWSKI AND KROSNICKI 1994] -- (b) and (c).",
        "texts": [
            " The E-M friction disc, ring or drum brake is free from oil and the operating brake-forceactuator motor\u2019s armature winding is not affected by moisture or vibration. A major advantage could also be in reducing the mass of the E-M friction brakes: discs, rings and drums can be made of silicon-carbide-reinforced aluminium instead of cast iron. Disengagement of the E-M friction disc, ring or drum brakes may be easily arranged electrically by connecting the brake\u2019s ASIM DC-AC macrocommutators to the automotive vehicles\u2019onboard mains in front of the brake-force-actuator E-M motors. Figure 3.58 shows the layout of a friction (a) disc EMB with the conven- tional rotary brushed DC-AC mechanocommutator brake-force-actuator motor [BALZ ET AL. 1996], designed by ITT Automotive, as well as (b) disc EMB and (c) ring EMB with the short-stroke linear tubular brushless DC-AC macrocommutator IPM magnetoelectrically-excited brake-force-actuator motor [FIJALKOWSKI AND KROSNICKI 1994]. 3.9 Electro-Mechanical Friction Disc, Ring and Drum Brakes 533 In these types of EMB, force is applied equally to both sides of the disc or ring rotor and braking action is achieved through the frictional action of inboard and outboard brake friction pads against the disc or ring rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003349_j.measurement.2020.107623-Figure9-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003349_j.measurement.2020.107623-Figure9-1.png",
        "caption": "Fig. 9. Finite element analysis results of the mechanism under each individual force",
        "texts": [
            " (26) as follow: Gt \u00bc 0:06439 0:01283 0:15594 0:54856 7:68379 1:56663 0:01283 0:06439 0:15594 7:68379 0:54856 1:56663 0:01283 0:06439 0:15594 7:68379 0:54856 1:56663 0:06439 0:01283 0:15594 0:54856 7:68379 1:56663 0:06439 0:01283 0:15594 0:54856 7:68379 1:56663 0:01283 0:06439 0:15594 7:68379 0:54856 1:56663 0:01283 0:06439 0:15594 7:68379 0:54856 1:56663 0:06439 0:01283 0:15594 0:54856 7:68379 1:56663 2 66666666666664 3 77777777777775 \u00f028\u00de Using ANSYS finite element simulation software platform, the single-dimensional force of 1000 N and the single-dimensional moment of 5 N\u2219m are applied to the geometric centers of the moving platform of the force sensing mechanism model in the directions of X and Z, respectively. Fig. 9 shows the results of finite \u00f028\u00de element analysis for the six-component F/T force sensing mechanism for loads of Fx, Fz, Mx, Mz. The stress values at the geometric center of the long rectangular beams in the measuring branches are obtained, in order to facilitate the comparison with the theoretical values, the size of the axial pull/pressure of each flexible measuring branch is further gained. Accuracy comparison between theoretical and simulation values of each flexible measuring branch axial pull/pressure of the force sensing mechanism is shown in Table 3 and Table 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003461_j.oceaneng.2020.108054-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003461_j.oceaneng.2020.108054-Figure2-1.png",
        "caption": "Fig. 2. Definition of positive deflection for x-rudder.",
        "texts": [
            " For further simplification, let a1w = (m \u2212 Zw\u0307), a2w = Zq\u0307 a1q = \u2212 Mw\u0307, a2q = ( Iyy \u2212 Mq\u0307 ) q\u0307 f1w = ( Zuq + m ) uq + Zwuw + Zw|w|w|w| + Zq|q|q|q| f1q = Muwuw + Mquq + Mw|w|w|w| + Mq|q|q|q| \u2212 M\u03b8 sin \u03b8 (7) Then the dynamic model of vertical subsystem reduces to { w\u0307 = ( a2qf1w + a2q\u03c4w + a2wf1q + a2w\u03c4q )/( a1wa2q + a2wa1q ) q\u0307 = ( a1wf1q + a1w\u03c4q \u2212 a1qf1w \u2212 a1q\u03c4w )/( a1wa2q + a2wa1q ) (8) Finally, one can obtain the simplest form of the dynamic model: { w\u0307 = fw + b1w\u03c4w + b2w\u03c4q q\u0307 = fq + b1q\u03c4w + b2q\u03c4q (9) where fw = ( a2qf1w + a2wf1q )/( a1wa2q + a2wa1q ) b1w = a2q /( a1wa2q + a2wa1q ) b2w = a2w / a1wa2q + a2wa1q fq = ( a1wf1q \u2212 a1qf1w )/( a1wa2q + a2wa1q ) b1q = \u2212 a1q /( a1wa2q + a2wa1q ) b2q = a1w /( a1wa2q + a2wa1q ) (10) In dynamic models above, the unmodelled dynamics, parameter uncertainty and time-varying property, and external disturbance (Liu et al., 2017) are not characterized. This is supposed to be acceptable because these characteristics and corresponding treatments are beyond the scope of this paper. In general, the derived models can be used for controller design in this paper\u2019s research. For deriving detailed relationship between maneuvering forces and moments \u03c4 = {\u03c4v,\u03c4r,\u03c4w,\u03c4q}before allocation, we assume that the control efforts are linear with the deflection. Define the positive deflection in Fig. 2, then the relationship can be presented as \u23a7 \u23aa \u23a8 \u23aa \u23a9 \u03c4v = Y\u03b41 u2\u03b41 + Y\u03b42 u2\u03b42 + Y\u03b43 u2\u03b43 + Y\u03b44 u2\u03b44 \u03c4w = Z\u03b41 u2\u03b41 + Z\u03b42 u2\u03b42 + Z\u03b43 u2\u03b43 + Z\u03b44 u2\u03b44 \u03c4q = M\u03b41 u2\u03b41 + M\u03b42 u2\u03b42 + M\u03b43 u2\u03b43 + M\u03b44 u2\u03b44 \u03c4r = N\u03b41 u2\u03b41 + N\u03b42 u2\u03b42 + N\u03b43 u2\u03b43 + N\u03b44 u2\u03b44 (11) where Y\u03b4* ,Z\u03b4* ,M\u03b4* ,N\u03b4* are the corresponding hydrodynamic parameters related to the rudders. Usually, roll torque \u03c4p is undesired as it may make the attitude un-Fig. 1. X-rudder underwater vehicles and its reference frames. W. Wang et al. Ocean Engineering 216 (2020) 108054 stable and enhance the difficulty of dynamics control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003199_j.oceaneng.2020.107310-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003199_j.oceaneng.2020.107310-Figure1-1.png",
        "caption": "Fig. 1. Vessel steering coordinate system.",
        "texts": [
            " Second 2 formulates the nonlinear heading model with the drift angle effects and the cascade state\u2013space steering model. The design process of the adaptive backstepping heading controller is expressed in Section 3. In Section 4, the simulation results are displaced to demonstrate the effectiveness of the control method, and the conclusion is given in Section 5. The surface vessel steering system is described by two coordinate systems (i.e. the earth fixed coordinate system \ud835\udc4b0\ud835\udc420\ud835\udc4c0 and body fixed coordinate system \ud835\udc4b\ud835\udc4f\ud835\udc42\ud835\udc4f\ud835\udc4c\ud835\udc4f). The yaw motion of a surface vessel is shown in Fig. 1. Note that there is a small nonzero drift angle \ud835\udefd in turnings, which is typically less than 5\u25e6. Because of this drift angle, the desired course angle cannot be followed accurately when the heading error is defined as \ud835\udf13\ud835\udc52 = \ud835\udf13 \u2212\ud835\udf13\ud835\udc51 in the control design process; therefore, the drift angle should be known. In the present investigations, model based steering control methods for marine vehicles are usually based on Nomoto models. As the firstorder Nomoto model is suitable for course keeping control rather than course-changing control, the model must consider the nonlinear steering conditions as presented by Amerongen and Cate (1975)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000332_tim.2009.2016388-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000332_tim.2009.2016388-Figure1-1.png",
        "caption": "Fig. 1. Two inverted pendulums connected by a spring.",
        "texts": [
            " A continuous saturation function sat((eT i Pibi)/\u03b7) with \u03b7 constant (see [23]) can be used to overcome this issue. Remark 5: The choices of controller parameters are important in obtaining a desired control performance. Generally, the larger the number of NN nodes, the smaller the approximation errors \u03b5Mi and \u03b4Mi . However, the direct determination of the number of NN nodes is still an open problem in control. IV. ILLUSTRATIVE EXAMPLE In this section, an inverted pendulum that is connected by a spring, as shown in Fig. 1 [7], is used as a case study to illustrate the capability of the proposed decentralized adaptive control. Each pendulum may be positioned by a torque input ui applied by a servomotor at its base. It is assumed that both \u03b8i and \u03b8\u0307i (angular position and rate) are available to the ith controller for i = 1, 2. The nonlinear equations that describe the motion of the pendulums are defined as follows: \u23a7\u23aa\u23a8 \u23aa\u23a9 x\u03071,1 = x1,2 x\u03071,2 = ( m1gr j1 \u2212 kr2 4j1 ) sin(x1,1) + kr 2j1 (l \u2212 b) + sat(u1) j1 + kr2 4j1 sin(x2,1) , y1 = x1,1 \u23a7\u23aa\u23a8 \u23aa\u23a9 x\u03072,1 = x2,2 x\u03072,2 = ( m2gr j2 \u2212 kr2 4j2 ) sin(x2,1) \u2212 kr 2j2 (l \u2212 b) + sat(u2) j2 + kr2 4j2 sin(x1,1) , y2 = x2,1 (60) where x1,1 = \u03b81 and x2,1 = \u03b82 are the angular displacements of the pendulums from vertical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003404_j.mechmachtheory.2020.103997-Figure15-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003404_j.mechmachtheory.2020.103997-Figure15-1.png",
        "caption": "Fig. 15. The 5-DOF parallel manipulators: (a) 2T2R + 1-DOF with the Bennett linkage (b) 2T2R + 1-DOF with the four-bar linkage.",
        "texts": [],
        "surrounding_texts": [
            "After consolidating the configurable platforms, 6-DOF parallel manipulators with configurable platforms can degenerate\ninto 5-DOF manipulators. The wrench system of 3T2R parallel mechanisms is a constraint-couple. Two combinations are\nadequate for the wrench system. They are the L 0 F 1 C -limb and L 0 F 0 C -limb, L 0 F 1 C -limb and L 0 F 1 C -limb. For the manipulators with two L 0 F 1 C -limbs, the constraint-couples are parallel. Afterward, the 3T2R parallel mechanism with the planar fourbar platform is obtained, as shown in Fig. 14 (b). For 2T3R parallel manipulators, the wrench system only consists of one\nconstraint-force. The valid combinations to realize one constraint-force can be the L 1 F 0 C -limb and L 0 F 0 C -limb, L 1 F 0 C -limb and L 1 F 0 C -limb. It is noteworthy that two parallel constraint-forces generate a constraint-couple with the direction vertical to the plane defined by the constraints. When three-drive L 1 F 0 C -limbs are adopted to build the 2T3R parallel manipulators, the two constraint-forces must be collinear. Otherwise, one constraint-couple will be generated in the mechanism, then the 6-DOF parallel manipulators degenerate into 2T2R + 1-DOF parallel manipulators with configurable platforms, as shown in\nFigs. 15 and 16 .",
            "For full-controlled parallel mechanisms, the number of active joints is demanded to be equal to the dimension of outputs.\nWhen all active joints are locked, the dimension of the twist system for the end-effectors degenerates into null-space. Oth-\nerwise, the designed manipulator is uncontrollable. The mapping between output and input is demonstrated by the screw\ntheory [ 6 , 40 ]. As the attitude and the position of the platform are determined in the workspace, at least one set of actuating\nparameters is available. Different from CPMs, the derived manipulators are characterized by nonrigid configurable platforms.\nWhen the platform is rigidified, the manipulator can be decomposed into one bottom CPM and one top single-loop mecha-\nnism. For the bottom mechanism, the number of qualified actuators is signified by n a1 . For the top mechanism, the number of required actuators n a2 equals the dimension of the twist system. As a result, ( n a1 + n a2 ) actuators are necessary for the full-controlled GPMs with configurable platforms.",
            "mechanisms. For the planar four-bar configurable platform, the movement between two end-effectors of the platform is\nviewed as a 1-DOF translation. The direction is collinear with the line determined by two relevant points E 1 and E 2 . For the Bennett platform, the motion of two end-effectors can be taken as a rotation. The axis of the rotation is passing through\nthe intersecting point O . It is perpendicular to the plane determined by E 1 , E 2 , and O . It is noteworthy that there is a dependent translation between E 1 E 2 and E 3 E 4 , and the direction is parallel to OO \u0301. Similarly, the relation motion between the end-effectors of other single-loop platforms can be obtained in the following Table 6 [28] .\nTaking the type 4 parallel manipulator shown in Fig. 10 (b) as an example, the qualified actuators of the bottom mecha-\nnism n a1 equals to 3. The dimension of the screw system for the single-loop mechanism is 1. Then the number of actuators ( n a1 + n a2 ) is matched. When all actuators are locked, the mechanism is transformed into a five-bar structure. And the DOF of the derived structure is zero. Therefore, the deployment of driving motors for this manipulator is reasonable. For the 2T3R + 1DOF mechanism shown in Fig. 16 (b), the equation ( n a1 + n a2 ) = 6 is carried out. When all actuators are locked, the mechanism is transformed into a five-bar rigid structure. As a result, the driving scheme of the manipulator is valid. The\ndriving schemes of other manipulators can be analyzed in the same way. Consequently, the driving schemes of manipulators\nshown in Figs. 9\u201312 , 13 (b), 14 (a), 15 and 16 are reasonable.\nThe multi-drive hybrid limbs have the potential to avoid the limbs\u2019 interference to enlarge the workspace of the manip-\nulators. In the premise of the same limb workspace, the proposed parallel manipulators have large workspace because of\nthe fewer connected limbs [14] . By reconfiguring the shapes of moving platforms, the integrated end-effectors can perform\ncooperative motions. In other words, the end-effectors can output parallel or intersecting motions. Therefore, the parallel manipulator has the potential to grasp large objects with irregular shapes. The 3T1R + 1-DOF type 2 manipulator can be applied to designing spatial pick-and-place devices, which are performing in a slanted plane. The 2T2R + 1-DOF manipulator\nhas the potential to be utilized for the oscillating screen equipment in the agricultural production or mining industry.\nAs for the 2T3R + 1DOF parallel manipulators drawn in Figs. 15 and 16 , all active joints are fixed on the base. The floating\nweight from actuators in these manipulators is capable of being eliminated. On the contrary, the floating actuators of serial counterparts have significant unpredictable influence over dynamic performance. As a result, the 2T2R + 1-DOF manipulators\nhave the potential to replace serial automatic assembly robots. Furthermore, the proposed manipulators with configurable\nplatforms can realize multipoint attachment with the environment. Therefore, the obtained manipulators can be utilized for\nthe force-reflecting equipment or the micro-positioning device after grasping objects.\nIn this paper, a systematic approach for synthesizing parallel manipulators with configurable platforms has been pro-\nposed. Two classes of linkages with two or more integrated end-effectors have been designed, and five closed-loop con-\nfigurable platforms have been proposed. Base on the screw theory, the serial limbs and the multi-drive hybrid limbs for\nconstructing mechanisms have been enumerated. The derived limbs can provide various constraints (from none constraint\nto full constraints). Besides, the relationships among all kinds of limbs have been revealed. According to the constraint syn-\nthesis method, a novel family of 4/5/6-DOF parallel manipulators with configurable platforms has been constructed. The\nderived manipulators have been decomposed into 3/4/5-DOF bottom mechanisms and 1-DOF single-loop mechanisms. The\nrequirement that all the actuators are fixed on the base is satisfied. Furthermore, the relative movements between the end-\neffectors of the platforms are equivalent to 1-DOF motions. Finally, the active driving schemes and the potential applications\nof the presented manipulators have been obtained.\nDeclaration of Competing Interests\nThe authors declare that they have no known competing financial interests or personal relationships that could have\nappeared to influence the work reported in this paper."
        ]
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure7.16-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure7.16-1.png",
        "caption": "Figure 7.16. Motion on a smooth cycloid .",
        "texts": [
            "To study the finite amplitude motion, however, the curve geometry must be specified . The finite amplitude motion on a cycloidal curve is investigated, and it is shown that the cycloidal oscillator is exactly simple harmonic, hence isochronous. Moreover, the cycloid is the only plane curve having this property. Momentum, Work, and Energy 7.11.1. Equation ofMotion on an Arbitrary ConcavePath 273 Consider a particle P of massm free to slide on a smooth and concave upward, but otherwise arbitrary curve {i in the vertical plane. The free body diagram of P is shown in Fig. 7.16a. The normal , surface reaction force N is workless, and the gravitational force has potential energy V(y) = mgy. The system is conservative with kinetic energy K (P, t) = ims2,where s(t ) is the arclength along {imeasured from point 0 at y = 0, say. The energy principle (7.73) requires (7.92a) Differentiation of (7.92a) with respect to s yields s+ gdy jds = O. Noting in Fig. 7.16a that . dy smy(s)=-, ds where -1 dyy = tan - ,dx (7.92b) we obtain the equation of motion of P on 0': s+ g sin yes) = o. (7.92c) This is the tangential component of the intrinsic equation of motion of P. Let v(s) == set) and Vo == v(so), So == s(O) at y = Yo initially. Introducing these initial data in (7.92a), integrating the first relation in (7.92b), and noting that ds/ v(s) = dt, we obtain the general solution in terms of set ): v2(s) = v5 - 2g1s sin y(s)ds , So 1s ds t- - - So v(s) ' (7.92d) To do more, we shall need to know the shape function yes)",
            "92c) reduces to the equation for the simple harmonic oscillator: p = (T = v'iKO. V~ (7.93c) The small amplitude frequency f = p12rr and period T = 11f are determined by the radius ofcurvature of the path at the equilibrium point O. For a circular arc of radius Ro = t, (7.93c) describes the small amplitude oscillations of a simple pendulum of length e, for example. 7.11.3. Finite Amplitude Oscillations on a Cycloid Now consider the finite amplitude oscillations of a particle on a smooth cycloid generated by a point P, starting at 0, on a circle of radius a, as shown in Fig. 7.16. As the circle rolls toward the right, without slipping on the horizontal line at y = 2a, the radial line turns counterclockwise through the angle fJ E [0, rr] measured from its initial vertical direction at O. Hence, the parametric equations of the cycloid are described by the Cartesian coordinates of P, namely, x = a(fJ+ sin fJ) , y = a(l - cos fJ) . (7.94a) Clearly, y E [0,2aJ, and for symmetric oscillations , fJ E [-rr, rr] and x E [-rra , rra]. (See Example 2.5, page 109, in Volume I.) The tangent angle yes) in (7.92b) and the curvature K(S) of the cycloid are readily determined from (7.94a). With the aid of the double angle trigonometric Momentum, Work, and Energy identities, we first obtain 275 f3 f3 dx = 4a COS 2 \"2d\"2' These yield dy = 4a sin f!.- cos f!.-df!.- . 2 2 2 dy f3 - = tandx 2' 1 ds f3 R = - = --- =4acos- . K d (f312) 2 (7.94b) Therefore, from the second relation in (7.92b), the tangent angle y(s) in Fig. 7.16 and the radius of curvature R(y) of the cycloid are given by f3 ds y = -2' R(y) = - = 4a cos y . (7.94c) dy Hence, y E [-Jr12, n 12] and R(y) decreases from R(O) = 4a to R(\u00b1Jr12) = O. The greatest amplitude is restricted by the curve geometry shown in Fig. 7.16 for y E [-Jr12, n 12]. Integration of the last equation in (7.94c) determines the function y(s): s = l Y 4a cos ydy = 4a sin y(s). (7.94d) Use of this relation in (7.92c) yields the exact equation ofmotion ofa particle free to slide on a smooth cycloid in the vertical plane: .. + 2 0s P s = , p = Jgl4a . (7.94e) We thus find a most interesting result: The finite amplitude, cycloidal motion is exactly simple harmonic and hence isochronous. The period of the cycloidal pendulum for all amplitudes is a constant given by r = 4Jrl ",
            "94f) is truly astonishing: If a particle ofarbitrary mass slides from a position ofrest at any point whatsoever on a smooth cycloid, it reaches the bottom always in the same time t* = r 14 = n Jalg. We notice from (7.94c) that Ro == R(O) = 4a at the equilibrium position y = O. Hence, the small amplitude formulas (7.93c) are the same, of course, as the exact relations (7.94e) for arbitrary amplitudes. Exercise 7.16. The analysis reveals some additional geometrical properties of the cycloid. Consider the cycloidal curve from 0 to its orthogonal intersection with the line y = 2a at S in Fig. 7.16 and derive the following properties. (a) The length a of the cycloid from 0 to S is equal to its radius of curvature at 0: a = 4a = Ro. (b) The slope of the cycloid at a point P situated at a distance s from 0 is equal to theproduct of the curvature K(S) = 1I R(s) and the arc length 276 Chapter 7 dy y = tan- 1 - , dx (7.95a) s at P: tan y = KS =S/ R. (c) At a point P on a cycloid, the sum of squares of its radius of curvature and its arc length from 0 is a constant equal to the square of the radius of curvature Ro= 4a at its lowest point: R2 + s2 = l6a 2, and hence S and R(s) at every point on a cycloid describe the same circle of radius Ro in the Rs-plane",
            "17, the evolute of the cycloid arc 0 S is the similar cycloid arc QS, both are generated by a circle of radius a. As P moves from S toward 0, the center of curvature T of the arc 0 S traces the arc from S to Q. In other words, if a string of length 4a is tied to a fixed point Q that forms the cusp of an inverted cycloidal curve in Fig . 7.17, and the string is pulled over the contour arc QS to point S where the bob is rele ased from rest, the bob will describe the same cycloidal path as as our sliding particle in Fig. 7.16 . On the basis of these unique 278 Chapter 7 (7.96a) properties of the cycloid,Huygens's isochronalpendulummaybeconstructedwith shortened cycloidal surfaces at the cusp support Q so that the bob P moves on a shorter cycloidal path of some practical design dimensions. Subsequent inventors introduced certain drivecontrol devices to adjust for energy losses due to frictional effects that would otherwise lead to variations in the amplitude. 7.12. Orbital Motion and Kepler's Laws Consider a body P ofmassm movingrelative to an inertial frame qJ= {O ;ek} under a central directed gravitational force (7",
            " A particle is given a small displacement from a stable equilibrium state on a smooth Archimedean spiral r = a</> in the vertical plane. Here a is a positive constant. Find the frequency of the oscillation about the first stable equilibrium state. Is the frequency about other stable equilibrium states larger or smaller? Explain this and support your answer with an example. See Problem 4.51 in Volume I. 7.64. A particle of mass m, initially at rest, slides in the vertical plane on a smooth cycloid shown in Fig. 7.16, page 273, and described by (7.94a) . Let yes) denote the slope angle of the curve at s, and Yo its value at the particle 's initial position . (a) Find as a function of y and Yo the time to reach a lower point on the curve . Do this two ways: (i) apply the energy integral (7.92a) and (ii) use the general solution of (7.94e). (b) Hence, show that regardless of its initial position, the particle will always reach the minimum point on the cycloid in the time t = r / 4. 7.65. A bead of mass m slides on a smooth wire in the vertical plane ",
            " If its speed is proportional to the distance traveled from the highest point on the curve , determine the path. 7.67. A particle of mass m is at rest at the vertex of a smooth , inverted cycloid in the vertical plane . When slightly disturbed, it slides down the cycloidal surface . (a) Find the vertical distance Momentum, Work, and Energy 299 below the vertex at which the particle leaves the surface . (b) Determine the distance traveled and the speed at that instant. 7.68. Consider an arbitrary point P on a smooth cycloid (7.94a) in the vertical plane frame <P = {o; i , j] in Fig. 7.16, page 273. A particle of mass m is released from rest to slide on a smooth, straight wire from the point P to the origin o. (a) Derive an equation for the normalized time of descent Ti = t[ / J(i1g along the wire, as a function of the angle fJ at the initial point P on the cycloid . (b) Show that for all values of fJ E [0, Jr] the normalized time of descent Tt exceeds the normalized time of descent T; = te / J(i1g of a particle sliding on the cycloid from the same point P. In particular, show that for fJ E [0, rr], Ti E [4, (Jr2+ 4)1/2], which is everywhere greater than Te \u2022 Hence, no matter where the motion starts, a particle that slides on the cycloid from point P always is the first to reach 0; moreover, the result is independent of the particle 's mass "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001801_rpj-04-2014-0046-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001801_rpj-04-2014-0046-Figure4-1.png",
        "caption": "Figure 4 (a) Desired object; (b) sliced model; (c) laser beam tracks; (d) layer treatment process; (e) recorded signal",
        "texts": [
            " Transversal and longitudinal profiles of brightness temperature captured by the CCD camera were obtained after treatment and averaging of five consecutive images. The values of brightness temperature presented in Figures 6(b), 10 correspond to the maximum temperature value in the HAZ. For the further discussion, it is necessary to specify the meaning of \u201ctrack\u201d and \u201chatch distance\u201d. A track is the result of the laser beam scanning with a constant speed along a straight line over the powder bed. The hatch distance, , [Figure 4(d)] is the distance between neighboring tracks. To monitor the SLM thermal phenomena, a 10 10-mm2 surface area was subjected to laser beam scanning. The scanning strategy is presented in Figure 4: the scanning direction is the same within each layer. The tracks are unidirectional to avoid heat accumulation at their end points (Figure 4). One may note that the laser beam jumps between the consecutive tracks with a much higher speed (3 103 mm/s) than the beam scanning speed (120 mm/s) during track formation. The experiments were carried out using Phenix PM100 machine (see SLM schematic in Figure 1). Laser source was YLR-50 a continuous wave Ytterbium fiber laser by IPG Photonics operating at 1,075-nm wavelength with P 50 W maximum output power. In the present study, 32-W power was delivered to the powder layer. The laser spot size on the surface of the powder bed was 70 m in diameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002182_s1672-6529(16)60323-2-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002182_s1672-6529(16)60323-2-Figure3-1.png",
        "caption": "Fig. 3 The experimental SUH.",
        "texts": [
            " The top k particles that have relatively low fitness levels are selected to create a virtual particle and generate a new global best position. These particles will keep track of the new best position in the predefined search space and finally find the global best solution. As a result, the proposed IPSO method can achieve a fast exploration speed during the search, and the stability of the whole algorithm can be guaranteed. The flowchart of the IPSO method is shown in Fig. 2. The end condition is that either fitness is lower than the predefined error bound, EBerr, or iteration reaches the upper limit, ULmax. As shown in Fig. 3, an experimental SUH is developed and implemented as a test bed for evaluation purposes. The experimental SUH is equipped with an AHRS that can provide three-axis linear acceleration, three-axis earth-magnetic field data, and three-axis an- gular velocity. The position information is obtained from GPS. By using an extended Kalman filter, the three-axis linear velocity information can be estimated by fusing data from AHRS and GPS. The onboard flight control modules are used to generate command inputs and record the flight data to an 8GB SD memory card"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003704_s00170-021-06768-2-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003704_s00170-021-06768-2-Figure3-1.png",
        "caption": "Fig. 3 Schematic of powder consolidation in EBSM",
        "texts": [
            " Similarly, this stochastic depostition model can also generate powder layers with desired characteristics in 2-D cases. Figure 2 shows the generated 2-D random powder layers with different characteristics. The powder particles are heated, melted, and solidified through an electron beam scanning and then consolidated into layers. This process involves complicated physical phenomena at multiscale, e.g., heat transfer, phase transformation of materials, flow of molten pool driven by surface and volume forces, and so on. The focus in this work is the consolidation process of powder particles, as shown in the Fig. 3. Therefore, the underlying incompressible Navier-Stokes equations [25] are solved with high fidelity to demonstrate the individual particles, and meanwhile, some source terms to model the heat input, surface tension, melting, and solidification are added [26, 27]: \u2202 \u03c1\u00f0 \u00de \u2202t \u00fe \u2207\u22c5 \u03c1V ! \u00bc 0; \u00f01\u00de \u2202 \u03c1 v! \u2202t \u00fe \u2207\u22c5 \u03c1 v!\u2297 v! \u00bc \u2207\u22c5 \u03bc\u2207 v! \u2212\u2207p\u00fe Sst \u00fe Amush 1\u2212 f l\u00f0 \u00de2 f 3l \u00fe \u03b4 v!; \u00f02\u00de \u2202 \u2202t \u03c1H\u00f0 \u00de \u00fe \u2207\u22c5 \u03c1V ! H \u00bc \u2207\u22c5 \u03be\u2207T\u00f0 \u00de \u00fe Qinput; \u00f03\u00de where Sst represent the momentum source term induced by surface tension. Qinput is the input heat source induced by the incident electron beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000436_bf02991399-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000436_bf02991399-Figure1-1.png",
        "caption": "FIG. 1. Schematic diagram of the microbial electrode. 1, Immobilized Cl. butyricurn; 2, platinum electrode; 3, silver peroxide electrode (Ag202); 4, O-ring; 5, electrolyte (0.I M phosphate buffer); 6, anion exchange membrane.",
        "texts": [
            " The solution was then saturated with nitrogen gas. Then 0.5 ml of the solution was cast on the platinum electrode covered with nylon net (effective surface area 9.1cm2). The polymerization reaction was initiated with 0.03 ml of 10% dimethylaminopropionitrile and 0.1 mg of potassium persulfate and was allowed to proceed anaerobically for 30 min at 37~ The resulting microbial electrode was stored in 0.1 M phosphate buffer (pH 7.0) containing 0.5% of glucose at 5~ A schematic diagram of the microbial electrode is shown in Fig. 1. The cathode was silver peroxide (Ag202) and the anode was a platinum electrode. The electrolyte was 50 ml of 0.1 M phosphate buffer (pH 7.0) and anion exchange membrane (Selemion Type AMV, Asahi Glass Company) was used as a separator. Standard solution (0.1 M phosphate buffer, pH 7.0) containing glucose and glutamate was employed as a model wastewater according to JIS (7). Wastewaters were diluted to 0-220 ppm (BOD) by 0.1 M phosphate buffer (pH 7.0). The microbial electrode was immersed in the sample wastewater and the current of the microbial electrode was measured by a millivoltammeter (Kikusui Electronics Model 114) and the signal obtainedwas displayed on a recorder (Riken Denshi, Model SP-J5C)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure10.2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure10.2-1.png",
        "caption": "Figure 10.2. Schema for the law of mutual action.",
        "texts": [
            " On that occasion, however, there was no explicit identification of his second law; this followed in the work published in 1771. Discussion of Euler's laws will continue following some observations on the law of action and reaction. So far, a principle of mutual action corresponding to Newton's third law, already applied repeatedly to interactions between pairs of bodies, has not been formally set down. We are going to show that the law of mutual action for bodies may be derived from Euler's laws of motion. + Consider the force distribution dF(P , t) at time t acting over the free body g'j shown in Fig. 10.2a, so that the total force on g'j is given by 00.9). Now suppose that g'j is divided into separate parts g'j] and g'j 2 so that g'j = g'j l Ug'j2 , as shown in Fig. 1O.2a.Letf, denote the part of the total force 00.9) that acts on the part g'jk,namely, fk == f( qjk, t) = LkdF(Pk, t) , 00.12) j The theorem on mutual action of force s is due to Noll . See the sources listed in the chapter references. Dynamics of a Rigid Body 415 where Pk is a material point belonging to \u00a3?13k \u2022Then by (10.9) and (10",
            " To prove this, let us consider the moment about a fixed point 0 of all forces that act on 9i3 = 9i31U 9132 and its separate parts 9131 and 9132. For the body 913 in Fig. 1O.2a, by (10.3) and (10 .10), ' 1 dho(9i3, t)M o(9i3, t) = xo(P, t) x dF(P , t) = . ~ dt In addition, since f 1 and f2 are those portions of the total force F(9i3, t ) that act on the contiguous parts 913 , and 9132, respectivel y, we have M o(9i3, t) =1xo(PI , t ) X dfl (P I , t )+1XO(P2, t ) X df2(P2, t ), ~I ~2 (10.20) where Pk denotes a material point of the part 9i3k \u2022 And for the separate parts 9131 and 9132 in Fig. 10.2b, wherein db j k is the elemental mutual force exerted on the disjoint part a3 j by 9i3k \u2022 Adding the last two equations and introducing (10 .20), we obtain MO(.'X3 I , t) +MO(~2 , t ) = M o(9i3 , t) + f -!!3\\ xo(P1, t) X db 12(PI, t) dho(~l , t ) dho(~2 , t)+ f d> XO(P2, t) X db21(P2, t ) = + . ~'J2 dt dt (10.21) Since 913 = 9131U9132, also hO(9?3 I , t )+hO(9i32, t )= hO(9i31U9132, t) = ho(9i3, t ). Hence , using this relation in (10.21) and recalling (10.19 ), we conclude that the 418 Chapter 10 resultant moment about 0 ofthe mutual forces vanishes: 1XO(Pl, t) X db 12(Pj , t) +1XO(P2 , t) X db21(P2, t) = O",
            "31 b) that acts on the part YB I , while f2 = W2 + T is that part of the total force (10.31b) that acts on the part YB2\u2022 Hence, F(YB, r) = f l + f2 in (10.13) is equivalent to (10.3lb). We shall ignore the mutual body force between YB] and YB2\u2022 Then N = b'2 is the mutual contact force Dynamics of a Rigid Body 421 exerted on a'l l by a'l2; and in accordance with the law of mutual action, we wish to demonstrate that b21= -b12 = -N for the mutual contact force exerted on a'l2 by a'l ]. (The reader should now draw the free body diagrams suggested in Fig. 10.2. for the problem in Fig. 10.3a.) Therefore, with the aid of (10.15) and the foregoing identification of terms, the total force (l 0.14) on the free body a'l ], the crate alone, is (l0.31c) and on a'l2, the elevator alone, is F2 =W2+ T + b21 = - . (l0.31d) dt Adding (l0.31c) and (l0.31d) and noting (l0.31b), we reach A A d F 1+ F2 = F(a'l, t) + N + b21 = dt (PI + P2). (l0.31e) However, by (5.11), p(a'l, t) == pea'll U a'l2, t) = p(a'l] , t) + P(a'l2, t), and hence the far right-hand side of (l0.31e) is the total force F(a'l , t) on a'l "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002700_j.jmapro.2019.12.016-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002700_j.jmapro.2019.12.016-Figure3-1.png",
        "caption": "Fig. 3. Coordinate system of grinding the worm tooth surface.",
        "texts": [
            " Following the approach introduced in [14], this equation is expressed as \u0394E = f(\u0394a, \u0394\u03c62, \u0394\u03b1, \u0394c, \u0394d, \u0394\u03b2, \u0394R) (1) In above equation, \u0394a represents the error in center distance between the grinding rod and the worm blank; \u0394\u03c62 denotes the error in axial feeding of the grinding rod; \u0394\u03b1 is the error of angular pitch; \u0394c represents the error generated by the grinding apparatus along the k2 axis; \u0394d means the axial error motion between the worm and worm wheel along the k1 axis and \u0394d = \u0394x1 + \u0394x2; \u0394\u03b2 denotes the motion error of the grinding apparatus along the perpendicular direction (along the k2 axis); and \u0394R is the error caused by the change of the radius of the grinding rod due to abrasive wear. Based on the principles of worm gear grinding and engagement, coordinate systems between the worm and worm wheel and between the worm and the grinding rod can be established as depicted in Fig. 3a and b. The displayed coordinate systems are defined as follows: S0 (i0, j0, k0) is a coordinate system fixed at the center of the grinding rod (O0); S01 (i01, j01, k01) and S02 (i02, j02, k02) are ideal coordinate systems fixed on the worm and worm wheel, respectively; S1 (i1, j1, k1) and S2 (i2, j2, Nomenclature A Center distance between the worm and worm wheel i Speed ratio, i = \u03c92/\u03c91 R Radius of the grinding rod Ra Radius of base circle of the worm wheel da Diameter of base circle of the worm wheel u Parameter of the contact point on cylindrical surface of the grinding rod v12 Relative velocity vector n Unit normal vector at the contact point Op \u03b8 Rotation angle of the grinding rod \u03c62 Directional angle of the grinding rod \u03c91, \u03c92 Rotation speed for worm and worm wheel, respectively \u0394a Error in center distance between the grinding rod and the worm blank \u0394\u03c62 Error in directional angle of the grinding rod \u0394\u03b1 Error of angular pitch \u0394c Error generated by the grinding apparatus along the k2 axis \u0394d Axial error motion between the worm and worm wheel along the k1 axis, \u0394d = \u0394x1 + \u0394x2 \u0394\u03b2 Motion error of the grinding apparatus along the perpendicular direction (along the k2 axis) \u0394R Error caused by the change of the radius of the grinding rod due to abrasive wear \u0394E Overall error M02\u2019 and Mpa\u2019 Transformation matrices M1, M2, M3 Coefficients of equation of meshing S0 (i0, j0, k0) Coordinate system fixed at the center of the grinding rod S01 (i01, j01, k01) Ideal coordinate system (error free) fixed on the worm S02 (i02, j02, k02) Ideal coordinate system (error free) fixed on the worm wheel S1 (i1, j1, k1) Practical coordinate system fixed on the worm S2 (i2, j2, k2) Practical coordinate system fixed on the worm wheel S1\u2019 (i1\u2019, j1\u2019, k1\u2019) Practical, movable coordinate system attached to the worm S2\u2019 (i2\u2019, j2\u2019, k2\u2019) Practical, movable coordinate system attached to the worm wheel Sp (ip, jp, kp) Practical, movable coordinate system attached to the contact point Op k2) are practical coordinate systems that are affected by the seven error parameters in Eq. (1), which are fixed on the worm and worm wheel, respectively; S1\u2019 (i1\u2019, j1\u2019, k1\u2019) and S2\u2019 (i2\u2019, j2\u2019, k2\u2019) are practical and movable coordinate systems attached to the worm and worm wheel, respectively; and Sp (ip, jp, kp) is a practical, movable coordinate system attached to the contact point Op As shown in Fig. 3, coordinates of the origin of the coordinate system S0, O0, in S2 are (a2, 0, \u0394c2), where a2 = da/2 and da is the diameter of base circle of the worm wheel. Transformation matrix from S0 to the movable coordinate system at worm wheel S2\u2019 can be derived as = \u23a7 \u23a8 \u23aa \u23a9\u23aa \u2212 \u2212 \u2212 \u23ab \u23ac \u23aa \u23ad\u23aa \u2032M sin\u03b1 cos\u03b1 cos\u03b1 a sin\u03b1 \u0394c 0 0 0 1 0 0 0 0 0 1 02 2 (2) Similarly, the transformation matrix from Sp to S2\u2019 can be obtained as = \u23a7 \u23a8 \u23aa \u23a9\u23aa \u2212 \u2212 \u2212 \u2212 \u2212 \u23ab \u23ac \u23aa \u23ad\u23aa \u2032M sin\u03b1cos\u03b8 cos\u03b1 cos\u03b1cos\u03b8 sin\u03b1 sin\u03b1sin\u03b8 a cos\u03b1sin\u03b8 sin\u03b8 cos\u03b8 \u0394c 0 0 0 0 0 1 p2 2 (3) The vector equation of the surface of the grinding rod in S0 is expressed as \u23a7 \u23a8 \u23aa \u23a9 \u23aa = + + = = = r i j kx y z x R \u03b8 y R \u03b8 z u cos sin 0 0 0 0 0 0 0 0 0 0 (4) where R is the radius of the grinding rod, \u03b8 and u are parameters of the contact point on cylindrical surface of the grinding rod, as indicated in Fig. 3. According to the theory of gear meshing [15], relative velocity of the contact point Op in the movable coordinate systems S1\u2019 and S2\u2019 has to satisfy \u22c5 =\u03bd n 012 (5) where v12 is the relative velocity vector of the worm with respect to the worm wheel on the contact point, and n is the unit normal vector at Op. Eq. (5) means that the relative velocity at the contact point should be perpendicular to the normal direction at that point. During gear meshing, tooth surfaces of the meshing gears will remain contact only if Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001735_j.mechmachtheory.2015.03.018-Figure2-1.png",
        "caption": "Fig. 2. The 8/4-4 type platform structure sensor with isometric legs.",
        "texts": [
            " Besides, it will complicate the sensor structure and go against the improvement of measuring precision. Eight measuring limbs are determined to be a reasonable redundant allocation in order to keep the symmetric structure and present fault-tolerance. Therefore, the 8/4-4 type platform structure sensor with isometric legs is proposed, considering isotropic configuration and the high-reliability that redundant parallel structure holds. The drawing of the 8/4-4 type platform structure sensor with isometric legs is shown in Fig. 2. The Cartesian coordinate O-XYZ called frame {\u03a9}, is set up with its origin located at the geometrical center of the upper platform. The configuration is determined by the following parameters: Rn, Rw, r, H, \u03b11, \u03b12, \u03b21 and \u03b22. Rn and Rw denote the radii of the two concentric circles on the lower platform, on which the centers of spherical joints are located. r denotes the radius of the upper platform. Ai (i= 1,2\u2026,8) and Bi (i= 1,2\u2026,8) are the centers of the i-th spherical joints of the upper and the lower platforms, respectively",
            " As a result, the 4/8/4 type platform structure sensor with isometric legs is proposed. The 8/4-4 structure is a parallel structure with its legs being placed on one platform and divided into two sets. If the axes of either set are lengthened in the direction along the upper platform, the result is the 4/8/4 type platform structure sensor with isometric legs. The latter case is shown in Fig. 3. Still, this type possesses a half-symmetric structure and all the legs are equal in length. Therefore, it is similar to the 8/4-4 type which is shown in Fig. 2. Besides, three platforms includes the upper one used for pre-stress, themiddle one used formeasurement and the lower one used for fixation. This structural distribution realizes full pre-stress on all themeasuring legs and results in better mechanical characteristics. The configuration is determined by the following parameters: Rs, Rw, r, Hs, \u03b11, \u03b12, \u03b21 and\u03b22. Rs denotes the radius of the upper platform. r denotes the radius of themiddle platform, onwhich the centers of eight spherical joints are located. Hs denotes the distance between the upper andmiddle platforms. The other parameters: Rw, \u03b11, \u03b12, \u03b21 and \u03b22, have the same meanings as those in Fig. 2. Similarly, the force Jacobian matrix can be obtained by screw theory. The relation among size parameters can be obtained by analyzing the lineage between the 4/8/4 type platform structure and 8/4-4 type platform structure as shown in Eq. (11). ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rs cos \u03b32\u2212r cos\u03b12\u00f0 \u00de2 \u00fe Rs sin \u03b32\u2212r sin \u03b12\u00f0 \u00de2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rw cos \u03b22\u2212r cos\u03b12\u00f0 \u00de2 \u00fe Rw sin \u03b22\u2212r sin \u03b12\u00f0 \u00de2 q \u00bc Hs H \u00bc l l \u00f011\u00de Then, the size changes between the two structures can be expressed as Hs \u00bc H R2 s\u22122Rsr cos \u03b32\u2212\u03b12\u00f0 \u00de \u00bc R2 w\u22122Rwr cos \u03b22\u2212\u03b12\u00f0 \u00de : \u00f012\u00de In order to measure the six-axis force acted on shaft and hole parts, ring structure is introduced into the design of parallel sensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0003379_j.ijmecsci.2020.105709-Figure5-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003379_j.ijmecsci.2020.105709-Figure5-1.png",
        "caption": "Fig. 5. The sliding boundary constraint where the direction that is perpendicular to \ud835\udc52 \ud835\udc58 \ud835\udc50 is free.",
        "texts": [
            " Note that \ud835\udf3dfh is required o be 0 for first-order compatible displacements. Given the nodal coorinates and bar connections, the nodes that are associated with each inge can be identified using the codes given in Appendix A.4 . The fold ngles and compatibility matrix for all hinges can be computed using he codes given in Appendix A.5 . .3. Boundary conditions Different boundary conditions and special constraints can be applied o the nodes. Here, a sliding boundary condition for node k in the xy lane is demonstrated and shown in Fig. 5 . Computing the distances of boundary nodes of x i,j from the sliding lane [35] gives deformation \ud835\udc1e \ud835\udc56,\ud835\udc57 \ud835\udc50 . First-order compatibility gives cos \ud835\udefc\ud835\udc50 \ud835\udc62 \ud835\udc58 \u2212 sin \ud835\udefc\ud835\udc50 \ud835\udc63 \ud835\udc58 = \ud835\udc52 \ud835\udc58 \ud835\udc50 , (15) here \ud835\udc52 \ud835\udc58 \ud835\udc50 is the displacement perpendicular to the sliding boundary, and c is the angle between the reaction bar and the horizontal plane, which, w c c f f i v \ud835\udf0b t c 3 a r s m s c g t d fi i \ud835\udefc t a n m c [ c S S S S r r 3 a r d e 3 t P t d \ud835\udc1d s p i u \ud835\udc1d C w s 3 b [ g m d a t i \ud835\udf49 a c a \ud835\udc1d w g 3 j D t here C ch has size n ch \u00d7 3 n , and n ch is the number of activated local ontacts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure1-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000558_j.mechmachtheory.2008.06.005-Figure1-1.png",
        "caption": "Fig. 1. Relative position of the pinion and the gear in mesh.",
        "texts": [
            " The real geometry and kinematics of the hypoid gear pair is applied, thus the exact geometrical separation of the mating surfaces is included in the oil film shape, and the real velocities of these surfaces are used in the Reynolds and energy equations. By using the corresponding computer program the influence of machine tool setting applied for pinion teeth finishing on maximum oil film pressure and temperature, EHD load carrying capacity, and on power losses in the oil film was investigated. A hypoid gear pair with the generated pinion and the non-generated gear is treated (Fig. 1). The pinion is the driving member. In order to reduce the sensitivity of the gear pair to errors in teeth surfaces and to the mutual position of the mating members appropriately chosen modifications are introduced into the teeth of the pinion. As a result of these modifications theoretically point contact of the meshed teeth surfaces appears instead of linear contact. The machine tool setting for pinion teeth finishing is shown in Fig. 2. The concave side of pinion teeth is in the coordinate system K1 (attached to the pinion) defined by the following system of equations: ~r\u00f01\u00de1 \u00bcMp4 Mp3 Mp2 Mp1 ~r\u00f0T1\u00de T1 ; \u00f01:1\u00de ~v\u00f0T1 ;1\u00de 0 ~e\u00f0T\u00de0 \u00bc 0; \u00f01:2\u00de where~r\u00f0T1\u00de T1 is the radius vector of tool surface points, matrices Mp1, Mp2, Mp3 and Mp4 provide the coordinate transformations from system KT1 (rigidly connected to the cradle and head-cutter T1) to system K1 (rigidly connected to the being generated pinion)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001582_s12206-015-0903-6-Figure4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001582_s12206-015-0903-6-Figure4-1.png",
        "caption": "Fig. 4. FE model of a profile shifted gear with crack.",
        "texts": [
            " Mesh stiffness KB at moment B (moment B stands for the double-tooth engagement ending moment over the mating duration of a cracked tooth) and contact ratio under different modification coefficients are shown in Fig. 3. In the figure, there is a distinct reduction of stiffness when the tooth crack is introduced. In addition, the mesh stiffness increases and contact ratio decreases with the increasing modification coefficients, and the mesh stiffness decreases with the growth of crack. To verify the validity of the analytical model, an FE model is also established in this paper. To reduce the computational time, the analysis is performed by a 2D model with only one tooth under plane strain assumption (see Fig. 4), which is widely used and accepted in Refs. [9, 15]. Crack tips with different modification coefficients and crack depths in tooth root are established by 2D singularity elements and a parabolic curve is adopted to simulate crack propagation path. The load is considered to apply to the plane of the gear body and uniformly distributed along the tooth width. Without considering the influence of contact between two gear teeth, meshing forces are applied on the tooth profile. The inner ring nodes of the gear are coupled with the master node (the geometric center of gear), and the master node is restrained from all degrees of freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0002356_2015-01-0505-Figure7-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0002356_2015-01-0505-Figure7-1.png",
        "caption": "Figure 7. Piston temperature distribution detail. Cooled piston (top).",
        "texts": [
            " In Figure 6, temperature distribution across a gasoline piston has been shown for the original piston model (without cooling gallery) and for the modified piston by introducing an oil cooling gallery. In order to simplify the analysis, same color scale has been used for both cases. As it can be observed, temperature differences between both models are evident, appearing the higher temperature at piston top land and rings for the non-cooled case as it was expected. The lower temperature observed at those regions for the cooled piston is beneficial since they can prevent from abnormal combustion events such as knocking or pre-ignition. On Figure 7 same results are presented for a cutting view of the piston solid model, as it was described before it is at the top land and rings area where the higher temperature reductions are found for the cooled piston. Averaged temperature results have been summarized on Table 3, main differences observed on temperature distribution across the piston can be explained due to the fact that literature survey data for the cooled piston have been obtained from diesel piston works. That is due to gasoline cooled pistons have not been widely used and there was not enough detailed information on that topic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0001209_imece2012-86513-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0001209_imece2012-86513-Figure3-1.png",
        "caption": "FIGURE 3. 3D SKETCH OF GEAR MOUNTED IN THE TESTING MACHINE.",
        "texts": [],
        "surrounding_texts": [
            "The first step in root stress calculation consists in determining the radii where tooth flank touch anvil load face (i.e. the radii where the load is applied on the gears): RL = OCL = \u221a X2 + r2 b (1) RR = OCR = \u221a (Wk \u2212X)2 + r2 b Let S0 be the shim thickness corresponding to a symmetric loading condition, and \u03b4S the increment of this thickness. If the thickness is equal to S0, then X =WK/2, while, for any other value of the shim thickness (S = S0 +\u03b4S), X is equal to WK/2+\u03b4S. Substituting this expression of X in Equation 1, the contact radii can be determined by means of the following equations: RL = OCL = \u221a (WK/2+\u03b4S)2 + r2 b (2) RR = OCR = \u221a (WK/2\u2212\u03b4S)2 + r2 b These radii have been used to determine the point where the load is actually applied. Due to the slight difference between the geometries of the two families of specimens, the results can be compared only in terms of bending stress and not of applied load. The bending stress has hence been determined by means of Equation 3, obtained adapting the ISO formula of the nominal tooth root stress (\u03c3F0) (defined in Clause 5.2.2 of [7]). Method B (described in [7]) has been adopted to determine the relevant factors. The nominal stress can be determined by means of Equation 3, since Y\u03b2 (helix angle factor), YB (rim thickness factor) and YDT (deep tooth factor) are all equal to one. The tooth form factor and stress correction factor have been determined applying the load at its actual radius (RR or RL). The geometric entities corresponding to the symbols are shown in Figure 5. Load (F) is normal to tooth flank and it is applied at radius RL or RR (determined by means of Equations 2), depending on the considered tooth. Table 2 lists the values of these parameters for each specimen family. \u03c3F0 = Ft b \u00b7m \u00b7YF \u00b7YS (3) 4 Copyright c\u20dd 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 10001-A 10002-E High 10002-E Low hF [mm] 10.811 11.006 8.054 lx [mm] 9.886 10.049 7.522 \u03b1Fen [deg] 23.8769 24.0671 20.9330 sFn [mm] 17.357 17.357 17.357 \u03c1F [mm] 3.383 3.383 3.383 qs [/] 2.565 2.565 2.565 L [/] 1.605 1.577 2.155 YF [/] 1.676 1.704 1.275 YS [/] 2.012 2.000 2.239 \u03c3F0/F [MPa/kN] 19.807 20.012 16.768 TABLE 2. PARAMETERS USED TO DETRMINE STANDARD STRESS where Ft : tangential load [N] m : module [mm] b : face width [mm] YF = 6 \u00b7 hFe mn \u00b7 cos(\u03b1Fen) ( sFn mn )2 \u00b7 cos(\u03b1) : tooth form factor YS = (1.2+0.13 \u00b7L) \u00b7q L (1.21\u00b7L+2.3) s : stress correction factor L = sFn hF qs = sFn 2 \u00b7\u03c1F The last row of Table 2 shows the ratio between the applied load and the nominal stress (\u03c3F0). Even though the more loaded tooth is expected to fail, a failure (Test No. 24 - Coated gear) occurred also on the less loaded tooth. Hence, the last column of Table 2 shows the data also for this loading condition. The run-out has been set at 5 \u00b7106 cycles, taking into account the position at 3 \u00b7106 cycles of the knee of the S-N diagram according to ISO standards ( [7]). In the next sections, the results of the bending tests performed on coated and uncoated gears will be presented and discussed."
        ]
    },
    {
        "image_filename": "designv10_12_0003239_tro.2020.2998613-Figure6-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003239_tro.2020.2998613-Figure6-1.png",
        "caption": "Fig. 6. (a) Corresponding angles of a UAV and its connected cable in the plane and (b) corresponding FBD.",
        "texts": [
            " If a vertical line is extended from point Bi, it crosses x\u2212 y plane in pointEi. Accordingly, a plane can be considered which includes three points P ,Bi, andEi. Both vectors of \u03c4\u2032i andmig are in such plane and are able to balance a third force in the same plane only. Accordingly, in order to hold the static equilibrium conditions, ti needs to be in PBiEi plane. By having ti in the same plane of \u03c4\u2032i and mig, the 3-D static equilibrium problem is transformed into a planar (2-D) static equilibrium problem. Accordingly, one can consider Fig. 6(a) with the FBD of Fig. 6(b), where \u03c4\u2032i denotes the tension magnitude of the UAV-connected cable. In this figure, \u03bb\u2032 i = tan\u22121(u\u2032 zi/u \u2032 xi) denotes the angle of cable with respect to the horizontal axis x, u\u2032 xi and u\u2032 zi are the entries of u\u2032 i, and \u03b3i denotes the angle of UAV with respect to the vertical axis z of frame xyz. Frame xyz is attached to the moving platform and is always parallel with XY Z frame. Based on the FBD of Fig. 6(b), the static equilibrium equations of the UAV in x and z directions can be written as tisin(\u03b3i) = \u03c4\u2032icos(\u03bb\u2032 i), ticos(\u03b3i) = \u03c4\u2032isin(\u03bb\u2032 i) +mig (6) where ti is the magnitude of ti and g denotes the magnitude of gravity acceleration. As (6) and Fig. 6(b) indicate, \u03c4\u2032i is a function of ti and the angles \u03bb\u2032 i and \u03b3i. In order to find \u03c4\u2032i, the summation of squares of both sides of (6) gives (tisin(\u03b3i))2 + (ticos(\u03b3i))2 = (\u03c4\u2032icos(\u03bb\u2032 i)) 2 + (\u03c4\u2032isin(\u03bb\u2032 i) + mig) 2, which is simplified to \u03c4\u20322i + 2mig\u03c4 \u2032 i sin(\u03bb \u2032 i)\u2212 t2i + (mig) 2 = 0. (7) Accordingly, \u03c4\u2032i, as the solution of (7), is obtained as \u03c4\u2032i(\u03bb \u2032 i) = \u221a t2i + (migsin(\u03bb\u2032 i)) 2 \u2212 (mig)2 \u2212migsin(\u03bb\u2032 i) (8) which concludes \u03c4\u2032maxi(\u03bb \u2032 i) = \u221a t2maxi + (migsin(\u03bb\u2032 i)) 2 \u2212 (mig)2 \u2212migsin(\u03bb\u2032 i) (9) Authorized licensed use limited to: University of Canberra"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_12_0000149_978-0-387-31255-2-Figure5.4-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000149_978-0-387-31255-2-Figure5.4-1.png",
        "caption": "Figure 5.4. Schema for the moment of a vector about a point.",
        "texts": [
            " Moment of a Vector About a Point The moment of a vector about a point occurs frequently in future work. This operation is first defined in general terms; and the transformation rule that describes the effect of a change of the reference point follows. The familiar idea of the moment of a force about a point is then reviewed ; and the momen t of momentum vector is introduced in the next section. We start with the general idea. Let x Q ( P) be the position vector of a point P from a point Q, and let u (P) denote a vector quantity at P in Fig. 5.4. The moment about Qofthe vector u(P ) is a vector entity J-LQ(P) defined by the rule J-LQ(P) == xQ(P) x u (P ) . (5.18) This vector is perpendicular to both x Q (P) and u (P) . It is represented in Fig. 5.4 as a vector line with an arrow turning about it in the right-hand sense of (5.18). 16 5.3.1. Reference Point Transformation Rule Chapter 5 The vector J.LQ (P) depends on the choice of Q. The moment of the same vector u(P) about another reference point 0 in Fig. 5.4 is given by J.Lo (P) = Xo (P) x u (P) , where xo(P) is the position vector of P from O. It is seenin Fig. 5.4 that xo(P) = rOQ + xQ(P) , in which rOQ == ro(Q) is the position vector of Q from O. Hence, substitution of this relation into the previous equation and use of (5.18) yields the transformationrule relatingthemomentsofthe same vectoru(P) about thepoints o and Q: J.Lo (P) = J.LQ (P) + rOQ x u (P). (5.19) It is seen that J.Lo (P) = J.LQ (P) when and only when the nonzero vector rOQ is parallel to u(P). 5.3.2. Moment of a Force About a Point We recall the familiar idea of the moment of a force about a point. In Fig. 5.4, let u(P) == F(P) denote a force acting on a particle P whose position vector from point Q is xQ (P), and write J.LQ (P) == MQ(P). Then, by (5. I8), the moment about Qofthe force F (P) is the vectorMQ(P) definedby the rule MQ(P) == xQ (P) x F (P). (5.20) The moment vector is a measure of the turning or twisting effect of the force about the reference point. Hence , the moment of a force is also called the torque; its physical dimensions are [MQl = [FLl. If a is a vector from Q to any point A on the action line of F(P) , the vector defined by r == xQ(P) - a is parallel to F(P) ",
            "22) where XQk =xQ (Pk) is the position vector of particle Pk from Q; and the total , or resultant, force is defined by F(f3) = I::Z=lFk \u00b7 The same rule may be applied to determine the total moment about a point Q of all the concentrated and distributed force s that act on a rigid body \u00a313. For the elemental force distribution dF d (P) acting on a material parcel at P , for example, the total torque about a point Q of the distributed force is defined by MQ( \u00a313) = rxQ (P) x dFd (P) ,1.0/) where xQ (P) is the position vector from Q to the parcel at P. A formula similar to (5.21) holds for n concentrated forces Fk(\u00a313) acting on \u00a313. Now consider the point transformation rule. Clearly, the turning effect of a force about another reference point at 0 in Fig. 5.4 will be different from that about Q.The transformation rule (5.19) shows that the moment ofthe same force about the reference point 0 is related to its moment (5.20) about the point Q by the rule M o (P) = M Q (P) + rOQ x F(P) . (5.23) We recall that rOQ is the position vector of point Qfrom 0 ; and hence rOQ x F (P) is the moment about 0 of the total force as though it were placed at Q. The same point transformation rule applies to (5.21) and (5.22); thus, Mo(\u00a313) = MQ(\u00a313) + rOQ x F(\u00a313), (5.24) where the total force acting on \u00a313, namely, F( \u00a313) = Fd(\u00a313) + Fc(\u00a313) , is the sum of the total distributed force Fd(\u00a313) = f8(3dFd (P) and the total of all concentrated forces Fc(\u00a313) = I:~=l Fk(\u00a313) "
        ],
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    },
    {
        "image_filename": "designv10_12_0003353_j.mechmachtheory.2020.103841-Figure3-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0003353_j.mechmachtheory.2020.103841-Figure3-1.png",
        "caption": "Fig. 3. Tooth surface of the medium gear.",
        "texts": [
            " In the fixed coordinate system \u03c3 m , the equation of right flank tooth surface r 1 R can be represented as follows: r 1 R ( u , \u03b8 ) = [ x R 1 y R 1 z R 1 ] = [ r b cos ( \u03b4\u2212\u03b8\u2212u ) \u2212r b u sin ( \u03b4\u2212\u03b8\u2212u ) \u2212r b sin ( \u03b4\u2212\u03b8\u2212u ) \u2212r b u cos ( \u03b4\u2212\u03b8\u2212u ) r b cos \u03b1 tan \u03b2R \u03b8 ] (1) Similarly, the equation of left flank tooth surface r 1 L is expressed as follows: r 1 L ( u , \u03b8 ) = [ x L 1 y L 1 z L 1 ] = [ r b cos ( \u03b4 + \u03b8\u2212u ) \u2212r b u sin ( \u03b4 + \u03b8\u2212u ) r b sin ( \u03b4 + \u03b8\u2212u )+ r b u cos ( \u03b4 + \u03b8\u2212u ) r b cos \u03b1 tan \u03b2L \u03b8 ] (2) where, u and \u03b8 represent the surface parameters of 1 , \u03b4 is the half of the angular tooth thickness on the base circle, and \u03b1 is the pressure angle of reference circle. As shown in Fig. 1 , the helical angles of two flanks on the IHB gear should be satisfied the following condition: \u03b2L > \u03b2R (3) The tooth surface g of medium gear is actually an oblique plane that is in line contact with the IHB gear tooth surface. The inclination angles on both sides of the tooth surface are also different. The tooth surface of oblique planar gear can be formed as shown in Fig. 3 . In the fixed coordinate system \u03c3 m , the equation of right flank tooth surface r g R of the medium gear is expressed as follows: r g R (v , t) = [ x gR 1 y gR 1 z gR 1 ] = [ v \u2212 r g b + t sin \u03b2bR t cos \u03b2bR ] (4) Similarly, the equation of left flank tooth surface r g L can be expressed as follows: r g L (v , t) = [ x gL 1 y gL 1 z gL 1 ] = [ v r g b \u2212 t sin \u03b2bL \u2212 t cos \u03b2bL ] (5) Here, v and t represent the planar parameters of tooth surface g . The OPE worm tooth surface is considered to be a conjugate surface, which is generated by the medium gear tooth surface"
        ],
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    },
    {
        "image_filename": "designv10_12_0000427_elt.2008.104-Figure2-1.png",
        "original_path": "designv10-12/openalex_figure/designv10_12_0000427_elt.2008.104-Figure2-1.png",
        "caption": "Figure 2. Cross-section of the three-phase 12/8 structure switched reluctance generator.",
        "texts": [
            "20050290510, and the Natural Science Foundation of Jiangsu Province under Grant No.BK2007039. 978-1-4244-1833-6/08/$25.00 \u00a92008 IEEE 1 detector, an excitation power converter and a controller. The block diagram of the system is shown in Fig. 1. The switched reluctance generator is a three-phase 12/8 structure doubly-salient reluctance machine. The stator and the rotor core of the generator are made of non-oriented silicon steel laminations. The cross-section of the switched reluctance generator is shown in Fig. 2. It has 12 teeth poles in the stator and 8 teeth poles in the rotor. There is a centrailzed coil wound on each stator tooth, and there are four coils in each phase, so that the A phase winding could be made up of the coils \u201c1\u201d, \u201c4\u201d, \u201c7\u201d and \u201c10\u201d, the B phase winding could be made up of the coils \u201c2\u201d, \u201c5\u201d, \u201c8\u201d and \u201c11\u201d, and the C phase could be made up of the coils \u201c3\u201d, \u201c6\u201d, \u201c9\u201d and \u201c12\u201d. By taking A phase winding for an example, the four coils- \u201c1\u201d, \u201c4\u201d, \u201c7\u201d and \u201c10\u201d, could be connected in series to form the winding of the phase A, which is shown in Fig"
        ],
        "surrounding_texts": []
    }
]