[
    {
        "image_filename": "designv10_4_0001008_j.engfailanal.2021.105260-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001008_j.engfailanal.2021.105260-Figure6-1.png",
        "caption": "Fig. 6. Mesh converge study for stress analysis.",
        "texts": [
            " Since the geometry may change slightly for different pressure angles and rim thickness, the number of elements and nodes will also differ. An example of a mesh structure created in this study was shown in Fig. 5. A mesh convergence study was performed to show the reliability of the mesh structure. Five different mesh sizes were used for the FEA, and the maximum bending stress results were obtained for each analysis. The result of the mesh independency study for 14000, 17000, 24000, 38300, and 53,500 elements, as shown in Fig. 6. Up to 38,300 elements, the stress was continually decreasing. It is seen that the stress changes very little in 53,500 elements. For this reason, the number of elements of the analysis was determined as 38,300 elements to avoid creating unnecessary data in the computer area. After determining the mesh structure of the analysis, the boundary conditions of the system were defined. Boundary conditions of the static structural analysis were shown in Fig. 7. A single 500 N static load was applied to the point of the highest point of single tooth contact (HPSTC point)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000658_j.ymssp.2021.107711-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000658_j.ymssp.2021.107711-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a rolling element rolls across the spall area: (a) diagram of a spalled REB, (b) entry, (c) impact, and (d) exit.",
        "texts": [
            " As mentioned above, the vibration characteristics associated with the passing process of the rolling element across the spall zone located on the raceway consist of two main components: a step response with lower frequency contents originates from the entry of the rolling element into the spall area, and an impulse response with higher frequency components results from the exit of the rolling element as it strikes on the trailing edge of the spall area [7,9]. The overall passing process of a rolling element across the spall area is shown in Fig. 1. When the rolling element reaches the spall area, the rolling element comes in contact with the leading edge of the spall area (see Fig. 1(b)), and then the rolling element rolls into the spall area driven by the bearing cage. As a result, the equivalent radius of contact curvature between the rolling element and the bearing raceways increases, resulting in the decreases of curvature summation. According to the Hertzian contact theory, the contact force between the rolling element and the bearing races decreases, and the rolling element loses part of its load carrying capacity (i.e., de-stressing process of the rolling element). This results in a step response of the entry of the ball. Then, the center of the rolling element reaches the midway through the spall zone as shown in Fig. 1 (c). At this moment, the rolling element strikes on the trailing edge of the spall area, leading to an impulse response event which contains a high frequency components related to the resonances of bearing, and then the rotation center of the rolling element moves from the point E to the point L. Thereafter the rolling element rotates about L, and finally exits the spall area, that is, the rolling element re-stresses to its normal state of carrying radial load. It is generally accepted that the dynamic behavior of the bearing is significantly different when a spall defect occurs on the bearing raceway"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.4-1.png",
        "caption": "Figure 12.4. Meshing diagram of an internal gear pair.",
        "texts": [
            "18) It can be seen in Figure 12.3 that the tip circle of an 266 Internal Gears internal gear lies inside the standard pitch circle, while the root circle lies outside it. The addendum as and the dedendum bs are still defined in the usual way, as the radial distances from the standard pitch circle to the tip circle and the root circle. Hence, as and bs are related to the various radi i in the following manner, ( 12.19) (12.20) Meshing Geometry of an Internal Gear Pair The meshing diagram of an internal gear pair is shown in Figure 12.4, with the pinion as gear 1 and the internal gear as gear 2. The position of the pitch point, and the radii of Meshing Geometry of an Internal Gear Pair 267 the pitch circles, were given by Equations (12.5 and 12.6). The common tangent E,E2 to the base circles is the line of act ion, and the angle t/I between thi s line and the common tangent to the pitch circles is the operating pressure angle of the gear pair. The lines C1E1 and C2E2 are both perpendicular to the line of action, so they each make an angle t/I with the line of centers. By expressing the center distance C in terms of the base circle radii, we obtain an equation for the operating pressure angle t/I, cos t/I (12.21) We can also use Figure 12.4 to write down a relation between Rb2 and Rp2 ' = 268 Internal Gears The operating pressure angle ~P2 of the internal gear is defined as the profile angle at the pitch circle, and its value is therefore found from Equation (12.11), if we substitute Rp2 in place of R, cos ~P2 A comparison of the last two equations shows that ~P2 is equal to ~, and we can show in the same way that the operating pressure angle ~Pl of the pinion is also equal to ~. We therefore use the symbol ~p for the operating pressure angle of either gear, and its value is equal to the operating pressure angle of the gear pair, (12",
            "29) Contact Ratio We defined the contact ratio of an external gear pair in Chapter 4, as the rotation of either gear during one meshing cycle, divided by the angular pitch of the same gear. We then showed that this definition is equivalent to the length of the contact path, divided by the base pitch. For an internal gear pair, the contact ratio is defined in the same manner as for an external gear pair. Once again, we can replace the definition by the alternative description, and this time we will not prove their equivalence, since the proof is identical to the proof given in Chapter 4. In the meshing diagram shown in Figure 12.4, the line of action is the common tangent to the base circles, and the ends T1 and T2 of the path of contact are the points where the two tip circles intersect the line of action. The length T1T2 is related to the other lengths on the line of action, We express each of these lengths in terms of quantities defined on the gears, and divide by the base pitch, to obtain the contact ratio mc ' Internal Gears 271 As always, there is non-conjugate contact if the path of contact extends beyond the interference points. The first condition, therefore, for no interference at the fillets of the pinion in Figure 12.4 is that T2 should lie above E1, or in other words, E2 T 2 must be larger than E2E 1 ' > (12.31) There is no corresponding condition relating to the position of point T1, since in principle the involutes of the internal gear can extend out to any radius, and conjugate contact is theoretically possible, however large the tip circle radius of the pinion. In practice, of course, the involute section of the tooth profile in each gear ends at the fillet circle, and we must therefore ensure that contact ceases a suitable distance away from the fillet circle. The active section of the tooth profile in either gear is the part which comes into contact with the other gear. The end point of the active section of the profile nearest the root is called the limit point, and the circle through this point is the limit circle. In the pinion, the limit circle is the circle through point T2 , while in the internal gear, it is the circle through T1. The radii RL1 and RL2 of the limit circles can be read from Figure 12.4, (12.32) (12.33) To ensure that there is no contact at the fillets, the limit circle of the pinion must be larger than its fillet circle, and because the teeth of the internal gear face inwards, its limit circle must be smaller than its fillet circle. It is customary to leave a margin of at least O.025m between the circles, to allow for possible errors in the center distance, and we therefore obtain the following conditions, which must be satisfied by the radii Rf1 and Rf2 of the fi llet ci rcles, 272 Internal Gears (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure8-1.png",
        "caption": "Fig. 8. Planar two-legged platform.",
        "texts": [
            " Since one common constraint couple constrains the rotation about z-axis, two more constraint couples constrain the rotations about xand y-axes, two constraint forces constrain the translations along x-and y-axes, the elementary platform mechanism can only translates along the z-axis. This makes this platform mechanism moves radially inwards or outwards the center of the ball. This can also be found by a further observation that the elementary four-legged platform is composed of two sets of planar linkages which are perpendicular to each other [21]. Removing two pairs of scissor-pair in the orthogonal plane, a two-legged planar platform mechanism is thus obtained in Fig. 8. Due to the special geometric dimensions that BC \u00bc AF , DC \u00bc EF , and ED and AB are arcs of two concentric circles, and the constraint that the platform mechanism is situated in a circular loop-chain, there exist two relative constraint equations, h1 \u00bc p h3, and h2 \u00bc 2h1. These constraints indicate that hubs ED and AB move along a radial vector, z, that c \u00bc z, and rest on surfaces of two concentric changeable circles. Hence, this produces two constraints on the motion plane and gives the mobility 1",
            " 10 of all four-legged elementary platforms are removed. The remaining mechanism forms a circular loop-chain in Fig. 10. It is a kinematic chain joined by parallelograms and planar two-legged platform on the x\u2013y plane. The mobility of the loop chain does not change. In this kinematic loop-chain, the symmetrical mechanism is composed of basic units each of which consisting of a planar two-legged platform and two parallelogram mechanisms as in Fig. 11a. Fig. 11b is the corresponding topological graph [22]. From the similar analysis in Fig. 8 and the constraints mentioned in Section 4, the mobility of the basic unit is one. From the above result that the basic unit has mobility one, calculating the mobility of the circular loop-chain, the topological graph of the chain can be simplified. Similar to the analysis of the basic unit, the mobility of this kinematic chain is one. Thus, the mobility of the equatorial circular loop-chain is one and that indicates that the mobility of the ball mechanism is one. This can further be proved from the mobility analysis of the supplementary kinematic chains which are removed during the mechanism decomposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.2-1.png",
        "caption": "Figure 3.2. Base pitch of a rack.",
        "texts": [
            "1 will coincide with the pitch point if the length CP' is equal to the pitch circle radius Rp' We equate the two expressions given in Equations (3.3 and 3.4), and rearrange the terms to put the condition in the following form., p~ cos 4l~ 271\"Rb N (3.5) 56 Gears in Mesh The base pitch Pb of the pinion is given by Equation (2.22), 211'Rb N (3.6) and the base pitch Pbr of the rack, defined as the distance between adjacent teeth measured along a common normal, can be expressed in terms of the pitch and the pressure angle with the help of Figure 3.2, P~ cos ~~ (3.7) Hence, the condition given by Equation (3.5) implies that the base pi tch of the rack must be equal to that of the pinion, (3.B) When we replace CP' in Equation (3.3) by the pitch circle radius Rp' the equation takes the following form, (3.9) We have shown that if the length CP' is equal to the pitch circle radius, the base pitches of the pinion and the rack must be equal. The converse is also true, as we can prove A Pinion Meshed Wi th a Rack 57 by considering Equations (3.3 - 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003427_978-94-017-0657-5_48-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003427_978-94-017-0657-5_48-Figure2-1.png",
        "caption": "Figure 2. Leg-surfaces of legs for TPMs.",
        "texts": [
            " By inspecting the list of legs for TPKCs, all legs for linear TPMs are determined in section 3. Then, all linear TPMs are obtained in section 4. All 1-0 (input-output) decoupled linear TPM are revealed in section 5. Finally, conclusions are drawn. TPMs When the actuator of a given leg of a TPM is locked, the moving platform will translate along a surface with its orientation unchanged under the action of the total constraints on the moving platform by all of the legs of the TPM. For brevity, the above surface is referred to as the leg-surface (Fig. 2) of the leg. Thus, the forward displacement analysis of the TPM can be described geometrically as follows: it consists in finding the intersection of three leg-surfaces. The higher the degree of the leg-surfaces, the more complicated the forward displacement analysis of the TPM. The simplest cases are TPMs with three planar leg-surfaces. As the intersection of three planes can be obtained by solving a set of linear equations, a TPM is a linear TPM if all of its three leg-surfaces are planes. Thus, type synthesis of linear TPMs is reduced to the type synthesis of legs for TPMs whose leg-surfaces are planes (Fig. 2(b)), which are referred to as legs for linear TPMs in the following. The type synthesis of linear TPMs can be performed in two steps. The first is to perform the type synthesis of legs for linear TPMs, the second is to perform the type synthesis of linear TPMs. In the type synthesis of legs for linear TPMs, we make the assumption that the first joint, i.e., the joint located on the base, is actuated while the other joints are unactuated. The type of a leg is denoted by a chain of characters denoting the joint types starting from the base to the moving platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003544_tmag.2004.843311-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003544_tmag.2004.843311-Figure8-1.png",
        "caption": "Fig. 8. Demonstration of (18)\u2013(20) for = 0:1, = 0:6.",
        "texts": [
            " In the first subperiod, which occupies portion of the \u201con period\u201d bandwidth, the phase current is defined as the first bisection of a \u201chalf-sine\u201d waveform multiplied by in such a way that this bisection starts from the point and reaches the point , where is the peak angle of this \u201chalf-sine\u201d waveform and can be defined by using as the following: (18) In the third subperiod, which occupies portion of the \u201con period\u201d bandwidth (so that ), the phase current is defined as the second bisection of another \u201chalf-sine\u201d waveform multiplied by in such a way that this bisection starts from the point and reaches the point , where is the peak angle of the other \u201chalf-sine\u201d waveform and can be defined by using as the following: (19) In the second subperiod (which is between the first and third subperiods), the point is connected to the point by a horizontal line at the height of . In order to mathematically define the phase current, let us first define the following angles: (20) Fig. 8 demonstrates the meaning of , , , and . Now, the phase current in this case can be defined as (21) The objective function in this optimization procedure is given by (22) In order to implement the above-described procedures, the motor indicated in the Appendix of this paper has been used. Each of the new procedures has been adapted to both the genetic algorithm and the simplex method. As mentioned before, the optimization objective function is chosen to minimize the SRM torque variance, which in turn indicates the SRM torque ripple"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003385_mcs.2002.1077786-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003385_mcs.2002.1077786-Figure2-1.png",
        "caption": "Figure 2. Rotational/translational proof-mass actuator.",
        "texts": [
            " Furthermore, since m( )\u03b8 and c( )\u03b8 are functions of \u03b8, we cannot ignore the angular position \u03b8. Hence, since \u03b8does not converge, it is clear that (1) is unstable in the standard sense but partially asymptotically stable with respect to \u03b8 (see Definition 1 below). Our next example involves a nonlinear system originally studied as a simplified model of a dual-spin spacecraft to investigate the resonance capture phenomenon [12] and more recently studied to investigate the utility of a rotational/translational proof-mass actuator for stabilizing translational motion [13]. The system (see Fig. 2) involves an eccentric rotational inertia on a translational oscillator giving rise to nonlinear coupling between the undamped oscillator and the rotational rigid-body mode. The oscillator cart of mass M is connected to a fixed support via a linear spring of stiffness k. The cart is constrained to one-dimensional motion, and the rotational proof-mass actuator consists of a mass m and mass moment of inertia I located at a distance e from the cart\u2019s center of mass. Lettingq, q, \u03b8, and \u03b8denote the translational position and velocity of the cart and the angular position and velocity of the rotational proof mass, respectively, the dynamic equations of motion are given by 66 IEEE Control Systems Magazine December 2002 LECTURE NOTES Chellaboina (ChellaboinaV@missouri"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001027_tpel.2021.3081618-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001027_tpel.2021.3081618-Figure3-1.png",
        "caption": "Figure 3: FEM model of the experimental SRM in Flux2D.",
        "texts": [
            " These parameters provided by the manufacturers are not always accurate and the electromagnetic properties of the ferromagnetic material may change during the manufacturing process [28]. In [29], it claims that the actual air gap could be different than that shown on the datasheet because of the complication of the manufacturing process, which yields a significant difference between the measured and simulated results. Compared with measurement, FEM is a less accurate but low-effort way to obtain the unsaturated phase inductance characteristic. The FEM model of the exemplary machine is built in the commercial FEM software Flux2D, which is shown in Fig. 3. Due to the symmetry of SRM configuration, only 1/4 of the machine requires to be considered for the simulation. By applying low-level current to one phase winding for all positions, the unsaturated phase inductance characteristic can be simulated. The measured unsaturated inductance characteristics are compared with the FEM results, as shown in Fig. 4. In Fig. 4, the symbol of \u201cel\u201d represents for electrical degree. The measured inductance values are marked by the circle and connected into the line forming the measured inductance profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003450_s0389-4304(03)00035-3-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003450_s0389-4304(03)00035-3-Figure1-1.png",
        "caption": "Fig. 1. Rolling contact fatigue test rig and hydrogen analysis method for thrust ball bearings.",
        "texts": [
            " It has been observed in recent years that the bearings used in automotive powertrains and peripheral auxiliaries often suffer a short service life due to flaking that occurs accompanying the formation of a subsurface white structure of a peculiar type [3\u20135]. It is important to identify the cause of this problem and to implement measures to prevent it from the standpoint of guaranteeing bearing durability and reliability. This peculiar short-life flaking mode was investigated in various tests in this study, focusing on hydrogen. The results have revealed the factors causing this phenomenon and an effective measure has been found for preventing it. The bearing test rig shown in Fig. 1 was used to evaluate the rolling contact fatigue life of thrust ball bearings, having races made of carbonitrided, quenched and tempered SCM420H, Japanese Industrial Standard (JIS) and balls made of SUJ2, JIS. Vickers hardness at surface layer of the races was Hv 720 and that of the balls was Hv 770. The effective case depth of the races was 2mm. Two types of traction fluid (oils #1 and #2) which contain different additives were used as the lubricant in the tests, which were conducted under conditions of an oil temperature of 120 C and maximum Hertz stress, Pmax, of 3.6 GPa. Following testing under identical conditions for a certain period of time, the races of some of the tested bearings were immediately cooled in liquid nitrogen. Three test pieces (4 4 2mm thick) were then cut from the rolling contact area of the races and their contact surface was polished to eliminate contamination. These pieces were used to measure the hydrogen content in the steel, as shown in Fig. 1. The width of test pieces is 4mm, which is approximately the same as the width of contact area and the thickness of test pieces is 2mm, which is reduced as much as possible, because our interest is focused on the hydrogen content in rolling contact zone, i.e. surface layer. The hydrogen content was measured with a programmed temperature gas chromatograph (Model UPM-ST-200R, ULVAC, Inc.) using a quadrupole mass spectrometer as the detector. Measurements were made in a temperature range of room temperature to 900 C with a rate of temperature increase of 10 C/min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003713_j.mechmachtheory.2005.10.012-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003713_j.mechmachtheory.2005.10.012-Figure1-1.png",
        "caption": "Fig. 1. The parallel manipulator and its schematic representation.",
        "texts": [
            " This paper contributes to previous efforts in regard to the application of screw theory to formulate the forward kinematics equations in a closed form, and subsequently to analyse the singularity of parallel manipulators such that the singularity configurations of the manipulators can easily be determined without explicitly calculating the actuator inputs making the determinant of the manipulator Jacobian zero. It follows that the singularity analysis and singular configuration determination does not require significant computational power. The proposed mechanism, see Fig. 1, is composed of a moving platform connected to a fixed platform by means of three unsymmetrical actuated limbs. One limb is a CPS1 serial manipulator that provides the parallel manipulator with two degrees of freedom, one due to the free translational motion of the cylindrical pair and the other due to the actuated prismatic joint. The second limb is a PS2 serial manipulator which forces the point O, fixed to the moving platform, to move along the Y-axis providing one degree of freedom to the parallel manipulator. The last limb is a typical HPS3 serial manipulator, where the actuated prismatic joint provides the fourth degree of freedom of the parallel manipulator. As far as the authors aware, the architecture of the parallel manipulator shown in Fig. 1 has not been previously reported in the literature. A screw is a six-dimensional vector composed of two three-dimensional vectors as follows: $ \u00bc s\u0302 ~sO ; \u00f01\u00de where the primal part, s\u0302, is a unit vector along the screw axis, whereas the dual part, ~sO, is the moment produced by s\u0302 around a point O fixed to the reference frame which is calculated, according to the pitch h of the screw and a vector~rO, as follows: ~sO \u00bc s\u0302 ~rO \u00fe hs\u0302. Any lower kinematic pair can be represented either by a screw or a group of screws",
            " This set of possible displacements does not form a subgroup of the Euclidean group, however the set has four degrees of freedom. Since the two first serial chains allow general displacements, then considering the three serial connecting chains, the parallel platform under study is a trivial chain of Tanev s type with four degrees of freedom. The four degrees of freedom can be chosen as the freedoms associated with the third serial chain PS2. The forward position analysis of the parallel manipulator shown in Fig. 1 is stated as follows. It must be recalled that the lengths associated with the limbs, {q1,q2,q3,q4}, are given, and it is required to determine the pose, position and orientation, of the moving platform w.r.t. the fixed platform via the computation of the coordinates of the three spherical joints attached to the moving platform and expressed in the reference frame XYZ. It must be noted that the computation of the coordinates of the spherical joint S1 does not depend on q4. With this in mind, a closed loop can be written as follows: ~b1 \u00fe~q3 \u00fe~a1 \u00bc~q1 \u00fe~q2. \u00f08\u00de Please note that ~ai ~ai \u00bc a2 i i \u00bc 1; 2; 3; ~bi ~bi \u00bc b2 i i \u00bc 1; 2; 3; ~qi ~qi \u00bc q2 i i \u00bc 1; . . . ; 4. 9>= >; \u00f09\u00de With reference to Fig. 1, the components of the vector ~a1 \u00bc a1X i\u0302\u00fe a1Y j\u0302\u00fe a1Z k\u0302 are found as a1X \u00bc q1 b1X ; \u00f0q2 3 \u00fe b2 1Z\u00dea2 1Y \u00fe 2K1q3a1Y \u00fe K2 1 \u00fe b2 1Z\u00f0a2 1X a2 1\u00de \u00bc 0; a1Z \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 1 a2 1X a2 1Y p ; 9>= >; \u00f010\u00de where K1 is K1 \u00bc \u00f0q2 3 \u00fe b2 1Z \u00fe a2 1 a2 1X q2 2\u00de=2. After the vector ~a1 is calculated, the components of the vector ~S1 \u00bc S1X i\u0302\u00fe S1Y j\u0302\u00fe S1Z k\u0302 result in S1X \u00bc q1; S1Y \u00bc q3 \u00fe a1Y ; S1Z \u00bc b1Z \u00fe a1Z . 9>= >; \u00f011\u00de In order to compute the coordinates of the spherical joint S3, the following two-loop closure equations can be employed: ~b3 \u00fe~q4 \u00fe~a3 \u00bc~S1; ~b1 \u00fe~q3 \u00fe~a2 \u00bc~b3 \u00fe~q4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003663_tac.2004.825959-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003663_tac.2004.825959-Figure1-1.png",
        "caption": "Fig. 1. Sun-avoidance constraint.",
        "texts": [
            "i(t)j 1 and jui(t)j 2; i = 1; 2; 3; t 2 [t0; tf ] (given the constants 1; 2 > 0), norm preserving kinematic constraint _q(t) = 1 2 (t)q(t) (2.4) with (t) = 0 !3(t) !2(t) !1(t) !3(t) 0 !1(t) !2(t) !2(t) !1(t) 0 !3(t) !1(t) !2(t) !3(t) 0 guaranteeing that kq(t)k = 1; for t 2 [t0; tf ] and, finally, the attitude constraints q(t)T ~Ai(x; y; )q(t) 0; for i = 1; . . . ;m (2.5) with ~Ai(x; y; ) = ~Ai = Ai bi bTi di 2 R4 4 (2.6) and Ai := xiy T i + yix T i x T i yi + cos I3 bi := xi yi di := x T i yi cos see Fig. 1. To see how constraints of the form (2.5) specify the exclusion zones in the attitude space-cones emanating from the spacecraft\u2019s sensitive instruments that need to exclude the bright objects in the sky during the maneuver\u2014one proceeds as follows [1]. First, consider the unit celestial vector x (specified in the inertial coordinates) and the unit body vector y (specified in the body coordinates).3 We would like the time evolution of the cone with a half-angle around the inertially represented vector y; yI , to exclude x at all times"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001012_j.triboint.2021.106927-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001012_j.triboint.2021.106927-Figure15-1.png",
        "caption": "Fig. 15. Contour lines of the lubricant film thickness and the calculated Hertzian area according to Hamrock and Dowson [26].",
        "texts": [
            " Consequently the measured capacity represents a plate distance that is calculated to be between the central and the minimum lubrication film thickness. To eliminate this uncertainty, it is proposed to subdivide the Hertzian area into two capacitors in a parallel arrangement. One capacitor for the minimum and one for the central lubrication film thickness. In addition to the lubricant film thickness, the area in the Hertzian region is also assumed with an uncertainty. According to Hamrock and Dowson [26], Fig. 15 compares the Hertzian area with the contour lines of the lubricant film thickness. It is shown that Hertz underestimates the area which is deflected. The underestimated deflected area, is currently considered by the undeflected capacitor CR. Assuming the non-deformed geometry, the distance and thus the impedance is overestimated by CR. Both errors, the overestimation of the plate distance and the underestimation of the Hertzian area reduce the calculated capacity. Taking both into account could reduce the deviation between measurement and calculation even further"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure5-1.png",
        "caption": "Fig. 5. Growth of a cylinder from a fixed growth surface G",
        "texts": [
            " In the growth of some horns, teeth and seashells it is known that the generating cells are, in fact, oriented at an angle to G, as shown in Fig. 4C. The following examples are chosen to illustrate growth from fixed and changing surfaces, starting with elementary examples to illustrate general principles and proceeding to more realistic biological cases. Example 3.1. Fixed growth surface Suppose G is a fixed circular area in the x 1 , x 2 plane, centered at the origin with radius a as shown in Fig. 5. Further, suppose that g is given as a constant vector over G: g\"v 0 i 3 , (30) where v 0 is a constant and i 3 is a unit vector in the x 3 direction. Assume the generating cells on G are fixed in position. Then choose h 1 \"x 1 , h 2 \"x 2 and h 3 \"q where q is the time at which any material point is first generated. In this case Eq. (25) gives x\"x0#P t h 3 v 0 i 3 dq\"x0#v 0 (t!h 3 )i 3 . (31) Equation (31) gives the components x 1 \"h 1 , x 2 \"h 2 , x 3 \"v 0 (t!h 3 ) . (32) Equation (32) is the explicit expression of Eq. (1) for this case and is valid in the domain h2 1 #h2 2 6a2 and 06h 3 6t. The grown length is \u00b8\"v 0 t. The particle paths and cell tracks are the same set of straight lines as shown in Fig. 5. Example 3.2. Growth surface accreting on edges Consider a case in which G is again a circular area fixed at x 3 \"0, but with a radius \u2018\u2018a\u2019\u2019 which grows so that a\"kt , (33) where k is a constant. Suppose the growth velocity is again given by Eq. (30). Then with the same choices of h i as in Example 3.1, Eqs. (31) and (32) also hold here. The only difference is that the domain in h space is now limited to (h2 1 #h2 2 )6k2h2 3 and 06h 3 6t. The solution implies that the cells on G are fixed in position once they are generated and new cells are added at the periphery of G as G grows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.23-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.23-1.png",
        "caption": "Figure 13.23. Transverse and normal tooth thickness.",
        "texts": [
            " In the developed base cylinder, as in every developed cylinder, both sides of the 350 Tooth Surface of a Helical Involute Gear teeth are straight. However, when we consider the base tangent plane, we are almost always interested in the sides of the teeth which coincide with the generators, so it is common practice to regard the base tangent plane and the developed base cylinder as identica1. Tooth Thickness For helical gears, we define the tooth thickness in both the transverse and the normal directions, in exactly the same manner as we defined the transverse and normal pitches. Figure 13.23 shows the developed cylinder of radius R, and each pair of diagonal lines represents the intersection between the cylinder and the two faces of a tooth. The transverse and the normal tooth thickness at radius Rare defined as the distances between the tooth lines on the developed cylinder, measured in the transverse and normal directions. The relation between the transverse thickness ttR and the normal thickness tnR can be read from Figure 13.23, (13.112) At the standard pitch cylinder, the tooth thicknesses are represented by the symbols tts and t ns \u2022 When we refer to the transverse and normal tooth thickness, without specifying any particular radius, it is generally understood that we Profile Shift 351 mean tt and t , the tooth thicknesses at s ns the standard pitch cylinder. These values must of course satisfy Equation (13.112), ( 13. 113) The transverse tooth thickness is defined in essentially the same manner as the tooth thickness of a spur gear, so the results derived in Part 1 for the spur gear tooth thickness apply equally to the transverse tooth thickness of a helical gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000513_j.addma.2020.101531-Figure41-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000513_j.addma.2020.101531-Figure41-1.png",
        "caption": "Fig. 41. Distortion seen in test geometry 1K.",
        "texts": [
            " Jo u na l P r -p ro of It can be concluded that there was local overheating at these build heights due to insufficient heat dissipation while printing and thus the deformation of thin walls led to recoater contact. The recoater removed the newly printed layer, so the next layer of powder could not adhere to the part, leading to the molten powder\u2019s balling during exposure. This cycle of non-adhered layers and subsequent removal by recoater was repeated until the end of the job. The test geometry selected was a representation of a possible real part with a wall thickness of 0.3 mm. Using a soft recoater during printing, it was seen that the part had three distinct regions of deformations (Fig. 41). While regions 1 and 2 distorted inwards, region 3 distorted outward. The maximum distortion was 1.73 mm at region 2. The simulation software tools were used to see if they could predict these distortions seen in printed test geometry 1K and how well they could compensate for these distortions. Figs. 42A to 42E show predictions of distortion by each software. Scan data of compensated test geometry for the predicted distortion Figs. 43A, 43B and 43C. Scan data of compensated part from Amphyon, Simufact, and Netfabb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000658_j.ymssp.2021.107711-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000658_j.ymssp.2021.107711-Figure3-1.png",
        "caption": "Fig. 3. Illustration of displacement increment: (a) zoomed-in detail of ball-spall zone contact; (b) geometrical relatioshipn of ball-inner race contact.",
        "texts": [
            " 2(a)) of the first rolling element with respect to x coordinate axis, Nball represents the total number of the rolling elements, xc refers to the rotational speed of the cage and can be calculated by xc \u00bc 0:5xr\u00f01 v\u00de \u00f07\u00de wherexr is the rotational speed of the shaft. v \u00bc Dball cosa=Dm, with a and Dm being the contact angle and the pitch diameter of the REB, and Dball is the rolling element diameter. In this work, a single inner race surface spall is studied theoretically and experimentally. The contact deformation between the inner race and the kth rolling element has an additional change (see Fig. 3(b)) when the rolling element rolls over the spall zone. Thus, the radial displacement of the inner race needs to be modified with consideration of localized surface spall on the inner race of REB. As shown in Fig. 3(a), during the rolling process of the rolling element across the spall area, the displacement increment increases from zero and reaches its maximum value when the rolling element is halfway Illustration of the contact deformation: (a) radially loaded REB, (b) radial contact deformation between the rolling element and both the inner and ces, and (c) geometrical detail illustration of radial displacement. through the spall area at first. Then, the displacement increment decreases from its maximum value to zero as the rolling element rolls from the midway through the spall zone to trailing edge of spall zone. Based on the above analysis, it can be determined that the location of the rolling element centre, during this whole interaction with the spall area, is the blue full line C1-C2-C3 as shown in Fig. 3(a). Refering to previous works [17,18], the spall shape studied in this work is selected to be a rectangular one. Based on the above analysis and the geometrical relationship as shown in Fig. 3(b)), the displacement increment dd can be formulated as a piecewise function, that is dd \u00bc 0 0 6 mod\u00f0hk;2p\u00de 6 mod\u00f0/spall;2p\u00de hspall dm cos p\u00f0mod\u00f0hk ;2p\u00de mod\u00f0/spall ;2p\u00de\u00de 2hspall p 2 h i mod\u00f0/spall;2p\u00de hspall < mod\u00f0hk;2p\u00de < mod\u00f0/spall;2p\u00de dm mod\u00f0hk;2p\u00de mod\u00f0/spall;2p\u00de \u00bc 0 dm cos p\u00f0mod\u00f0/spall ;2p\u00de mod\u00f0hk ;2p\u00de\u00de 2hspall p 2 h i mod\u00f0/spall;2p\u00de < mod\u00f0hk;2p\u00de < mod\u00f0/spall;2p\u00de \u00fe hspall 0 mod\u00f0/spall;2p\u00de \u00fe hspall 6 mod\u00f0hk;2p\u00de 2p 8>>>>>>>>>>>< >>>>>>>>>>>: \u00f08\u00de where mod( ) represents the modulus after the division arithmetic operation, Lspall is the spall width measured along the raceway, dm \u00bc 0:5Dball \u00f00:5Dball\u00de2 \u00f00:5Lspall\u00de2 h i0:5 ;g denotes the included angle between line segments ObA and ObB in the principal xoy plane(see Fig. 3(b)), /spall refers to the angular position of the center of the spall area with respect to x coordinate axis, which is determined by /spall \u00bc xrt \u00fe /0 \u00f09\u00de where /0 is the initial angular offset of the spall center relative to x coordinate axis, and hspall represents the size of the half central angle of the spall area along the tangential direction relative to the center of the inner race, which can be defined by hspall \u00bc arcsin\u00f0Lspall=Din\u00de \u00f010\u00de where Din is the diameter of the REB, and the ball-spall contact angle g can be defined based on the geometrical relationship as illustrated in Fig. 3(b), that is g \u00bc arcsin\u00f0Lspall=Dball\u00de \u00f011\u00de Based on the aforementioned analysis, the comprehensive displacement excitation model can be formulated by dhk \u00bc x cos h\u00fe y sin h 0:5Cd\u00f01 coswl\u00de kkdd \u00f012\u00de where kk is a parameter indicating the presence of ball-spall contact for the kth rolling element. kk = 1 stands for the passing process of the kth rolling element over the spall area within the load zone, while 0 stands for the other case. Thus, it can be formulated by kk \u00bc 1 mod\u00f0/spall;2p\u00de hspall 6 mod\u00f0hk;2p\u00de 6 mod\u00f0/spall;2p\u00de \u00fe hspall and wm 6 mod\u00f0/spall;2p\u00de 6 wmand wm 6 mod\u00f0hk;2p\u00de 6 wm 0 otherwise 8>< >: \u00f013\u00de Similarly to the application of external radial load on the bearing, the magnitude of the load acting on the rolling element when it rolls though a spall-free location within the load zone, Qw, is classically formulated as in [16] by Qw \u00bc Qm \u00f02 1\u00fe cosw\u00de=2 \u00bd 1:5 wm 6 w 6 wm 0 elsewhere ( \u00f014\u00de where wm refers to the angular limit of the load zone (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003019_s1350-4533(00)00062-x-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003019_s1350-4533(00)00062-x-Figure3-1.png",
        "caption": "Fig. 3. Static compression tests, according to the ASTM.",
        "texts": [
            " As response sensitivity cannot be avoided, the sensor output is measured for each individual implant in a calibration step before implantation. The fatigue limit is then individually defined as half of the sensor signal at the elastic limit [12]. The elastic limit is measured by loading to failure, for several implants and an average value is taken. However, even if no significant failure was observed, taking the minimum value instead of the average should be considered. Static compression tests, according to the ASTM (designation F-384-73,1987) have been performed on the hard-wired nail-plate type implants, loaded as presented in Fig. 3. The response of strain gauges, bonded at critical spots, as indicated in Fig. 4, has been monitored in combination with the load-deformation curve of the implant. Linear deformation is observed up to 750 N as shown in Fig. 5. Fig. 5 shows the load-deformation curve of one of the implants (number 47), for three repetitive loadings to 750 N and the final destructive test. The structural importance of the lid is demonstrated as well as the relatively poor response of the bottom strain gauge (SG1, Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure21-1.png",
        "caption": "Fig. 21. Tetrahedron element mesh for the complex component with homogenized support structures.",
        "texts": [
            " As a preliminary study, for the component with a height of 44mm, the model is sliced into 25 layers and accordingly, a large layer activation thickness of 1.76mm is employed. In other words, nearly 44 thin layers are lumped into an equivalent layer in the layered simulation. Though an overestimation of the residual deformation is expected according to the previous work [25], the computational cost for modeling such a complex geometry can be saved significantly. In addition, tetrahedron elements are adopted to mesh the component as shown in Fig. 21. Especially for the interface between the solid and thin-walled support structures, element mesh is refined for better accuracy in the simulation for layerwise material addition and post cutting process. Moreover, a small substrate with a thickness of 2.0 mm is attached to the bottom of the bracket and its bottom surface is fixed in displacement as the boundary condition for the entire inherent strain model. This setup has been proved to be helpful in avoiding stress overestimation at bottom surface of the bracket and having the simulation converged smoothly when a tetrahedron element mesh is employed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure11.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure11.9-1.png",
        "caption": "Fig. 11.9 Computer-aided design of a car",
        "texts": [
            " This system was initially developed on the IBM 704 computer for the purpose to use simple cubic polynomials to describe the outlines of components such as automobile hoods. This was widely credited as the earliest application of CAD in engineering (Krull 1994). The latter half of the 1960s saw significant progress in the development of computer graphics devices. The introduction of microcomputers after the 1970s greatly accelerated the pace of commercialization of CAD technology. Application was expanded to many fields, from creating simple circuit diagrams to designing very complicated airplanes and automobiles (Fig. 11.9). At the same time, many commercialized CAD systems were put in the market. During the 1980s, the Very-Large-Scale Integration (VLSI) technology made the micro-processor and computer memory more powerful and much cheaper. 404 11 Mechanical Design in New Era Workstations appeared and CAD became popularized in mid and small-sized businesses. Autodesk Inc. released the AutoCAD in 1982, a landmark in the course of CAD technology. The 1990s saw rapid popularization of CAD in almost every industry. One important driving force behind was the tougher market competition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000763_j.bbe.2020.12.010-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000763_j.bbe.2020.12.010-Figure6-1.png",
        "caption": "Fig. 6 \u2013 Static analysis of a squatting posture.",
        "texts": [
            " The junction plate is loose from the B or C plane when the user in a standing posture or walking. The ankle joint can realize flexion/dorsiflexion and abduction/adduction. The ankle structure of the engineering prototype is made of carbon fiber, leading to an increase in the strength of the ankle components and a reduction in the overall weight (Fig. 5). The maximum stress position of the exoskeleton was analyzed and the human squatting model was established to find the boundary conditions. Static analysis of a sitting position is illustrated in Fig. 6, where m1 is the mass of the calf, m2 is the mass of the thigh, m3 is the mass of the trunk, F1 and F2 are the forces exerted by the legs on the exoskeleton. Fs is the reactive force that the ground act on the exoskeleton. F01 and F02 are both the reactive force that the exoskeleton act on the structure of ratchet. human thigh. l1 is the length from the foot sole to the knee joint. l2 is the length of the thigh. l3 is the length from the center of trunk mass to the hip joint. u1 is the ankle joint",
            "76 mm), which also meets the requirement of practical application. The reduction rate of mass is 40% with the initial value of 0.42 kg and the optimal value of 0.25 kg. The optimal equivalent stress and total deformation are exhibited in Fig. 9. The optimization procedure of shank link rod is similar to thigh. The strength analysis of overall device is carried out based on software. First, the foot soles of the exoskeleton are fixed. Then, the downward forces F1 and F2 are applied in the positions illustrated in Fig. 6. Next, the model is imported into ANSYS to mesh the exoskeleton. The whole stress distribution results, deformation results, and strain diagram are exhibited in Fig. 6. The maximum stress is 118.4 MPa, which meets the needs of material strength. The maximum deformation range is 4.46 mm. The maximum strain range meets the requirements (Fig. 10). Ratchet equivalent stress and total deformation are presented in Fig. 11. The maximum simulation equivalent stress is 27.16 MPa, which less than the allowable stress of steel and can meet the stiffness requirement. It can be revealed from Fig. 11(a) that the maximum total deformation value of ratchet can be ignored. External forces or sudden external perturbations may be occurred when using the exoskeleton in dynamic working situations, for example, sudden impact force, external vibration, interaction with machines or rotation between different tasks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002867_la0267903-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002867_la0267903-Figure9-1.png",
        "caption": "Figure 9. Cyclic voltammograms simulated with the Digisim software package (third scan, scan rate of (A) 1, (B) 2, (C) 5, (D) 10 mV s-1) obtained for a one-electron reduction process under finite diffusion boundary conditions with a layer thickness of 800 nm, a diffusion coefficient of 2\u00d710-14 m2 s-1, a concentration of 24 mM, a standard rate constant for electron transfer of 3 \u00d7 10-8 m s-1, a transfer coefficient of 0.5, and an equilibrium potential of 0.0 V vs SCE.",
        "texts": [
            " Langmuir 2001, 17, 1184. (39) Forzani, E. S.; Perez, M. A.; Teijelo, M. L.; Calvo, E. J. Langmuir 2002, 18, 9867. (40) Calvo, E. J.; Wolosiuk, A. J. Am. Chem. Soc. 2002, 124, 8490. causing a widening of the peak-to-peak separation. Both effects can be successfully reproduced by assuming a finite diffusion space and suitable values for the concentration of cytochrome c, the effective diffusion coefficient for cytochrome c within the membrane, and an apparent standard rate constant for electron transfer (see Figure 9). The physical interpretation of parameters such as the diffusion coefficient and the standard rate constant obtained by comparison of voltammetric data with numerical simulation data is not immediately obvious. The match between experiment and simulation for several scan rates is very good, but the nature of the processes responsible for the electron transfer is revealed only in part. The concentration of cytochrome c in the membrane, 24 mM, is very high compared to the solution concentration, 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001029_j.mechmachtheory.2021.104357-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001029_j.mechmachtheory.2021.104357-Figure2-1.png",
        "caption": "Fig. 2. a.) Gear tooth crack model, b.) Crack profile, c.) Tooth slice.",
        "texts": [
            " 1 provides an insight into the initial crack locations and the natural propagation paths. Due to the unceasing engagement and disengagement of the gear teeth, the gear mesh stiffness is a time-dependent parameter. The TVMS results in the parametric excitation and depicts the health condition of the gear system. Thus, the evaluation of TVMS plays an essential role in gear tooth modelling. In the present work, the potential energy method is used [38,39] . In this method, the gear tooth is modelled as a cantilever beam starting from the root circle [24] . Fig. 2 a shows the single gear tooth to be considered a cantilever beam, acted upon by a force F at a pressure angle of \u03b11 . During the regular operation, gear teeth are subjected to a continuous bending load. Thus, resulting in the accumulation of strain energy. The accumulated strain energy provides the gear pair mesh stiffness. The methodology adopted by Mohammed and Rantatalo [21] is followed. Mathematically, the strain energy accumulated in a gear tooth under the action of contact force F is expressed as; U b = F 2 2 K b , U s = F 2 2 K s , U a = F 2 2 K a (1) where U b , U s , and U c represent the strain energy associated with bending, shear, and axial compressive loads, respectively. The terms K b , K s , and K a are the bending, shear, and axial stiffness, respectively. According to the Cantilever beam theory, the strain energy stored in meshing gear can be expressed as; U b = \u222b d 0 M 2 2 EI x d x, U s = \u222b d 0 1 . 2 F 2 b 2 GA x d x, U a = \u222b d 0 F 2 a 2 EA x d x (2) where F and M are the contact force and the transmission moment at the contact point; and F b , F a , and M are expressed as; where h , x , d are shown in the gear tooth geometry, in Fig. 2 a. The variables h and d represent the position of the contact point from the gear tooth center and the root of the gear tooth. From the properties of the involute curve [24] ; h = r b [(\u03b11 + \u03b12 ) cos (\u03b11 ) \u2212 sin (\u03b11 )] (4) d = r b [(\u03b11 + \u03b12 ) sin (\u03b11 ) + cos (\u03b11 )] \u2212 r r cos (\u03b13 ) (5) where r b and r r are the base circle radius and root circle radius, \u03b12 and \u03b13 are the respective gear tooth angles subtended by the involute profile at the base circle and the root circle. The shear modulus is given as; where E and \u03bd are the Elastic modulus and the Poisson\u2019s ratio",
            " The continuous bending load promotes the crack initiation at the root of a gear tooth. The crack affects the gear tooth stiffness, and the stiffness reduction further affects the vibration characteristics. The bending stiffness is given as; 1 K b = \u222b d 0 ((d \u2212 x ) cos \u03b11 \u2212 h sin \u03b11 ) 2 EI x dx (7) the shear stiffness is given as; 1 K s = \u222b d 0 1 . 2 cos 2 \u03b11 GA x dx (8) the axial stiffness is given as; 1 K a = \u222b d 0 sin 2 \u03b11 EA x dx (9) The terms I x and A x represent the area moment of inertia and the cross-sectional area of the section xx at a distance x (shown in Fig. 2 a) given as; I x = { (1 / 12)(h x + h x ) 3 db ; h x \u2264 H c (1 / 12)(h x + H c ) 3 db ; h x > H c (10) A x = { (h x + h x ) db ; h x \u2264 H c (h x + H c ) db ; h x > H c (11) where H c = h c \u2212 h l .sin\u03b1c , H c represents the gear tooth height affected with the crack, h c gives the distance of the crack initiation point on the involute profile from the gear tooth center, \u03b1c is the crack inclination angle, and h l is the effective arc length of the crack path. A simplified parabolic crack profile is proposed to describe the gear tooth crack extending into the gear tooth body. The crack path function is represented by q (u ) , as shown in Fig. 2 b. It has a resemblance to the crack paths shown in Fig. 1 . Mathematically, it is expressed as follows; q (u ) = \u221a (q h + q ) 2 q l u (12) where q l , q , and q h represent the crack initiation point distance, crack width, and the distance of crack initiation point on the involute profile from the gear base circle, respectively. The crack parameters are shown in Fig. 2 b. The arc length of the crack (h l ) is given as; h l = \u222b 2 c 0 \u221a 1 + ( (q h + q ) 2 2 q l v ) 2 dv (13) A set of crack parameters governs the crack path, i.e., q (u ) = f (\u03b1c , q l , q h , q ). The crack angle, \u03b1c is set at 70 0 , q l at 1.35 mm, q h at 0.35 mm, two values for crack width ( q ) of 0.5 mm and 0.7 mm are used. The stiffness for a slice of gear tooth along the width ( z-axis) is given as; K t (z) = 1 1 K b + 1 K s + 1 K a (14) For the complete tooth width b, the tooth mesh stiffness, K T is given as; K T = \u222b b 0 K t (z) dz (15) The presence of tooth fillet affects the dynamics of gear tooth loading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002834_02783649922066628-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002834_02783649922066628-Figure6-1.png",
        "caption": "Fig. 6. A general parallel robot having two-connectivity after link splitting.",
        "texts": [
            ") By simple extension of the arguments, it can be shown that the same asymptotic complexity result applies to l-connected mechanisms for any fixed value of l. This is a new complexity result. In particular, note that there is no limit on the number of loops in an l-connected mechanism. The actual computational cost will, of course, be larger for l > 1 than l = 1, and it grows cubically with increasing l, so this result is really only of practical use for small values of l. Fortunately, many practical closed-loop mechanisms are two-connected or three-connected, and many that are not can be converted by link splitting. For example, Figure 6 shows a generic parallel robot mechanism in which the platform and base have each been split into three parts. The original mechanism is six-connected, but the link-split mechanism is only two-connected. Figure 6 also illustrates how to deal with multiple connections to ground. Recall that connections to ground are done by at BROWN UNIVERSITY on December 16, 2012ijr.sagepub.comDownloaded from the root node. While it would certainly be possible to program the root node to perform a multijoint connection to ground, it is generally better to keep the root-node calculation as short as possible on the grounds that while the root-node processor is active, all others are idle. The solution is to invent a floating base that is rigidly connected to ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002812_a:1016559314798-Figure19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002812_a:1016559314798-Figure19-1.png",
        "caption": "Figure 19. Fourier transform of the 3R robot joint 3 velocity, for 500 cycles, versus the radial distance r and the frequency ratio \u03c9/\u03c90, for \u03c1 = 0.1 m, \u03c90 = 3 rad/sec.",
        "texts": [],
        "surrounding_texts": [
            "In the last group of experiments, after elapsing an initial transient, we calculate the Fourier transform of the robot joint velocities for a large number of cycles of circular repetitive motion with frequency \u03c90 = 3 rad/sec. Figures 17\u201323 shows the results for the 3R and 4R robots versus the radial distance r, the center of the circle, with radius \u03c1 = 0.10 m. Once more we verify that for 0 < r < rs we get a signal energy distribution along all frequencies, while for rs < r < 3 m the major part of the signal energy is concentrated at the fundamental and multiple harmonics. Moreover, the DC component, responsible for the position drift, presents distinct values, according to the radial distance r and \u03c1: |q\u0307i (\u03c9 = 0)| = a\u03c1d/(b + r)c, i = 1, 2, . . . , n. (28) Tables 6 and 7 show the values of the parameters of Equation (28) for the 3R and 4R robots, respectively. Based on these results we conclude that the velocity drift changes with the robot endeffector radial distance r. Furthermore, the DC component is \u2018induced\u2019 by the repetitive motion with a quadratic-like dependence with \u03c1."
        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.10-1.png",
        "caption": "Figure 12.10. The end points of single-tooth contact.",
        "texts": [
            " For 278 Internal Gears example, radial assembly of 20\u00b0 pressure angle gear pairs can generally be carried out when (N2-N 1) is 17 or larger. In some cases it may also be possible, for gear pairs with lower values of (N2-N 1). However, since the positions of the tooth tip points in each gear depend on the tooth thickness and the radius of the tip circle, as well as on the pressure angle, the checks should be made whenever there is a danger that radial assembly may be impossible. Highest and Lowest Points of Single-Tooth Contact The meshing diagram for an internal gear pair is shown in Figure 12.10. The ends of the path of contact are labelled T1 and T2 , and the two points on the path of contact, a distance Pb inside each end, are shown as Q and Q'. There is single-point contact whenever the contact point lies between Q and Q' \u2022 Cutting Internal Gears 279 On the pinion, the highest and lowest points of single-tooth contact correspond to Q' and Q on the path of contact. The radii of the circles through these points can be read directly from the diagram, (12.45) Simi larly, on the internal gear, the highest and lowest points of single-tooth contact correspond to Q and Q', and again the radii of the circles through these points can be read from the diagram, (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure4-1.png",
        "caption": "Fig. 4. Elementary open kinematic chain (0A \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b72C -1C) associated with the loop A-C of parallel Cartesian robotic manipulator: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " The motion parameter b1 is given by the number of independent motions between the extreme elements 1B and 0 in the serial open kinematic chain 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b7 -2B -1B associated with the first loop when no other loop is closed (Fig. 3). We can observe that five independent motions (vx, vy, vz,\u03c9x,\u03c9y) exist between the extreme elements 1B and 0 (Fig. 3). These velocities form the base of RF(1). The motion parameter b2 is given by the number of independent motions between the extreme elements 1C and 0 in the serial open kinematic chain 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 -2C -1C associated with the second loop when no other loop is closed (Fig. 4). Five independent motions (vx, vy, vz,\u03c9x,\u03c9z) exist between the extreme elements 1C and 0 (Fig. 4). These velocities form the base of RF(2). The dimension of the range of the restriction of F2 to the kernel of F1 can also be obtained by inspection. dim(RF(2)/KF(1) ) is given by the number of independent motions between the extreme elements 1C and 0 in the complex open kinematic chain from Fig. 5 obtained by concatenating the closed loop A-B and the elementary open kinematic chain associated with the leg C. Only four independent motions (vx, vy, vz,\u03c9z) exists in this case between the extreme elements 1C and 0 (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000704_j.addma.2021.102116-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000704_j.addma.2021.102116-Figure9-1.png",
        "caption": "Fig. 9. (a) Imported connecting rod CAD model; (b) Voxelized finite element model; (c) Generated islands of each layer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            "41% in this case. It should be emphasized here that the experimentally measured residual deformation value is smaller than the predicted value in optimization. This deformation overestimation is attributed to the elastic finite element analysis performed in the optimization which neglects the plastic behavior. Despite not considering plasticity in the optimization model, the optimized scan pattern still performs well. The second case is a connecting rod and the dimension is 95 \u00d7 35 \u00d7 18 mm3, as shown in Fig. 9(a). In this case, 60 physical layers are merged as one layer and the part is voxelized with element size of 1.25 \u00d7 1.25 \u00d7 1.8 mm3. The finite element model of this connecting rod employed in scan pattern optimization is shown in Fig. 9(b), which has 21,280 elements and 24,563 nodes. The island size is 5 \u00d7 5 mm2 in the build design. Each island is divided into 16 elements as shown in Fig. 9 (c). The initial scan pattern is the same as the block structure case in Section 3.1. Each island is filled with bi-directional horizontal scan lines as shown in Fig. 10. Build path reconstruction is employed for each island depending on the intersection between island and geometry as shown in Fig. 10(b). The reconstructed build paths of initial scan pattern are used to build the connecting rod. The optimized results for the connecting rod case are presented in Fig. 11 including the deformation profile after cutting off with initial and optimized scan pattern, layer-wised optimized scan pattern and reconstructed building path, and the convergence history. As shown in Fig. 11(a), the upward bending after partially cutting off the first layer is reduced significantly with optimized scan pattern compared to the deformation with initial scan pattern. The deformation of the selected tip point on the top surface along the center line, as indicated by the red dot in Fig. 9(a), is 0.83 mm before optimization and is reduced to 0.45 mm after optimization. The layer-wise scan pattern and reconstructed build path of layer 1, 3, 7 and 9 are presented in Fig. 11(b). The convergence history is presented in Fig. 11(c). The optimization converges with 80 iterations and takes 2.3 h to with Intel Xeon Gold 6136 3.0 GHz CPU (two processors) and 256GB RAM. Different from the optimized scanning pattern of the block structure, which mainly consists of vertical scanning tracks, the optimized scanning pattern for connecting rod has islands with horizontal scanning Q"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure6.26-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure6.26-1.png",
        "caption": "Figure 6.26. Schematic showing spherical aberration in TEM.",
        "texts": [
            " Unfortunately, the information transferred by the optical system suffers various aberrations, which limit the performance of phase contrast high-resolution imaging. In this section, we introduce the different aberrations and derive the transfer function of the objective lens. 6.3.3.1. SPHERICAL ABERRATION. Spherical aberration refers to a change in focal length as a function of the electron scattering angle. The focal plane is a curved surface, and the electrons scattered to different angles are focused at different positions along the optic axis (Fig. 6.26). As pointed out, we can use the ray diagram for a single- 291 ELECTRON CRYSTAL LOGRAPHY FOR STRUCTURE ANALYSIS 292 CHAPTER 6 lens TEM to show the aberration effect. At the front focal plane, the image of a point object is replaced by a finite disk due to spherical aberration. The radius of the disk is (6.48) where Cs is the spherical aberration coefficient, which is an important parameter characterizing the resolution of the lens, and e is the angle of the scattered electron with respect to the optic axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000504_j.matchar.2020.110468-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000504_j.matchar.2020.110468-Figure1-1.png",
        "caption": "Fig. 1. Schematic geometry of: (a) vertically-built (Z direction) and (b) horizontally-built (XY direction) samples: The vertically-built sample was cut along the scanning-direction plane (XY) and investigated in the scanned surface. The horizontally-built sample was cut along the building-direction plane (XZ) and investigated in the multilayered surface. The beam scans the surface by the orthogonal (cross) strategy.",
        "texts": [
            " Hence, systematic research is required to unveil the process\u2013properties relation during AM processing. In the present work, we aim to investigate the effects of heat treatment and building direction on the microstructural evolution and mechanical properties of AM 15-5 PH. AM 15-5 PH samples were fabricated by EOS GmbH M290 in a nitrogen atmosphere using the following process parameters: spot size of ~70 \u03bcm, scanning speed of 1200 \u03bcm/s, layer thickness of ~40 \u03bcm and scanning as cross strategy (see Fig. 1). Two types of cylindrical samples were fabricated: one is the axial direction of the cylinder is parallel to the z-axis (denoted as vertically-built sample, Fig. 1(a)), and another is the axial direction of the cylinder is perpendicular to the z-axis (denoted as horizontally-built sample, Fig. 1(b)). The tested samples were cut along the scanning-direction (SD) plane for the vertically-built materials and along the building-direction (BD) plane for the horizontally-built ones (see Fig. 1) from a cylindrical tensile sample (10\u201313 mm diameter). Commercially extruded 15-5 PH was used in this study for comparison with the AM samples. Following the DMLS process, the samples were submitted to various heat-treatment conditions, as listed in Table 1. Note that WC and AC indicate water quenching and air cooling, respectively. The samples were further metallographically prepared using SiC papers (up to 4000 grit) and polished with ~40 nm OP-S (oxide polishing suspensions). The polished surface was etched using a solution of nitrohydrochloric acid (i",
            " This preparation process was repeated 2\u20133 times until the grain structure was clearly visible with polarized light microscopy. EBSD was used to investigate the local microstructure and texture distributions at a step size of 0.1\u20130.5 \u03bcm, an accelerating voltage of 20 kV and a working distance of 5 mm. The chemical composition was evaluated using a JEOL JSM-7800F instrument equipped with an energy-dispersive X-ray spectrometer (EDX), showing that all the samples have compositions similar to standard 15- 5 PH stainless steel (see Table 2). For measuring the local hardness on the investigated surfaces (see Fig. 1), a nanoindentation experiment was performed using an Anton Paar NHT3 apparatus (equipped with a Berkovich indenter tip) at a constant loading rate of 0.05/s and a maximum indent depth up to 1000 nm. The hardness of individual samples was mapped with 75 points (5 \u00d7 5 matrix at a total of three areas) on randomly selected central and edge areas and calculated using the Oliver and Pharr method (Eq. (1)) [24]: =H P A max (1) where \u0420max is the maximum indentation load and A is the projected area by a penetration of the indenter",
            " Note that these mechanical tests were repeated in 2\u20133 samples fabricated under the same conditions in order to confirm the repeatability and reproducibility. X-ray diffraction (XRD) was applied to perform phase analyzes on diverse microstructures induced by different building directions and heat treatments using an Xstress 3000 X-ray diffractometer equipped with a copper (Cu) X-ray source (wavelength: 1.54 \u00c5). The XRD is analyzed using Rietveld refinement method with X'pert Highscore software. Series of experiments were carried out on the XY and XZ planes of the vertical and horizontal samples, respectively, as shown in Fig. 1. Fig. 2 shows the microstructure and texture of conventional and asbuilt AM samples. Conventional 15-5 PH shows a lath martensite structure in blocks. The as-built samples are composed of finer equiaxed and columnar grains, as shown in Fig. 2(b) and (c). In the as-built samples, a columnar grain growth is exhibited, similarly to the microstructure in the fusion zone of the welded part. Fig. 2(b) shows the scanned XY surface of V-AB. The microstructure shows columnar grain growth perpendicular to the scanning line, which is accompanied by a melting pool and equiaxed grains located on the scanning line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000763_j.bbe.2020.12.010-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000763_j.bbe.2020.12.010-Figure5-1.png",
        "caption": "Fig. 5 \u2013 The mechanical structure of ankle joint. Plane A is Groove surface. B is inside plane when the junction plate is connected with plane A and plane B, the ankle joint is locked to support the wearer. C is outside plane, when the junction plate is loose from the A and connected with plane C, the ankle joint is active.",
        "texts": [
            " Specifically, the left and right ankle swing are locked to ensure the steady support of the exoskeleton when the junction plate is connected with A plane. The junction plate is loose from the B or C plane when the user in a standing posture or walking. The ankle joint can realize flexion/dorsiflexion and abduction/adduction. The ankle structure of the engineering prototype is made of carbon fiber, leading to an increase in the strength of the ankle components and a reduction in the overall weight (Fig. 5). The maximum stress position of the exoskeleton was analyzed and the human squatting model was established to find the boundary conditions. Static analysis of a sitting position is illustrated in Fig. 6, where m1 is the mass of the calf, m2 is the mass of the thigh, m3 is the mass of the trunk, F1 and F2 are the forces exerted by the legs on the exoskeleton. Fs is the reactive force that the ground act on the exoskeleton. F01 and F02 are both the reactive force that the exoskeleton act on the structure of ratchet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000896_j.rcim.2021.102133-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000896_j.rcim.2021.102133-Figure3-1.png",
        "caption": "Fig. 3. The mechanism diagram of the 3-TPS hybrid robot.",
        "texts": [
            " A gas bottle is used to keep air pressure more stable. The differential pressures of the compressed air in two chambers push the piston of the cylinder to generate the output force. The polishing tool is driven by the piston, and the compressed air is provided by an air pump. As an end-effector, the pneumatic system is assembled on the 3-TPS hybrid robot [43] to conduct 5 DOF movement, thus a polishing force experimental platform has been built. The 3-TPS hybrid robot mechanism diagram is shown in Fig. 3. The 3-TPS robot, a hybrid machine tool with horizontal-vertical conversion, is driven by parallel mechanism as basic structure and constrained by serial mechanism. The parallel mechanism is constituted by 3 telescopic rods. As driving rods they are assembled on the fixed platform by 3 Hooke hinges (B1, B2, B3), and connected to the moving platform by 2 spherical hinges and 1 revolute pair (b1, b2, b3). Main parameters of the servo motors of the driving rods include rated output 1kw, rated revolution 3000 r/min and rated torque 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure8-16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure8-16-1.png",
        "caption": "Figure 8-16. Simple shear, (a) Double sandwich test piece; (b) sandwich test piece showing shear deformation; (c) shearing of rubber block. 1,1' undeformed shape; 2, 2' bending deformation; 3, 3' true shear deformation; 4,4' resultant bending plus shear deformation",
        "texts": [],
        "surrounding_texts": [
            "The stress/strain curve in simple shear is approximately linear up to relatively large strains and can be represented by: A ^ where: F = applied force, A = cross-sectional area, G = shear modulus, and y = shear strain. With reference to Figure 8.16, the strain is x/h and area A is 1 x the width of the rubber (not shown in the diagram) for a single sandwich and twice this for the double sandwich."
        ]
    },
    {
        "image_filename": "designv10_4_0003620_iros.1992.594498-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003620_iros.1992.594498-Figure13-1.png",
        "caption": "Figure 13: Locus of a finger in deformation of object.",
        "texts": [
            " The solid line indicates the case with force sensation, and the dashed line indicates the case without force sensation. In the case without force, Re showed (7) an initial rapid increase after which the subject stopped deformation(Fig,12(b)). On the other hand, in the case with force, the shape drew near to the target shape with- (8 ) Fig.11 shows R, and Re of three subjects at the time when the shape seemed to draw nearest to the target shape. The vertical axis shows R,, and horizontal axis out sudden error(Fig.U(a)). Fig.13 is part of the locus of the finger. The horizontal axis indicates distance from the object axis and the vertical axis indicates height. In the case with force, the finger moves more regularly and less wastefully than in the case without force. These results show the importance of force sensation in assisting with the task of deformation of an object in the virtual work space. 5 Conclusion We have investigated a virtual space where we can manipulate object models on a computer by finger. We have shown the importance of realization of the perception cycle in the virtual work space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003244_02640410152006135-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003244_02640410152006135-Figure6-1.png",
        "caption": "Fig. 6. Model of forces acting on the shot during the delivery phase.",
        "texts": [
            " The expression for the height of the shot at the instant of release (i.e. the release height) is: hrelease = hshoulder + larm sin h (3) where hshoulder is the height of the athlete\u2019 s shoulders when standing upright and larm is the length of the athlete\u2019 s outstretched throwing arm and shoulder. When shot-putting on level ground, the landing height is equal to the radius of the shot, and so the height di\u00fe erence between the release and the landing (equation 2) becomes: h(h) = hshoulder + larm sin h - rshot (4) where rshot is the radius of the shot. Figure 6 shows a model where the shot-putting action is reduced to just the delivery phase. The athlete applies to the shot a force, F, at an angle Q to the horizontal. The combined e\u00fe ect of the applied force and the weight of the shot, mg, is a resultant force, R, that produces acceleration of the shot along a straight line path, l, at an angle h to the horizontal (Tricker and Tricker, 1967). This acceleration path is at the same angle to the horizontal as the release angle (Susanka and Stepanek, 1988)",
            " In Proceedings of the First International Conference on Techniques in Athletics, Vol. 1 (edited by G.P. Br ggemann and J.K. R hl), pp. 118\u00b1 125. K\u201d ln: Deutsche Sporthochschule. Zatsiorsky, V.M. (1995). Science and Practice of Strength Training. Champaign, IL: Human Kinetics. Zatsiorsky, V.M. and Matveev, E.I. (1969). Investigation of training level factor structure in throwing events (in Russian). Theory and Practice of Physical Culture (Moscow), 10, 9\u00b1 11. In the model of the delivery phase shown in Fig. 6, the work done by the athlete in exerting a constant force F to cause acceleration of the shot along a path length l is given by the projection of F onto l: W = F \u00b4 l W = Fl cos (Q - h) (13) where Q - h is the angle included between the directions of F and l. The trigonometric identity sin2 x + cos2 x = 1 may be rearranged as cos x = (1 - sin2 x)1/2 Letting x = Q - h gives cos (Q - h) = [1 - sin2 (Q - h)]1/2 and so equation (13) may be written as W = Fl [1 - sin2 (Q - h)]1/2 (14) The law of sines, applied to the triangle formed by the force vectors F, mg and R, gives sin (Q - h) mg = sin a F \\ sin (Q - h) = mg F sin a (15) D ow nl oa de d by [ T em pl e U ni ve rs ity L ib ra ri es ] at 0 5: 53 2 1 N ov em be r 20 14 The sum of the angles internal to the triangle formed by the force vectors F, mg and R must be equal to 180\u00b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure6-7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure6-7-1.png",
        "caption": "Figure 6-7. Principles of oscillating disc and oscillating die curemeters. (a) Oscillating disc; (b) Oscillating die.",
        "texts": [],
        "surrounding_texts": [
            "The reciprocating paddle instrument is now largely a matter of history and a third type, the rotorless curemeter, has rapidly become the most popular. The rotorless type is a curemeter in which one half of the die enclosing the test piece, rather than a paddle or disc within the test piece, oscillates or reciprocates (Figure 6.7). Despite the widespread use of curemeters, progress to international standardisation was relatively slow, partly because of patent difficulties as a Test on unvulcanized rubbers 85 result of the virtual monopoly of certain commercial instruments. However, the oscillating disk curemeter was eventually standardized as ISO 3417^^ .\u0302 The apparatus is described in some detail, based on commercially available equipment, with requirements for construction, dimensions, frequency and amplitude of oscillation, closing pressure and temperature control. The ASTM standard, D2084^^^ preceded and was the model for the ISO method. It is considered to be technically the same as ISO 3417 with minor differences not being significant. The British standard, BS 903 Part A60-2'^^ is identical to ISO 3417. ISO does not have a standard specifically for rotorless curemeters, but instead has a guide to the use of curemeters, ISO 6502^^ .\u0302 This covers both oscillating disc and rotorless curemeters and distinguishes three types of rotorless instrument - reciprocating, oscillating unsealed cavity and oscillating sealed cavity. It points out the principal advantages of rotorless curemeters as being that the test temperature is reached in a shorter time and there is better temperature distribution in the test piece. The rationale for this approach to stadardising is that a general guide can apply to different types of curemeter and is not restricted to a particular commercial design. All the general matter such as the principles of the different types of instrument, the level of temperature control desirable and the measures which can be taken from the cure trace etc can be in one place, without the problems of specifying in detail the various instrument geometries and constructions available. Also, material common to both oscillating disk and rotorless instruments would not need repetition. The aim as regards covering various designs of rotorless instrument has been achieved but has failed in respect of preventing repetition as the standard refers to ISO 3417 as having particular requirements for oscillating disk instruments. The basic principles of curemetering are covered and typical vulcanization curves illustrated together with the parameters that can be derived from them. By way of illustration the curve for a plateau type cure on an oscillating disc curemeter is shown in Figure 6.8. Minimum torque, maximum torque or the slope of the curve (cure rate) can be taken but perhaps the most useful single figure is the time to achieve a given degree of cure which is the time for the torque to increase to: where y is the percentage cure required, (usually 90% for a 'practical' cure, MHF is the plateau torque and ML is the minimum torque. A similar estimate of cure time is taken from an oscillating paddle or rotorless curemeter curve."
        ]
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure2-1.png",
        "caption": "Fig. 2. A singular con\u00aeguration of class (RPM, IO, II).",
        "texts": [
            " , G, are 3-dimensional planar screws, SP=(1, yP, \u00ffxP) T, mPG=(yP\u00ffyG, xG\u00ffxP) T, and I2 is the 2 2 unit matrix. To \u00aend all the singularities and establish their types, the procedure described in Section 3.2 is followed: 1. Check for IIM singularities. For the given mechanism, it is established that condition (vi) has no solution compatible with the given link lengths. 2. Check for RPM singularities. The condition (iii) is satis\u00aeed only when the determinants of both [ SBSOSD] and [ SCSGSD] vanish. This gives eight distinct singular con\u00aegurations (one of them is shown in Fig. 2) 3. (3.2) For each of the eighth con\u00aegurations in {2}, conditions (i) and (ii) are checked and it is found that neither is satis\u00aeed. (3.5) It is concluded that the (RPM, IO, II) class consists of the eight elements of {2}. (4) Condition (vii) is applied. (vii) is equivalent to the singularity of at least one of the matrices [ SBSCSD] or [ SCSGSF]. The solution of each of these equations (combined with the loop equations) is a 1-dimensional submanifold of the 2-dimensional con\u00aeguration space. The \u00aerst manifold has four connected components, and the second one has three components",
            " However, it can be seen that if a non-trivial linear combination of these 8-dimensional column vectors equals zero, then both sets of screws { SB, SC, SD} and { SC, SD, SG} must be linearly dependent. (Indeed, since mFG is never zero, the coe cient of the last column must be zero. Moreover, since SB is always di erent from SC, the coe cients of three columns preceding the last one (columns 7, 8, 9, of L in (6)) are not all zero. This implies that { SC, SD, SG} are linearly dependent. From the properties of planar screws it then follows that an RPM-type singularity of the mechanism shown in Fig. 1 occurs when both sets of points {B, C, D} and {C, D, G} are colinear (Fig. 2). Thus, using screw theory, the singularity conditions can be interpreted as geometric criteria, as illustrated by the example analysed later in Section 5. It should be noted that, such a screw theory based approach provides a better geometrical insight into the problem of singularity identi\u00aecation, and it is not dependent on the speci\u00aec values of the link parameters. This allows the study of singularities that occur for a given kinematic chain regardless of the values of the link parameters. For complex mechanisms with many loops, the dimension of the velocity equation can be quite large"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000690_j.rcim.2021.102138-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000690_j.rcim.2021.102138-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of collision detection. (a) Sphere, (b) Cylinder, (c) Cuboid.",
        "texts": [
            " Meanwhile, there are k regular geometric objects in the simplified model of the robot, and Gj is one of them, and the centroid of Gj is Oj. Considering that the position coordinates of Oj are a function of the joint angle \u0398 of the robot, then the functional form of the collision detection constraint can be defined as g4(\u0398i) = dmin ( Pi,Gj ) \u2265 0, { i = 1, 2,\u22ef,m j = 1, 2,\u22ef, k (17) Q. Fan et al. Robotics and Computer-Integrated Manufacturing 70 (2021) 102138 where, dmin(\u22c5) represents the minimum distance from point Pi to the surface of regular geometry Gj. As shown in Fig. 3, when regular geometry is a sphere, a cylinder and a cuboid, dmin(\u22c5) can be defined as Eqs. 18 to 20 respectively, as follows dmin(P,G) = dist(P,O) \u2212 s\u22c5r (18) dmin(P,G) = max ( dist(P1,O) \u2212 s\u22c5r dist(P2,O) \u2212 s\u22c5h/2 ) (19) dmin(P,G) = max \u239b \u239d dist(P2,O) \u2212 s\u22c5l/2 dist(P3,O) \u2212 s\u22c5w/2 dist(P4,O) \u2212 s\u22c5h/2 \u239e \u23a0 (20) where r, l,w, h are the size parameters of the regular geometry; s is a safety factor greater than 1, and its recommended value is 1~1.5; dist(\u22c5) is the function of distance between two points. Further, if the minimum distance (denoted as dmin) from the point P to the surface of the regular geometry G is positive, the point P is not inside the geometry G, otherwise the point P is inside the geometry G"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.5-1.png",
        "caption": "Figure 7.5: N-trailer robot",
        "texts": [
            " However, dim ~c = 4 only away from the singularity rjJ = \u00b17r /2, that corresponds to a loss of controllability for the vehicle. The relevance of this singularity is limited, due to the restricted range of the steering angle rjJ in many practical cases. N-Trailer Robot A more complex wheeled vehicle is obtained by attaching N one-axle trailers to a car like robot with rear-wheel drive. For simplicity, each trailer is assumed tobe connected to the axle midpoint of the previous one (zero hooking), as shown in Fig. 7.5. The car length is f, and the hinge-ta-hinge length of the i-th trailer is f;. One possible generalized coordinate vector that uniquely describes the configuration of this system is q = (x, y, r/J, Bo, el, ... , eN) E IRN+4, obtained by Setting Bo = e and extending the configuration of the car-like robot with the orientation B;, i = 1, ... , N, of each trailer. As a consequence, n = N + 4. The N + 2 nonholonomic constraints are Xf sin(Bo + r/J)- ilt cos(Bo + r/J) 0 x sin 80 - iJ cos Bo 0 x; sin{1; - i;; cos ei 0, i = 1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003642_j.robot.2005.04.004-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003642_j.robot.2005.04.004-Figure1-1.png",
        "caption": "Fig. 1. Body-fixed frame and earth-fixed frame for AUV.",
        "texts": [
            " In order to demonstrate the effectiveness of the proposed control scheme, certain simulation studies are presented in Section 4. Finally, we make a brief conclusion on the paper in Section 5. The dynamical behavior of an AUV can be described in a common way through six degree-of-freedom (DOF) nonlinear equations as [28] M(\u03bd)\u03bd\u0307 + CD(\u03bd)\u03bd + g(\u03b7) + d = \u03c4, \u03b7\u0307 = J(\u03b7)\u03bd, (1) where \u03b7 = [x, y, z, \u03c6, \u03b8, \u03c8]T is the position and orientation vector in earth-fixed frame, \u03bd = [u, v,w, p, q, r]T the velocity and angular rate vector in body-fixed frame as shown in Fig. 1, M(\u03bd) \u2208 6\u00d76 the inertia matrix (including added mass), CD(\u03bd) \u2208 6\u00d76 the matrix of Coriolis, centripetal and damping term, g(\u03b7) \u2208 6 the gravitational forces and moments vector, d denotes the unstructured uncertainty vector, such as exogenous input term and unmodeled dynamics and \u03c4 is the input torque vector. And J(\u03b7) is the transformation matrix defined as J(\u03b7) =   c\u03c8 c\u03b8 \u2212s\u03c8 c\u03c6 + c\u03c8 s\u03b8 s\u03c6 s\u03c8 s\u03c6 + c\u03c8 c\u03c6 s\u03b8 s\u03c8 c\u03b8 c\u03c8 c\u03c6 + s\u03c6 s\u03b8 s\u03c8 \u2212c\u03c8 s\u03c6 + s\u03b8 s\u03c8 c\u03c6 \u2212s\u03b8 c\u03b8 s\u03c6 c\u03b8 c\u03c6 0 0 1 s\u03c6 t\u03b8 c\u03c6 t\u03b8 0 c\u03c6 \u2212s\u03c6 0 s\u03c6/c\u03b8 c\u03c6/c\u03b8   , (2) where s\u00b7 = sin(\u00b7), c\u00b7 = cos(\u00b7) and t\u00b7 = tan(\u00b7). Underwater vehicles are generally designed to have symmetric structure; therefore, it is reasonable to assume that the body-fixed coordinate is located at the center of gravity with neutral buoyancy. In this paper, we consider an AUV as shown in Fig. 1, which has one propeller, two stern planes and two rudders to control the vehicle. For this kind of AUV, we decouple the sway motion of the vehicle and consider the heave velocity as a disturbance. And in the diving plane, we assume that the roll and yaw angular velocities are also close to zeroes. This could be acquired by properly adjusting the propeller\u2019s RPM and the rudders\u2019 angles. Under the above assumptions, the heave dynamics of the vehicle could be expressed as z\u0307 = \u2212u sin \u03b8 + v cos \u03b8 sin \u03c6 + w cos \u03b8 cos\u03c6 = \u2212u sin \u03b8 + d\u2032 z"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001704_jphysiol.1913.sp001601-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001704_jphysiol.1913.sp001601-Figure5-1.png",
        "caption": "Fig. 5.",
        "texts": [
            " If a current was passed from the platinum in C to that in B the nerve was excited at the lower end of the slot between C and B, the cathode being the point where the density of current in the nerve sud(denly decreased owing to the increase of the sectional area of the Ringer's solution surrounding it. In a similar way the nierve could be excited at the lower end of the slot between D and C. The method used here is essentially the same as that used for localising the excitation in the 'fluid electrodes' which I have described elsewhere2. There is no danger with this method of exciting elsewhere than close to the slot 1 This drawing may be more easily understood by comparison with Fig. 16, which is a plan of a trough differing from that of Fig. 5 only in the number and the size of the chambers. 2 This Journal, xxxvii. p. 114. 1908. See also Proc. Physiol. Soc. p. xxxii. 1913. AQ0 ACTION OF ALCOHOL ON NERVE. until the current-strength is raised to such an extent that its density in the whole chamber becomes equal to that which it previously had in the slot itself, and even then excitation will occur within the chamber B or C and not in the part of nerve which has passed out into the chamber A. This point is illustrated by an experiment in which the nerve was rendered unable to propagate an impulse at various points by compression",
            " If then under two different conditions we determine the position of any point along A B we discover whether the rate of recovery of the nerve is altered. I shall deal first with this second method of experiment, in which the rate of recovery of the nerve is measured by determining a point K. LUCAS. oD the curve A B, that is by finding the interval for muscular summation with a second stimulus falling so late as to be well clear of the least interval for muscular summation represented by the vertical line B C. Exp. 6 is an example of this type. It was carried out in a trough similar to that shown in Fig. 5, with the exception that there were only two chambers for the nerve instead of three, so that only one point of stimulation was available'. The length of the chambers was 18 5 mm. the propagated disturbance had therefore to pass through about 17 mm. of narcotised nerve on its way from the point of stimulation to the muscle. The experiment was conducted as follows. Ringer's solution was first allowed to flow until steady results for the threshold currentstrength were obtained. Then the curve relating strength of stimulus to interval for muscular summation was mapped out, the result being that shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure16-1.png",
        "caption": "Fig. 16. Robotic milling: (a) part with a spherical surface within a square area, (b) CL data, and (c) a selected robot configuration during the milling process.",
        "texts": [
            " Thanks to the balancing force which generated deflections opposite to the gravity force, smaller total deflections can be obtained. Similarly, Fig. 15 shows the contribution of each link on the linear deflections and the angular deflections in the horizontally extended configuration. By comparing Fig. 15 with Fig. 13 , one can find that the influence of the link arm (link 2) and arm (link 3) also become significant, although the in-line wrist still plays a key role. As a case study, we further investigate the deflections of the end-effector during the robotic milling process. Fig. 16 (a) gives a part with a spherical surface within a square area. By using CAM (Computer-aided manufacturing) system, tool path (Cutter Location data, CL data) is generated in the workpiece frame as shown in Fig. 16 (b), which includes the tooltip coordinates and the tool axis orientation vectors. The CL data is then transformed into the joint angles by using the inverse kinematic model of the robot. A specific configuration of the robot during the milling process is selected as shown in Fig. 16 (c), where \u03b8 = [6.68 \u00b0, 35.24 \u00b0, 41.74 \u00b0, 11.98 \u00b0, -48.76 \u00b0, -13.63 \u00b0] T . According to Ref. [46] , an external cutting force f E = [150, 250, 200] T N and \u03c4E = [0, 0, 0] T Nm is applied on the end-effector at this configuration. With the parameters setting above, the deflections of the robot end-effector can be calculated through the model described in Eq. (30) . Fig. 17 shows the total linear deflections and angular deflections in three different directions. It also shows the contributions of the three different factors on the total deflections, including external force, link weights and balancing force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003187_0301-679x(90)90041-m-Figure21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003187_0301-679x(90)90041-m-Figure21-1.png",
        "caption": "Fig 21 Schematic of NASA flywheel rotor module 63",
        "texts": [
            " The high surface energy of hydrocarbon oils provides the stabilizing force for the lubricant droplet on the applicator tip. The system is best suited for large bearings where there is sufficient space between the retainer dynamic envelope and the raceway to accept the applicator 62. NASA research 63 with a terrestrial experimental 46 cm (19-in.) diameter, 58 kg (128-1b) flywheel showed the feasibility of using a wick lubrication system in a vacuum environment to lubricate moderate speed bearings. The flywheel with its lubrication system is shown in Fig 21. In this system a lightly spring-loaded Metering bellows / Release valve Adjus~ble \\ Metering valve . . . . . . . I . . . . . i I X l . i A p p l i c o t o r ~ ! Delivery tube Standoff~ ~'x~ jRotat ing inner race / I n n e r race riding retainer -------Stationary outer race E. V. Zaretsky--liquid lubrication in space wick saturated with oil contacts a conical sleeve adjacent to the bearing inner race. Frictional contact against the sleeve causes a small amount of oil to be deposited. This oil migrates along the sleeve to its large end and into the bearing under the centrifugal force field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003993_05698190600614874-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003993_05698190600614874-Figure2-1.png",
        "caption": "Fig. 2\u2014Principle of the two-disc machine.",
        "texts": [
            " Then, a parameter analysis is presented that shows that tooth friction can strongly affect dynamic transmissibility through bearing mounts and leads to significant power losses. In order to evaluate the tribological properties of lubricants, EHL test rigs such as ball-on-disc apparatus or two-disc machines (Ville, et al. (8)) can be used to simulate gear mesh conditions. In the present study, a two-disc machine was used consisting of two independently driven discs mounted on the spindle of a threephase AC motor (Fig. 2, Ville, et al. (8)). A wide speed range from 1000 to 14,000 rpm can be covered by varying the supply frequency and tests can be performed under sliding conditions. The load is applied with a pneumatic jack. As the disc radii lie between 10 and 50 mm and as the raceway curvatures are between 10 mm and \u221e (no crowning), maximum Hertzian pressures from 0.1 to 4 GPa can be obtained. Finally, one of the motors mounted on two cylindrical hydrostatic bearings can rotate about an axis normal 260 D ow nl oa de d by [ D al ho us ie U ni ve rs ity ] at 1 8: 15 0 1 A ug us t 2 01 3 Ac = Actual average contact area (m2) Ao = Apparent contact area (m2) cfdry = Coulomb friction coefficient, which was set to 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000095_j.ijfatigue.2020.105654-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000095_j.ijfatigue.2020.105654-Figure1-1.png",
        "caption": "Fig. 1. (a) Assemble map and (b) physical map of the grips for tensile and fatigue testing at high temperature, schematics showing the geometrical dimensions of high-temperature (c) tensile and (d) fatigue specimens.",
        "texts": [
            " To quantify the profile of surface defects, rectangular HA-treated samples with the un-machined surface (as-built rough surface) were scanned using the 3D-XRT technique. The cross-sectional area (perpendicular to building direction) of the sample is around 1 mm2 and the voxel resolution was 2.1 \u03bcm. High-temperature fatigue specimens specified by the ASTM standards are generally columnar with a large geometrical dimension. Hence, grips were fabricated to evaluate the high-temperature fatigue properties by using relatively small rectangular specimens, as shown in Fig. 1(a) and (b). All the mechanical test specimens were taken from the same height of build plates (nominal thickness of 1.3 mm and 3.3 mm) by EDM. The geometry and nominal dimensions of tensile and fatigue specimens were schematically shown in Fig. 1(c) and (d), respectively. The actual cross-sectional area of the tensile and fatigue specimens was measured by using a vernier caliper. Tensile specimens with a nominal thickness of 3.3 mm were subsequently mechanically grounded, polished and finally electropolished before testing. Fatigue specimens with different combinations of cross-sectional geometries and surface conditions were presented in Table 1. To investigate the geometry effect, more specifically, the effect of the specimen thickness, geometry 1 (G1) specimens with the nominal thickness of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.24-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.24-1.png",
        "caption": "Figure 13.24. Normal helix in the developed cylinder of radius R.",
        "texts": [
            "116) The three relations between tts' mt , IP ts ' and the corresponding quantities in the normal section, were given by Equations (13.113,13.29 and 13.83), When these equations are substituted into Equation (13.116), we obtain the relation between the normal tooth thickness and the profile shift, (13.117) Chordal Tooth Thickness in the Normal Section The simplest method by which we can measure the tooth thickness of a helical gear is to measure the normal tooth thickness at the standard pitch cylinder, using a gear-tooth caliper. However, the normal thickness is defined along a line in the developed cylinder, as shown in Figure 13.24, so that on the actual gear it is a measurement along a helix. As we described in Chapter 8, the gear-tooth caliper measures the tooth thickness along a straight line, or in other words, it measures the chordal thickness. In order to derive a relation between the normal tooth thickness and the corresponding chordal thickness, we must first find the Chordal Tooth Thickness in the Normal Section 353 radius of curvature of the helix along which the normal tooth thickness is defined. We will use the symbol PR to represent the radius of curvature of the helix at radius R, with helix angle ~R",
            "52), dn~ - sin ~R deA n~ Since the length of the unit vector is unchanged, the magnitude of the angle through which it has turned is (sin ~R deA). The corresponding distance moved along the helix is (R deA/sin ~R). Hence, the radius of curvature, which is equal to the distance moved divided by the angle through which the tangent turns, can be expressed as follows, R (13.118) sin2~R The normal tooth thickness at any radius R is measured along a helix known as the normal helix, which is shown in Figure 13.24 as a line perpendicular to the teeth. Its helix angle is (?r/2-~R)' and its radius of curvature PnR can therefore be found from Equation (13.118), R (13.119) 354 Tooth Surface of a Helical Involute Gear The relation between the normal tooth thickness t ns at the standard pitch cylinder, and the corresponding chordal thickness t nsch ' can be read from Figure 13.25. t 2 P n s sin ( 2 pnnss ) and we use Equation (13.119) to express Pns in terms of the radius and the helix angle at the standard pi tch cylinder, 2 Rs "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000032_j.rcim.2020.101959-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000032_j.rcim.2020.101959-Figure1-1.png",
        "caption": "Fig. 1. 3D model and joint model of TX60 and camera module.",
        "texts": [
            " However, this is only appropriate for customers with one or few robots and the deployment of measuring equipment in complex factory environments is difficult and time consuming. A cost-effective closed-loop calibration method has great potential for promotion. In Section 2, we introduce the robot kinematic model. In Section 3, we present the measurement process and simulation measurement experiment. In Section 4, we present the calibration method and parameter identification method. In Section 5, we present the calibration experiment of TX60. In Section 6, we present the conclusions. The robot used in this paper is the Sta\u00fcbli 6R robot TX60 as shown in Fig. 1. The repetitive positioning error is within 0.02 mm. Similar to other robotic manipulators, the absolute positioning accuracy is not mentioned in the product manual. As shown in Eq. (1). the MDH model [19] is built on the robot with joint parameter deviations. Each joint has a useless joint parameter (the bold zero in Table 1). Parameter d is zero for adjacent parallel joints, and \u03b2 is zero for other joints. =\u2212 \u2212 \u2212T Rot z \u03b8 Trans z d Trans x a Rot x \u03b1 Rot y \u03b2( , ) ( , ) ( , ) ( , ) ( , )i i i i i i i i i i i i 1 1 1 (1) Among the parameters in Table 1 d1 and \u03b81 can be transformed to the joint parameters of robot mounting base, and calibrated separately after the robot is installed. The parameters for joint 7 represent the nominal transformation from the robot flange coordinate system to an intermediate coordinate system whose axes are parallel to the camera coordinate axes and whose origin is at the intersection of the camera optical axis and the flange plane. Joint 6 is rigid coupled with and can be considered part of joint 7, as shown in Fig. 1. Parameter deviations of joint 6 are skipped and included in tool parameter deviations. Tool calibration is not the focus of this paper and most robot manufacturers provide this function. The 22 unmarked joint parameters in Table 1 are the parameters to be calibrated and are recorded as vector JP. The inverse solution based on the parameters that describe the physical robot kinematics exactly needs to be solved iteratively with the inverse solution based on nominal joint parameters as the initial value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000658_j.ymssp.2021.107711-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000658_j.ymssp.2021.107711-Figure2-1.png",
        "caption": "Fig. 2. outer ra",
        "texts": [
            " It is generally accepted that the dynamic behavior of the bearing is significantly different when a spall defect occurs on the bearing raceway. In addition, the additional contact displacement and the contact force will be produced when the rolling element moves across the spall area of the bearing. As a result, it is crucial to establish the time-varying displacement and force models of rolling element-race contact for modeling the spalled REB and investigating the dual-impulse behavior. According to the geometrical relationships of the fault-free REB as shown in Fig. 2 and the simplified model in [15], x and y, as shown in Fig. 2(b), are assumed as the initial displacements of the center of the inner race along x and y coordinate axes, respectively. Geometrically, the total deflection dk between the kth rolling element and bearing races along the normal direction of contact, at any angular position hk, is derived as follows. dk \u00bc dbi \u00fe dbo Ck \u00f01\u00de where dbi and dbo refer to the elastic deformation of the rolling element to the inner and outer races respectively, k denotes the kth rolling element, and Ck is the internal radial clearance of the kth rolling element within the loaded zone and can be expressed as in [16] by Ck \u00bc 0:5Cd\u00f01 coswl\u00de \u00f02\u00de where Cd denotes the diametrical clearance of the whole bearing, and w is the azimuth measured from the maximum load direction (see Fig. 2(a)). Based on the geometrical relationship as shown in Fig. 2, the total elastic deflection dk can be equivalently formulated by dk \u00bc d1 \u00fe d2 Ck \u00f03\u00de where the contact geometrical relationship d1 and d2, shown in Fig. 2(c), can be expressed such as d1 \u00bc x cos hk \u00f04\u00de d2 \u00bc y sin hk \u00f05\u00de where hk is the angular position of the kth rolling element relative to x coordinate axis, which can be given by hk \u00bc h0 \u00fexct \u00fe 2p\u00f0k 1\u00de=Nball \u00f06\u00de where h0 denotes the initial angular offset (see Fig. 2(a)) of the first rolling element with respect to x coordinate axis, Nball represents the total number of the rolling elements, xc refers to the rotational speed of the cage and can be calculated by xc \u00bc 0:5xr\u00f01 v\u00de \u00f07\u00de wherexr is the rotational speed of the shaft. v \u00bc Dball cosa=Dm, with a and Dm being the contact angle and the pitch diameter of the REB, and Dball is the rolling element diameter. In this work, a single inner race surface spall is studied theoretically and experimentally. The contact deformation between the inner race and the kth rolling element has an additional change (see Fig",
            " Thus, it can be formulated by kk \u00bc 1 mod\u00f0/spall;2p\u00de hspall 6 mod\u00f0hk;2p\u00de 6 mod\u00f0/spall;2p\u00de \u00fe hspall and wm 6 mod\u00f0/spall;2p\u00de 6 wmand wm 6 mod\u00f0hk;2p\u00de 6 wm 0 otherwise 8>< >: \u00f013\u00de Similarly to the application of external radial load on the bearing, the magnitude of the load acting on the rolling element when it rolls though a spall-free location within the load zone, Qw, is classically formulated as in [16] by Qw \u00bc Qm \u00f02 1\u00fe cosw\u00de=2 \u00bd 1:5 wm 6 w 6 wm 0 elsewhere ( \u00f014\u00de where wm refers to the angular limit of the load zone (see Fig. 2(a)), Qm denotes the maximum load, and is the load distribution factor and given by \u00bc 0:5\u00f01 Cd=2dr\u00de, in which dr represents the radial shift of the ring at w \u00bc 0. All these above parameters can be calculated as in [16]. However, the magnitude of the radial load component carried by the rolling element alters when the rolling element comes in contact with the spall zone, and it can not be governed by Eq. (14) because of the interaction between the rolling element and the spall zone. Kinematically, the speed of the rolling element changes sharply from its entry to strike on the trailing edge of the spall zone, resulting in the collision force and vibration of bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.4-1.png",
        "caption": "Figure 16.4. A hob cutting a gear.",
        "texts": [
            " In practice, it is generally the magnitude of the lead angle which is given in the specification, together with a statement to indicate whether the hob is right or left-handed. It is clear that the lead angle can be determined from the helix angle, and vice versa. In describing the geometry of the hobbing process, we will specify the shape of the hob by means of its helix angle, since the symbols will then agree with the notation used in Chapter 15, where we described the geometry of crossed helical gears. Figure 16.4 shows a hob in position to cut a gear blank, and since their axes are not parallel, it is clear that they form a crossed helical gear pair. During the cutting process, the hob and the gear blank are rotated about their axes with angular veloci ties wh and wg ' I n order to cut the teeth of the gear across the entire face-width, the hob is moved slowly in the direction of the gear axis, and the velocity of the hob center is called the feed velocity vh . The values required for the three variables wh ' Wg and vh are achieved by means of change gears or stepping motors in the hobbing machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003510_pime_proc_1994_208_345_02-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003510_pime_proc_1994_208_345_02-Figure4-1.png",
        "caption": "Fig. 4 Rolling EHD interferometric test rig",
        "texts": [
            " It was realized that EHD film thicknesses are of Table 2 Methods for studying lubricant films in contacts References Method Measurement Optical interferometry Ultra-thin film interferometry Laser fluorescence Infra-red emission Infra-red emission spectroscopy Infrared reflectionabsorption spectroscopy Raman spectroscopy Visual observation Film thickness (2,3) Very thin film (4, 5) Film thickness (6, 7) Temperature (&lo) Shear stress (11) Film chemistry (12) Alignment (13) Film chemistry (14) Molecular alignment (15) Film pressure (16 17) Film chemistry Particle flow (18) Large-scale chemical (19) thickness film formation 5 THE BEHAVIOUR OF LUBRICANTS IN CONTACTS: CURRENT UNDERSTANDING AND FUTURE POSSIBILITIES the same order as the wavelength of visible light, and so should produce interference patterns (Newton's rings), from which film thicknesses might be determined. Figure 4 shows a typical test rig. A glass disc, coated with a thin semi-reflecting layer, is loaded and rolled against a steel ball. Light is shone into the contact through the glass so that some is reflected back from the semi-reflecting layer while the rest passes through any oil-film present, to be reflected back from the metal ball. The two reflected beams of light interfere constructively or destructively depending upon the path difference and thus upon the thickness of the lubricant film, as illustrated in Fig",
            " The results at 23\u00b0C were made using conventional optical interferometry whereas those at the higher tem- analysis then calculates which particular frequency has peratures were measured using the ultra-thin film been constructively interfered, and thus the film thick- method. It would not have been possible to measure ness. The method is fully described in reference (4). A film thicknesses at 80 and 100\u00b0C using the conventional conventional optical test rig is employed, as shown in approach since, at these temperatures, the viscosity of Fig. 4. the oil becomes so low that the film thickness generated Part J : Journal of Engineering Tribology 0 IMcchE 1994 at Freie Universitaet Berlin on November 18, 2016pij.sagepub.comDownloaded from THE BEHAVIOUR OF LUBRICANTS IN CONTACTS: CURRENT UNDERSTANDING AND FUTURE POSSIBILITIES is less than 70 nm over the speed range. It is interesting to note that all the results closely obey the predicted EHD film thickness/speed equation: h = k,UO.' (1) even down to very thin films of less than 20 nm, showing, for the first time, that EHD film thickness equations are valid down to this region",
            " The other two methods looked at film thickness, temperature and rheology. This monitors the chemistry of lubricant films in contacts. A lubricated contact is formed between a rotating steel ball and an infra-red transparent flat. The contact can be a sliding one, in which case a small diamond flat is used in a test rig similar to Fig. 13. Diamond is used since, unlike sapphire, it can transmit infra-red wavelengths in the chemical region of the infra-red spectrum. Alternatively, a rolling contact can be produced using a test rig similar to that in Fig. 4 but with an infra-red, transparent, calcium fluoride disc. Infra-red radiation is focused into the contact using an FTIR microscope system and this is reflected back from the lubricant/steel interface and collected by the microscope optics for analysis. Spectra can be taken of discrete areas of the contact, typically 75-200 pm in diameter, the area being defined by the aperture used. For most work carried out so far an aperture of 100 pm diameter has been employed. Figure 17 shows small portions of the infra-red spectrum from the lubricant film, representing the absorption by the C-H bonds, taken respectively from the inlet, the centre and the exit of the contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002812_a:1016559314798-Figure17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002812_a:1016559314798-Figure17-1.png",
        "caption": "Figure 17. Fourier transform of the 3R robot joint 1 velocity, for 500 cycles, versus the radial distance r and the frequency ratio \u03c9/\u03c90, for \u03c1 = 0.1 m, \u03c90 = 3 rad/sec.",
        "texts": [],
        "surrounding_texts": [
            "In the last group of experiments, after elapsing an initial transient, we calculate the Fourier transform of the robot joint velocities for a large number of cycles of circular repetitive motion with frequency \u03c90 = 3 rad/sec. Figures 17\u201323 shows the results for the 3R and 4R robots versus the radial distance r, the center of the circle, with radius \u03c1 = 0.10 m. Once more we verify that for 0 < r < rs we get a signal energy distribution along all frequencies, while for rs < r < 3 m the major part of the signal energy is concentrated at the fundamental and multiple harmonics. Moreover, the DC component, responsible for the position drift, presents distinct values, according to the radial distance r and \u03c1: |q\u0307i (\u03c9 = 0)| = a\u03c1d/(b + r)c, i = 1, 2, . . . , n. (28) Tables 6 and 7 show the values of the parameters of Equation (28) for the 3R and 4R robots, respectively. Based on these results we conclude that the velocity drift changes with the robot endeffector radial distance r. Furthermore, the DC component is \u2018induced\u2019 by the repetitive motion with a quadratic-like dependence with \u03c1."
        ]
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure1-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure1-2-1.png",
        "caption": "Figure 1-2 (a) The motion of a ball after several impacts with an elliptically shaped billiard table. The motion can be described by a set of discrete numbers (s,, <\u00a3,) called a map. (b) The motion of a particle in a two-well potential under periodic excitation. Under certain conditions, the particle jumps back and forth in a periodic way, that is, LRLR \u2022 \u2022 \u2022 , or LLRLLR \u2022 \u2022 \u2022 , and so on, and for other conditions the jumping is chaotic that is, it shows no pattern in the sequence of symbols L and R.",
        "texts": [
            " His work on problems of celestial mechanics led him to questions of dynamic stability and the problem of finding precise mathematical formulas for the dynamic 4 Introduction: A New Age of Dynamics this essay on Science and Method: It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible. In the current literature, chaotic is a term assigned to that class of motions in deterministic physical and mathematical systems whose time history has a sensitive dependence on initial conditions. Two examples of mechanical systems that exhibit chaotic dynamics are shown in Figure 1-2. The first is a thought experiment of an idealized billiard ball (rigid body rotation is neglected) which bounces off the sides of an elliptical billiard table. When elastic impact is assumed, the energy remains conserved, but the ball may wander around the table without exactly repeating a previous motion for certain elliptically shaped tables. Another example, which the reader with access to a laboratory can see for oneself, is the ball in a two-well potential shown in Figure l-2b. Here the ball has two equilibrium states when the table or base does not vibrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-11-1.png",
        "caption": "Figure 5-11 First and second iteration functions for the quadratic map (5-3.3) [see also Eq. (5-3.6)].",
        "texts": [
            " Now a fixed point, or equilibrium point can be stable or unstable. That is, iteration of x can move toward or away from x0. The stability of the map depends on the slope of /(*) at *0; that is, dx dx < 1 implies stability > 1 implies instability (5-3.5) 170 Criteria for Chaotic Vibrations Since the slope /' = X(l - 2x) depends on X, XQ becomes unstable at Xi = \u00b11/|1 \u2014 2x0\\. Beyond this value, the stable periodic motion has period 2. The fixed points of the period 2 motion are given by The function f ( f ( x ) ) is shown in Figure 5-11. Again there are stable and unstable solutions. Suppose the XQ solution bifurcates and the solution alternates between x+ and x~ as shown in Figure 5-12. We then have x+ = Xx~(l - x~) and x~ = X.x + (l - x + ) (5-3.7) To determine the next critical value X = X 2 at which a period 4 orbit emerges, we change coordinates by writing *\u201e = ** + !)\u201e (5-3.8) Putting Eq. (5-3.8) into (5-3.7), we get (5-3.9) Theoretical Predictive Criteria 171 X2 Figure 5-12 Diagram showing two branches of a bifurcation diagram near a period-doubling point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003751_s0263574708004748-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003751_s0263574708004748-Figure4-1.png",
        "caption": "Fig. 4. Circles centered at P and O.",
        "texts": [
            " When \u03b8 changes from \u03b80 to 0 or 2\u03c0 , the contact point reaches the position given by x2 = x1 \u2212 cos \u03b10 \u00d7 \u03b80 y2 = y1 + sin \u03b10 \u00d7 \u03b80 } for 0 < \u03b80 \u2264 \u03c0 x2 = x1 + cos \u03b10 \u00d7 (2\u03c0 \u2212 \u03b80) y2 = y1 \u2212 sin \u03b10 \u00d7 (2\u03c0 \u2212 \u03b80) } for \u03c0 \u2264 \u03b80 < 2\u03c0. At the end of this maneuver, the configuration of the sphere is given by q2 = (x2, y2, \u03b10, 0, \u00b1\u03c0 2 ). Figure 3 shows how the sphere rolls in Steps 1 and 2. As the angle \u03c60 is in the range \u03c0 \u2264 \u03c60 \u2264 2\u03c0 , Step 1 is carried out to change the angle \u03c6 from \u03c60 to \u2212\u03c0 2 . Step 3: Let the point of contact at the end of Step 2 be P = (x2, y2). If O is the origin of the inertial frame attached to the XY plane, then the geometrical construction shown in Fig. 4 helps reconfiguration of the sphere. We construct two circles, one with center P and radius 2\u03c0n1 and another with center O and radius 2\u03c0n2; n1, n2 \u2208 Z. At the point P the zb-axis is vertical and circle centered at P and radius 2\u03c0n1 gives all possible locations where the sphere can be reconfigured with zb-axis vertical again. Similarly, the circle centered at O and radius 2\u03c0n2 gives all possible locations where the zb-axis will be vertical. The values of n1 and n2 can be suitably chosen based on the distance OP",
            " We obtain the transformation between the two Euler angle systems and obtain a set of ZXY Euler angles from the ZYZ Euler angle system describing the orientation of the sphere at the end of Step 2 as \u03be2 = \u03b10 \u00b1 \u03c0/2; \u03b22 = 0; \u03b32 = 0. Consider the path PM such that the line PM is at an angle \u03b61 w.r.t. the inertial positive x-axis. To roll the sphere along the line PM using input u1, the xb-axis must be aligned http://journals.cambridge.org Downloaded: 29 Nov 2014 IP address: 132.203.227.62 perpendicular to the line PM as xb3 as shown in Fig. 4. This is achieved by changing the angle \u03be from \u03be2 to \u03be3 = \u03b61 + \u03c0/2 using the control input u3. Using model (9), and the initial conditions x = x2, y = y2, \u03be = \u03be2, \u03b22 = 0, \u03b32 = 0 and control u1 = 0, u3 = 0, we obtain x\u0307 = 0 y\u0307 = 0 \u03be\u0307 = u3 \u03b2\u0307 = 0 \u03b3\u0307 = 0. This is pivoting as expected and the contact point does not move giving x3 = x2 and y3 = y2. The angles \u03b2 and \u03b3 are also unchanged giving \u03b23 = \u03b22 = 0 and \u03b33 = \u03b32 = 0. Only the angle \u03be changes from \u03be2 to \u03be3 aligning the xb-axis perpendicular to the line PM",
            " It can be observed that during this step, only the angle \u03b2 changes from 0 to 2\u03c0n1 keeping \u03be and \u03b3 constant. At the end of this maneuver, the zb-axis is vertical at the point M and the configuration of the sphere is described by q4 = (x4, y4, \u03be3, 0, 0). Step 5: Control inputs u1 = 0 and u3 = 0. This step is similar to Step 3. Let the line MO be at an angle \u03b62 w.r.t. the positive inertial x-axis. In this step, the angle \u03be is changed from \u03b61 + \u03c0/2 to \u03b62 + \u03c0/2 using the control input u3 such that \u03be5 = \u03b62 + \u03c0/2 and xb-axis is aligned perpendicular to the line MO as xb5 as shown in Fig. 4. Similar to Step 3, this is pivoting of the sphere and its contact point does not move giving x5 = x4 and y5 = y4. At the end of this maneuver, the configuration of the sphere is described by q5 = (x5, y5, \u03be5, 0, 0). Step 6: Control inputs u1 = 0 and u3 = 0. This step is similar to Step 4 and the sphere is rolled using the control input u1. The contact point travels along the line MO given by x = x5 + \u03b2(cos \u03b62) y = y5 + \u03b2(sin \u03b62). At the end of this maneuver, the contact point of the sphere reaches the point O which is origin of the inertial frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.14-1.png",
        "caption": "Figure 13.14. Triangle to determine cos tPR and sin tPR\u2022",
        "texts": [
            "46) To obtain a vector parallel to the helix tangent at A, we differentiate the position vector with respect to the variable eA, eAn eAn + Rb - R sin x + R cos y tan..pb n z (13.47) We then divide this vector by its length, to obtain a unit vector nA in the direction of the helix tangent at A, /.I A eAn + Rb ----'--::::--{ - R sin e n + R cos n ) R2 x y tan..pb z v[R2+ b ] tan 2..pb (13.48) An alternative expression for the helix angle of the gear at radius R can be found by rearranging Equation (13.34), (13.49) and from the triangle shown in Figure 13.14, we can write down expressions for the sine and cosine of ..pR' which can be used to simpiify Equation (13.48). We then obtain the final expression for n~, 328 Tooth Surface of a Helical Involute Gear We now differentiate n~ to obtain a vector in the direction of the principal normal to the helix at A. dnA --E. d9A (13.51) This vector is in the direction from A towards point C, the centre of the transverse section through A. For the purpose of describing the tooth surface geometry, it is rather more convenient to define a uni t vector n~ in the opposi te direction, in other words from C towards A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure8-1.png",
        "caption": "Figure 8 The closed loop.",
        "texts": [
            " g i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + = \u2211 (27) Similar to the former examples, the numbers of common constraints and parallel-redundant-constraints are invariable at any possible configuration of this mechanism. The mobility is global. The Cardan joint, as shown in Figure 7, is one of the most famous counter-examples besides the Bennett and Goldberg mechanisms pointed out by Merlet[30]. It is a chain which consists of four closed loops connected by five links in series. If each closed loop including two links and two joints is regarded as a generalized pair, the serial chain contains four generalized pairs and five links. We take one closed loop into consideration. As shown in Figure 8, the origin point locates on the center of one joint, and z-axis is along its axis. Then its kinematic screw system expressed by Pl\u00fccker coordinates is ( ) ( ) 1 2 0 0 1; 0 0 0 , 0 0 1; 0 0 0 , = = $ $ (28) Since the Pl\u00fccker coordinates of the two screws are completely identical, the two screws are linearly dependent and just equivalent to the one based on the screw theory. Therefore, the closed loop has one rotation freedom around z-axis. Because the Cardan joint consists of four identical loops, namely it contains four single-mobility pairs, the Cardan joint has four freedoms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.12-1.png",
        "caption": "Figure 5.12. Pinion cutter tooth tip geometry.",
        "texts": [
            " The tooth profile in some pinion cutters is rounded at the tip, so that the profile makes a smooth transition with the tip circle. In other pinion cutters, the profile follows the involute right out to the tip circle, and there is a sharp 134 Gear Cutting I, Spur Gears corner where the profile meets the tip circle. We will consider the geometry of a cutter wi th a ro'unded corner at the tooth tip, of radius r cT ' and we can then regard the cutter with no rounding as a special case, in which the value of r cT is equal to zero. A pinion cutter with rounded tooth tips is shown in Figure 5.12. The circular section ha~ a radius r cT ' and it meets the tooth profile at Ahc ' and the tip circle at ATc \u2022 The symbol Ahc was chosen, because it is the highest point of the involute section of the cutter tooth profile. The center of the circular arc is shown as A~. In order to calculate the fillet shape in the gear, which is cut by the circular section of the cutter tooth, it is first necessary to find the coordinates of points Ahc and A~. Since the circular section of the profile is tangent to the tip circle, the polar coordinate R~ of point A~ is equal to the radius of the tip circle, minus the radius of the rounded tip section, Cutter Tooth Tip Geometry R' c 135 (5",
            "35) The tangent to the tooth profile at Ahc makes an angle Yhc with the tooth center-line, and the value of Yhc is given by Equation (2.38), (5.36) The Cartesian coordinates x~ and Y~ of point A~ can be read from the diagram, and the polar coordinate 8~ is then expressed in terms of x~ and y~, x' c Rhc cos 8hc - rcT sin Yhc (5.37) y' Rhc sin 8hc - rcT cos Yhc (5.38) c 8' arctan (y~) (5.39) c x' c For a pinion cutter with no rounding at the tooth tips, we set the value of r rT equal to zero, and the radi i Rhc and R~ are then equal to the tip circle radius RTc ' In.the cutter tooth profile shown in Figure 5.12, the center A' of the circular tip section lies above the tooth c center-line. It is essential that A' should always be above c 136 Gear Cutting I, Spur Gears the center-line, in order to allow the circular section of the profile to merge smoothly with the tip circle. If A' were to c lie below the center-line, the cutter tooth would be slightly pointed. Hence, the value of y~ given by Equation (5.38) must always be positive, and a negative value would indicate that the radius r cT of the circular section is too large",
            "084916 radians 4.865\u00b0 (9.6) R = 8.4000 (9.7) Examples 8R = 1.004\u00b0 = 0.017526 radians tR = 2R8R = 0.2944 inches For a gear with no tip relief, Rb = 7.5175 41T = 26.499\u00b0 tT = 0.3043 inches Reduction in tooth thickness = 0.0098 inches Example 9.3 227 (9.8) (2.36) Repeat the calculations of Example 9.1, assuming that the gear is cut by a 16-tooth pinion cutter with a tip circle diameter of 113.4 mm, a profile shift of 1.8 mm, and rounding at the tooth tips with a radius of 1.5 mm. This is the cutter shown in Figure 5.12. m=6, 41 s =200, Nc =16, RTc =56.7, ec =1.8, r CT=1.5 Ng=24, eg=1.5 We must first find the polar coordinates (R~,8~) of the center of the circular section at the tip of the cutter tooth. Rsc = 48.000 mm Rbc = 45.105 R~ 55.200 41hc = 36.454\u00b0 Rhc = 56.078 tsc = 10.735 0.024246 radians 35.065\u00b0 x' c 55.200 y~ = 0.132 8' = 0 137\u00b0 c \u2022 (5.32) (5.33) (5.34) (6.1) (5.35) (5.36) (5.37) (5.38) (5.39) Next, we determine the center distance at which the cutter wi 11 cut the requi red tooth thickness in the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003056_s0094-114x(03)00003-x-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003056_s0094-114x(03)00003-x-Figure7-1.png",
        "caption": "Fig. 7. Direction of the loads.",
        "texts": [
            " (24) in this equation, the following equation is obtained for the axial clearance: j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f02Pr \u00fe A\u00de2 \u00f02h\u00de2 q 2a \u00f025\u00de Thus, taking the axial clearance into account, the initial coordinates on the Z axis of the centres of curvature Cei1 and Ces1 are modified, where ZCei1 \u00bc a j \u00f026\u00de ZCes1 \u00bc a j \u00f027\u00de Once the clearance has been overcome, the outer loads (Fr, Fz and M) are applied on the outer ring, and these cause displacements of the centres of curvature of the outer raceways, dr, dz and h. The moment axis has been established as axis y, and the angle between the radial force and this moment is defined as U (Fig. 7). The final coordinates (represented by 2) of the centres of curvature will be as follows: XCii2 \u00bc XCii1 \u00f028\u00de YCii2 \u00bc YCii1 \u00f029\u00de ZCii2 \u00bc ZCii1 \u00f030\u00de XCis2 \u00bc XCis1 \u00f031\u00de YCis2 \u00bc YCis1 \u00f032\u00de ZCis2 \u00bc ZCis1 \u00f033\u00de XCei2 \u00bc XCei1 \u00fe dr sinU \u00f034\u00de YCei2 \u00bc YCei1 \u00fe dr cosU \u00f035\u00de ZCei2 \u00bc ZCei1 \u00fe dz h dm 2 h cosw XCes2 \u00bc XCes1 \u00fe dr sinU \u00f036\u00de YCes2 \u00bc YCes1 \u00fe dr cosU \u00f037\u00de ZCes2 \u00bc ZCes1 \u00fe dz h dm 2 h cosw \u00f038\u00de In a four contact-point bearing with one row of ball bearings, the contact can be happened between two diagonally opposed centres of curvature; the contact can therefore be happened between the centres of curvature Cii and Ces and/or the centres of curvature Cis and Cei (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure12.10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure12.10-1.png",
        "caption": "Fig. 12.10 Gleason process",
        "texts": [
            " This demand in turn inspired the development of corresponding gear manufacturing technologies (Hotchkiss 1969; Maiuri 2007). William Gleason, an Irish immigrant to the U.S., founded a machine shop in New York in 1865 to build gear-cutting machine tools. This was the origin of the later Gleason Corporation, a prominent machine tool maker in the world. At the beginning, only machines for cutting spur gears were made in this company. In 1913, Gleason invented a method for cutting spiral bevel gears with face milling as shown in Fig. 12.10. This is the well know Gleason method, a single indexing method. The tooth trace of the bevel gear in the Gleason method is a circular arc and the tooth depth at the larger diameter is larger than that at the smaller diameter (tapered teeth). The Gleason method can also be used in grinding and lapping. In 1927, the company successfully developed the process of manufacturing hypoid gears. In 1946, Oerlikon, a Swiss company, developed a continuous indexing method of cutting spiral bevel gears, called Oerlikon method as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.1-1.png",
        "caption": "Figure 12.1. An internal gear pair.",
        "texts": [
            " In the case of an internal gear, it is clear that the gear cannot mesh with any rack, so a different method is required for defining its tooth shape. We first determine what shape the tooth profile of the internal gear must have, if the gear is to mesh correctly with an involute pinion. And we will then show that the tooth profile of the internal gear can still be regarded as conjugate with the basic rack, 260 Internal Gears provided the basic rack is an imaginary rack of the sort discussed earlier. Figure 12.1 shows an involute pinion meshed with an internal gear. The pinion is numbered as gear 1, and the internal gear as gear 2. We proved in Chapter 1 that, for the Law of Gearing to be satisfied, the common normal at the contact point must always pass through the pitch point P, which is a fixed point on the line of centers. The position of P is such that, when we draw the pitch circles touching each other at P, the angular velocity ratio of the two gears is the same as it would be if the two pitch circles were to make roll ing contact wi th no slipping",
            "4), the corresponding relation for an external gear pair. The direction of rotation of the pinion is always the same as that of the internal gear, so w1 has the same sign as w2 , as indicated by Equation (12.1). If the radii of the pitch circles are RP1 and Rp2 ' and the circles roll together without slipping, their angular velocities must be related as follows, (12.2) It is evident from Equations (12.1 and 12.2) that the pitch circle radii are proportional to the tooth numbers, (12.3) In addition, we can see from Figure 12.1 that the difference between the pitch circle radi i is equal to the center distance C, C (12.4) We solve Equations (12.3 and 12.4), to obtain the values of RP1 and Rp2 ' ( 12.5) (12.6) We have now found the position of the pitch point P, since it is the point where the pitch circles touch each other. We next determine the shape of the internal gear tooth profile, if the common normal at the contact point is to pass through P. Since the tooth profile of the pinion is an involute, the normal to the profile at any point touches the pinion base circle. To find the position of the contact point, when the pinion is in the position shown in Figure 12.1, we 262 Internal Gears first draw the tangent from P to the pinion base circle, touching the base circle at E1. The point A1 where this line cuts the pinion tooth profile must be the contact point, since it is the only point of the profi Ie whose normal passes through P. A point on the tooth profile of the internal gear must therefore coincide with A1, since A1 is the contact point. This point on the internal gear is labelled A2 , and the normal to the internal gear tooth profile at A2 lies along A1PE 1, because the normals to both profiles must coincide at the contact point",
            " We have therefore proved that the normal to the tooth profile at every point of the profile must touch the base circle. This is exactly the manner in which the involute was defined in Chapter 2, so the tooth profile of an internal gear is identical to that of an external gear with the same number of teeth. The difference between the two types of gear, however, is that the teeth of the internal gear lie outside the profile, while those of the external gear lie inside it. In other words, the teeth of the internal gear have exactly the same shape as the tooth spaces in an external gear. We now make use again of Figure 12.1. Since lines C2E2 and C1E1 are both perpendicular to line E2E1, the two triangles C2E2P and C1E1P are similar. The ratio of the base circle radii is therefore equal to that of the pitch circle radii, which we showed in Equation (12.3) is also equal to the ratio of the tooth numbers, (12.7) The base pitches of both gears are defined by Equation (2.22), Tooth Profile of an Internal Gear 263 (12.8) (12.9) Since, as we have just proved, the base circle radii are proportional to the tooth numbers, it follows from Equations (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003307_1.2791809-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003307_1.2791809-Figure4-1.png",
        "caption": "Fig. 4 A three-degrees-of-freedom manipulator",
        "texts": [
            " 6 Examples For the illustration of the inverse and forward dynamics algorithms developed in Sections 5.1 and 5.2, respectively, two manipulators, namely, a three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm, as shown in Figs. 4 and 7, respectively, are analyzed using RIDIM and RFDS!M software. 6.1 A Three-Degrees.of-Freedom Planar Manipulator. The manipulator under study is assumed to move in the X - Y plane, whereas the gravity is working in the negative Y direction, as indicated in Fig. 4. Let i and j be the two unit vectors parallel to the axes, X and Y, respectively, and k =-- i \u00d7 j. The expressions for the three joint torques, namely, \u00a21, z2, and %, are evaluated explicitly from the inverse dynamics algorithm given in Section 5.1, which exactly match with those reported in Angeles (1997). Moreover, RIDIM is used to find the joint torques for the following normal j oint angle trajectories and their corresponding 1 st and 2nd time derivatives: 0 i = ~ t with T = 10.0 sec. The joint torques obtained from RIDIM are plotted in Fig",
            " tau_2\" and \"tau_3\" denote the joint torques, T~, z2, and $3, respectively. The plots are also verified with the plots obtained from the explicit expressions. In order to test RFDSIM, free fall simulation, i.e., motion due to gravity only, without any external joint torque, of the manipulator is carried out with the initial conditions as 0g(0) = 0r(0) = 0, for i = 1, 2, 3. The variations of the simulated joint angles are shown in Figs. 6, where \"th_l,\" \"th_2,\" and \"th 3\" represent 01,02, and 03, respectively. Note from Fig. 4 that due to gravity the first joint angle, 0~, will increase initially in the negative direction, as evident from Fig. 6. Moreover, the system under gravity behaves as a triple pendulum. These is evident from all the joint angle variations, namely, 0~, 02, and 03 of Fig. 6. 6,2 A Stanford Arm. As a second example, a more general six-axis six-degrees-of-freedom manipulator, namely, the Stanford arm, as shown in Fig. 7, is taken whose Denavit-Hartenberg (DH) parameters, along with the mass and inertia properties are given in Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure11-5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure11-5-1.png",
        "caption": "Figure 11-5. Principle of DIN abrader",
        "texts": [],
        "surrounding_texts": [
            "V Abrasion resistance index = ^ x 100% where Vs = volume loss of standard rubber and Vr = volume loss of rubber under test. Abrasion resistance is the reciprocal of volume loss. If the volume loss or abrasion resistance only is quoted, it is desirable to have some certification of the abradant used. This is naturally supplied to some extent by specifying a particular grade and source of supply but leaves open to question the variability of that source of supply. Some workers prefer to use a standard rubber to test the abradant and to calculate a relative volume loss: V xV. Relative volume loss = -^ where Vr = volume loss of rubber under test, Vd = the defined volume loss of the standard rubber and Vs = the measured volume loss of the standard rubber. Whichever approach you take, the result is still dependent on the variability of the standard rubber and, arguably, it could be better to rely on the reproducible manufacture of, for example, an abrasive wheel. It would not seem beyond the bounds of ingenuity to find a standard material which is inherently more reproducible than rubber! It could then be used either to certify the abradant or to use in the calculation of abrasion index. If abrasion loss is measured as a function of test parameters such as speed, temperature, degree of slip, contact pressure etc, it may be possible to combine the results in some way to produce a composite measure of abrasion resistance. Obtaining data as a function of test parameters is impossible, or at least very tedious, with most apparatus, but can be achieved automatically with the LAT system (see Section 2.6)."
        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.6-1.png",
        "caption": "Figure 14.6. Transverse section with imaginary racks.",
        "texts": [
            "13 showing the tooth profiles, and two imaginary racks between the teeth. The tooth thicknesses of the imaginary racks were chosen exactly equal to those of the two gears, measured at Backlash 389 their pitch circles. In Figure 4.14 we showed the pitch plane section through the imaginary racks, and we then proved that the circular backlash of the gear pair is equal to the distance that either imaginary rack can move, when the other is held fixed. We follow the same procedure for the case of a helical gear pair. Figure 14.6 shows a transve~se section through the gear pair, with the imaginary racks drawn in, and Figure 14.7 shows the pitch plane section through the imaginary racks. A typical pair of teeth are in contact along line ArA~, and the gaps between the teeth are represented by the narrow un shaded bands. As we proved earlier in this chapter, the transverse pi tch, normal pi tch and helix angle of the imaginary racks are equal to the corresponding quantities in the gears, measured at their pitch cylinders. The transverse tooth thicknesses of the imaginary racks are chosen equal to those of the gears, 390 Helical Gears in Mesh and it then follows that the corresponding normal tooth thicknesses are also equal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003471_28.502168-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003471_28.502168-Figure12-1.png",
        "caption": "Fig. 12. netization of magnets. Flux plot for the same motor as in Fig. 4 but with parallel mag-",
        "texts": [
            " 11 compares the cogging torque curves for the two motors ~ 514 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 3, MAY/JUNE 1996 shown in Figs. 9 and 10. It can be observed that bifurcated teeth double the frequency and simultaneously reduce the peak cogging torque by about 50%. D. Varying the Magnetization of Magnets Just like varying the magnet arc, varying the magnetization (radial or parallel) of magnets has an effect on the shape and the magnitude of cogging torque. This can be illustrated with an example. The motor shown in Fig. 4 has radial magnetization of magnets. Fig. 12 shows flux plot for the same motor except that it has parallel magnetization of magnets. Fig. 13 compares the cogging torque curves for the two motors shown in Figs. 4 and 12. It can be seen that parallel magnetization of magnets leads to about 20% less peak cogging torque as compared to the radial magnetization. E. Other Methods The method of shifting alternate magnet poles by one-half stator slot pitch in multipole-pair designs and the method of varying the radial air-gap length around the full circumference of a machine can both be analyzed using the flux-MMF diagram technique"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.14-1.png",
        "caption": "Figure 12.14. Cutting the end point of the fillet.",
        "texts": [
            " The coordinates of A can be read immediately from Figure 12.13, R (12.68) arctan (_1/_) - Q RC +~ 1'g pg (12.69) Shape of the Fi llet 285 Equations (12.60 - 12.69) are used to calculate the coordinates of points on the internal gear tooth fillet, corresponding to any chosen values of a. The first point which needs to be considered is Af , where the fillet meets the involute. In this case, the cutting point must lie at He on the path of contact, and line PAc therefore makes an angle ~c with the ~ axis, as shown in Figure 12.14. The value of a at which this occurs can be read from the diagram, a R arccos (R~c) - ~c c (12.70) The last point to be considered is cut when line C A' c c lies along the E axis, and the value of a is then zero, a o (12.71) In this case, the cutter has reached its maximum penetration, and A is the point at which the fillet meets the root circle. The entire fillet shape can be constructed by choosing a sequence of values for a, between the values given by Equations (12.70 and 12.71), and then calculating the corresponding coordinates Rand lI R\u2022 286 Internal Gears Fillet Radius of Curvature In Chapter 10, we derived the Euler-Savary equation relating the radii of curvature of two conjugate profiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000245_ijvd.2019.109873-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000245_ijvd.2019.109873-Figure7-1.png",
        "caption": "Figure 7 Rolling element bearing design (see online version for colours)",
        "texts": [
            " The problem has been solved using PVS, GA (Savsani and Savsani, 2016), WCA, teaching learning based optimisation (TLBO) and artificial bee colony (ABC) (Rao et al., 2011). The statistical results for the algorithms are given in Table 9. According to the table, we can see that ABC is not able to give the optimal global solution for this problem. In terms of the robustness, NAMDE is the best with standard deviation of 00E+00. The goal here is to maximise the dynamic load carrying capacity of the rolling element bearing (Gupta et al., 2007), as shown in Figure 7. There are ten continuous variables and the number of balls is discrete. The design is subject to nine nonlinear constraints on kinematic conditions and manufacturing requirements. The problem has been optimised previously using: moth-flame optimisation (MFO), ant lion optimiser (ALO), grey wolf optimiser (GWO), whale optimisation algorithm (WOA) (Yildiz et al., 2019a), spotted hyena optimiser (SHO) (Dhiman and Kumar, 2017), RankiMDDE, TLBO, ABC, mine blast algorithm (MBA) (Sadollah et al., 2013), WCA, and GA (Gupta et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000574_j.ijnonlinmec.2020.103627-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000574_j.ijnonlinmec.2020.103627-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of a rolling element bearing.",
        "texts": [
            " For the 4# bearing, we consider the nonlinear factors, as it is a ball earing. To meet the different requirements of aero-engine dynamics esign, the connection between the bearing and the cage is elastic and ard connected. The hard connection is not affected by the damper actors, such as the oil film damper. In this case, the nonlinear charcteristics of the ball bearing will be more prominent. It is assumed hat the 4# bearing in Fig. 1 is hard supported and connected directly o the cage through the bearing housing. Fig. 2 shows a cross-sectional iew of the 4# bearing. For the ball bearing shown in Fig. 2, the outer ring of the ball earing is directly fixed to the cage through the bearing housing. Thus, he relationship between the speed of the outer ring and the linear peed of the inner ring of the ball bearing can be expressed as = \ud835\udefa \u00d7 \ud835\udc5f , (1) \ud835\udc56 1 \ud835\udc56 a \ud835\udc63 \ud835\udefa \ud835\udf03 w \ud835\udeff \ud835\udeff w t o b \ud835\udc39 w f \ud835\udc65 \ud835\udc39 2 i b t \ud835\udc2a w r h \ud835\udc2a \ud835\udc2a r \ud835\udc0c w ( w \ud835\udc0c \ud835\udf11 \ud835\udc5f \ud835\udc40 where \ud835\udc5f\ud835\udc56 is the inner ring radius of the bearing. The relationship between the linear speed \ud835\udc63\ud835\udc50\ud835\udc4e\ud835\udc54\ud835\udc52, the rotational speed \ud835\udefa\ud835\udc50\ud835\udc4e\ud835\udc54\ud835\udc52 of the cage, nd the rotation speed \ud835\udefa1 of the high-pressure rotor is \ud835\udc50\ud835\udc4e\ud835\udc54\ud835\udc52 = 1 2 (\ud835\udc63\ud835\udc56 + \ud835\udc630), (2) \ud835\udc50\ud835\udc4e\ud835\udc54\ud835\udc52 = \ud835\udc63\ud835\udc50\ud835\udc4e\ud835\udc54\ud835\udc52 (\ud835\udc63\ud835\udc56 + \ud835\udc630)\u22152 = \ud835\udefa1 \u00d7 \ud835\udc5f\ud835\udc56 \ud835\udc5f\ud835\udc56 + \ud835\udc5f0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001021_0142331221994380-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001021_0142331221994380-Figure1-1.png",
        "caption": "Figure 1. Autonomous underwater vehicle with the inertial-fixed frame and the body-fixed frame.",
        "texts": [
            " Q, Q1, P and P1 are symmetric positive definite matrices and satisfy the following equation relations PA+AT P= Q, P1A1 +A1 T P1 = Q1. lmin( ) and lmax( ) are defined as the maximum and minimum eigenvalues of the matrix, respectively. Lemma 3: (Zuo, 2015) Let e1, e2, , eM \u00f8 0, subsequently PM i= 1 ex i \u00f8 PM i= 1 ei x 0\\x\\1 PM i= 1 ex i \u00f8 M1 x PM i= 1 ei x 1\\x\\\u2018 8>>< >>: \u00f06\u00de System modeling and problem formulation The dynamics of autonomous underwater vehicle contains two frames of reference called the body-fixed frame (b) and the earth-fixed frame (e), respectively (see Figure 1). Assumed that AUV is symmetric in all planes and the origin of the body-fixed reference frame is positioned at the center of gravity of the AUV. The 5-DOF mathematical model of AUV can be described as Chen et al. (2016) and Liu et al. (2017) _h= J (h)y M _y +C(y)y +D(y)y + g(h)= t \u00f07\u00de Considering the external disturbances of the system, the above model can be rewritten as follows _h= J (h)y M _y +C(y)y +D(y)y + g(h)= t + td \u00f08\u00de where, y = \u00bdu v w q r T denotes the velocity in the body-fixed frame, u, v and w denote the surge, sway and heave velocity of AUV, q and r represent pitch and yaw rate of AUV, here omit the roll motion; h= \u00bdx y z u c T denote the position coordinates in the earth-fixed frame, x, y and z represent the position coordinates of AUV in three directions in the inertial coordinate system, u and c denote the orientation of vehicle in the earth-fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.5-1.png",
        "caption": "Figure 7.5. Calculation of the undercut circle radius.",
        "texts": [
            " The only methods known to the author of this book, for finding the radius Ru of the undercut circle, all involve some form of trial and error. The problem is simplified slightly, if we find the point where the locus of Ahc intersects the involute, rather than the point where the fillet intersects the involute. The two points are not identical, so the value we obtain for Ru is only approximate, but the error is negligible. The value of Ru can then be found by the following procedure. An undercut tooth profile is shown in Figure 7.5, Undercut Circle 181 with the involute extended to the point where it meets the base circle at B, and the diagram also shows the locus of point Ahc ' A typical circle of radius R cuts the involute and the locus at points A and A', and the polar coordinates of these points are labelled 9R and 9R. If 9R is larger than 9R, the radius R is smaller than Ru' as we can see in Figure 7.5. The radius Ru of the undercut circle can be found by calculating 9R and 9R at a number of different radii, and eventually finding the value of R at which 9R and 9R are equal. The polar coordinate 9R of the point on the involute at radius R was given by Equation (2.35), (7. 7) The corresponding value of 9R depends on the type of cutter used, and we will deal first with the case when the gear is cut by a pinion cutter. Figure 7.6 represents the gear and the pinion cutter, in their positions when point Ahc of the cutter lies on the gear circle of radius R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.16-1.png",
        "caption": "Figure 5.16. Undercutting.",
        "texts": [
            " However, when the cutting point reaches Eg , there is still part of the cutter involute near point Ahc ' which has not yet made a final cut on the gear tooth. It is impossible to cut the gear tooth involute any further, since the involute does not exist inside the base circle. In Chapter 9, we will describe the exact shape cut in the gear by the tooth tip of the cutter. At this stage, we will simply state that the path followed by point Ahc ' relative to the gear blank, is a curve that intersects the involute near the base circle, as shown in Figure 5.16. The result is that part of the involute in the gear tooth profile is cut away. This phenomenon is called undercutting, because a section of the correct involute profile is undercut by the tip of the cutter tooth. Undercutting is essentially the same as interference between the cutter and the gear blank. There is, however, one important difference between interference and undercutting. Undercutting 141 Interference occurs in a gear pair, if there is non-conjugate contact between the tooth tips of one gear and the tooth fillets of the other, and the gear pair is then unusable",
            "50) Examples 189 This quantity is negative, so the gear will be undercut. The radius of the undercut circle is found by trial and error, using Equations (7.11-7.13). In order to save space, only the final set of calculations is given below. Choose R = 56.555 mm ur - 23.378 - 0.651431 radians = - 37.324\u00b0 9' 8.345\u00b0 R tsg = 15.708 4>R = 4.488\u00b0 9R = 0.145643 radians = 8.345\u00b0 (7.11) (7.12) (7.13) (5.31) (2.18) (7.7) Since 9R is equal to 9R, we have chosen the correct value of R, and the undercut circle radius Ru is equal to 56.555 mm. This particular gear is shown in Figure 5.16. Example 7.3 The gear pair shown in Figure 7.9 has the following specification. Gear 1 is the gear which was described in Example 7.2, with a tip circle diameter of 140 mm, and the radius of its undercut circle was calculated in that example. Gear 2 has 25 teeth, and the diameter of its tip circle is 285 mm. The center distance is 195 mm. Show that the form circle of gear 1 is larger than its undercut circle, and then calculate the contact ratio. m=10, 4>5=20\u00b0, N1=12, N2=25 RT1 =70.0, RT2 =142.5, C=195"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000000_j.oceaneng.2019.02.023-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000000_j.oceaneng.2019.02.023-Figure1-1.png",
        "caption": "Fig. 1. Frames and states of the surface vessel.",
        "texts": [
            " It is proved that the tracking errors are uniformly ultimately bounded and converge to a small neighborhood of zero. The rest of this paper is organized as follows. The problem statement and several useful assumptions and lemmas are presented in next section. In section 3, the design process of controller is introduced in detail. Simulation results and comparisons are provided in section 4. Conclusion is given in section 5. In this paper, we consider 5 degree-of-freedom (DOF) model of an underactuated AUV which is subjected to environmental disturbances (Do and Pan, 2009). The frame of AUV is shown as Fig. 1.The mathematical model of AUV can be described as = + = + + = + = = x u v w y u v w z u w q r cos cos sin sin cos sin cos cos sin sin sin cos /cos (1) = + + = + = + = + + = + + u vr wq u d v ur v d w uq w d q uw q d r uv r d m m m m d m m u u m m d m v m m d m w m m m d m gGM m m q q m m m d m m r r 1 ( ) sin 1 ( ) 1 L 22 11 33 11 11 11 11 11 22 22 22 11 33 33 33 33 11 55 55 55 55 55 11 22 66 66 66 66 (2) where x y z( , , ) defines the position of AUV and ( , ) defines the orientation of vehicle in the inertial reference frame (IRF); u v w q r( , , , , ) represents the surge velocity, sway velocity, heave velocity, pitch velocity and yaw velocity respectively; the available controls u, q and r represent the surge control force, pitch control force and yaw control force which are provided by propellers and thrusters; d d d d d, , , ,u v w q r are unknown environmental disturbances caused by wind, waves and ocean currents; = \u2026m i( 1, , 6)ii denote the added masses and the inertia of vehicle; = \u2026d i( 1, , 6)ii denote the hydrodynamic parameters; g is the buoyancy of AUV and GML is the vertical distance between center of gravity and center of buoyancy (Fossen, 2002)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002935_iros.1993.583168-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002935_iros.1993.583168-Figure8-1.png",
        "caption": "Fig. 8 Linearized model of biped wallcing robot",
        "texts": [
            " -_-- -__- ma,(zo'~o*-xotzot) + %(0 + zq)(F0 + x, + g,) computing approximate solutions of linearized equations. A!Co mnutat - ion of App roximate Solut ions: By assuming that neither the waist nor the uunk particles do not move vertically, Le., the trunk arm rotates on the horizontal plane only, the equations are decoupled and Linearized. Then, the yaw-axis moment generated by the yaw-axis actuator is described by the rotational angle of the yaw-axis actuator By and 56 3 the radius of the trunk's arm R ( shown in Fig. 8 ), and the linearized equations (3, (6) and (7) are obtained. m0,RZ8, = -Mzo(t) -Mz(t) ( 7 ) In these equations, My(t), Mx(t) and Mz(t) are known, because they are derived from the lower-limbs motion and the time trajectory of Z M P . Also Mz,(t) is known when the trunk motion of the pitch and roll-axis motion is derived. Considering the case of the steady walking, My(t), Mx(t) and Mz(t) are periodic functions, because each particle of the lower-limbs and the time trajectory of Zh4P move perioditally for the moving coordinate W-XYZ"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003235_amc.2004.1297665-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003235_amc.2004.1297665-Figure1-1.png",
        "caption": "Fig. 1. Over view of the bicycle coordinate Fig. 3. The bicycle coordinate from side position",
        "texts": [
            " Explanation of Centrifugal force Centrifugal force is a force that occurs when an object moves on circular orbit. This force is acting the direction of normal line of the circular orbit. The equation of centrifugal force is shown in follow equation. Here, FCF, Mob, Vob and R,, mean centrifugal force, mass of the object, moving velocity of the object and radius of circular orbit respectively. B. Equibrilium of bicycle robot From eq(l), it is known that intensity of centrifugal force applying running bicycle is determined by the radius of turning circle and the moving velocity. Fig.1 shows the over view of the bicycle coordinate. In Fig.1, L means the wheel base, p means the direction angle, a1 means the slip angle of the front wheel and a2 means the slip angle of rear wheel. Assuming that the turning radius R is much bigger than the wheel base L, the turning radius R is represented as follows approximately. R = Lcot(@ - a1 +a*) (2) 0-7803-8300-1/04/$20.00 82004 IEEE. 193 AMC 2004 - Kawasaki, Japan If the side slip doesn't occur, the turning radius R is written as follows. R = L c o t p (3) The angle formed by vertical axis and a bicycle is named camber angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.12-1.png",
        "caption": "Figure 13.12. Relation between the pitches.",
        "texts": [
            " We follow the same pattern in the description of a helical gear, except that in this case there is more than one type of tooth pitch. We first define the tooth pitches at a cylinder of arbitrary radius R, and then we describe the corresponding quanti ties at the standard pitch cylinder and at the base cylinder. The operating pitches will not be introduced until Chapter '4, where we discuss the meshing of helical gears. The tooth pitches at any radius R are defined as lengths on the developed cylinder of radius R, which is shown in Figure 13.12. The cylinder is drawn wi th a length equal to the gear lead L, so that the teeth appear as lines parallel to the diagonal, making an angle \"'R with the z direction, and in this length each tooth makes exactly one revolution round the gear. A typical tooth is shown as a broken line such as T,T2T3T4 \u2022 A transverse section through the cylinder appears on the developed surface as a vertical line with a constant value of z. Hence, if the gear has N teeth, there must be N teeth cutting any vertical line through the rectangle, and since the lines representing the teeth are parallel with the diagonal, there will also be N teeth cutting any axial line. The axial pitch Pz is defined as the distance between adjacent teeth, measured in the axial direction. Since any axial line in Figure 13.12 is crossed by N teeth, the axial Tooth Pi tches 325 pi tch is equal to the lead di vided by the number of teeth, ~ N (13.36) The axial pitch is independent of the radius R, as we can see from Equation (13.36). It is also clear, from the same equation, that the axial pitch Pz must obey the same sign convention as the lead L. In other words, Pz is positive for right-handed gears, and negative for left-handed. It should perhaps be pointed out that in North America the standard symbol for the axial pitch is Px' The use of Pz was chosen here, because with the coordinate system used in this book, the axial pitch is measured in the z direction. The transverse pitch PtR at radius R is defined as the distance between adjacent teeth, measured in the transverse direction. Its value can be read from Figure 13.12, 211'R N (13.37) From this definition, it is clear that the transverse pitch of a helical gear at any radius is identical with the corresponding circular pi tch of a spur gear. Next, the normal pitch PnR at radius R is defined as the distance between adjacent teeth, measured along a line perpendicular to the teeth in the developed cylinder, as shown in Figure 13.12. We can use the diagram to derive relations between the various pitches, PnR PtR cos \"'R (13.38) Pz PnR (13.39) sin \"'R The transverse pitch and the normal pitch at the standard pitch cylinder are generally called the transverse pitch and the normal pitch of the gear. They are represented by the symbols Pts and Pns' and their values can be obtained if we replace R by Rs in Equations (13.37 and 13.38), 211'Rs N (13.40) 326 Tooth Surface of a Helical Involute Gear Pts cos \"'s (13.41) We can also write down the relation between the axial pitch and the normal pitch at the standard pitch cylinder, corresponding to Equation (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002771_s0924-0136(00)00850-5-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002771_s0924-0136(00)00850-5-Figure3-1.png",
        "caption": "Fig. 3. Illustration of the powder accumulated at the base of the clad in single cladding path: (a) \u00aerst layer; (b) second layer; (c) third layer.",
        "texts": [
            " Firstly, only cladding was employed to build the designed part until the height of the part could not be increased. The maximal height was only 5 mm. The height at all corners was greater was that the speed at the corner was lower than at other positions because of the effect of the acceleration and deceleration of the moving table near to the corner. Also the cross-sectional view of the clad pro\u00aele was of arc type because of surface tension and the Gaussian distribution of laser beam intensity. An illustrated diagram of some unmelted residual powders accumulated at the base of the \u00aerst clad is shown in Fig. 3. The reason for these accumulated powders is that the powder \u00afow rate was too high or the powder stream was bigger than the spot size of the focused beam. In the second clad, the clad pro\u00aele became sharper. Also some of the residual powders from the previous clad were melted in the successive cladding operation, and this melted residual powder made the clad pro\u00aele even more sharp, as shown in Fig. 3(b). Again, the same situation happened in successive cladding operations, as shown in Fig. 3(c). Hence, the height of the clad could no longer be increased because the clad pro\u00aele was too sharp to accumulate any melted powder. In order to increase the accumulation of the melted powder on the surface of the clad, machining was employed to smooth the clad surface. Secondly, after every three claddings, the melted metals were machined to a thickness of 0.15 mm. This was continued until a height of 10 mm was achieved. There was a lot of powder attached at the edge of the part. Also the ripple effect at the edge was excessive before machining",
            " As shown in this \u00aegure, there is no porosity at the top surface after milling, which means that there is no porosity in the clad, if the cladding operation parameters were carefully selected. The geometry of the mold cavity was not stepwise as is general in layer manufacturing processes. A sloping surface of the mold cavity was formed because of the surface tension of the clad and the accumulated powder melting. Although the milling operation was applied on the clad every two layers, the results of the accumulated powder and the sloping surface of the clad were similar to that of the single clad as shown in Fig. 3. The reason for this phenomenon is that the layer thickness of 0.5 mm was set too thick. The dimensions of the mold cavity were measured at eight different positions. The average error of the mold cavity was about 0.15 mm. The objective of the mold modi\u00aecation is to investigate the feasibility of the mold modi\u00aecation and repair using the hybrid processes of SLC and milling. An original mold was designed and machined using CNC from raw material in mild steel with 17.5 mm height, 112 mm length, and 40 mm width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003655_j.talanta.2005.07.007-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003655_j.talanta.2005.07.007-Figure1-1.png",
        "caption": "Fig. 1. The diagram of the integrated three screen-printed electrodes. Diameter of the working electrode and the counter electrode are 4 mm and 10 mm, respectively.",
        "texts": [
            " All of other chemicals were analytical grade and were used without further purification. Buffer solutions used in experiments were prepared with doubly distilled water. Before screen-printing, the AgCl particle was prepared: excess HCl (0.1 mol L\u22121) was titrated slowly into the stirred 0.1 mol L\u22121 AgNO3 solution. Then the AgCl deposit was filtrated and incubated to dry. Grinded AgCl particle (can pass through 0.2 mm mesh) was mixed thoroughly with the silver printing ink (1/1 to g/g). The screen-printed electrodes with integrated three electrodes (Fig. 1) were fabricated as follows: firstly, the carbon ink was printed through the mesh to the PET support to form the conducting layer and also to work as the working electrodes and the counter electrodes, and then it was dried at 120 \u25e6C for 15 min. Secondly, the Ag/AgCl ink was printed on the reference electrodes position, and then dried at 120 \u25e6C for 45 min. Lastly, the insulating ink was printed to cover the non-working and non-conducting region of the SPE, and then it was dried under the UV lamp for 5 h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003220_s0304-8853(01)01181-7-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003220_s0304-8853(01)01181-7-Figure5-1.png",
        "caption": "Fig. 5. The spiral-type-magnetic micromachine with heating function.",
        "texts": [
            " The field frequency was reduced to 1Hz again, the velocity of machine C became smaller, while machine A moved faster because the machine could be synchronized again to the field. This experiment suggested that we could control several machines in a uniform magnetic field by changing the frequency or the intensity of the field. For the medical application of this machine, the important point is its function after arriving at its destination. We proposed a heating mechanism attached to this machine. It is well known that magnetic materials placed in an alternating magnetic field produce heat due to iron loss. We produced a heating machine by attaching a permalloy rod. Fig. 5 shows the view of the machine. By applying the rotational magnetic field for moving and the alternating field for heating at the same time, the machine heated and moved in agar. Fig. 6 shows the experimental system. We set the heating machine in the agar. A thermo-sensitive sheet was set beneath the machine. The color of the sheet changes from white to red at 501C. The field of 12 kA/m with a rotation frequency of 1Hz and the alternating field of 100 kHz and 6.4 kA/m were applied at the same time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure7-1.png",
        "caption": "Fig. 7. A singular con\u00aeguration of class (RPM, IIM, II, IO).",
        "texts": [
            " In the table, for each singularity class, it is denoted whether the class is non-empty (YES) or empty (NO), the steps in which the singularities of the class are obtained (or it is proven that the class is empty), and the \u00aegure that shows a representative con\u00aeguration of the class. It is determined that the mechanism has singularities belonging to 13 di erent singularity classes. Seven \u00aegures (Figs 6\u00b112) illustrate the singularities of the mechanism. Except for Figs 11 and 12, which represent the same (RO, II) singularity class, the \u00aegures depict con\u00aegurations belonging to di erent singularity classes. One \u00aegure (Fig. 7) is used to illustrate two singularity classes after a re-labelling of the sub-chains (Step 3.3). Four \u00aegures (Figs 6, 7, 9 and 10) can il- lustrate four additional classes if a small perturbation in the depicted con\u00aeguration is performed (Step 3.5). The remaining two classes, which are not directly illustrated by \u00aegures, consist of singularities that are comparatively easy to describe and envision (Step 6). 5.3.2. The identi\u00aecation procedure. Below, the steps of the identi\u00aecation procedure are detailed",
            " The \u00aerst component has 13 con\u00aegurations, and one of them is shown in Fig. 6. In this con- \u00aeguration, the points P are on the SP 1 axes and the three axes SP 2 intersect in one point, D. The 13 con\u00aegurations can be obtained by varying the elevation of the moving platform and moving the intersection point, D, in the base plane (D can also be at in\u00aenity). Several 2-dimensional manifolds of IIM-type singularities are attached to the 3-dimensional set. One of these can be obtained from the con\u00aeguration shown in Fig. 7 by rotating the moving platform about the line BC (and varying the elevation of points B and C). The second component is 1-dimensional and consists of con\u00aegurations like the one in Fig. 8, where the three supporting legs are fully extended and the two platforms are in the same plane. (2) RPM-type singularities From Equation (11) it is evident that L\u00c3 p is singular only when either mB 1 or mC 1 are zero, i.e. when either B or C are on the axis of the \u00aerst-joint screw of the corresponding subchain",
            " From condition (iv), it follows that an element of {1} is an II-type singularity if and only if the 6 6 matrix L\u00c3 I has a null-space dimension of at least two. Next, we check whether this condition is satis\u00aeed for the di erent IIM-type singularities as determined in Step (1). For all the 13 con\u00aegurations of the type shown in Fig. 6, where for all three serial subchains point P is on the SP 1 axis, the condition is satis\u00aeed since mB 1 and mC 1 are zero vectors. For the IIM-type con\u00aegurations with three extended legs (as in Fig. 8) the condition is not satis\u00aeed. If only two subchains are singular (similar to Fig. 7), the condition is always satis\u00aeed when the singular subchains are B and C (as in the \u00aegure). When, however, one of the singular subchains is A, then, generally, the matrix A is of rank 5. There are two exceptions. The \u00aerst is represented in Fig. 9, where the singular subchains are A and B and additionally the point Co lies in the plane ABC. The second exception is shown in Fig. 10, where not only points B and C are located on screws SB 1 and SC 1 , but also point A lies in the (vertical) plane de\u00aened by the two screws. Each of Figs 9 and 10 represents, in fact 11 con\u00aegurations, since the elevation of point A can vary. Thus, the set of singularities belonging to the IIM, IO and II types consists of a main 3- dimensional set (Fig. 6), a 2-dimensional set (Fig. 7) and two 1-dimensional sets (Figs 9 and 10). The set of singularities in the IIM and IO types has two 2-dimensional components (similar to Fig. 7. with subchain A as one of the singular ones) and a 1-dimensional component (Fig. 8). (3.2) According to condition (i) and Equation (13), a con\u00aeguration is an RI-type singularity if and only if at least one of the following conditions is satis\u00aeed: either the subchain A is singular (in any way); or subchain B is fully extended; or subchain C is fully extended. Condition (ii) and Equation (12) imply that an RPM-singularity is also of the RO-type in the following three cases: (a) When C is on the SC 1 axis and the plane ABC is perpendicular to mC 2 (Fig",
            " 9, though subchain A need not be singular). Thus, four sets are obtained: 15 RPM-type singularities, 14 RPM and RI-type singularities, 14 RPM and RO-type singularities and RPM, RI and RO-type singularities. (3.3) The intersections of the subsets of {3.1} and {3.2} give the 10 singularity classes (Table 2) of con\u00aegurations that are both IIM and RPM. Of these, only \u00aeve classes are non-empty for the mechanism under consideration: (a) (IIM, IO, RPM, RI) has 12 con\u00aegurations with two singular subchains similarly to Fig. 7, but subchain A must be one of the singular subchains. When the two singular subchains are A and B, point Co should not lie in the plane ABC (i.e. unlike Fig. 10). Alternatively, if the singular subchains are A and C, then the plane ABC should not contain Co and Ao. (b) (IIM, IO, II, RPM) has 12 con\u00aegurations as in Fig. 7. The singular subchains must be B and C. The plane ABC must not contain Co and Bo (unlike Fig. 10). (c) (IIM, IO, II, RPM. RI) has 13 con\u00aegurations with three singular subchains as in Fig. 6. (d) (IIM, IO, II, RPM, RO) has 11 con\u00aegurations like the one depicted in Fig. 10. The moving plane ABC contains the points Co and Bo and the subchains B and C are singular in the same way as in Fig. 7. (e) (IIM, IO, II, RPM, RI, RO) has 11 con\u00aegurations in two 1-dimensional sets. The \u00aerst is represented by the con\u00aeguration in Fig. 9. It is similar to Fig. 7 with singular subchains A and B, but point Co is in the plane ABC, allowing for a RO-singularity. The second set is similar to the con\u00aeguration in Fig. 9, however, the non-singular subchain must be B rather than A. (3.4) Only one of the four classes of IIM but not RPM singularities is non-empty: (IIM, IO, RI, RO) consists of 11 con\u00aegurations as in Fig. 8. (3.5) All of the four RPM but not IIM classes are non-empty. (RPM, II, IO) has 15 con\u00aegurations. An example for this class can be obtained from the con\u00aeguration in Fig. 7 by an arbitrarily small perturbation of the subchain C while subchains A and B remain \u00aexed. (RPM, RI, II, IO) has 14 con\u00aegurations and can be illustrated by a variation of Fig. 6 obtained by maintaining the depicted position of the subchains A and B and slightly perturbing subchain C. (RPM, RO, II, IO) has 12 con\u00aegurations. An example is obtained from the con\u00aeguration in Fig. 10 by a small rotation of subchain C about SC 1 . (RPM, RI, RO, II, IO) has 12 con\u00aegurations and a representative can be obtained from Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-25-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-25-1.png",
        "caption": "Figure 5-25 Basins of attraction for different initial conditions for the unforced, two-well potential oscillator [from Dowell and Pezeshki (1986) with permission of the American Society of Mechanical Engineers, copyright 1985].",
        "texts": [
            " The method outlined in this section has also been used on a three-well potential problem and has been tested successfully in experiments on a vibrating beam with three equilibria by Li (1985). r Figure 5-24 Overlap criteria for a multiwell problem using semiclassical analytic methods. 190 Criteria for Chaotic Vibrations Dowell and Pezeshki (1986) have posited another heuristic criterion for the two-well potential problem (5-3.36). Instead of comparing the size of periodic orbits with the undamped, unforced problem, they compare the prechaotic, periodic, subharmonic orbits for the driven oscillator with the boundary of the basin of attraction for the damped, unforced problem (Figure 5-25). This boundary represents the set of initial conditions (.4(0), A(0)) for which the orbit goes to the left or right equilibrium point without crossing ^ 4 = 0 . They also observe, through numerical simulation, that the driven motion becomes chaotic when the force level of /0 is larger than the value for which a periodic orbit touches the basin boundary. (See Chapter 6 for a discussion of basin boundaries.) Criteria Derived from Classical Perturbation Analysis. The novitiate to the field of nonlinear dynamics may be misled by the current interest in chaos to conclude that the field lay dormant in the prechaos era"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure18-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure18-2-1.png",
        "caption": "Figure 18-2. Rubber to fabric peel test",
        "texts": [],
        "surrounding_texts": [
            "difference between their acoustic impedances. For example, at a rubber/air interface there is a large difference in acoustic impedance and less ultrasonic energy will be transmitted than at a well-bonded rubber to metal interface. Hence, if there is an area of debonding at the rubber/metal interface and there is a thin layer of air or a vacuum between the two this can be detected by loss in the transmitted, or increase in the reflected, ultrasound. Attractive and simple as the technique is in theory, in practice there are a number of difficulties which severely limit its value. Only areas of disbond, not a weak bond, can be detected although very weak areas can be made to part by pre-stressing, which is in any case necessary to separate the debonded areas. Notwithstanding these remarks, there have been considerable developments in ultrasonic flaw detection over the years although there has not been any widespread adoption of the technique in the rubber industry generally. Other non-destructive tests have been suggested to estimate bond quality, but such techniques as holography and radiography, and also ultrasonics, have mostly been used in the rubber industry for detection of flaws in tyres. It is not considered appropriate to cover non-destructive flaw detection in general here but an account of applications to polymers has been given by Gros in Handbook of Polymer Testing^ .\u0302"
        ]
    },
    {
        "image_filename": "designv10_4_0002967_s0165-0114(97)00195-4-FigureI-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002967_s0165-0114(97)00195-4-FigureI-1.png",
        "caption": "Fig. I, Fuzzy membership functions of s and uf~.",
        "texts": [],
        "surrounding_texts": [
            "In this section, we study the properties of the control law. We first make some assumptions about the system (6). Assumption. For unknown functions f ( x ) and g(x), we can determine (1) I~(x)l ~O(x) , x ~ R ~, (2) I f ( x ) l ~<M0(x), xEA~t, (3) O < M l ( x ) ~ y ( x ) < ~ M 2 ( x ) , x 6 A ~ , (4) 1 0 - * ( x ) l - - I ~ q - * ( x ) x l ~< M3(x), x 6 R \" , where D ( x ) , M o ( x ) , M l ( x ) , M 2 ( x ) and M3(x) are known functions. Choose the following control law u and adaptive law to adjust the parameter vector 0 as follows: u = - (1 - rn(t))Uad -- m(t)kl (s, t)Ufs - k2(s, t)Ufs, where kl(s , t ) -- - - k2(s, t) - [\" ql(1 - m(t))sz~(t)p(x) , O = / r/l(1 - m ( t ) ) s A ( t ) p ( x ) , = r/e(1 -- m(t)) lSA(t) 1. 1 [M0(x) + I~/sA(t) + .if(t) -- e ~'1 + x.,/\" I J, MI(x) M3(x)]s~(t)l ~o + D(x) 2M2(x) + M1 (x) ' if (lO] < M ) or (I/~] = M and sA( t )OTp(x) <~ 0), if (I/~1 = M and sA(t)OTp(x)>O), (19) (20) (21) Substituting (19) into (6) and by (10) yields ~(t) + qsA(t) = g(X)[U* -- U(X]/})] + ~l~osat(s(t)/~o) -- = g(x)( l -- m(t))[u* -- u(xl/}) + gufs] +m(t)g(x)(u* + kl(s, t)ufs) + g(x)k2(s,t)Ufs + qqgsat(s(t)/~o) = g(x)(1 - m(t))dPTp(x) + g(x)(1 -- m(t))[u* -- u(xlO ) + 6~uf~] + m(t)g(x)(u* + kl(s,t)uf~) + g(x)k2(s,t)uf~ + rl~o sat(s(t)/~o) - ~, (22) where ~b = 0 - 0, sA(t) = s(t) - q~ sat(s(t)/~o) and ~p is a parameter which describes the width of the dead zone. Theorem 2. Consider the nonlinear (1) with Assumption (1) - (4) . I f we take the adaptive control law (19) - (21) , then we have (i) IOI <~M, u, x E L ~ , (ii) e(t) converges' to a neighborhood o f zero. Proof. The proof of 10[ ~< M is similar to [12]. We only prove the other conclusions\u2022 Consider the Lyapunov function candidate V ( t ) = l -1 2 1 ~bv~ b + 1 2. (23) 2g SA + 2r/1 2q2 Differentiating V(t) with respect to time, we have V ( t ) - S ~ A O(X)S~ + l bTq b + l g ~ . (24) g(x) 292(X) ql r/2 If Isl <~o, then AA=0, it follows /2=0. If I s l ~ , then dzz =s. By (22), we have f,(t) = - ~ - - o(x)sL y(x) 202(x) + sA(1 - m(t))q~Tp(x) + S~(I -- m(t))[u(x[O) -- u* + guf~] 1 _ 1 _ + sAm(t)(kluf~ + u*) + sz~(k2uf~ + qtp sat(s(t)/~p)/g(x) - ~/.q(x)) + ~ T ~ + \u00b1gf,. ~11 112 (25) By assumptions (1) and (2), it is known If(x)t ~< Mo(x), Ml(x) <~ Io(x)l ~ M2(x), and Iq9 sat(s,/~p)l ~< q~, we have ( ) i?(t ) <~ _ ) ~,~ Z (p+D(x) M~(x)ls~l M(x ) + IsAI M~(x) + 2M2(x) k2 +m(t)+s~(lu*l- k,) +s~(l --m(t))OTP(X)IOT~\u00f7IS~I(I m(t))~+ I~. (26) i l l ) 1 Since I.*1 ~< [1/M,(x)][Mo(x)+ Is( t )+ 2 s ( t ) e 0) +Xm ], from the parameter adaptive law (20) and (21), if we take 1 k, (s, t) - [Mo(x) + I~IsA(t) + Ls(t) -- e (m + x~,~ '~ ], Mj (x) k2(s , t )= M3(x)IsA(t)[ + tffp + D(x) 2M2(x) Mj(x ) then S~ . . . . (2 T OOYp( X ) I2(t) <~ - t I M ~ - ~ + IsA(1 - mUD ~ 2 ' (27) where I = 0 ( 1 ) if the first (second) condition of (20) is true. If I = 1, then 101 = M ~ I 0 I, by the following formula: oT6 \u00bd1012- \u00bdtO[ 2 - (28) therefore, sL I2(t) <~ - -qMl(x)\" (29) Therefore, all signals in the system are bounded. Since s(t) is uniformly bounded, if e(0) is bounded, then e(t) is also bounded, and Xm(t) is bounded by design, so x ( t ) E L ~ . From (19), we can get u E L ~ . To complete the proof and establish asymptotic convergence of the tracking error, it is necessary to show that szz--* 0 as t ~ co. This can be accomplished by applying Barbalat's lemma to the continuous, nonnegative function Vl(t) = V(t) - I?(r) s~(,) ) s~(t) +q M,(,~---)J dz, with Vt(t)=-qM,(t~- ~. (3o) It can be easily shown that every term in (7) is bounded, hence s~ is bounded, which implies that /)l is a uniformly continuous function of time. Since Vt is bounded below by 0, and Vj(t) ~< 0 for all t. Barbalat's lemma proves that l?l ~ 0 and hence from (29) that sz~(t)--, O. This means that inequality Is[ ~< ~o is obtained asymptotically, so the tracking error e(t) converges to a neighborhood of zero. 6 . S i m u l a t i o n In this section, we consider the following nonlinear system: 1 - e -x 2 - - - - + (1.02 + sin 7x)u + sin 3t. (31) 1 + e - x Use the adaptive fuzzy controller developed in the last section to regulate the system to the origin, i.e., Xm = O. In the simulation, choose Employ five fuzzy rules as follows: Ri: I f x is A j, then y is B j j = - 2 , - 1 , 0 , 1 , 2 , where [ A j = e x p - j = - 2 , - 1 , 0 , 1,2. Define Ai(x) (32) pi(x) = i=2 ~ / : - - 2 Ai(x) ' then 2 y(x ) = Z OiPi(X)\" i = - 2 (33) Using the fuzzy logic system (32) to approximate u*. Take initial conditions: x(0) = 1, g(0) = 1.5, Oi(O) is taken randomly in the interval [ - 2 , 2] choose r /= 20, ql = 0 . 6 , /72 = 0 . 9 , m 0 ~ 1, Mt = 0.2, M2 = 2.02, M3 = 7, (p = 0.5. The simulation results are shown in Figs. 2 and 3, which confirm that the proposed algorithm is accurate."
        ]
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure14.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure14.5-1.png",
        "caption": "Fig. 14.5 Die forging (www.dropforging.net)",
        "texts": [
            " Impression die forging was initially conducted by hand in shops, and gradually evolved into a forging operation widely used in the industry around 1870. The main driving forces behind the development came from the automobile and aeroplane industries. Impression die forging has several advantages, among which the following two are especially attractive to the auto-industry and the aero-industry. (1) it is conservation of metal and has favorable grain orientation, thus higher strength/ weight ratio (compared with machining); (2) it is a near-net-shape or net shape operation, requiring very little, or not at all, machining (Fig. 14.5). Nowadays parts made through impression die forging become larger, heavier and with more intricate shapes. At the same time, the dimensional tolerance becomes tighter. To meet these requirements, impression die forging is developing toward a net shape operation. On the equipment side, presses are more common 14.2 Development of Metal Forming 517 than hammers because of the lower vibration and noise level (Lange and Mayer-Norkemper 1977). The conceptual origin of rolling is traced back to Leonardo da Vinci who made the sketch on his notebook of a hand rolling mills in 1480 for rolling soft metals like gold and silver"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000833_j.cirpj.2021.06.022-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000833_j.cirpj.2021.06.022-Figure5-1.png",
        "caption": "Fig. 5. 3D scan of deposited wall.",
        "texts": [
            " Samples were deposited using a Qineo pulse 450A welding power source with synergic control in w O r m F C a F W s a b o c w p f m t d d d F m 0 P as obtained, and part alignment was corrected when necessary. nce the scanned WAAM part was aligned correctly with the eference CAD model, the maximal allowance to be removed was easured with respect to the middle plane of the reference part. inally, the aligned scans were exported and used as a blank in AM software to program the required milling tool paths. The dditive-subtractive manufacturing process chain is shown in ig. 4. Additionally, flatness deviations (FD) of the as-deposited AAM components were calculated based on the analysis of 3D cans (Fig. 5). For this purpose, five sections were created along the ligned component's length with an equal distance of 15 mm etween them. The corresponding (x, y, z) coordinates were btained. The start and stop points of the welds were not onsidered in the FD calculation. The surface modulation in the idth direction (Y direction) was obtained by fitting a regression lane y 0 \u00bc ax \u00fe bz \u00fe c. The distance of each point on the surface (di) rom the regression plane was calculated. The absolute sum of aximum and minimum distance from the regression plane gives he FD (Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002924_978-94-009-1718-7_36-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002924_978-94-009-1718-7_36-Figure1-1.png",
        "caption": "Fig. 1: Wunderlich Mechanism as a kinematotropic linkage.",
        "texts": [
            " Wunderlich published a paper [5] in which he describes a planar twelve-bar mechanism with six parallelogram or antiparallelogram loops which can be arranged in four different closure modes, all of them movable with either one or two degrees of free dom. What makes this mechanism especially remarkable is the fact that by passing a sin gularity position the mechanism might change its movability. In that case the singularity position is, therefore, not a simple bifurcation position, but a sort of mobility turning posi tion. Fig. 1 shows Wunderlich's mechanism in two different positions. In the position in which it is has two parallelogram and four antiparallelogram loops, the mechanism is movable with mobility 1 because the two position angles If! and <p are related by the equa tion: wherein k) = (a+ b)/(a-b), k2 = (c + b)/(c - b) are the system parameters. In the posi tion, however, in which Wunderlich's mechanism has four parallelogram and two antipar allelogram loops, its mobility is 2, as If! and <P can be chosen arbitrarily"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000288_j.msea.2020.139456-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000288_j.msea.2020.139456-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the scanning strategies used in this study.",
        "texts": [
            " A powder layer with thickness (d) of 30 \u03bcm was deposited on a carbon-steel building platform. Samples of Co\u2013Cr\u2013Mo alloy were then fabricated from the powder in a chamber filled with argon gas to minimize oxidation. For simplicity, the term \u201cvolumetric energy density (\u03b7)\u201d is commonly used to describe the SLM parameters [29]. The value of \u03b7 is inversely related to the scanning speed (v) as shown below: \u03b7 \u00bc P v hd ; where h is the hatch spacing (120 \u03bcm). The number of laser passes was also varied, and two different scanning strategies were adopted as schematically illustrated in Fig. 1. The other process conditions for the six samples are shown in Table 2. Different cylindrical and tensile samples were produced by SLM, using various processing conditions, for simple compression and tensile testing with no further finishing. The average dimension of the cylindrical samples was about 9.5 mm (diameter) \ufffd 6.5 mm (height), while the tensile samples were produced as per the ASTM E8 standard, with a gauge length of 25 mm. At least four samples were produced and tested for each set of processing conditions listed in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000914_j.msea.2021.141587-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000914_j.msea.2021.141587-Figure1-1.png",
        "caption": "Fig. 1. Tensile specimen extraction schemes used to assess mechanical property in different DED 15-5PH geometries and locations. (a) DC model, and (b) DW model; (c) and (d) are as-deposited DC and DW parts,respectively.",
        "texts": [
            " [21], an argon atmosphere is more effective than a nitrogen atmosphere at suppressing the formation of austenite in 17-4PH AM materials. The DED parameters, including the laser power, deposition speed, distance between laser scanning paths, and the thickness of single layer powder were systematically changed until the optimization parameters were obtained, which ensures the relative density of DED component is higher than 99.1%. The processing parameters employed to produce all parts are given in Table 2. The parts were fabricated using a serpentine hatch strategy was depicted in Fig. 1, with the laser scanning paths parallel to each other. An identical scanning strategy was used for successive layers. A structure of cuboid geometry model (Fig. 1a) have dimensions of 50 mm \u00d7 15 mm x 5 mm and thin wall geometry model (Fig. 1b) have dimensions of 50 mm \u00d7 3 mm x 26 mm was illustrated, and tensile specimens with rectangular gauge sections ~1.8 mm \u00d7 3 mm x 14 mm were machined from different locations. As-deposited DC and DW parts are displayed in Fig. 1c and d, respectively. The initial 15-5PH had good strength and ductility performance, but at levels below those typically recommended for use. Thus, a postdeposition heat-treatment was required to improve the strength of the material to the desired level. The heat treatment applied to the DED 15- 5PH was based on H900 to obtain the maximum strength, which includes an initial solution heat treatment at 1040 \u25e6C for 30 min followed by an aging heat treatment of 482 \u25e6C for 1 h. Structural analysis and global texture analysis were performed by using X-ray diffraction (XRD; Bruker D8 Advance) with Cu K\u03b1 target (\u03bb = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000094_j.jmapro.2020.03.018-Figure23-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000094_j.jmapro.2020.03.018-Figure23-1.png",
        "caption": "Fig. 23. 3D model of the third sample and Deposited near-net shape.",
        "texts": [
            " A 30-layered thin-walled cylinder with an overhang feature is shown in Fig. 22. As a result of the new strategies used, the appearance and the profile of the thin-walled cylinder is reasonably good, and the whole deposition process was quite stable. It also demonstrates the proposed multi-directional WAAM strategy is capable of depositing at any angle on the vertical surface, from horizontal to vertical. In the third case, multi-directional WAAW was used to fabricate a horizontal wall on a curved surface, with the 3D model shown in Fig. 23. Typically, in practice with the WAAM, the welding surface is not a flat surface. This case is designed to examine the performance of multi-directional WAAM that used to deposit on an irregular surface. In the deposition process, a thin-walled cylinder was built up vertically to create a curved surface, the WFS and TS were set to 2 m/min and 0.1 m/min, respectively. Subsequently, WFS and TS were changed to 1 m/ Fig. 19. The appearance of weld beads geometries and their cross-section with welding torch angle varied from 45\u02da to 90\u02da. Fig. 20. A modified force model for a pendent molten pool with welding torch angle at 45 \u02da. min and 0.1 m/min. The torch angle was controlled to be perpendicular to the tangent line curved surface at all times. The start of the deposit alternated of each layer. A total of 35 layers were deposited horizontally resulting in a satisfactory flat surface, as shown in Fig. 23. This study focused on a new strategy of fabricating parts with overhangs using the multi-directional WAAM. Due to the negative impact of gravitational force, it is difficult to transfer the molten droplet to the target position and form a regular bead geometry in the multi-directional deposition process. To achieve a stable deposition process, the forming mechanism of positional deposits is initially investigated. Based on the analysis, GMAW using the CMT technology was selected for the multi-directional WAAM process due to its excellent position accuracy and ability to reduce the system heat input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure7-1.png",
        "caption": "Fig. 7. Some SP-equivalent parallel kinematic chains. (a) 2-R\u0302R\u0302\u00f0RRR\u00dekE and (b) 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE.",
        "texts": [
            " (3) can be reduced to j f1 t; 6 j f2 t; 6 j f3 t; 6 j f4 t; 6 j j 6\u00bc 0 \u00f04\u00de Eq. (4) shows that a simplified validity condition of actuated joints for SP-equivalent parallel mechanisms can be stated as follows: A set of 4 actuated joints is valid for a 4-DOF SP-equivalent parallel mechanism if and only if, in a general configuration, the t-components of the actuation wrenches of the four actuated joints fi 6 j are linearly independent. One candidate SP-equivalent parallel mechanism corresponding with the 2-R\u0302R\u0302\u00f0RRR\u00dekE SP-equivalent parallel kinematic chain (Fig. 7(a)) is the 2-R\u0302R\u0302\u00f0RRR\u00dekE SP-equivalent parallel mechanism (Fig. 9(a)). The axes of all the actuation wrenches pass through the center of the common point of the R\u0302 joints and are all parallel to one plane. We have j f1 t; 6 j f2 t; 6 j f3 t; 6 j f4 t; 6 j j \u00bc 0 0 0 0 \u00bc 0. where * denotes a generic number. According to the validity condition of actuated joints, the set of actuated joints is invalid. The candidate 2-R\u0302R\u0302\u00f0RRR\u00dekE SP-equivalent parallel mechanism is thus discarded. One candidate SP-equivalent parallel mechanism corresponding with the 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE SP-equivalent parallel kinematic chain (Fig. 7(b)) is 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE SP-equivalent parallel mechanism (Fig. 9(b)). The axis of the actuation wrench of an actuated joint is along the intersection of the plane determined by the axes of the two R joints within \u00f0RR\u00dekE and the plane determined by the axes of the R\u0302 joints except for the actuated joint considered (Fig. 8(b)). Using the validity condition of actuated joints, it can be proved that the set of actuated joints is valid. nism and (b) 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE candidate SP-equivalent parallel mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003508_robot.1995.525390-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003508_robot.1995.525390-Figure10-1.png",
        "caption": "Fig. 10 Crabbing for Inspection",
        "texts": [
            " 9 shows a L-shaped pipe measuring 200 mm in diameter. The right side of the reflection becoming dim indicates that the L-shaped pipe is turning right. In this system, the images are not clearly influenced by the diameters of the pipe. With the inspection device, the robot must follow the weld line in order to inspect the full circumference of the line. Basically this is made possible by rotating the robot wheels 90\" as shown from Figs. 10 (a) to (b) and climbing in the pipe. Unfortunately, the position of the robot as shown Fig. 10 (b) is not so steady in terms of vibrations and acceleration. To overcome this problem, the robot body is angled as shown in Fig. 10 (c) for a more steady posture that allows travel in the circumferential direction. 5 Development of the prototype A prototype has been built featuring the newly developed devices described above. Measuring 410 mm long overall, 90 mm wide, and 140 mm height, the robot is able to navigate narrow pathways like valve locations and can negotiate obstacles like plug valves. The bottom as well as the front and rear sections of the robot are cut down as shown in Figs. 11 and 12 in order for it to travel through L-shaped pipes measuring 150 mm in diameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure5-1.png",
        "caption": "Fig. 5. A 6-DOF hybrid-chain manipulator.",
        "texts": [
            " Reciprocal screws have been used by di erent authors to obtain input-output velocity equations of parallel and hybrid-chain manipulators [5], [13\u00b115]. A similar approach can be used for general closed-loop mechanisms: by multiplying the twist equation for each loop by one or more reciprocal screws part of the passive velocities are eliminated. However, if the reciprocal screws are not chosen in a correct way, the resulting equation may no longer be a necessary and su cient condition and would not be suitable for singularity analysis [15]. 5. EXAMPLE To illustrate the above techniques, herein, the singularities of the mechanism shown in Fig. 5 are identi\u00aeed. This is a 6-DOF platform manipulator with an asymmetric distribution of the actuated joints (\u00aerst described in [16]). The output link (the end-e ector) is the moving platform ABC, the six input joints are: the \u00aerst three joints of sub-chain A, the second and third joint in subchain B and third joint in subchain C. The base AoBoCo and the moving platform are equilateral triangles with sides AB = AoBo=a. The two non-zero links in each serial subchain have the same length, l. It is assumed that 2 l/ 3 p EaE2l",
            " From Equation (7) it can be deduced that rank L = rank L\u00c3 +6 (and, therefore, rank L=rank L\u00c3 \u00ff 3), where L\u00c3 is the 12 18 matrix, L\u0302 JA \u00ffJB O O JB \u00ffJC ; 10 Above, JP are the 6 6 sub-chain Jacobians. From Equation (9), it follows that rank Lp=rank L\u00c3 p, where L\u00c3 p is the 6 6 matrix, L\u0302p mB 1 0 0 0 mC 1 mC 2 : 11 Also from (9), the rank of L can be expressed by the matrix L\u00c3 I, L\u0302I ~b mB 1 0 0 ~c 0 mC 1 mC 2 ; 12 for which: rank LI=rank L\u00c3 I+3 Finally, rank LO=rank L\u00c3 O, where L\u00c3 O is obtained by rearranging the columns of LO, LO diag MA 123;M B 123;M C 123 : 13 Thus, the conditions from Section 2.3 can be expressed for the mechanism in Fig. 5 in terms of the matrices from Equations (10)\u00b1(13) as follows: (i) q $ {RI}\\ rank L\u00c3 O<rank L\u00c3 p+6, (ii) q $ {RO}\\ rank L\u00c3 I<rank L\u00c3 p+3, (iii) q $ {RPM}\\ rank L\u00c3 p<3. (iv) q $ {II}\\ rank L\u00c3 I<rank L\u00c3 \u00ff6, (v) q $ {IO}\\ rank L\u00c3 O<rank L\u00c3 \u00ff3, (vi) q $ {IIM}\\ rank L\u00c3 <12, (vii) q $ {RO} or q $ {RPM}\\ q $ {II} or q $ {IIM}\\L\u00c3 I is singular, (viii) q $ {RI} or q $ {RPM}\\ q $ {IO} or q $ {IIM}\\L\u00c3 O is singular. 5.3.1. Summary. We apply the identi\u00aecation algorithm from Section 3.2 to the mechanism in Fig. 5 using conditions (i)\u00b1(viii) listed above in Section 5.2. At each step, the conditions are resolved through geometric analysis of the screws composing the corresponding matrices. The singularities obtained are summarized in Table 2. In the table, for each singularity class, it is denoted whether the class is non-empty (YES) or empty (NO), the steps in which the singularities of the class are obtained (or it is proven that the class is empty), and the \u00aegure that shows a representative con\u00aeguration of the class"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.9-1.png",
        "caption": "Figure 4.9. Clearance at the root circle of gear 1.",
        "texts": [
            " In order to avoid this possibility, a gear pair must be designed with adaquate clearances at each root circle. The clearance c 1 at the root circle of gear 1 was defined in Equation (3.67) as the difference between the dedendum of gear 1 and the addendum of gear 2, (4.24) By expressing a p2 and bP1 in terms of the radi i of the corresponding tip circle, pitch circle and root circle, we can show that the clearance at the root circle of gear 1 is equal to the amount by which the tooth tips of gear 2 clear Backlash 97 the root circle of gear 1, as shown in Figure 4.9. C-Rroot1-RT2 (4.25) We stated in Equation (3.70) that a value of 0.25 modules is the recommended minimum for the clearance at each root circle. One of the reasons for this recommendation is to help avoid the possibility of interference. The designer of a gear pair should therefore ensure that the clearances are adaquate, as well as checking that the conditions for no interference are satisfied. In practice, interference is more likely to occur at the fillets of the pinion than at those of the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure4-17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure4-17-1.png",
        "caption": "Figure 4-17 Construction of a one-dimensional return map in a three-dimensional phase space.",
        "texts": [
            " This is because VL = -<p, where <p is the magnetic flux in the inductor, and <p = <p(/), so Experimental Poincare Maps 139 that when <p = 0, the flux is at a maximum or minimum. The Poincare map is then a collection of pairs of points (Vsn, ILn) which can be displayed on a storage or digital oscilloscope. Construction of One-Dimensional Maps from Multidimensional Attractors There are a number of physical and numerical examples where the attracting set appears to have a sheetlike behavior in some three-dimensional phase space as illustrated in Figure 4-17. [The Lorenz equations (1-3.9) are such an example.] This often means that a Poincare section, obtained by measuring the sequence of points that pierce a plane transverse to the attractor, will appear as a set of points along some one-dimensional line. This suggests that if one could parameterize these points along the line by a 140 Experimental Poincare Maps 141 variable x, it would be possible that a function exists that relates xn+l and xn: *\u201e + !=/(*\u201e) The function (called a return map) may be found by simply plotting xn+l versus xn"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000593_j.msea.2021.141384-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000593_j.msea.2021.141384-Figure3-1.png",
        "caption": "Fig. 3. Dimensions of tensile bars (a: SLM b: EBM c: Mill-annealed).",
        "texts": [
            "1% was employed to prevent from detrimental oxidation and lessen severe evaporation during the entire building process. Ti\u20136Al\u20134V plate with a thickness of 10 mm was commercially available under mill-annealed condition. The last processing steps involve hot-rolling and subsequently annealed at 750 \u25e6C for 1 h. The actual chemical compositions of the testing samples were examined using XRF (ZSX-100e) at the condition in Table 2. The SLMed and EBMed bars were vertically fabricated based on the tensile testing design. The dog bone-shaped dimensions were shown in Fig. 3a and b for the SLMed and EBMed tensile samples, respectively. Three tensile bars for each additive manufactured alloy were used to determine the mechanical properties. Two tensile testing samples with the dimensions as given in Fig. 3c were cut from the mill-annealed Ti\u20136Al\u20134V alloy plate by electrical discharge machining (EDM). All the samples are machined to improve surface finish before the tensile test. The tensile loading direction is parallel to the build direction (BD) for the additive manufactured samples and the rolling direction (RD) for the mill-annealed Ti\u20136Al\u20134V alloy samples, respectively. The yield strength, ultimate strength, and elongation percentage were measured by the tensile tests, which were carried out on a universal testing machine (Instron 5969) with a cross-head velocity of 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000967_j.optlastec.2021.107161-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000967_j.optlastec.2021.107161-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of acoustic emission signal propagation.",
        "texts": [
            " However, the strength of acoustic emission signal of many materials is very weak, which cannot be heard directly by human ears, and sensitive electronic instruments are therefore needed for AE (acoustic emission) signal detection. AE detection technology possesses many advantages, including the fact that the energy detected by AE comes from the measured object itself, rather than the energy provided by the detection instrument, such as ultrasonic acquisition ray detection. In addition, AE detection technology can detect real-time continuous signals of active defects changing with time, temperature, and other factors [19,20]. The propagation process of AE signals in the medium is shown in Fig. 2. Material and shape of a component will have different influences on the attenuation of AE signal amplitude. For components with regular shape and uniform material, the propagation law [21] of AE signals can be described by Eq.(1) A = A0exp ( \u2212 \u03c0f VQ d ) (1) where A0 is the amplitude of the source, f is the frequency, V is the propagation velocity, d the propagation distance, and Q the quality factor of the material(it is related to the constitutive equation of dielectric materials, which is generally obtained by experiment)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003682_j.matdes.2007.01.023-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003682_j.matdes.2007.01.023-Figure2-1.png",
        "caption": "Fig. 2. Scheme of a typical laser track with its main geometric characteristics: clad height H; clad width W and depth penetration p.",
        "texts": [
            " The powder used in the experiments was the commercial nickel alloy \u2018\u2018diamalloy 2002\u2019\u2019 supplied by Sulzer Metco , whose characteristics and chemical composition are listed in Table 2. After the tests the samples were sectioned transverse by (Fig. 1) to the clad track and polished successively with SiC paper with several granulometries in water. The samples were then etched with Nital (2%). The geometry of the clad track was studied by shop microscopy, with 30\u00b7 magnification and 1 lm resolution. Fig. 2 shows the scheme with a typical cross section of one laser track and defines the main geometrical quantities usually used for laser track characterization: clad height (H), clad width (W) and depth penetration (p). A plan of experiments with 27 tests was performed with the purpose of evaluating the processing parameters laser power (P), the second column is the scanning velocity (V), the fifth is the powder mass flow rate (C) under the geometric form of clad (clad height (H), clad width (W) and depth penetration (p)) and establishing the multiple regression analysis between these parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure8-15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure8-15-1.png",
        "caption": "Figure 8-15. Definition of shape factor",
        "texts": [],
        "surrounding_texts": [
            "applied to the circular faces. There are, in theory, two conditions under which the test pieces can be compressed: either with perfect slippage between the rubber and the compressing members or with complete absence of slip. Generally, perfect slippage is impossible to achieve and most applications involve either rubber bonded to metal or compressed between surfaces that virtually eliminate slip. If there were perfect slippage, every element of the test piece would be subjected to the same stress and strain and a cylindrical test piece would remain a true cylinder without any barrelling. Under these conditions stress and strain are approximately related by (but see also Section 1): ^ = G ( A - - A ) = | ( A - - A ) where: F = compression force, A = initial cross-sectional area of test piece, E = Young's modulus G = shear modulus, X = ratio of compressed height to initial height. The strain expressed as a fraction of the original height is 8, so that numerically A. = 1 - s. Further approximations to the relation between stress and strains are sometimes seen:- For strains up to about 30%, ignoring third and higher powers of e: Es = E{r'^A) A \\-s For strains up to about 5%, 1-s - 1 and it reduces to: A The more usual case, both in applications and experiment, is where it is assumed that there is complete absence of slip, stress and strain are not uniform throughout the test piece and 'barrelling' takes place on compression. The pressure distribution over the flat ends of the test piece under these circumstances has been investigated by Hall\u0302 .\u0302 The relationship between stress and strain in a test piece with bonded end pieces is very dependent on the shape factor of the test piece. This is usually defined as the ratio of the loaded cross-sectional area to the total force-free area (Figure 8.15). The larger the shape factor the more stiff the rubber appears and this property is much exploited in the design of rubber springs and mountings. Short term stress-strain properties 151 The approximate stress/strain relationship incorporating the shape factor has been expressed in several ways but perhaps the most usual is: F \u00a3 in its most general form: A 2>^ ^ E^=E(A = BS') where Ec = effective compression modulus, E = Young's modulus, F = compression force, A = initial cross-sectional area, = ratio of compressed height to initial height and S = shape factor. The shape factor, S is the ratio of the loaded area to the force free area which for a disc is: S = diameter 4 X thickness and for a rectangular block (see Figure 8.15): lb 2h{Ub)"
        ]
    },
    {
        "image_filename": "designv10_4_0003905_robot.2005.1570171-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003905_robot.2005.1570171-Figure5-1.png",
        "caption": "Fig. 5. Outlook of rotary-type soft actuator.",
        "texts": [
            " The both sides with length 50[mm] from the end are reinforced for inhibiting axial expansion. The bending side at center part of bellows with length 60[mm] is reinforced. Since the other side of the bellows expands to the (a) Palm side (b) Arm side Fig. 3. Shape of appliance. axial direction by reinforcement at the only bending side, this actuator bends circumferentially when the compressed air is supplied into the actuator. The part between the bending and fixed parts of the bellows is not reinforced for releasing the palm appliance. Fig.5 shows the outlook of actuator. Depending on the reinforcement of bellows, when the compressed air is supplied to the actuator, the actuator expands to the axial direction as shown in Fig.5(b). Fig.6 shows the size of the rotary-type soft actuator used for type II. The outer and inner diameter and length of rubber tube are 16, 12, 180[mm], respectively. The outer and inner diameter of polyester bellows are 28, 22, respectively The both sides of the bellows with length 60[mm] from the end are reinforced for inhibiting axial expansion. The bending side at center part of bellows with length 60[mm] is reinforced. Fig.7 shows the fundamental characteristics of actuator. Enough bending angle \u03b4\u03b8 for assisting with human wrist can be obtained as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003571_bf01212271-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003571_bf01212271-Figure2-1.png",
        "caption": "Fig. 2. The general 1-trailer system.",
        "texts": [
            " These constraints describe a Pfaffian system of dimension 2 in five variables, I := {cos ~ dx + sin ~b dy + a cos 0 dO + a do, - s i n ~ dx + cos ~ dy + a sin 0 dO}, which is linearizable (dim 11 = 1 and dim 12 = 0). Alternatively, we could consider this Pfaffian as a driftless system with three inputs and five states (for instance, by choosing three velocities as the inputs). If we set X := x + a sin ~ cos 0 and Y:= y - a cos ~ cos O, I = {dX + a cos ~k dq~, dY + a sin ~ d~0}, and only four variables are needed. Notice that X and Y are the coordinates of the point of contact M between the hoop and the plane. Example 2 (The General 1-Trailer System). This nonholonomic system (see Fig. 2) generalizes the 1-trailer system considered in [LS] and [MS]: here the trailer is hitched to the car not directly at the center of the car rear axle, but more realistically at a distance d of this point. The two inputs are the driving velocity ul of the car's rear wheels, and the steering velocity u2 of the car's front wheels. The wheels are assumed to roll and spin without slipping. With the notation of Fig. 2, the kinematic equations are : u 1 COS 0, P = u l sin 0, ~--- U2, Ul 0 = T tan q~, 01 = ~ sin(0 - 01) - 7 tan q~ cos(0 - 01) 9 By Theorem 7, the system is feedback linearizable: notice [f2, [ f l , f2]] is collinear to [f t , f2], hence E2 = { fD f2, [ f l , f2], [ f l , [ f l , f2]]} and has dimension 4. This proves that the system is linearizablc. More details and computations can be found in [RFLM]. This is no longer true when there is more than one trailer [RFLM]: notice the difference with the standard n-trailer system (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000567_tro.2020.3000290-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000567_tro.2020.3000290-Figure3-1.png",
        "caption": "Fig. 3. CTR sketch is annotated to describe the PDE boundary value problem. A main contribution of this article is deriving the equations of motion for a concentric tube collection (13), and a simplified set of PDEs (18) is obtained under the assumption that tubes are held straight below the base.",
        "texts": [
            " Note that the linear velocity of points along the robot is still included with appropriate Coriolis effects arising from the rotating reference frame. 7) Frictional energy dissipation is described by a conventional Coulomb-plus-viscous model applied at points where tubes abruptly change curvature or terminate. 8) A linear constitutive law is assumed to relate internal moment to the curvature and torsion variables; however, the overall model is still geometrically nonlinear, and a nonlinear material law could easily be accommodated in the framework. Let there be N inextensible tubes. As shown in Fig. 3, the arc length parameter s is defined so that pi(t, 0) = 0 is the fixed location of a constraining baseplate hole through which all tubes pass. An actuator translation \u03b2i is defined so that the global position of the ith tube base is [0 0 \u03b2i(t)] . Note that \u03b2i will be a negative number since the actuators are behind the baseplate. Each tube has a total length of li. Note that our convention of prescribing s = 0 at the baseplate means that a particular value of the parameter swill describe different material tube points over time since the tubes can slide in and out of the base plate as they are actuated",
            " After a few more algebraic steps, we can finally extract x and y components of mb s as \u2202mb xy \u2202s = {\u2212u\u03021m b \u2212 e\u03023R 1n+ (\u03c1I)\u03c91,t } xy + [ \u03c91,y \u2212\u03c91,x ] N \u2211 i=1 \u03c1iIi(\u03c91,z + \u03b3i) (12) where (\u03c1I) = \u2211N i=1 \u03c1iIi. Pulling together all the results in this section, we can succinctly state the set of PDEs for a concentric tube system in the form of a first-order vector system ys = f (y,yt) where the state vector y contains state variables p, R, q, \u03c9, n, mb xy , mb 1,z , and mb i,z , \u03b8i, and \u03b3i for i \u2208 [2 N ], as shown in Fig. 3. The full system can be summarized as ps = R1e3 R1,s = R1u\u03021 q1,s = \u2212u\u03021q1 + \u03c9\u03021e3 Authorized licensed use limited to: Carleton University. Downloaded on August 03,2020 at 23:45:05 UTC from IEEE Xplore. Restrictions apply. \u03c91,s = u1,t \u2212 u\u03021\u03c91 ns = \u2212f +R1 ( \u03c9\u03021q1 + q1,t ) (\u03c1A) \u2202mb xy \u2202s = {\u2212u\u03021m b \u2212 e\u03023R 1n+ (\u03c1I)\u03c91,t } xy + [ \u03c91,y \u2212\u03c91,x ]( (\u03c1I)\u03c91,z + N \u2211 i=1 \u03c1iIi\u03b3i ) \u2202mb i,z \u2202s = \u2212e 3 u\u0302im b i + 2\u03c1iIi (\u03c91,z,t + \u03b3i,t) \u03b8i,s = ui,z \u2212 u1,z \u03b3i,s = ui,z,t \u2212 u1,z,t. (13) This system is analogous to the classical PDEs for a single rod in (1), but it accounts for multiple concentric tubes",
            " The friction torque between tube 1 and tube 2 is then applied to each tube in opposite directions leading to the following transition conditions at s: mb 1,z(s +) = mb 1,z(s \u2212)\u2212 \u03c4f mb 2,z(s +) = mb 2,z(s \u2212) + \u03c4f . (23) Authorized licensed use limited to: Carleton University. Downloaded on August 03,2020 at 23:45:05 UTC from IEEE Xplore. Restrictions apply. To apply friction at the point where the outer tube terminates, the boundary condition in (20) is re-written as Mz(t)\u2212mb 2,z(t, \u03b22 + l2)\u2212 \u03c4f = H2,zz\u03c92,z,t mb 1,z((\u03b22 + l2) +) = mb 1,z((\u03b22 + l2) \u2212)\u2212 \u03c4f . Friction also occurs at the point where the outer tube passes through a hole in the base plate (see Fig. 3). This introduces another frictional torque on the outer tube, given by \u03c4base = \u03bc\u2032 base \u2225 \u2225mb xy(0) \u2225 \u2225 sig(\u03c92z(0)) + \u03bdbase\u03c92z(0) mb 2,z(0 +) = mb 2,z(0 \u2212) + \u03c4f (0) + \u03c4base. (24) Note that frictional forces between the tubes may also be present in the axial direction. While these forces are significant, they do not significantly affect the robot shape because of the axial stiffness of the tubes and their concentric constraints. No shape hysteresis is observed when translating the tubes relative to one another",
            " Let the states over the whole grid be joined in a state vector defined as Y = [ y 1 y 2 \u00b7 \u00b7 \u00b7 y N ] , then a vector containing the residual errors of the differential equations may be expressed as E(Y ) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 y2\u2212y1 s2\u2212s1 \u2212 f( s1+s2 2 , y1+y2 2 ) y3\u2212y2 s3\u2212s2 \u2212 f( s2+s3 2 , y2+y3 2 ) ... yN\u2212yN\u22121 sN\u2212sN\u22121 \u2212 f( sN\u22121+sN 2 , yN\u22121+yN 2 ) \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 . (25) The boundary conditions are strongly satisfied so that some elements of y are specified. Note that the the concentric tube problem involves the concatenation of systems (1), (13), and (18), as shown in Fig. 3. We use a Levenberg\u2013Marquardt algorithm to solve the nonlinear system so that \u2016E\u20162 < 10\u22129, using standard SI units for all variables. The time discretization is implemented using BDF2 [48] which, in the context of (15), has nonzero coefficients c0 = 3/(2\u0394t), c1 = \u22122/\u0394t, and c2 = 1/(2\u0394t). The Jacobian of the aforementioned system is sparse (in fact, tridiagonal), so we use sparse matrix data structures and sparse linear solving routines implemented in C++ using the matrix library Eigen [49]. The Jacobian is calculated by first-order finite differences with appropriately chosen increments for the magnitudes of the variables"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003185_j.automatica.2004.11.002-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003185_j.automatica.2004.11.002-Figure3-1.png",
        "caption": "Fig. 3. The LPRS and oscillations analysis.",
        "texts": [
            " If we derive the function that satisfies the above requirements we will be able to obtain exact values of the frequency of the oscillations and of the equivalent gain. Let us call the function J ( ) defined above as well as its plot on the complex plane (with the frequency varied) the locus of a perturbed relay system (LPRS). Suppose, we have computed the LPRS of a given system. Then (like in the DF analysis) we are able to determine the frequency of the oscillations and the equivalent gain kn (Fig. 3). The point of intersection of the LPRS and of the straight line, which lies at the distance b/(4c) below (if b > 0) or above (if b < 0) the horizontal axis and parallel to it (line \u201c\u2212 b/4c\u201d) offers computing the frequency of the oscillations and the equivalent gain kn of the relay. According to (4), the frequency of the oscillations can be computed by solving the equation Im J ( ) = \u2212 b/(4c) (5) (i.e. y(0) = \u2212b is the condition of the relay switch) and the gain kn can be computed as kn = \u22121/(2Re J ( )) (6) that is a result of the definition of the LPRS",
            " This formula can be used for linear parts containing a dead time J ( ) = \u221e\u2211 k=1 (\u22121)k+1 ReWl(k ) + j \u221e\u2211 k=1 ImWl[(2k \u2212 1) ]/(2k \u2212 1). (17) It can be easily shown that series (17) converges for every strictly proper transfer function. With the formulas of the LPRS derived, an input\u2013output analysis can be done in the same manner as with the use of the DF method. Main result of this paper is, therefore, a method of solution of the periodic and input\u2013output problems for relay servo systems (formulas (5) and (6) and Fig. 3) that involves a new frequency-domain characteristic of the linear part\u2014the LPRS (formulas (16) and (17))\u2014and does not require involvement of the filtering hypothesis. Consider an example of the input\u2013output analysis of the electro-pneumatic relay servomechanism (Fig. 4), which represents the first step in the servomechanism design that was carried out (Boiko, 2000). The specified bandwidth of the input signal is [1Hz, 8Hz] ( \u2208 [=6.28 rad/s, 50.2 rad/s]) with the maximum amplitude of the input Amax=1V"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000958_tie.2021.3068674-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000958_tie.2021.3068674-Figure13-1.png",
        "caption": "Fig. 13 Torque generation mechanism of FSPM machines",
        "texts": [
            " where six kinds of dominant harmonics are defined with the PPN of |Ppm-Pr|, Ppm, Ppm+Pr, |3Ppm-Pr|, 3Ppm, and 3Ppm+Pr and the sum of harmonic torques generated by these harmonics of four machines covers at least 98% of the total torque. In addition, the harmonic with the PPN of |3Ppm-Pr| is the main source of the negative harmonic torque. According to the above analysis, the electromagnetic torque generation mechanism of a FSPM machine with arbitrary stator slot/rotor pole combinations is summarized in Fig. 13. Firstly, the energized winding and PM array of FSPM machines establish primitive air-gap armature MMF and PM MMF, respectively. Then, the stator and the rotating rotor act as modulators to modulate the primitive air-gap MMFs, and the resultant air-gap flux densities contain fruitful harmonics. The rotor modulation effect working on the magnetic circuit can be regarded as a series of FMR rotors for the corresponding eigen-magnetic circuits. Only when |mPw\u00b1vPr|=Ppm, mrvMfm\u2260 0, and \u03c9e=Pr\u03c9r are met, the armature flux density has the harmonics with the same PPN and electrical speed as the dominant harmonics of the PM flux density and the FMR rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000666_j.addma.2021.102068-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000666_j.addma.2021.102068-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic presentation of a plastic injection mold machine, (b) disassembled mold presenting the conventionally fabricated 420 (brown) and additively manufactured Corrax (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " Corrax is an ultrahigh strength Mo-added maraging stainless steel with much less Ni < 10 wt% compared to typical maraging steels. The lower Ni level reduces the formation of reverted austenite, while the addition of Mo enhances the corrosion resistance, and the low carbon content enables crack free additive manufacturing of this stainless steel grade. The goal of this work is to introduce a cost-effective novel HAM 420/ Corrax for the manufacturing of complex plastic injection molding dies with superior corrosion resistance properties. Fig. 1a shows a typical plastic injection molding machine. A simple plastic injection molding die set includes core and cavity, as shown in Fig. 1b. The molten plastic is forced into the empty volume between the core and cavity to produce a part after cooling. A more complex injection molding die may include core, cavity, neck ring, core ring, gauge insert, cavity flange, etc. Currently, typical plastic injection molding dies are fabricated using 420 stainless steel and by conventional manufacturing techniques. The cooling channels are drilled in the dies; therefore, there are design limitations due to the manufacturing technology constraints",
            " One solution to this problem is to decrease the operating temperature by designing appropriate cooling channels in the dies. Studies suggest that molds with complex conformal cooling channels, which can be manufactured with HAM, would decrease the cycle time of injection molding up to 50% whilst improving plastic injection molding die life by more than 30% [37]. Furthermore, conformal cooling instead of straight water lines, which is made possible by hybrid AM, may prevent hot spots and increase the accuracy of the parts produced [38]. As presented in Fig. 1b, we suggest using 420 (brown) as the base and print Corrax (red) on 420 to enable the cost-effective manufacturing of complex molds with optimized cooling channels for higher performance and durability. In general, HAM is a process that integrates additive manufacturing and subtractive manufacturing, which can be used for rapid prototyping [39]. In the current work, we suggest fabricating plastic injection molding dies using additive manufacturing involving cooling channels and the more geometrically complex volumes of dies followed by the final shaping of the die (substrate) by subtractive manufacturing",
            " A major cause of failure in a plastic injection molding die is pitting corrosion in the cooling pathways. Pitting corrosion is a localized type of corrosion by which microscopic holes are initiated in the material. Growth of those pits can lead to the early fracture of the dies under cyclic loading, i.e. corrosion-fatigue failure, during continuous production. Since injection molding is a cost-sensitive industry, it is not applicable in practice to use expensive stainless steels such as the 3xx series with superior corrosion resistance. As shown in Fig. 1, we suggest using 420 as the base and print the core and cavity, including cooling channels using Corrax as affordable stainless steel with enhanced corrosion resistance. To examine it, we subject the 420/Corrax interface in the asbuilt condition to potentiodynamic polarization corrosion tests using 200 and 2000 ppm NaCl solution as the electrolyte. The 2000 ppm NaCl media is considered as a harshly corrosive environment. As can be seen in Fig. 12b, the size of the pits on the Corrax side is significantly smaller compared to the 420 side in the 200 ppm NaCl environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure20-1.png",
        "caption": "Fig. 20. Geometrical dimensions of a complex bracket with thin-walled support structures.",
        "texts": [
            " For those thin-walled lattice support structures of larger volume densities, the speedup will be more considerable since the simulation with all the lattice features considered will consume much longer time, while the half-size modeling utilizing the homogenized inherent strains and material properties always consumes nearly half an hour regardless of the specific volume densities. Therefore, the proposed approach is promising for wider applications of the L-PBF process. In order to show scalability of the proposed method, a complex bracket with overhang features is studied in this section. Thin-walled support structures are needed to support the overhangs in L-PBF processing of the bracket. An image of the complex part together with the support structures is shown in Fig. 20. Some geometrical dimensions are also annotated in the figure. The volume density of the thin-walled support structures is set as 0.36 which corresponds to a wall gap size of 0.5 mm. Similar to Section 5.1, the entire component is modeled through a layer-by-layer simulation where different inherent strain values are employed for the bulk solid regions and homogenized thin-walled support structures, respectively. As a preliminary study, for the component with a height of 44mm, the model is sliced into 25 layers and accordingly, a large layer activation thickness of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000079_j.rcim.2019.101916-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000079_j.rcim.2019.101916-Figure8-1.png",
        "caption": "Fig. 8. The different deposition positions in the tests (a) downhand (flat), (b) horizontal, (c) vertical-down, and (d) vertical-up.",
        "texts": [
            " The rest of welding parameters were set to the system optimal regarding different filler material, which can be found in [54]. To investigate the humping formation under different welding settings during multi-layer multi-directional WAAM, the influence of CMT welding variables, Wire Feed Speed (WFS) and Travel Speed (TS), and welding position were examined by depositing a ten-layer 100 mm thinwalled structure. In addition, the base plates were orientated vertically, so that the welding torch is perpendicular to the base plate as shown in Fig. 8. The experiments are divided into three subsections with five groups of tests, as shown in Table 2. Fig. 8 demonstrates the deposition positions, including downhand(a), horizontal(b), vertical-down(c) and vertical-up(d). Firstly, based on the observation of molten pool behaviour, the presented mechanism of humping formation was validated through depositing horizontal walls in test 1 group A. Besides, another trial in downhand position was conducted for comparison. Secondly, the effect of WFS and TS on humping formation were investigated thorough the tests in group B and C, respectively. Finally, in the practical WAAM process, the deposition path may be designed along multiple directions rather than just horizontally, and therefore the effects of gravitational force on metal flow may be different"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000664_j.jnucmat.2021.153041-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000664_j.jnucmat.2021.153041-Figure3-1.png",
        "caption": "Figure 3: Build 1. (a) As-built sample surfaces, before removal from start plate. (b) Optical micrographs of vertical sections near midline. Sample 3 is fully dense but warped.",
        "texts": [
            " The use of higher speeds (and therefore lower energy densities) 3 Figure 2: Detail of sample and support structure geometry: The dense region of interest is built on a porous support structure, which sits on an interface region of mixed W and Ti64. (Shown: Build 2, Part 2) The primary variables explored in this experiment were beam speed, focus offset, and preheat temperature. Speed was varied using the ARCAM control function Speed Function (SF), and beam size was varied using the control function Focus Offset (FO). Beam current was maintained at 21 mA and hatch spacing was maintained at 32.5 \u00b5m. Build 1 varied actual beam speed from 324 to 588 mm/s and FO from 20 to 40 mA. Fig.3a shows the resulting parts in their as-built state, Fig.3b shows optical microscopy of XZ sections taken near the center of the cuboid (midline). The resulting variations in energy density and beam size resulted in noticeable changes in geometric fidelity and porosity. Increasing spot size and decreasing speed tend to decrease porosity, but also result in the balling of the Figure 4: Build 2. (a) As-built sample surfaces, before removal from start plate. (b) Optical micrographs of vertical sections near midline. Sample 3 (bottom right) shows a region of full density atop a porous support structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000307_j.jmatprotec.2020.116970-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000307_j.jmatprotec.2020.116970-Figure1-1.png",
        "caption": "Fig. 1. (a) Tensile Sample, (b) Hexagonal Structure, (c) Tensile Sample Locations.",
        "texts": [
            " Feldhausen et al. Journal of Materials Processing Tech. 290 (2021) 116970 Fabrication of the hexagonal geometry was performed using a Mazak VC500A/5x AM hot wire deposition system. This system has 5-axis machining capability integrated with laser hot-wire fed directed energy deposition. A 1.14 mm (0.045\u2032\u2032) diameter 316 L stainless steel wire was used to fabricate the component. Argon was used as a local shielding gas with a volumetric flow rate of 21.2 L per minute. The hexagonal structure, as shown in Fig. 1, is dimensioned such that it can be used to produce tensile samples conforming to the ASTM E8/E8M-16a standard for tension testing of metallic materials (Standard 2016 ASTM E8 / E8M-16e1, 2016). Tensile specimens were produced in both horizontal and vertical orientations to characterize mechanical properties between and along the additively manufactured layers. Table 3 details the parametric evaluation. Two machining sequences were selected: one sequence where the component will be machined directly after deposition while it is still hot, and one sequence where the component is allowed to naturally cool before machining"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.3-1.png",
        "caption": "Figure 4.3. A gear pair, with two pairs of teeth in contact.",
        "texts": [
            "6) In these equations, circles, Rb1 and Rb2 operating pressure Equation (3.44), 2 2 Rb2 tan t/I - v'(RT2 -Rb2 ) (4. ?) RT1 and RT2 are the radii of the are the base circle radii, and t/I is angle of the gear pair, given tip the by cos t/I (4.8) The final expression for the contact ratio, which is the one generally used to calculate its value, is found by expressing the contact length as the difference between the s coordinates of points T1 and T2 , and then substituting into Equa t ion (4. 5) , (4.9) Contact Ratio 87 A pair of meshing gears is shown in Figure 4.3, in positions such that there is one pair of teeth in contact near T l' and a second pair near T2\u2022 The contact points lie, as always, on the path of contact between Tl and T2\u2022 In order that there should be two simultaneous contact points, the distance between the contact points must of course be less than the length ~sc of the path of contact. The distance between the contact points is the same as the distance between a pair of adjacent tooth profiles of either gear, measured along the common normal, and we showed in Chapter 2 that this distance is equal to the base pitch Pb' At the beginning of the present chapter, we pointed out that there must be parts of each meshing cycle during which two pairs of teeth are in contact. We have now shown that this requirement will be met, provided the length ~sc of the path of contact is greater than the base pitch Pb' This condition implies, as we can see from Equation ~4.5), that the value of the contact ratio must be greater than 1.0. It is possible to imagine a set of points, spaced at 88 Contact Ratio, Interference and Backlash intervals of Pb along the common tangent to the base circles, as shown in Figure 4.3, and moving upwards along that line as the gears rotate. The points within the line segment from T2 to T 1 would represent the contact points between the gears. At any particular instant, there might be either one or two such points within this interval, but over a period of time the average number of points in the interval would be equal.to the length asc of the interval, divided by the distance Pb between the points. Since this quantity is exactly equal to the contact ratio, as it is represented by Equation (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003824_physreve.74.031915-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003824_physreve.74.031915-Figure2-1.png",
        "caption": "FIG. 2. Sketch of the interaction of two microtubules, S is the distance from the motor to the center point of microtubule.",
        "texts": [
            " Collision rules Here we specify these rules by integrating the equations of motion of the two tubules. This calculation is based on a number of simplifications. We assume that two infinitely rigid rods of equal length l interact with one molecular motor. We assume that the motor moves with constant speed V along the rods the results can are trivially generalized for the case of V const . To simplify the system even further, we consider a symmetric case: the distance of the motor from the center point of the rod S, \u2212l /2 S l /2 is the same for both rods; see Fig. 2. We choose the orientation of x axis along the bisector of the angle between the tubules, and we denote the angle between a tubule and a bisector note that = 2\u2212 1 /2 . Since the size of a motor 30 nm is much smaller than the length of a microtubule l 5\u201310 m , we 031915-4 consider a limit of zero motor size. Since the motor\u2019s bending elasticity is rather small, we approximate the motor by a soft spring and prescribe that the force F exerted on the tubules due to motor motion is perpendicular to the bisector of the angle between the tubules i.e., along the motor , which in the symmetric case is along the x axis; see Fig. 2. Even if the symmetry is initially broken and the force is exerted at an angle to the x axis, the force will initiate a relative displacement of the tubules in the y direction, which will shift the binding points in such a way as to restore the symmetry. The equations governing evolution of the angle between the microtubule and the bisector and the coordinates X ,Y of the center of mass of the microtubule are obtained from balance of torques and forces due to motor motion and viscous drag forces t = r \u22121S cos F , 15 tX = \u22121 cos2 + \u22121 sin2 F , 16 tY = \u22121 \u2212 \u22121 sin cos F ",
            " However, for moderate values we observed that asters and vortices become even less localized; see Fig. 9. This delocalization is because the absorbed motors advect the microtubules in the direction opposite to their orientation. Consequently, these motors move the tubules from the asters and make a small depression of density for 0 contrary to the density peak for =0, compare images in Fig. 9. Similar results were also obtained for vortices. Remarkably, the suppression of density of microtubules in the core of vortex is also observed experimentally; see Fig. 2 a in Ref. 5 . The presence of motors attached to the substrate may also explain differential rotation of vortices absent in our previous analysis. Indeed, since these motors generate net motion of individual microtubules with the velocity , they can support rotating configurations similar to those observed in the system of vibrated rods 32 . Obviously, no rotation anticipated for asters due to pure radial orientation of microtubules: the forces induced by motors attached to substrate will be compensated by \u201cpressure\u201d gradient due to redistribution of density of microtubules"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000529_j.msea.2021.141141-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000529_j.msea.2021.141141-Figure1-1.png",
        "caption": "Fig. 1. (a) Selective laser melted (SLM) AlSi10Mg samples in 0\u25e6, 15\u25e6, 45\u25e6 and 90\u25e6 building directions; (b) Rotating bending fatigue and SEM in-situ fatigue samples; (c) Microstructures of the SLM AlSi10Mg samples.",
        "texts": [
            " Finally, the variation tendencies of crack aspect ratios were measured from the RBF and in-situ fatigue sample fracture surfaces, respectively. It was an important parameter for the residual fatigue life estimations of the SLM AlSi10Mg components. In the present work, to study the effect of building directions on the fatigue performance and crack propagation behavior of the SLM AlSi10Mg alloy, RBF and SEM in-situ fatigue samples were fabricated from the SLM AlSi10Mg blocks in 0\u25e6, 15\u25e6, 45\u25e6 and 90 building directions, as shown in Fig. 1a and b. The main chemical compositions (9.70% Si, 0.45% Mg, 0.25% Fe in wt.%) and mechanical properties (elastic modulus E, 0.2% offset yield strength \u03c30.2, ultimate tensile strength \u03c3b and elongation after fracture \u03b4, as shown in Table 1) of the SLM AlSi10Mg alloys were provided by TSC Laser Technology Development (Beijing) Co., Ltd. The detail SLM process and equipment parameters were described in Ref. [9]. To reduce the negative effect of residual stress on the fatigue performance of the samples [9,20], the stress relieving anneal (SRA) process at 520 \u25e6C (2 h) was conducted for the SLM AlSi10Mg samples with furnace cooling and argon shielding gas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003957_0022-0728(88)80004-4-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003957_0022-0728(88)80004-4-Figure6-1.png",
        "caption": "Fig. 6. Cyclic voltammograms recorded at 50 mV/s in 5x10 -2 M H 2SO, saturated with oxygen. (a) PMeT-Pd electrode, Pd/PMeT-9%, average particle diameter 15 nm ; (b) PMeT electrode, deposition charge 1 C/cm2 ; (c) Pt electrode covered with a 3 .6 jig Pd deposit .",
        "texts": [
            " It was therefore interesting to use this reaction as a model to analyze the electrocatalytic properties of our modified electrodes and to correlate these properties to the factors controlling the structure of these electrodes . For this purpose, PMeT electrodes containing palladium particles of various average sizes have been characterized with regard to their activity for oxygen reduction in aqueous acidic medium, using cyclic voltammetry and rotating disk voltammetry . (It was confirmed using X-ray fluorescence spectroscopy that no contamination of the Pd by Pt occurred .) Figure 6 shows the voltammograms of PMeT and PMeT-Pd electrodes in 5 x 10 -z M H2SO4 saturated with oxygen. Comparison of the PMeT curve with that of Fig. 2 indicates that PMeT is inactive for 0 2 reduction. On the other hand, the PMeT-Pd curve shows two reduction peaks . The first peak (A) at 0.425 V(SCE) corresponds to the reduction of the oxide layer formed at the surface of the metal, and the second peak (B) at 0.320 V(SCE), which appears only in the presence of oxygen, corresponds to its reduction "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003003_1.1320821-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003003_1.1320821-Figure4-1.png",
        "caption": "Fig. 4 Bearing force measurement system",
        "texts": [
            " and 13 mm ~helical gears! amplitude over 20 percent of the active profile. The test gears were lubricated by jet and the temperature of the oil ~ISO VG 100! in the sump was kept at 55\u00b0C. Gear, shaft and lubricant data are listed in rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 04/13/20 Table 2 and a sketch of the test rig is given in Fig. 3. Bearing forces were sensed by four three-dimensional piezoelectric transducers mounted between the test stand base and the bearing pedestals ~Fig. 4!. Figures 5, 6 and 7 show the measured and simulated bearing forces on the input and output shafts for spur and helical gears ~bearing labels are given in Fig. 3!. Simulations were performed in the following conditions: i! no friction, ii! a constant friction coefficient of 0.1, iii! using the formula of Benedict and Kelley @6# and iv! the formula proposed by Kelley and Lemanski @20#. A number of significant observations can be made: ~a! the influence of tooth friction on bearing forces at low speeds is certainly non negligible particularly in the s\u0304 direction ~horizontal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000175_j.matdes.2020.109185-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000175_j.matdes.2020.109185-Figure14-1.png",
        "caption": "Fig. 14. Schematic of the inactive elements model and the relatively lower temper",
        "texts": [
            " The inactive elements are attributed with ordinary material properties but excluded from the structural stiffness at the beginning of the calculation [41], so that the track forming procedure can be represented by sequentially activating the designated element sets. However, since the temperature of the interface nodes is obtained by the interpolation between active and inactive elements, the interface nodal temperature will be lower than the desired value as the temperature for an inactive element is set to be zero by default(shown in Appendix Fig. 14). Such problem had been described in detail by Michaleris et al. [43] who built a 1D model to analyse the temperature calculation scheme on the node shared by two elements, active and inactive respectively. For the pure mechanical analysis proposed in this study, the heat transfer mechanism is superseded by the direct loading of the temperature, thus the inactive element method is not applicable since the temperature compensation for the interface nodes is quite knotty. In thiswork,we develop a high-fidelitymodelling approach for thermal stress by mapping the temperature profiles from the thermal-fluid model [8,44] to the mechanical model, to ensure the accuracy of the temperature profile and to incorporate the realistic geometry including both rough surfaces and internal pores and voids"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000035_j.triboint.2020.106496-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000035_j.triboint.2020.106496-Figure4-1.png",
        "caption": "Fig. 4. a) Discretization of the intermediate plane and b) final grid extruded in both directions.",
        "texts": [
            " The plane was meshed with a Netgen algorithm [53], which uses a top-down strategy: starting from the nodes in the angles it discretizes the edges and extends the mesh towards the internal faces. The mesh creation is managed by a fast Delaunay algorithm and by a backtracking algorithm which guarantees a valid mesh. At this point, the 3D extrusion-meshing algorithm is exploited: the elements corresponding to the teeth flanks are extruded in only one direction while the remaining area is extruded in both directions (Fig. 4). The mesh is made of approximately 520,000 elements and requires about 30 s on a single-core 19.2 GFLOPS machine to be generated. As shown by Concli et al. [33], the meshing time is about 1/12th compared to the local remeshing process (with tetrahedrons) in a commercial code. The effectiveness of the presented algorithm is supported by the fact that even the complete remeshing of the gearbox domain is less computationally expensive with respect to the local remeshing in the gear boundary region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002812_a:1016559314798-Figure18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002812_a:1016559314798-Figure18-1.png",
        "caption": "Figure 18. Fourier transform of the 3R robot joint 2 velocity, for 500 cycles, versus the radial distance r and the frequency ratio \u03c9/\u03c90, for \u03c1 = 0.1 m, \u03c90 = 3 rad/sec.",
        "texts": [],
        "surrounding_texts": [
            "In the last group of experiments, after elapsing an initial transient, we calculate the Fourier transform of the robot joint velocities for a large number of cycles of circular repetitive motion with frequency \u03c90 = 3 rad/sec. Figures 17\u201323 shows the results for the 3R and 4R robots versus the radial distance r, the center of the circle, with radius \u03c1 = 0.10 m. Once more we verify that for 0 < r < rs we get a signal energy distribution along all frequencies, while for rs < r < 3 m the major part of the signal energy is concentrated at the fundamental and multiple harmonics. Moreover, the DC component, responsible for the position drift, presents distinct values, according to the radial distance r and \u03c1: |q\u0307i (\u03c9 = 0)| = a\u03c1d/(b + r)c, i = 1, 2, . . . , n. (28) Tables 6 and 7 show the values of the parameters of Equation (28) for the 3R and 4R robots, respectively. Based on these results we conclude that the velocity drift changes with the robot endeffector radial distance r. Furthermore, the DC component is \u2018induced\u2019 by the repetitive motion with a quadratic-like dependence with \u03c1."
        ]
    },
    {
        "image_filename": "designv10_4_0003195_tmag.2004.824127-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003195_tmag.2004.824127-Figure12-1.png",
        "caption": "Fig. 12. Synchronous generator with a starting cage and damper windings.",
        "texts": [
            " In all examples, the iron cores are treated as nonlinear materials. A single-phase induction motor with shaded rings is shown in Fig. 7. The ratings of the motor are 390 V, four poles, 50 Hz. The simulation is under the locked-rotor operation. Fig. 8 shows the starting torque response. The currents in the stator phase and the shaded ring are shown in Figs. 9 and 10, respectively. The distribution of typical eddy-current density in the shaded ring is shown in Fig. 11. This example is a synchronous generator with the ratings of 6 kVA, 390 V, four poles, 50 Hz (Fig. 12). The rotor has a field winding, a starting cage, and damper windings. The starting cage and damper windings are modeled as solid conductors to consider induced eddy-current effect. For the simulation of open-circuit condition each stator winding is connected with a very large resistor 10 . Then, these terminal resistors are subsequently set to zero to model the terminal fault. Fig. 13 gives the waveforms of stator phase currents. Based on the computed stator phase currents, the parameters of transient reactance , subtransient reactance , transient time constant , and subtransient time constant can be further extracted by the procedures specified in [16]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000696_tie.2021.3063869-Figure21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000696_tie.2021.3063869-Figure21-1.png",
        "caption": "Fig. 21. Test platform for electromagnetic performance.",
        "texts": [
            " For fair comparison, a prototype with skewing slots with the same machine dimensions is also made and tested. The appearance of stator and rotor of the two prototypes are shown in Fig. 19, while the silicon sheets of the conventional rotor and the proposed rotor configuration are given in Fig. 20. For the proposed rotor, two keybars are needed to facilitate assembling of the two staggered 180\u00b0 rotor segments. A commercial bench with integrated torque sensor and induction motor is used to test the prototypes, as shown in Fig. 21. The measured three-phase line back-EMF of the proposed motor at the rated speed 3000 rpm is shown in Fig. 22. Fig. 23 shows the measured three-phase current of the proposed motor under the rated load 32N\ua78fm. The measured line back-EMF of the proposed motor is compared to the FEA simulated results in Fig. 24. The measured back-EMF of the IPM motor with the proposed rotor and skewing slots at the rated speed 3000rpm are compared in Fig. 25. The measured results show that amplitude of the fundamental component of back EMF of the two prototypes are almost the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure5-1.png",
        "caption": "Fig. 5. Eight-bar mechanism.",
        "texts": [
            " Parallelogram mechanisms are distributed uniformly in the ball mechanism and are the result of the connection between two elementary four-legged platforms or that of the connection between an elementary three-legged and four-legged platforms. The mobility analysis of the ball mechanism needs decomposing the mechanism into an equatorial circular chain and into elementary platforms and parallelograms. Based on the principle of superposition, a mechanism can be decomposed into several kinematic sub-chains which possess the same mobility. This can be illustrated from a particular eight-bar mechanism in Fig. 5. The mechanism is a parallelogram type integrated with two pairs of extra links which act as motion guiding linkages [19,20]. These extra links form two kinematic sub-chains. Dismantling the two sub-chains by removing two pairs of guiding links, the mechanism has the same motion. Hence, the mobility analysis can be given by decomposing the mechanism into a closed loop and two sub-kinematic chains. The mobility of the closed loop can hence be obtained and is the same as that of the whole mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000377_j.triboint.2020.106322-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000377_j.triboint.2020.106322-Figure7-1.png",
        "caption": "Fig. 7. Datastream consisting of a series of first interface reflected pulses recorded by sensor CH1. The insert shows a magnified section showing four such pulses. As a roller passes over CH1 the reflected pulse is reduced in magnitude. Two such roller passes can be seen in this stream of data.",
        "texts": [
            " 6, the first pulse recorded is the initial excitation sent to excite the transducer. The subsequent pulses are the first, second and third reflections from the raceway-roller interface. Although not used in this work, it is interesting to observe the reflection from the opposite roller interface; the pulse has travelled through the outer raceway-roller contact and been reflected from the inner racewayroller contact. The first reflection from the raceway interface provides the best signal to noise ratio and was selected for further processing; a window was assigned over it. Fig. 7 shows the raw ultrasonic datastream consisting of an assembly of each first interface reflected pulse obtained from the sensor CH1. The datastream consists of a series of reflected pulses plotted alongside their respective capture time. Due to their rapid capture rate, the datastream forms a dense compact shape with the pulse peak amplitudes determining the bounds. A magnified view of a section of the datastream shows four reflected interface pulses with very similar pulse shape. In the data stream shown in Fig. 7 two dips in signal amplitude can be observed; these are caused by roller passes. When a roller is directly within the sensor transmission path, a portion of the ultrasonic energy is transmitted through the roller and thus causes a reduction in signal amplitude. In the gap between the roller passes, a subtle reduction in pulse amplitude can also be observed. This is a result of a change in the lubrication condition of the bearing surface and will be discussed further in x4.3. Fig. 8 shows the data processing scheme applied to the interface reflected pulses to obtain the reflection coefficient and raceway deflection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure5-1.png",
        "caption": "Fig. 5 Coordinate systems betwee",
        "texts": [
            " If the imaginary enerating gear were fed the full cutting depth without rolling, the ooth surface of the work gear would be a molded surface of the maginary generating gear, a cutting process known as \u201cformate\u201d r nongenerating. In such a nongenerating process, the cradle is ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 fixed q= c , and the speed ratio of the rotation of the cutter head and work gear is equal to the teeth ratio of the work gear and cutter head starts. Figure 5 describes the coordinate systems between the generating gear and the work gear. The coordinate system S1 x1 ,y1 ,z1 is rigidly connected to the work gear, and Se, Sf, and Sg are auxiliary coordinate systems that describe the relative motion between the generating gear and work gear. Matrices transformation from Sd to S1 gives the locus of the cutting tool r1 u, , c2, 1 = M1g 1 \u00b7 Mgf \u00b7 M fe \u00b7 Med c2 \u00b7 rd u, = M1d 1, c2 \u00b7 rd u, 12 Here Med c2 = cos c2 sin c2 0 0 \u2212 sin c2 cos c2 0 0 0 0 1 0 0 0 0 1 13 M fe = 1 0 0 0 0 1 0 Em 0 0 1 \u2212 B 0 0 0 1 14 Mgf = cos m 0 sin m \u2212 A 0 1 0 0 \u2212 sin m 0 cos m 0 0 0 0 1 15 M1g 1 = 1 0 0 0 0 cos 1 \u2212 sin 1 0 0 sin 1 cos 1 0 0 0 0 1 16 where c2 is the secondary cradle rotation angle for the generating motion, Em is the vertical offset, B is the sliding base feed setting, m is the machine root angle, A is the increment of machine center to back, and 1 is the rotation angle of the work gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003584_we.173-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003584_we.173-Figure13-1.png",
        "caption": "Figure 13. Rigid multibody model of the complete drive train",
        "texts": [
            " The categorization presented in subsection two of section two for a planetary system is used, but an extra category of out-of-plane modes is introduced, since the out-of-plane motion is not fixed here. The relevance of the out-of-plane modes is indicated by the fact that they lie in the same frequency range as the other modes, which could interfere with the range of e.g. the gear mesh excitations. Furthermore, these excitations imply out-of-plane forces because of the helix angle, which enables energy input in the out-of-plane modes. This subsection discusses the analysis of the complete drive train with a purely torsional and a rigid multibody model. Figure 13 shows the latter model, which demonstrates the layout of the drive train. 1. The low-speed planetary gear stage consists of three planets and its ring wheel is fixed to the gearbox housing. The wind turbine\u2019s rotor is considered rigid and its large inertia is added to the inertia of the planet carrier, which can rotate freely. The helix angle of this stage is zero and its sun is connected to the planet carrier of the second planetary stage through an appropriate stiffness matrix. 2. The high-speed planetary stage was presented and investigated separately in subsection two"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002863_978-94-011-4120-8_32-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002863_978-94-011-4120-8_32-Figure1-1.png",
        "caption": "Figure 1. Orthoglide general architecture Figure 2. Leg kinematics",
        "texts": [
            " A hybrid paralle1fserial PKM with three parallel inclined linear joints and a two-axis wrist is the GEORGE V (IFW Uni Hanover). To be complete, one should add the ECLIPSE machining center which does not fall into the aforementioned two PKM families. This is a 6-DOF over actuated machine with three vertical struts which can move independently on an horizontal circular prismatic joint. The orthoglide presented in this paper belongs to the family of 3-axis translational PKM with variable foot points and fixed length struts (figure 1). This machine has three parallel PRPaR identical chains (where P, R and Pa stands for Prisinatic, Revolute and Parallelogram joint, respectively). Figure 2 shows the kinematics of each leg. The actuated joints are the three orthogonal linear joints. These joints can be actuated by means of linear motors or by conventional rotary motors with ball screws. The output body is connected to the prismatic joints through a set of three parallelograms, so that it can move only in translation (note that two parallelograms would be enough)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.10-1.png",
        "caption": "Figure 2.10. Tooth profile tangent at radius R.",
        "texts": [
            "35) Having found the polar coordinate 8R of point A, we can immediately write down an expression for the tooth thickness at radius R, In order to find a relation between the thicknesses at any two radii R1 and R2, we use Equation twice to write down the tooth thicknesses tR and tR ' h 1 \" b h ,1 2 t en e lmlnate ts etween t e two expressIons, tR tR = R2[r + 2(inv 'R - inv'R )] 2 1 1 2 (2.36) tooth (2.36) and we (2.37) where 'R and /fiR are the prof ile angles at the two radi i. 1 2 44 Tooth Profi Ie of an I nvol ute Gear There is another quantity which will be useful in the description of a gear tooth profile, in particular in Chapter 11, where we discuss the tooth strength of a gear. We define an angle YR, as shown in Figure 2.10, as the angle between the profile tangent at point A and the tooth center-line, which coincides with the x axis. Since line CE in Figure 2.10 is parallel to the profile tangen~ at A, the angle between CE and the x axis is equal to YR' and we can therefore express YR as follows, (2.38) We replace 8R by the expression given in Equation (2.35), and the equation for YR then takes the following form, Standard Basic Rack Forms 45 and bs between these circles and the standard pi tch circle are called the addendum and the dedendum, and for this reason the tip and root circles are also called the addendum and dedendum circles. The sum of the addendum and the dedendum is known as the whole depth of the gear teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002908_jsvi.1999.2264-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002908_jsvi.1999.2264-Figure1-1.png",
        "caption": "Figure 1. Non-linear model of a geared rotor-bearing system.",
        "texts": [
            " The Jacobian matrix and the residue vector arising in the IHB formulations are derived explicitly. In addition to the familiar period doubling bifurcation scenario leading to chaos, in this example, a quasiperiodic route to chaos is also observed which occurs through an initial Hopf bifurcation. The periodic, subharmonic solutions and the bifurcation points obtained by the IHB method compare very well with the results obtained by numerical integration. The geared rotor-bearing model considered in this study is shown in Figure 1(a). The model is essentially the same as considered by Kahraman and Singh [2]. The same model was also considered by numerical integration and the IHB method by the \"rst author [3] for the system without parametric excitation. In this model, friction forces at the mesh point are assumed to be negligible. Because of this the transverse vibrations along the directions of pressure line and the vibrations along the direction perpendicular to the pressure line are uncoupled. Bearings and shafts that support the gears are represented by equivalent damping and non-linear sti!ness elements as shown in Figure 1. The damping elements are characterized by linear viscous damping coe$cients c 1 and c 2 , and the non-linear sti!ness elements are de\"ned by non-linear force}displacement functions f 1 and f 2 with corresponding scaling constants k 1 and k 2 . The e!ect of the prime mover and the load inertias are not considered. Also it is assumed that the system is symmetric about the plane of the gears and that the axial motion parallel to the shafts is negligible. A high-frequency internal excitation arising out of static transmission error is included in the equations of motion",
            " The displacement force relation at the bearings is taken as linear in the current study but the algorithm presented is more general and can be used to get the solution by including the bearing non-linearities together with gear mesh clearance. In the present analysis at the gear mesh displacement force relationship is taken as clearance-type dead space functions with backlash 2b h which is piecewise linear and can be written as f h (p)\"G p(q)!b h /b c , 0 p(q)#b h /b c , p(q)'b h /b c , !b h /b c )p(q) b h /b c , p(q)(!b h /b c . (8) The value of b h /b c in the present study is taken as unity. This function is shown in Figure 1(b). Consider the set of non-linear ordinary di!erential equations (ODE) representing the non-linear dynamical system of the following general form: f(xK , x5 , x, F, X, h)\"0. (9) In this vector equation, x\"x(h) is the response of the non-linear system, or in general, the dependent variable vector, F is the vector of amplitudes of external harmonic excitations, X represents a set of non-dimensional frequencies of relevance (non-dimensionalized with respect to a reference frequence), h is a nondimensional time and the number of overdots represents the order of di"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003618_j.optlaseng.2005.08.005-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003618_j.optlaseng.2005.08.005-Figure2-1.png",
        "caption": "Fig. 2. The schematic arrangement of LRM.",
        "texts": [
            " In the present study, the effect of processing parameters has been studied; these were optimized and near net shape were fabricated. Then, they were machined using cubic boron nitride (CBN) tooling and ground with Al2O3 grinding wheel to meet the required dimensional accuracy and surface finish. The fabricated bushes were characterized by various mechanical and metallographic examinations. Results are compared with those produced by GTAW technique. LRM machine consists of a high power laser system integrated with beam delivery system, powder-feeding system and job/beam manipulation system. Fig. 2 presents the schematic arrangement of LRM machines. In the present experiment, laser beam was generated using a 10 kW continuous wave (CW) CO2 laser system [12] and was transferred to the fabrication point at 3- axis laser workstation [13] using a couple of water-cooled gold-coated plane mirrors and a concave mirror of 600mm radius of curvature. At fabrication point, a defocused laser beam spot of 3mm was used for powder deposition. Colmonoy-6 powder (size range: 45\u2013106 mm) was fed into the molten pool using a volumetric controlled powder feeder [14] through a co-axial powder-feeding nozzle [15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure8-11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure8-11-1.png",
        "caption": "Figure 8-11. Gavin type grips for dumb-bell tensile test pieces",
        "texts": [],
        "surrounding_texts": [
            "Short term stress-strain properties 139\nOne grip is fixed and the other attached to a crosshead which is motor driven so as to extend the test piece whilst the force is monitored by the load cell. The output of the load cell, and an extensometer (or crosshead movement), is fed to a computer.\nISO 37 refers to ISO 5843^^ for specification of the test machine. This standard was produced to avoid the need to attempt description of a complex engineering instrument in a testing standard. It is intended that all test methods using a tensile machine will refer to this document, which specifies requirements quite comprehensively, including tolerances on the measurement of force and extension.\nRings are held by a pair of pulleys mounted on roller bearings, a mechanism being provided to rotate one or both pulleys automatically during the test. It is not satisfactory to use pegs or fixed pulleys because the rubber does not readily slip over the surfaces and is therefore not uniformly stretched. However, lubricated spindles are specified in ASTM D412 to try and overcome the problem.\nDumb-bells are rather less easy to grip and considerable ingenuity has been devoted to the design of a grip that will hold the end of a dumb-bell with a pressure uniform across its width and adequate to prevent slipping, but without setting up local strains liable to cause failure. The essential design feature is that the grip should close automatically as the tension increases. A widely used and successful design is that due to Gavin shown in\nFigure 8.11.\nThe dumb-bell end is held between rollers A, the ends of which pass through slots in the members B and C; the slots in C are horizontal and those in B steeply sloping. By depressing C by hand against the spring D, the rollers are forced apart for the insertion of the dumb-bell; on release the spring pushes C up until the rollers grip the dumb-bell. During the test the tension on the dumb-bell tends to pull the rollers further up and, hence, by reason of the inwardly sloping slots, closer together, thus increasing the grip.\nAnother mechanical design is a roller closing against a flat plate and in certain extreme cases this type of grip with the dumb-bell wrapped around the roller is the most successful. The alternative to achieving self closing by a mechanical device is to use pneumatic or hydraulic grips where flat parallel faces are pushed on to the dumb-bell end under air or fluid pressure. Although more expensive, this type of grip can be very effective and convenient to use.\nRather surprisingly, lubrication of the dumb-bell ends with talc sometimes improves gripping, presumably by permitting just enough slip to equalise the gripping pressure.",
            "The test piece must be stretched smoothly at substantially constant speed and to meet this requirement the drive must have sufficient power to maintain the speed even under maximum force. The standard rate of grip separation is 500\u00b150 mm/min but this does not necessarily mean that the actual rate of strain in the test piece is being kept constant between equally close limits. If the dumb-bell slips in the grips or the loads cell has rather low stiffness, the rate of extension is less than the speed of the moving grip. In addition, with a dumb-bell, the rate of strain is not constant throughout its length. The actual strain rate in the centre narrow portion will depend on the free length of test piece between the grips, on the dumb-bell shape (especially the ratio of widths of central and end portions) and on the shape of the stress/strain curve. Hence, the strain rate in the centre portion will not always be the same in different tests or even constant during one test.\nGenerally, speed variations of \u00b110% have a negligible effect on the measured tensile strength at the effective strain rates realised in the standard test\u0302 ^ (i.e. about 650%/min for large rings and 800-1300%/min for type 1 and 2 dumb-bells). Considering the closeness of results on types 1 and 2 dumb-bells, it is probable that rather larger variations from the arbitrary standard would not be significant. However, it is possible that for thermoplastic rubbers or tests made at low temperatures there could be",
            "Short term stress-strain properties 141\ngreater sensitivity to strain rate, so it is sensible to avoid unnecessary variation. Very large changes in strain rate will affect tensile properties but there seems to have been little interest in very high rates for rubber since a falling weight driven machine for strain rates between 2.5 and 12.7 m/sec was described^ .\u0302 Measures of modulus over decades of strain rate can be obtained with dynamic tests as discussed in chapter 9.\nInstead of constant rate of traverse, it would be perfectly feasible to use a constant rate of strain testing machine for rubbers, but this complication and expense has never been considered worthwhile.\nThe days of reading force off the dial of a pendulum force measuring system are long gone (although these are still mentioned in ASTM D412) and tensile machines now use electrical force transducers that feed their signal directly to a computer. This means that there are negligible errors due to inertia or friction and the system is inherently stiff (i.e. there is little movement of the force measuring element). There is also the convenience of multiple force scales and automatic manipulation of data. The sophistication of tensile machines varies and the choice has to be one based on balancing range, accuracy, quality of construction and convenience against cost. It should be noted that increased sophistication of data manipulation does potentially introduce problems of verification of the software as computers cannot make value judgements in the same manner as a trained technician.\nISO 5893 specifies four grades of steady state accuracy and gives reference to detailed methods of verification. ISO 37 specifies Grade 2 which is \u00b12%. Although ISO 5893 considers dynamic calibration to be too difficult to specify at present, it does give recommendations to ensure that the recording system used with electrical load cells does not introduce significant inertia errors - it is not often realised that recorders may have very significant dynamic errors and, hence, lessen the inherent advantage of an 'inertialess' load cell. Modem instruments use a data capture system and a computer to store the force and displacement data in digital form.\nASTM also specifies a tolerance of \u00b1 2% on force and refers to a calibration standard for force verification of testing machines in general.\nAs with pendulum force measuring systems, the use of a ruler or a piece of string to measure elongation of dumb-bells is largely history- to the relief of technicians whose fingers were frequently stung by the recoiling halves of the test piece after rupture.\nAs long as the deflection of the load cell is insignificant, the elongation"
        ]
    },
    {
        "image_filename": "designv10_4_0000265_j.matdes.2019.108138-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000265_j.matdes.2019.108138-Figure3-1.png",
        "caption": "Fig. 3. Commercially implemented block-type support structure (blue). Frangibility is increased by the inclusion of triangular gaps (teeth) that also allow unmelted powder to escape.",
        "texts": [
            " Support structures can resist this deformation [19] both by increasing heat transfer and by physically grounding the fabricated geometry to the build platen. Frangibility is defined as \u2018the property which allows an object to break, distort, or yield at a certain impact load while absorbing minimal energy\u2019 [20]. AM support structures should be adequately frangible to allow easy removal and minimise post-processing difficulty. Frangibility of SLM support structures is improved by the inclusion of teeth (Fig. 3) which encourage fracture at the component and build platen interfaces. Support structures are commonly used to provide a frangible interface to offset the manufactured component from the build platen. This interface protects the component and platen from damage and reduces post-processing time [21]. 2.1. Specific support structures A range of support structure designs have been implemented in commercial software (Fig. 4) or proposed in academic literature (Fig. 5). These support structures have various technical attributes that are appropriate for specific applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000696_tie.2021.3063869-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000696_tie.2021.3063869-Figure1-1.png",
        "caption": "Fig. 1. Topology of the proposed machine.",
        "texts": [
            " The acceleration response on the stator core are finally calculated and compared to estimate electromagnetic vibration, indicating that the proposed rotor structure can reduce the vibration to be the same level as that using slot skewing. Two machines, i.e. the proposed machine and the conventional machine with slot skewing are prototyped. Extensive experiments are done and compared in terms of back-EMF, current, static average torque, instantaneous torque and efficiency. II. TOPOLOGY AND SIZE DETERMINATION The structure of a V-shaped IPM machine using the proposed rotor configuration is shown in Fig. 1. Compared to original rotor, the intersection angle between two magnets of one V-shaped pole is different to the others, resulting in a different pole arc to pole pitch ratio. The rotor has been segmented along the axial direction. The two segments are staggered 180 mechanical degrees. It can be seen from Fig. 2 that all the magnets have the same dimensions as the original rotor, so the total volume of magnets keep unchanged after using the proposed method. In addition to this, the two opposing segments can compensate the unbalanced magnetic pull caused by the unequal pole width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure9.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure9.6-1.png",
        "caption": "Figure 9.6. Meshing diagram of an undercut gear and a rack cutter.",
        "texts": [
            "21) To construct the entire fillet of the gear tooth, we consider a number of positions of the cutter, starting with the ur value given by Equation (9.20) and ending with the value given by Equation (9.21). We then use Equations (9.10 - 9.18) to calculate the positions of the corresponding points on the fi llet. Fillet Shape of an Undercut Gear The method described in the previous section for finding the shape of a gear tooth fillet can still be used when the gear is undercut. The meshing diagram for the gear and the cutter is shown in Figure 9.6. Since the gear is undercut, we are considering a situation in which the end point Hr of the path of contact lies below the interference point Eg \u2022 The point of the cutter tooth profile which passes through Eg is labelled AEr \u2022 The tooth profile of the undercut gear is shown in Figure 9.7. Although the shape of the involute part of the profile is already known, and it is therefore unnecessary to use the general theory described at the beginning of this chapter, it is nevertheless helpful to consider the results we would obtain if we were to do so. A typical point of the cutter tooth profile is shown as Ar in Figure 9.6. In order to use the general method, we need a relation between the coordinates xr and Yr of point Ar' and this relation can be Fillet Shape of an Undercut Gear 217 read from the diagram, - 11Tm - x t .. 4 r an \"'r (9.22) Equations (9.3-9.8) can then be used to find the position of the corresponding point A on the gear tooth profile, which is shown in Figure 9.7. We consider a sequence of points on the rack cutter tooth, starting near the root and moving towards the tip. As we move along the profile to AEr , the cutting point moves down the path of contact to Eg , and on the gear tooth the corresponding points lie on the involute, down to point B where the involute meets the base circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002841_1.1623761-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002841_1.1623761-Figure1-1.png",
        "caption": "Fig. 1 A ball screw and nut mechanism",
        "texts": [
            " The influence of differing these parameters at two contact areas is considered in this study. The drag force created by a ball moving in a viscous oil is also taken into account in the force balance. The results of ball screw\u2019s mechanical efficiency achieved by the present model are compared with those evaluated by the model of Lin et al. 003 by ASME DECEMBER 2003, Vol. 125 \u00d5 717 13 Terms of Use: http://asme.org/terms Downloaded F In the study of the kinematics and dynamics of the ball screw mechanism ~Fig. 1!, four coordinate systems are needed to describe the motion of three components and their contact behavior. The rotating coordinate system, ~x,y,z!, is fixed in space with its z axis coincident with the axis of the screw ~see Fig. 2!, even though it rotates with the same speed as the screw. The Frenet coordinate system, ~t,n,b!, is defined to describe the moving path of the ball center. The motion of a ball enables us to study the kinematics of a ball and the slip behavior arising at the contact areas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000013_j.isatra.2019.04.034-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000013_j.isatra.2019.04.034-Figure3-1.png",
        "caption": "Fig. 3. Interval type-2 Gaussian MFs.",
        "texts": [
            " The general form of the lth rule of the type-2 Takagi\u2013Sugeno\u2013Kang (TSK) fuzzy logic system can be written as: If x1 is F\u0303 l 1 and x2 is F\u0303 l 2 and . . . xn is F\u0303 l n, Than yl = G\u0303ll = 1,M (8) where: The output of type-2 fuzzy system for the rule l is represented by G\u0303l, x = [x1, x2, . . . , xn]T are the inputs, the type-2 fuzzy system of the input state k of the lth rule is represented by F\u0303 l k, and M is the number of rules. As can be seen, the rule structure of type-2 fuzzy logic system is similar to type-1 fuzzy logic system except that type-1 membership functions are replaced with their type-2 counterparts. In Fig. 3, the footprint of uncertainty of each membership function (MF) can be represented as a bounded interval in terms of the upper MF \u00b5F\u0303 ik (xk) and the lower \u00b5 F\u0303 ik (xk), where \u00b5F\u0303 ik (xk) = exp [ \u2212 1 2 ( xk \u2212 mk \u03c3k )] and \u00b5 F\u0303 ik (xk) = 0.8\u00b5F\u0303 ik (xk) (9) In fuzzy system interval type-2 using the minimum or product t-norms operations, the lth activated rule F i (x1, . . . , xn) gives us the interval that is determined by two extremes f l (x1, . . . , xn) and f l (x1, . . . , xn) [53]: F l (x1, . "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure1.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure1.4-1.png",
        "caption": "Figure 1.4. A rack and pinion.",
        "texts": [
            " However, before looking at the case of two gears meshing together, we will consider that of a gear meshing with a rack. Rack and Pinion Rack and Pinion 13 A rack is a segment of a gear whose radius is infinite. I f the number of teeth N2 of gear 2 in Figure 1.3 were extremely large, the radius of the gear would also be large, relative to the tooth size, and the teeth near the meshing area would lie almost on a straight line. In the limit, as N2 becomes infinite, the teeth would lie exactly on a straight line, as shown in Figure 1.4. When two gears mesh, the smaller of the two is called the pinion, and the larger is usually referred to as the gear. Any gear meshed with a rack is considered smaller than the rack, since the rack is part of a gear with an infinite number of teeth. Hence, it is common to speak of a rack and pinion. Whereas a gear pair is used to transmit rotary motion between shafts, a rack and pinion are used to convert rotary motion into linear, or vice-versa. One well-known application is the rack and pinion steering of many automobiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000946_s11548-020-02300-1-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000946_s11548-020-02300-1-Figure4-1.png",
        "caption": "Fig. 4 Novel coordinate systems in which the X3 axis is always parallel to the needle. a Coordinate system of the puncture robot and b coordinate system of the US image",
        "texts": [
            " In the first two types of US-guided needle insertion robotic systems (mentioned in the \u201cIntroduction\u201d section) the calibration between the US image and the needle is complicated and mainly consists of two sub-calibrations: sub-calibration between the US image and the robot-end effector, and subcalibration between the robot and the needle [19, 25]. We proposed a novel calibration method for the third type of robotic system to directly calibrate the transformation matrix between the US image and the needle-driving mechanism. Based on the movement characteristics of the puncture robot, we established a novel coordinate system for the US image and puncture robot separately by combining Cartesian and polar coordinates, as shown in Fig.\u00a04. The coordinate system of the puncture robot, which is represented as U R , consists of three coordinate axes. The X1 axis is parallel to the direction of the first DOF of the mechanism. Its coordinate value RX1 denotes the distance between the RCM of the mechanism and the origin of the coordinate system. The X2 axis is the swing angle from the vertical direction of the X1 axis to the needle orientation, and its value RX2 indicates the orientation of the needle. The X3 axis is always parallel to the needle, and its coordinate value RX3 indicates the insertion depth (the distance between the needle tip and RCM)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002841_1.1623761-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002841_1.1623761-Figure4-1.png",
        "caption": "Fig. 4 \u201ea\u2026 Ball-nut contact, \u201eb\u2026 ball-screw contact",
        "texts": [
            ", four unknowns, b, b8, vR and v t , can be achieved from numerical solutions. For example, the rotational speed of the screw is 1070 rpm, and the helical angle is 8.74 deg, the numerical solution of v t is 217 rad/sec, the b angle is 48.99 deg vR is 359.22 rad./s and the b8 angle is 24.136 deg. If the sliding behavior between a ball and the screw is taken into ac- count, the solution of b8 should be smaller than this value and is thus negligible in calculations. Since the b8 angle is so small, it can be ignored in the following study of the ball-screw mechanisms. Figure 4~a! shows the schematic diagram of a ball in contact with the nut; whereas Fig. 4~b! shows the schematic diagram of the same ball in contact with the screw. The angular velocity of the nut relative to a moving and rotating ball is defined to be vo , it points to the direction parallel to the 1-axis. The 1-axis, as shown in Fig. 4~a!, is parallel to the b-axis. At the contact area formed between a ball and the nut, there DECEMBER 2003, Vol. 125 \u00d5 721 13 Terms of Use: http://asme.org/terms Downloaded F exists a point at which it is in a state of pure rolling. This point is not necessarily the center of the contact ellipse, but is very close to this center. If the distance between this point and the ball center is ro8 , the linear velocities of the ball and the screw at this point must be equal. As Fig. 4~a! shows, the equivalence is given as: S dm 2 cos ao 1ro8Dvo cos ao52ro8~vb cos ao1vn sin ao! (22) where dm52rm ; and ao denotes the contact angle at the nut. Substituting Eq. ~14b! and Eq. ~14c! into Eq. ~22! gives the rearranged form as: vR vo 5 2S dm 2 1ro8 cos aoD ro8~cos b cos b8 cos ao1sin b sin ao! > 2S dm 2 1ro8 cos aoD ro8~cos b cos ao1sin b sin ao! (23) Similarly, there exists a point in the contact area formed between the ball and the screw, at which it is pure rolling. As Fig. 4~b! shows, the distance between this point and the ball center is defined to be ri8 . The angular velocity of the rotating screw relative to the ball is defined to be v i . Equating the linear velocities of the ball and the screw at this point gives S 2 dm 2 cos a i 1ri8Dv i cos a i52ri8~vb cos a i1vn sin a i! (24) where a i is the contact angle formed at the screw. The substitution of Eq. ~14b! and Eq. ~14c! into Eq. ~24! gives vR v i 5 2S dm 2 2ri8 cos a iD ri8~cos b cos b8 cos a i1sin b sin a i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000343_j.matdes.2020.108880-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000343_j.matdes.2020.108880-Figure1-1.png",
        "caption": "Fig. 1.Manufacturing process of SLMed Ti6Al4V alloy (a) as-received Ti6Al4V powder, (b) SLM equipment RenAM 500 M, (c1) 0\u00b0 linear scanning scheme, (c2) 90\u00b0 rotational scanning scheme, (c3) 67.5\u00b0 rotational scanning scheme and (d) the 67.5\u00b0 SLMed Ti6Al4V sample.",
        "texts": [
            " Compared to conventional annealed Ti6Al4V alloy, the influence of anisotropic microstructure and mechanical properties of SLMed Ti6Al4V alloy produced by different laser scanning strategies on themachining performance has not been investigated at present. Therefore, this paper focuses on investigating the effects of the machining surface and the laser scanning strategy on machining performance of SLMed Ti6Al4V alloys in milling. In this paper, SLMed Ti6Al4V samples fabricatedwith three different laser scanning strategies are illustrated in Fig. 1. As shown in Fig. 1 (a), the fully dense spherical Ti6Al4V powder (provided by Renishaw Corp., UK) was employed in SLM and the adhesion and agglomeration phenomena of the as-received titanium alloy powder were negligible. The detailed chemical composition of Ti6Al4V ELI-0406 (Extra Low Interstitial) powder is given in Table 1 (provided by Renishaw Corp.). Ti6Al4V ELI-0406 powder can be considered as a higher purity version of themost commonly used titanium alloy Grade 5. The SLMed titanium alloy samples were manufactured by a RenAM 500 M machine (Renishaw Corp., UK), which is equipped with a 500 W Yb-fibre laser beam, an automated powder and waste handling systems, as shown in Fig. 1 (b). To prevent titanium alloy material from being contaminated or oxidized by air during powder bed fusion, an argon inert atmosphere was maintained with b1000 ppm (0.1%) oxygen throughout the build process. The laser scanning strategy in SLM is of great significance to microstructure, mechanical property and material anisotropy of AMed components. To investigate the effect of the laser scanning strategy on machining performance of SLMed Ti6Al4V alloy, three distinct laser scanning schemes were employed to fabricate Ti6Al4V samples during continuous SLM building strategy, as illustrated in Fig. 1(c). The laser beam moved along the zigzag trajectory in each layer of the three laser scanning schemes. The laser scanning strategy for successive layers was identical or rotated by a certain angle. In the 0\u00b0 linear scanning scheme, the laser scanning vector moved back and forth in the Table 1 Chemical composition of Ti6Al4V powder for SLM. Element Ti Al V Fe O C N H Residuals Mass (%) Balance 5.50\u20136.50 3.50\u20134.50 \u22640.25 \u22640.13 \u22640.08 \u22640.05 \u22640.012 \u22640.405 horizontal plane without a laser scanning vector rotation in subsequent layers",
            "5\u00b0 in subsequent layers, respectively, which means the subsequent layers are different. In addition to different laser scanning strategies, the preparation of Ti6Al4V samples was carried out using the identical SLM parameters recommended by Renishaw: laser power of 200 W, scanning velocity of 1500mm/s, slice thickness of 30 \u03bcm, and hatch distance of 65 \u03bcm. Finally, the rectangular Ti6Al4V samples of 30mm(L) \u00d7 20mm (W) \u00d7 15 mm (H) were manufactured using 0\u00b0 linear, 90\u00b0 and 67.5\u00b0 rotational SLM process, as shown in Fig. 1(d). Moreover, annealed ASTM B265 Ti6Al4V Grade 5 was used as referencematerial in this research to evaluate the machinability of SLMed Ti6Al4V alloy. The element composition of ASTM B265 Ti6Al4V provided by the supplier is given in Table 2. In this research, all milling experiments were carried out on a CNC vertical machining centre MAKINO V55 with a maximum spindle speed of 14,000 rpm. The annealed ASTM B265 Ti6Al4V alloy samples were pre-machined to 30 mm (L) and 20 mm (W), which is the same as the SLMed Ti6Al4V samples",
            " 2(b)), which consists of a piezoelectric dynamometer 9254B, a multichannel charge amplifier 5019A, a corresponding data acquisition systemand the data processing software Dynoware. SLMed Ti6Al4V samples exhibit significant anisotropy features due to the differences inmicrostructure andmechanical properties in different directions. Thus, the machining performance on the front surface (xoz plane) and the top surface (xoy plane) of SLMed Ti6Al4V alloy samples is investigated in this research, as illustrated in Fig. 1(d). Since annealed Ti6Al4V alloy is a typical isotropic material, only machining properties on the top surface were considered. Because the postmachining of AMed components is generally deemed semi-finishing or finishing operations, the feed rate varies within a small range to ensure themachined surface quality. Since AM technology has the advantage of near-net forming, the axial depth of cut remains a small constant value to ensure a lower amount of removal. In addition, rough milling should be performed to obtain a flat and smooth surface before the designed machining experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003675_0022-0728(90)87185-m-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003675_0022-0728(90)87185-m-Figure9-1.png",
        "caption": "Fig. 9. Cyclic voltammograms of the Au electrode modified by cysteamine and naphthoquinone carboxylic derivative (see the formula in the text) using the carbodiimide technique (1) ; of a similar electrode treated by the same quinone without carbodiimide and rinsed with ethanol (2); and of the same electrode after treatment with 2,3-dichloro-1,4naphthoquinone (3). 0.01 M boric buffer, pH 9.18, potential scan rate, 0 .167 V/s .",
        "texts": [
            " The present study deals only with one of the possible variations, namely when 2-aminopropionic acid is used . An amino group reacts easily with quinone [22] . In the case with amino acids, to functionalize quinone by a carboxyl group, inorganic alkali is added to the solution 183 184 for the deprotonation of amino groups during their reaction with quinone [7]. The carbodiimide technique is used for binding the carboxyl group of this quinone with the amino group of cysteamine previously immobilized at the electrode surface : 0 P or j Au 0 . . HS- fCH2),-NH-C'-tCHpJ~ -- NH *10 Figure 9 (curve 1) shows the cyclic voltammogram for a chemically modified electrode obtained by this method . The quinone was not immobilized at the electrode in the control in the absence of carbodiimide (Fig . 9, curve 2) as a linking reagent. However, in this case the reactivity of the surface amino groups is preserved, as proved by their reaction with 2,3-dichloro-l,4-naphthoquinone (Fig . 9, curve 3). Comparison of curves I and 3 (Fig. 9) shows that naphthoquinone aminoderivatives immobilized at the electrode via spacers of various length have the same redox potential. However, the surface concentration of the quinone immobilized by the carbodiimide technique is greater than in the case of direct reaction of the quinone with the surface amino groups of cysteamine . This difference is reproduced well and indicates that not all surface amino groups can react directly with quinone and that a greater number of them is capable of carbodiimide binding "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure14-1.png",
        "caption": "Fig. 14. A horn grown from an expanding surface G by growth velocities such that all cell tracks are expanding logarithmic spirals",
        "texts": [
            " Logarithmic spirals were extensively discussed by D\u2019arcy Thompson (1942), primarily with respect to shells in which the spiral angle is constant for all points of the shell. The use of inward and outward spirals for horns as in Fig. 11 was not developed. In Fig. 11, the stippled area indicates a possible cross-section of a hollow horn. The solid tip may be produced by a change of G from a circle to a ring as growth proceeds as shown schematically in Fig. 13. Example 3.7. A curvilinear horn of flatter spirals Another example of growth of a horn is illustrated in Fig. 14. In this example, no cell track is a circle, but all cell tracks are flat logarithmic spirals, similar to a long-horn steer. Here the parameters in Eq. (54) are chosen as follows. The values in Table 2 produce the curves starting at A and B in Fig. 14. To define the rest of the horn, planes are chosen so that they intersect the curves C 1 and C 2 at equal angles. In this b 1 \"b 2 \"82.10\u00b0 in Fig. 14. Such surfaces are assumed to be generating surfaces and the cross-sections of the horn on such planes are assumed to be circles Hq which were on the generating surface Gq at earlier times. Table 2. Dimensions and constants of cell tracks in Fig. 14 Curve b (cm) a (deg) C 1 40 63.01 C 2 60 78.81 Fig. 15. Computer generated 3-D-view of the horn shown schematically in Fig. 14 The above is sufficient information to develop the full external geometry of the horn. Interior cell tracks are also assumed to be logarithmic spirals in the x 1 , x 2 plane and to be connected by circular cross-sections. A 3-D view of this horn generated by a computer program is shown in Fig. 15. The region ADB in Fig. 14 is considered to be part of the skull and is omitted in Fig. 15. Example 3.8. Horns with 3-D spirals All of the examples shown in Figs. 5\u201415 have a plane of symmetry. In this example and in Example 3.9, horns with a three dimensional spiral component will be produced by introducing tangential and asymmetric components of the growth velocity distribution. Here we consider the simplest example of this type of horn or tusk, which is straight but has several screw-like threads similar to the horn of the narwhal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000220_s00170-020-05197-x-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000220_s00170-020-05197-x-Figure5-1.png",
        "caption": "Fig. 5 Specimens placement on a building platform",
        "texts": [
            " The laser power is in the range 275\u2013325 W, the scanning speed is 655\u20131032 mm/s, the hatching step is 0.09\u20130.12 mm, the volumetric energy density (VED) is 60\u201380 J/mm3, and the layer thickness is 0.05 mm. The samples were manufactured according to the various combinations of SLM process parameters shown in Table 2. After optimal SLM process parameter determination, the cylindrical specimens were fabricated for analyzing of mechanical anisotropy that occurs during melting of this material [31]. The building angles of specimens are 0, 30, 45, 60, and 90\u00b0 (Fig. 5). To study the effect of heat treatment on the material mechanical properties, cylindrical samples were subjected to treatment in two modes. Based on the data presented in [32], the first heat treatment option (T1) was proposed, the thermogram of which is shown in Fig. 6. In the second version (T2), the standard heat treatment modes of the Inconel 738 alloy were used (Fig. 6). Heating to a temperature of 1125 \u00b0C was carried out at a rate of 35 \u00b0C/min. Exposure time for 2 h leads to the appearance of the \u03b3\u00b4 phase in the form of large particles of irregular shape, and subsequent exposure time for 24 h at a temperature of 840 \u00b0C leads to the appearance of its finely divided precipitates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.13-1.png",
        "caption": "Fig. 7.13 Geneva mechanism in a film projector",
        "texts": [
            " In 1893, W. Dickson went further to develop a film projector which was able to move the film continuously, and project the pictures one by one in sequence to the same position of a screen. A light with on and off synchronized with the film speed was used; consequently, continuous motion could be seen due to the persistence of vision. Later, it was further improved with a series of small holes punched on both sides, through which a Geneva mechanism was used to drive the film in intermittent motion (see Fig. 7.13). In 1894, Auguste Lumi\u00e8re and Louis Lumi\u00e8re, the brothers in France, developed independently the Cin\u00e9matograph, which combined a film camera and a projector. In 1895, they showed a movie in Paris publicly for the first time. In 1912, T. Edison invented sound film. Later on wide screen film and color film appeared in 1927 and 1940 respectively (Jiang 2010; Pan and Wang 2005). 172 5 Second Industrial Revolution In 1938, Chester Carlson, an America engineer, invented and patented an electrostatic copying machine (Owen 2004)",
            ", the Soviet Union, Japan and other countries, 234 7 Birth and Development of Modern Mechanical Engineering Discipline generally related to the valve mechanism in a internal combustion engine (Zhang 2009; Furman 1921; Pe\u0448e\u0442o\u0432 1934). However, the elasticity of parts was not considered in all these studies; vibration theory was not applied either. The earliest intermittent motion mechanism is the ratchet mechanism, which could only be used at very low speeds. Later, Geneva mechanisms were invented by a watchmaker in Geneva, the Swiss watch-making center, and widely used. One application is in film projectors for driving the film as shown in Fig. 7.13. It was also widely used in machine tools and light industry machines to produce 7.2 Development of Modern Mechanism Subject 235 intermittent rotation of a worktable. When designing a Geneva mechanism, once the indexing number is determined, the ratio between rotation time and stop time is determined as well, and cannot be changed any more. This feature tuned out to be a main drawback of Geneva mechanisms. A Geneva mechanism has lower vibration and noise compared with a ratchet mechanism; however, the driven wheel in Geneva mechanisms experiences sudden changes of acceleration at the starting and stopping instants, leading to severe impacts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003965_tac.2008.2010992-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003965_tac.2008.2010992-Figure4-1.png",
        "caption": "Fig. 4. Possible evolutions of the auxiliary system in Case 1.1. Note that the",
        "texts": [
            " Starting from any point in interval (23), considering that , at , the state trajectory crosses the abscissa axis, i.e., , with (24) The fact that is ensured by , while the left extreme of the interval is obtained if the auxiliary state variables starts at with , (that ensures that the control variable does not saturate), and at any time instant in the considered interval. One can verify that, imposing , and if holds, then . The possible evolutions of the auxiliary system at the described iteration is shown in Fig. 4. If the initial condition is , the proof is the same as in the foregoing case, with reversed extremes of the intervals. This ensures the contraction property. Case 1.2: Considering now a starting point with and , one has that, in any case, or , and this value is kept until the first switching time instant . From (7), (13), (15) and (16), it follows that , , that is, the trajectory of the auxiliary system moves toward the -axis an crosses it, if the control keeps its value without commutating to before the -axis is reached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000035_j.triboint.2020.106496-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000035_j.triboint.2020.106496-Figure1-1.png",
        "caption": "Fig. 1. Overview of the test rig.",
        "texts": [
            " This approach has been proven to be accurate even on complex geometries as epicyclic gears and cycloidal architecture for the prediction of flows and power losses. The details of this methodology are explained in paragraph 3.1. The goal of this paper is to validate the approach also in terms of capability to predict the micro scale flows. The standard FZG test rig is used as a base for the configuration used in the current study. The gearbox consists of two mating gears with geometrical specifications as listed in Table 1. A gear and a pinion were mounted on their respective shafts and driven by an electric motor, as shown in Fig. 1. The drive gears were replaced with a belt-driven transmission to reduce the total weight of the test rig. The torque was measured by a KISTLER torque sensor (variant number: 4503A20L00B1CD1) which in this study was mounted on the shaft of the gear, thus measuring only the torque of the gear. In order to maximize the optical access for the PIV measurements, the test box and the gears were made of transparent PMMA and the test oil was Nytex 810 from Nynas, chosen for its clear appearance. The averaged torque loss was measured for several speed steps (250 \ufffd 2000 RPM)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000972_s11694-021-01032-3-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000972_s11694-021-01032-3-Figure2-1.png",
        "caption": "Fig. 2 Schematic illustration of the preparation of GCE surface using tyrosinase, AuNP and pyrroquinoline quinone reduction. Reprinted from Reference [32] with permission from Elsevier",
        "texts": [
            " In order to overcome the disadvantages of inhibition-based enzymes such as insolubility and non-reusability, other groups of enzymes such as tyrosinase and acid phosphatase are being studied in the field of biosensor development [28, 31]. Tyrosinase is responsible for the oxidation of phenol groups in pesticides, but it can also interact with other compounds as substrates resulting in selectivity problems [28]. While choosing other enzymes in the biosensor development for pesticides, the ability to be used for multiple measurements, regeneration, and selectivity are key parameters [28, 31]. In their recent work, Kim et\u00a0al. [32] fabricated a biosensor based on tyrosinase enzyme (Fig.\u00a02) for the detection of pesticides. This study suggests a more sensitive and simpler electrochemical biosensor that is applicable for diluted samples. In addition to the other well-known enzymes, acid phosphatase is also an inhibition based-enzyme, however its reversible mechanism of inhibition differ from inhibitionbased enzymes [28]. Parameters affecting enzyme biosensor performance Enzyme-based biosensors are highly dependent on the type of sample, target analyte, measurement regularity, and other factors such as the selectivity of electrically conductive materials that play a key role in the electrochemical 1 3 behavior of the enzyme electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure7-1.png",
        "caption": "Fig. 7. An elementary four-legged platform.",
        "texts": [
            " Thus the mobility of these elementary platforms is essential to the mobility analysis of the ball. The elementary four-legged platform is the basis of a circular loop-chain. It acts to connect two orthogonal circular loop-chains and to connect the loop chains to a Y-shaped unit in an octant. The platform consists of two square hubs as a platform and a radially movable base and four legs in the form of scissors structure. Four scissors-pairs as legs are located in two perpendicular planes as in Fig. 7. Every leg has three revolute pairs and their axes are parallel to the base plane, the x\u2013y plane. Looking at leg 1 where the axes of the kinematic pairs are perpendicular to x- and z-axes, the screws of the kinematic pairs can be established as follows: $11 : \u00f0 0 1 0 0 0 b1 \u00deT; $12 : \u00f0 0 1 0 a2 0 b2 \u00deT; $13 : \u00f0 0 1 0 a3 0 b1 \u00deT; in which ai and bi are the parameters determined by the positions of axes. As to the screw notation, the first subscript denotes the leg number, the second subscript denotes the joint number"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.12-1.png",
        "caption": "Figure 4.12. Displaced positions of the rack and pinion.",
        "texts": [
            " Before we discuss the general case of the backlash in a gear pair, we consider first a rack and pinion, and we will determine the tooth thickness of the rack, if its teeth are in contact with both faces of the pinion teeth. This is the situation known as close-mesh operation, when there is no backlash. Figure 4.11 shows the pinion and rack, in positions such that the contact point between one tooth of the pinion and the rack lies exactly at the pi tch point. The same pinion and rack are shown in Figure 4.12, and the pinion has been rotated until the opposite profile of the same tooth passes through the pitch point. Since both faces of the pinion tooth are in contact with the rack, the pitch point again coincides wi th a contact point. The rotation ~p between the two positions of the pinion Backlash 101 can be expressed in terms of its tooth thickness at the pitch circle, A{1 (4.29) and the displacement AU r of the rack is equal to its space width wpr ' measured at the pitch line, (4.30) The rack displacement and the pinion rotation are related by Equation (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.9-1.png",
        "caption": "Figure 5.9. A hob.",
        "texts": [
            " In order that the total number of teeth can be cut in the gear, the cutting process is stopped each time the gear has turned through one or two angular pitches, and the cutter is moved back the same number of pitches. This procedure naturally adds to the time required to cut the gear, and also contributes to errors in the shape of the gear. It is impossible to give a complete explanation of the hobbing process, except in the context of cutting helical gears. The description given in this chapter is therefore very brief, and many statements are made without proof. A full description, containing all the necessary proofs, will be given in Chapter 16. A typical hob is shown in Figure 5.9. It has basically the same shape as a screw, with one or more threads, and each thread is cut by a number of gashes, either at right angles to the thread, or parallel with the hob axis, so that cutting Hobbing 129 faces are formed. Figure 5.10 shows the positions of a hob and a gear blank during the cutting process. The cutting action of the hob is very similar to that of a rack cutter. The gear blank and the hob are each rotated about their axes, the gear blank slowly and the hob more quickly. Since the hob has the shape of a screw, its threads appear to move in the direction of its axis, so that they simulate the movement of a rack cutter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003767_s026357470400092x-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003767_s026357470400092x-Figure8-1.png",
        "caption": "Fig. 8. Cancellation of the components of the longitudinal thrust vector.",
        "texts": [
            " 13. F is the attitude feedback gain in Eq. 15, and g is gravitational acceleration. Xu and Yv are speed derivatives. We set Xu and Yv to zero, when the speed is low. Figure 7 shows bode plots of G(s)x\u03b8r and G(s)y\u03c6r . The plots include notches due to unstable zeros i.e., flapping states (a, b) and attitude state (\u03b8 , \u03c6) cancel the lateral and longitudinal components of the thrust vector, respectively, in the manner of a pendulum. Cancellation of the components of the thrust vector is depicted in Figure 8. 4.2. LQI position feedback controller design We designed an LQI feedback controller for position control. The system can be described by x\u0307(t) = Ax(t) + Bu(t) (23) The input u(t) is a multi-input consisting of \u03b8r and \u03c6r , the references of the attitude actuator. u(t) = [\u03b8r (t) \u03c6r (t)]T (24) r is the position reference, the output y is the x \u2212 y position of the helicopter. r(t) = [xr (t) yr (t)]T , y(t) = [x(t) y(t)]T (25) e(t) = t\u222b 0 r(t) \u2212 y(t) dt, e\u0307(t) = r(t) \u2212 y(t) The extended state-space system description involves error (e(t)) is described by d dt [ x(t) e(t) ] = [ A 0 \u2212C 0 ] [ x(t) e(t) ] + [ B 0 ] u(t) + [ 0 I ] r(t) (26) The LQR cost function is the sum of the steady-state meansquare weighted state xe(t) = [x(t) e(t) ]T , and the steadystate mean-square weighted attitude actuator reference signals u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003384_rspa.2004.1371-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003384_rspa.2004.1371-Figure3-1.png",
        "caption": "Figure 3. Schematic of a puckered cylinder. (a) Puckering of a cylindrical surface of radius R into another of smaller radius b. The puckering can be described by using a two-dimensional geometry, so that the deformation is given by the vector v(s) = (v1(s), v2(s)). (b) Definition of the trihedron {t1, t2, n}.",
        "texts": [
            " In the following sections we will consider two concrete examples that apply the preceding equations to the packing of a naturally flat sheet into a slightly smaller cylindrical drum via either cylindrically or conically deformed sheets. 3. The puckered cylinder (a) Geometry We consider a very long sheet rolled into the shape of a circular cylinder of radius R. The lateral ends of the sheet are glued to each other, and the resulting long cylindrical Proc. R. Soc. A (2005) sheet is then introduced into a cylinder of radius b < R as shown in figure 3. The excess length of the sheet causes it to pucker with a natural dimensionless control parameter to describe the packing in this system given by \u03b52 = (R \u2212 b) b . (3.1) Assuming that the deformation of the sheet is cylindrical, the position vector describing the sheet can be written as r(s, z) = v(s) + ze3, (3.2) where v(s) = v1(s)e1 + v2(s)e2, s is the arc length of the two-dimensional curve defined by v(s) and z is the length along the axis of the cylinder (see figure 3a). We observe that this class of one-dimensional deformations automatically satisfies the Gauss\u2013Codazzi relations (2.12). The metric tensor associated with this deformation is gss = 1, gsz = 0, gzz = 1, and the orthonormal vector triad describing the surface is t1 = t, t2 = e3, n = t \u00d7 e3. (3.3) Here t = \u2202sv is the tangent and n is the oriented normal to the planar curve that completely describes the cylindrical sheet. In terms of the angle \u03c6 between t and the horizontal (figure 3b), we have t = cos \u03c6e1 + sin\u03c6e2 and n = sin\u03c6e1 \u2212 cos \u03c6e2. The components of the curvature tensor are given by bss = \u03ba, bzz = bsz = 0, where \u03ba = \u2212n \u00b7 \u2202st = \u03c6\u0307 is the curvature of the planar curve shown in figure 3. Here and elsewhere, we use the notation \u02d9(\u00b7) \u2261 \u2202s(\u00b7). The lines z = const. and s = const. are the lines of curvature for all possible deformations, so that the geodesic torsion \u03c4 = 0 identically. Therefore, msz = mzs = 0. Since the normal curvature along the line s = const. is zero, mss = B\u03ba, mzz = B\u03c3\u03ba. Finally, torque equilibrium in the n-direction yields Nsz = Nzs. Here we see an example where the local torques and forces are symmetric. (b) Mechanical equilibrium In the absence of any frictional interactions with the confining cylinder the external force must be along the normal so that K = \u2212kn (k > 0)",
            "7) The first two correspond to force balance in the tangential and normal directions, while the last equation is a consequence of torque equilibrium. By using the relation (3.7) in (3.5) we can integrate it once so that Nss + B\u03ba2/2 = \u2212Ba2, where a2 is a constant of integration. Substituting the result in equation (3.6) yields B[\u03ba\u0308 + (a2 + 1 2\u03ba2)\u03ba] = k(s), (3.8) which, together with appropriate boundary conditions, describes the equilibrium shape of the Elastica of Euler. For the confined cylindrical sheet shown in figure 3, the radius of curvature is constant and equal to the radius of the external cylinder \u03ba = 1/b in the region where the sheet is in contact with the rigid cylinder. Therefore, it follows from (3.8) that k = kc = const. in this region. Furthermore, in the contact region \u03ba\u0307 = 0 so that (3.7) implies Qs = 0 and (3.6) implies Nss = \u2212bkc, i.e. the sheet is under purely normal compression due to confinement. To characterize the free region, we define s = 0 as the generator at the centre of the fold. Solving (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure1-1.png",
        "caption": "Fig. 1. Vector diagrams in d-q axis coordinates. (a) Conventional IPM machine. (b) AIPM machine.",
        "texts": [
            " In Section IV, several selected AIPM machines are redesigned based on the conventional IPM machine benchmark for Toyota Prius 2010 and their performance are compared. Besides, experimental results of an AIPM machine prototype are provided for verification. Section V is the conclusion. In this section, the principle of utilizing MFS effect in AIPM machines to enhance torque density is introduced by a simplified analytical model that ignores saturation, crossmagnetization and harmonics. The vector diagrams of stator current and PM flux linkage in conventional IPM and AIPM machines are shown in Fig. 1, where is, id, and iq are the vectors of stator current and d- and q-axis currents, respectively; \u03c8pm, \u03c8fd, and \u03c8fq are the vectors of synthetic PM flux linkage and d- and q-axis PM flux linkages, respectively, \u03b2 is the current advancing angle, and \u03b1s is the asymmetric angle in AIPM machine. The d-q axis coordinates in Fig. 1 are defined by the rotor saliency. The d- and q-axis flux linkages can be generally expressed as (1), where \u03c8d and \u03c8q are the d- and q-axis flux linkages, Ld and Lq are the d- and q-axis inductances. d fd d d q fq q d L i L i          (1) According to Fig. 1 and (1), the d- and q-axis flux linkages in IPM and AIPM machines are expressed as (2) and (3), respectively, P Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (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. BA-05 2 sin cos d pm d s q q s L i L i          (2) cos sin sin cos d pm s d s q pm s q s L i L i              (3) The general torque equations for IPM machines are shown in (4), which includes the PM torque component produced by the interaction between q-axis PM flux linkage \u03c8fq and d-axis current id for AIPM machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure4-1.png",
        "caption": "Fig. 4. Variations in A i \u2013B i chain.",
        "texts": [
            " , 3 , j = 1 , 2 , and O \u2013A i \u2013B i \u2013C i \u2013P, i = 1 , for the RUU linkage. Vectors o , a i , b i , b i j , c i j , c i , p , are the Cartesian coordinates of points O, A i , B i , B i j , C i j , C i , P in the reference coordinate frame F b , respectively. According to Fig. 3 , a i \u2212 o = (R + \u03b4R i ) R z (\u03b7i + \u03b4\u03b7i ) j + \u03b4a zi k (4) where \u03b4R i and \u03b4\u03b7i are the variations in the nominal geometric parameters R and \u03b7i , respectively, and \u03b4a zi is the positioning error of A i along z-axis. According to Fig. 4 , b i \u2212 a i = (b i + \u03b4b i ) R Bi j (5) with R Bi = R z (\u03b7i + \u03b4\u03b7i )(I + [ \u03b4\u03c6i ]) R z (\u03b8i + \u03b4\u03b8i ) (6) where [ \u03b4\u03c6i ] represents the cross-product matrix (CPM) 2 of vector \u03b4\u03c6i = [ 0 \u03b4\u03c6yi \u03b4\u03c6zi ]T , and I is the 3 \u00d7 3 identity matrix. Moreover, \u03b4b i is the variation in b i , \u03b4\u03b8i is the error of input angle \u03b8i of the i th actuator and \u03b4\u03c6i represents the angular variations of manufacturing errors. According to Fig. 5 , b i j \u2212 b i = 1 2 \u03b5( j)(d i + \u03b4d i j ) R Bi (I + [ \u03b4\u03c8 i ]) i ; \u03b5( j) = { 1 , j = 1 \u22121 , j = 2 (7) where \u03b4\u03c8 i = [ 0 \u03b4\u03c8 yi \u03b4\u03c8 zi ]T is the orientation error of link B i 1 B i 2 with respect to the axis of rotation of the i th active revolute joint, and \u03b4d i is the variation of B i 1 B i 2 that is supposed to be equally shared by the connecting bar of the parallelogram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure1-17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure1-17-1.png",
        "caption": "Figure 1-17 Poincare section: construction of a difference equation model (map) from a continuous time dynamical model.",
        "texts": [
            " (See Crutchfield and Packard (1982) or Wolfram (1986), for a discussion of symbol dynamics.) In a periodically forced vibratory system, a Poincare map may be obtained by stroboscopically measuring the dynamic variables at some particular phase of the forcing motion. In an n-state variable problem, one can obtain a Poincare section by measuring the n \u2014 1 variables when the nth variable reaches some particular value or when the phase space trajectory crosses some arbitrary plane in phase space as shown in Figure 1-17 (see also Chapters 2 and 4). If one has knowledge of the time history between two penetrations of this plane, one can relate the position at tn+l to that at tn through given functions. For example, for the case shown in Figure 1-17, The mathematical study of such maps is similar to that for differential equations. One can find equilibrium or fixed points of the map and one can classify these fixed points by the study of linearized maps about the fixed point. If xn+l = f(xw) is a general map of say n variables represented by Maps and Flows 25 the vector x, then a fixed point satisfies (1-3.2) The iteration of a map is often written f(f(x)) = f (2)(x). Using this notation, an \"w-cycle\" or w-periodic orbit is a fixed point that repeats after m iterations of the map; that is, * = f (m)(v \\ h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000032_j.rcim.2020.101959-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000032_j.rcim.2020.101959-Figure3-1.png",
        "caption": "Fig. 3. Point constraint calibration 3D schematic diagram.",
        "texts": [
            " Then, the camera is used to capture the fixed sphere from different angles, the camera position is adjusted to position the sphere in the center of the image and maintain a certain distance between the sphere and camera so that the sphere image is the same size. Finally, the robot joint angles are recorded separately when the angle-change motion is completed. While keeping the sphere in the same position, the camera optical axis at different poses are supposed to intersect at a point, which is the center of the sphere, as shown in Fig. 3. The actual measurement is shown in Fig. 4. In the measured point constraint data, the joint angles are recorded as the vector JAp. The coordinates of the sphere in the camera coordinate system are recorded as vector \u0394Ppc, which is called centering error and obtained by image processing. The unknown actual sphere coordinates in the robot basal coordinate system are marked as vector PBp. The distance constraint measurement process is as followed. First, the sphere is placed at two positions in sequence with several gauge blocks in between, which means the distance of the two positions is known, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000772_tcyb.2021.3063139-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000772_tcyb.2021.3063139-Figure9-1.png",
        "caption": "Fig. 9. One-link manipulator.",
        "texts": [
            " Downloaded on June 30,2021 at 08:27:27 UTC from IEEE Xplore. Restrictions apply. Remark 8: By observation of the simulation images, we can obtain that the devised C1 AFFTC scheme can drive the system output fast following the desired signal. From Figs. 6 and 7, we can know that the virtual control law \u03b11 and control input are continuous and bounded. It is worth mentioning that unlike the C0 AFFTC methods that exist, the singularity issue in the developed method is excluded. Example 2: Consider an one-link manipulator with the actuator, in Fig. 9, is governed by [39] { Mq\u0308 + Cq\u0307 + G sin(q) = \u03c5 Bm\u03c5\u0307 + Hm\u03c5 = u \u2212 Kmq\u0307 (67) where q, q\u0307, and q\u0308 are the link position, velocity, and acceleration. u is the control input and \u03c5 is the joint dynamic torque. The detailed parameters of the manipulator are listed in Table I. Letting x1 = q, x2 = q\u0307, and x3 = \u03c5, then the dynamic equation of (67) can be expressed as \u23a7 \u23a8 \u23a9 x\u03071 = x2 x\u03072 = 1 M (\u2212Cx2 \u2212 G sin x1) + 1 M x3 x\u03073 = 1 Bm (\u2212Kmx2 \u2212 Hmx3) + 1 Bm u (68) The desired signal is governed by yd = 0.5 sin(0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure6.21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure6.21-1.png",
        "caption": "Figure 6.21. Schematic showing the disappearance of dislocation contrast under the g . R = 0 condition.",
        "texts": [
            " There are two methods: one is the traditional diffraction contrast imaging technique (described below); the other is the convergent beam diffraction technique (Section 6.5). We now outline the principle of using diffraction contrast imaging for this analysis. From Eq. (6.29), the crystal potential is identical to the potential for a perfect crystal if g. R = 0; i.e., g is perpendicular to R. If only two beams are excited in the diffraction pattern, one being the transmitted beam (000) and the other being the diffracted beam g, g. R = 0 results in the disappearance of dislocation contrast in the image. This result can be easily understood from Fig. 6.21. Since g is perpendicular to the reflection plane, the condition g. R = 0 means that the atom displacement R must be confined in the reflection plane, so there is no modulation to the interplanar distance dg (with g = 1/ dg ) of the reflection planes. Since the amplitude of the g beam is only affected by the component of lattice distortion in the direction parallel to g under the two beam condition, no contrast is produced if R is parallel to the reflection plane. This result is exact if the two-beam condition is precisely met"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003537_tro.2006.870649-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003537_tro.2006.870649-Figure2-1.png",
        "caption": "Fig. 2. Explanation of our proposed method. (a) 3-D convex hull of supporting points. (b) The moment about an edge of the convex hull.",
        "texts": [
            " However, the balance can be kept even when only the heel contacts the floor. Defining the ZMP as the COP of contact between the feet and the floor, this means that the balance can be kept even when the ZMP exists on the edge of the foot-supporting area. Since we cannot determine whether or not the robot keeps balance by using this ZMP, we consider generalizing the ZMP as the COP, also including the contact between the hands and the environment. When a hand contacts the environment as shown in Fig. 2, the convex hull of the supporting points forms a 3-D convex polyhedron. For simplicity, let us consider modeling the robot using a massless convex polyhedron and a mass connected with the polyhedron through the joints [Fig. 2(b)]. Here, if the acceleration is small, the convex polyhedron will maintain its initial posture. However, if the acceleration becomes larger, the convex polyhedron might rotate about an edge, and the robot may fall down. By defining the ZMP, considering the interaction between the hand and the environment as the GZMP, we obtain the region of the GZMP in this research. If the GZMP is included strictly inside this region, the robot keeps balance. The region will be obtained by using the following algorithm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000437_j.commatsci.2020.109686-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000437_j.commatsci.2020.109686-Figure3-1.png",
        "caption": "Fig. 3. Geometric model used in LPBF calculation.",
        "texts": [
            "00%, respectively. Based on the open-source CFD code OpenFOAM, the dynamic behavior of the molten pool during the LPBF process was predicted, and the molten pool evolution and influences of various process parameters (laser power, scanning speed, powder bed thickness, and hatch space) on the pore defect were analyzed. The calculation time step was set to 1 \u00d7 10\u22128 s. Dimensionless analysis of the molten pool evolution during the LPBF formation process was conducted first, and the geometric model is shown in Fig. 3. The thickness, length, and width of the powder bed were 50, 1000, and 150 \u03bcm, respectively, and the substrate thickness was 50 \u03bcm. The powder material used was 316L stainless steel, and its alloy composition (mass percentage) was 65.395% Fe, 0.03% C, 1.0% Si, 2.0%Mn, 0.045% P, 0.03% S, 12.0% Ni, 17.0% Cr, 2.5%Mo. Table 1 shows the required material properties calculated by JMatPro v7.0. Table 2 shows the laser processing parameters. The calculation was a single-track formation process, in which the initial temperature of the metal particles and substrate was 300 K, and the laser moved linearly from the coordinate (50 \u03bcm, 75 \u03bcm) horizontally to the coordinate (950 \u03bcm, 75 \u03bcm), then the laser stopped heating, and the system continued to cool for 100 \u03bcs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003903_acc.2008.4587329-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003903_acc.2008.4587329-Figure1-1.png",
        "caption": "Fig. 1. Flexible joint robotic arm.",
        "texts": [
            " y(t) = Cx(t) instead of yk = Cx(tk) in (1), its convergence behavior with nonuniformly sampled measurements can be analyzed via the less conservative function [7] V (t) = eT (t)Xe(t) + \u222b t t\u2212\u03c4(t) (\u03b4 \u2212 t + s)e\u0307T (s)Y e\u0307(s) ds + (\u03b4 \u2212 \u03c4(t))(e(t) \u2212 \u01eb(t))T Z(e(t) \u2212 \u01eb(t)), (14) where X,Y,Z are symmetric positive definite matrices. Note that (6) is obtained from (14) by setting P = X = Y = Z. In this section the applicability of the proposed observer design for Lipschitz nonlinear systems with nonuniformly sampled measurements is demonstrated via two examples. In the following observer (3) is applied to estimate the state of a flexible joint robotic arm [6] shown in Figure 1. The dynamics of this robotic arm is described by (1) with system state xT = [x1 x2 x3 x4] , system matrices A =     0 1 0 0 \u221248.6 \u22121.25 48.6 0 0 0 0 1 19.5 0 \u221219.5 0     , B =     0 21.6 0 0     , G =     0 0 0 \u22121     ,HT =     0 0 1 0     , CT =     0 1 1 0 0 0 0 0     , function \u03c1(t, u) = Bu, and nonlinearity \u03c3(Hx) = 3.3 sin x3 with Lipschitz constant \u03b3 = 3.3. Furthermore, it is assumed that \u03b4 = 0.1. Solving the LMI conditions of Theorem 1 with the above specified matrices and constants, one obtains the observer matrix LT = \u00bb \u221252 20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure11.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure11.1-1.png",
        "caption": "Figure 11.1 \u2022. Tooth force applied to gear 1.",
        "texts": [
            " The second type of stress which is often responsible for tooth damage is the tensile stress in the fillet, caused by a tooth load on the face of the tooth. If the tensile stress is too large, fatigue cracks will be formed in the fillet, and the tooth will eventually fracture. It is clear that both the contact stress and the fillet stress must always be calculated, and compared with values which the gear material can sustain without damage. Contact Force Intensity 243 Contact Force Intensity In the abSence of friction, the tooth force W is directed along the normal to the tooth prof i Ie, which is tangent to the base circle, as shown in Figure 11.1. If the torque applied to gear 1 is M1, the corresponding tooth force W is found by taking moments about the gear axis, (11.1) A similar relation exists between the contact force and the torque applied to gear 2, (11.2) and, by eliminating W from these equations, we obtain a relation between M1 and M2 , (11.3) When a gear pair is designed, the value of either M1 or M2 is known. We use Equation (11.3) to find the other torque, 244 Tooth Stresses in Spur Gears and the contact force is then found from Equation (11.1 or 11. 2) \u2022 Point Aw in Figure 11.1 is usually referred to as the contact point, but of course the gear is a solid object, and the contact really takes place along the entire axial line through Aw' whose length is equal to the gear face-width F. The contact length Lc is the total length of all the contact lines in the gear pair, and is therefore equal to either F or 2F, depending on whether the gear pair has one or two pairs of teeth in contact. The load intensity w is defined as the tooth force per unit length of the contact line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003179_s0030-3992(99)00046-8-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003179_s0030-3992(99)00046-8-Figure5-1.png",
        "caption": "Fig. 5. Coaxial laser cladding nozzle of the present study.",
        "texts": [
            " The main performance criterion is the catchment ef\u00aeciency, Z, which is de\u00aened as the ratio of the powder trapped in the formed clad to the powder delivered. For commercial needs, an e cient process design is required. The catchment e ciency is hence one of the primary factors used to assess the success of the cladding process [15]. Powder catchment was evaluated in these experiments by weighing the substrate before and after cladding. The measured catchment divided by the powder feed rate and cladding time is the catchment e ciency. In the cladding tests using a coaxial nozzle as illustrated in Fig. 5, the powder catchment was measured for di erent powder \u00afow rates and clad speeds with 1 kW CW CO2 laser radiation at a \u00aexed clad length of 200 mm with a stand-o distance of 10 mm. As shown in Fig. 6, the powder catchment increases with increasing powder \u00afow (varying the drill speed of the powder feeder at a constant carrier \u00afow rate of 6 l/min) and decreasing cladding speed [1]. For clad forming before the particles have fully melted, the catchment e ciency will be mainly determined by the ratio of the laser generated melt area to the impact area of the powder stream [5,6]",
            " Z 1 exp \u00ff 3:5d=D 2 2 6 The numerical relationship of Eq. (6) between catchment e ciency and diameter ratio of beam spot diameter to powder impact diameter (d/D ) in a powder stream is shown in Fig. 7. Clearly, the catchment ef\u00aeciency increases with d/D and approaches 80% at d/ D = 0.5. In the chosen optics setting and nozzle size, the d '/D ' ratio is about 0.26 and could be used in Eq. (3) to calculate the value of d/D through the beam axis. The catchment e ciency of the powder stream of the coaxial nozzle illustrated in Fig. 5 was theoretically and experimentally examined. According to Eqs. (3) and (6), the theoretical catchment e ciency was calculated at a beam divergent angle of 88 with various powder spraying angles along the beam direction. An important relationship between the catchment ef\u00aeciency, the stand-o distance and the spraying angle is plotted in Fig. 8. The computational results were veri\u00aeed with the catchment test at various stream jet velocities. In reality, the jet velocities U1 and U0 have an adverse in\u00afuence on the spraying angle which has been con\u00aermed by \u00afow images analysis in the previous study [16]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure7-1.png",
        "caption": "Fig. 7. Fully-parallel robotic manipulator with Sch\u00f6nflies motions: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " In this case, leg C has just a guiding role by constraining the mobile platform to a planar motion. This mechanism has p = 11 joints (2 prismatic and 9 revolute joints) and q = 2 independent loops. Each joint has one degree of mobility (fi = 1). The two independent loops have also the same motion parameter b1 = b2 = 5 whichever set of independent loops is chosen. Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s mobility criteria give M = 11 \u2212 (5 + 5) = 1. This is an erroneous result. In fact Eq. (26) gives r = 5 + 4 = 9 and Eq. (6) indicates two degrees of mobility M = 11 \u2212 9 = 2. This is the right result. Fig. 7 presents a parallel robotic manipulator with decoupled Sch\u00f6nflies motions (Gogu, 2002). The mobile platform has four degrees of freedom: three independent translations and one rotation about an axis of fixed direction. The parallel mechanism has four legs integrating p = 20 joints (4 prismatic and 16 revolute joints) and q = 3 independent loops. The three independent loops have the same motion parameter b = b1 = b2 = 6 whichever set of independent loops is chosen. Chebychev\u2013Gr\u00fcbler\u2013 Kutzbach\u2019s mobility criteria give M = 20 \u2212 (6 + 6 + 6) = 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002935_iros.1993.583168-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002935_iros.1993.583168-Figure7-1.png",
        "caption": "Fig. 7 Definition of vectors for trunk",
        "texts": [
            " (3) A Cartesian coordinate system 0-XYZ is set, where the Z-axis is vertical, the X-axis and Y-axis form a plane which is the same as that of the floor (Fig. 5) . (4) The contact region between the foot and the floor is a set of contact points. ( 5 ) The coefficient of friction for rotation around X , Y and Z-axis is zero at the contact point. In (l), the machine model is regarded as a model that has three particles in the hunk and n particles in the lower-limbs as shown in Fig. 6. On the 0 - X Y Z , let each vector to be established as shown in Fig. 5 and Fig. 7. An equation of the motion at an arbitrary point P is obtained by applying DAlembert's Principle as follows: n m,,r;'xf0'+~mi(ri -P)x(r i+G)+T=O ( 1 ) i=O P(xp, yp, ZJ i s defined as ZMP, so we denote P(x,, yp, z,,) as Pmp(x,p, y,, z-,). To consider the relative motion of each part, a translationally moving coordinate W(X, Y, 2) is established on the waist of the robot on a parallel with the fixed coordinate 0-XYZ ( shown in Fig. 6 ), Q(x,, y,. z,) is defined as the origin of W(X, Y, 2) on the 0 - X Y Z "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000508_soro.2020.0006-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000508_soro.2020.0006-Figure5-1.png",
        "caption": "FIG. 5. Representative deformed shape of the catheter with constant bending radius.",
        "texts": [
            " As an alternative to the mechanistic approach, the inverse kinematic problem was divided into learning-based classification and regression problems. For a given desired position P , the classifier, that is, C(h , u ) would determine tendon(s) to be pulled, while the regressor would determine the length of the said tendon(s) (desired lengths). Therefore, the objective of the inverse kinematics would be to determine the catheter configuration, that is, (Ck : i j, Li, Lj) in joint space, for a given desired position P in the task space. Degrees of freedom. Figure 5 depicts a representative deformation of the catheter, where the Cartesian coordination system X Y Z\u00f0 \u00deT represents the fixed global frame, P is the position of the tip of the catheter, that is, the center of the red tip marker marked by the bright \u00fe , r is the bending radius, G is the bending plane, and Ob is the center of the bending arc cOP. Due to the relatively larger longitudinal stiffness compared with the bending stiffness, the compression of the catheter along its spine was neglected. Therefore, cOP \u00bc 2rh\u00bc 40mm constant: (1) Also, ~P : \u00bc~OP was presented in the global Cartesian coordinates and spherical coordinates as follows: ~P\u00bc x y z\u00f0 \u00deT 2 S\u00fe , (2) and ~P\u00bc q h u\u00f0 \u00deT 2 S , (3) where S\u00fe 2 R3 and S 2 R3 are the Cartesian and spherical representations of the working space (surface) of the catheter, and q 2 R, h 2 0, p\u00bd , and u 2 ( p, p]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000852_j.compscitech.2021.108667-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000852_j.compscitech.2021.108667-Figure1-1.png",
        "caption": "Fig. 1. (a) Unit cell of origami-inspired sandwich material; (b) Exploded view of unit cell of origami-inspired sandwich material.",
        "texts": [
            " Analytical models are developed to provide the upper and lower bounds of the out-of-plane compressive strength of the origami-inspired composite sandwich materials. Finite element analyses and experiments are then conducted to characterize the out-of-plane compressive behaviors and verify the validity of the analytical models. The compressive strength and energy absorption are analyzed in comparison with origami-inspired sandwich materials without PMI foam and other competing types of sandwich materials. The geometrical design of the unit cell of the origami-inspired sandwich material is shown in Fig. 1(a). As can be seen in the exploded view of the unit cell shown in Fig. 1(b), it is composed of a curved-crease CFRP origami core, PMI foam blocks, and upper and lower CFRP face sheets. The shapes of the PMI foam block and curvedcrease origami core are identical so that the PMI foams can be used as substrates and the CFRP prepregs (see Fig. 1) can be attached perfectly to the surface of the PMI foams. Curved-crease origami structures are adopted because they are suitable for fabrication using fiber-reinforced composites [33]. Circular arcs are selected as the crease lines (red lines in Fig. 1(b)) for simplicity, as used by Du et al. [33]. The curved-crease origami core has been proved to be foldable and developable to ensure that pre-damage will be minimized in the composite prepregs during the folding process [37]. As shown in Fig. 1, there are six independent geometrical parameters: the height of the origami core hc, the wall thickness of the origami core tc, the thickness of the face sheets tf , the angle \u03b2, the angle \u03b8 and the length l. The density of the sandwich core can be expressed as \u03c1= \u03c1FoamVFoam+\u03c1OrigamiVOrigami VFoam+VOrigami = ( \u03c1Origami \u2212 \u03c1Foam ) tc 2hc sin 2 \u03b8 cos \u03b2 \u222b \u03c0\u2212 2\u03b8 0 \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 sin 2 \u03b2 + cos 2 \u03d5cos 2 \u03b2 \u221a d\u03d5+ \u03c1Foam (1) where \u03c1Origami is the density of the CFRP used to fabricate the origami core, VOrigami is the volume occupied by the origami core, \u03c1Foam is the density of the PMI foam, and VFoam is the volume occupied by the PMI foam blocks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.2-1.png",
        "caption": "Figure 7.2: Lie bracket motion",
        "texts": [
            " If the two inputs u1 and u2 are never active at the same instant, the solution of eq. (7.11) is obtained by composing the flows relative to 91 and 92 . In particular, consider the input sequence { u 1 ( t) = + 1, u2 ( t) = 0, t E [ 0, c), u(t) = u1(t) = 0, u2 (t) = +1, t E [c, 2c), u1(t) = -1,u2 (t) = 0, t E [2c,3c), u1(t) = O,u2(t) = -1, t E [3c,4c), (7.12) where c is an infinitesimal interval of time. The solution of the differential equation at time 4c is obtained by following the flow of 91, then 92 , then -91, and finally -92 ( see Fig. 7.2). By computing x(c) as a series expansion about x0 = x(O) along 91, x(2c) as a series expansion about x(c) along 92 , and so on, one obtains 'a calculation which everyone should do once in his life' (R. Brockett). Note that, when 91 and 92 commute, no net motion is obtained as a result of the input sequence (7.12). The above computation shows that, at each point, infinitesimal motion is possible not only in the directions contained in the span of the input vector fields, but also in the directions of their Lie brackets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000613_s11071-020-05764-7-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000613_s11071-020-05764-7-Figure6-1.png",
        "caption": "Fig. 6 Schematic diagram of linkage structure of small \u2018\u20188\u2019\u2019 and large \u2018\u20188\u2019\u2019",
        "texts": [
            ";FT frnJ h iT \u00f031\u00de where Fdr m 1\u00f0 \u00dep\u00fej \u00bc F m 1\u00f0 \u00dep\u00fej s m 1\u00f0 \u00dep\u00fej \" # , Ffr m 1\u00f0 \u00dep\u00fej \u00bc Ff m 1\u00f0 \u00dep\u00fej sf m 1\u00f0 \u00dep\u00fej \" # . 3.3 Resolved the linkage force It is assumed that the pretensioning force applied by the linkage cable is largely enough to prevent slippage between the linkage cable and the joint. To achieve synchronous pitching and yaw of the four sub-joints in the segment, the (m - 1)p ? j universal joint and (m - 1)p ? j ? 1 universal joint in the mth segment are linked through small \u2018\u20188\u2019\u2019 cables and large \u2018\u20188\u2019\u2019 cables, respectively. The linkage diagram of the small \u2018\u20188\u2019\u2019 and large \u2018\u20188\u2019\u2019 is shown in Fig. 6. As shown in Fig. 6a, the two adjacent sub-joints are moved in the opposite direction at the same angular velocity by the principle of the synchronous belt. Assume that the length of the two cables that are not in contact with the joint is Los, the cross-sectional area of the cable is As, the Young modulus of the cable is Es, the radius of rotation joint is rs, the deformation of the cable is DLs \u00bc 2rsDh m 2i 1, and the control torque caused by the inconsistent deformation of the cable on both sides is: DT \u00bc ks Dhm1 \u00fe Dhm2 \u00bc 2ksDh m 2i 1 \u00f032\u00de where ks \u00bc 2EsAsrs Los . Therefore, the equivalent stiffness of small \u2018\u20188\u2019\u2019 linkage is: k\u0302 m 1\u00f0 \u00dep\u00fej s \u00bc 2ks \u00f033\u00de As shown in Fig. 6b, assume that the length of the two cables that are not in contact with the joint is Lol, the cross-sectional area of the cable is Al, the Young modulus of the cable is El, and the radius of rotation joint is rl. Similarly, the equivalent linkage stiffness of large \u2018\u20188\u2019\u2019 is: k\u0302 m 1\u00f0 \u00dep\u00fej l \u00bc 4ElAlrl Lol \u00f034\u00de Therefore, the resultant moment of the linkage cable acting on the universal joint (m - 1)p ? j is: sL m 1\u00f0 \u00dep\u00fej \u00bc k m 1\u00f0 \u00dep\u00fej ls qmi \u00f035\u00de where k m 1\u00f0 \u00dep\u00fej sl \u00bc 0 2k\u0302 m 1\u00f0 \u00dep\u00fej l 2k\u0302 m 1\u00f0 \u00dep\u00fej s 0 \" # "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003768_rob.4620050502-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003768_rob.4620050502-Figure3-1.png",
        "caption": "Figure 3. A 3-D redundant robot derived from the PUMA geometry.",
        "texts": [
            " SIMULATION The above control schemes for higher efficiency and mechanical advantage were applied to a seven-degree-of-freedom redundant robot. Simulations for this robot were performed in Fortran 77 on a VAX 11/780 computer running on V4.2 VMS system. The scalar constant R was selected heuristically to avoid joint velocity limits. The graphical display of robot configurations along a desired trajectory was obtained by using DI3000 (Precision Visuals) graphics package. The robot used for simulation was derived from the PUMA geometry. The robot and the Denavit-Hartenberg table for it are shown in Figure 3. Redundancy was obtained by adding a prismatic joint in the forearm of the PUMA robot. Thus the length of the forearm, a r . varies according to the movement of the prismatic joint. In Figure 3, z i , i = 1 to 6 are the unit vectors representing axes of rotation for the corresponding rotational joints and z r is the axis of translation for the prismatic joint. The control schemes developed to improve robot\u2019s efficiency and mechanical advantage were applied to the seven-degree-of-freedom redundant robot of Figure 3. Desired end-effector motion was also obtained by locking the prismatic joint and, by using the pseudo-inverse solution. The weighting matrices W,, W o , W,, and W, were selected suitably to incorporate different units associated with the components of vectors x, d, f and 7 respectively. A line diagram of the robot, shown in Figure 4, was used to draw the robot configurations along the trajectory. The offset, upper arm and forearm are drawn as straight lines in proportion to their lengths u 2 , 1 2 , and a, respectively",
            " This results in higher MVR along the trajectory as compared to the case in Figure 5 in which the prismatic joint is locked. Thus the addition of extra joint results in lower velocities at the other joints. This is particularly useful in the singularity re- Dubey and Luh: Redundant Robot Control 427 2 I Flgun 8. 3-D redundant robot trajectory along AB - null space used to improve mechanical advantage. Dubey and Luh: Redundant Robot Control 429 430 Journal of Robotic Systems-1988 gion where the joint velocities required are extremely high in the absence of redundancy. In Figure 7, as seen from Figure 3, MVR in the direction of motion is consistently much higher compared to the cases in Figures 5 and 6. The redundancy is utilized to improve MVR in Figure 7. This results in joint configurations requiring lower joint velocities for the desired end-effector motion. Thus more efficient motion is obtained in Figure 7 as compared to the cases in Figures 5 and 6. Improvement in MMA in Figure 8 as compared to Figures 5 and 6 can be noted from Figure 10. The redundancy is utilized in Figure 8 to improve MMA in the direction of motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003832_0094-5765(88)90189-0-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003832_0094-5765(88)90189-0-Figure2-1.png",
        "caption": "Fig. 2. Geometry of the system (present analysis).",
        "texts": [
            " The special case of maintaining the middle mass at the system centre of mass was considered in detail by them. They also considered the stabilization of the dynamics by adding two spring-dashpot dampers or through appropriate reel control laws. The present paper re-examines the inplane dynamics of three-body tethered systems by treating them as double-dumbbell systems. This makes the formulation and analysis somewhat more convenient and facilitates obtaining some interesting new results. The tethered system under consideration consists of three bodies having masses rn~, m2 and rn 3 as shown in Fig. 2. The dimensions of the bodies are much smaller compared to the lengths of the tethers and hence, the bodies can be approximated as point 1059 masses. The mass of the tether(s) is assumed to be negligible. The instantaneous centre of mass C is assumed to follow a circular orbit. The orbital coordinate axes x, y, z located at C are such that z-axis is directed towards the centre of the Earth and x-axis is in the direction of flight. The length of the tether between one end-mass mt and the middle mass m 3 is denoted by l~",
            " The formulation for case (i) is considered first; that for case (ii) is slightly different due to the constraint equation and is considered later. 2.1. Equations o f motion when l I and 12 are independent The motion is assumed to be confined to the orbital plane; thus only the co-ordinates x~ and zi, i = 1, 2, 3, are nonzero. Furthermore, since C is the centre of mass of the system, 3 3 E m i x i = O, E mizi = 0 . ( 1 ) i = 1 i = 1 Because of the two constraint eqns (1), the motion can be described by four independent generalized co-ordinates; here they are chosen as ll, 12, 01 and 0 z as shown in Fig. 2, 01 and 02 being the angles of inclination of the two tethers to the local vertical. From geometry, Xl = It sin 01 + x3, Zl = 11 cos 01 + z3 (2a) x2 = - (l: sin 02 - x3), z2 = - (lz cos 02 - z3). (2b) Substituting eqns (2a) and (2b) into eqns (1) one obtains {-,} ,.':\" sir\" O, x: = [A] ) j : , X3 {zl} ,lcoso, , z, = [A] ( t , cos 0. 3 Z (3a) (3b) where 1 --/~j M2 ] [ A ] = [ - P l - 1 + # 2 , L P2 d (3c) Pl, P2 being the mass ratios given by p l=rn l /m , i t2=m2/m, (3d) while m = rn I + m 2 + m3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of vector velocities at a growth surface. See text for definitions and equations",
        "texts": [
            " Now the growth velocity g is defined as the velocity of a material point leaving G relative to the generating cell on G. Thus, vg i \"x5 m i !x5 G i on G , (13) where x5 m refers to the velocity of a material point as it leaves G, Eq. (10). Using Eqs. (10) and (12) in Eq. (13) gives vg i \"! Lx i Lh 3 df 3 dt \"vg i (h 1 , h 2 , t) on G (14) where the functions x i (h 1 , h 2 , h 3 , t) are those given by Eq. (1) and the derivatives Lx i /Lh 3 in Eq. (14) are evaluated on G t . The general case of velocities g, x5 m and x5 G are shown schematically in Fig. 2. If the generating cells on G are assumed to have a long axis, which is parallel to the direction in which they extrude new material (like a tube of tooth paste), then the angle a that g makes with the normal n (Fig. 2) is also the inclination of the generating cells with respect to n. The new material extruded by the generating cells must, of course, be supplied to them by diffusion or the blood circulation which is not described in the present discussion. Two special cases using the above vocabulary give simple forms which are useful in particular examples. The first case is that of G being a fixed surface and the generating cells having fixed locations on G. Then xR G i \"0 and it follows from Eq. (12) that A Lx i Lt Bh 1 , h 2 , h 3 \""
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure13.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure13.7-1.png",
        "caption": "Fig. 13.7 Harmonic drive",
        "texts": [
            " For this reason, the Novikov gearing was called Wildhaber-Novikov gearing in the U.S. for some time. However, this is not appropriate because Wildhaber\u2019s concept is fundamentally different from the 476 13 Development of Theories in Mechanical Engineering of New Era Novikov\u2019s (Litvin n.d.; Radzevich 2012). Novikov gears have been used in some applications of high-power transmissions, particularly in the Soviet Union and China. In 1957, Clarence Musser, an American engineer, invented the harmonic drive as shown in Fig. 13.7 (Musser 1960). In this drive, a flexible spline is deformed through the rotation of a wave generator and the flexible spline meshes with a rigid circular spline in two regions of opposite sides. Due to the difference between the flexible spline teeth and the rigid spline teeth is small, a very large speed ratio can be achieved. Other advantages of harmonic drives include compactness, light weight, no backlash, and co-axial input and output shafts etc. It has found application in many fields, including the Apollo Lunar Roving Vehicle, the Skylab Space Station, as well as many robots (Shen and Ye 1987)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000903_j.asoc.2021.107226-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000903_j.asoc.2021.107226-Figure1-1.png",
        "caption": "Fig. 1. Free body diagram for lower limb exoskeleton.",
        "texts": [
            " Further, in Section 5, t F a S 2 i o e e l o j ( T M m a C C w F he experimental set-up for gait data acquisition is described. urthermore, the simulation results obtained for presented work re discussed in Section 6, are followed by conclusion section in ection 7. . Mathematical model for exoskeleton In this section, the mathematical model used for simulation s presented which provides the relation between the position f the links (\u2205exoi ) of the exoskeleton and the external force xerted on them (\u03c4exoi ) [10]. The design structure of lower limb xoskeleton, as shown in Fig. 1, is a two-degree of freedom lower imb exoskeleton wherein two links imitate the femur and tibia f the lower limb of the human body, and there is one revolute oint present at each link and is mathematically expressed as Mexo ( \u2205exoi ) + Mexo ( \u2205exoi ) )\u2205\u0308exoi + (Cexo ( \u2205exoi , \u2205\u0307exoi ) + C exo ( \u2205exoi , \u2205\u0307exoi ) )\u2205\u0307exoi + Gexo ( \u2205exoi ) + Gexo ( \u2205exoi ) = \u03c4exoi + Fexoi (t) + \u2206(t,\u2205exoi , \u2205\u0307exoi , \u2205\u0308exoi ) (1) he inertia matrix for exoskeleton considered is given by exo(\u2205exoi ) = [ Me11 Me12 Me21 Me22 ] (2) Me11 = mexo1d 2 exo1 + mexo2 ( l2exo1 + d2exo2 + 2lexo1dexo2 cos(\u2205exo2 ) ) + Iexo1 + Iexo2 (3) Me12 = mexo2 ( d2exo2 + lexo1dexo2 cos ( \u2205exo2 )) + Iexo2 (4) Me21 = Me12 (5) Me22 = mexo2d 2 exo2 + Iexo2 (6) where mexo1 represents the mass of the femur or link 1; mexo2 represents the mass of the tibia or link 2; lexo1 is the length of the femur or link 1; lexo2 represents the length of the tibia or link 2; g is the acceleration due to gravitation; \u03c4exoi is the external force on the links; dexo1 is the distance from joint to the centre of mass of link 1; dexo2 is the distance from joint to the centre of mass of link 2; Iexo1 = 1 3mexo1 l 2 exo1 is the moment of inertia for link1; Iexo2 = 1 12 exo2 l 2 exo2 is the moment of inertia for link 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.17-1.png",
        "caption": "Fig. 7.17 Rotor of turbo-generator unit",
        "texts": [
            " In 1870, only 4 years after the invention of generator, a Canadian, H. Martinson, filed a patent of dynamic balancing technology. In 1915, Schenck Company made the first double-face balancing machine, and quickly occupied the world market (ANON1 n.d.). To this point, the problem of balancing of rigid rotors was basically solved. Rotors working at a speed higher than the fundamental critical speed is regarded as flexible rotors. The rotor in a large turbo-generator unit is a typical and the most important example of flexible rotors (Fig. 7.17). Balancing of a flexible rotor is much more complicated than that of a rigid rotor. Rotor dynamics is the branch of machine dynamics devoted to the study of flexible rotors. In 1869, William Rankine, a British physicist, published the earliest recorded paper on flexible rotors. However, the model he used in the analysis was not appropriate, leading to a wrong conclusion: for a rotor of a given length, diameter and material there was a limit of speed, and supercritical operation was impossible. The wrong conclusion influenced for half a century (Nelson 2003)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000567_tro.2020.3000290-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000567_tro.2020.3000290-Figure5-1.png",
        "caption": "Fig. 5. Validation was performed using a two-tube robot as in [26]. The outer tube was rigidly attached to the baseplate, and the inner tube was rotated at a distance from the baseplate \u03b21, which is constant for any given trial and varied between trials.",
        "texts": [
            " The Jacobian is calculated by first-order finite differences with appropriately chosen increments for the magnitudes of the variables. Note that the accuracy of this Jacobian approximation does not affect the accuracy of the model, only the convergence of the iterative solution. To illuminate the discussion here and facilitate future work, an example simulation of a snap-through bifurcation is provided at codeocean.com/capsule/1121798. Our experimental setup (see Fig. 4) consists of a two-tube robot with the outer tube rigidly attached to the baseplate, as shown in Fig. 5. A Phantom v310 high-speed camera (Vision Research, Inc., Wayne, NJ, USA) was used to study the robot as it was actuated through an elastic instability, followed by oscillations. The high-speed camera collected data at 50 000FPS (\u0394t = 20\u03bcs) with a resolution of 256 \u00d7 128 pixels. Disk-shaped markers were affixed to each tube at its tip, so that the relative angle, \u03b8f between the tubes, could be easily reconstructed from video data. Authorized licensed use limited to: Carleton University. Downloaded on August 03,2020 at 23:45:05 UTC from IEEE Xplore"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000306_tmech.2020.3034640-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000306_tmech.2020.3034640-Figure14-1.png",
        "caption": "Fig. 14. FEA tip force of the PneuNets of the Design A (2 mm lg) at the applied pressure of: (a) 0.01 MPa, (b) 0.02 MPa, (c) 0.03 MPa, (d) 0.04 MPa, (e) 0.05 MPa, (f) 0.06 MPa.",
        "texts": [
            " This is because the small deformation displacement of the lateral wall of the chamber, and no large extrusion of the lateral walls of the adjacent chambers. The results have a good agreement when the pressure is less than 0.045 MPa. When the pressure is larger than 0.045 MPa, the lateral walls of the adjacent chambers begin to extrude with the increase of pressure, and the analytical predication results will be lower than the FEA simulation results. The FEA simulation results of tip force of the Design A (2 mm lg) at the zero bending angle are shown in Fig. 14. The tip force of the Design A (2 mm lg) at the zero bending angle is analyzed as shown in Fig. 15. The tip force model has a good agreement with the experimental results and FEA simulation results over the entire range of the test parameters. The experimental tip force shows the nonlinear relationship with the pressure. This is because the contact and squeeze of adjacent chamber walls will raise with the increase of the pressure and the calculation of the contact moment Mc has some simplifications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000094_j.jmapro.2020.03.018-Figure22-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000094_j.jmapro.2020.03.018-Figure22-1.png",
        "caption": "Fig. 22. 3D model of the first sample and Deposited near-net shape.",
        "texts": [
            " The torch angle was varied accordingly so that it was parallel to the growth direction of each layer. NTWD was kept constant at 8 mm. The start of the bead alternated at each end after every deposit. Fig. 21 also shows the final product, with a total of 32 layers deposited successfully. It demonstrates that the proposed multidirectional WAAM strategy is capable of fabricating an inclined wall from 0 to 90 degrees with proper welding settings. In the second case study, the multi-directional WAAM was used to fabricate a cylinder horizontally, with the 3D model shown in Fig. 22. Firstly, a vertical wall was produced with the WFS and TS set to 5 m/ min and 0.3 m/min, respectively. Process parameters for the horizontal cylinder were WFS 2 m/min and TS 0.3 m/min. The torch angle was set to 90\u02da, and the NTWD was set to 8 mm. In the deposition process, the start point was selected randomly, and the welding direction (anticlockwise or clockwise) was alternated for each layer to minimise uneven joint height. A 30-layered thin-walled cylinder with an overhang feature is shown in Fig. 22. As a result of the new strategies used, the appearance and the profile of the thin-walled cylinder is reasonably good, and the whole deposition process was quite stable. It also demonstrates the proposed multi-directional WAAM strategy is capable of depositing at any angle on the vertical surface, from horizontal to vertical. In the third case, multi-directional WAAW was used to fabricate a horizontal wall on a curved surface, with the 3D model shown in Fig. 23. Typically, in practice with the WAAM, the welding surface is not a flat surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.27-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.27-1.png",
        "caption": "Figure 13.27. Transverse section at plane z=O.",
        "texts": [
            " Having now defined tts and t ns ' the two measures of tooth thickness in a helical gear, we are able to specify the involute profile in the plane z=O, and we can then determine the position of AO. We have used the coordinates (R,eA,Z) to represent the position of point A, and we will now derive an expression for eA as a function of Rand z. In other words, we will find the position of the point on the tooth surface that lies at radius R in the transverse section at plane z. It is convenient to choose the (x,y,z) coordinate system in the position shown in Figure 13.27, so that the x axis coincides with a tooth centre-line in the transverse section z=O. As always, since the profile in a transverse section is an involute, the results derived for spur gears can be used directly, apart from the changes in notation. Hence, if AO is the point at radius R on the tooth profile in the transverse section z=O, the angular coordinate BAO can be found from Equations (2.18 and 2.35). (13.131) (13.132) If point A lies on the surface of the same tooth, at the same radius R as point AO' the gear helix through AO must also pass through A, and the difference between the angular coordinates of the two points is given by Equation (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure8-1.png",
        "caption": "Fig. 8. A singular con\u00aeguration of class (RI, RO, IO, IIM).",
        "texts": [
            " The 13 con\u00aegurations can be obtained by varying the elevation of the moving platform and moving the intersection point, D, in the base plane (D can also be at in\u00aenity). Several 2-dimensional manifolds of IIM-type singularities are attached to the 3-dimensional set. One of these can be obtained from the con\u00aeguration shown in Fig. 7 by rotating the moving platform about the line BC (and varying the elevation of points B and C). The second component is 1-dimensional and consists of con\u00aegurations like the one in Fig. 8, where the three supporting legs are fully extended and the two platforms are in the same plane. (2) RPM-type singularities From Equation (11) it is evident that L\u00c3 p is singular only when either mB 1 or mC 1 are zero, i.e. when either B or C are on the axis of the \u00aerst-joint screw of the corresponding subchain. Each of these two conditions corresponds to a set of 15 con\u00aegurations. They intersect in a 4-dimensional set. (3) Classi\u00aecation of {1} [ {2} (3.1) It can be observed that in all existing singularities of {1} the rank of L decreases by only one, while the rank of L\u00c3 O decreases by at least two",
            " From condition (iv), it follows that an element of {1} is an II-type singularity if and only if the 6 6 matrix L\u00c3 I has a null-space dimension of at least two. Next, we check whether this condition is satis\u00aeed for the di erent IIM-type singularities as determined in Step (1). For all the 13 con\u00aegurations of the type shown in Fig. 6, where for all three serial subchains point P is on the SP 1 axis, the condition is satis\u00aeed since mB 1 and mC 1 are zero vectors. For the IIM-type con\u00aegurations with three extended legs (as in Fig. 8) the condition is not satis\u00aeed. If only two subchains are singular (similar to Fig. 7), the condition is always satis\u00aeed when the singular subchains are B and C (as in the \u00aegure). When, however, one of the singular subchains is A, then, generally, the matrix A is of rank 5. There are two exceptions. The \u00aerst is represented in Fig. 9, where the singular subchains are A and B and additionally the point Co lies in the plane ABC. The second exception is shown in Fig. 10, where not only points B and C are located on screws SB 1 and SC 1 , but also point A lies in the (vertical) plane de\u00aened by the two screws. Each of Figs 9 and 10 represents, in fact 11 con\u00aegurations, since the elevation of point A can vary. Thus, the set of singularities belonging to the IIM, IO and II types consists of a main 3- dimensional set (Fig. 6), a 2-dimensional set (Fig. 7) and two 1-dimensional sets (Figs 9 and 10). The set of singularities in the IIM and IO types has two 2-dimensional components (similar to Fig. 7. with subchain A as one of the singular ones) and a 1-dimensional component (Fig. 8). (3.2) According to condition (i) and Equation (13), a con\u00aeguration is an RI-type singularity if and only if at least one of the following conditions is satis\u00aeed: either the subchain A is singular (in any way); or subchain B is fully extended; or subchain C is fully extended. Condition (ii) and Equation (12) imply that an RPM-singularity is also of the RO-type in the following three cases: (a) When C is on the SC 1 axis and the plane ABC is perpendicular to mC 2 (Fig. 10 is an example, though subchain B need not be singular)",
            " (e) (IIM, IO, II, RPM, RI, RO) has 11 con\u00aegurations in two 1-dimensional sets. The \u00aerst is represented by the con\u00aeguration in Fig. 9. It is similar to Fig. 7 with singular subchains A and B, but point Co is in the plane ABC, allowing for a RO-singularity. The second set is similar to the con\u00aeguration in Fig. 9, however, the non-singular subchain must be B rather than A. (3.4) Only one of the four classes of IIM but not RPM singularities is non-empty: (IIM, IO, RI, RO) consists of 11 con\u00aegurations as in Fig. 8. (3.5) All of the four RPM but not IIM classes are non-empty. (RPM, II, IO) has 15 con\u00aegurations. An example for this class can be obtained from the con\u00aeguration in Fig. 7 by an arbitrarily small perturbation of the subchain C while subchains A and B remain \u00aexed. (RPM, RI, II, IO) has 14 con\u00aegurations and can be illustrated by a variation of Fig. 6 obtained by maintaining the depicted position of the subchains A and B and slightly perturbing subchain C. (RPM, RO, II, IO) has 12 con\u00aegurations. An example is obtained from the con\u00aeguration in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.6-1.png",
        "caption": "Figure 12.6. Path followed by the pinion tooth tip.",
        "texts": [
            " If these general rules were invariably true, it would be sufficient to check for interference at the pinion fillets, and for clearance at the internal gear root circle. Since there are some exceptions to the general rules, it is still necessary to check that all three interference conditions are satisfied, and that both clearances are adaquate. However, the general rules do form the basis of a design procedure, which will be described later in this chapter. Tip Interference There is a second type of interference which can occur in an internal gear pair. Figure 12.6 shows the path followed, relative to the internal gear, by point AT1 on the tooth tip of the pinion. This curve is called a hypotrochoid, and it touches the tooth profile of the internal gear at its limit circle. In a well-designed gear pair, the path of AT1 lies within the tooth space of the internal gear, as shown in Tip Interference 273 Figure 12.6. However, in certain circumstances, the path of AT1 passes through the corner of the internal gear tooth, and this phenomenon is known as tip interference. It is obvious that when tip interference takes place, the gear pair is unusable. The shape of the path followed by point AT1 is a convex curve. It is because the teeth of the internal gear are concave that tip interference can occur. I f the teeth of gear 2 were convex, as in the case of an external gear pair, then there would be no possibility of tip interference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.16-1.png",
        "caption": "Figure 4.16. Measuring the backlash.",
        "texts": [
            " For additional information, the reader is referred to design references, such as the Gear Handbook [2]. The specification of a pair of spur gears generally includes maximum and minimum values for the circular backlash. When the gear pair is checked to see whether the actual backlash falls within the specified range, the simplest procedure is to measure the backlash B' along the common normal, and then to calculate the circular backlash, using the relation given by Equation (4.40). The backlash B' can be measured directly with a feeler-gauge, or by means of a dial gauge, as shown in Figure 4.16. The gauge is positioned so that its moveable arm lies along a base circle tangent of one of the gears. If this gear is rocked while the other gear is held fixed, the displacement measured by the dial gauge is then equal to the backlash along the common normal. 108 Contact Ratio, Interference and Backlash Numerical Examples Example 4.1 A gear pair has a module of 8 mm, a pressure angle of 20\u00b0, and a center distance of 453 mm. The tooth numbers are 16 and 95, the tooth thicknesses 14.90 mm and 16"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002820_s0956-5663(03)00225-2-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002820_s0956-5663(03)00225-2-Figure2-1.png",
        "caption": "Fig. 2. Organisation of the ECL multifunctional bio-sensing chip. GCE: glassy carbon electrode, Pt: platinum pseudo-reference electrode, S: silicone spacer, W: plexiglas window.",
        "texts": [
            " To this solution, 5 ml of luminol charged beads were added to design the self containing reactant chip. Those different preparations were then spotted with a micropipet as a 0.3 ml drop every 3 mm, on the surface of a freshly polished glassy carbon square (25 mm2), giving spots of 800 mm in diameter. The drops were dried under tungsten lamp and exposed to UV radiation for 30 min in order to obtain dry photopolymerised spots. Choline, glucose, glutamate, lactate, lysine and urate sensing layers could be spotted at the same time in a particular channel (see Fig. 2), producing in each channel a six-parameters biosensor. The ECL measurements were performed with a CCD camera LAS-1000 Plus (FUJIFILM). The experimental set-up is shown on Fig. 2. The glassy carbon electrode (25 mm2, from Goodfellow) was poised at a fixed potential (vs. a platinum pseudo-reference) during all the camera acquisition time (180 s). A piece of silicone, bring into contact with the glassy carbon electrode, patterned six different channels with a 200 ml inner volume. Pictures obtained were quantified with a FUJIFILM image analysis program (Image Gauge 3.12). All ECL measurements were performed in 30 mM Veronal (diethyl barbiturate) buffer, 30 mM KCl, pH 8.5, and given as arbitrary unit per surface unit (a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003182_jsvi.1997.1301-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003182_jsvi.1997.1301-Figure2-1.png",
        "caption": "Figure 2. Typical finite rotor element co-ordinates.",
        "texts": [
            " To investigate the effects of misalignment on the rotor dynamic characteristics, we derived a dynamic model for coupling-rotor-ball bearing systems with three types of misalignment as shown in Figure 1: angular, parallel and combined misalignment. In this model, we introduced the reaction forces and moments of bearing and coupling elements as the misalignment effects. Then, we calculated the time responses under misalignment and unbalance force. In this study, we utilized the finite element model (FEM) for the flexible shaft and rigid disc elements [13]. Axial vibration, which is known to be an important indication for the presence of misalignment [1\u20133], is also included in the model. Using the co-ordinates given in Figure 2, the equation of motion for the shaft and disc elements is expressed in partitioned form as &m s+ d 0 0 0 ms+ d 0 0 0 ma'8y\u0308z\u0308x\u03089+ & 0 \u2212gs+ d 0 gs+ d 0 0 0 0 0'8y\u0307z\u0307x\u03079+ &k s 0 0 0 ks 0 0 0 ka'8yzx9= 8fy fz fx9, (1) where {y}= {q1 q2 q3 q4}T, {z}= {q5 q6 q7 q8}T, {x}= {q9 q10}T. Here, the superscripts s and d mean the shaft and disc elements, respectively; the superscript a means the axial direction; the matrices, [m], [g] and [k], are the mass, gyroscopic and stiffness matrices, respectively; the force vectors, {fy} and {fz}, include the unbalance, gravity and external forces, and the axial force vector, {fx}, has the axial component of unbalance force and the axial force developed by the axial deformation of the shaft element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure4-1.png",
        "caption": "Fig. 4. Velocity streamline of a simple water jacket with elbows.",
        "texts": [
            " The maximum temperature difference appears at this inflection point. In the water jacket design, the inflection point should be avoided. C. Impact of the Water Jacket Shape The analytical calculation of the CHTC is only effective for the water jackets with no elbows, such as circumferential water jackets. When the water passes through an elbow, the interfacial structures and interaction mechanisms, in the water jacket walls, are significantly affected. The computational fluid dynamics (CFD) is used to analyze the impact of elbows. Fig. 4 shows the velocity streamline of a simple water jacket with elbows. The vortex and backflow exist in the elbows, which causes a different velocity distribution. The circumferential and axial water jackets, with same inlet velocity and configuration parameters, are studied with CFD. The structured mesh and turbulent model (k-epsilon) are used in the CFD model. As shown in Fig. 5, the velocity distribution of the circumferential water jacket is uniform, which matches with Authorized licensed use limited to: Carleton University"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003526_j.oceaneng.2006.10.014-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003526_j.oceaneng.2006.10.014-Figure1-1.png",
        "caption": "Fig. 1. AUV model.",
        "texts": [
            " Simulation results show that AUV can be effectively controlled in the dive phase in spite of the presence of parameter uncertainties and the constraints on the control fin deflection. The organization of the paper is as follows. Section 2 presents the AUV model and the output regulation problem. Suboptimal control laws for the constrained and unconstrained cases are derived in Sections 3 and 4, respectively. Then simulation results are presented in Section 5. A schematic of the AUV model with its body-fixed coordinate system is shown in Fig. 1. The earth-fixed frame is treated as an inertial frame. The motion of the AUV lies in a vertical plane. Let \u00f0xB; yB; zB\u00de be the coordinates of the center of buoyancy. The origin of the body-fixed coordinate system is fixed at the center of buoyancy (i.e. \u00f0xB; yB; zB\u00de \u00bc 0). We denote the coordinates of the center of gravity of the vehicle with respect to the center of buoyancy by \u00f0xG; yG; zG\u00de. The heave and pitch equations of motion of the vehicle with respect to the body-fixed moving frame are described by a set of nonlinear differential equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.16-1.png",
        "caption": "Figure 12.16. Checking for tip interference during cutting.",
        "texts": [
            " However, in order to ensure that there is no tip interference, we will assume for the purpose of the calculations that the involute profile of the cutter tooth extends right out to the tip circle, meeting it at point ATc \u2022 To check that there is no tip interference, we calculate the distance between the tooth tip corner ATg of the gear, and the point where the path of ATc intersects the tip circle of the gear. This distance should exceed a specified value, such as 0.02 modules. The radius of point ATc on the cutter is of course equal to RTc , the radius of the tip circle. The profile angle ~Tc at this point, and the polar coordinate 9Tc ' are found from Equations (2.18 and 2.35), cos ~Tc Rbc (12.82) RTc 9' tsc inv ~s - inv ~Tc (12.83) -- + Tc 2Rsc Undercutting 291 The remaining equations are similar in form to Equations (12.38 - 12.43), where we discussed tip interference in an internal gear pair. Figure 12.16 shows the position of point ATc on the cutter, as it passes through the tip circle of the gear. The angle 9g is the polar coordinate of ATc ' relative to the axes fixed in the gear. By considering triangle CgCcATc' we can write down the following two equations, ( 2 2 2) Cf+RTc-RTg 2C f RTc (12.84) if- sin (fJ +9 ) Tc g g (12.85) The angular position of the cutter is found from Equation (12.84), ( 2 _ 2_ 2 ) RTg Cf RTc arccos 2C R f Tc - 9' Tc (12.86) The corresponding angular position of the gear is then given by Equation (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000071_j.promfg.2019.06.214-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000071_j.promfg.2019.06.214-Figure1-1.png",
        "caption": "Fig. 1. A schematic diagram of direct metal laser sintering (DMLS) process [6]",
        "texts": [
            " STL file slices the overall part into many layers with respect to the layer thickness and a laser beam sinters/melts each layer. Selective laser melting (SLM) and selective laser sintering (SLS) are the main two PBF processes. Unlike the SLM process, where the powder is completely melted d wn to fo m a homogeneous part, the SLS \u2217 Corresponding author. E-mail address: emalekip@purdue.edu (Ehsan Malekipour). process partially melts the material (sinter the powder) layerby-layer at the molecular level [5]. The schematic diagram in Fig. 1 shows the overall process of the PBF process [6]. The 3D printer machine consists of a supply station for the metal powder and a sintering/melting unit. A laser selectively sinters/melts the powder with respect to the layer geometry along a prescribed pattern. After sintering/melting of a layer, the powder dispenser platform moves upward a distance equals to the thickness of a layer to supply the material required for printing a new layer and a recoater arm or a roller transfers the material powder to the sintering/melting zone",
            " STL file slices the overall part into many layers with respect to the layer thickness and a laser beam sinters/melts each layer. S lective laser melting (SLM) and selective laser sintering (SLS) are the main two PBF processes. Unlike the SLM process, where the powder is completely melted down to form a homogeneous part, the SLS \u2217 Corresponding author. E-mail address: emalekip@purdue.edu (Ehsan Malekipour). process partially melts the material (sinter the powder) layerby-layer at the molecular level [5]. The schematic diagram in Fig. 1 shows the overall process of the PBF process [6]. The 3D printer machine consists of a supply station for the metal powder and a sintering/melting unit. A laser selectively sinters/melts the powder with respect to the layer geometry along a prescribed pattern. After sintering/melting of a layer, the powder dispenser platform moves upward a distance equals to the thickness of a layer to supply the material required for printing a new layer and a recoater arm or a roller transfers the material p wder to the sin ering/melting zone",
            " STL file slices the overall part into many layers with respect to the layer thickness and a laser beam sinters/melts each layer. Selective laser melting (SLM) and selective laser sintering (SLS) are the main two PBF processes. Unlike the SLM process, where the powder is completely melted down to form a homogeneous part, the SLS \u2217 Corresponding author. E mail address: emalekip@purdue.edu (Ehsan Malekipour). process partially melts the material (sinter the powder) layerby-layer at the molecular level [5]. The schematic diagram in Fig. 1 shows the overall process of the PBF process [6]. The 3D printer machine consists of a supply station for the metal powder nd sintering/melting unit. A laser selectively sinters/melts the powder with respect to the layer geometry along a prescribed pattern. After sintering/melting of a layer, the powder dispenser platform moves upward a distance equals to the thickness of a layer to supply the material required for printing a new layer and a recoater arm or a roller transfers the material powder to the sintering/melting zone",
            " STL file slices the overall part into many layers with respect to the layer thickness and a laser beam sinters/melts each layer. Selective laser melting (SLM) and selective laser sintering (SLS) are the main two PBF processes. Unlike the SLM process, where the powder is completely melted down to form a homogeneous part, the SLS \u2217 Corresponding author. E-mail address: emalekip@purdue.edu (Ehsan Malekipour). process partially melts the material (sinter the powder) layerby-layer at the molecular level [5]. The schematic diagram in Fig. 1 shows the overall process of the PBF process [6]. The 3D printer machine consists of a supply station for the metal powder and a sintering/melting unit. A laser selectively sinters/melts the powder with respect to the layer geometry along a prescribed pattern. After sintering/melting of a layer, the powder dispenser platform moves upward a distance equals to the thickness of a layer to supply the material required for printing a new layer and a recoater arm or a roller transfers the material powder to the sintering/melting zone",
            " STL fil slices the over l pa t i to ma y layers with respect to the layer thickn ss a d a laser b am sin ers/melts each layer. Sel ctive laser melting (SLM) and s lective laser sinte ing (SLS) are the main two PBF processes. Unlike the SLM process, where the powder is completely melt d down to form a homogeneous part, the SLS \u2217 Corresponding author. E mail address: emalekip@purdue.edu (Ehsan Malekipour). process partially m lts the material (sinter the pow er) layerby-layer at the m le ular level [5]. T schematic diagram in Fig. 1 shows the overall process of the PBF process [6]. The 3D printer m chin consists of a supply station for th metal powder an a sintering/melting unit. A s s lectively sin ters/melts the owder with r pect to the layer geometry al ng a prescribed pattern. After sintering/melting of a layer, the powder dispenser pl tform moves upward a distance equals to the thickness of a lay t supply the material equired for printing a new layer and a rec ater arm or a roller tr nsfers the material powder t t sintering/melting zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000093_tie.2020.2982112-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000093_tie.2020.2982112-Figure9-1.png",
        "caption": "Fig. 9 Lock position selection",
        "texts": [
            " 3(b), if all power switches maintain switched off except K4 and K5, the windings of A and B phases, the exist two power switches K4 and K5, the four freewheel diodes D2, D3, D5 and D6 are utilized for constructing the bridgeless AC-DC rectifier based on-board battery charger. Thus, no additional power devices should be added to realize the charging function. However, as the phase windings of two adjacent phases are selected for using as the energy-storage inductors of the bridgeless rectifier, it is necessary to avoid the variation of the phase inductance caused by rotation and magnetic saturation effects. As shown in Fig. 9, by exciting phase-C alone, the rotor will rotate to the C-phase aligned position, where the center lines of the rotor poles are aligned with the center lines of the C-phase stator poles. Thus, to lock the rotor in this position with a mechanical fixture, the winding inductance value of phase A and B are equal. As can be seen in Fig. 9, their inductances are equal to Lth, which is the inductance value in the lower intersection position of the three phase unsaturated inductance characteristics. Besides, in the C-phase aligned position, both of the A and B phases are located nearby their unaligned positions individually. Thus, their phase inductance will not sensitive to the magnetic saturations, even though there are high input currents flowing through the windings. The basic operational modes of the constructed bridgeless rectifier are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002789_s1350-6307(97)00006-x-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002789_s1350-6307(97)00006-x-Figure4-1.png",
        "caption": "Fig. 4. Combination of sliding and rolling in gear teeth.",
        "texts": [
            " The effect of the latter is that the surface material is rolled in one direction, and pushed (sliding) in another, therefore resulting in higher stresses than those encountered in positive sliding [4]. The modified stress distribution in the surface and near-surface material resulting from combined rolling and sliding is shown in Fig. 3. The position of maximum shear stress is moved closer to the contacting interface, and crack initiation therefore occurs at the surface. Gear teeth have complex combinations of sliding and rolling, which vary along the profile of each tooth, as illustrated in Fig. 4. In the addendum, the direction of rolling and sliding is the same, and positive sliding conditions therefore prevail. In the dedendum, however, the direction of rolling is opposite to that of sliding, and negative sliding conditions exist. Contact fatigue is therefore more likely to initiate in the dedendum, and pitting in this region is usually very severe, and often acts as a precursor to tooth bending fatigue [1]. In practice, it is common that contact fatigue damage will first occur in the dedendum of the smaller gear (which is usually the driving gear) of a gear set [4, 5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000658_j.ymssp.2021.107711-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000658_j.ymssp.2021.107711-Figure6-1.png",
        "caption": "Fig. 6. Schematic diagram of ball-race contact: (a) a radially loaded REB, and (b) a simplified spring-damper model under EHL condition.",
        "texts": [
            " (36) gives the formula of load-film thickness Q \u00bc 2:5955 106h 14:9254 c U10G7:9104\u00f01 0:61e 0:73j\u00de14:9254EeqR 15:9254 c \u00f039\u00de According to the definition of contact stiffness, the oil film stiffness, Koil, can be given by Koil \u00bc lim Ddfilm!0 DQ Dd \u00bc dQ dh \u00f040\u00de in which dfilm represents the deformation of the oil film in contact area. Combining Eqs. (39) and (40), Koil can be formulated by Koil \u00bc 3:8746 107h 15:9254 c U10G7:9104\u00f01 0:61e 0:73j\u00de14:9254EeqR 15:9254 c \u00f041\u00de For the ball-race contact under EHL (see Fig. 6(b)), the normal load Q en in the inlet zone can be calculated considering the following simplified hypotheses [22,23]. (1) The elliptical shape area of the Hertzian contact can be approximately considered as a rectangle with length 2a and width 2b. The major axis of the contact ellipse is here much larger than its minor axis (viz., 2a 2b). In this case, the sideleakages effects are neglected. (2) The variation of the film thickness on perpendicular direction is neglected, and the oil film viscosity is considered, initially, as a constant",
            " (54) in the Hertzian contact area considering Eqs. (40) and (55) gives [23,24] d \u00bc Koil \u00fe Kre\u00f0 \u00dehc=Kre \u00f056\u00de Referring to Eq. (56), Eq. (53) can be further written as Q en \u00bc 4Kreg0uyRya h2 c \u00f0Koil \u00fe Kre\u00de d\u00fe i 13:329g0R 1:5 y a h1:5 c xd \u00f057\u00de According to the definition of stiffness, in the inlet region, the stiffness of oil film can be formulated by [23,24] Ken \u00bc dQen dhc \u00bc 4g0uyRya h2 c \u00f0Koil \u00fe Kre\u00de Kre \u00f058\u00de and the damping coefficient can be formulated by [23,24] Cen \u00bc dQ en dux \u00bc 13:329g0R 1:5 y a h1:5 c \u00f059\u00de Fig. 6 shows a ball-race contact under EHL condition. Because of the application of normal load on the rolling element, there will be a elastic contact stiffness Kre in series with Koil (see Fig. 6(b)). The deformation of the ball will cause the surfaces in the oil film inlet zone to come together, and this case allows the generation of stiffness Ken and damping Cen [24], which will act in parallel with other stiffnesses and dampings (see Fig. 6(b)).From Fig. 6(b), the total stiffness of the ball-race contact under the EHL condition can be formulated by KB IR=OR \u00bc dQ ddk \u00bc KreKen \u00fe KoilKen \u00fe KoilKre Kre \u00fe Koil \u00f060\u00de For the contact pair in the Hertzian contact region, the minimum thickness of oil film is extremely small and thus very stiff, and the damping Coil can be neglected. In addition, metallic components possess very low inherent damping characteristic because of the existence of the oil film, and thus the bearing system damping Cc in the Hertz contact area can be ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure4.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure4.6-1.png",
        "caption": "Fig. 4.6 J. Watt\u2019s steam engine. a Watt\u2019s engine (https://dazeinfo.com), b centrifugal governor (https://en.wikipedia.org/wiki/Centrifugal_governor)",
        "texts": [
            " For this issue, Watt installed a flywheel to smooth out the speed fluctuation of the output rotation. The speed of the engine output is also affected by the amount of steam into the engine. Without proper control, the amount of steam, also the output speed of the 4.2 Steam Engine and Transportation Revolution 101 engine, can\u2019t keep constant. In 1782 Watt made another important improvement. Under the suggestion of Matthew Boulton, an entrepreneur and his partner, he installed a centrifugal governor in his engine, making the amount of steam supply close to a preset value (Fig. 4.6b). Thus, the output speed of the engine could be kept stable. This improvement paved the way for the engine to be applied in trains and ships. Neither flywheel nor centrifugal governor was Watt\u2019s invention. Governors had already been applied in mills of Europe since the 17th century while flywheels first appeared in Germany early in 1430. About the centrifugal governor, another two things are worth of mentioning. First, it is the early application of the modern automatic control theory. Second, further application of and investigation on centrifugal governors triggered an extremely important topic of system stability in mechanics, see Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000247_pime_proc_1950_163_020_02-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000247_pime_proc_1950_163_020_02-Figure10-1.png",
        "caption": "Fig. 10. Dimensions Used for Calculating Fillet Stress",
        "texts": [
            " Thus, the use of a ilominal fillet stress based on the bending moment, although satisfactory for the long cantilever, was a guess for the gear tooth. A closer estimate of the nominal stress could probably be achieved by the introduction of a second factor, the magnitude of which should vary inversely as the square root of the distance of the point of tooth contact from the fillet. That factor increased the nominal tensile fillet-stress, and had been suggested by him in a recent paper$. By simplification of the formula, the maximum tensile fillet-stress became :- D(l?iu/e2+ 1/0.3/be)M Dimensions a, b, e, and R were indicated in Fig. 10, W was the * CARTER, B. C., and FORSHAW, J. R. 1942 Aeronautical Research Committee Report and Memoranda No. 1982, \u201cDesign and Development of a Torsiograph having a Serrated Condenser Pick-up Unit\u201d. CARTER, B. C., SHANNON, J. F., and FORSHAW, J. R. 1945 Proc. I.Mech.E., vol. 152,p;,219, \u201cMeasurement of Displacement and Strain by Capacity Methods , j- LINDSEY, W. H. 1949 J1. Roy. Aeronautical SOC., vol. 53, p. 141, \u201cThe Development of the Armstrong Siddeley \u2018Mamba\u2019 Engine\u201d. # HEYWOOD, R. B. 1948 Proc",
            " The fundamental investigation of dynamic stresses in gear teeth involved masses and elasticities, and the problem was therefore basically a vibration problem. The possibilities of overstressing by resonance were ominous: he was relieved 10 hear that damping would tend to prevent that occurrence. It would Seem prudent in design not to search too diligently for possible vibration dangers but preferably to avoid any proximity between the frequency of a single-node torsional vibration and the frequency of tooth engagement. The meaning of the figure 10,000 in the last line of Table 1 was that, according to the theory developed, with elp = 1-5/1,000 the permissible bending stress at any speed higher than 10,000 r.p.m. was at least as high as that allowed by British Standard formula for 10,000 r.p.m. He did not suggest that British Standard allowable stresses were undesirably high. Any case in which the present theory seemed to require a lower allowable stress than British Standard should be taken merely as confirming that one or more of the underlying assumptions made in the paper was purposely pessimistic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003019_s1350-4533(00)00062-x-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003019_s1350-4533(00)00062-x-Figure5-1.png",
        "caption": "Fig. 5. Load deformation curve of implant 47.",
        "texts": [
            " However, even if no significant failure was observed, taking the minimum value instead of the average should be considered. Static compression tests, according to the ASTM (designation F-384-73,1987) have been performed on the hard-wired nail-plate type implants, loaded as presented in Fig. 3. The response of strain gauges, bonded at critical spots, as indicated in Fig. 4, has been monitored in combination with the load-deformation curve of the implant. Linear deformation is observed up to 750 N as shown in Fig. 5. Fig. 5 shows the load-deformation curve of one of the implants (number 47), for three repetitive loadings to 750 N and the final destructive test. The structural importance of the lid is demonstrated as well as the relatively poor response of the bottom strain gauge (SG1, Figs. 4 and 6) as compared to the response of the gauges SG2 and SG3, distant from the neural axis. The varied or changeable response of the lid strain gauges shown in Fig. 7, suggests failure at the lid/nail-plate weld. The stress concentration in an implanted device can compromise its hermeticity, induce moisture leakage and disturb the sensor signal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000712_j.oceaneng.2021.109724-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000712_j.oceaneng.2021.109724-Figure2-1.png",
        "caption": "Fig. 2. Wind turbine two-mass model.",
        "texts": [
            " Cp(\u03bb, \u03b2)= \u03bbCq(\u03bb, \u03b2) (5) Power coefficient for the under-studied wind turbine is presented in Fig. 1. Through regulating \u03b2, the pitch system controls the amount of wind energy captured by the turbine. For hydraulic pitch control systems, each actuator is considered as a linear second-order system with the following transfer function. \u03b2 \u03b2r = \u03c92 n s2 + 2\u03b6\u03c9n + \u03c92 n (6) where \u03b2r, \u03b6 and \u03c9n show the reference pitch angle, damping ratio and natural frequency, respectively. The mechanical part of drivetrain system can be modeled as a nonlinear two-mass spring damper system as shown in Fig. 2. Its dynamic model can be represented by the following state space equations (Esbensen and Sloth, 2009). \u03c9\u0307r = 1 Jr ( Pr(\u03c9r , \u03b2,U) \u03c9r \u2212 \u03c9rDs + \u03c9gDs Ng \u2212 \u03b8Ks ) \u03c9\u0307g = 1 Jg ( \u03c9rDs Ng \u2212 \u03c9gDs Ng 2 + \u03b8Ks Ng \u2212 Tg ) \u03b8\u0307 = \u03c9r \u2212 \u03c9g Ng (7) in which \u03b8 shows torsional angle. The definition of other parameters and their corresponding values for the reference turbine are listed in Table 1. Defining the state and the input vectors as, x= [ \u03c9r \u03c9g \u03b8 \u03b2 \u03b2\u0307 ]T , ...u = \u03b2r (8) the nonlinear dynamic model of the wind turbine in affine form is expressed as, x\u0307= f (x, x\u0307) + gu (9) where f(x, x\u0307) represents the nonlinear term in wind turbine model and g is the coefficient of control input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.8-1.png",
        "caption": "Figure 16.8. Right-handed hob and right-handed gear.",
        "texts": [],
        "surrounding_texts": [
            "The most commonly used method for cutting helical gears is by hobbing. As always in generating cutting, one gear is used to cut another. A typical hob is shown in Figure 16.3, and it can be seen that, apart from the gashes forming the cutting faces, the hob is simply a helical gear, in which each tooth is referred to as a thread. A hob. 458 Gear Cutting II, Helical Gears Since the hob is similar in shape to a screw, its helix angle \"'sh is always large, particularly when there is only one thread. It is cust~mary to specify the shape of a hob by means of its lead angle, rather than its helix angle. For a right-handed hob, the lead angle Ash is defined as the complement of the helix angle, (16.13) where Ash and \"'sh are measured in degrees. For a left-handed hob, whose helix angle is negative, the lead angle can be def ined as follows, - 90 0 - '\" sh ( 16.14) so that we obtain a negative lead angle for a left-handed hob. In practice, it is generally the magnitude of the lead angle which is given in the specification, together with a statement to indicate whether the hob is right or left-handed. It is clear that the lead angle can be determined from the helix angle, and vice versa. In describing the geometry of the hobbing process, we will specify the shape of the hob by means of its helix angle, since the symbols will then agree with the notation used in Chapter 15, where we described the geometry of crossed helical gears. Figure 16.4 shows a hob in position to cut a gear blank, and since their axes are not parallel, it is clear that they form a crossed helical gear pair. During the cutting process, the hob and the gear blank are rotated about their axes with angular veloci ties wh and wg ' I n order to cut the teeth of the gear across the entire face-width, the hob is moved slowly in the direction of the gear axis, and the velocity of the hob center is called the feed velocity vh . The values required for the three variables wh ' Wg and vh are achieved by means of change gears or stepping motors in the hobbing machine. There are two additional settings which must be made when the hobbing machine is being set up. These are the shaft angle ~, which is the angle between the axes of the hob and the gear blank, and the cutting center Hobbing 459 distance CC, which is the distance between the two axes. In the remainder of this section, we will determine the values required for the machine parameters wh ' wg ' vh ' E and CC, if the hob is to cut a gear with Ng teeth, normal module mn , normal pressure angle ~ns' helix angle ~sg' and normal tooth thickness t nsg Before we discuss the details of the cutting process, we will first prove that, as usual, the gear will have the same normal module and normal pressure angle as those of the hob. We showed in Chapter 15 that the minimum condition for correct meshing of two crossed helical gears is that their normal base pitches should be equal. The corresponding result, when we consider a gear being cut by a hob, is that the normal base pitch of the gear will always be equal to that of the hob. Since the normal base pitch of the hob is equal to that of the basic rack, we can conclude that the normal base pitches of the gear and the basic rack are equal, and the gear can therefore mesh correctly with the basic rack. As always, the standard pitch cylinder of the gear is defined as its pitch cylinder when it is meshed with the basic rack. The normal pitch Pns and the normal pressure angle ~ns of the gear must 460 Gear Cutting II, Helical Gears then be equal to those of the basic rack, and hence equal to those of the hob. This result remains true, whether or not the cutting pitch cylinders of the gear and the hob coincide with the i r standard pi tch cylinders. In order to cut the gear described earlier, we must therefore use a hob with the same normal module and normal pressure angle as those specified for the gear. We consider next how to cut the required number of teeth, and the correct helix angle. When a rack cutter is used to cut a gear, the helix angle of the gear depends on the angle at which the cutter is set, so it might be expected that the helix angle of a gear being hobbed would be determined by the value of the shaft angle ~. This is not the case, however, and we will now show that the number of teeth cut in the gear blank, and the helix angle at which they are cut, depend only on the values chosen for wh ' Wg and vh \u2022 In Chapter 5, we defined the cutting point as the point where the cutter makes a cut on the final tooth surface, and we showed that this point corresponds to the contact point when the gear blank and the cutter are regarded as a pair of meshing gears. The situation is no different when the cutter is a hob. We described in Chapter 15 how to find the position of the contact point in a crossed helical gear pair, and this point becomes the cutting point when we consider a hob cutting a gear. As in any metal-cutting process, the shape of each tooth cut in a gear blank is the envelope of positions through which the hob moves, relative to the gear blank. For the purpose of determining this shape, it is helpful to neglect the gashes in the hob thread, so that the threads are regarded as continuous, and we can imagine that the teeth are formed in the gear blank by grinding, rather than by cutting. If the hob and the gear blank were a pair of crossed helical gears, there would always be at least one thread of the hob making contact with the gear. Hence, for the hob and the gear blank, there is always at least one thread which is in contact with the final tooth surface of the gear. We label the points in contact AOh on the hob, and AOg on the gear. After the hob turns through exactly one angular pitch, the position of the thread containing point AOh is occupied by the Hobbing 461 next thread, and the corresponding point Alh on this thread will now be the cutting point, touching a point A1g on the gear tooth adjacent to the tooth containing AOg. As the hob rotates, we can identify a sequence of points such as AOh and Alh on the hob threads, and AOg and A1g on the gear teeth. The points on the hob lie in the same transverse section and are evenly spaced, at angular intervals equal to the angular pitch. Of course, if the hob has only one thread, the angular pitch is 360 0 , and the points all coincide. On the other hand, the gear points do not lie in one transverse section, due to the feed of the hob in the direction of the gear axis, and each point is displaced axially a small amount relative to the next point. We now consider the position on the gear of point ANg , the cutting point when the hob has turned through Ng angular pitches. Since the gear is to have Ng teeth, points AOg and ANg must be on the same tooth. Hence, if the gear is a spur gear, ANg must lie on the axial line through AOg' while if the gear is a helical gear, ANg must lie on the gear helix through AOg. The distance through which the hob is fed during one revolution of the gear blank is called the feed rate f. Since the magnitude of f is small compared with the tooth dimensions, point ANg always lies close to the axial line through AOg. The gear blank must therefore turn through approximately one revolution while the hob turns through Ng angular pitches, which is a rotation equal to (Ng/Nh ) revolutions. In order to meet this requirement, the angular velocity ratio (wh/wg ) must be approximately equal to (Ng/Nh ), or exactly equal, when a spur gear is being cut. In the case of a helical gear, the small difference between the two ratios is one of the factors which determine the helix angle of the gear, as we will show later in this section. Once the settings are chosen for the hobbing machine, the value of (wh/wg ) is established, and the number of teeth that will be cut in the gear is then given by the following expression, NhWh Integer closest to (--) Wg (16.15) 462 Gear Cutting II, Helical Gears Having found how the value of Ng depends on the hobbing machine angular velocities wh and wg ' we now consider the helix angle. If points AOg and A1g lie at radius R, the positions of these points at various times can be plotted on a developed cylinder of radius R, as shown in Figure 16.5. The times at which the hob touches points AOg and A1g are called T and T', and the diagram shows the positions of AOg at time T, and A1g at time T'. Since the feed of the hob is in the direction of the gear axis, the line in the diagram joining AOg and A1g is in the same direction. The diagram also shows the gear helices through these points, which appear as straight lines making an angle ~Rg with the gear axis, and these are labelled helix 0 and helix 1. The point on helix 0 in the transverse section through A1g is labelled Ag \u2022 The position of helix 0 at time T' is shown by the dotted line, and the positions of Aog and Ag at this time are shown as AOg and Ag \u2022 In Figure 16.5, the length AOgA1g represents the hob feed between the times T and T', and AgAg represents the arc Hobbing 463 length moved by point Ag in the same time interval. Since helix 0 and helix 1 are gear helices on adjacent teeth at the same radius, their positions at any instant are exactly one tooth pitch apart. A1g and Ag lie on the two helices in their positions at time T', so the distance between these points is equal to the transverse pitch. We therefore obtain the following expressions for the three lengths, A A' 9 9 A A' 19 9 The time interval required for the hob to rotate through one angular pitch can be expressed in terms of the hob angular velocity, T' - T We now use triangle AOgA1gAg to relate the three lengths, A A' - A A' 19 9 9 9 and when their values are substituted, we obtain the following relation between wh ' Wg and vh ' 211' vh -N-- tan l/IR hWh 9 ( 16.16) The feed rate f of the hob was defined earlier as the distance moved by the hob during one revolution of the gear blank. It is customary to express the feed velocity vh in terms of f, _f_ (211') Wg (16.17) and with this substitution, Equation (16.16) takes the following form, tan l/IRg 211'R ( 16.18) 464 Gear Cutting II, Helical Gears The helix angle of the gear at radius R is expressed in terms of the lead Lg by Equation (13.31), tan IPRg and Equation (16.18) then becomes a relation giving the lead that will be cut in the gear, l(NhWh ) f - Ng Wg ( 16.19) The quantity (Ng/Lg) is equal to the reciprocal of the axial pitch, as we showed in Equation (13.36), and this can be expressed in terms of the helix angle IPsg by means of Equation (13.42), _1_ Pzg sin IPSg Pns (16.20) Hence, Equation (16.19) can be put into two alternative forms, giving either the axial pitch or the helix angle of the gear, _1_ Pzg l(NhWh ) f - Ng Wg (16.21 ) (16.22) It is an interesting result that, as we pointed out earlier, the helix angle cut in a gear is not affected by the shaft angle ~ of the hobbing machine. This angle is generally set equal to the standard shaft angle ~s' or in other words, equal to the sum of the helix angles of the gear and the hob, ~s (16.23) We showed in Chapter 15 that a pair of crossed helical gears can mesh correctly, even when the shaft angle is not equal to the standard shaft angle. It therefore follows that a hob can cut an accurate involute gear, even when ~ is not exactly equal to ~s. However, for the remainder of this section, we will assume that the shaft angle is set equal to ~s' and in a Hobbing 465 later section of the chapter we will discuss the consequences of a small change in this value. The last setting of the hobbing machine to be considered is the cutting center distance CC , and its effect on the tooth thickness of the gear. As we discussed earlier, the cutting process can be considered as equivalent to meshing with zero backlash. An expression for the normal backlash in a crossed helical gear pair was given in Equation (15.96), The length ~Cp Equation (15.47), in this expression (16.24) was defined by (16.25) and all the other quanti ties are defined on the pitch cylinders, as indicated by the notation. We are considering, at present, a hob cutting a gear blank when the shaft angle ~ is set equal to the standard value ~s. In this case the cutting pitch cylinders coincide with the standard pitch cylinders, as we proved in Chapter 15. If we replace RP1 and Rp2 in Equation (16.25) by Rsg and Rsh ' and set the backlash in Equation (16.24) equal to zero, these two equations give an expression for the normal tooth thickness cut in the gear, (16.26) The expression in brackets in this relation represents the hob offset. When the normal tooth thickness t h of the hob is ns equal to O.5Pns' Equation (16.26) has exactly the same form as Equation (16.12), which gave the normal tooth thickness of a gear cut by a rack cutter. If the normal tooth thickness of the hob is greater than O.5Pns' the normal tooth thickness of the gear is reduced by the same amount. Whatever the value of t nsh ' the effect of a change in the hob offset on the tooth thickness of the gear is identical to the corresponding effect caused by a change in the offset of a rack cutter. In Chapter 5, we stated that the tooth thickness of a gear cut by 466 Gear Cutting II, Helical Gears a hob is generally calculated as if the gear were cut by a rac k cutter. We have now shown that thi s procedure is essentially correct, prpvided the hobbing machine is set with its shaft angle ~ equal to the standard value ~s' There is a second manner in which the cutting action of a hob resembles that of a rack cutter. In the discussion following Equations (15.74 and 15.77), we showed that the path of contact in a crossed helical gear pair touches each base cylinder, and makes an angle (~- 'tp1) with the line of centers, when viewed in the direction of the axis of gear 1. Hence, in the case of a hob cutting a gear, the path followed by the cutting point touches the base cylinders of the gear and the hob, and makes an angle (~- 'tpg) with the line of centers, when viewed in the direction of the gear axis. If the shaft angle is set at the standard value, this angle becomes (1[2 - 't ), as shown in Figure 16.6, and the path of the sg . cutting point then appears identical with the corresponding path when the gear is cut by a rack cutter. It is for this reason that, when we check for undercutting in a gear, we can regard the hob as equivalent to a rack cutter. We check that Swivel Angle 467 there would be no undercutting if the gear was cut by the rack cutter, and this implies that there will also be no undercutting when in fact the hob is used. Swi vel Angle Earlier in this chapter, we stated that it is common practice to specify the lead angle of a hob, instead of its helix angle. It is also customary to specify the angular setting of the hobbing machine by means of the swivel angle, rather than by the shaft angle. Since a hob is shaped like a screw, its helix angle is always large, particularly in the case of a single-thread hob, for which the helix angle is typically about 85\u00b0. The helix angle of the gear being cut may of course have any value, but in the majority of gears, the magnitude of the helix angle is between 0\u00b0 and 30\u00b0. In general, right-handed hobs are used to cut right-handed gears, and left-handed hobs are used for left-handed gears. In most cases, therefore, the shaft angle is approximately equal to a right angle, and the swivel angle is defined as the amount by which the shaft angle differs from a right angle. For example, if the axis of the gear is vertical during the cutting process, the swivel angle a is defined as the angle which the hob axis makes with the 468 Gear Cutting II, Helical Gears horizontal. The standard shaft angle was defined by Equation (16.23), as the sum of the gear and the hob helix angles. We express the helix angle of the hob in terms of its lead angle, by means of Equation (16.13 or 16.14), and we obtain the following expression for the standard shaft angle, ,f, + 90\u00b0 - A \"'sg - sh (16.27) where the plus and minus signs refer to a right or Hobbing Machine Gear Train Layout 469 left-handed hob. We now define the standard swivel angle os' so that it differs by a right angle from the standard shaft angle, (16.28) As discussed earlier, the hobbing machine is generally set so that the shaft angle is equal to the standard shaft angle, and it then follows that the swivel angle is equal to the standard swivel angle. Figures 16.7 and 16.8 show the relations between the shaft angles and the swivel angles when a right-handed hob is used to cut a spur gear or a right-handed helical gear, while Figures 16.9 and 16.10 show the corresponding relations when a left-handed hob is used to cut a spur gear or a left-handed helical gear. Hobbing Machine Gear Train Layout We showed in Equations (16.15 and 16.22) that the number of teeth and the helix angle cut in a gear depend on the feed rate f and the angular velocity ratio (wh/wg ) in the hobbing machine, NhWh Integer closest to (----) Wg (16.29) 470 Gear Cutting II, Helical Gears sin I/I sg l(NhWh ) f - Ng Wg (16.30) It is helpful to examine how the gear trains in some typical hobbing machines are arranged, in order to achieve the values of Ng and I/I sg required in the gear. One type of hobbing machine is shown schematically in Figure 16.11. The rectangular boxes in the diagram represent gear pairs or gear trains, with the output-input ratio in each case given by the constant k. The symbol ki stands for the ratio of the index change gears, kf is the ratio of the feed change gears, and the other k values represent the gear trains built into the machine, whose ratios cannot be altered by the user. The values of wh and wg , and of the hob feed velocity vh ' can be read from the diagram in terms of the input angular velocity w 1 ' (16.31) (16.32) Hobbing Machine Gear Train Layout 471 (16.33) The feed rate f was given by Equation (16.17), in terms of Wg and vh ' and when these are expressed by means of Equations (16.32 and 16.33), we obtain a relation between the feed rate and some of the gear ratios in the hobbing machine, f The terms in brackets are combined into a single constant, known as the machine feed constant Cf , whose value is provided by the manufacturer of the hobbing machine. The feed rate is then expressed solely as a function of the ratio kf of the feed change gears, f (16.34) To obtain the ratio (wh/wg ) in terms of the hobbing machine gear ratios, we express wh and Wg by means of Equations (16.31 and 16.32), As before, the terms in brackets are combined into another constant, the machine index constant Ci , whose value is also provided by the manufacturer, and the angular velocity ratio is then given by the following expression, C\u00b7 1 k.\" 1 (16.35) We substitute this expression into Equations (16.29 and 16.30), and we obtain the number of teeth that will be cut in the gear, and its helix angle, in terms of the hobbing machine gear ratios, NhC. Integer closest to ( __ l) k i (16.36) {16.37l We now determine how the machine ratios should be 472 Gear Cutting I I, Helical Gears chosen, in order to cut a gear with the number of teeth and helix angle required. The feed rate f and the hob angular velocity wh are chosen to obtain good metal-cutting characteristics. The values depend on the size of the hob, the hardness of the material being cut, and the surface finish required. For more details, the reader should consult references such as the Gear Handbook [2]. Once a value for f is. chosen, the required ratio kf for the feed change gears is found from Equation (16.34), f Cf (16.38) The value chosen for wh is obtained by setting the input speed change, shown in Figure 16.11, to a suitable value. With the feed change gear ratio already selected, the index change gear ratio is used to determine both the number of teeth cut in the gear, and its helix angle. We choose the ratio ki so that it satisfies Equation (16.37), in order to obtain the required helix angle, NhCi ki f sin ~Sg (16.39) (1rm + N ) n g When this value for ki is substituted into Equation (16.36), we find that we also obtain the correct number of teeth, because the magnitude of the term (f sin ~Sg/1rmn) in the expression for ki is always very much less than 0.5. It is sometimes difficult to find change gears which provide exactly the value of ki given by Equation (16.39). Once the change gears have been chosen, their actual ratio ki should be calculated, and this value is substituted into Equation (16.37), to give the helix angle that will in fact be cut in the gear. Use of a Differential in the Hobbing Machine There is one major problem associated with hobbing machines, when they are designed in the manner shown in Figure 16.11. If a second cut is required, as is often the case, it is necessary to disconnect the feed drive, in order Use of a Differential in the Hobbing Machine 473 to return the hob quickly to its starting position. It is then very difficult to reset the machine, with the work table and the hob in exactly the correct positions. This problem can be overcome if a differential is incorporated into the hobbing machine. In order to determine the relation that must be maintained between the hob feed, the work table rotation and the hob rotation, we once again consider Equation (16.30), We use Equation (16.17) to express the hob feed rate f in terms of the feed velocity vh ' and we obtain the relation which must be maintained throughout the cutting process between the hob feed velocity, the table angular velocity, and the hob angular veloci ty, (16.40) A gear train with one degree of freedom can always be represented by a linear equation relating the angular velocities of the input and the output shafts. A differential is a gear train with two degrees of freedom, and it has three shafts, either two input and one output, or one input and two output. The angular velocities of the three shafts are always related by a single linear equation. Hence, as we can see from Equation (16.40), if the hob feed, the work table drive and the hob drive were all connected to the three shafts of a suitable differential, they would then always maintain the correct relative positions. The differential may be a simple planetary gear train, or one which is constructed of bevel gears. In either case, the output angular velocity w3 is a linear combination of the input angular velocities w1 and w2 ' and can therefore be represented by the following equation, (16.41) The constants k7 and ka of the differential depend on the design of the gear train, and need not concern us here. 474 Gear Cutting II, Helical Gears The complete layout of the hobbing machine is shown in Figure 16.12, where the differential is represented as a simple planetary gear train. The hob drive is connected to the sun gear of the differential, the table drive is connected to the planet carrier, and the feed is connected to the internal gear. As before, the index change gears and the feed change gears are represented by symbols ki and kf , and now there is a third set of change gears, the differential change gears, represented by the symbol kd \u2022 The constants k1 to k6 are the fixed ratios of the gear trains in the hobbing machine. The constant k6 represents the ratio of a worm and gear, connecting the differential change gears to the internal gear of the differential. This ratio is shown with a minus sign, since the hand of the helix in the worm is chosen so that a positive angular velocity in the worm produces a negative angular veloci ty in the gear. We pointed out earlier that the number of teeth and the helix angle cut in the gear depend on the feed rate f and the Use of a Differential in the Hobbing Machine 475 angular velocity ratio (wh/wg ). We therefore need to express these two quantities in terms of the hobbing machine gear ratios. We start by writing down a number of relations between the angular velocities, Wh k1w1 (16.42) Wg k2ki k3w3 (16.43) vh k2kik4kfw3 (16.44) w 2 k2kik4kfkd(-k6)w3 (16.45) The feed rate f, which was given by Equation (16.17), can now be expressed in terms of the gear ratios, f As before, the terms in brackets are combined into a single quantity, the machine feed constant Cf , and the feed rate is then given simply in terms of the feed change gear ratio, f (16.46) When Equations (16.42 and 16.43) are used to express wh and wg ' the angular velocity ratio takes the following form, wh k1w1 Wg k2k3kiw3 and the relation between w 1 and w3 is found from Equations (16.41 and 16.45), The last two equations are combined to give the angular velocity ratio in terms of the gear ratios, and we use Equation (16.46) to express the ratio kf in terms of the feed rate f, (16.47) 476 Gear Cutting II, Helical Gears We now define the machine index constant Ci and the machine di fferent ial constant Cd as follows, C. 1 k1 k2 k3k7 k3 k7Cf k1k4 k6kS As usual, the values of the machine constants Cf ' Ci and Cd are all provided by the manufacturer of the hobbing machine. Ci is a ratio, but Cf and Cd are lengths, since they are defined in terms of the feed rate f, which is the distance moved by the hob during one revolution of the work table. When the constants are substituted into Equation (16.47), we obtain the final expression for the angular velocity ratio, (16.4S) This expression is substituted into Equations (16.29 and 16.30), and we obtain the number of teeth and the helix angle that will be cut in the gear, corresponding to the feed rate f and the change gear ratios ki and kd in the hobbing machine, C\u00b7 fkd Integer closest to [Nh(k: + c)] 1 d (16.49) (16.50) Once again, we must determine how the change gear ratios kf , k i and kd should be chosen, in order to cut a gear with Ng teeth and helix angle ~sg' As before, we choose the feed rate f from metal-cutting considerations, and the ratio kf is then given by Equation (16.46), (16.51) If we are cutting a spur gear, or in other words a gear with zero helix angle, we can satisfy Equation (16.50) by setting the value of kd equal to zero, and choosing the value of ki as follows, Use of a Differential in the Hobbing Machine k. 1 477 (16.52) The conventional method for cutting a helical gear is to use the same value for ki , and to choose kd in a manner which then satisfies Equation (16.50), Cd sin IPsg Nh '/I'mn (16.53) An alternative expression for the required differential change gear ratio is found by combining Equations (16.20 and 16.53), (16.54) When we compare the last two equations, it is clear that it is much easier to select suitable change gears, giving the correct value for kd , if we design the gear so that its axial pitch Pzg is a round number, rather than its helix angle IPsg. There are times when it is difficult, or even impossible, to find change gears which provide the exact values for ki and kd , given by Equations (16.52 and 16.53). For example, when the value required for Ng is a large prime number, we cannot obtain the exact value for ki , since most sets of change gears do not contain gears with more than 120 teeth. Also, when the helix angle ~sg is very small, it may be difficult to obtain a sufficiently accurate value for kd \u2022 When these situations occur, we can choose the index gears so that their ratio ki differs slightly from the value given by Equation (16.52), and the differential change gears are then used to ensure that Equation (16.50) is still satisfied with sufficient accuracy. Since the index change gear ratio is close to the value given by Equation (16.52), it can be represented by an expression with the following form, k. 1 (16.55) where the quantity ~ may be either positive or negative. This expression for ki is substituted into Equation (16.50), and we obtain the corresponding value of the differential change gear ratio required to cut the correct helix angle, 478 Gear Cutting II, Helical Gears (16.56) We have determined the values of ki and kd in a manner that satisfies Equation (16.50), so we know that the correct helix angle will be cut. It is now necessary to substitute the values of ki and kd into Equation (16.49), in order to confirm that the gear will also be cut with the correct number of teeth. The expressions for ki and kd given by Equations (16.55 and 16.56) are substituted into the right-hand side of Equation (16.49), with the following result, (16.57) As we pointed earlier, the magni tude of the term (f sin ~sg/wmn) is always less than 0.5, so with these values of ki and kd , the number of teeth cut in the gear will indeed be equal to the number required. The change gear ratios given be Equations (16.55 and 16.56) can be used for cutting either helical or spur gears, whenever it is difficult to obtain the values given by Equations (16.52 and 16.53). It is interesting that the quantity a has cancelled out from the expression in Equation (16.57). This means that there is no theoretical limit to the value of a which can be used, and the ratio ki may therefore differ considerably from the value given by Equation (16.52). In practice, however, it is usually easier to select the differential change gears to obtain an accurate value for kd , if the index gears are chosen so that their ratio is close to the value given by Equation (16.52), and the magnitude of a is therefore small compared wi th 1. It is evident that a differential is useful in the design of a hobbing machine, since it facilitates the selection of the necessary change gears. However, the original purpose for which the differential was introduced, as we discussed earlier in the chapter, was to maintain the correct relation between the hob feed, the work table rotation and the hob rotation, during a rapid return of the hob to its starting position. Figure 16.13 shows how this purpose is achieved. The drive is disconnected, by means of a dog clutch, between the feed change gears and the feed drive. An auxiliary motor, Theoretically Correct Shape for the Hob Thread 479 known as the hob rapid traverse motor, is then used to drive the hob feed. The drive passes through the di fferent ial, causing the work table to turn at exactly the correct speed, so that the helical teeth in the gear mesh continuously with the threads of the hob. During the entire return motion of the hob, only a very small rotation of the table is required, compared with the many revolutions that take place while the gear is being cut. Hence, the return of the hob can be carried out quite quickly, without damage to the gearing driving the work table. Theoretically Correct Shape for the Hob Thread We stated in Chapter 5 that a hob whose thread profile is straight-s;ded in the normal section will not cut exact involute tooth profiles. We are now in a position to estimate the amount of error, and to determine the correct normal 480 Gear Cutting II, Helical Gears profile in the hob thread. In Chapter 15, we proved that two involute helical gears can mesh with crossed axes, and maintain a constant angular velocity ratio. The hobbing process is essentially the same as the meshing of a pair of crossed helical gears. It therefore follows that, in order to cut correct involute profiles in the gear, the thread of the hob must also have the shape of an involute helicoid. In other words, the thread has an involute profile in the transverse section. The corresponding profile in the normal section is a convex curve, and not a straight line. However, because the helix angle of a hob is so large, the profile in the normal section is extremely close to the straight line. Hence, when a straight-sided hob is used to cut gears, the resulting error in the gear tooth profiles is generally small. We can estimate this error in the following manner. We described a method in Chapter 13 for calculating the profile of the normal section through a helicoid. We now use this method to find the profile of the normal section through the hob thread. We calculate the distances, at the thread tip and at the top of the fillet, between this profile and its tangent at the standard pitch cylinder, as shown in Figure 16.14. The profile of a straight-sided hob would coincide with this tangent, and a hob of that type would therefore cut too deeply into the teeth of the gear, in the regions near the fillet and near the tip. Figure 16.15 shows the normal section through an Effect of a Non-Standard Shaft Angle 481 exact involute helicoid tooth, and it also shows the profile we obtain when the gear is cut by a straight-sided hob. The maximum differences between the two profiles are approximately equal to the distances described earlier, by which the normal section profile of the involute hob deviates from the straight line. As we can see in Figure 16.15, the tooth shape cut by a straight-sided hob is similar to the shape of a tooth cut with tip and root relief. The errors caused by the use of a straight-sided hob are therefore sometimes beneficial, and this is one of the reasons for the continued use of straight-sided hobs, when true involute hobs are also readily obtainable. There are times, however, when the errors caused by straight-sided hobs may be excessive. This is often the case for gears cut by multi-thread hobs, or by single-thread hobs of large module, whose helix angles are usually less than 85\u00b0. Whenever there is a possibility that a straight-sided hob may cut too much tip and root relief in a gear, the procedure just described can be used to determine whether a true involute hob should be used. Effect of a Non-Standard Shaft Angle In an earlier section of this chapter, we described how to calculate the tooth thickness cut in a gear, when the shaft angle ~ of the hobbing machine is set equal to the standard value ~s. We stated at that time that we would still obtain a 482 Gear Cutting II, Helical Gears correct involute profile in the gear tooth, even if the values of E and Es wer~ not the same. The only effect of the altered shaft angle is a change in the tooth thickness, and we will now discuss briefly how the new tooth thickness can be found. Since it is not generally necessary to make this calculation, we will simply outline the steps, without presenting all the equations. When the shaft angle is not equal to its standard value, the cutting pitch cylinders of the gear and the hob do not coincide with their standard pitch cylinders. The first step is therefore to calculate the cutting pitch cylinder radii R~g and R~h. Knowing the normal thread thickness t nsh of the hob at its standard pitch cylinder, we then calculate its normal thread thickness t nph at the cutting pitch cylinder. To find the normal tooth thickness cut in the gear, we regard the hobbing process as the meshing of a crossed helical gear pair with zero backlash. An expression was given in Equation (15.96) for the normal backlash in a crossed helical gear pair, The length ~cp in this equation was defined by Equation (15.47), as the difference between the center distance and the sum of the pitch cylinder radii. For the situation of a hob cutting a gear, ~cp would represent the difference between the cutting center distance and the sum of the cutting pitch cylinder radii, We combine these equations, and set the backlash Bn equal to zero, to obtain the normal tooth thickness t npg cut in the gear. The final step is to calculate the corresponding normal tooth thickness t nsg of the gear at its standard pi tch cylinder. If we carry out this calculation, we will find that the normal tooth thickness t nsg cut in the gear is almost independent of the shaft angle E. In other words, the tooth thickness is hardly affected by a small change in the shaft Geometric Design of a Helical Gear Pair 483 angle, provided of course that the cutting center distance is left unchanged. However, the radii of the cutting pitch cylinders are very sensitive to the shaft angle value. In particular, a small change in the value of ~ can move the cutting pitch cylinder of the hob right off the surface of the hob thread. In the absence of experimental evidence, it is not certain what effect this may have on the tooth surface quality. Therefore, although the shaft angle need not theoretically be set equal to its standard value, it is nevertheless recommended that in practice this value should continue to be used. Geometric Design of a Helical Gear Pair In the final section of this chapter, we outline a procedure by which we can choose the helix angle, the profile shift values and the gear blank diameters, for a pair of helical gears intended to mesh on parallel shafts at an arbi trary center di stance C. Since the standard center distance depends on the helix angle, (16.58) it would appear that we can always choose the helix angle so that the standard center distance Cs is equal to the center distance C. In this case, the pitch cylinder of each gear would coincide with its standard pitch cylinder. However, as we will show, it is not always practical to choose the helix angle in this manner, and there is no particular advantage in doing so. When the gears are cut by a pinion cutter, the helix angle of each gear is equal to that of the cutter, so the choice of ~s is limited by the cutters that are available. When a rack cutter is used to cut the gears, the cutter veloci ty v r and the gear blank angular veloci ty must be related by Equation (16.11), 484 Gear Cutting II, Helical Gears This equation must be satisfied exactly, because an incorrect value for vr would result in uneven spacing of the teeth on the gear. However, when ~s is chosen so that Cs is equal to C, it may be impossible to find change gears giving the exact relation between vr and wg \u2022 In general, it is probably easiest to obtain the required helix angle when the gear is cut by a hob, and the differential change gear ratio is given by either Equation (16.53) or Equation (16.56). Even in this case, it may be difficult to find a set of change gears giving a sufficiently small error. The effort required is seldom justified, because a gear pair can be designed quite satisfactorily, assuming only that Cs is approximately equal to C. The procedure is essentially the same as the one described in Chapter 6, for the design of a spur gear pair. For the reasons just outlined, it is generally best to choose the helix angle ~s so that the gears can be cut wi thout difficulty, and at the same time the standard center distance Cs is slightly less than the center distance C. The value of Cs should lie within the range given by Equation (6.14), C (16.59) The design procedure now consists in the choice of suitable profile shift values, and the gear blank diameters, in order to obtain the backlash required, and adaquate values for the working depth and the clearances at each root cylinder. We consider the meshing geometry in a transverse plane, and the design steps are then identical to those used in the design of a spur gear pair. For a helical gear pair, it is customary to specify the normal backlash Bn' rather than the circular backlash B. It is therefore necessary to calculate a number of the gear parameters in the transverse plane, before we can consider the transverse plane geometry. The values of mt' Rs1 ' ~ts' Rb1 , Rp1 ' ~p' ~tP' Ptp' and Bare found from Equations (13.148, 13.150, 13.151, 13.152, 14.28, 14.7, 14.8, 14. 10 and 14.72). (16.60) (16.61) Geometric Design of a Helical Gear Pair B tan tl>ns cos \"'s Rp1 tan \"'s Rs1 Rb1 Rp1 21TC 485 (16.62) (16.63) (16.64) (16.65) (16.66) (16.67) (16.68) The design of a helical gear pair with parameters mn and tl>ns' and normal backlash Bn' has now been effectively replaced by the design of a spur gear pair with parameters mt and tl>ts' and circular backlash B. We use the method described in Chapter 6, and in particular Equations (6.45 - 6.53), to carry out the necessary steps. Since the procedure was explained in Chapter 6, the equations will be presented here with very little explanation. We start by writing down the transverse tooth thicknesses at the pi tch cylinders, 1 2\"(Ptp-B) + tlttp (16.69) 1 2\"(Ptp -B) - tlttp (16.70) where tlttp is a quantity chosen by the designer, to increase the tooth thickness in one gear, and reduce it in the other. The next four equations are given for gear 1 only, since the corresponding equations for gear 2 are found by interchanging the subscripts 1 and 2. t ttsl R [.:..!E..!. + 2(inv tP tp - invtl>ts\u00bb) (16.71) s 1 Rpl 1 tI> (tts11 (16.72) e 1 2 tan 2\"1Tmt ) ts bs1 a r - e 1 (16.73) 486 Gear Cutting II, Helical Gears b + R - R sl p1 sl (16.74) The addendum values ap1 and ap2 are chosen to give a working depth of 2.0mn , and equal clearances at each root cylinder, mn - ~(bp1 - bp2 ) 1 mn + 2(bp1 - bp2 ) (16.75) (16.76) And finally, we obtain the diameters of the two gear blanks, (16.77) (16.78) Once the dimensions of the gear pair are all chosen, the designer should of course check, as in the design of a spur gear pair, that there is no interference or undercutting, and that the contact ratio, the root cylinder clearances, and the tip cylinder tooth thicknesses are all adaquate. Gear Cutting II, Helical Gears 487 Numerical Examples Example 16. 1 A 55-tooth helical gear with normal module 4 mm, normal pressure angle 20 0 and helix angle 30 0, is to be cut with a normal tooth thickness of 6.915 mm. Calculate the cutting center distance, and the radius of the root cylinder in the gear, if it is cut by a 32-tooth pinion cutter with a normal tooth thickness of 6.40 mm, and a tip cylinder diameter of 158.12mm. mn=4, ~ns=200, ~s=300, Ng=55, t nsg=6.915 Nc =32, t nsc =6.40, RTc =79.06 Example 16.2 Rsg = 127.017 mm ~ts 22.796 0 Rbg = 117.096 ttsg = 7.985 73.901 68. 129 7.390 inv ~~p = 0.024565 ~~p = 23.471 0 201.932 mm 122.872 mm (13.113) (13.113) (16.6) (2.16,2.17) (16.7) (16.8) A hobbing machine has an index constant C. of 24, and a 1 differential constant Cd of 25 mm. Calculate the change gear ratios required to cut a 49-tooth gear with a normal module of 5 mm and a l)elix angle of 23 0, using a 2-thread hob. C.=24, Cd=25, N =49, Nh=2, m =5, ~ =23 0 1 g n s 488 Gear Cutting II, Helical Gears k. = (48/49) 1 kd = 0.3109340 40.201 mm (16.52) (16.53) (16.20) The index change ratio can obviously be provided by a single gear pair. The differential ratio can be achieved with good accuracy by two gear pairs, having ratios of (24/66) and (59/69). It is not always easy, however, to find change gears which give the required ratio. In the case described in this example, it would have been simpler if the gear pair had been designed with an axial pitch of 40 mm, in which case the required differential change gear ratio would have been exactly (25/80). Example 16.3 When lead screws and other transfer mechanisms are converted from inches to mms, it is sometimes necessary to introduce a factor of 25.4 into their drives. This factor requires a gear with 127 teeth, which is difficult to cut using conventional change gear ratios, because 127 is a prime number, and most sets of change gears do not contain gears with more than 120 teeth. Use Equations (16.55 and 16.56) to choose the ratios to cut a 127-tooth spur gear wi th a single-thread hob, when the hobbing machine has a feed rate of 0.020 inches, and the machine constants Ci and Cd are 24 and 0.5 inches. Required ki = 0.1889764 (16.52) Choose index change gears with ratios (24/41) and (31/96). (24/41) x (31/96) - (1/31) 0.8064516 (16.55) (16.56) The differential ratio can be provided by a single gear pair with a ratio of (25/31). Chapter 17 Tooth Stresses in Helical Gears Introduction The calculation of the tooth stresses in a helical gear is considerably more complicated than the corresponding calculat ion for a spur gear. The contact stress and the fillet stress in each tooth depend on the intensity of the load, and on its position. Since the load intensity varies, as the position of the contact line moves up or down the tooth face, it is not easy to decide when the maximum stresses will occur. As we pointed out in Chapter 11, we consider in this book only the static stresses that would occur if the gears were not rotating. The actual stresses that exist in normal operation are found by multiplying the static stresses by various factors, to account for dynamic effects, type of loading, and so on. Values for these factors are given in the AGMA Standard referred to in Chapter 11 [6]. The method described in this chapter for calculating the static stresses is based on the AGMA method, but differs from it in certain respects. A summary of the differences will be presented at the end of the chapter. Tooth Contact Force In a helical gear pair, there are generally several tooth pairs which are simultaneously in contact. The contact in each tooth pair takes place along a straight line, which coincides with one of the generators in each tooth. In order to calculate the tooth stresses, we assume that the load intensity w is constant along all the contact lines. The value 490 Tooth Stresses in Helical Gears of w at any instant is then equal to the total contact force W, divid.d by the total contact length Lc' w (17.1) In this section of the chapter, we determine the value of W, corresponding to any specified value of the applied torque. And in the following section, we will describe how to calculate the contact length Lc. The direction n~ of the normal to the tooth surface at A, when A is a point on the contact line, was given by Equation (14.94), n~ = cos \"'b [sin t/ltp nx(O) + cos t/ltp ny(O)] - sin \"'b nz(O) (17.2) In the absence of friction, the contact force acts in the direction opposite to n~, and its component parallel to the gear axis is therefore (w sin \"'b). Hence, the component perpendicular to the gear axis, which is the useful component, is equal to (W cos \"'b) \u2022 The base cylinder of gear 1 is shown in Figure 17.1, with Contact Length 491 the plane of action of the contact force touching the base cylinder. The diagram also shows the component of the contact force perpendicular to the gear axis. We take moments about the axis, to obtain a relation between the applied torque M1 and the contact force W, (17.3) and we use the same method to find the corresponding relation between the contact force and the torque M2 appl ied to gear 2, (17.4) The contact force is found from either of these equations. By combining the two equations, we obtain a relation between M1 and M2 , which is the same as Equation (11.3), the corresponding relation between the torques applied to a pair of spur gears. (17.5) Contact Length As we stated earlier, there generally several tooth pairs in contact at any instant, and the contact length Lc is the sum of the contact lengths on each of these tooth pairs. In this section, we will derive a general expression for Lc' It turns out that we do not often need to make use of the general expression, since the cases required for the stress analysis are always special, and therefore simpler. However, it is a matter of interest to have the general result, and it also helps to determine when the maximum and minimum values of Lc occur. A transverse section through the gear pair is shown in Figure 17.2, with the plane of action touching the two base cylinders. As usual, the ends T1 and T2 of the path of contact are the points where the tip cylinders intersect the plane of action. Figure 17.3 shows the plane of action, with the axial lines through T1 and T2 meeting the transverse plane z=O at T10 and T20 , and meeting the transverse plane z=F at T1F and T2F \u2022 The region of contact is the rectangle T10T20T2FT1F. We stated in Chapter 14 that the lines of contact on the different contacting tooth pairs can be represented by a set of diagonal lines in the region of contact, each making an angle \"'b with the gear axis, and with a vertical spacing equal to the transverse base pi tch Ptb. To find the length of the contact lines in the rectangle, it is helpful to construct two additional triangles T'T 10T1F and T10T\"T20 , as shown in Figure 17.3. The value of Lc is then found as the length of the diagonal lines in triangle T' T\"T 2F' minus the lengths in triangles T'T 10T1F and T10T\"T20 \u2022 We proved in Chapter 14 that the lengths T' T 1 F and T 1 F T 2F are equal to mFPtb and mpptb' where mF and mp are the face contact ratio and the profile contact ratio, given by Equations (14.68 and 14.64), _1_ Ptb F tan \"'b (17.6) Contact Length 493 The plane of action. In addition, the length T'T2F is equal to mcptb' where mc is the total contact ratio, equal to the sum of mF and mp , (17.8) In order to find the value of Lc' we first consider a general triangle of height mPtb' where m can represent any of the contact ratios me' mF or mp. This triangle is shown in Figure 17.4, and the upper contact line is shown in a typical position, lying a vertical distance ePtb below the top corner of the triangle, where e is any number between 0 and 1. The number of contact lines in the triangle is equal to 494 Tooth Stresses in Hel ical Gears (n +1), where n represents the integral part of the number e e (m-e). If e is greater than m, there are no contact lines in the triangle, and the value required for ne is -1. We therefore define a function, n int(f) (17.9) where f is any number, and n is the largest integer which is less than or equal to f. If, for example, f has the values 2.2, 1.0 and -0.3, the corresponding values of n are 2, 1 and -1. The val ue of n e can then be expressed by the funct ion, n e int(m-e) (17.10) In the triangle shown in Figure 17.4, the upper contact line has a length (m-w)ptb/sin ~b' The next contact line is shorter than the first by Ptb/sin ~b' and so on. The total contact length Le can therefore be expressed as an arithmetic series, whose sum is given by the following expression, (17.11) We now apply this result to the three triangles in If we use this method to calculate the contact length Lc for various values of e, we will find the following results. Minimum and Maximum Values for Lc 495 The value of L is always a minimum when e is zero, and a c contact line passes through the upper corner T10 of the region of contact. And the value of L is a maximum when e is equal to c [mF - int(mF)], and a contact line passes through the other upper corner T1F of the contact region. Minimum and Maximum Values of Lc For the purpose of the stress analysis, we would expect to be most interested in the minimum value of Lc' since this corresponds to the maximum load intensity. Now that we know that the contact length is a minimum when a contact line passes through T10 , it is possible to find simpler expressions for the value Lcmin \u2022 We can simplify the expressions further, if we consider only gear pairs in which every transverse section has either one or two contact points. This condition means that the profile contact ratio lies between the following limits, < 2 (17.16) and this range includes all gear pairs of normal design. In the transverse section shown in Figure 17.2, there are two points Q and Q' marked on the plane of action. Point Q lies a distance Ptb below T l' and Q' lies a distance Ptb above T2\u2022 If the diagram represented a spur gear pair, Q and Q' would be the points on the path of contact corresponding to the ends of the period of single-tooth contact. In a helical gear pair, there is generally no period of single-tooth contact, because the total contact ratio mc is usually larger than 2. However, Q and Q' would represent the ends of the period of single-tooth contact in any particular transverse section, and it is therefore still customary to refer to these points as the end points of single-tooth contact. The region of contact is shown again in Figure 17.5, with the axial lines through Q and Q' cutting the transverse plane z=O a~ QO and QQ' and cutting the transverse plane z=F at QF and Qp.. We have stated that the value of Lc is a minimum when a contact line passes through point T 10. There must simultaneously be a second contact line through QO' since the distance between T10 and QO is equal to the transverse base pitch Ptb' Due to the symmetry of the rectangle, we can also argue that Lc is again a minimum when there are contact lines through T 2F and QF' We now consider a particular gear pair, with the contact lines shown in Figure 17.5. One contact line passes through point T10 , while a second line starts at QO' and intersects the plane z=F at point AF , somewhere between QF and QF' For this situation to be possible, the length mFPtb must be less than (2-mp)ptb' as we can see from the diagram. Such a gear pair is therefore defined by the condition, (17.17) and will be referred to as a very low face contact ratio (VLFCR) gear pair. A spur gear pair, in which the face contact ratio is zero, would fit into this category. The condition given by Equation (17.17) is equivalent to the statement that the total contact ratio mc is less than 2. This means that there are periods of the meshing cycle when only one tooth pair is in contact, which is the situation shown in Figure 17.5. The contact length Lcmin for this case can be read directly from the diagram, L . cmln F cos \"'b (17.18) Minimum and Maximum Values for Lc 497 The same region of contact is shown in Figure 17.6, but the contact line has moved up, so that it now passes through point Qp., and a new contact line is about to enter the region at T2F \u2022 During the period when the contact line moves between the positions of Figures 17.5 and 17.6, there is only one tooth pair in contact, and the contact length Lc remains constant, with the value equal to Lcmin given by Equation (17.18). The region of contact for a second gear pair is shown in Figure 17.7. The contact line which starts at QO now intersects the plane z=F at a point between QF and T1F \u2022 The face contact ratio must lie wi thin the following range, 498 Tooth Stresses in Helical Gears < (17.19) and this type of gear pair will be described as a low face contact ratio (LFCR) gear pair. We know that the contact length is at its minimum value, since one contact line passes through T10 \u2022 To calculate the value of Lcmin ' we take the length of the contact line through QO' and we add the length of the short contact line near T2F , L . cmln F cos 1/Ib + Ptb (m +m -2) sin 1/Ib F P The expression is simplified if we use Equation (17.6) to express Ptb in terms of F, L . cmln (17.20) Lastly, we consider gear pairs in which the face contact ratio is greater than 1, > (17.21) Gear pairs that fall within this category are known as normal helical gear pairs, since most helical gear pairs are designed with a face contact ratio larger than 1. The region of contact for a gear pair of this type is shown in Figure 17.8, with the contact lines in the positions Minimum and Maximum Values for Lc 499 corresponding to the minimum contact length. Starting from the left, there is one contact line passing through QQ' then there are a number of complete contact lines stretching from the bottom edge to the top edge of the region, and finally there are either one or two lines which intersect the right-hand edge. To find the value of Lcmin' we consider in turn each of the three groups of contact lines just described. We start by defining two new quantities nc and nF , as the integer parts of mc and mF , (17.22) (17.23) The number of contact lines crossing the upper edge of the region is nF , which means that the number of complete lines is (nF-1). The total number of contact lines is nc ' so the number crossing the right-hand edge is (nc-nF). Hence, the contact length Lcmin is found as follows, L . cmln Ptb \u2022\u2022 1. [1 + mp (nF-1) + (m -n ) + (m -n +l)(n -nF-1)] sIn \"'b c c c c c The result is then simplified, and expressed in terms of the face-width F, L . cmln 500 Tooth Stresses in Helical Gears We pointed out earlier that the maximum load intensity on a gear tooth corresponds to the minimum contact length, and for this reason we derived expressions for Lcmin ' However, as we will show later in this chapter, the fillet stress is often a maximum when the contact line passes through the corner T1F of the contact region, and this occurs when the load intensity is a minimum. We therefore also need expressions for Lcmax ' the maximum contact length. Minimum and Maximum Values for Lc lie in the following range, < The contact length is again the sum of the two lengths, and, as usual, we express the result in terms of F, 5{)1 (17.27) 502 Tooth Stresses in Helical Gears lower edge of the region is then equal to (nFP+2), and the total number of contact lines in the region is (nF+2). Hence, the number of complete contact lines is (nFP+1), and the number of lines crossing the left-hand edge of the region is (nF-nFP)' By considering the three groups of contact lines described earlier, we-obtain the following expression for the contact length, As before, we simplify this result, and express Lcmax in terms of F, Contact Stress In the last section of Chapter 14, we proved that when A is a contact point between a rack and a pinion, the line of contact through A and the common normal at A both, lie in the plane of action. The same is true when A is a contact point between a pair of helical gears. To prove this statement, we need only consider the imaginary rack between the gears, and make use of the result just stated, first for one gear and the imaginary rack, and then for the second gear and the imaginary rack. The plane of action for a gear pair is shown in Figure 17.12, with the contact line GA making an angle..pb with the n direction, as we proved in Equation (14.93). Near z point A, the tooth surfaces can be represented by two circular cylinders in contact, with their axes lying in the plane of action. Their radi i are shown as Pc 1 and Pc2' with the subscript c indicating that these are the radii of curvature when we make a section through the cylinders perpendicular to the line of contact. If we make a transverse section, as shown in the diagram, the cylinders appear as ellipses. For gear 1, the semi-minor axis of the ellipse is Pc1 ' while the semi-major axis is equal to (pc 1/cOS ..pb)' The radius of Contact Stress 503 curvature Pt 1 at point A in the transverse section through the tooth profile is then equal to the radius of curvature at the corresponding point of the ellipse, 2 Pc l (17.31) The corresponding equation for gear 2 can be written down immediately, (17.32) The maximum contact stress 0c between two cylinders of radii Pc1 and Pc2 was given by Equation (11.5),"
        ]
    },
    {
        "image_filename": "designv10_4_0000959_j.apm.2021.03.051-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000959_j.apm.2021.03.051-Figure4-1.png",
        "caption": "Fig. 4. Effect of tip relief on the delay of the start of contact.",
        "texts": [
            " (15) can be used for the determination of \u03d52 ( \u03be inn ) and \u03d52 ( \u03be o ), whose values are required to calculate \u03bemin and \u03bemax with Eq. (4) . In fact, the specific values of \u03bemin and \u03bemax are not necessary to compute \u03d52 ( \u03be inn ) and \u03d52 ( \u03be o ) with Eq. (15) . Exceptionally, the number of teeth-pairs in simultaneous contact at each contact position \u03bemin and \u03bemax , may increase by one due to the load-induced deflections and output gear delay. In these cases, the sums in Eq. (15) should consider one more teeth-pair with K = 0 to account such a qualitative variation of the effective contact ratio. M Fig. 4 shows how a tip relief at the driven teeth delays the effective start of contact. If the amount of relief is equal to the length of delay at the theoretical inner point of contact \u03b4( \u03be inn ), the start of contact will be shifted to the theoretical location at point e, and the mesh-in impact will be avoided. This adjusted amount of modification is therefore expressed as: R \u2212inn = \u03b4R ( \u03beinn ) = \u03b4( \u03beinn ) (18) Fig. 5 presents the LSR, QSTE, and TVMS curves for a spur gear with adjusted linear tip relief at the driven tooth tip (left diagrams), and at both tooth tips (right diagrams)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure8-1.png",
        "caption": "Fig. 8. Actuation wrenches of some legs for SP-equivalent parallel kinematic chains. (a) R\u0302R\u0302\u00f0RRR\u00dekE leg and (b) R\u0302R\u0302R\u0302\u00f0RR\u00dekE leg.",
        "texts": [
            " The selection of actuated joints for an f-DOF parallel mechanism should satisfy the validity condition for actuated joint of parallel mechanisms [9]: For an f-DOF parallel mechanism in which all the twists within the same leg are linearly independent in a general configuration, a set of f actuated joints is valid if and only if, in a general configuration, all the actuation wrenches, fi 6 j, of the f actuated joints together with a basis of the wrench system W of the parallel kinematic chain constitute a basis of the 6-system. Here, the actuation wrench fi 6 j of joint j in leg i is any one wrench which is not reciprocal to the twist of joint j and reciprocal to all the twists of the other joints within leg i. In the R\u0302R\u0302\u00f0RRR\u00dekE leg (Fig. 8(a)), the first R joint is actuated. The actuation wrench is a f0 whose axis intersects the axis of the second R\u0302 joint, is parallel to the axes of the R joints in \u00f0RRR\u00dekE and does not intersect the axis of the actuated joint. Here and throughout, R and P denote an actuated R joint and an actuated P joint respectively. In the R\u0302R\u0302R\u0302\u00f0RR\u00dekE leg (Fig. 8(b)), the first R joint is actuated. The actuation wrench is any f0 whose axis is the intersection of the plane passing through the axes of two unactuated R\u0302 joints and the plane passing through the axes of the two R joints in \u00f0RR\u00dekE. Considering that the order of a screw system is coordinate frame free and for simplicity reasons, all the actuation wrenches and wrenches are expressed in a coordinate system with its origin at the center of the wrench system of the SP-equivalent parallel kinematic chain and the Z-axis perpendicular to all the wrenches within the wrench system of the SP-equivalent parallel kinematic chain",
            " The candidate 2-R\u0302R\u0302\u00f0RRR\u00dekE SP-equivalent parallel mechanism is thus discarded. One candidate SP-equivalent parallel mechanism corresponding with the 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE SP-equivalent parallel kinematic chain (Fig. 7(b)) is 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE SP-equivalent parallel mechanism (Fig. 9(b)). The axis of the actuation wrench of an actuated joint is along the intersection of the plane determined by the axes of the two R joints within \u00f0RR\u00dekE and the plane determined by the axes of the R\u0302 joints except for the actuated joint considered (Fig. 8(b)). Using the validity condition of actuated joints, it can be proved that the set of actuated joints is valid. nism and (b) 2-R\u0302R\u0302R\u0302\u00f0RR\u00dekE candidate SP-equivalent parallel mechanism. For practical reasons, the selection of actuated joints for m-legged SP-equivalent parallel mechanisms should satisfy the following criteria: (1) The actuated joints should be distributed among all the legs as evenly as possible. (2) The actuated joints should preferably be on the base or close to the base. (3) No unactuated P joint exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002750_s0043-1648(00)00384-7-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002750_s0043-1648(00)00384-7-Figure4-1.png",
        "caption": "Fig. 4. Illustration of tooth stiffness model.",
        "texts": [
            "PII: S0043-1648 00 00384-7 where: j F s F 2\u017d .\u00ddsliceyk i ,k is1 j is the number of simultaneous contacts for one thin sliced cylindrical gear wheel, P is the total power throughput and r is the radius of the base circle of the gear andg v is the angular velocity of the same. F will equal:i,k F sd C 3\u017d .i ,k i k \u00dd i k where C is the combined tooth stiffness for contact i,\u00ddik slice k and d is the deformation of the same. C can bei k \u00dd i k regarded as a composite spring made of a weak and a stiff \u017d .spring in series see Fig. 4 . The stiff spring represents the surface stiffness, C , and the weak spring, C ,surface bendrshear represents the bendingrshearing of a tooth. C hasbendrshear w xbeen calculated from the results of Wang and Cheng 7 as w xwell as by a method described by Simon 8 . The results w xfrom Wang and Cheng 7 have been used previously by the authors to calculate a constant C .\u00dd i k w xSimon 8 has calculated tooth deflection using FEA, w xsimilarly to Wang and Cheng 7 , but from the results, he also derived an empirical expression for tooth deflection and tooth shearing depending on loading position and geometry",
            " The details of Simon\u2019s empirical solution are not discussed here; however, it complies well with the findings w xof Wang and Cheng 7 . Simulations with constant and as well as with varying tooth stiffness will be shown later in this paper. d is a function of the bending and shearing of thei k tooth as well as deformation of the tooth surface. d cani k be divided into: d sd qd 4\u017d .i k bend r shear surface For a given load on ordinary involute shaped gear teeth, the surface deflection, d , is relatively small comparedsurface to the bendingrshearing deflection, due to the relative \u017d .weakness of the teeth see Fig. 4 . The tooth surface is about 20 to 40 times stiffer than the tooth itself in this paper. This has been checked by equalising the contact with an elliptical Hertz contact, and the tooth stiffness has been calculated by using the results of w xSimon 8 . The variation depends on where on the line of action the contact occurs. The surface deflection will therefore be neglected due to its relative smallness. This means that C sC in the simulations.\u00dd i k Bendrshear If a slice has two teeth in contact, the total contact force has to be divided between the teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003920_3.20230-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003920_3.20230-Figure3-1.png",
        "caption": "Fig. 3 DRAPER II space telescope structure.",
        "texts": [
            "5512 The DRAPER I model14 is a tetrahedral truss connected to the ground by three right-angled bipods as shown in Fig. 2. These bipods take on the duties of rate sensors and force actuators, all in the direction of the members, giving the colocation necessary for a positive real model. The model has 12 dynamic degrees of freedom and thus a maximum of 12 modes. The natural frequencies for the model, as found by a NASTRAN analysis, are given in Table 1. The DRAPER II model15 is a model of a space telescope consisting of two subsystems as shown in Fig. 3. The optical support structure contains the four optical surfaces that are assumed to be rigid and kinematically mounted onto the structure. The equipment section is assumed to be a rigid central section with two flexible solar panels cantilevered from it. Because of the complexity of the finite-element model, a truth model for the DRAPER II model was formed using the first 50 nonzero modes, obtained from a NASTRAN analysis of the full DRAPER II model. The natural frequencies for the first 17 modes are given in Table 2",
            " There is considerable design flexibility in the choice of A and B to move the closed-loop eigenvalues of (Fm \u2014 GmK) and in the choice of Q to move the estimator eigenvalues of (Fm -KFHm). In this study, A is taken as al and B is taken as /. The same value of a is used when finding the closed-loop eigenvalues for all controller methodologies and design models. The specific values used for a in each controller design are 103 and 1010 for the DRAPER I and DRAPER II structures respectively. For the DRAPER I structure, only the x andy line-of-sight (LOS) errors are considered in the evaluation of K, whereas the x and y LOS errors and z \"defocus\" error (refer to Fig. 3) are considered for the DRAPER II structure. The estimator gain matrix KF is determined by the choice of the matrix Q in Eq. (14). In this study, Q was chosen as Q = <?/ where the scalar q was chosen to give an equal \"expected\" control cost for all controllers being evaluated. The control cost was evaluated by considering the integral (uTRu) = where FT satisfies (17) (18) x0 is the initial condition on the augmented state vector, and Fa and Ka for each controller are given in the Appendix. The scalar cost was evaluated by a \"pseudospectral\" norm, which consists of the maximum eigenvalue of the top (leading diagonal) n x n block of W (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure1.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure1.7-1.png",
        "caption": "Figure 1.7. pitch point of a rack and pinion.",
        "texts": [
            " Rack and Pinion y (x - ~) 211\" A cot 1/1 r 17 (1.14) Equation (1.14) can be interpreted in the following manner. There is a fixed point P, at a distance (Np/211\") from C on the line through C perpendicular to the rack reference line, such that the slope of line PA is equal to cot I/IAr \u2022 This means that line PA makes an angle (11\"/2 _I/iAq with the n~ direction, and it is therefore the common normal at the contact point A, since the common tangent makes an angle I/IA r with the n~ direction. The position of point P is shown in Figure 1.7. The result just proved is known as the Law of Gearing, as it relates to a rack and pinion. It may be stated in the following way. The condition that must be satisfied by the tooth profiles of a rack and pinion, in order that the relation between rack velocity and pinion angular velocity should remain constant, is that the common normal at the contact point should at all times pass through a fixed point P. The position of P is at a distance (Np/211\") from the pinion center C, on the perpendicular from C towards the rack reference line",
            "8), we gave the relation that we require between the rack velocity and the pinion angular velocity. We used that relation to prove the Law of Gearing, which lead us to define the pitch point and the pinion pitch circle. Having now derived an expression in Equation (1.15) for the pitch circle radius, we can combine Equations (1.8 and 1.15), and we obtain a simpler form for the relation between the rack velocity and the pinion angular velocity, (1.16) The line in the rack which touches the pinion pitch circle at P, as shown in Figure 1.7, is known as the rack 18 The Law of Gearing pitch line. When the pinion and rack are in motion, the velocity of any point on the pinion pitch circle is equal to RpW, and the velocity of any point on the rack pitch line is equal to vr ' Since these velocities are equal, as we can see from Equation (1.16), the motion of a rack and pinion is identical to the motion that would be obtained if the rack pitch line and the pinio~ pitch circle were to make rolling contact with no slipping. Ci rcular pi tch The circular pitch of the pinion teeth at any radius R is defined as the distance between corresponding points of adjacent teeth, measured around the circumference of the circle of radius R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003077_0094-114x(95)00100-d-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003077_0094-114x(95)00100-d-Figure2-1.png",
        "caption": "Fig. 2. Rototranslation.",
        "texts": [],
        "surrounding_texts": [
            "To extend the transformation matrices approach to a full kinematics analysis, two new matrices W and H must be introduced. The angular and linear velocity of a body with respect to a reference frame can be represented by the velocity matrixt W: W = 0 - - (D r COy (D. 0 - - cox - - CO)' (D.r 0 0 0 0 V X V.r V- = _0 _ ~ - b - - 6 - _ - v \u00b0 _ ' 6 i where ~ indicates the angular velocity of the body and v o is the velocity of the point, considered belonging to the body (called the pole) that in a considered instant is passing through the origin of the reference frame. he velocity P of a point P on the body can be obtained as: /6 = W P = .~p ~p zv -[~- I i i i \u00a2..0 ~ Y o \" I I o- o -o- : o Xp Ye Zp (6)"
        ]
    },
    {
        "image_filename": "designv10_4_0000300_s11684-020-0781-x-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000300_s11684-020-0781-x-Figure9-1.png",
        "caption": "Fig. 9 (A) Gripper design with sensor integrated in the jaws, reprinted with permission from IEEE [97], (B) Stewart type sensor embedded in the wrist, reprinted with permission from John Wiley and Sons [109], and (C) working principle of the intrinsic force sensing.",
        "texts": [
            " Force sensing in surgical robotic systems can generate faithful force feedback to the operating surgeon and can potentially help increase the safety of typical surgical tasks, including tissue manipulation [91] and blunt dissection [92]. Force sensing during surgery mainly include two types: (1) measuring the tissue gripping force and (2) measuring the interaction force with environment. Sensing approaches include extrinsic force sensing and intrinsic force sensing. Extrinsic force sensing integrates a sensing element at the location of contact and directly measures the force, whereas intrinsic force sensing, proposed in Reference [93], uses actuator-level information to calculate the contact force, as shown in Fig. 9C. However, the former may provide a more accurate result. The increased complexity of sensor-integrated instruments may lead to reduced reliability, providing challenges to sterilization and higher costs. Gripping force sensing using the extrinsic approach includes the use of a strain gauge [94], polyvinylidene difluoride (PVDF) elements [95], fiber Bragg grating (FBG) [96], and capacitive sensing cells (Fig. 9A) [97]. Given that a gripping force is always actively applied, the intrinsic sensing approach might be more suitable. Representative examples include measuring the driving shaft tensions [51], driving pulley strains [98], driving pulley torques [99], and motor currents [100]. Interaction force sensing with environment adopting the extrinsic approach includes the use of strain gauges [101,102] with one design (Fig. 9B) [101], optical intensity [103,104], FBG [105], and PVDF piezoelectric film [106]. On the other hand, intrinsic sensing is implemented by measuring the backbone actuation forces [107], motor currents [108], and actuation pulley strains [98]. Compared with the extrinsic sensing approach, the intrinsic sensing approach allows versatile extracorporeal sensor arrangement, which enables structural simplification of the inserted instruments. However, intrinsic force sensing through actuation cables or motor currents is affected by friction and moving inertia"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000690_j.rcim.2021.102138-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000690_j.rcim.2021.102138-Figure14-1.png",
        "caption": "Fig. 14. Schematic diagram of machining target (a) and measuring point distribution (b).",
        "texts": [
            " Robotics and Computer-Integrated Manufacturing 70 (2021) 102138 be obtained according to Algorithm B2 as shown in Fig. 13. Then, the positions of the workpiece in the six sets of comparative milling experiments were determined. The distribution of these locations is also shown in Fig. 13. Their position coordinates and corresponding MSPI values are shown in Table 2. In each set of experiments, a reference plane was first milled on the upper surface of the workpiece and then four slots were milled on the reference plane, as shown in Fig. 14-a. The distance between the center line of the slot and the y-axis of the workpiece frame is 20, 40, 60, 80 mm, the slot width is 12 mm, and the slot depth is 0.5 mm. In addition, it should be noted that the reference plane was by repeating the toolpath trace several times, and the slot surface was formed by tracing the toolpath once. The cutting parameters in the experiment are shown in Table 3. After the milling experiments are completed, the machining quality is evaluated by the coordinate measuring machine shown in Fig. 11-b. Here, the machining error is defined as the average of the distance between the multiple measuring points on the slot surface and the reference plane. And the distribution of measuring points is shown in Fig. 14- b. The machining errors of the 6 sets of milling experiments are shown in Table 4. Due to the only variable in each set of experiments is the relative position of the frames {WP} and {BP}, the validity of the BP optimization method can be determined by evaluating the machining error. Here, the machining error is defined as the difference between the actual cutting depth and the ideal cutting depth. The actual cutting depth is measured by CMM, and it is defined as the average distance between multiple evenly distributed points on the machined surface and the reference surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000965_j.jmst.2021.03.006-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000965_j.jmst.2021.03.006-Figure16-1.png",
        "caption": "Fig. 16. Schematic diagrams showing the overlapping of the tracks under the continuous-wave and pulsed-wave modes.",
        "texts": [
            " A high scan speed favors increasing he length of the melt pool ( \u03bb), thus promoting the formation of he Rayleigh instability [43] and deteriorating the surface quality n the PWed sample, as presented in Fig. 9 (f). Wave troughs and ave crests were induced along the laser beam path by the flucuation as the Rayleigh instability occurred. A strong metallurgical onding was generated once the 2 wave crests belonging to adjaent tracks overlapped. However, a big void appearing as a pocket orphology could contain several un-melted powders as 2 wave roughs adjoined, leading to the pores due to lack of fusion in the Wed sample, as depicted in Fig. 16 (b). Compared with the pulsed- ave mode, the CWed track was straight and stable, as shown in igs. 9 (c) and 16(a). This ensured the adequate overlapping beween the tracks, thus effectively avoiding the pore formation. Another type of pores observed in the PWed sample was he metallurgical pore. This was ascribed to the residual bubble n the melt pool during solidification. Viscosity is known as a emperature-dependent thermophysical property, and generally, it s negatively correlated with temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.13-1.png",
        "caption": "Figure 12.13. Cutting a point on the gear tooth fillet.",
        "texts": [
            " When the cutting point reaches Hc on the path of contact, point Ahc of the cutter touches point Af on the gear tooth profile, the point where the involute section of the profile meets the fillet. The fillet circle of the internal gear is the circle passing through Af , and its radius Rfg is equal to the length CgHc' which can be read from the diagram, (12.59) We use the geometry of non-involute generation, described in Chapter 9, to find the coordinates of points on the tooth fillet of the internal gear. Part of the meshing diagram during the cutting process is shown in Figure 12.13. On the cutter tooth, the center of the circular section at the tip is labelled A', and its polar coordinates (R' ,0') are c c c given by Equations (5.32 and 5.39). The line PA' meets the c cutter tooth profile at Ac' and this must be the point at which the cutter touches the tooth fillet of the gear, since the normal at Ac passes through the pitch point. We use the (~,~) coordinate system whose origin is at the pitch point, and we consider the geometry when the line from the pinion center to point A~ makes an angle a with the ~ axis",
            "66) The relation between the angular positions of a pinion and an internal gear was given by Equation (12.29), When the equation is used for a plnlon cutter and an internal gear, the sum of the tooth thicknesses is equal to the circular pitch P~ on the cutting pitch circles. The equation is simplified if it is multiplied throughout by the ratio (C~/CC), and we then obtain an expression for the angular position of the gear, (12.67) Since point Ac on the cutter is the contact point, it coincides with a point A on the tooth fillet of the gear. The coordinates of A can be read immediately from Figure 12.13, R (12.68) arctan (_1/_) - Q RC +~ 1'g pg (12.69) Shape of the Fi llet 285 Equations (12.60 - 12.69) are used to calculate the coordinates of points on the internal gear tooth fillet, corresponding to any chosen values of a. The first point which needs to be considered is Af , where the fillet meets the involute. In this case, the cutting point must lie at He on the path of contact, and line PAc therefore makes an angle ~c with the ~ axis, as shown in Figure 12.14. The value of a at which this occurs can be read from the diagram, a R arccos (R~c) - ~c c (12",
            "50), and we obtain the following expression for RO' NgNCCC (N -N )2 g c (12.75) Since the radius of curvature of the cutter tooth profile is known, and we want to calculate the corresponding radius of curvature in the gear tooth profile, we solve Equation (12.73) for Pg , (12.76) Fillet Radius of Curvature 287 To calculate the radius of curvature Pf at a point A on the tooth fillet of the internal gear, we first use Equations (12.60 - 12.65) to find the position (L11) of A when it is cut. The corresponding values of ~ and s can be read from Figure 12.13, tan q, s _E_ sin q, (12.77) (12.78) The gear tooth fillet is cut by the circular tip section of the cutter tooth, whose radius is r cT \u2022 We therefore find the radius of curvature at A, by substituting r cT in place of Pg in Equation (12.76), (12.79) The minimum radius of curvature r f occurs at the point where the fillet meets the root circle. This point is cut when line AcA~ in the cutter coincides with the E axis, and the angle a which we have used to describe the cutter position is equal to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000868_j.engfailanal.2021.105444-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000868_j.engfailanal.2021.105444-Figure2-1.png",
        "caption": "Fig. 2. Force model of a normal gear.",
        "texts": [
            " In this paper, the mesh stiffness of normal gear system is calculated based on improved energy method. Liang [15] improved the time-varying mesh stiffness model established by Tian [37] based on energy method. Comparing with Tian\u2019s model, Liang added shear stiffness to the modeling process and fully considered the influence of gear tooth root, then modeled the mesh stiffness of external-external and external-internal spur gear pairs. According to material mechanics, the gear teeth are simplified to a cantilever beam with variable cross-section as shown in Fig. 2. The mesh stiffness during gear mesh consists of bending stiffness kb, axial compression stiffness ka, shear stiffness ks and Hertzian contact stiffness kh. The comprehensive mesh stiffness of a single pair of teeth can be obtained as: kt = 1 ( 1 kh + 1 ks1 + 1 kb1 + 1 ka1 + 1 ks2 + 1 kb2 + 1 ka2 ) (1) L. Xiang et al. Engineering Failure Analysis 125 (2021) 105444 where 1, 2 represent active and passive gears engaged in meshing, respectively. Considering the contact ratio of gears, the combined mesh stiffness can be expressed as: kt = \u22112 i=1 1 ( 1 kh + 1 ks1,i + 1 kb1,i + 1 ka1,i + 1 ks2,i + 1 kb2,i + 1 ka2,i ) (2) where i = 1, 2 represent the first and second pairs of teeth engaged in meshing respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000868_j.engfailanal.2021.105444-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000868_j.engfailanal.2021.105444-Figure4-1.png",
        "caption": "Fig. 4. Gear spalling fault model.",
        "texts": [
            " Table 1 is the basic parameters of a wind turbine gear system. Taking the gear system as an example, the gear time-varying mesh stiffness analysis is carried out. It can be seen from Fig. 3 that the mesh stiffness of each gear pair in the wind turbine gear system changes periodically with the rotation of the gear. Due to uneven load and low hardness of tooth surface, spalling fault will occur on gear. It is assumed that spalling occurs near the pitch line and takes the shape of a rectangular \u0394L \u00d7 \u0394W \u00d7 \u0394D as shown in Fig. 4. When the fault occurs on the tooth surface, the tooth width L, section area Ay and inertia moment Iy of the gear teeth will change. The modified calculation method is as follows: Table 1 Basic parameters of the gear system. Gear Number of teeth rb/m I/(kg.m2) Material s 31 0.17 5.75 17CrNiMo6 pi 47 0.27 29.65 17CrNiMo6 c 0.0.44 85.36 17CrNiMo6 r 125 0.71 40CrMo g1 119 0.51 306.03 17CrNiMo6 g2 25 0.11 0.59 17CrNiMo6 g3 106 0.35 39.98 17CrNiMo6 g4 27 0.09 0.17 17CrNiMo6 L. Xiang et al. Engineering Failure Analysis 125 (2021) 105444 Lz = \u23a7 \u23a8 \u23a9 L \u2212 \u03b11 < \u03b1 < \u2212 \u03b1a L \u2212 \u0394L \u2212 \u03b1a < \u03b1 < \u2212 \u03b1b L \u2212 \u03b1b < \u03b1 < \u2212 \u03b12 (3) where \u03b1a and \u03b1b are the mesh position correlation angles of a and b, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure2-1.png",
        "caption": "Fig. 2. Kinematic structure of the parallel Delta-RU robot.",
        "texts": [
            " This paper presents the error modeling and kinematic calibration of a modified parallel Delta robot, with the implementation by the following steps: 1 \u00a9 formulation of the kinematic sensitivity matrix and error model by considering all possible geometric error sources; 2 \u00a9 sensitivity analysis of the influence of the geometric variations onto the end-effector postures; 3 \u00a9 identification of geometric parameters by position measurement using a laser tracker; 4 \u00a9 kinematic calibration for accuracy improvement. With the derived error model, the parameter identification is realized by solving an unconstrained C nonlinear optimization problem, by means of the least square minimization method, for updating the kinematic model to be inserted into the controller. After calibration, the position error of the robot end-effector is significantly improved throughout the operational workspace. Fig. 2 depicts the parameterizations of the Delta-RU robot. The global coordinate frame F b is built with the origin located at the geometric center of the base frame, of which the x -axis is parallel to the axis of rotation of the first actuate joint and z-axis points downwards. The moving coordinate frame F p is attached to the mobile platform and the origin is at the geometric center, with the axes parallel to the reference frame. Here and after, i , j and k represent the unit vectors of x -, y - and z-axis, respectively",
            " This is the reason that we did not show the isocontours at z = 373 mm due to poor graphical representation caused by the significant differences of the co-existing minimum and maximum indices. Fig. 12 shows the percentage of the distributions of the sensitivity indices throughout the cylindrical workspace, together with the max-/minimum indices listed in Table 2 . Although the maximum \u03bdp and \u03bd\u03c9 can reach up to 4.9 and 1.4, respectively, the indices at the most positions are bounded between 0.1 and 0.5, with very few exceptions as indicated in Fig. 2 and the mean values in Table 2 . Contrary to its original counterpart, the end-effector pose errors of the Delta-RU robot is slightly less sensitive to the geometric variations, which can be concluded from Figs. 10 , 12 and Table 2 . Moreover, the kinematic error model, namely, Eq. (23) , is able to calculate the pose errors of the robot end-effector with known variations in design parameters. For instance, let suppose the linear and angular tolerance to be 0 . 1 mm and 0 . 05 \u25e6, respectively, the pose errors at five positions [62] shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003371_0925-4005(96)01834-5-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003371_0925-4005(96)01834-5-Figure2-1.png",
        "caption": "Fig. 2. Redox scheme and cyclic voltamnmgrams of a microperoxidase MP-I! modified gold electrode in 0.1 M phosphate buffer (pH 7.0). Scan rates: (a) 25 mV s +1, (b) 50 mV s -I, (c) 100 mV s -I.",
        "texts": [
            " It has been immobilized at a cystamine-modified gold electrode by means of a carbodiimide-activated coupling of a carboxylic residue at the peptide chain or the two propionic acids at the hemin group with the amino functions of the thiol monolayer. Due to its small size, microperoxidase MP-11 shows the largest surface concentration of all investigated catalytic structures and the highest electrocatalytic activity for the reductioa of H202 (Table 1)+ By means of cyclic voitammetry, we have been able to observe the reversible oxidation and reduction wave of the iron porphyrin (see Fig. 2; E \u00b0 =-398 mV/SCE; AE= 25 mV; ks= 12s - J ;F=6x l0 -I\u00b0 tool cm -9) [19]. The reduction of H202 could be obtained at potentials smaller than +300 mV/SCE (Fig. 3), indicating a catalytic pathway via an intermediate iron-(IV)-oxo-porphyrin cation radical [20]. These microperoxidase-monolayer modified gold electrodes have been tested in a conventional electrochemical three-electrode stationary system at an applied constant potential of +50 mV/SCE. On addition of H202 aliquots, the increase in reduction current was recorded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000461_j.apor.2020.102342-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000461_j.apor.2020.102342-Figure1-1.png",
        "caption": "Fig. 1. Frames about underwater vehicles (Liu et al., 2019b).",
        "texts": [
            " In general, the dynamic model of an fully-actuated AUV subject to ocean current can be described as the following form Fossen (2011). = J ( ) (1) + + + + =M C C D G( ) ( ) ( ) ( )RB A r r r r (2) where \u03b7 is a 6 \u00d7 1 vector whose first three elements, respectively, describe AUVs location in the Xe, Ye, Ze axles in the earth inertial frame and the last three are the Euler angles representing the AUV\u2019s attitude about the same axles; J(\u03b7) denotes the transformation matrix using xyz convention in terms of Euler angles from the body-fixed frame to the earth frame, and these frames are described in Fig. 1; is a 6 \u00d7 1 vector whose first three elements, respectively, describe the AUV\u2019s linear velocities in the Xb, Yb, Zb axles in the body-fixed frame and the last three, respectively, describe the AUV\u2019s angular velocity with respect to the body-fixed frame. M is a 6 \u00d7 6 inertia matrix including the added mass matrix; =r c; c is the velocity of ocean current with respect to the body-fixed frame, and it is always assumed that the ocean current is slowly varying and irrotational, i.e., 0c ; C ( )RB and C ( )A r are 6 \u00d7 6 matrixes to respectively describe the rigid-body and hydrodynamic centripetal and Coriolis terms; D ( )r is a hydrodynamic damping matrix; G(\u03b7) is a 6 \u00d7 1 vector of gravity and buoyancy forces and moments; \u03c4 is a 6 \u00d7 1 vector to denote the force/moment applied to the AUV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000249_admt.201800692-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000249_admt.201800692-Figure11-1.png",
        "caption": "Figure 11. Rolled-up capacitors. a) Fabrication process for rolled-up capacitors from left to right: deposition and patterning of the sacrificial layer (Ge), which is further oxidized to form GeOx; deposition of the 1st plate (Au/Ti) and oxide multilayer stack; deposition of 2nd plate (Cr) and oxide multilayer stack; deposition of bond pads (Cr/Au) and opening of the trench; rolling of the capacitors, starting from the dashed line. b) Layer sequence of the planar structure. a,b) Adapted with permission.[13] Copyright 2014, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. c) Layer sequence used to create the nanomembrane-based rolled-up capacitors shown in their planar and rolled states. Adapted with permission.[18] Copyright 2010, American Chemical Society. d) Actual structures in their planar and rolled-up state, which is obtainable in an array form on a wafer scale. Adapted with permission.[13] Copyright 2014, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. Magnified view (right) on one of the capacitors. Adapted with permission.[18] Copyright 2010, American Chemical Society.",
        "texts": [
            " Additionally, modern integrated circuits may have several power lines fed at various positions and thus require numerous decoupling capacitors connected through a PCB (Figure 3 or 9c) with an integrated circuit and power supply. This leads to a substantial use of the PCB area and requires newer small-scale devices with higher areal capacitance density for each new generation of the product. Swiss-roll architectures favor the fabrication of capacitors using a simple initially planar layout that corresponds to the double plate electrostatic capacitor (Figure 11a,b).[13,18] Selfassembly of this initially planar structure leads to a Swiss-roll (Figure 3) with several windings, where capacitance increases to almost twice its initial value due to overlapping of neighboring windings (Figure 11c) and as result increasing the effective area of the capacitor. This process is significantly simpler than the sequential layer by layer fabrication of capacitor plates used for conventional surface mounted device capacitors (Figure 3), and is performed in a parallel fashion on the wafer scale (Figure 11d). The demonstrated structures can possess more than 1 \u00b5F mm\u22122 with a footprint area of only 13 \u00d7 200 \u00b5m2 and more than 20 windings. If electrochemically active materials are used instead of simple metallic plates, more sophisticated energy storage devices can be realized, such as lithium ion batteries as outlined in a recent review.[129] The Swiss-roll architecture is useful in making soft electrical contacts with brittle or low modulus materials. These contacts Adv. Mater. Technol. 2019, 1800692 www",
            "[18] made tiny energy storage elements based on 3D ultracompact hybrid organic/inorganic strained multilayers to form microcapacitors with amorphous Al2O3 as dielectric and polycrystalline metallic plates. It was possible to adjust the leakage current by growing an additional self-assembled molecular layer on top of the oxide. Sharma et al.[13] extended this technique to the wafer scale, starting with the microstructuring of planar double-plate capacitors via sequential deposition of metal and oxide layers on top of a sacrificial layer (Figure 11). The Ge sacrificial layer was evaporated on top of a Si/SiO2 wafer with a subsequent oxidation procedure to form germanium oxide (GeOx) to make it water soluble. Then, the first strained plate of the capacitor was prepared by sequential deposition of Au and Ti (10\u2019s of nm). Gold was used to reduce the adhesion of the entire device to assist in the delamination of the capacitors, and the sample was also covered by a multilayer stack consisting of Al2O3, HfO2, and TiO2 via atomic layer deposition (ALD)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure7.51-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure7.51-1.png",
        "caption": "Figure 7.51 Schematic ray diagrams showing the (a) bright-field TEM, (b) dark-field TEM, and (c) reflection electron microscopy.",
        "texts": [
            " It is generally desirable to examine the crystal surface before thinning. Reflection electron microscopy (REM) can fulfill this task (Wang, 1996b). REM is usually performed in TEM because of the requirement for a high-resolution optic system. REM is a technique that can be applied to image the surfaces of single crystalline bulk specimens. The REM technique is easily introduced after examining the 401 STRUCTURE ANALYSIS OF FUNCTIONAL MATERIALS 402 CHAPTER 7 conventional operation modes of a TEM. Figure 7.51 shows ray diagrams corresponding to TEM bright-field (BF) , TEM dark-field (DF), and REM. For TEM imaging, a thin specimen is held perpendicular to the incident beam (Fig. 7.51a). In TEM, electron scattering by a thin crystal gives a diffraction pattern in the back focal plane (Le., the plane where the objective aperture is located) of the objective lens. If one of the diffracted beams is selected by the objective aperture, preferably with the objective aperture axially aligned and the incident beam tilted so as to minimize the spherical aberration effect, a dark-field image is formed (Fig. 7.51b). In REM, the specimen is replaced by a thick bulk crystal and the near-flat surface of a bulk specimen is oriented so that the incident electron beam strikes the surface at a glancing angle (Fig. 7.51c), resulting in a reflection high-energy electron diffraction (RHEED) pattern on the back focal plane of the objective aperture. The dark-field image formed by selecting a reflected beam with the objective aperture is a surface image. Intensity variations in the image may be attributed to variations of the diffraction intensity resulting from changes of crystal structures, surface chemical composition, crystal lattice orientation, or phase contrast arising from a variation of electron path lengths due to surface morphology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003089_s1727719100003348-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003089_s1727719100003348-Figure3-1.png",
        "caption": "Fig. 3 Tractions on side 2-3",
        "texts": [
            "> = \u2014 J The Jacobian is yt ud s - ys uf xs ut - xt us 0 xs uf - xt ud s yt ud s - ys uf (37) xs is an abbreviation of the derivative dx/ds. Substitutions of Eqs. (34), (35), and (36) into Eq. (37) yield B B= 0 xsNu-xtNUs t - xt Ni, s yt h s - ys , i = 3, 4 B= = 0 xs N2,t-xtN2 In which, 128 Journal of Mechanics, Vol. 20, No. 2, June 2004 Nis=dNt/ds, Nit=dNtldt 5.1 Three-Node Triangular Element A = Z NJ, *yj> * * = Z NJ, XJ Consider a three-node triangular element with nodal numbers (1, 2, 3). A distributed force vector is acting on the 2-3 side of element boundary (see Fig. 3). The work equivalent forces based on a virtual work formulation are defined as Using the virtual work, the nodal internal forces are L L fy L > = t e BT isdA (38) The nodal forces flx, fy and f2 at nodes 1 and 2 are found from the equilibrium equations. fly=-(f2y+f3y+f4y) fy = -i-flJl + fyX] ~ (39) fyX4 -f^yd For assemblage, the internal forces are transformed to global coordinates: (CY={fu fy f* fly f3x f (40) 3y f4y} T = \u00a3 2 0 0 0 0 \u00a32 0 0 0 0 \u00a32 0 0 0 0 \u00a32 For an incremental deformation formulation, the internal forces become (41) at is the stress and E the tangent modulus matrix of the element material at time t"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003859_detc2007-34210-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003859_detc2007-34210-Figure5-1.png",
        "caption": "Figure 5: Trace of generating roll",
        "texts": [
            " In addition, change of zero order ratio of generating roll 0aR , offset 0mE , work head 0pX , and root angle 0m\u03b3 also introduces second-order profile and spiral angle modifications. Change of zero-order cutter radial setting 0rs primarily introduces spiral angle change. Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/05/2016 We notice that the universal motions are higher order polynomials in terms of the generating roll angle q. Application of higher order motions will modify the tooth surfaces diagonally along the trace of generating roll as shown in Figure 5. On the concave tooth flank, the rolling direction is from toetop ( 1T ) to heel-bottom ( 2H ). But the rolling is from heel-tip ( 1H ) to toe-bottom ( 2T ) on the convex side. Therefore, normally, the 1st, 2nd, 3rd and 4th order universal motions introduce tooth flank form higher order \u2018warping\u2019 or \u2018twisting\u2019 modifications along the direction of generating roll. Table 2 and 3 show the difference surfaces 1\u03b4 and 2\u03b4 of the concave side and convex side respectively corresponding to a positive change of 1st, 2nd, 3rd and 4th order coefficients of ratio of generating roll aR and radial setting rS "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003233_jsvi.2000.3169-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003233_jsvi.2000.3169-Figure2-1.png",
        "caption": "Figure 2. Co-ordinate system of a helical spring.",
        "texts": [
            " For clarity, the equations of a helix are introduced \"rst and used to derive the equations of motion of a helical spring. Figure 1 shows a helical coil spring, the axis of which lies along the x-axis. The helix radius is R and the helix angle is a. The variable s is used to measure the distance along the wire and is related to the angle / by /\"s cos a/R. (1) The global (x, y, z) co-ordinates are related to / by x\"R/ tan a, y\"R cos/, z\"R sin / . (2) At any point on the helix, local co-ordinates are de\"ned as shown in Figure 2, with u( radial, w( tangential and v( binormal to the other directions. The displacements (u, v, w) in these local co-ordinates are related to those in global co-ordinates (u x , u y , u z ) by i g j g k u v w e g f g h \" 0 !cos/ !sin/ cos a sin a sin/ !sin a cos/ sin a !cos a sin/ cos a cos/ i g j g k u x u y u z e g f g h \"[Q] i g j g k u x u y u z e g f g h . (3) Similar equations apply for rotations, forces and moments. Frenet formulation [17] allows all the displacements and resultant forces to be given as functions of s",
            " The curvature i and tortuosity q of the helix are de\"ned by i\" cos 2 a R , q\" sin a cos a R . (4) The relations between these parameters and the three unit vectors [14] can be written in matrix form as L Ls i g j g k u( v( w( e g f g h \" 0 q !i !q 0 0 i 0 0 i g j g k u( v( w( e g f g h . (5) Consider the situation in which the spring is subjected to an arbitrary dynamic load F1 , as shown in Figure 1. Then at any cross-section the wire is subjected to three components of force P u , P v , P w and three moments M u , M v , M w about the u( , v( and w( directions (see Figure 2). These forces and moments result in the linear and rotational displacements of the wire and cause the coupling e!ects of motion of the spring. It will be assumed that the cross-section of the wire has two axes of symmetry which coincide with the directions u( and v( . Suppose that the components of the linear displacements d, rotations h, concentrated forces P and moments M at position s are de\"ned by i g g j g g k d h( P M e g g f g g h \" d u d v d w h u h v h w P u P v P w M u M v M w i g j g k u( v( w( e g f g h "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000099_s00170-020-05394-8-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000099_s00170-020-05394-8-Figure10-1.png",
        "caption": "Fig. 10 a Confocal and (b) transmitted light microscope images of lattice structure nodes. b Minimum (Dmin) and maximum (Dmax) node dimensions in the build direction (BD) and non-build direction (nonBD) are shown",
        "texts": [
            "41), then the node diameter will be smaller than the intersection of the struts, and so functionally, it will be as if no node is present at all. To demonstrate this, specimens were manufactured with node-to-strut diameter ratios below this value (1 and 1.25) and slightly above (1.5). For the identification of manufacturing defects and surface morphology of as-manufactured lattice structures, micrographs and transmitted light microscope images were acquired using a Keyence VHX-5000 microscope. An example of a confocal and transmitted light image of a lattice cell is presented in Fig. 10. Six repetitions of each premutation of cell size, node size, and strut size were collected. As the diameter of as-manufactured nodes varies significantly, a means of quantifying the size of as-manufactured nodes is necessary. For this reason, the minimum (Dmin) and maximum (Dmax) dimensions of as-manufactured nodes were measured in the build direction (BD) and the direction perpendicular to the build direction, referred to as the non-build direction (non-BD). Transmitted light images (Fig. 11(a)) are automatically cropped to show only a single cell and analysed to identify the 2D boundary of the struts and nodes (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002881_ias.1996.556993-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002881_ias.1996.556993-Figure1-1.png",
        "caption": "Fig. 1. Model of salient PM motor.",
        "texts": [
            " An experimental system consisting of an Interior Permanent Magnet (IPM) synchronous motor and a voltagesource PWM inverter has been constructed and tested to verify the effectiveness and versatility of the approach to position estimation at zero and low-speed. The IPM motor has the magnetic saliency of the q-axis inductance being larger than the d-axis inductance. Experimental results show that the proposed approach has the capability of estimating the rotor position of at standstill and at such an extremely low-speed as 1 r/min. 11. HARMONIC MODEL OF P M MOTOR Fig.1 shows the simplified model of a PM motor with magnetic saliency. The equations describing the PM motor are given by Lo + L1 cos 20 L1 sin 20 d LO -L1cos20 1 - dt + [ L1sin20 -sin20 cos20 dt - sin 0 where, Ld - Lq L1= Ld + Lq 2 Lo = -2 ' 0-7803-3544-9196 $5.00 0 1996 IEEE 29 The equations can be simplified by applying the space vector theory. v = ri + L- + eo ( 3 ) di dt Here, the inductance matrix is represented by Lo + L1 cos 20 L1 sin 28 ] (4) L1 sin 26' LO - LI cos 26' L = [ and it contains the rotor position information of the PM motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.13-1.png",
        "caption": "Figure 14.13. Normal section through the rack tooth.",
        "texts": [
            "19) that the rack helix angle ~~ is equal to the operating helix angle ~p of the pinion, and in relating the various sets of unit vectors, it will be convenient to describe all the angles in terms of those defined on the pinion. We therefore obtain the following relations from Figure 14.11, pinion at plane z=O, when the pinion has rotated through an angle p. The vectors n x ' ny and n z are expressed in terms of their reference directions by the following set of relations, 396 Helical Gears in Mesh (14.82) (14.83) (14.84) We now introduce another pair of unit vectors fixed in the rack. A normal section through the rack tooth is shown in Figure 14.13, and the vectors nnr and nTr are defined in the direction normal to the tooth surface, and in the direction of the tangent pointing towards the tooth tip. The normal pressure angle I/l~r of the rack is equal to the operating normal pressure angle I/l np of the pinion, as we proved in Equation (14.20). Once again, we use the angle defined on the pinion when we express the relations between the different un i t vectors, - sin I/l np n~ - cos I/l np n'T/ (14.85) (14.86) In order to determine which of the pinion generators is in contact with the rack, we make use of the following condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.26-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.26-1.png",
        "caption": "Figure 13.26. Span measurement.",
        "texts": [
            " The chordal tooth thickness is then given by the following equation, proved in exactly the same manner as Equat ion (13.120), R t cos2~R 2 sin( nR 2R ) (13.121) cos2~R In Chapter 8, we described the span measurement of the tooth thickness, in the case of a spur gear. The same method Span Measurement 355 can be used for a helical gear, and the measurement is made in a base tangent plane, since in this plane the normals to the surfaces of different teeth all lie in the same direction. A base tangent plane is shown in Figure 13.26, with the shaded areas representing the sections through the teeth. The span measurement is made in the direction perpendicular to the teeth, and is shown in the diagram as the length S. Since the base tangent section is essentially the same as the developed base cylinder, as we pointed out earlier in this chapter, the pitch and the tooth thickness in the direction of the span measurement are equal to the normal base pitch Pnb and the normal tooth thickness t nb at the base cylinder. Hence, if the span is measured over N' teeth, the span length is equal to (N'-1) normal base pitches, together with the tooth thic kness, S (13.122) By expressing Pnb and t nb in terms of the corresponding quantities in the transverse plane, and then relating these to the quantities in the standard pitch cylinder, we can express the span length S in the following manner, (13.123) 356 Tooth Surface of a Helical Involute Gear Once the length S is measured, the normal tooth thickness is found by rearranging Equation (13.123), S - (N'-1)7I'm - Nm inv'ts cos 'ns n n (13.124) The radius R at which the measurement is made can be read from Figure 13.26, R (13.125) We now have to choose the value of N' so that the span measurement is made near the middle of the tooth face, or in other words, at a radi us of approximately (Rs +e). The value of S which would give the ideal measurement radius is found by setting R equal to (Rs+e) in Equation (13.125), (13.126) We follow the same procedure that was used in the case of spur gears. We express Rb in terms of Rs ' and expand the expression for S as a power series in (e/Rs )' retaining only the first two terms, ( 13",
            "75-(2/N)], exactly as we did for spur gears, and once again the angle 'ts in the second term is expressed more conveniently in degrees, so that the final expression Position of a Typical Point A on the Tooth Surface 357 for N' takes the following form, N' ~ 1 + N1~8tos + N tan ~ns ::n2~b + 2e[0.75-(2/N)] (13.129) - 2 'II' cos 'II'mn tan cfl ns This equation generally gives a non-integer value for N' , and the number of teeth to be spanned is equal to the integer closest to this value. There is one condition that must be met, for the span measurement of a helical gear to be possible. The measurement must obviously be made inside the end faces of the gear. The projection of the span length in the axial direction, which is shown in Figure 13.26, must therefore be less than the face width, S sin ~b < F (13.130) Position of a Typical Point A on the Tooth Surface We stated earlier that the tooth surface of a helical gear is formed by a family of helices, each passing through a specified profile in the transverse section z=O. So far in this chapter, whenever we have discussed the position of a typical point A, we have essentially given its position relative to AO' the point where the gear helix through A cuts the transverse plane z=O. However, we have not yet established the position of AO"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003243_978-94-011-4120-8_45-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003243_978-94-011-4120-8_45-Figure1-1.png",
        "caption": "Figure 1. Exemplification of the problem",
        "texts": [
            " In this section it is analyzed how the screw system of a serial chain, that represents the motion of its last link, evolves in time. Then the ex- 433 1. Lenarcic and M.M. Stanisi,; (eds.), Advances in Robot Kinematics, 433-440. \u00a9 2000 Kluwer Academic Publishers. pression of the screw systems after an infinitesimal displacement is derived with a first-order approximation of velocities. In order to simplify the problem, first it is analyzed the case of a serial chain composed of only three rigid bodies, as shown in figure 1. Let us call the angular velocity between body i and j as j wi and the velocity of an arbitrary point P of body i, measured in a coordinate system fixed in body j, as jv~. Assuming the same conventions, the angular and linear accelerations will be called j Qi and ja~. A unitary screw Si of pitch hi can be associated to each helical pair: (1) where i-1wiSi = i- 1 w i . In an arbitrary coordinate system CS, with origin coincident at time t with point P of body 2, the moment part Soi of screw Si is given by the velocity of the frame origin, when the frame is moving around Sr (2) where Pi is a generic vector joining a point on the screw axis Si to P",
            " (9) By substitution of (9) and (8) into (7), we find that, using (2), \u00b0a~ can be expressed in CS as: \u00b0a~ = (Owl ) 2Sl /\\ Sol + ew2 )2S2 /\\ S02 + 2 0W l Sl /\\ I W2So 2 + O~ISol + 1~2s02 (10) This expression can be rewritten in a more meaningful way as: 0a~ = (OW 1Sl +1 W2S2) 1\\ (OWl Sol +1 W2S0 2) + O~lSol +1~2S02 + (OW1S11\\1 W2So2 _1 W2S2 1\\0 W1So1) (11) The first component of (11) is equal to 0 w 2 (t) 1\\ \u00b0v~ and it is the centripetal acceleration of the screw motion St. The centripetal acceleration vector field constrains the velocities of body 2 to be tangent at time t + dt to the helicoidal trajectories of the screw motion St, as shown in figure 1. This implies that the screw system SHdt is unchanged with respect to St as an effect of the centripetal acceleration, and its expression does not depend on the centripetal term of the acceleration. In fact from (6), by using (11), it is: So(t + dt) =0 W1Sol +1 W2So2 + O~lSoldt (12) +1~2S02dt + (OW1S11\\1 W2So2 _1 W2S2 1\\0 W1So1)dt The angular acceleration 0 0 2 is obtained by deriving \u00b0w2 : where in (13) the derivative ~~ is made in a coordinate system fixed in body 1. So the angular velocity part of the screw St+dt is given by (4): s(t + dt) = \u00b0W 1Sl + lW2S2 + \u00b0W1Sldt + lW2S2dt + \u00b0W1Sl 1\\ lW2s2dt (14) By adopting the definition of Lie Bracket as: [S S] [ Sl 1\\ S2 ] 1, 2 = Sl 1\\ S02 - S2 1\\ Sol (15) with the aid of (12) and (14), the screw system SHdt can be expressed in CS as: Neglecting second-order terms, we can rewrite the above equation as: SHdt = (Owl + \u00b0wldt)Sl + (lw2 + lw2dt)(S2 + \u00b0Wl [Sl' S2]dt) = (17) Owl (t + dt)Sl +1 w2 (t + dt)(S2 + \u00b0Wl [Sl' S2]dt) (18) Comparing the (3) and (18) and assuming that Ti =i-l wiSh we see that after an infinitesimal time dt the screw S2 has been transformed into the screw 82 + [Tl' 8 2 ]dt, while the screw 8 1 is unchanged. This means that the screw system varies by reason of the movement of 82 along the trajectories of Tl, Sugimoto (1990), and so it can be evaluated by the Lie derivative of 82 with respect to T I . The expression (18) can be generalized for an arbitrary serial chain. Suppose that a third screw 8 s is added to the serial chain of figure 1. The total motion can be split in two consecutive movements, the first due to joint 2 and the second to joint 1. After a movement of joint 2, the screw 8s becomes by (18): (19) Further, after a movement of joint 1: 82 -+ 82 + [Tl' 8 2 ]dt 8~ -+ 8~ + [Tl' 8~]dt = 8 s + [Tl, 8s]dt + [T2' 8s]dt + o(dt) (20) Clearly the movement due to joint 3 does not affect the screw system. Indeed by extending iteratively the process to more joints, it is possible to state a general rule: a screw 8i is determined at time t + dt by the series of twists Tl, T2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003129_a:1008106331459-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003129_a:1008106331459-Figure10-1.png",
        "caption": "Figure 10. Robot motion during micromanipulation.",
        "texts": [
            " In this case, the center of rotation of the robot is the point A or B, correspondingly, on the endeffector tip (Figures 10 (a) and 10 (b)). However, both the linear and the rotational motion phase are performed sequentially by using both these methods so that the whole operation time of the robot is generally not optimal. When performing a navigation task by the third method, the center of rotation is point OA (Figure 9 (c)). In this case, the route length between points OA and OB is minimized. When performing a micromanipulation task, the center of rotation is the tip of its manipulator (in the initial state \u2013 point A, Figure 10 (c)). In the latter case, the route length between points A and B is minimized to keep the endeffector tip under the microscope objective. An advantage of the third method is the possibility to move along an optimal trajectory in minimal time. However, as the actual direction of the linear robot motion is determined by its current orientation, the motion direction must be continuously corrected. Generally, independent of the movement method used, it is hardly possible to navigate a microrobot exactly along a calculated trajectory by using an open-loop control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure18-4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure18-4-1.png",
        "caption": "Figure 18-4. Direct tension adhesion test: A is the rubber-fabric test piece; B and B' are metal cylinders; C is adhesive.",
        "texts": [],
        "surrounding_texts": [
            "coming from products with various thickness of the plies. The speeds are dependent on the method, 0.8 mm/s for 180 ,\u0302 2.5 mm/s for 90^ and 0.4 mm/s for rings, but the logic is not too clear. ASTM D413 also gives simple dead load methods for adhesion strength whereby a mass, large enough to cause peeling, is hung from one leg of the test piece and the rate of separation noted. The problems of interpreting the results are discussed but tensile machines are common enough that there would seem to be little use for this type of procedure. Because coated fabrics are generally dealt with in separate standards committees, and because the thinner coatings are not strong enough to allow the use of the peel methods described above, separate standards have been developed for these products. The problem of failure in the coating is overcome by using reinforcements of fabric or cement. These methods are really product tests and outside the scope of this book but the appropriate references can be noted. The international standard for coated fabrics is ISO 2411'\u0302 ^ the British methods are identical as BS EN ISO 2411 and the ASTM methods are in D751'\u0302 ^ There are also methods for conveyor belts in ISO 252-1^^ When using peel tests on such products as belts to separate the plies, it can be difficult to obtain interfacial failure. Loha et al\"\u0302 ^ successfully used test pieces including a perforated metal sheet at the interface to measure rubber to rubber adhesion strength. Adhesion, corrosion and staining 2.2 Direct Tension Tests 373 Borroff and Wake'\u0302 ^ and later Meardon\"\u0302 ,\u0302 developed a direct tension method which was claimed to more nearly measure the 'true' adhesion between fabric and rubber. It is particularly useful for discriminating between adhesive systems, when the peel tests can be misleading. The main objection to the method is practical in that the preparation of test pieces is rather difficult. The method is covered in ISO 4637^ .\u0302 The test piece consists of two metal cylinders, 25 mm diameter, between which the composite to be tested is cemented (see Figure 18.4). The metals are gripped in a tensile machine and separated at a rate of 50 mm/min and the maximum force recorded. The most important part of the test is the preparation of the metal/rubber/fabric test piece and international interlaboratory tests showed that, unless very careful preparation of the metals was carried out, failure occurred at the metal surface. ISO 4637 gives considerable detail on surface preparation; after machining, the ends are lapped and degreased with trichloroethylene whilst the test piece is wiped with a solution of ammonium hydroxide in acetone. The assembly is cemented together with a cyanoacrylate adhesive using a special jig and it should be noted that the piece of fabric/rubber under test is a square of side approximately 32 mm and, hence, larger than the metal cylinders. ISO 4637 was developed from the British standard, BS 903:Part A27^\\ which was eventually revised to be identical with the international method. It is one of those regrettable lapses in standardisation that this revision had to"
        ]
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure10-1.png",
        "caption": "Fig. 10. A singular con\u00aeguration of class (RPM, RO, IIM, II, IO).",
        "texts": [
            " For the IIM-type con\u00aegurations with three extended legs (as in Fig. 8) the condition is not satis\u00aeed. If only two subchains are singular (similar to Fig. 7), the condition is always satis\u00aeed when the singular subchains are B and C (as in the \u00aegure). When, however, one of the singular subchains is A, then, generally, the matrix A is of rank 5. There are two exceptions. The \u00aerst is represented in Fig. 9, where the singular subchains are A and B and additionally the point Co lies in the plane ABC. The second exception is shown in Fig. 10, where not only points B and C are located on screws SB 1 and SC 1 , but also point A lies in the (vertical) plane de\u00aened by the two screws. Each of Figs 9 and 10 represents, in fact 11 con\u00aegurations, since the elevation of point A can vary. Thus, the set of singularities belonging to the IIM, IO and II types consists of a main 3- dimensional set (Fig. 6), a 2-dimensional set (Fig. 7) and two 1-dimensional sets (Figs 9 and 10). The set of singularities in the IIM and IO types has two 2-dimensional components (similar to Fig",
            " with subchain A as one of the singular ones) and a 1-dimensional component (Fig. 8). (3.2) According to condition (i) and Equation (13), a con\u00aeguration is an RI-type singularity if and only if at least one of the following conditions is satis\u00aeed: either the subchain A is singular (in any way); or subchain B is fully extended; or subchain C is fully extended. Condition (ii) and Equation (12) imply that an RPM-singularity is also of the RO-type in the following three cases: (a) When C is on the SC 1 axis and the plane ABC is perpendicular to mC 2 (Fig. 10 is an example, though subchain B need not be singular). (b) When C is on the SC 1 axis while point B is not on the SB 1 axis, and b_mB 1 . (c) When B is on the SB 1 axis, while point C is not on the SC 1 axis, and the point Co lies in the plane ABC (Fig. 9, though subchain A need not be singular). Thus, four sets are obtained: 15 RPM-type singularities, 14 RPM and RI-type singularities, 14 RPM and RO-type singularities and RPM, RI and RO-type singularities. (3.3) The intersections of the subsets of {3.1} and {3.2} give the 10 singularity classes (Table 2) of con\u00aegurations that are both IIM and RPM. Of these, only \u00aeve classes are non-empty for the mechanism under consideration: (a) (IIM, IO, RPM, RI) has 12 con\u00aegurations with two singular subchains similarly to Fig. 7, but subchain A must be one of the singular subchains. When the two singular subchains are A and B, point Co should not lie in the plane ABC (i.e. unlike Fig. 10). Alternatively, if the singular subchains are A and C, then the plane ABC should not contain Co and Ao. (b) (IIM, IO, II, RPM) has 12 con\u00aegurations as in Fig. 7. The singular subchains must be B and C. The plane ABC must not contain Co and Bo (unlike Fig. 10). (c) (IIM, IO, II, RPM. RI) has 13 con\u00aegurations with three singular subchains as in Fig. 6. (d) (IIM, IO, II, RPM, RO) has 11 con\u00aegurations like the one depicted in Fig. 10. The moving plane ABC contains the points Co and Bo and the subchains B and C are singular in the same way as in Fig. 7. (e) (IIM, IO, II, RPM, RI, RO) has 11 con\u00aegurations in two 1-dimensional sets. The \u00aerst is represented by the con\u00aeguration in Fig. 9. It is similar to Fig. 7 with singular subchains A and B, but point Co is in the plane ABC, allowing for a RO-singularity. The second set is similar to the con\u00aeguration in Fig. 9, however, the non-singular subchain must be B rather than A. (3.4) Only one of the four classes of IIM but not RPM singularities is non-empty: (IIM, IO, RI, RO) consists of 11 con\u00aegurations as in Fig",
            "5) All of the four RPM but not IIM classes are non-empty. (RPM, II, IO) has 15 con\u00aegurations. An example for this class can be obtained from the con\u00aeguration in Fig. 7 by an arbitrarily small perturbation of the subchain C while subchains A and B remain \u00aexed. (RPM, RI, II, IO) has 14 con\u00aegurations and can be illustrated by a variation of Fig. 6 obtained by maintaining the depicted position of the subchains A and B and slightly perturbing subchain C. (RPM, RO, II, IO) has 12 con\u00aegurations. An example is obtained from the con\u00aeguration in Fig. 10 by a small rotation of subchain C about SC 1 . (RPM, RI, RO, II, IO) has 12 con\u00aegurations and a representative can be obtained from Fig. 9 by a small rotation of subchain C about SC 1 . (4) RO- and II-type singularities There are 15 con\u00aegurations that are of the RO and II types but are not IIM nor RPM-singu- larities. From Equation (12), the conditions for RO-type singularity are: (a) Either Co must be in the plane ABC (Fig. 11), or (b) The point A must be in the plane of subchain B (Fig. 12), i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure15.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure15.1-1.png",
        "caption": "Figure 15.1. A helical rack and pinion.",
        "texts": [
            " However, even though their use is far less frequent than that of parallel-axis gears, it is important to understand the meshing geometry of a crossed helical gear pair, since it forms the theoretical basis of the hobbing process. The technique of hobbing is the most common method by which gears are cut. It is essentially a process in which the gear blank 406 Crossed Helical Gears and the hob operate as a pair of crossed helical gears. A brief description of hobbing was given in in Chapter 5, but for a more detailed explanation, it is first necessary to describe the meshing geometry of crossed helical gears. A helical rack and pinion, of the type discussed in Chapter 14, is shown in Figure 15.1. The rack is supported in guides which allow movement only in the direction perpendicular to the pinion axis. We showed in Chapter 14 that a rack and pinion will mesh correctly, provided the normal base pi tch and the transverse base pi tch of the rack are equal to those of the pinion. The pi tch cylinder radi us of the pinion is given by Equation (14.6), (15.1) where Ptr is the transverse pitch of the rack. We also proved that on the pinion the normal and transverse pitches, the Rack and Pinion 407 helix angle, and the normal and transverse pressure angles, all measured at the pitch cylinder, are equal to the corresponding quantities on the rack",
            " The velocity of the rack in Figure 15.2 can be resolved into two non-perpendicular components v~ and v~, the first in the direction perpendicular to the pinion axis, and the second parallel to the rack teeth, as shown in Figure 15.2. A motion of the rack in the direction of its teeth would cause no rotation of the pinion, so the only component of the rack velocity related directly to the pinion angular velocity is v~. The value of v~ for the rack in Figure 15.2 is therefore equal to the velocity of the rack in Figure 15.1, and the other component v~ must be such that the resultant velocity is in the direction allowed by the guides. Since the angle between the component directions is fixed, the components\u00b7 v~ and v~ remain in a constant ratio, and a constant angular velocity of the pinion will therefore produce a constant velocity of the rack. To distinguish between the two types of rack shown in Figures 15.1 and 15.2, we regard each rack as the limiting case, when the number of teeth becomes infinite, of a gear whose axis is perpendicular to the direction of motion of the rack. In the case of Figure 15.1, the axis of this gear is parallel to the pinion axis, so the rack and pinion can be thought of as a special case of a parallel-axis gear pair. On the other hand, the rack in Figure 15.2 is the limiting case of a gear whose axis is not parallel to the pinion axis, and the angle between these two axes is shown in the diagram as t. Since the axes are not parallel, the rack and pinion can be regarded as a crossed helical gear pair. The two types of rack and pinion will be referred to as either a parallel-axis, or a crossed helical, rack and pinion",
            " The concept of the pitch cylinder does turn out to be useful in the geometric analysis of a crossed helical rack and pinion. We start by defining it, and then we will explain the reasons for the way in which it is defined. The pitch cylinder of a pinion, meshed with a rack in a crossed helical manner, is defined as the cylinder with the same radius as the pinion pitch cylinder in the equivalent parallel-axis rack and pinion. With this definition, the radius of the pinion pitch cylinder in Figure 15.2 is equal to that in Figure 15.1. The pitch cylinder radius for the pinion in Figure 15.1 was given by Equation (15.1) in terms of the transverse pitch of the rack, We cannot use the same equation for the pinion in Figure 15.2, because the transverse pitches of the two racks are different. We therefore use Equation (14.1) to express the transverse pitch of the rack in Figure 15.1, in terms of its Pinion pi tch Cylinder 411 normal pitch and its helix angle. We then obtain the following expression for the pitch cylinder radius, 271' cos I/I~ (15.4) This equation can now be used to give the pitch cylinder radius for the pinion in Figure 15.2, since the values of the rack normal pitch and the rack helix angle are the same in the two diagrams. The most important advantage of defining the pi tch cylinder in this manner is that we know, from the meshing geometry of the parallel-axis rack and pinion described in Chapter 14, that the normal pitch, the normal pressure angle, and the helix angle of the rack are equal to the corresponding quantities on the gear, measured at this particular radius, 1/1' r 4>np (15.5) (15.6) (15.7) There is, of course, no longer any relation between the transverse quantities of the rack and those of the pinion, since the transverse quantities on the rack are all different from those on the parallel-axis rack in Figure 15.1. The only disadvantage we find, when the pitch cylinder is defined in this way, is that the rack velocity is no longer equal to RpW, as it is in the case of a parallel-axis rack and pinion. However, it is not difficult to express the rack velocity in terms of the pinion angular velocity. We proved earlier that if the pinions in Figures 15.1 and 15.2 have the same angular velocity, the velocity of the rack in Figure 15.1 is equal to v~, the velocity component of the rack in Figure 15.2 perpendicular to the pinion axis. We know that the rack in Figure 15.1 has a velocity equal to R w. For the rack p in Figure 15.2, it is therefore the velocity component v~, rather than the resultant veloc i ty, which is equal to Rpw, v' r (15.8) 412 Crossed Helical Gears We now use the velocity vector triangle in Figure 15.2, to express the resultant rack velocity vr in terms of the pinion angular velocity, cos \"'~ v~ cos(\"'~-~) cos \"'~ cos(\"'~-~) Rpw (15.9) If we combine Equations (15.4 and 15.9), we obtain an alternative expression for the rack velocity, 211' cos(\"'~-~) W (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.5-1.png",
        "caption": "Figure 12.5. Gear positions, with contact at the pi tch point.",
        "texts": [
            "6) for RPl and Rp2 ' it is clear that the operating circular pitches are equal. The symbol Pp is therefore used to represent the operating circular pitch of either gear, and its value is given by the following expression, (12.23) Relation Between the Gear positions In an internal gear pair, the angular position of the internal gear is indicated in the same manner as that of the pinion, by the angle ~2 measured from the line of centers counter-clockwise to the x2 axis. An internal gear pair is shown in Figure 12.5, with the contact point coinciding with Relation Between the Gear positions 269 the pitch point. When the gears are in these positions, their angular positions can be read from the diagram, (12.24) (12.25) where tP1 and tP2 are the tooth thicknesses at the pi tch circles. After rotations AP1 and AP 2 , the new angular positions are as follows, P 1 -~ + AP 1 (12.26) 2Rp1 P2 ~+ 2Rp2 AP 2 (12.27) The angular velocities of the two gears are related by Equation (12.2), 270 Internal Gears Rp1 w1 Rp2w2 This equation is integrated, giving a relation between the gear rotations, RP1~/J1 RP2~/J2 (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002987_ias.1999.799162-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002987_ias.1999.799162-Figure1-1.png",
        "caption": "Fig. 1. (a) Eddy current generation at the entry and exit of the air gap when the primary coil moves with velocity v . (b) Polarity and decaying profile of the entry and exit eddy currents. (c) Air gap flux profile.",
        "texts": [
            " Hence, they can not be directly applied for the vector control. An accurate equivalent circuit model is indispensable for high performance vector control. Some researches have modified the \u2018per-phase\u2019 equivalent circuits used in roundrotor machine analysis [2][3]. However, they are mainly focused on evaluating the characteristics of the motor. This paper presents a new equivalent circuit model in which the end effect is modeled and quantified for the rotor-flux oriented(RF0) control of a LIM. . Fig. 1 (a) shows a conceptual construction of a linear induction motor. The primary is simply a rotary-motor primary cut open and rolled flat. The secondary usually consists of a sheet conductor with an iron return path for the magnetic flux. In a LIM, as the primary moves, the secondary is continuously replaced by a new material. This new material will tend to resist a sudden increase in flux penetration and only allow a gradual build up of the flux density in the air gap. Such a flux variation along the motor length is illustrated in Fig",
            " The eddy current in the entry grows very rapidly to mirror the primary current, nullifying the- primary MMF and reducing the flux to nearly zero at entry [6]. On the other hand, the eddy current at the exit generates a kind of wake field, dragging the moving motion of the primary core. The rise and decay of the secondary eddy current are controlled by the 0-7803-5589-X/99/$10.00 1999 IEEE 2284 sheet leakage time constant ZT = LIT/r, and total secondary time constant T, = LT/r,, respectively [6]. Since Tl, is small compared with T,, the eddy current at the entry grows very rapidly to the primary current level, and then decay slowly (See Fig. 1 (b)). Hereafter, we consider the problem of incorporating the end effects into an equivalent circuit model. Note from the previous argument that, the secondary eddy current generated by the end effect is in phase opposition to the primary current. In RFO vector control of a RIM, the synchronous reference frame is aligned to d axis rotor flux A:, yielding A& = 0, i:,. = 0, and i:, = -Lm/L, . i& in the steady state. Similar concept can be applied to the LIM. Since we align the reference frame with the reaction rail flux and call it d axis, it results in As,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.18-1.png",
        "caption": "Fig. 7.18 Jeffcott\u2019s rotor",
        "texts": [
            " All these were apparently in distinct contradiction with Rankine\u2019s theory. To this point, Rankine\u2019s error should have been corrected. However, Rankine was so famous in his field and his wrong prediction was so widely accepted that his wrong conclusion remained influential for almost 50 years after the right work done by the above scholars. In 1916, the Royal Society of London commissioned Henry Jeffcott to resolve this conflict between Rankine\u2019s theory and the practice of engineers. In 1919, Jeffcott published his classic paper using a rotor model depicted in Fig. 7.18 in which the curve of the vibration amplitude against frequency was given. He concluded that self-centering effect was created when the rotor operating at a super-critical speed and the amplitude would tend to a constant value with further increase of rotational speed (Jeffcott 1919). The existence of stable super-critical speed was an important new finding which laid the theoretical basis to design turbines, pumps and compressors with higher speed and efficiency. Soon in 1920s, flexible rotors operating at super-critical speed were designed according to the new finding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003123_s0094-114x(03)00065-x-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003123_s0094-114x(03)00065-x-Figure4-1.png",
        "caption": "Fig. 4. Stewart platform manipulator.",
        "texts": [
            " Denoting the fixed axis direction in a leg by ki, the leg-vector is given by Si \u00bc t\u00fe qi bi Diki; \u00f08\u00de where the displacement of prismatic joint at the base of the leg Di is given by Di \u00bc \u00f0t\u00fe qi bi\u00de ki: \u00f09\u00de The platform-connection-points are transformed according to Eq. (5), where the rotation matrix R is given in terms of roll-pitch-yaw angles as R \u00bc RPY \u00f0hz; hy; hx\u00de \u00bc Rot\u00f0z; hz\u00deRot\u00f0y; hy\u00deRot\u00f0x; hx\u00de: \u00f010\u00de The force-transformation matrix for R \u00bc \u00bd Fx Fy Fz Mx My Mz T is given by H \u00bc k1 k2 k3 s1 s2 s3 q1 k1 q2 k2 q3 k3 q1 s1 q2 s2 q3 s3 : \u00f011\u00de Fig. 4 shows a Stewart platform manipulator. This manipulator has one prismatic actuation in each leg. The rotation matrix is given by Eq. (10). The force-transformation matrix is given by H \u00bc s1 s2 s3 s4 s5 s6 q1 s1 q2 s2 q3 s3 q4 s4 q5 s5 q6 s6 : \u00f012\u00de The Eqs. (3), (7), (11), and (12) give the expressions for the force-transformation matrix H for the 5-bar, 8-bar, 3-PRPS and Stewart platform manipulators, respectively. When H is singular, the transformation is degenerate and some loads ( R) on the platform cannot be supported by the actuator forces (F), leading to loss of constraint, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003195_tmag.2004.824127-Figure17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003195_tmag.2004.824127-Figure17-1.png",
        "caption": "Fig. 17. Slot section of a form-wound coil and its flux plot when t = 10 s.",
        "texts": [
            " Power electronic inverter-fed motors have become commonly used in variable speed drives. Because the high , fast switching, and possible long feeder cable, the repetitive steep-fronted voltage is becoming a source of premature winding insulation failures [17], [18]. The fast rising wavefronts have high frequency contents in the range of megahertz and, hence, the skin effect is very significant and the parasitic capacitive effects need to be considered in the solution. An example to demonstrate how to analyze such problems is presented. Fig. 17 shows one side of a coil with eight turns in a slot. All solid conductors are connected with external circuit as in Fig. 18. The turn-to-ground capacitance and turn-to-turn capacitance are first computed using electrostatic field solver as a preprocessing. The capacitance between nonadjacent turns is negligible. The calculated capacitance is divided into two halves and appears at both ends of the longitudinal impedance. A step voltage (simulating PWM wavefront) having 50 ns rise time and 800 V magnitude is applied to the terminal of the coil"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002785_s0951-8320(00)00106-x-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002785_s0951-8320(00)00106-x-Figure3-1.png",
        "caption": "Fig. 3. A two-link planar manipulator.",
        "texts": [
            " Conduct a large number of such experiments and compute the two types of dynamic reliability as: CDR number of acceptable trejectory points total number of trejectory points examined or 23 SPDR number of acceptable trajectories total number of trajectories examined 24 A \u00aerst-order auto-regressive vector process [13] is used to represent the random joint torque vector t(t) in step (a) of the simulation procedure, as indicated below ~t i t f ~t i t 2 Dt 1 ri t ; i 1; n 25 where ~t i t ti t 2 t i t ; 21 , f , 1 for stationary processes, and ri t is a series of random numbers with zero mean and constant standard deviation given by sri sti 1 2 f2 1=2: 26 The reliabilities are computed for the two-link manipulator shown in Fig. 3. The various kinematic and dynamic parameters of this manipulator are considered to be independent random variables following Gaussian distributions, and with the mean values and standard deviations as given below: \u0300 1 50 cm; \u0300 2 40 cm; s`1 0:01 cm; s`2 0:01 cm; m1 8 kg; m2 6 kg; sm1 0:005 kg; sm2 0:005 kg; I1 1400 kg 2 cm2 ; I2 800 kg 2 cm2 ; sI1 1:5 kg 2 cm2 ; sI2 1:5 kg 2 cm2 ; t1 5000 N 2 cm; t2 1500 N 2 cm where `1 and `2 are the link lengths, ml and m2 the link masses, I1 and I2 the link inertias about the axes through the centers of mass and perpendicular to the plane of the paper, and t 1 and t 2 are the joint torques"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure8-1.png",
        "caption": "Fig. 8 Coordinate systems fo",
        "texts": [
            " 6 The relative position between the outer and inside lades Table 2 Machine settings for the proposed m Items Convex Tilt angle i Swivel angle j Radial setting SR Initial cradle angle setting c Vertical offset Em Increment of machine center to back A Sliding base feed setting B Machine root angle m JANUARY 2007, Vol. 129 / 43 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use p p c c a T d a t e d c s t n t s 4 Downloaded Fr osition between the imaginary generating gear and the work gear. The tooth contact analysis TCA is used to verify the contact attern and kinematic characteristics of the example gear set. The oordinate systems of the gear assembly are shown in Fig. 8. The oordinate systems S1 x1 ,y1 ,z1 , S2 x2 ,y2 ,z2 , and Ss xs ,ys ,zs re rigidly connected to the pinion, gear, and frame, respectively. he auxiliary coordinate systems Sp, Sq, and Sr are established to escribe the relative position between this gear pair. Here, V and represent the shortest distance and crossing angle between the xes of gear rotation, and H1 and H2 represent the axial settings of he pinion and gear, respectively. The position and unit normal quations for the tooth surfaces of the pinion and the gear are erived from above-mentioned equations and represented in the oordinate systems S1 and S2, respectively. As shown in Fig. 8, the pinion is assembled to the coordinate ystem S1 and rotates about axis xp, while the gear is assembled to he coordinate system S2 and rotates about axis xs. Using coordiate transformation, position vectors and unit normal vectors of he pinion and gear can be represented in the frame coordinate ystem Ss as follows: rs P u P , P , 1 P , 1 = Msr \u00b7 Mrq \u00b7 Mqp \u00b7 Mp1 1 \u00b7 r1 u P , P , 1 P = Ms1 1 \u00b7 r1 u P , P , 1 P 4 / Vol. 129, JANUARY 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 ns P u P , P , 1 P , 1 = Ls1 1 \u00b7 n1 u P , P , 1 P 22 Here Mp1 = 1 0 0 0 0 cos 1 sin 1 0 0 \u2212 sin 1 cos 1 0 0 0 0 1 23 Mqp = 1 0 0 H1 0 1 0 0 0 0 1 0 0 0 0 1 24 Mrq = cos 0 \u2212 sin 0 0 1 0 0 sin 0 cos 0 0 0 0 1 25 s for the example: \u201ea\u2026 pinion and imaginary rating gear ion ene r assembly of the gear pair Transactions of the ASME 6 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003187_0301-679x(90)90041-m-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003187_0301-679x(90)90041-m-Figure16-1.png",
        "caption": "Fig 16 Radiometer spindle assembly for TIROS 1I meteorological satellite 53",
        "texts": [
            " It is therefore important that the lubricant evaporated from these surfaces into the space environment be replenished. As a result, Ahlborn et al 2 recommend that the lubrication system be designed whereby the lubricant lost to space during the life of a mission is 10% of the internal lubricant supply. This can be achieved by controlled leakage. The premier work related to controlled leakage was reported by Weinreb 53 for the bearings in a mechanism for the TIROS II meteorological satellite. The mechanism, shown in Fig 16, was a five-channel infra-red radiometer which consisted of five optical mirrors mounted on five gears and eight ball bearings driven by a low-power motor whose output torque was 2.12 x 10 -4 N m (0.03 in.-oz). The design was based on the fact that, on a molecular scale, even smooth surfaces appear rough, and, according to Knudsen 54, the direction in which a molecule rebounds after a collision with a wall is statistically independent of the angle of incidence. For this reason, the molecular flow resistance of small orifices can be made relatively high. The vapour pressure inside the chamber can be 87 E. V. Zaretsky--l iquid lubrication in space maintained and vaporization of the lubricant can be minimized. The mechanism shown in Fig 16 was designed with lubricant reservoirs of oil-impregnated sintered nylon. The lubricant was a MIL-L-6085A diester oil with a vapour pressure of approximately 10 -4 torr. When the outside pressure reaches a value below 10 -2 torr, a molecular flow occurs around the shaft through the small clearance. The clearance was a nominal 0.0127 mm (0.0005 in.). Using the equation derived by Knudsen 54, it was possible to calculate the escape rate of oil from the bearing assembly. Based upon the required life of the satellite and the escape rate of the lubricant, the amount of oil required in the reservoirs was determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003461_tsmcb.2002.1033184-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003461_tsmcb.2002.1033184-Figure3-1.png",
        "caption": "Fig. 3. PUMA 560 robot arm with a long tool.",
        "texts": [
            " From the previous results of position error estimation, we know that the error can be made smaller by decreasing the design parameter c to expedite the convergence of neural network (12); whereas, although a smaller value of tf makes the position error decrease faster, it may cause large joint acceleration or velocity. The ensuing simulation results will verify the soundness of the proposed error estimation. The Unimation PUMA 560 robot arm has six joints [24]. When both the Cartesian position and orientation are considered, the PUMA 560 arm is not a redundant robot. However, if we consider only the positioning of the end-point of its attached tool, the PUMA 560 arm, as shown in Fig. 3, becomes a redundant manipulator and the associated Jacobian matrix J( ) 2 R3 6. Table I shows the Denavit and Hartenberg parameters of the system with joint limits expressed in radians. In this subsection, by applying the proposed dual network model (12) to the PUMA 560 robot arm with the capacitive parameter c = 10 6, we discuss the torque minimization problem of redundant manipulators when its end-effector tracks circular paths. The first desired motion of the end-effector is a circle of radius r = 10 cm with the revolute angle about the x axis =6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure14.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure14.1-1.png",
        "caption": "Fig. 14.1 Centrifugal casting. a Vertical, b horizontal",
        "texts": [
            " However, the real industrial production did not appear until 1919 when Dimitri de Lavaud, an American engineer of Brazilian origin, invented the watering cooling pipe casting machine. His invention then was widely used for casting of iron pipes, making the centrifugal 512 14 Development of Other Manufacturing Processes casting the second most commonly used casting method next only to sand casting (Zhang 2004). Now, it is still widely used in casting many other types of hollow parts, such as bushings in internal combustion engines, as shown in Fig. 14.1. Centrifugal casting has a series of advantages as below: (1) gating systems and risers are not needed; (2) high output; (3) castings have a higher density and a finer grained structure with less porosity, and (4) two materials can be cast by introducing a second material during the process. Due to these features, it is suitable for making hollow, cylindrical, and thin-walled parts, such as pipes, bushings, and flywheel etc. The modern investment casting was formed during the 1940s on the basis of earlier development (DeGarmo et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure13-3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure13-3-1.png",
        "caption": "Figure 13-3. Tracking test, (a) Electrode system; (b) effect of voltage on number of electrolyte drops causing 'failure'. CTI is the comparative tracking index.",
        "texts": [],
        "surrounding_texts": [
            "standards to aid this process but there is also an lEC guide on high voltage testing techniques'\u0302 '\u0302'\u0302 ^"
        ]
    },
    {
        "image_filename": "designv10_4_0002924_978-94-009-1718-7_36-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002924_978-94-009-1718-7_36-Figure7-1.png",
        "caption": "Fig. 7: Workspace of point P (F = 1).",
        "texts": [
            " To find the regions in which the point P is possibly moving we introduce a second coordinate system (YI' Y2' Y3) fixed on one of this three plates (see Fig. 6 and 7). By actuating both angles <P and lfI simultaneously we get for the relation between the position vectors X and y: x = a {O, 1,0} + c {costfJ,cos l{I,sintfJ + sin I{I} + Y. (12) Point P with the given position vector Y = {Yl' Y2' Y3} in (Yl' Y2' Y3) is then moving with two degrees of freedoms in its workspace, an algebraic surface of order four: But with I{I:=} tfJ and tfJ:=} -tfJ (Fig. 7) formula (12) yields: X(tfJ) = a {O,l,O}+c {costfJ,costfJ,O}+ Y (14) and the workspace ofP reduces to a straight line in the plane X3 = Y3 \u2022 The two workspace are in contact at the singularity position ~ = 0 A l/f = 0 . The four accessible singularity positions of the queer square mechanism are shown in the Fig. 8 and Fig. 9. 368 Summary Some linkages show \"kinematotropy\", i.e., from a singularity position they can open up into regions with different global mobilities. In the paper three examples of such kinema totropic linkages are given, one of them is new"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003160_20.620439-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003160_20.620439-Figure8-1.png",
        "caption": "Fig. 8. Experimental setup.",
        "texts": [],
        "surrounding_texts": [
            "4306 IEEE TRANSACTIONS ON MAGNETICS, VOL. 33, NO. 5, SEPTEMBER 1997\nC. Enlarged Plot: ( z = 0, Np = 10, N, = 1)\nIn Figs. 5 and 6, it is seen that, for z = 0, the mutual inductance increases as the off-center distance y increases. This increment is shown in greater detail in Fig. 7 . With the coil dimensions of calculation 2, the mutual inductance as a function of off-center distance y for z = 0 is plotted as y is varied from 0.0 to 7.2 mm.\nFrom Figs. 5-7, it can be concluded that the mutual inductance increases as the off-center distance y gets larger. However, if the air gap is relatively small, the fractional change in the mutual inductance is not very significant.\nIV. EXPERIMENTAL MEASUREMENTS The computer calculations were compared to the results\nof actual experiments in the laboratory. Three experiments\nwere performed with the setup shown in Figs. 8 and 9. If a sinusoidal ac current is applied to the primary coil, the change in the primary coil flux induces a voltage in the secondary coil. Assuming plane wave propagation in the secondary conductor, the electric field may be expressed as\nSince the secondary conductors are taken to be good conductors, the skin depth is expressible as\nwhere p is the permeability and a is the conductivity. With a frequency of 1 W z (as used in experiments 1-3)\napplied by the ac power source, (22) gives a skin depth of",
            "4307 KIM ef al.: MUTUAL INDUCTANCE OF NONCOAXIAL CIRCULAR COILS\n2.575 mm for aluminum ( p = 2.62 x lo-' R . m) and 2.09 mm for copper ( p = 1.724 x lo-' R . m). If the frequencies are 60,1250, and 2500 Hz, skin depth for aluminum conductor would be 10.5, 2.3, and 1.63 mm, respectively. These values are to be compared to the secondary copper wire diameter of 0.2 mm in experiments 1 and 3, and an aluminum tube thickness of 1.6 mm in experiment 2. The internal impedance of the oscilloscope was set to be 1 Ma, while the secondary coil had a resistance of less than 0.2 R, and an inductance of 0.3 mH. Thus, the induced voltage in the secondary coil is given by\nE2 = 2 7 ~ f Ml2Ip (23)\nand the mutual inductance is\nE2 M12 = (24)\nwhere E2 and Ip are rms values.\nA. Experiment I The experiment was done at 1 kHz with the setup shown in Figs. 8 and 9. The primary coil was fixed to one end\nplate of the frame so that it could not move. Another coil, the secondary, was attached to the movable plate in the middle of the frame. It could be shifted horizontally, and also could be moved to vary the off-center distance. Fig. 9 represents the equipment for the measurement of the mutual inductance. An ac current input was applied to the primary coil and was measured by an ammeter in the power meter. The induced voltage in the secondary coil was measured by the oscilloscope.\nFor the first experiment, a primary coil of 85 mm average diameter having 150 tums of 0.65-mm-diameter copper wire was selected; the secondary coil had an average diameter of 40 mm and had 50 tums of 0.20-mm-diameter copper wire. Results of the experiment are listed in Table I.\nThe discrepancy between calculated and experimental results does not exceed 6%.\nB. Experiment 2 The results of a second experiment performed at 1 kHz with a single-tum secondary coil are listed in Table 11. The secondary coil was a 2024 T-30 reinforced aluminum ring having a diameter of 1 inch, a width of 10 mm, and a thickness of 1.6 mm. It was cut at one end to make a very small air gap to connect electric wire for measurement of the induced",
            "4308\nIEEE TRANSACTIONS ON MAGNETICS, VOL. 33, NO. 5 , SEPTEMBER 1997\nvoltage. The primary coil was formed of ten layers of solid copper bar, which made its cross-sectional dimension 30.2 mm x 22.0 mm. The coils were placed with an off-center distance of 1 mm, which is the maximum air gap of the model-3 linear induction-type coil gun at Polytechnic University. Here, the discrepancy between calculated and experimental results does not exceed 7%.\nC. Experiment 3\nIn Section 111-C, it was shown that the mutual inductance increases as the off-center distance gets larger. However, in experiments 1 and 2, the changes of the mutual inductance with off-center distance y were quite small. In order to determine the nature of this dependence clearly, a third experiment was performed (also at 1 Wz) with a primary coil, wound with a larger radius, Rp = 77.0 mm, using 60 turns of 2-mmdiameter copper wire . The secondary coil was moved up and down in a radial direction, while the primary coil remained fixed. The longitudinal distance between the primary coil and the secondary coil z was zero. The results of this experiment are listed in Table 111.\nFrom Table 111, it can be seen that the mutual inductance increases as the off-center distance increases, as indicated in Figs. 3 and 4. The discrepancy was less than 4%.\nV. CONCLUSION\nA procedure has been provided for the accurate calculation of the mutual inductance of axially and laterally displaced circular coils; the procedure has been verified experimentally. It was shown in Figs. 4-6, and proved by the experiments, that the mutual inductance increases as the off-center distance gets bigger. The physical meaning of this result is that,\nwith a dynamically oscillating secondary coil, the induced current and the restoring force [l], [22] in the secondary coil get bigger as the secondary coil approaches close to the primary coil. The maximum off-center distance in induction circular coil machines is limited by the air gap distance of the machines. Therefore, it is obvious that the effect of the mutual inductance increment in small air gap machines is less than that in machines with large air gaps. It should be noted, however, that the restoring force is proportional to the gradient of the mutual inductance and, as can be seen from Fig. 7, this gradient increases rapidly as the offcenter distance increases and, therefore, the minimal air gap distance decreases. In all cases, the error in the calculated results is well within engineering tolerance. In all cases, the discrepancy between the calculated and experimental results did not exceed 7%.\nK. B. Kim, Z. Zabar, E. Levi, and L. Birenbaum, \u201cIn-bore projectile dynamics in the linear induction launcher (LIL). Part 1: Oscillations,\u201d IEEE Trans. Magn., vol. 31, pp. 484-488, Jan. 1995. Z. Zabar, \u201cNovel schemes for electromagnetic launchers,\u201d final rep., SDIODST, Polytechnic Univ., Jan. 30, 1991 (Contract DASG60-88-C0047). M. W. Garrett, \u201cCalculation of fields, force and mutual inductances of current systems by elliptic integrals,\u201d J. Appl. Phys., vol. 34, no. 9, pp. 2567-2573, Sept. 1963. T. H. Fawzi and P. E. Burke, \u201cThe accurate computation of self- and mutual inductances of circular coils,\u201d IEEE Trans. Power Appar. Syst., vol. PAS-97, pp. 464-468, Mar./Apr. 1978. Z. X. Feng, \u201cThe treatment of singularities in calculation of magnetic field by using integral method,\u201d IEEE Trans. Magn., vol. MAG-21, no. 6, pp. 2207-2210, Nov. 1985. B. Azzerboni, E. Cardelli, M. Raugi, and A. Tellmi, \u201cSome remarks on the current filament modeling of electromagnetic launchers,\u201d IEEE Trans. Magn., vol. 29, pp. 643-648, Jan. 1993. B. Azzerboni, E. Cardelli, M. Raugi, A. Telliui, and G. Tina, \u201cMagnetic field evaluation for thick annular conductors,\u201d IEEE Trans. Magn., vol. 29, pp. 2090-2094, May 1993. B. Azzerboni, E. Cardelli, M. Raugi, G. Tina, and A. Tellini, \u201cAnalytical expressions for magnetic field from finite curved conductors,\u201d IEEE Trans. Magn., vol. 27, pp. 750-757, Mar. 1991. B. Azzerboni, E. Cardelli, and A. Tellini, \u201cComputation of the magnetic field in massive conductor system,\u201d IEEE Trans. Magn., vol. 25, Nov. 1989. W. A. Perkins and J. C. Brown, \u201cMAFCO-Magnet field code for handling general current elements in three dimensions,\u201d J. Appl. Phys., vol. 35, pp. 3337-3343, 1964. V. I. Danilov and M. Ianovici, \u201cMagnetic field of thick finite dc solenoids,\u201d Nucl. Instrum. Meth., vol. 94, pp. 541-550, 1971. I. R. Ciric, \u201cSimple analytical expressions for the magnetic field of current coils,\u201d ZEEE Trans. Magn., vol. 27, pp. 669-673, Jan. 1991. L. Urankar, \u201cVector potential and magnetic field of current-canying finite arc segment in analytical form. Part I: Filament approximation,\u201d IEEE Trans. Magn., vol. MAG-16, pp. 1283-1288, Sept. 1980. -, \u201cVector potential and magnetic field of current-carrying finite arc segment in analytical form. Part II: Thin sheet approximation,\u201d IEEE Trans. Magn., vol. MAG-18, pp. 911-917, May 1982."
        ]
    },
    {
        "image_filename": "designv10_4_0003749_robot.2006.1642140-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003749_robot.2006.1642140-Figure4-1.png",
        "caption": "Fig. 4. Dorsal Reference Curve",
        "texts": [
            " This enables the frame {e1, ea, eb} to be separated from the shape of a curve and represent the posture of an ACM\u2019s body. (3) can be integrated analytically or numerically with given initial condition and \u03c4 , \u03baa and \u03bab, and a solution {c, e1, ea, eb} is obtained. Now we note that the frame {e1, ea, eb} represent the posture of ACM\u2019s body but we do not need to fix the direction of ea and eb here like \u201cea shows the belly and eb shows the right side\u201d. It is free how to decide the physical direction of ea and eb. Fig. 4 shows an example of a solution of (3). This figure shows the backbone curve and the locus drawn by ea(s), eb(s), which are fixed to the backbone curve. Because this figure looks like a slender fish which has a long dorsal fin, let us call a solution of (3) as a \u201cdorsal reference curve\u201d, and let us call a frame {e1, ea, eb} as a \u201cdorsal reference frame\u201d. Dorsal reference curve consists of a backbone curve and a dorsal reference frame. In addition, we call 3 functions \u03c4 (s), \u03baa(s) and \u03bab(s) as shape functions after Chirikjian\u2019s research"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure5-1.png",
        "caption": "Fig. 5. Velocity streamlines of the circumferential and axial water jackets.",
        "texts": [
            " When the water passes through an elbow, the interfacial structures and interaction mechanisms, in the water jacket walls, are significantly affected. The computational fluid dynamics (CFD) is used to analyze the impact of elbows. Fig. 4 shows the velocity streamline of a simple water jacket with elbows. The vortex and backflow exist in the elbows, which causes a different velocity distribution. The circumferential and axial water jackets, with same inlet velocity and configuration parameters, are studied with CFD. The structured mesh and turbulent model (k-epsilon) are used in the CFD model. As shown in Fig. 5, the velocity distribution of the circumferential water jacket is uniform, which matches with Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 01:31:42 UTC from IEEE Xplore. Restrictions apply. the assumption of straight piping flow. However, for the axial water jacket, the velocity changes steeply near the elbows. The impact of the elbows on the CHTC is shown in Fig. 6. The CHTC distribution of the circumferential water jacket is more uniform than that of the axial water jacket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000083_j.addma.2019.100935-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000083_j.addma.2019.100935-Figure4-1.png",
        "caption": "Fig. 4. Three-dimensional finite element mesh for forty-layer cylinder part.",
        "texts": [
            " Thus, a controlled technique should be developed to deal with this problem, and the finite element model is first established to study the thermal behavior on the additively manufactured component. The Simufact.welding software (version 6.0.0) is used for thermal simulations. According to our previous study [21], it can provide the thermal distribution and the distortion prediction for the welding process with high accuracy. The geometric size of the FEM model is shown in Fig. 2(a). The wall thickness was set at 4.5 mm and the layer height was 1.5 mm. Fig. 4 shows the three-dimensional finite element mesh for the cylinder model. In the present model, linear brick elements with eight-node hexahedrons are used for thermal simulation. In addition, the software can automatically refine the elements for the area near the deposited layer from level 0 to 10. All the elements of the deposited layer were deactivated before deposition, and then activated sequentially following the heat source. The Goldak double ellipsoidal heat source was used to apply the heat to the additive manufactured deposits [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure4-1.png",
        "caption": "Fig. 4. Force analysis of substructure 5.",
        "texts": [
            " (8) results in the reaction force exerted on the joint 6 \u03c1w, 6 = W T 6 $ w, 6 (9) where $ w, 6 = $ w,E + $ w,G E , $ w,E = [ f E \u03c4E ] , $ w,G E = \u2212m E g [ \u02dc z ( R E r E G E ) \u00d7\u02dc z ] , \u03c1w, 6 = [ \u03c1w, 6 , f \u03c1w, 6 ,\u03c4 ] , W 6 = [ R 6 \u02c6 r6 R 6 0 R 6 ] , r 6 = R E r E 6 $ w, 6 is the resultant externally applied wrench imposed at point O E for joint 6, $ w,E is the external wrench applying on point O E , $ w, G E is the equivalent gravitational wrench of link 6 applying on point O E , \u03c1w, 6 is the reaction force at joint 6, \u02c6 r6 is the skew-matrix of the position vector r 6 , W 6 denotes an adjoint transformation matrix, which can also be derived directly with the screw theory [39 , 40] . Fig. 4 shows the force diagram of substructure 5. In a similar approach, the reaction force at joint 5 can be calculated. The static equilibrium equations of the substructure can be derived as { f E \u2212 m E g \u0303 z \u2212 m 5 g \u0303 z = R 5 \u03c1w, 5 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z \u2212 m 5 g ( R E r E 6 + R 6 r 6 G 5 ) \u00d7\u02dc z = ( R E r E 6 + R 6 r 6 5 ) \u00d7 ( R 5 \u03c1w, 5 , f )+ R 5 \u03c1w, 5 ,\u03c4 (10) where \u03c1w, 5 , f = [ \u03c1w, 5 , f x \u03c1w, 5 , f y \u03c1w, 5 , f z ] T , \u03c1w, 5 ,\u03c4 = [ \u03c1w, 5 ,\u03c4x \u03c1w, 5 ,\u03c4y \u03c1w, 5 ,\u03c4 z ] T , \u03c1w, 5 , f and \u03c1w, 5 ,\u03c4 are the reaction force and torque of joint 5 acting at point O 5 , m 5 is the mass of link 5, G 5 denotes the mass center of link 5, r 6 G 5 is the position vector from point O 6 to point G 5 evaluated in { O 6 }, and r 6 5 is the position vector from point O 6 to point O 5 evaluated in { O 6 }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003518_j.ymssp.2004.10.006-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003518_j.ymssp.2004.10.006-Figure1-1.png",
        "caption": "Fig. 1. Diagram of the dynamic gear model.",
        "texts": [
            " Gear monitoring measurements can therefore be taken with one less analogue-to-digital channel so as to indicate the deterioration in gear condition under fluctuating load conditions. A distinction between cyclic stationary load conditions and non-cyclic stationary load conditions was proposed. It was found that non-cyclic stationary load modulation could be averaged out with RDA. A test rig was built to apply non-cyclic stationary load conditions to a test gearbox. Measurements were taken with an accelerometer and a shaft encoder for three different levels of induced flank wear on the gear wheel in order to validate the postulates. Fig. 1 is a diagram of a simplified dynamic gear model. The model comprises four degrees of freedom and was developed to explore the utilisation of the IAS for the purposes of monitoring the condition of gears. A unique feature of the model is the incorporation of a translating mass. This degree of freedom is utilised to represent conventional vibration monitoring on the gear case, which is compared with IAS monitoring. The equations of motion describing the model are presented in Eqs. (1)\u2013(4) and the model parameters are given in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003957_0022-0728(88)80004-4-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003957_0022-0728(88)80004-4-Figure2-1.png",
        "caption": "Fig. 2 . Comparison of the cyclic voltammograms of (a) PMtT electrode in 0 .1 M LiC1O, in H,, O, S = 2 mA; (b) Pt electrode in 0.05 M K 2PdCI, and 0.1 M HCO4 , S-0.2 mA .",
        "texts": [
            " I shows clearly that the fibrillar structure is the most adequate for the preparation of modified electrodes of high specific area . Electrodeposition ofpalladium particles in PMeT The electrocatalytic properties of modified electrodes prepared by electrochemical inclusion of metallic particles in a given polymer matrix depend on several parameters, e.g. the concentration of active centers, their size, and their spatial distribution . The control of these various parameters requires analysis of the effects of the electrical conditions used for metal deposition . Figure 2 shows the cyclic voltammogram of PMeT in aqueous medium and the current-potential curve corresponding to the electrodeposition of palladium in PMeT in an aqueous solution containing 0.05 M K2 PdCl4 and 0.1 M HCI04 . Comparison of these two curves shows that at the potential corresponding to the metal deposition (-0.6V(SCE), the polymer is undoped and thus almost insulating. As a consequence of this poor conductivity and of the hydrophobic character of the polymer, 57 the use of a constant applied potential for metal deposition results in a very heterogeneous distribution of the metal which is deposited predominantly on the external surface of the PMeT electrode",
            " For this purpose, PMeT electrodes containing palladium particles of various average sizes have been characterized with regard to their activity for oxygen reduction in aqueous acidic medium, using cyclic voltammetry and rotating disk voltammetry . (It was confirmed using X-ray fluorescence spectroscopy that no contamination of the Pd by Pt occurred .) Figure 6 shows the voltammograms of PMeT and PMeT-Pd electrodes in 5 x 10 -z M H2SO4 saturated with oxygen. Comparison of the PMeT curve with that of Fig. 2 indicates that PMeT is inactive for 0 2 reduction. On the other hand, the PMeT-Pd curve shows two reduction peaks . The first peak (A) at 0.425 V(SCE) corresponds to the reduction of the oxide layer formed at the surface of the metal, and the second peak (B) at 0.320 V(SCE), which appears only in the presence of oxygen, corresponds to its reduction . This potential value is in good agreement with that reported by Peuckert et al. in the case of oxygen reduction on small supported Pt particles [31] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000528_s11661-021-06211-x-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000528_s11661-021-06211-x-Figure2-1.png",
        "caption": "Fig. 2\u2014The computer models showing three specimen layouts as the flat, side, and vertical layouts of tensile specimens. The cross sections AA, BB, and CC are used for explanation in Fig. 10.",
        "texts": [
            "97 lm (D50) and a polymeric blended binder, which acts as plasticizer and backbone, with a solid loading of 63 vol. pct. The 1.75 mm diameter filament as displayed in Figure 1 was used to fabricate specimens using a commercially closed system of multi-material-fused filament printing machine. Figure 1 shows good homogeneity of the filament. The nozzle size for the metal filament is 0.3 mm. The printing parameters were listed in Table I. The specimens were printed in three layouts, which were the flat, side, and vertical layouts as shown in Figure 2. The tensile specimens printed in the side layout required a support at the gauge length to avoid specimen sagging during debinding and sintering. The support was separated from the tensile specimen by a printed ceramic layer, which was manually detached after sintering as shown in Figure 3. The printed dimensions for tensile specimens were 120.7 mm in length, 12.0 mm in width (grip), and 3.6 mm in thickness. The desirable final dimension after sintering were 100.9 mm in length, 10.0 mm in width at grip (5 mm width at gauge length), and 3",
            " However, the relative density of specimens in all layouts is different even though the specimens have been sintered using the same sintering profile. This is attributed to the difference in the characteristics of voids between perimeter walls and of the porosity which were affected by the different specimen layouts, especially for vertical layout. For better understanding, the schematics of cross-sectional specimens and related voids between perimeter walls of specimens printed in the flat (section AA in Figure 2) and side layouts (section BB in Figure 2) are shown in Figures 10(a) and (b), respectively. For the vertical layout (section CC in Figure 2), the schematics, displaying cross sections of voids lines, are shown in Figure 10(c). These voids are commonly present in FDM processed material having different shapes due to differences in the printing strategy and parameters.[28] The formation of triangular-shaped voids, found in the flat and side layouts, is shown in Figure 10(d). During printing, the printing path is compressed, densified, and adhered to the previous adjacent layers but it still needs to maintain their shape, which cannot be fully dense",
            "[32] It is proposed that the load-bearing and stress concentration around the voids are suitable factors for quantitative explanation of the change in tensile properties due to voids.[33,34] The ultimate tensile stress of the alloy containing voids (r) can be calculated as r \u00bc r0 1 p\u00f0 \u00de \u00bd1 where r0 is the ultimate tensile strength of fully dense alloy and p is the area fraction of voids per the overall area at the gauge length region. Here, p is determined by p \u00bc 6a A hz lt 1 \u00bd2 where a is an average void area (Table III), hz is the height basing on the specimen layout in Figure 2 (3 mm for the flat layout and 5 mm for the side layout), lt is the layer thickness after sintering (0.125 mm), and A is the overall area at the gauge length region (3 9 5 mm2). The calculated value of p is reported in METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 52A, MAY 2021\u20142007 Table III. The fraction of ultimate tensile strength of the flat per side layout, ignoring the effect of stress concentration, can be calculated as rFlat rSide \u00bc 1 pFlat\u00f0 \u00de 1 pSide\u00f0 \u00de : \u00bd3 The calculated value of the fraction of ultimate tensile strength of the flat per side layout, following the load-bearing model is approximately 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003235_amc.2004.1297665-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003235_amc.2004.1297665-Figure4-1.png",
        "caption": "Fig. 4. equilibrium of gravity and centrifugal force",
        "texts": [
            " = dsinq (6) From eq(l),eq(5) and eq(6), centrifugal force FCF can be represented as follows. Mu2 sinq. 4 FCF = M means the whole mass of the bicycle and u means the running velocity, A torque by gravitational force TGR is represented by gravitational constant g and height of COG h. TGR = -MghsinB (8 ) Assuming that the rider doesn't move upper body, the dynamic equation of bicycle is represented as follows. I 8 = T G R + F c F . ~ = -MghsinB+=sinq .4 L (9) I means the moment of inertia. The equilibrium of centrifugal force and gravitational force is shown in Fig.4. Assuming that the camber angle 0 is relatively small, this parameter is approximated as sin0 E 0 and cos0 Y 1. By using state space, dynamic equation eq(9) is transformed into eq(l0). 111. STEERING CONTROLLER A. Setting gain values From eq(lO), it is known that camber angle 0 is related to steering angle $5. Setting the desired camber angle as @d and the steering angle as $5 = Ki ( 6 d - e) - K$3, transfer function from @d to 0 is represented in eq(11). M h A is A = - + and B is B = canonical form is represented as follows in general"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000051_s12555-018-0383-4-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000051_s12555-018-0383-4-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed frame and body-fixed frame.",
        "texts": [
            " Problem formulation The mathematic model of DP vessels can be described as [21] \u03b7\u0307i = Ji (\u03d5i)\u03c5i, (3) Mi\u03c5\u0307i +Di\u03c5i = \u03c4i +di(t), (4) where Ji (\u03d5i) is the rotation matrix and given by: Ji (\u03d5i) = cos(\u03d5i) \u2212sin(\u03d5i) 0 sin(\u03d5i) cos(\u03d5i) 0 0 0 1  , (5) with the properties: \u2225Ji (\u03d5i)\u2225= 1 and JT i (\u03d5i)Ji (\u03d5i) = I3\u00d73. In order to facilitate the following written, we omit without confusion, such as Ji = Ji (\u03d5i) and JT i = JT i (\u03d5i). \u03b7i = [xi,yi,\u03d5i] T denotes the position and yaw angle in the earthfixed reference frame XEOEYE (see Fig. 1). The vector \u03c5i = [ui,vi,ri] T denotes the velocity vector in the bodyfixed frame XBOBYB. Mi = MT i \u2208 \u211c3\u00d73 denotes the inertia matrix included added mass, which is positive definite, invertible and M\u0307i = 0. Di \u2208 \u211c3\u00d73 denotes the damping matrix, which is positive definite. \u03c4i = [\u03c4i1,\u03c4i2,\u03c4i3] T denotes the control input produced by thrusters. di(t) = [di1,di2,di3] T consists of the total environmental disturbances caused by wind, waves, ocean currents in surge, sway and yaw, respectively. In practice, the control forces and moment produced by the thrusters are limited"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.11-1.png",
        "caption": "Figure 4.11. Rack and pinion, in close-mesh operation.",
        "texts": [
            " If the angle (measured in radians) through which the second gear can be turned is multiplied by the radius of its pitch circle, we obtain the length of the path moved by a point on the pitch circle, during the rocking of the gear. We will now prove that the length just described is equal to the circular backlash. For this reason, the circular backlash is also known as the backlash, measured at the pitch circle. Before we discuss the general case of the backlash in a gear pair, we consider first a rack and pinion, and we will determine the tooth thickness of the rack, if its teeth are in contact with both faces of the pinion teeth. This is the situation known as close-mesh operation, when there is no backlash. Figure 4.11 shows the pinion and rack, in positions such that the contact point between one tooth of the pinion and the rack lies exactly at the pi tch point. The same pinion and rack are shown in Figure 4.12, and the pinion has been rotated until the opposite profile of the same tooth passes through the pitch point. Since both faces of the pinion tooth are in contact with the rack, the pitch point again coincides wi th a contact point. The rotation ~p between the two positions of the pinion Backlash 101 can be expressed in terms of its tooth thickness at the pitch circle, A{1 (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.7-1.png",
        "caption": "Figure 3.7. Common tangent to the base circles.",
        "texts": [
            " We find the position of a typical contact point, and then check to see if the common normal at the contact point cuts the line of centers at the pitch point. Any normal to the tooth profile of gear 1 must touch the base circle of gear 1, while any normal to the tooth profile of gear 2 must touch the base circle of gear 2. Hence, the common normal at the contact point must touch both base circles, which means it must coincide with the common tangent to the base circles. If the common tangent touches the base circles at E1 and E2 , as shown in Figure 3.7, then the posi tion of the tooth contact point must be somewhere on line E1E2 , and the common normal at the contact point lies along E1E2 . The point where this line intersects the line of centers is labelled P', and we must now check to see whether P' coincides with the pitch point P. The radii C1E1 and C2E2 in Figure 3.7 are each perpendicular to E1E2 , and they are therefore parallel. 66 Gears in Mesh Hence, the triangles E,C,P' and E2C2P' are similar, and we obtain the following relation between the sides of the triangles, The lengths E,C, and E2C2 are equal to the base circle radii, which we express by means of Equations (3.35 and 3.36), and the relation then takes the following form, (3.37) We proved in Chapter' that the pitch point P divides the line of centers C'C2 in the ratio N, :N2 \u2022 If point P' is to coincide with P, the right-hand side of Equation (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000494_ab710f-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000494_ab710f-Figure1-1.png",
        "caption": "Figure 1. Illustration of the variable stiffness rigid-soft finger. (a) Structure design of the finger with a self-locking exoskeleton. (b) Demonstration of the gripper carrying a load of 9 kg.",
        "texts": [
            " The experiments and results of the stiffness, driving force, actuation performance and gripping tests of the gripper are demonstrated in Experiments and Results section. The relevant discussion and the conclusion of this study is presented in the Discussion and Conclusion section. The variable stiffness rigid-soft gripper consists of two soft fingers and two sets of exoskeleton structures. The exoskeleton structure is mounted on both sides of the soft finger, which can help to achieve the variable stiffness of the gripper. As shown in Figure 1(a), the exoskeleton contains a ratchet-and-pawl, a self-locking spring and an unlocking actuator, which dominate the main stiffness of the finger. The ratchet-and-pawl is the core part of the self-locking structure to ensure the reliability of the self-locking process. The tooth profile of the ratchet is triangle, and the ratchet arm is integrated with ratchet. In addition, only one ratchet is used to match with each pawl, which aims to simplify the exoskeleton 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 M an us cr ip t structure and reduce its weight. The free end of the pawl is extended to the upper position of the unlocking actuator, increasing the arm length of the unlocking torque, thereby the required unlocking force is reduced. The soft gripper is mounted on the fixed base with its free end connected to a rigid rod of the exoskeleton. When the gripper is actuated, the ratchet arm can rotate with the gripper end. As shown in the Figure 1(b), the soft-rigid gripper with self-locking exoskeleton can make its load carrying capacity above 9 kg. 2.2. Working principle Figure 2. Working principle of the variable stiffness rigid-soft gripper. (a) The finger is relaxed at its initial state. (b) When the soft finger is actuated, it bends to drive the rotation of the ratchet arm. (c) The soft finger maintains its bending configuration by the self-locking of the exoskeleton even after the air supply is removed. (d) When the unlocking actuator is inflated, the ratchet and pawl is separated and the finger returns to the initial state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure12.11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure12.11-1.png",
        "caption": "Fig. 12.11 Oerlikon process",
        "texts": [
            " This is the well know Gleason method, a single indexing method. The tooth trace of the bevel gear in the Gleason method is a circular arc and the tooth depth at the larger diameter is larger than that at the smaller diameter (tapered teeth). The Gleason method can also be used in grinding and lapping. In 1927, the company successfully developed the process of manufacturing hypoid gears. In 1946, Oerlikon, a Swiss company, developed a continuous indexing method of cutting spiral bevel gears, called Oerlikon method as shown in Fig. 12.11. The tooth trace of the gear in this method is elongated epicycloid and the tooth depth along the face width is constant. Spiral bevel gears made from different methods cannot be engaged. This is different from spur gears. The Oerlikon method was actually coincident with a patent of Gleason in 1914. The continuous indexing Oerlikon method is obviously more productive than the single indexing Gleason method. One may wonder why Gleason did not develop its own continuous indexing method based on the patent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000813_j.msea.2021.141111-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000813_j.msea.2021.141111-Figure3-1.png",
        "caption": "Fig. 3. Position of cantilever specimens on the build platform: (a) before and (b) after cutting them from the platform.",
        "texts": [
            " In the light of the results cited in the previous paragraph, the process parameters specified in Tables 2 and i.e., low heat input, small layer thickness, build platform preheat and scanning strategy with short hatch rotation (Fig. 2), should prevent thermal distortion of specimens during building. Three kinds of specimens were prepared, whose shape, dimensions and build orientation are presented in Table 3. Cantilever beams for distortion measurement were made in horizontal position at 0\u25e6, 45\u25e6 and 90\u25e6 in relation to the x axis (Fig. 3a). Specimens for microstructure examination, for hardness measurements and for tensile testing were prepared in the form of cylinders in perpendicular position to the build platform. Final dimensions of gauge lengths of tensile specimens were obtained by turning and peripheral grinding according to ASTM E8-04. Scope of the examinations included: 1. Measurements of maximum z-displacement of one-end fixed specimens with low structural stiffness after cutting them from the platform (see Fig. 3b), without previous stress-relief annealing and after stress relieving together with the build platform. This test was aimed at evaluating maximum stresses left in LPBF-ed specimens with use of process parameters specified in Table 2, in the as-built condition and after stress-relieving together with the platform at 1150 \u25e6C (i.e., above recrystallization temperature) and at 1065 \u25e6C as recommended by ASTM F3055-14a. 2. Determination of influence of the suggested stress-relieving parameters on tensile properties at ambient temperature and at elevated temperatures, as well as on hardness and microstructure of cylindrical specimens subjected to solution annealing after removing from the platform and then turned, ground, and finally aged acc",
            " They suggested however, that the residual stress Type II (micro-stress) was not completely released. This is consistent with the results of Cao et al. [26], who found, by EBSD measurements, presence of residual plastic strains inside columnar grains after 1-h annealing at 1080 \u25e6C. On the grounds of the measured deflections, residual stresses were calculated from the common formula \u03c3max = F\u22c5l/W, using the formula wzmax = F\u22c5l3/3 EJ for maximum deflection of a cantilever beam loaded at its end by the force F (see Fig. 3), where moment of inertia J = 27 mm4 and cross-section modulus W = 18 mm3. Considering the range of Young\u2019s modulus values given in literature for horizontally LPBF-ed specimens, like 193 GPa [27], 195 GPa [28], 200 GPa [29] and 203 GPa [30], the value E = 200 GPa was accepted. It should be stressed that the above E values are significantly higher than those obtained for vertical specimens subjected to tension in parallel to the build direction. This difference results from crystallographic texture, specific cellular substructure of columnar grains created by the dislocation network Table 1 Chemical composition of IN718 powder (acc. to SLM Solutions Certificate). Element Ni Cr Fe Ta + Nb Mo Ti Al Si C Co B Mn Cu P S O N wt% 52.83 18.97 18.16 5.05 2.99 0.96 0.46 0.35 0.045 0.03 0.003 < 0.03 < 0.03 < 0.015 < 0.015 0.01 166 ppm Table 3 Shape, dimensions, and destination of LPBF specimens. Destination Shape ( Fig. 3a) Dimensions of gauge length Build orientation Distortion measurement Cantilever beam l \u00d7 b \u00d7 h = 60 mm \u00d7 12 mm \u00d7 3 mm Horizontal Microstructure examination Cylindrical Diameter 7.5 mm \u00d7 71 mm Vertical Tensile test Cylindrical Diameter 4 mm, gauge length 19 mm, screw thread 250-20 UNC Vertical K. Gruber et al. Materials Science & Engineering A 813 (2021) 141111 [29], and residual stress distribution since residual stresses add up to tensile stresses during the tensile test. As results from the calculations, maximum deflection of free-end of the beam (Table 5) corresponds with high level of maximum tensile stresses at bending in the as-built condition, ranging between 785 and 865 MPa"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure11-1.png",
        "caption": "Fig. 11. A singular con\u00aeguration of class (RO, II).",
        "texts": [
            " (RPM, RO, II, IO) has 12 con\u00aegurations. An example is obtained from the con\u00aeguration in Fig. 10 by a small rotation of subchain C about SC 1 . (RPM, RI, RO, II, IO) has 12 con\u00aegurations and a representative can be obtained from Fig. 9 by a small rotation of subchain C about SC 1 . (4) RO- and II-type singularities There are 15 con\u00aegurations that are of the RO and II types but are not IIM nor RPM-singu- larities. From Equation (12), the conditions for RO-type singularity are: (a) Either Co must be in the plane ABC (Fig. 11), or (b) The point A must be in the plane of subchain B (Fig. 12), i.e. b_mB 1 . (5) RI- and IO-type singularities There are 15 con\u00aegurations which satisfy (viii) without being RPM or IIM-type. In these con\u00aegurations the subchain A is singular or one of the other two serial chains is fully extended. (6) Classi\u00aecation of {4} [ {5} The last three singularity classes are obtained as the intersection and di erences of {4} and {5}. (RI, IO) and (RO, II) have 15 con\u00aegurations, while (RI, RO, IO, II) is of dimension 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.3-1.png",
        "caption": "Figure 7.3: Unicycle",
        "texts": [
            " However, we shall focus on open-loop control, because this allows to introduce concepts (e.g., the chained form) that are of great relevance also for the synthesis of feedback stabilizing laws. The mostintuitive approach to open-loop control for a nonholonomic system is to find canonical paths, i.e., feasible paths that allow us to achieve any desired reconfiguration. The corresponding feedforward control u(t) is derived by using the kinematic model. In Section 7.1, we have already seen an example of such procedure for the rolling disk. Example. The unicycle of Fig. 7.3 may be steered from any initial configuration qo = (xo, Yo, Oo) to any final configuration ql = (x I\u2022 Yl\u2022 01) through the motion sequence below: 1. Rotate the unicycle so as to align the projection of its midplane with the straight line joining (xo, Yo) and (x I\u2022 Yl ). 2. Roll forward until the contact point with the ground is ( x 1, y 1). 3. Rotate the unicycle to achieve the final orientation 01. From the kinematic model (7.26) it is apparent that the above motion prescribes the sequential activation of u2 , u1 and u2 again"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000011_jsen.2019.2918018-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000011_jsen.2019.2918018-Figure6-1.png",
        "caption": "Fig. 6. SPMSM model in simulations: (a) Cross-section view. (b) 3D view.",
        "texts": [
            " When all of the measured kn are equal to 1, the stator windings operate under the normal operation condition; otherwise, the windings suffer from the faulty operation with short-circuit faults. Therefore, by finding the abnormal pattern of the measured ratio kn, the inter-turn short-circuit faults can be detected and located. To validate the analytical stray magnetic field model for the inter-turn short-circuit fault detection, an SPMSM model with 8-pole/36-slot was chosen as the test motor in the simulation, as shown in Fig. 6. In order to accurately obtain the stray magnetic field distribution, totally 24 magnetic-field-sensing points (i.e., S1~S24) were set in the simulation, which corresponded to 24 TMR sensor units uniformly distributed outside the stator yoke for sensing both radial and tangential components of stray magnetic field. The specifications of the test motor are shown in Table I. The FEM model of the test motor was simulated by the commercial software JMAG Designer 14. The test motor with parallel-connected distributed windings was fed by the three-phase voltage source in the simulation, as shown in Fig. 7. Two winding short-circuit faults at different locations were alternatively set by controlling the switches S1 and S2. When the switch S1 is turned on, the winding a1 is shorted by a fault resistor Rf. Similarly, when the switch S2 is turned on, the winding a7 is shorted by the fault resistor Rf. The winding a1 and a7 are located at two different places with a 180-degree difference, as illustrated in Fig. 6(a). The resistance of the fault resistor Rf in the simulation is 0.02 \u03a9. Fig. 8 shows the simulated flux vector distribution of the test motor which rotated at 1500 rpm. It can be observed that the stray magnetic flux \u03a6st originated from the windings in stator slots and leaks outside the stator yoke. Hence, the changes in the phase currents and winding healthy conditions led to the change of \u03a6st. Fig. 9 shows the simulation results of winding currents (i.e., ia1, ia2 and ia3), fault resistor current (iRf), radial components (Brad) and tangential components (Btan) of stray magnetic field at the four sensing points (i",
            " Its main specifications and parameters are given in Table I. The SPMSM was fed through space vector control using an adjustable-speed motor drive. The motor was also coupled with a high-speed flywheel and a generator to adjust the load level in experiments. During the experiments, the phase currents (i.e., ia, ib and ic) of test motor as well as the fault resistor current (iRf) were monitored by four AC current probes (Tektronix TCPA300). The three-phase parallel-connected winding configuration of the test motor is illustrated in Fig. 6 and Fig. 7. In order to simulate the inter-turn short-circuit faults in test motor, the winding a1 and a7 were alternatively shorted by the fault resistor Rf in experiments by controlling the switches S1 and S2, same as in simulation. Three electrical taps were extracted outside the motor cover to connect the switches and as fault resistors for producing the short-circuit faults (see Fig. 10(a) and Fig. 10(b)). The aluminum housed resistors (from Arcol HS series [34]) with maximum tolerance of \u00b110% were chosen as the fault resistors in the experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure6-1.png",
        "caption": "Fig. 6. Some legs for SP-equivalent parallel kinematic chains. (a) R\u0302R\u0302\u00f0RRR\u00dekE leg and (b) R\u0302R\u0302R\u0302\u00f0RR\u00dekE leg.",
        "texts": [
            " The types that were obtained are listed in rows 5 and 6 of Table 2. For a better understanding of the notation used, several single-loop kinematic chains involving an SP virtual chain are shown in Fig. 5. In Fig. 5, the SP virtual chain is drawn with dashed lines. By removing the virtual chain in a 4-DOF single-loop kinematic chain involving an virtual chain, one leg for SP-equivalent parallel mechanisms can be obtained. For example, by removing the virtual chain in an R\u0302R\u0302R\u0302\u00f0RR\u00dekEV kinematic chain (Fig. 5(b)), an R\u0302R\u0302R\u0302\u00f0RR\u00dekE leg (Fig. 6(b)) can be obtained.2 Such a leg has a 1-f0-system. The f0 passes through the common point of the axes of three R\u0302 joints and is parallel to the axes of the R joints within \u00f0RR\u00dekE. In this way, all the legs for SP-equivalent parallel mechanisms have been obtained and are listed in Table 3. Based on the results obtained in steps 1 and 2, we can construct types of SP-equivalent parallel kinematic chains using the following three sub-steps. Step 3a: Take one combination of leg-wrench systems from Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.6-1.png",
        "caption": "Figure 16.6. Path of the cutting point, viewed in the direction of the gear axis.",
        "texts": [
            "77), we showed that the path of contact in a crossed helical gear pair touches each base cylinder, and makes an angle (~- 'tp1) with the line of centers, when viewed in the direction of the axis of gear 1. Hence, in the case of a hob cutting a gear, the path followed by the cutting point touches the base cylinders of the gear and the hob, and makes an angle (~- 'tpg) with the line of centers, when viewed in the direction of the gear axis. If the shaft angle is set at the standard value, this angle becomes (1[2 - 't ), as shown in Figure 16.6, and the path of the sg . cutting point then appears identical with the corresponding path when the gear is cut by a rack cutter. It is for this reason that, when we check for undercutting in a gear, we can regard the hob as equivalent to a rack cutter. We check that Swivel Angle 467 there would be no undercutting if the gear was cut by the rack cutter, and this implies that there will also be no undercutting when in fact the hob is used. Swi vel Angle Earlier in this chapter, we stated that it is common practice to specify the lead angle of a hob, instead of its helix angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.5-1.png",
        "caption": "Figure 3.5. position of the contact point.",
        "texts": [
            "25) Position of the Contact Point When we discussed the condition for correct meshing of a pinion and rack, at the beginning of this chapter, we showed that a typical contact point lies on the base circle tangent which is perpendicular to the rack tooth profile. Since the contact point always lies on this line, the path of contact is a segment of the same line. We can therefore specify the position of a contact point by its distance along this line from the pitch point. We introduce the length s, as shown in Figure 3.5, and it is defined in the manner of a coordinate, so that it is positive for points which lie above P, and negative for those lying below P. To derive an expression for s, we use a method which is very similar to the procedure just used when we found a relation between the pinion and rack positions. When the contact point is at the pitch point, the angular position of the pinion is given by Equation (3.19), 62 Gears in Mesh and the value of s is zero. After a pinion rotation ~~, the angular position of the pinion is given by Equation (3.21), fJ (3.26) The rack will have displaced a distance Rp~~' as we showed in Equation (3.24), and the corresponding value of s can then be read from Figure 3.5, s (3.27) We eliminate ~~ between Equations (3.26 and 3.27), and we use Equation (3.11) to replace (Rp cos~) by Rb\u2022 We then obtain an expression for s as a function of the pinion angular position ~, s Rb~ + lt cos ~ 2 P (3.28) If we use Equation (3.28) to find the values of s corresponding to any two positions of the subtract one result from the other, expression for the displacement ~s of pinion, we can then and we obtain an the contact point Sliding Velocity 63 corresponding to a rotation llfJ of the pinion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure10.17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure10.17-1.png",
        "caption": "Fig. 10.17 Work cycle of Wankel rotary engine",
        "texts": [
            " The kinetic energy of the gas is converted directly to electric energy. An MHD generator has the potential of an ultimate efficiency in the range of 60 to 65% which is much better than the 30\u201340% of the steam and gas turbines in traditional power plants (Brogan 1964). The speed of internal combustion engines in the 1970s was already several times of that made in the early century. Nowadays the engine speed in race cars reached 10,000 and 5000 rpm for gas and diesel engines respectively. A German engineer, John Wankel, invented rotary engine in 1957 (Hege 2006) (Fig. 10.17). This type of engines are simple, compact and light-weight. However, they have several shortcomings, including poor fuel efficiency, no diesel option, and relatively high position of output shaft, making it difficult to fit into an automotive vehicle. Moreover, the poor manufacturability and high cost also prevented its application. It seems that it was installed only on some Mazda vehicles. 374 10 Summary of Mechanical Engineering in New Era A ring spinner was invented in the U.S. in 1828. After continuous improvement, ring spinners almost replaced self-acting mule during the 1960s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003508_robot.1995.525390-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003508_robot.1995.525390-Figure1-1.png",
        "caption": "Fig. 1 Magnetic Wheel Robot",
        "texts": [
            " However, a simple wheeled robot would have difficulty navigating vertical pipes. A wheeled robot equipped with springs or magnets could cope with vertical pipes. Because the use of springs would greatly increase the pipe cross-sectional area occupied, it would be difficult to resolve Problem 1. Moreover the ordinary spring-wheeled robot can not overcome Problem 2. In contrast, the use of magnets is limited to iron and similar pipes because of the basic property of magnets, but the lower cross-sectional area would resolve Problem 1 and the method of movement shown in Fig. 1 wauld overcome Problem 2 without complex mechanisms and controls. For these reasons, we settled on a magnetic wheel-type mechanism basically. Unfortunately, another difficulty is that there are multiple bumps insidepipes, such as joints, and a significant amount of energy is required to negotiate these with ordinary magnetic wheels. In general, crawler-type mechanisms are the most effective means of dealing with the bumps, but these require so many wheels that the mechanism could not navigate L- and - 858 T-shaped pipes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003129_a:1008106331459-Figure21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003129_a:1008106331459-Figure21-1.png",
        "caption": "Figure 21. Microgripper design: top view (left) and side view (right).",
        "texts": [
            " For a cantilever type endeffector (Figure 20), as the one used in our prototype, the theoretical relation between force F applied at a certain point and strain \u03b5 induced in another point, is expressed by Equation (5): \u03b5 = 6Fl Ebh2 . (5) Parameters l, b, h are illustrated in Figure 20; E is the Young modulus of the material of the endeffector. If we use strain gauges to detect the strain in the material, we obtain a resistance change of the strain gauge\u2019s nominal resistance value, that is linked to the strain \u03b5 by following equation: 1R = kR\u03b5, (6) where R is the nominal resistance of the gauge, k is the gauge factor. The microgripper used for our experiments has the structure shown in Figure 21. It consists of three piezoceramic (PZT) bimorph actuators: one actuator permits up-and-down movements along the z-axis, the other two are used to perform the gripping process in the xy-plane. High-grade steel endeffectors are mounted at the end of these two PZT actuators. Two pairs of metal-foil strain gauges have been glued at the base of the endeffectors; one strain gauge of each pair is used in tension and the other in compression load, in order to obtain a double output signal compared to the use of a single gauge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002881_ias.1996.556993-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002881_ias.1996.556993-Figure5-1.png",
        "caption": "Fig. 5. PWM scheme using redundant voltage vectors. The average voltage vector exists on the a axis.",
        "texts": [
            " Lumping the equations together gives the following equation. In the above equation, c k has to be decided so that the PWM inverter outputs the average voltage vector e during the modulation period. No general solution to (25) exists because the number of unknown variables is more than the number of equations. However, introduction of a right pseudo inverse matrix[g] enables to solve <k as follows: As the result of the calculation, one can decide a suitable PWM pattern under any combination of v k during the modulation period. Fig.5(a) shows a PWM pattern in the case that the average voltage vector e exists on the a: axis. Note that V s is selected during an interval of time, different from VO being selected during the corresponding interval in the conventional sinusoidal PWM scheme. As shown in Fig.5(b), V3' and Vs' produce @-axis components in the harmonic current vectors while VI' and V7' produce a-axis components. Fig.5(c) shows the trajectory of the harmonic current vector. The trajectory starts from the origin toward the left at the beginning of the first modulation period. Since the harmonic current vector changes toward the direction near that of the corresponding harmonic voltage vector, the trajectory draws a rectangle and returns to the origin at the end of the first period. All of Ai?', Ais ' , Ail' and Ais ' are not linearly dependent vectors in the first period. The rotor position, therefore, can be estimated by the proposed algorithm, based on the harmonic component of the current variation, independent of the location of the average voltage vector. Note that the sum of the harmonic current vectors in the first modulation period shown in Fig.5 is not equal to zero vector. In order to compensate for the deviation, the sequence of selecting the voltage vectors should be modified as shown in the second modulation period. Fig.6 shows a PWM scheme, where the average voltage vector exists on the origin of the a-P coordinate. This situation corresponds to the case of position estimation at standstill. Each voltage vector is output for 1/6 of the modulation period. Note that the inverter selects neither V I nor V7. The sequence is scheduled so that the trajectory of the harmonic current vectors starts from the origin at the beginning of the modulation period and returns to the origin at the end"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.10-1.png",
        "caption": "Figure 16.10. Left-handed hob and left-handed gear.",
        "texts": [],
        "surrounding_texts": [
            "The most commonly used method for cutting helical gears is by hobbing. As always in generating cutting, one gear is used to cut another. A typical hob is shown in Figure 16.3, and it can be seen that, apart from the gashes forming the cutting faces, the hob is simply a helical gear, in which each tooth is referred to as a thread. A hob. 458 Gear Cutting II, Helical Gears Since the hob is similar in shape to a screw, its helix angle \"'sh is always large, particularly when there is only one thread. It is cust~mary to specify the shape of a hob by means of its lead angle, rather than its helix angle. For a right-handed hob, the lead angle Ash is defined as the complement of the helix angle, (16.13) where Ash and \"'sh are measured in degrees. For a left-handed hob, whose helix angle is negative, the lead angle can be def ined as follows, - 90 0 - '\" sh ( 16.14) so that we obtain a negative lead angle for a left-handed hob. In practice, it is generally the magnitude of the lead angle which is given in the specification, together with a statement to indicate whether the hob is right or left-handed. It is clear that the lead angle can be determined from the helix angle, and vice versa. In describing the geometry of the hobbing process, we will specify the shape of the hob by means of its helix angle, since the symbols will then agree with the notation used in Chapter 15, where we described the geometry of crossed helical gears. Figure 16.4 shows a hob in position to cut a gear blank, and since their axes are not parallel, it is clear that they form a crossed helical gear pair. During the cutting process, the hob and the gear blank are rotated about their axes with angular veloci ties wh and wg ' I n order to cut the teeth of the gear across the entire face-width, the hob is moved slowly in the direction of the gear axis, and the velocity of the hob center is called the feed velocity vh . The values required for the three variables wh ' Wg and vh are achieved by means of change gears or stepping motors in the hobbing machine. There are two additional settings which must be made when the hobbing machine is being set up. These are the shaft angle ~, which is the angle between the axes of the hob and the gear blank, and the cutting center Hobbing 459 distance CC, which is the distance between the two axes. In the remainder of this section, we will determine the values required for the machine parameters wh ' wg ' vh ' E and CC, if the hob is to cut a gear with Ng teeth, normal module mn , normal pressure angle ~ns' helix angle ~sg' and normal tooth thickness t nsg Before we discuss the details of the cutting process, we will first prove that, as usual, the gear will have the same normal module and normal pressure angle as those of the hob. We showed in Chapter 15 that the minimum condition for correct meshing of two crossed helical gears is that their normal base pitches should be equal. The corresponding result, when we consider a gear being cut by a hob, is that the normal base pitch of the gear will always be equal to that of the hob. Since the normal base pitch of the hob is equal to that of the basic rack, we can conclude that the normal base pitches of the gear and the basic rack are equal, and the gear can therefore mesh correctly with the basic rack. As always, the standard pitch cylinder of the gear is defined as its pitch cylinder when it is meshed with the basic rack. The normal pitch Pns and the normal pressure angle ~ns of the gear must 460 Gear Cutting II, Helical Gears then be equal to those of the basic rack, and hence equal to those of the hob. This result remains true, whether or not the cutting pitch cylinders of the gear and the hob coincide with the i r standard pi tch cylinders. In order to cut the gear described earlier, we must therefore use a hob with the same normal module and normal pressure angle as those specified for the gear. We consider next how to cut the required number of teeth, and the correct helix angle. When a rack cutter is used to cut a gear, the helix angle of the gear depends on the angle at which the cutter is set, so it might be expected that the helix angle of a gear being hobbed would be determined by the value of the shaft angle ~. This is not the case, however, and we will now show that the number of teeth cut in the gear blank, and the helix angle at which they are cut, depend only on the values chosen for wh ' Wg and vh \u2022 In Chapter 5, we defined the cutting point as the point where the cutter makes a cut on the final tooth surface, and we showed that this point corresponds to the contact point when the gear blank and the cutter are regarded as a pair of meshing gears. The situation is no different when the cutter is a hob. We described in Chapter 15 how to find the position of the contact point in a crossed helical gear pair, and this point becomes the cutting point when we consider a hob cutting a gear. As in any metal-cutting process, the shape of each tooth cut in a gear blank is the envelope of positions through which the hob moves, relative to the gear blank. For the purpose of determining this shape, it is helpful to neglect the gashes in the hob thread, so that the threads are regarded as continuous, and we can imagine that the teeth are formed in the gear blank by grinding, rather than by cutting. If the hob and the gear blank were a pair of crossed helical gears, there would always be at least one thread of the hob making contact with the gear. Hence, for the hob and the gear blank, there is always at least one thread which is in contact with the final tooth surface of the gear. We label the points in contact AOh on the hob, and AOg on the gear. After the hob turns through exactly one angular pitch, the position of the thread containing point AOh is occupied by the Hobbing 461 next thread, and the corresponding point Alh on this thread will now be the cutting point, touching a point A1g on the gear tooth adjacent to the tooth containing AOg. As the hob rotates, we can identify a sequence of points such as AOh and Alh on the hob threads, and AOg and A1g on the gear teeth. The points on the hob lie in the same transverse section and are evenly spaced, at angular intervals equal to the angular pitch. Of course, if the hob has only one thread, the angular pitch is 360 0 , and the points all coincide. On the other hand, the gear points do not lie in one transverse section, due to the feed of the hob in the direction of the gear axis, and each point is displaced axially a small amount relative to the next point. We now consider the position on the gear of point ANg , the cutting point when the hob has turned through Ng angular pitches. Since the gear is to have Ng teeth, points AOg and ANg must be on the same tooth. Hence, if the gear is a spur gear, ANg must lie on the axial line through AOg' while if the gear is a helical gear, ANg must lie on the gear helix through AOg. The distance through which the hob is fed during one revolution of the gear blank is called the feed rate f. Since the magnitude of f is small compared with the tooth dimensions, point ANg always lies close to the axial line through AOg. The gear blank must therefore turn through approximately one revolution while the hob turns through Ng angular pitches, which is a rotation equal to (Ng/Nh ) revolutions. In order to meet this requirement, the angular velocity ratio (wh/wg ) must be approximately equal to (Ng/Nh ), or exactly equal, when a spur gear is being cut. In the case of a helical gear, the small difference between the two ratios is one of the factors which determine the helix angle of the gear, as we will show later in this section. Once the settings are chosen for the hobbing machine, the value of (wh/wg ) is established, and the number of teeth that will be cut in the gear is then given by the following expression, NhWh Integer closest to (--) Wg (16.15) 462 Gear Cutting II, Helical Gears Having found how the value of Ng depends on the hobbing machine angular velocities wh and wg ' we now consider the helix angle. If points AOg and A1g lie at radius R, the positions of these points at various times can be plotted on a developed cylinder of radius R, as shown in Figure 16.5. The times at which the hob touches points AOg and A1g are called T and T', and the diagram shows the positions of AOg at time T, and A1g at time T'. Since the feed of the hob is in the direction of the gear axis, the line in the diagram joining AOg and A1g is in the same direction. The diagram also shows the gear helices through these points, which appear as straight lines making an angle ~Rg with the gear axis, and these are labelled helix 0 and helix 1. The point on helix 0 in the transverse section through A1g is labelled Ag \u2022 The position of helix 0 at time T' is shown by the dotted line, and the positions of Aog and Ag at this time are shown as AOg and Ag \u2022 In Figure 16.5, the length AOgA1g represents the hob feed between the times T and T', and AgAg represents the arc Hobbing 463 length moved by point Ag in the same time interval. Since helix 0 and helix 1 are gear helices on adjacent teeth at the same radius, their positions at any instant are exactly one tooth pitch apart. A1g and Ag lie on the two helices in their positions at time T', so the distance between these points is equal to the transverse pitch. We therefore obtain the following expressions for the three lengths, A A' 9 9 A A' 19 9 The time interval required for the hob to rotate through one angular pitch can be expressed in terms of the hob angular velocity, T' - T We now use triangle AOgA1gAg to relate the three lengths, A A' - A A' 19 9 9 9 and when their values are substituted, we obtain the following relation between wh ' Wg and vh ' 211' vh -N-- tan l/IR hWh 9 ( 16.16) The feed rate f of the hob was defined earlier as the distance moved by the hob during one revolution of the gear blank. It is customary to express the feed velocity vh in terms of f, _f_ (211') Wg (16.17) and with this substitution, Equation (16.16) takes the following form, tan l/IRg 211'R ( 16.18) 464 Gear Cutting II, Helical Gears The helix angle of the gear at radius R is expressed in terms of the lead Lg by Equation (13.31), tan IPRg and Equation (16.18) then becomes a relation giving the lead that will be cut in the gear, l(NhWh ) f - Ng Wg ( 16.19) The quantity (Ng/Lg) is equal to the reciprocal of the axial pitch, as we showed in Equation (13.36), and this can be expressed in terms of the helix angle IPsg by means of Equation (13.42), _1_ Pzg sin IPSg Pns (16.20) Hence, Equation (16.19) can be put into two alternative forms, giving either the axial pitch or the helix angle of the gear, _1_ Pzg l(NhWh ) f - Ng Wg (16.21 ) (16.22) It is an interesting result that, as we pointed out earlier, the helix angle cut in a gear is not affected by the shaft angle ~ of the hobbing machine. This angle is generally set equal to the standard shaft angle ~s' or in other words, equal to the sum of the helix angles of the gear and the hob, ~s (16.23) We showed in Chapter 15 that a pair of crossed helical gears can mesh correctly, even when the shaft angle is not equal to the standard shaft angle. It therefore follows that a hob can cut an accurate involute gear, even when ~ is not exactly equal to ~s. However, for the remainder of this section, we will assume that the shaft angle is set equal to ~s' and in a Hobbing 465 later section of the chapter we will discuss the consequences of a small change in this value. The last setting of the hobbing machine to be considered is the cutting center distance CC , and its effect on the tooth thickness of the gear. As we discussed earlier, the cutting process can be considered as equivalent to meshing with zero backlash. An expression for the normal backlash in a crossed helical gear pair was given in Equation (15.96), The length ~Cp Equation (15.47), in this expression (16.24) was defined by (16.25) and all the other quanti ties are defined on the pitch cylinders, as indicated by the notation. We are considering, at present, a hob cutting a gear blank when the shaft angle ~ is set equal to the standard value ~s. In this case the cutting pitch cylinders coincide with the standard pitch cylinders, as we proved in Chapter 15. If we replace RP1 and Rp2 in Equation (16.25) by Rsg and Rsh ' and set the backlash in Equation (16.24) equal to zero, these two equations give an expression for the normal tooth thickness cut in the gear, (16.26) The expression in brackets in this relation represents the hob offset. When the normal tooth thickness t h of the hob is ns equal to O.5Pns' Equation (16.26) has exactly the same form as Equation (16.12), which gave the normal tooth thickness of a gear cut by a rack cutter. If the normal tooth thickness of the hob is greater than O.5Pns' the normal tooth thickness of the gear is reduced by the same amount. Whatever the value of t nsh ' the effect of a change in the hob offset on the tooth thickness of the gear is identical to the corresponding effect caused by a change in the offset of a rack cutter. In Chapter 5, we stated that the tooth thickness of a gear cut by 466 Gear Cutting II, Helical Gears a hob is generally calculated as if the gear were cut by a rac k cutter. We have now shown that thi s procedure is essentially correct, prpvided the hobbing machine is set with its shaft angle ~ equal to the standard value ~s' There is a second manner in which the cutting action of a hob resembles that of a rack cutter. In the discussion following Equations (15.74 and 15.77), we showed that the path of contact in a crossed helical gear pair touches each base cylinder, and makes an angle (~- 'tp1) with the line of centers, when viewed in the direction of the axis of gear 1. Hence, in the case of a hob cutting a gear, the path followed by the cutting point touches the base cylinders of the gear and the hob, and makes an angle (~- 'tpg) with the line of centers, when viewed in the direction of the gear axis. If the shaft angle is set at the standard value, this angle becomes (1[2 - 't ), as shown in Figure 16.6, and the path of the sg . cutting point then appears identical with the corresponding path when the gear is cut by a rack cutter. It is for this reason that, when we check for undercutting in a gear, we can regard the hob as equivalent to a rack cutter. We check that Swivel Angle 467 there would be no undercutting if the gear was cut by the rack cutter, and this implies that there will also be no undercutting when in fact the hob is used. Swi vel Angle Earlier in this chapter, we stated that it is common practice to specify the lead angle of a hob, instead of its helix angle. It is also customary to specify the angular setting of the hobbing machine by means of the swivel angle, rather than by the shaft angle. Since a hob is shaped like a screw, its helix angle is always large, particularly in the case of a single-thread hob, for which the helix angle is typically about 85\u00b0. The helix angle of the gear being cut may of course have any value, but in the majority of gears, the magnitude of the helix angle is between 0\u00b0 and 30\u00b0. In general, right-handed hobs are used to cut right-handed gears, and left-handed hobs are used for left-handed gears. In most cases, therefore, the shaft angle is approximately equal to a right angle, and the swivel angle is defined as the amount by which the shaft angle differs from a right angle. For example, if the axis of the gear is vertical during the cutting process, the swivel angle a is defined as the angle which the hob axis makes with the 468 Gear Cutting II, Helical Gears horizontal. The standard shaft angle was defined by Equation (16.23), as the sum of the gear and the hob helix angles. We express the helix angle of the hob in terms of its lead angle, by means of Equation (16.13 or 16.14), and we obtain the following expression for the standard shaft angle, ,f, + 90\u00b0 - A \"'sg - sh (16.27) where the plus and minus signs refer to a right or Hobbing Machine Gear Train Layout 469 left-handed hob. We now define the standard swivel angle os' so that it differs by a right angle from the standard shaft angle, (16.28) As discussed earlier, the hobbing machine is generally set so that the shaft angle is equal to the standard shaft angle, and it then follows that the swivel angle is equal to the standard swivel angle. Figures 16.7 and 16.8 show the relations between the shaft angles and the swivel angles when a right-handed hob is used to cut a spur gear or a right-handed helical gear, while Figures 16.9 and 16.10 show the corresponding relations when a left-handed hob is used to cut a spur gear or a left-handed helical gear. Hobbing Machine Gear Train Layout We showed in Equations (16.15 and 16.22) that the number of teeth and the helix angle cut in a gear depend on the feed rate f and the angular velocity ratio (wh/wg ) in the hobbing machine, NhWh Integer closest to (----) Wg (16.29) 470 Gear Cutting II, Helical Gears sin I/I sg l(NhWh ) f - Ng Wg (16.30) It is helpful to examine how the gear trains in some typical hobbing machines are arranged, in order to achieve the values of Ng and I/I sg required in the gear. One type of hobbing machine is shown schematically in Figure 16.11. The rectangular boxes in the diagram represent gear pairs or gear trains, with the output-input ratio in each case given by the constant k. The symbol ki stands for the ratio of the index change gears, kf is the ratio of the feed change gears, and the other k values represent the gear trains built into the machine, whose ratios cannot be altered by the user. The values of wh and wg , and of the hob feed velocity vh ' can be read from the diagram in terms of the input angular velocity w 1 ' (16.31) (16.32) Hobbing Machine Gear Train Layout 471 (16.33) The feed rate f was given by Equation (16.17), in terms of Wg and vh ' and when these are expressed by means of Equations (16.32 and 16.33), we obtain a relation between the feed rate and some of the gear ratios in the hobbing machine, f The terms in brackets are combined into a single constant, known as the machine feed constant Cf , whose value is provided by the manufacturer of the hobbing machine. The feed rate is then expressed solely as a function of the ratio kf of the feed change gears, f (16.34) To obtain the ratio (wh/wg ) in terms of the hobbing machine gear ratios, we express wh and Wg by means of Equations (16.31 and 16.32), As before, the terms in brackets are combined into another constant, the machine index constant Ci , whose value is also provided by the manufacturer, and the angular velocity ratio is then given by the following expression, C\u00b7 1 k.\" 1 (16.35) We substitute this expression into Equations (16.29 and 16.30), and we obtain the number of teeth that will be cut in the gear, and its helix angle, in terms of the hobbing machine gear ratios, NhC. Integer closest to ( __ l) k i (16.36) {16.37l We now determine how the machine ratios should be 472 Gear Cutting I I, Helical Gears chosen, in order to cut a gear with the number of teeth and helix angle required. The feed rate f and the hob angular velocity wh are chosen to obtain good metal-cutting characteristics. The values depend on the size of the hob, the hardness of the material being cut, and the surface finish required. For more details, the reader should consult references such as the Gear Handbook [2]. Once a value for f is. chosen, the required ratio kf for the feed change gears is found from Equation (16.34), f Cf (16.38) The value chosen for wh is obtained by setting the input speed change, shown in Figure 16.11, to a suitable value. With the feed change gear ratio already selected, the index change gear ratio is used to determine both the number of teeth cut in the gear, and its helix angle. We choose the ratio ki so that it satisfies Equation (16.37), in order to obtain the required helix angle, NhCi ki f sin ~Sg (16.39) (1rm + N ) n g When this value for ki is substituted into Equation (16.36), we find that we also obtain the correct number of teeth, because the magnitude of the term (f sin ~Sg/1rmn) in the expression for ki is always very much less than 0.5. It is sometimes difficult to find change gears which provide exactly the value of ki given by Equation (16.39). Once the change gears have been chosen, their actual ratio ki should be calculated, and this value is substituted into Equation (16.37), to give the helix angle that will in fact be cut in the gear. Use of a Differential in the Hobbing Machine There is one major problem associated with hobbing machines, when they are designed in the manner shown in Figure 16.11. If a second cut is required, as is often the case, it is necessary to disconnect the feed drive, in order Use of a Differential in the Hobbing Machine 473 to return the hob quickly to its starting position. It is then very difficult to reset the machine, with the work table and the hob in exactly the correct positions. This problem can be overcome if a differential is incorporated into the hobbing machine. In order to determine the relation that must be maintained between the hob feed, the work table rotation and the hob rotation, we once again consider Equation (16.30), We use Equation (16.17) to express the hob feed rate f in terms of the feed velocity vh ' and we obtain the relation which must be maintained throughout the cutting process between the hob feed velocity, the table angular velocity, and the hob angular veloci ty, (16.40) A gear train with one degree of freedom can always be represented by a linear equation relating the angular velocities of the input and the output shafts. A differential is a gear train with two degrees of freedom, and it has three shafts, either two input and one output, or one input and two output. The angular velocities of the three shafts are always related by a single linear equation. Hence, as we can see from Equation (16.40), if the hob feed, the work table drive and the hob drive were all connected to the three shafts of a suitable differential, they would then always maintain the correct relative positions. The differential may be a simple planetary gear train, or one which is constructed of bevel gears. In either case, the output angular velocity w3 is a linear combination of the input angular velocities w1 and w2 ' and can therefore be represented by the following equation, (16.41) The constants k7 and ka of the differential depend on the design of the gear train, and need not concern us here. 474 Gear Cutting II, Helical Gears The complete layout of the hobbing machine is shown in Figure 16.12, where the differential is represented as a simple planetary gear train. The hob drive is connected to the sun gear of the differential, the table drive is connected to the planet carrier, and the feed is connected to the internal gear. As before, the index change gears and the feed change gears are represented by symbols ki and kf , and now there is a third set of change gears, the differential change gears, represented by the symbol kd \u2022 The constants k1 to k6 are the fixed ratios of the gear trains in the hobbing machine. The constant k6 represents the ratio of a worm and gear, connecting the differential change gears to the internal gear of the differential. This ratio is shown with a minus sign, since the hand of the helix in the worm is chosen so that a positive angular velocity in the worm produces a negative angular veloci ty in the gear. We pointed out earlier that the number of teeth and the helix angle cut in the gear depend on the feed rate f and the Use of a Differential in the Hobbing Machine 475 angular velocity ratio (wh/wg ). We therefore need to express these two quantities in terms of the hobbing machine gear ratios. We start by writing down a number of relations between the angular velocities, Wh k1w1 (16.42) Wg k2ki k3w3 (16.43) vh k2kik4kfw3 (16.44) w 2 k2kik4kfkd(-k6)w3 (16.45) The feed rate f, which was given by Equation (16.17), can now be expressed in terms of the gear ratios, f As before, the terms in brackets are combined into a single quantity, the machine feed constant Cf , and the feed rate is then given simply in terms of the feed change gear ratio, f (16.46) When Equations (16.42 and 16.43) are used to express wh and wg ' the angular velocity ratio takes the following form, wh k1w1 Wg k2k3kiw3 and the relation between w 1 and w3 is found from Equations (16.41 and 16.45), The last two equations are combined to give the angular velocity ratio in terms of the gear ratios, and we use Equation (16.46) to express the ratio kf in terms of the feed rate f, (16.47) 476 Gear Cutting II, Helical Gears We now define the machine index constant Ci and the machine di fferent ial constant Cd as follows, C. 1 k1 k2 k3k7 k3 k7Cf k1k4 k6kS As usual, the values of the machine constants Cf ' Ci and Cd are all provided by the manufacturer of the hobbing machine. Ci is a ratio, but Cf and Cd are lengths, since they are defined in terms of the feed rate f, which is the distance moved by the hob during one revolution of the work table. When the constants are substituted into Equation (16.47), we obtain the final expression for the angular velocity ratio, (16.4S) This expression is substituted into Equations (16.29 and 16.30), and we obtain the number of teeth and the helix angle that will be cut in the gear, corresponding to the feed rate f and the change gear ratios ki and kd in the hobbing machine, C\u00b7 fkd Integer closest to [Nh(k: + c)] 1 d (16.49) (16.50) Once again, we must determine how the change gear ratios kf , k i and kd should be chosen, in order to cut a gear with Ng teeth and helix angle ~sg' As before, we choose the feed rate f from metal-cutting considerations, and the ratio kf is then given by Equation (16.46), (16.51) If we are cutting a spur gear, or in other words a gear with zero helix angle, we can satisfy Equation (16.50) by setting the value of kd equal to zero, and choosing the value of ki as follows, Use of a Differential in the Hobbing Machine k. 1 477 (16.52) The conventional method for cutting a helical gear is to use the same value for ki , and to choose kd in a manner which then satisfies Equation (16.50), Cd sin IPsg Nh '/I'mn (16.53) An alternative expression for the required differential change gear ratio is found by combining Equations (16.20 and 16.53), (16.54) When we compare the last two equations, it is clear that it is much easier to select suitable change gears, giving the correct value for kd , if we design the gear so that its axial pitch Pzg is a round number, rather than its helix angle IPsg. There are times when it is difficult, or even impossible, to find change gears which provide the exact values for ki and kd , given by Equations (16.52 and 16.53). For example, when the value required for Ng is a large prime number, we cannot obtain the exact value for ki , since most sets of change gears do not contain gears with more than 120 teeth. Also, when the helix angle ~sg is very small, it may be difficult to obtain a sufficiently accurate value for kd \u2022 When these situations occur, we can choose the index gears so that their ratio ki differs slightly from the value given by Equation (16.52), and the differential change gears are then used to ensure that Equation (16.50) is still satisfied with sufficient accuracy. Since the index change gear ratio is close to the value given by Equation (16.52), it can be represented by an expression with the following form, k. 1 (16.55) where the quantity ~ may be either positive or negative. This expression for ki is substituted into Equation (16.50), and we obtain the corresponding value of the differential change gear ratio required to cut the correct helix angle, 478 Gear Cutting II, Helical Gears (16.56) We have determined the values of ki and kd in a manner that satisfies Equation (16.50), so we know that the correct helix angle will be cut. It is now necessary to substitute the values of ki and kd into Equation (16.49), in order to confirm that the gear will also be cut with the correct number of teeth. The expressions for ki and kd given by Equations (16.55 and 16.56) are substituted into the right-hand side of Equation (16.49), with the following result, (16.57) As we pointed earlier, the magni tude of the term (f sin ~sg/wmn) is always less than 0.5, so with these values of ki and kd , the number of teeth cut in the gear will indeed be equal to the number required. The change gear ratios given be Equations (16.55 and 16.56) can be used for cutting either helical or spur gears, whenever it is difficult to obtain the values given by Equations (16.52 and 16.53). It is interesting that the quantity a has cancelled out from the expression in Equation (16.57). This means that there is no theoretical limit to the value of a which can be used, and the ratio ki may therefore differ considerably from the value given by Equation (16.52). In practice, however, it is usually easier to select the differential change gears to obtain an accurate value for kd , if the index gears are chosen so that their ratio is close to the value given by Equation (16.52), and the magnitude of a is therefore small compared wi th 1. It is evident that a differential is useful in the design of a hobbing machine, since it facilitates the selection of the necessary change gears. However, the original purpose for which the differential was introduced, as we discussed earlier in the chapter, was to maintain the correct relation between the hob feed, the work table rotation and the hob rotation, during a rapid return of the hob to its starting position. Figure 16.13 shows how this purpose is achieved. The drive is disconnected, by means of a dog clutch, between the feed change gears and the feed drive. An auxiliary motor, Theoretically Correct Shape for the Hob Thread 479 known as the hob rapid traverse motor, is then used to drive the hob feed. The drive passes through the di fferent ial, causing the work table to turn at exactly the correct speed, so that the helical teeth in the gear mesh continuously with the threads of the hob. During the entire return motion of the hob, only a very small rotation of the table is required, compared with the many revolutions that take place while the gear is being cut. Hence, the return of the hob can be carried out quite quickly, without damage to the gearing driving the work table. Theoretically Correct Shape for the Hob Thread We stated in Chapter 5 that a hob whose thread profile is straight-s;ded in the normal section will not cut exact involute tooth profiles. We are now in a position to estimate the amount of error, and to determine the correct normal 480 Gear Cutting II, Helical Gears profile in the hob thread. In Chapter 15, we proved that two involute helical gears can mesh with crossed axes, and maintain a constant angular velocity ratio. The hobbing process is essentially the same as the meshing of a pair of crossed helical gears. It therefore follows that, in order to cut correct involute profiles in the gear, the thread of the hob must also have the shape of an involute helicoid. In other words, the thread has an involute profile in the transverse section. The corresponding profile in the normal section is a convex curve, and not a straight line. However, because the helix angle of a hob is so large, the profile in the normal section is extremely close to the straight line. Hence, when a straight-sided hob is used to cut gears, the resulting error in the gear tooth profiles is generally small. We can estimate this error in the following manner. We described a method in Chapter 13 for calculating the profile of the normal section through a helicoid. We now use this method to find the profile of the normal section through the hob thread. We calculate the distances, at the thread tip and at the top of the fillet, between this profile and its tangent at the standard pitch cylinder, as shown in Figure 16.14. The profile of a straight-sided hob would coincide with this tangent, and a hob of that type would therefore cut too deeply into the teeth of the gear, in the regions near the fillet and near the tip. Figure 16.15 shows the normal section through an Effect of a Non-Standard Shaft Angle 481 exact involute helicoid tooth, and it also shows the profile we obtain when the gear is cut by a straight-sided hob. The maximum differences between the two profiles are approximately equal to the distances described earlier, by which the normal section profile of the involute hob deviates from the straight line. As we can see in Figure 16.15, the tooth shape cut by a straight-sided hob is similar to the shape of a tooth cut with tip and root relief. The errors caused by the use of a straight-sided hob are therefore sometimes beneficial, and this is one of the reasons for the continued use of straight-sided hobs, when true involute hobs are also readily obtainable. There are times, however, when the errors caused by straight-sided hobs may be excessive. This is often the case for gears cut by multi-thread hobs, or by single-thread hobs of large module, whose helix angles are usually less than 85\u00b0. Whenever there is a possibility that a straight-sided hob may cut too much tip and root relief in a gear, the procedure just described can be used to determine whether a true involute hob should be used. Effect of a Non-Standard Shaft Angle In an earlier section of this chapter, we described how to calculate the tooth thickness cut in a gear, when the shaft angle ~ of the hobbing machine is set equal to the standard value ~s. We stated at that time that we would still obtain a 482 Gear Cutting II, Helical Gears correct involute profile in the gear tooth, even if the values of E and Es wer~ not the same. The only effect of the altered shaft angle is a change in the tooth thickness, and we will now discuss briefly how the new tooth thickness can be found. Since it is not generally necessary to make this calculation, we will simply outline the steps, without presenting all the equations. When the shaft angle is not equal to its standard value, the cutting pitch cylinders of the gear and the hob do not coincide with their standard pitch cylinders. The first step is therefore to calculate the cutting pitch cylinder radii R~g and R~h. Knowing the normal thread thickness t nsh of the hob at its standard pitch cylinder, we then calculate its normal thread thickness t nph at the cutting pitch cylinder. To find the normal tooth thickness cut in the gear, we regard the hobbing process as the meshing of a crossed helical gear pair with zero backlash. An expression was given in Equation (15.96) for the normal backlash in a crossed helical gear pair, The length ~cp in this equation was defined by Equation (15.47), as the difference between the center distance and the sum of the pitch cylinder radii. For the situation of a hob cutting a gear, ~cp would represent the difference between the cutting center distance and the sum of the cutting pitch cylinder radii, We combine these equations, and set the backlash Bn equal to zero, to obtain the normal tooth thickness t npg cut in the gear. The final step is to calculate the corresponding normal tooth thickness t nsg of the gear at its standard pi tch cylinder. If we carry out this calculation, we will find that the normal tooth thickness t nsg cut in the gear is almost independent of the shaft angle E. In other words, the tooth thickness is hardly affected by a small change in the shaft Geometric Design of a Helical Gear Pair 483 angle, provided of course that the cutting center distance is left unchanged. However, the radii of the cutting pitch cylinders are very sensitive to the shaft angle value. In particular, a small change in the value of ~ can move the cutting pitch cylinder of the hob right off the surface of the hob thread. In the absence of experimental evidence, it is not certain what effect this may have on the tooth surface quality. Therefore, although the shaft angle need not theoretically be set equal to its standard value, it is nevertheless recommended that in practice this value should continue to be used. Geometric Design of a Helical Gear Pair In the final section of this chapter, we outline a procedure by which we can choose the helix angle, the profile shift values and the gear blank diameters, for a pair of helical gears intended to mesh on parallel shafts at an arbi trary center di stance C. Since the standard center distance depends on the helix angle, (16.58) it would appear that we can always choose the helix angle so that the standard center distance Cs is equal to the center distance C. In this case, the pitch cylinder of each gear would coincide with its standard pitch cylinder. However, as we will show, it is not always practical to choose the helix angle in this manner, and there is no particular advantage in doing so. When the gears are cut by a pinion cutter, the helix angle of each gear is equal to that of the cutter, so the choice of ~s is limited by the cutters that are available. When a rack cutter is used to cut the gears, the cutter veloci ty v r and the gear blank angular veloci ty must be related by Equation (16.11), 484 Gear Cutting II, Helical Gears This equation must be satisfied exactly, because an incorrect value for vr would result in uneven spacing of the teeth on the gear. However, when ~s is chosen so that Cs is equal to C, it may be impossible to find change gears giving the exact relation between vr and wg \u2022 In general, it is probably easiest to obtain the required helix angle when the gear is cut by a hob, and the differential change gear ratio is given by either Equation (16.53) or Equation (16.56). Even in this case, it may be difficult to find a set of change gears giving a sufficiently small error. The effort required is seldom justified, because a gear pair can be designed quite satisfactorily, assuming only that Cs is approximately equal to C. The procedure is essentially the same as the one described in Chapter 6, for the design of a spur gear pair. For the reasons just outlined, it is generally best to choose the helix angle ~s so that the gears can be cut wi thout difficulty, and at the same time the standard center distance Cs is slightly less than the center distance C. The value of Cs should lie within the range given by Equation (6.14), C (16.59) The design procedure now consists in the choice of suitable profile shift values, and the gear blank diameters, in order to obtain the backlash required, and adaquate values for the working depth and the clearances at each root cylinder. We consider the meshing geometry in a transverse plane, and the design steps are then identical to those used in the design of a spur gear pair. For a helical gear pair, it is customary to specify the normal backlash Bn' rather than the circular backlash B. It is therefore necessary to calculate a number of the gear parameters in the transverse plane, before we can consider the transverse plane geometry. The values of mt' Rs1 ' ~ts' Rb1 , Rp1 ' ~p' ~tP' Ptp' and Bare found from Equations (13.148, 13.150, 13.151, 13.152, 14.28, 14.7, 14.8, 14. 10 and 14.72). (16.60) (16.61) Geometric Design of a Helical Gear Pair B tan tl>ns cos \"'s Rp1 tan \"'s Rs1 Rb1 Rp1 21TC 485 (16.62) (16.63) (16.64) (16.65) (16.66) (16.67) (16.68) The design of a helical gear pair with parameters mn and tl>ns' and normal backlash Bn' has now been effectively replaced by the design of a spur gear pair with parameters mt and tl>ts' and circular backlash B. We use the method described in Chapter 6, and in particular Equations (6.45 - 6.53), to carry out the necessary steps. Since the procedure was explained in Chapter 6, the equations will be presented here with very little explanation. We start by writing down the transverse tooth thicknesses at the pi tch cylinders, 1 2\"(Ptp-B) + tlttp (16.69) 1 2\"(Ptp -B) - tlttp (16.70) where tlttp is a quantity chosen by the designer, to increase the tooth thickness in one gear, and reduce it in the other. The next four equations are given for gear 1 only, since the corresponding equations for gear 2 are found by interchanging the subscripts 1 and 2. t ttsl R [.:..!E..!. + 2(inv tP tp - invtl>ts\u00bb) (16.71) s 1 Rpl 1 tI> (tts11 (16.72) e 1 2 tan 2\"1Tmt ) ts bs1 a r - e 1 (16.73) 486 Gear Cutting II, Helical Gears b + R - R sl p1 sl (16.74) The addendum values ap1 and ap2 are chosen to give a working depth of 2.0mn , and equal clearances at each root cylinder, mn - ~(bp1 - bp2 ) 1 mn + 2(bp1 - bp2 ) (16.75) (16.76) And finally, we obtain the diameters of the two gear blanks, (16.77) (16.78) Once the dimensions of the gear pair are all chosen, the designer should of course check, as in the design of a spur gear pair, that there is no interference or undercutting, and that the contact ratio, the root cylinder clearances, and the tip cylinder tooth thicknesses are all adaquate. Gear Cutting II, Helical Gears 487 Numerical Examples Example 16. 1 A 55-tooth helical gear with normal module 4 mm, normal pressure angle 20 0 and helix angle 30 0, is to be cut with a normal tooth thickness of 6.915 mm. Calculate the cutting center distance, and the radius of the root cylinder in the gear, if it is cut by a 32-tooth pinion cutter with a normal tooth thickness of 6.40 mm, and a tip cylinder diameter of 158.12mm. mn=4, ~ns=200, ~s=300, Ng=55, t nsg=6.915 Nc =32, t nsc =6.40, RTc =79.06 Example 16.2 Rsg = 127.017 mm ~ts 22.796 0 Rbg = 117.096 ttsg = 7.985 73.901 68. 129 7.390 inv ~~p = 0.024565 ~~p = 23.471 0 201.932 mm 122.872 mm (13.113) (13.113) (16.6) (2.16,2.17) (16.7) (16.8) A hobbing machine has an index constant C. of 24, and a 1 differential constant Cd of 25 mm. Calculate the change gear ratios required to cut a 49-tooth gear with a normal module of 5 mm and a l)elix angle of 23 0, using a 2-thread hob. C.=24, Cd=25, N =49, Nh=2, m =5, ~ =23 0 1 g n s 488 Gear Cutting II, Helical Gears k. = (48/49) 1 kd = 0.3109340 40.201 mm (16.52) (16.53) (16.20) The index change ratio can obviously be provided by a single gear pair. The differential ratio can be achieved with good accuracy by two gear pairs, having ratios of (24/66) and (59/69). It is not always easy, however, to find change gears which give the required ratio. In the case described in this example, it would have been simpler if the gear pair had been designed with an axial pitch of 40 mm, in which case the required differential change gear ratio would have been exactly (25/80). Example 16.3 When lead screws and other transfer mechanisms are converted from inches to mms, it is sometimes necessary to introduce a factor of 25.4 into their drives. This factor requires a gear with 127 teeth, which is difficult to cut using conventional change gear ratios, because 127 is a prime number, and most sets of change gears do not contain gears with more than 120 teeth. Use Equations (16.55 and 16.56) to choose the ratios to cut a 127-tooth spur gear wi th a single-thread hob, when the hobbing machine has a feed rate of 0.020 inches, and the machine constants Ci and Cd are 24 and 0.5 inches. Required ki = 0.1889764 (16.52) Choose index change gears with ratios (24/41) and (31/96). (24/41) x (31/96) - (1/31) 0.8064516 (16.55) (16.56) The differential ratio can be provided by a single gear pair with a ratio of (25/31). Chapter 17 Tooth Stresses in Helical Gears Introduction The calculation of the tooth stresses in a helical gear is considerably more complicated than the corresponding calculat ion for a spur gear. The contact stress and the fillet stress in each tooth depend on the intensity of the load, and on its position. Since the load intensity varies, as the position of the contact line moves up or down the tooth face, it is not easy to decide when the maximum stresses will occur. As we pointed out in Chapter 11, we consider in this book only the static stresses that would occur if the gears were not rotating. The actual stresses that exist in normal operation are found by multiplying the static stresses by various factors, to account for dynamic effects, type of loading, and so on. Values for these factors are given in the AGMA Standard referred to in Chapter 11 [6]. The method described in this chapter for calculating the static stresses is based on the AGMA method, but differs from it in certain respects. A summary of the differences will be presented at the end of the chapter. Tooth Contact Force In a helical gear pair, there are generally several tooth pairs which are simultaneously in contact. The contact in each tooth pair takes place along a straight line, which coincides with one of the generators in each tooth. In order to calculate the tooth stresses, we assume that the load intensity w is constant along all the contact lines. The value 490 Tooth Stresses in Helical Gears of w at any instant is then equal to the total contact force W, divid.d by the total contact length Lc' w (17.1) In this section of the chapter, we determine the value of W, corresponding to any specified value of the applied torque. And in the following section, we will describe how to calculate the contact length Lc. The direction n~ of the normal to the tooth surface at A, when A is a point on the contact line, was given by Equation (14.94), n~ = cos \"'b [sin t/ltp nx(O) + cos t/ltp ny(O)] - sin \"'b nz(O) (17.2) In the absence of friction, the contact force acts in the direction opposite to n~, and its component parallel to the gear axis is therefore (w sin \"'b). Hence, the component perpendicular to the gear axis, which is the useful component, is equal to (W cos \"'b) \u2022 The base cylinder of gear 1 is shown in Figure 17.1, with Contact Length 491 the plane of action of the contact force touching the base cylinder. The diagram also shows the component of the contact force perpendicular to the gear axis. We take moments about the axis, to obtain a relation between the applied torque M1 and the contact force W, (17.3) and we use the same method to find the corresponding relation between the contact force and the torque M2 appl ied to gear 2, (17.4) The contact force is found from either of these equations. By combining the two equations, we obtain a relation between M1 and M2 , which is the same as Equation (11.3), the corresponding relation between the torques applied to a pair of spur gears. (17.5) Contact Length As we stated earlier, there generally several tooth pairs in contact at any instant, and the contact length Lc is the sum of the contact lengths on each of these tooth pairs. In this section, we will derive a general expression for Lc' It turns out that we do not often need to make use of the general expression, since the cases required for the stress analysis are always special, and therefore simpler. However, it is a matter of interest to have the general result, and it also helps to determine when the maximum and minimum values of Lc occur. A transverse section through the gear pair is shown in Figure 17.2, with the plane of action touching the two base cylinders. As usual, the ends T1 and T2 of the path of contact are the points where the tip cylinders intersect the plane of action. Figure 17.3 shows the plane of action, with the axial lines through T1 and T2 meeting the transverse plane z=O at T10 and T20 , and meeting the transverse plane z=F at T1F and T2F \u2022 The region of contact is the rectangle T10T20T2FT1F. We stated in Chapter 14 that the lines of contact on the different contacting tooth pairs can be represented by a set of diagonal lines in the region of contact, each making an angle \"'b with the gear axis, and with a vertical spacing equal to the transverse base pi tch Ptb. To find the length of the contact lines in the rectangle, it is helpful to construct two additional triangles T'T 10T1F and T10T\"T20 , as shown in Figure 17.3. The value of Lc is then found as the length of the diagonal lines in triangle T' T\"T 2F' minus the lengths in triangles T'T 10T1F and T10T\"T20 \u2022 We proved in Chapter 14 that the lengths T' T 1 F and T 1 F T 2F are equal to mFPtb and mpptb' where mF and mp are the face contact ratio and the profile contact ratio, given by Equations (14.68 and 14.64), _1_ Ptb F tan \"'b (17.6) Contact Length 493 The plane of action. In addition, the length T'T2F is equal to mcptb' where mc is the total contact ratio, equal to the sum of mF and mp , (17.8) In order to find the value of Lc' we first consider a general triangle of height mPtb' where m can represent any of the contact ratios me' mF or mp. This triangle is shown in Figure 17.4, and the upper contact line is shown in a typical position, lying a vertical distance ePtb below the top corner of the triangle, where e is any number between 0 and 1. The number of contact lines in the triangle is equal to 494 Tooth Stresses in Hel ical Gears (n +1), where n represents the integral part of the number e e (m-e). If e is greater than m, there are no contact lines in the triangle, and the value required for ne is -1. We therefore define a function, n int(f) (17.9) where f is any number, and n is the largest integer which is less than or equal to f. If, for example, f has the values 2.2, 1.0 and -0.3, the corresponding values of n are 2, 1 and -1. The val ue of n e can then be expressed by the funct ion, n e int(m-e) (17.10) In the triangle shown in Figure 17.4, the upper contact line has a length (m-w)ptb/sin ~b' The next contact line is shorter than the first by Ptb/sin ~b' and so on. The total contact length Le can therefore be expressed as an arithmetic series, whose sum is given by the following expression, (17.11) We now apply this result to the three triangles in If we use this method to calculate the contact length Lc for various values of e, we will find the following results. Minimum and Maximum Values for Lc 495 The value of L is always a minimum when e is zero, and a c contact line passes through the upper corner T10 of the region of contact. And the value of L is a maximum when e is equal to c [mF - int(mF)], and a contact line passes through the other upper corner T1F of the contact region. Minimum and Maximum Values of Lc For the purpose of the stress analysis, we would expect to be most interested in the minimum value of Lc' since this corresponds to the maximum load intensity. Now that we know that the contact length is a minimum when a contact line passes through T10 , it is possible to find simpler expressions for the value Lcmin \u2022 We can simplify the expressions further, if we consider only gear pairs in which every transverse section has either one or two contact points. This condition means that the profile contact ratio lies between the following limits, < 2 (17.16) and this range includes all gear pairs of normal design. In the transverse section shown in Figure 17.2, there are two points Q and Q' marked on the plane of action. Point Q lies a distance Ptb below T l' and Q' lies a distance Ptb above T2\u2022 If the diagram represented a spur gear pair, Q and Q' would be the points on the path of contact corresponding to the ends of the period of single-tooth contact. In a helical gear pair, there is generally no period of single-tooth contact, because the total contact ratio mc is usually larger than 2. However, Q and Q' would represent the ends of the period of single-tooth contact in any particular transverse section, and it is therefore still customary to refer to these points as the end points of single-tooth contact. The region of contact is shown again in Figure 17.5, with the axial lines through Q and Q' cutting the transverse plane z=O a~ QO and QQ' and cutting the transverse plane z=F at QF and Qp.. We have stated that the value of Lc is a minimum when a contact line passes through point T 10. There must simultaneously be a second contact line through QO' since the distance between T10 and QO is equal to the transverse base pitch Ptb' Due to the symmetry of the rectangle, we can also argue that Lc is again a minimum when there are contact lines through T 2F and QF' We now consider a particular gear pair, with the contact lines shown in Figure 17.5. One contact line passes through point T10 , while a second line starts at QO' and intersects the plane z=F at point AF , somewhere between QF and QF' For this situation to be possible, the length mFPtb must be less than (2-mp)ptb' as we can see from the diagram. Such a gear pair is therefore defined by the condition, (17.17) and will be referred to as a very low face contact ratio (VLFCR) gear pair. A spur gear pair, in which the face contact ratio is zero, would fit into this category. The condition given by Equation (17.17) is equivalent to the statement that the total contact ratio mc is less than 2. This means that there are periods of the meshing cycle when only one tooth pair is in contact, which is the situation shown in Figure 17.5. The contact length Lcmin for this case can be read directly from the diagram, L . cmln F cos \"'b (17.18) Minimum and Maximum Values for Lc 497 The same region of contact is shown in Figure 17.6, but the contact line has moved up, so that it now passes through point Qp., and a new contact line is about to enter the region at T2F \u2022 During the period when the contact line moves between the positions of Figures 17.5 and 17.6, there is only one tooth pair in contact, and the contact length Lc remains constant, with the value equal to Lcmin given by Equation (17.18). The region of contact for a second gear pair is shown in Figure 17.7. The contact line which starts at QO now intersects the plane z=F at a point between QF and T1F \u2022 The face contact ratio must lie wi thin the following range, 498 Tooth Stresses in Helical Gears < (17.19) and this type of gear pair will be described as a low face contact ratio (LFCR) gear pair. We know that the contact length is at its minimum value, since one contact line passes through T10 \u2022 To calculate the value of Lcmin ' we take the length of the contact line through QO' and we add the length of the short contact line near T2F , L . cmln F cos 1/Ib + Ptb (m +m -2) sin 1/Ib F P The expression is simplified if we use Equation (17.6) to express Ptb in terms of F, L . cmln (17.20) Lastly, we consider gear pairs in which the face contact ratio is greater than 1, > (17.21) Gear pairs that fall within this category are known as normal helical gear pairs, since most helical gear pairs are designed with a face contact ratio larger than 1. The region of contact for a gear pair of this type is shown in Figure 17.8, with the contact lines in the positions Minimum and Maximum Values for Lc 499 corresponding to the minimum contact length. Starting from the left, there is one contact line passing through QQ' then there are a number of complete contact lines stretching from the bottom edge to the top edge of the region, and finally there are either one or two lines which intersect the right-hand edge. To find the value of Lcmin' we consider in turn each of the three groups of contact lines just described. We start by defining two new quantities nc and nF , as the integer parts of mc and mF , (17.22) (17.23) The number of contact lines crossing the upper edge of the region is nF , which means that the number of complete lines is (nF-1). The total number of contact lines is nc ' so the number crossing the right-hand edge is (nc-nF). Hence, the contact length Lcmin is found as follows, L . cmln Ptb \u2022\u2022 1. [1 + mp (nF-1) + (m -n ) + (m -n +l)(n -nF-1)] sIn \"'b c c c c c The result is then simplified, and expressed in terms of the face-width F, L . cmln 500 Tooth Stresses in Helical Gears We pointed out earlier that the maximum load intensity on a gear tooth corresponds to the minimum contact length, and for this reason we derived expressions for Lcmin ' However, as we will show later in this chapter, the fillet stress is often a maximum when the contact line passes through the corner T1F of the contact region, and this occurs when the load intensity is a minimum. We therefore also need expressions for Lcmax ' the maximum contact length. Minimum and Maximum Values for Lc lie in the following range, < The contact length is again the sum of the two lengths, and, as usual, we express the result in terms of F, 5{)1 (17.27) 502 Tooth Stresses in Helical Gears lower edge of the region is then equal to (nFP+2), and the total number of contact lines in the region is (nF+2). Hence, the number of complete contact lines is (nFP+1), and the number of lines crossing the left-hand edge of the region is (nF-nFP)' By considering the three groups of contact lines described earlier, we-obtain the following expression for the contact length, As before, we simplify this result, and express Lcmax in terms of F, Contact Stress In the last section of Chapter 14, we proved that when A is a contact point between a rack and a pinion, the line of contact through A and the common normal at A both, lie in the plane of action. The same is true when A is a contact point between a pair of helical gears. To prove this statement, we need only consider the imaginary rack between the gears, and make use of the result just stated, first for one gear and the imaginary rack, and then for the second gear and the imaginary rack. The plane of action for a gear pair is shown in Figure 17.12, with the contact line GA making an angle..pb with the n direction, as we proved in Equation (14.93). Near z point A, the tooth surfaces can be represented by two circular cylinders in contact, with their axes lying in the plane of action. Their radi i are shown as Pc 1 and Pc2' with the subscript c indicating that these are the radii of curvature when we make a section through the cylinders perpendicular to the line of contact. If we make a transverse section, as shown in the diagram, the cylinders appear as ellipses. For gear 1, the semi-minor axis of the ellipse is Pc1 ' while the semi-major axis is equal to (pc 1/cOS ..pb)' The radius of Contact Stress 503 curvature Pt 1 at point A in the transverse section through the tooth profile is then equal to the radius of curvature at the corresponding point of the ellipse, 2 Pc l (17.31) The corresponding equation for gear 2 can be written down immediately, (17.32) The maximum contact stress 0c between two cylinders of radii Pc1 and Pc2 was given by Equation (11.5),"
        ]
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        "image_filename": "designv10_4_0003158_robot.2002.1013705-Figure1-1.png",
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        "caption": "Figure 1: Coordinate frames",
        "texts": [
            " Finally, Section 5 provides conclusions. 2. Online pattern Generation 2.1 Coordinate Frames A 43-DOF biped model with rotational joints is considered in this study, which consists of two 6-DOF legs, two 7-DOF arms, two 3-DOF hands, a 4-DOF neck, two 2-DOF eyes and a torso with a 3-DOF waist. To define mathematical quantities, a world coordinate frame 3 is fixed on the floor where the biped robot can walk and a moving coordinate frame is attached on the center of the waist to consider the relative motion of each particle (see Figure 1). In modeling, five assumptions are defined as follows: (1) The biped robot consists of a set of particles, (2) The foothold of the biped robot is rigid and not moved by any force and moment, (3) The contact region between the foot and the floor surface is a set of contact points, (4) The coefficients of friction for rotation around the X, Y and Z-axes are nearly zero at the contact point between the feet and the floor surface and (5) The feet of the robot do not slide on the contact surface. 2"
        ],
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    {
        "image_filename": "designv10_4_0002785_s0951-8320(00)00106-x-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002785_s0951-8320(00)00106-x-Figure1-1.png",
        "caption": "Fig. 1. Link and joint parameters.",
        "texts": [
            " The classi\u00aecations for both the kinematic and the dynamic reliabilities can further be extended using the number of degrees of freedom constrained for the end-effector location. The procedure can also be generalized to categorize using the constraints on the end-effector velocity. Manipulator kinematics deals with the study of the spatial con\u00aeguration of the robot arm (in particular the relation between joint variables and the position and the orientation of the end-effector) as a function of time without regard to the forces/moments that cause the motion. The link and joint parameters of a general robotic arm are shown in Fig. 1. Four geometric parameters are associated with each link/ joint pair; the distance between the links di and the joint angle u i determine the relative position of neighboring links, and the link length ai and the twist angle a i determine the structure of links. For a revolute joint, di, ai, and a i are the arm parameters, and u i is the joint variable. For a prismatic joint, u i, ai and a i are the arm parameters, and di is the joint variable. The forward (or direct) kinematics problem, i.e. determination of the end-effector position and orientation from known arm parameters and joint variables, is solved using the Denavit\u00b1Hartenberg notation [10]"
        ],
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    },
    {
        "image_filename": "designv10_4_0000076_j.ijfatigue.2019.105353-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000076_j.ijfatigue.2019.105353-Figure11-1.png",
        "caption": "Fig. 11. Cumulative damage contour of the bogie frame after weld polishing.",
        "texts": [
            " Such assessment result clearly seems to be a dilemma that might not ensure the running safety and reliability of bogie frames, primarily due to improper selection of as-welded joints in BS 7608. Therefore, to further improve the design lifetime based on assessment procedures at the presence of MNIEF, a weld toe polishing method was determined in terms of BS 7608 and current manufacturing guidelines. The calculation clearly shows that the lifetime due to polishing is discounted to about 135 million kilometers (see Fig. 11) larger than that from as-welded joints. In view of potential failure hazard of welded defects inside the highspeed powered bogie under extreme service environments, the newlydesigned frame should be further examined for a higher life safety factor although current safety factor 12.5 has been acquired in terms of estimated 135 million kilometers to actual 10.8 million kilometers. According to BS 7608, after weld toe polishing, the knee point of fatigue S-N curve can be increased to 1.5 times of the as-welded joints. Meanwhile, the inverse slope can be increased from 3 to 3.5. Therefore, the weld toe polishing was virtually introduced by adopting the modified fatigue S-N curve, and the calculated cumulative damage D was plotted in Fig. 11. It can be clearly found that the maximum D is 0.08 around the journal guidance seat, thus indicating the significantly improved fatigue life of the bogie frame. Compared with original assessment procedure in Fig. 9, the maximum D has been significantly decreased from 0.86 to current 0.08 at the presence of MNIEF. Nevertheless, the service safety and reliability are still an important concern for high-speed railway with increased speed. It is well-known that complex environments can necessarily produce a detrimental effect on the damage of welded materials",
            "1 and measured fatigue P-S-N curves are adopted for revealing the maximum fatigue cumulative damage region of the bogie welded frame with gear meshing excitation and weld toe polishing treatment, as plotted in Fig. 14. Compared with well-defined material grade based on BS 7608, it can be clearly observed that no distinct damage still takes place on the BM region of entire welded frame. However, the maximum fatigue cumulative damage (Dmax) is 0.0009 located at the journal guidance seat (as a welded region), which is considerably lower than those than original Fig. 9 (Dmax= 0.86) and improved Fig. 11 (Dmax= 0.08). Therefore, such Dmax= 0.0009 can be discounted to the total life of about 12,000 million kilometers. The safety factor of key load-carrying Fig. 12. The picture of bogie frame details and specimens. Note that the frame was actually polished around the weld and then HCF specimens were also smoothed. components of powered bogie frame can be estimated as 12000/10.8 \u2248 1111. Such a fairly high safety factor of welded frames made of S355J2W validates the applications of new steel grade and weld toe polishing technique"
        ],
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    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.10-1.png",
        "caption": "Figure 4.10. Backlash.",
        "texts": [
            " Moreover, any change in the temperature will cause changes in the dimensions of both the gear-box casing and of the gears. A gear pair must therefore be designed in a manner that makes allowance for thermal expansion, for center distance error, and for cutting errors in the gear teeth. To prevent the teeth of the two gears from jamming together, the tooth thickness of each gear is chosen so that contact will occur on one face only, leaving a small gap at the opposite face. This gap, which can be seen in the gear pair shown in Figure 4.10, is known as the backlash. The size of the gap can be defined in a number of different ways, particularly in the case of a helical gear pair, and each method leads to a slightly different value for the backlash. It is common practice to refer simply to the backlash of a gear pair, without specifying which type of backlash is meant. This practice is quite acceptable, provided the word backlash is used in a general sense to refer to the gap between the teeth of the two gears. However, when a value is assigned to the backlash, it is preferable to specify which type of backlash is intended"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure10.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure10.1-1.png",
        "caption": "Figure 10.1. A rigid bar rolling on the fixed base circle.",
        "texts": [
            "33, 9.34) (9.36) (9.25) (9.26) (9.27) (9.28) (9.29 ) (9.30) (9.31) (9.32) (9.33, 9.34) Chapter 10 Curvature of Tooth Profiles Involute Radius of Curvature The radius of curvature at any point of an involute is found most easily, by making use of one of the special propert ies of the curve. We pointed out in Chapter 2 that the involute can be represented as the path followed by point A of a rigid bar, while the bar rolls without slipping on a circle of radius Rb \u2022 The bar and the circle are shown in Figure 10.1, and the contact point is labelled E. Since E is also the instantaneous center of the bar, the path of A coincides momentarily with the circle whose center is E, and the radius of curvature p of the involute at point A is therefore equal to the length EA, p EA ( 10. 1) If A is the point of the involute at radius R, as shown in Figure 10.2, the angle ECA is equal to the profile angle ~R' as we proved in Equation (2.9), and the radius of curvature can therefore be expressed as follows, p (10.2) Euler-Savary Equation The equation just derived gives a very simple method for calculating the radius of curvature, at any point on the involute section of a gear tooth profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000263_10426914.2019.1643473-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000263_10426914.2019.1643473-Figure1-1.png",
        "caption": "Figure 1. Schematic of GMAW additive manufacturing system.",
        "texts": [
            " The forming appearance and effective deposition rate per power of two depositions were compared, and the impact of welding processes on morphology, microstructure, and mechanical properties was studied. 316L stainless steel welding wire with 0.8 mm diameter and a sheet with a length of 250 mm, width of 100 mm, and thickness of 5 mm were selected in this study. The substrate surface was polished and dried with acetone before the test. The GMAW additive manufacturing system used in the test is given in Fig. 1, being consisted of LORCH S3 Robot MIG XT welding power supply, FANUC M-10ia six-axis robot, and R-30iB Mate robot control cabinet. Because of the fast heat dissipation of the substrate, it was difficult for the first two layers to weld with small-current welding, which affected the subsequent deposition. Therefore, the method of \u201c bottom layers with high current, upper layers with small current\u201d was adopted[10], and the scanning speed was 30 cm/min. The 99.999% of high-purity argon gas with the flow of 20 L/min was chosen as the protective gas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000127_s40964-019-00083-9-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000127_s40964-019-00083-9-Figure8-1.png",
        "caption": "Fig. 8 Simulation results as a temperature distribution while scanning over the bridge and b maximum temperature over time",
        "texts": [
            " That leads to a frequency of 100\u00a0Hz for a scan speed of 10\u00a0mm/s. Within the simulation, an ambient temperature of 22\u00a0\u00b0C was defined and the part is thermally isolated to the surrounding volume. As part material, stainless steel with a density of 7750\u00a0kg/m3, a heat transfer coefficient of 15.1\u00a0W/m\u00a0K and a specific thermal capacity of 480\u00a0J/kg\u00a0K was chosen. The results of the simulation can be evaluated in different ways. The main result of the simulation is the maximum temperature over time which can be used as the basis for different analysis. Figure\u00a08a shows an exemplary temperature distribution while scanning over the bridge structure and the results of the maximum temperature development, it is notable that the temperature rises within the five scans and that the maximum of each scan is at the bridge (see Fig.\u00a08b). To analyse the influence of the scan speed and the laser power on the maximum temperature, different parameter combinations (10, 20, 50, 100, and 1000\u00a0mm/s and 80, 160, 240, and 320\u00a0W) were applied, and the resulting maximum temperatures were compared. In Fig.\u00a09a, an almost linear increase of the maximum temperature for an increasing laser power is shown. The relation between the scan speed and the temperature shows a strongly increased temperature for slow scan speeds (see Fig.\u00a09b). To compare the influence of the parameters on the relative height of the steps, the quotient between the temperature on the bridge section and the temperature at the basis of the bridge is computed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003859_detc2007-34210-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003859_detc2007-34210-Figure1-1.png",
        "caption": "Figure 1: A Model of Universal Hypoid Generators",
        "texts": [],
        "surrounding_texts": [
            "As the basis of computerized design and analysis of spiral bevel and hypoid gear drives, a Universal Generation Model (UGM) has been developed and can be applied to the tooth surface geometric description of both face-milled and facehobbed spiral bevel and hypoid gears [14-17]. The UGM can calculate the coordinates of hypoid gear tooth surfaces generated by the cutting tools whose blade edge geometry is generally defined by four parts, tip edge, Toprem, profile, and Flankrem. Each machine setting is analytically described as a motion element associated with a coordinate system. The UGM incorporates the UMC which defines the machine settings in a dynamic manner by polynomials as, \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23a7 ++++= ++++= ++++= ++++= ++++= ++++= ++++= ++++= 4 4 3 3 2 210 4 4 3 3 2 210 4 4 3 3 2 210 4 4 3 3 2 210 4 4 3 3 2 210 4 4 3 3 2 210 4 4 3 3 2 210 4 4 3 3 2 210 qiqiqiqiii qjqjqjqjjj qqqq qXqXqXqXXX qEqEqEqEEE qsqsqsqsss qXqXqXqXXX qRqRqRqRRR mmmmmm pppppp mmmmmm rrrrrr bbbbbb aaaaaa \u03b3\u03b3\u03b3\u03b3\u03b3\u03b3 (1) Here, q is the cradle rotation angle; aR is the ratio of generating roll; bX is the sliding base; rs is the cutter radial setting; mE is the offset; pX is the work head setting; m\u03b3 is the root angle; j is the swivel angle; and i is cutter head tilt angle, respectively. 2 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/05/2016 Ter Figure (1) illustrates the kinematical description of the machine settings of a model of universal hypoid generators. Each machine setting is represented by a moving element whose motion is described a polynomial function in terms of cradle rotation angle. We call the machine settings represented by Equation (1) the universal motions. The universal motions can be implemented on CNC hypoid gear generating machines by machine software. The first terms in Equation (1) represent traditional basic machine settings. There are totally forty (8\u00d7 5) coefficients in Equation (1). In this paper, we will generally call them the universal motion coefficients. Since the cradle rotation angle is the parameter of the universal motions, the universal motions can only be applied to the generated members whose tooth flank form geometry can be generally represented by a position vector and a unit normal vector in a parametric form as, \u23aa \u23a9 \u23aa \u23a8 \u23a7 = = = 0),,( ),,( ),,( quf qu qu \u03b8 \u03b8 \u03b8 nn rr (2) Here, ( u ,\u03b8 ) are generating surface parameters and q is the parameter of the generating motion. And, 0),,( =quf \u03b8 is the equation of meshing relating the three parameters for a generated pinion or gear. Using Equation (2) the theoretical tooth surface geometry can be numerically represented by the coordinates of a group of surface points defined from Figure 2. A grid of n lines and m columns is defined in the L-R axial plane of the pinion or gear. A point called the reference point is specified on both concave and convex tooth surfaces. The reference point is usually chosen in the center of the grid and is used to define the tooth difference angle by which the tooth thickness or tooth size is calculated. Given a point by (L, R) the following system of nonlinear equations can be used to solve for the surface parameters. Copyright \u00a9 2007 by ASME Copyright \u00a9 2007 by The Gleason Works ms of Use: http://www.asme.org/about-asme/terms-of-use \u23aa \u23aa \u23a9 \u23aa\u23aa \u23a8 \u23a7 = = =+ 0),,( ),,( ),,(),,( 22 quf Lquz Rquyqux \u03b8 \u03b8 \u03b8\u03b8 (3) Consequently, the coordinates ( x , y , z ) and the unit normal components ( xn , yn , zn ) of the corresponding surface point can be obtained, which are called the tooth surface nominal data representing the theoretical target tooth surfaces. In case of inverse engineering, the target tooth flank form may be numerically represented by the measured coordinates of a group of grid points of a master hypoid pinion or gear. In order to visually represent the tooth flank form error, a local coordinate system S(X, Y,\u03b4 ) is defined for each side of tooth flank and shown in Figure 3. We assume that the positive direction of axis \u03b4 is the same as that of the tooth surface normals whose positive directions are defined as pointing out of the tooth from inside to outside. Under such assumption, a positive error indicates a thicker tooth than the target one, and a negative error indicates a thinner tooth. Each side of tooth surfaces is rotated at an angle 1\u03b1 and 2\u03b1 respectively so that at the reference point coordinate 0=y . The nominal data of the grid points of the convex and concave tooth surfaces are then transformed into the same coordinate system as that of the Coordinate Measuring Machine (CMM) and can be numerically represented by the position vectors and unit normals as, Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/05/2016 [ ] [ ]\u23aa \u23a9 \u23aa \u23a8 \u23a7 = = Ti z i y i x i Tiiii nnn zyx )()()()( )()()()( n r )2,...2,1( mni \u00d7= (4)"
        ]
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure2.18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure2.18-1.png",
        "caption": "Fig. 2.18 Chinese chain windmill",
        "texts": [
            "17, being surviving examples, are still in use, although only serving aesthetical purposes. The noria has 120 water collection compartments and could raise more than 95 L of water per minute. A noria in Iraq in the 10th century could lift as much as 2550 L per minute (Hill 1996a). Wind pumps have also been used in South-eastern Asia and China for much longer time than in Europe, mainly for irrigation and/or sea salt production which needs pumping sea water into drying pans. The Chinese sail windpump (Fig. 2.18) was first used thousands years ago (Fraenkel 1986). The traditional Chinese design was constructed from wire-braced bamboo poles carrying fabric sails. Many Chinese windmills rely on the wind generally blowing in one direction, because their rotors are of fixed orientation. 2.2 Various Ancient Machines 25 Al-Jazari invented five machines for raising water; all were described in his book in 1206 (Al-Jazari 1973). An example of them is shown in Fig. 2.19. The dynamic scale model, shown in Fig. 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000638_s11071-021-06826-0-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000638_s11071-021-06826-0-Figure3-1.png",
        "caption": "Fig. 3 The schematic diagram of the mechanical structure of the 2-DOF robot manipulator",
        "texts": [
            " 2 Using different initial values listed in Table 1, pictures a, b, c provide the evolution of \u03be , \u03b7, s with Ts = 3s and Tc = 0.5s; pictures d, e, f provide the evolution of \u03be , \u03b7, s with Ts = 1s and Tc = 0.1s; pictures g, h, i provide the evolution of \u03be , \u03b7, s with Ts = 0.01s and Tc = 0.02s 5.2 Simulations for robot manipulator In this subsection, the 2-DOF robot manipulator is selected to verify the effectiveness of the main results in Theorem 3. The mechanical structures of the 2- DOF manipulator are shown in Fig. 3, and the specific dynamics is presented as follows: [ M11 M12 M21 M22 ][ q\u03081 q\u03082 ] + [ C11 C12 C21 C22 ][ q\u03071 q\u03072 ] + [ g1 g2 ] = [ \u03c41 \u03c42 ] + [ d1(t) d2(t) ] (5.47) where M11 = p1 + 2p2 cos(q2), M12 = M21 = p3 + p2 cos(q2), M22 = p3, C11 = \u2212p2 sin(q2)q\u03072, C12 = \u2212p2 sin(q2)(q\u03071 + q\u03072), C21 = p2 sin(q2)q\u03071, C22 = 0, g1 = g p4cos(q1) + g p5cos(q1 + q2), g2 = g p5cos(q1 + q2), p1 = m1r21 +m2(l21 + r22 )+ I1 + I2, p2 = m2l1r2, p3 = m2r22 + I2, p4 = m1r1 + m2l1, p5 = m2r2, I1 = 1 3m1l21 , I2 = 1 3m2l22 , g = 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000072_s40192-019-00149-0-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000072_s40192-019-00149-0-Figure2-1.png",
        "caption": "Fig. 2 a Four bridge structures were built on a build plate of the same nominal chemical composition (IN625). b Parts were separated using wire EDM with the build plate attached for residual strain and distortion measurements after the build process",
        "texts": [
            " The AMB2018-01 tests consist of AM LPBF 3D metal alloy builds of a bridge structure geometry with 12 legs of varying size, as shown in Fig.\u00a01. The bridge-shaped structures were additively produced from virgin IN625 powder using an EOS M2701 system with modifications for in\u00a0situ measurements. The 12 legs consist of 4 replications of a section described in the green box in Fig.\u00a01. Each section consists of 3 distinct leg sizes: 5\u00a0mm, 0.5\u00a0mm, and 2.5\u00a0mm. The AM parts were built on build plates of nominally the same alloy (IN625) as shown in Fig.\u00a02. The build plates were 100\u00a0mm squares with 12.7\u00a0mm thickness, mounted to the middle of the build area of the LPBF machine. The bridge-shaped structures were built using the nominal parameter set for IN625. The contour laser power and scan speed were 100\u00a0W and 900\u00a0mm/s, respectively, and the infill laser power and scan speed were 195\u00a0W and 800\u00a0mm/s, respectively, with a hatch distance spacing of 100\u00a0\u00b5m. The build consisted of a total of 625 layers, with a 20-\u00b5m layer height. According to the manufacturer, the D4\u03c3 laser diameter on the build plane is 85\u00a0\u03bcm during the contour scans, but defocuses to 100\u00a0\u03bcm for the infill scans",
            " The part designs, build plate, build layouts, scan strategy, and scan parameters are further detailed on the AM-Bench website and another manuscript (Heigel et\u00a0al., unsubmitted). For residual stress/strain measurements, four (4) bridge-shaped 1 Mention of commercial products does not imply endorsement by the National Institute of Standards and Technology, nor does it imply that such products or services are necessarily the best available for the purpose. 1 3 parts were built on a build plate as shown in Fig.\u00a02. After the build was completed, each part including the surrounding attached build plate was separated from other parts using wire electric discharge machining (EDM). All residual stress/strain measurements were performed on individual sections extracted from the initial build plate. Each section included the part still attached to a portion of the build plate (as shown in Fig.\u00a02b). The parts were measured in the asbuilt condition. Figure\u00a02a shows the build plate with 4 parts attached after the build process and (B) the separation of two of the parts after the build process. The residual elastic strains within the as-built IN625 parts were measured using neutron diffraction on the BT8 diffractometer at the NIST Center for Neutron Research (NCNR), energy-dispersive synchrotron X-ray diffraction at the ID1A3 beamline at the Cornell High Energy Synchrotron Source (CHESS), and the contour method at University of California, Davis, and Hill Engineering, LLC",
            " For each location where zz = 0 applies, there are three equations of this kind (one d-spacing for each orientation measured) forming a system that can be solved for the three unknowns ( xx , yy , and d0). Equation\u00a01 can be used to obtain explicit expressions (Eq.\u00a02) for the three orthogonal measurement directions: X = (0\u00b0, 90\u00b0), Y = (90\u00b0, 90\u00b0), and Z = (0\u00b0, 0\u00b0): Once the d0 is calculated, the elastic strain components for all measured positions were calculated. This same system of equations can be used for the location where zz = xx = 0. Energy\u2011Dispersive X\u2011Ray Diffraction Measurements Energy-dispersive diffraction measurements were conducted on part 2 (Fig.\u00a02) on the ID1A3 beamline at the Cornell High Energy Synchrotron Source (CHESS). The ID1A3 beamline utilizes a continuous spectrum incident X-ray beam with (2a) xx = dx \u2212 d0 d0 = Fxx(0 \u25e6, 90\u25e6) xx + Fyy(0 \u25e6, 90\u25e6) yy + Fzz(0 \u25e6, 90\u25e6) zz (2b) yy = dy \u2212 d0 d0 = Fxx(90 \u25e6, 90\u25e6) xx + Fyy(90 \u25e6, 90\u25e6) yy + Fzz(90 \u25e6, 90\u25e6) zz (2c) zz = dz \u2212 d0 d0 = Fxx(0 \u25e6, 0\u25e6) xx + Fyy(0 \u25e6, 0\u25e6) yy + Fzz(0 \u25e6, 0\u25e6) zz effective spectrum from 40\u00a0keV to 200 + keV, which corresponds to a wavelength of 0.0248\u00a0nm to 8.2656 \u00d7 10\u22123\u00a0nm. Previous efforts by others have utilized energy-dispersive X-ray diffraction for high-resolution residual strain mapping of large engineering samples [11\u201313]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002933_02783640022066833-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002933_02783640022066833-Figure1-1.png",
        "caption": "Fig. 1. The snakeboard model and a robotic prototype",
        "texts": [
            " 1994) is a variant of the skateboard in which the passive wheel assemblies can pivot freely about a vertical axis. By coupling the twisting of the human torso with the appropriate at University of Bristol Library on March 18, 2015ijr.sagepub.comDownloaded from turning of the wheel assemblies (where the turning is controlled by the rider\u2019s foot movements), the rider can generate a snakelike locomotion pattern without having to kick off the ground. A simplified model of the snakeboard is shown in Figure 1. We assume that the front and rear wheel axles move through equal and opposite rotations. This is based on observations of human snakeboard riders who use roughly the same phase relationship. A momentum wheel rotates about a vertical axis through the center of mass, simulating the motion of a human torso. The snakeboard\u2019s position variables, (xc, yc, \u03b8) \u2208 SE(2), are determined by a frame affixed to its center of mass. The shape variables are (\u03c8, \u03c6), and so the configuration space is Q = M \u00d7 G = (S1 \u00d7 S 1) \u00d7 SE(2), with q = (\u03c8, \u03c6, xc, yc, \u03b8) \u2208 Q"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000189_j.jmapro.2019.04.019-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000189_j.jmapro.2019.04.019-Figure1-1.png",
        "caption": "Fig. 1. (a) 3D model of the thin wall without-support, and (b) half of finite element model.",
        "texts": [
            " (3) The surface of the molten pool is assumed to be flat without respect to evaporation and capillary flow. (4) Thermal conduction, thermal convection and thermal radiation are the three main heat transfer modes in SLM. In order to simplify the calculation of computer, thermal radiation is ignored. (5) The type of laser is assumed to be Gaussian laser. In this paper, the FEM is applied to replace the real experiment to simulate the forming process of the thin wall without-support during SLM. As shown in Fig. 1(a), 3D model of the thin wall without-support is presented. The blue part represents the powder bed, the black part represents the substrate and the red part represents the thin wall. Due to the ultra-high laser energy input, the local high temperature is generated on the surface of the powder layer. And the thermal resistance is generated due to the low thermal conductivity of the powder layer, which results in the high temperature gradient. Taking into account the limited computing power of the computer, the dimensions of the powder bed acted as the substrate are 3 \u00d7 2 \u00d7 0.5mm. The thin wall contains five layers. The dimensions of each layer are 3 \u00d7 0.6 \u00d7 0.03mm. Also the FEM is symmetric with respect to the X-Y plane, so only half of the model needs to be established for reducing the computation time. Half of the FEM is depicted in Fig. 1(b). The density of the powder layer is usually set 60% [26]. The main processing parameters are shown in Table 1. The scanning strategy is reciprocating. The dimensions of mesh are 60 \u00d7 30 \u00d7 30 \u03bcm. In actual SLM, the powder bed is difficult to be fully preheated. In this paper, the powder bed acted as the substrate is preheated by a 10W laser and the scan speed is 500mm/s. The simulation process is divided into the following three steps. First, the entire model which includes the added powder layers and the powder bed acted as the substrate is established and meshed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003195_tmag.2004.824127-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003195_tmag.2004.824127-Figure7-1.png",
        "caption": "Fig. 7. Single-phase induction motor with shaded rings.",
        "texts": [
            " 4, the equivalent values of the external resistance and inductance should be divided by four. If it is considered as in series connection as in Fig. 5, the values of the equivalent external resistance and inductance should be multiplied by four. The proposed procedure described above has been applied to many different types of electric machines and drives. Four application examples are presented here. In all examples, the iron cores are treated as nonlinear materials. A single-phase induction motor with shaded rings is shown in Fig. 7. The ratings of the motor are 390 V, four poles, 50 Hz. The simulation is under the locked-rotor operation. Fig. 8 shows the starting torque response. The currents in the stator phase and the shaded ring are shown in Figs. 9 and 10, respectively. The distribution of typical eddy-current density in the shaded ring is shown in Fig. 11. This example is a synchronous generator with the ratings of 6 kVA, 390 V, four poles, 50 Hz (Fig. 12). The rotor has a field winding, a starting cage, and damper windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003409_1.1899688-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003409_1.1899688-Figure4-1.png",
        "caption": "Fig. 4 Illustration of sliding distan positions r \u20209\u2021",
        "texts": [
            "org/terms Downloaded F Xij p r = Rr p R ij p Xij p r=0 + Tzp 4 where ij p =zptan i p /Ri p, i p is the helix angle at radius Ri p ,r p is the angular position of gear p measured from r=0, and R and T are the rotation matrix and the translation vector respectively, defined as R = cos sin 0 \u2212 sin cos 0 0 0 1 , 5 T = 0 0 \u2212 6 The sliding distance sij p r\u2192r+1 was defined as the distance by which a point represented by node ij on gear p slides with respect to its corresponding point on its mating gear as they rotate from position r to position r+1. Assume that the leading edge of the contact zone reaches a node ij of gear p at r=m as illustrated in Fig. 4 a . At this position, node ij meshes with node pq of gear g and is experiencing a nonzero pressure for the first time since the beginning of loading cycle. Position vector Xij p r=m of node ij at r=m is given by Eq. 4 , and since points ij and pq overlap in space, Xpq g r=m = Xij p r=m 7 When the gears are rotated by one incremental rotation to position to r=m+1, as in Fig. 4 b , Xij p r=m+1 is again defined by Eq. 4 . Meanwhile, node pq on gear g no longer overlaps with node ij on 660 / Vol. 127, JULY 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 06/06/201 gear p as gear g rotates about its center Og. The position vector of node pq is obtained by first translating the coordinate frame from the center of gear p Op to the center of gear g Og , then rotating it by g, and finally translating it back to Op: Xpq g r=m+1 = R g Xpq g r=m + TE \u2212 TE 8 Here, g=\u2212 Zp /Zg p, Zp and Zg are the number of teeth of gears p and g, respectively, and E is the center distance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure9-1.png",
        "caption": "Fig. 9. A singular con\u00aeguration of class (RPM, RI, RO, IO, II, IIM).",
        "texts": [
            " 6, where for all three serial subchains point P is on the SP 1 axis, the condition is satis\u00aeed since mB 1 and mC 1 are zero vectors. For the IIM-type con\u00aegurations with three extended legs (as in Fig. 8) the condition is not satis\u00aeed. If only two subchains are singular (similar to Fig. 7), the condition is always satis\u00aeed when the singular subchains are B and C (as in the \u00aegure). When, however, one of the singular subchains is A, then, generally, the matrix A is of rank 5. There are two exceptions. The \u00aerst is represented in Fig. 9, where the singular subchains are A and B and additionally the point Co lies in the plane ABC. The second exception is shown in Fig. 10, where not only points B and C are located on screws SB 1 and SC 1 , but also point A lies in the (vertical) plane de\u00aened by the two screws. Each of Figs 9 and 10 represents, in fact 11 con\u00aegurations, since the elevation of point A can vary. Thus, the set of singularities belonging to the IIM, IO and II types consists of a main 3- dimensional set (Fig. 6), a 2-dimensional set (Fig",
            "2) According to condition (i) and Equation (13), a con\u00aeguration is an RI-type singularity if and only if at least one of the following conditions is satis\u00aeed: either the subchain A is singular (in any way); or subchain B is fully extended; or subchain C is fully extended. Condition (ii) and Equation (12) imply that an RPM-singularity is also of the RO-type in the following three cases: (a) When C is on the SC 1 axis and the plane ABC is perpendicular to mC 2 (Fig. 10 is an example, though subchain B need not be singular). (b) When C is on the SC 1 axis while point B is not on the SB 1 axis, and b_mB 1 . (c) When B is on the SB 1 axis, while point C is not on the SC 1 axis, and the point Co lies in the plane ABC (Fig. 9, though subchain A need not be singular). Thus, four sets are obtained: 15 RPM-type singularities, 14 RPM and RI-type singularities, 14 RPM and RO-type singularities and RPM, RI and RO-type singularities. (3.3) The intersections of the subsets of {3.1} and {3.2} give the 10 singularity classes (Table 2) of con\u00aegurations that are both IIM and RPM. Of these, only \u00aeve classes are non-empty for the mechanism under consideration: (a) (IIM, IO, RPM, RI) has 12 con\u00aegurations with two singular subchains similarly to Fig",
            " The singular subchains must be B and C. The plane ABC must not contain Co and Bo (unlike Fig. 10). (c) (IIM, IO, II, RPM. RI) has 13 con\u00aegurations with three singular subchains as in Fig. 6. (d) (IIM, IO, II, RPM, RO) has 11 con\u00aegurations like the one depicted in Fig. 10. The moving plane ABC contains the points Co and Bo and the subchains B and C are singular in the same way as in Fig. 7. (e) (IIM, IO, II, RPM, RI, RO) has 11 con\u00aegurations in two 1-dimensional sets. The \u00aerst is represented by the con\u00aeguration in Fig. 9. It is similar to Fig. 7 with singular subchains A and B, but point Co is in the plane ABC, allowing for a RO-singularity. The second set is similar to the con\u00aeguration in Fig. 9, however, the non-singular subchain must be B rather than A. (3.4) Only one of the four classes of IIM but not RPM singularities is non-empty: (IIM, IO, RI, RO) consists of 11 con\u00aegurations as in Fig. 8. (3.5) All of the four RPM but not IIM classes are non-empty. (RPM, II, IO) has 15 con\u00aegurations. An example for this class can be obtained from the con\u00aeguration in Fig. 7 by an arbitrarily small perturbation of the subchain C while subchains A and B remain \u00aexed. (RPM, RI, II, IO) has 14 con\u00aegurations and can be illustrated by a variation of Fig. 6 obtained by maintaining the depicted position of the subchains A and B and slightly perturbing subchain C. (RPM, RO, II, IO) has 12 con\u00aegurations. An example is obtained from the con\u00aeguration in Fig. 10 by a small rotation of subchain C about SC 1 . (RPM, RI, RO, II, IO) has 12 con\u00aegurations and a representative can be obtained from Fig. 9 by a small rotation of subchain C about SC 1 . (4) RO- and II-type singularities There are 15 con\u00aegurations that are of the RO and II types but are not IIM nor RPM-singu- larities. From Equation (12), the conditions for RO-type singularity are: (a) Either Co must be in the plane ABC (Fig. 11), or (b) The point A must be in the plane of subchain B (Fig. 12), i.e. b_mB 1 . (5) RI- and IO-type singularities There are 15 con\u00aegurations which satisfy (viii) without being RPM or IIM-type. In these con\u00aegurations the subchain A is singular or one of the other two serial chains is fully extended"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002876_s0022-460x(02)01213-0-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002876_s0022-460x(02)01213-0-Figure13-1.png",
        "caption": "Fig. 13. Driven shaft analytical model.",
        "texts": [
            " Waves are assumed to propagate through the gear elements as if they were part of the same material as the shaft. The element material properties and geometry were made to reflect those of the steel gears available in the lab. The actual configuration for the transverse vibration testing is shown in Fig. 12. The model must also consider the added inertia of the bearings at either end of the shaft in order to accurately predict the propagation parameter. The analysis considers the bearings to be effectively pinned boundary conditions (see Fig. 13). The shaft was tested in two orientations (see Fig. 14). The propagation parameter for the periodic shaft in both configurations are shown in Figs. 15 and 16. Note that there are attenuation regions at lower frequencies for the periodic shaft including the bearing and gear inertias than for the shaft without their inclusion (see Fig. 17). The propagation parameter of a uniform shaft with the mass of the gear added is shown in Fig. 18. Note that although the shaft alone has no attenuation regions, that with the addition of the gear inertia introduces attenuation regions, albeit very small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002841_1.1623761-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002841_1.1623761-Figure2-1.png",
        "caption": "Fig. 2 The position of ball center in Cartesian coordinates and Frenet coordinates",
        "texts": [
            " The results of ball screw\u2019s mechanical efficiency achieved by the present model are compared with those evaluated by the model of Lin et al. 003 by ASME DECEMBER 2003, Vol. 125 \u00d5 717 13 Terms of Use: http://asme.org/terms Downloaded F In the study of the kinematics and dynamics of the ball screw mechanism ~Fig. 1!, four coordinate systems are needed to describe the motion of three components and their contact behavior. The rotating coordinate system, ~x,y,z!, is fixed in space with its z axis coincident with the axis of the screw ~see Fig. 2!, even though it rotates with the same speed as the screw. The Frenet coordinate system, ~t,n,b!, is defined to describe the moving path of the ball center. The motion of a ball enables us to study the kinematics of a ball and the slip behavior arising at the contact areas. The third coordinate system, ~U,V,W!, as Fig. 3 shows, is defined such that its origin is at the center of the ball and the U axis is coincident with the spinning axis of a ball. The fourth coordinate system, (U ,r ,f), is defined to describe to the inertia force and the inertia moment which are produced due to the motion of the ball with a mass of m",
            " and (U ,r ,f), are given as: t5U cos b sin b81r sin f cos b82r cos f sin b sin b8 (2a) n52U sin b2r cos f cos b (2b) b52U cos b cos b81r sin f sin b81r cos f sin b cos b8 (2c) Assuming that a ball has moved an angle w k\u0303 along the helical angle a of a screw with a lead d sin a, then d sin a5 wL 2p (3) where L is the pitch length of the screw, d is the distance between two origins, o and o8 ~ball center!; rm is now defined as the projection length of oo8 on the x-y plane. Then, the coordinate transformation between the ~x,y,z! coordinate system and the ~t,n,b! coordinate system, as Fig. 2 shows, is given as F x y z G5F rm cos w rm sin w wL 2p G1F 2cos a sin w 2cos w sin a sin w cos a cos w 2sin w 2sin a cos w sin a 0 cos a G 3F t n b G (4) 2.2 Inertia Forces of Ball Motion. The three components of the inertia force produced in x-, y- and z-directions respectively due to a ball motion along the screw surface are stated as: Fx52rE 2rb rb E 0 ~rb 2 2U2!1/2E 0 2p x\u0308rdfdrdU (5a) Transactions of the ASME 13 Terms of Use: http://asme.org/terms Downloaded F Fy52rE 2rb rb E 0 ~rb 2 2U2!1/2E 0 2p y\u0308 rdfdrdU (5b) Fz52rE 2rb rb E 0 ~rb 2 2U2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003083_1.1630812-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003083_1.1630812-Figure1-1.png",
        "caption": "Fig. 1 McKibben actuator model",
        "texts": [
            " Matsikoudi-Iliopoulou @20# combines fiber @21# and membrane @17# solutions to obtain the solution of a pressurized cylindrical membrane reinforced with one family of inextensible fibers. This paper combines the theory of Kydoniefs @18# and Matsikoudi-Iliopoulou @20# to generate and solve the static equations for initially cylindrical elastic membranes with two family fiber reinforcement under inner pressure and axial load. The actuator shape and fiber and membrane stresses are calculated and compared with experimental results. 2.1 Coordinate System. Figure 1 shows a McKibben actuator modeled by two families of inextensible fibers reinforcing an elastic, isotropic, and incompressible membrane with uniform undeformed thickness 2h0 . The fibers form constant angles 6a with the generators of the undeformed cylinder. Under the applied inner pressure P and axial force F, the polar coordinates ~R, Q, h! of the undeformed configuration (C0) become ~r, u, z! in the deformed configuration ~C!. The meridional arc length of C is j and the angle between the tangent to C and the z-axis is s ~see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.5-1.png",
        "caption": "Figure 13.5. The helical basic rack.",
        "texts": [
            "2 therefore indicate that the vectors point in the direction upwards out of the drawing. The spur gear and the rack are being viewed in the negative nS direction. A clockwise circular arrow would mean that the vector points downwards into the drawing. It will be the general pract ice, throughout Part 2 of thi s book, to include in each diagram a unit vector represented by a circular arrow, in order to specify the direction of the view being taken. The spur gear and rack of Figure 13.2 are shown again in The Basic Helical Rack 309 The Basic Helical Rack Figure 13.5 shows the basic helical rack, used to define the tooth surface of a helical gear. Just as the basic rack of a spur gear has teeth which are straight-sided, the basic rack in Figure 13.5 has teeth whose faces are flat planes. The angle between the gear axis and the direction of the rack teeth is shown as ~r' and it is called the basic rack helix angle. A plane cut through the rack perpendicular to the gear axis is known as a transverse section of the rack, and a plane cut perpendicular to the rack teeth, in other words perpendicular to n S' is called a normal section. The diagram also shows a transverse section and a normal section through the basic rack. The distances in the two sections between corresponding points of adjacent teeth are called the transverse rack pitch Ptr and the normal rack pitch Pnr",
            " It can be seen from triangle A1A2A3 that there is a relation between the two pitches, (13.1) We define a transverse module mt and a normal module mn in terms of the pi tches of the basic rack, 310 Tooth Surface of a Helical Involute Gear (13.2) (13.3) and the modules are then related in the same manner as the pitches, (13.4) The transverse diametral pitch Ptd and the normal diametral pitch Pnd are defined as the reciprocals of the two modules, (13.5) (13.6) The pressure angles shown in the transverse and normal Independent Parameters of the Basic Rack 311 sections in Figure 13.5 are called the transverse rack pressure angle ~tr and the normal rack pressure angle ~nr. They can be expressed in terms of the tooth dimensions as follows, tan ~tr ht H tan ~nr hn H where H is the tooth depth, and ht and hn are the lengths shown in Figure 13.5 in the transverse and normal tooth sections. These two lengths are related as follows, and from the last three equations, we obtain a relation between the two pressure angles and the helix angle, tan ~tr cos \"'r (13.7) The rack base pitches in the two sections are defined as the distances between adjacent tooth profiles, measured in each case along the common normal. The transverse base pitch Ptbr and the normal base pitch Pnbr are shown in Figure 13.5, and are related to the rack pitches Ptr and Pnr in the following manner, (13.8) (13.9) Independent Parameters of the Basic Rack We have specified the basic rack by means of the following seven quantities: Ptr' Pnr' Ptbr' Pnbr' ~tr' ~nr and \"'r. However, we have shown that there are four relations between the quantities, given by Equations (13.1, 13.7, 13.8 and 13.9). It is clear that only three of the quantities used to specify the basic rack are independent. We will choose to 312 Tooth Surface of a Helical Involute Gear regard Pnr' ~nr and Wr as the three independent parameters, and we now repeat the relations in a form suitable for calculating the remaining four quantities. tan ~tr Basic Rack Reference Plane Pnr cos Wr tan ~nr cos Wr (13.10) (13.11) (13.12) (13.13) In Chapter 2, when we discussed the basic rack profile, we defined the rack reference line as the line along which the tooth thickness and the space width are equal. In the context of a helical rack, the reference line would be a line in the transverse section, as shown in Figure 13.5. If we construct the reference lines in a number of different transverse sections, the lines will all lie in a plane perpendicular to n E, and this plane is known as the rack reference plane, or sometimes the datum plane. Because the tooth profile of an involute rack is straight-sided in the normal as well as the transverse section, a normal section will also intersect the reference plane in a line along which the tooth thickness and the space width are equal. Hence, the rack reference plane can be described as the plane at which the tooth thickness is equal to the space width in both the transverse and the normal sections",
            " We can therefore describe the pitch cylinders of a helical gear pair as the cylinders with radii RP1 and Rp2 ' where the values of these radii are found by applying the theory of spur gear geometry to any transverse section through the gear pair. A similar description can be given for the case of a helical gear and a rack. In this chapter we will consider only the geometry of a gear meshed with its basic rack, and in the following chapter we will discuss the geometry of a gear meshed with an ordinary rack, and that of a pair of gears. Standard pi tch Cylinder of a Heli cal Gear We now study the geometry of a gear with N teeth, whose tooth shape is defined as being conjugate to the basic rack in Figure 13.5. If we consider a single transverse plane through both the gear and the basic rack, as shown in Figure 13.6, the tooth profile of the gear must be conjugate to that of the rack. Hence, the gear tooth profile in the transverse plane can be found by means of the spur gear geometry described in Chapter 2. The profile is therefore an involute defined by a basic rack with pitch Ptr and pressure angle ~tr' The radii of the standard pitch circle and the base circle are then given by Equations (2.27 and 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003979_ac00197a022-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003979_ac00197a022-Figure6-1.png",
        "caption": "Figure 6. Effect of urea and amino acids on glucose response. Curves: glucose only (O), (b) glucose in presence of all amino acids at physiological maximum ( O ) , and glucose in presence of urea at physiological maximum (A). Sample size, 30 ML.",
        "texts": [
            " As the molar concentrations of urea are comparable to that of glucose in body fluids, its presence has always created difficulties in the development of the electrocatalytic glucose sensor. This is especially true for Pt black-based sensors, where the reported errors are as high as 20% resulting from the influence of urea (7). As urea is uncharged in neutral solution and is smaller than glucose, it is not trivial to realize a membrane that will selectively discard urea while allowing glucose to pass through. Fortunately, under the measurement conditions of the present experiment, urea was almost inactive, causing an error of less than 2% (Figure 6) at its physiological maximum (26 mg/dL). Amino acids are also potential physiological interferences, and a considerable amount of work has been done previously dealing with the elimination of their influence. A wide variety of membranes such as polysulfone (4) and Permion 1025 (7) have been employed for this purpose. In the pulsed amperometric mode, the potentials required for amino acid oxidation are much higher (+500 mV) than the one used for glucose oxidation. It is believed that the amino acid oxidation is catalyzed by the metal oxide formation (In, unlike the glucose oxidation, which is inhibited by such a process",
            " Despite this, interference from a mixture of all amino acids (present at their physiological maximum levels) for a bare electrode was so great that the response toward glucose was almost obscured. However, the transport of these amino acids was greatly restricted by the Nafion membrane, probably because of their zwitterionic character at neutral pH. For a modified electrode with a collagen membrane over the Nafion film, an error of approximately 19% resulted in the response of a 100 mg/dL glucose solution (Figure 6) when all amino acids were added at their physiological maximum level. However, the response for all glucose concentrations fluctuated within *3% when amino acid concentrations were varied from physiological average to the physiological extremes. Therefore, the error resulting from amino acid interference can be cut down to less than 3 % by adding amino acids at their average physiological concentrations to the calibration standards. A few other carbohydrates besides glucose are also found in body fluids, but at comparatively much lower concentrations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003089_s1727719100003348-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003089_s1727719100003348-Figure1-1.png",
        "caption": "Fig. 1 Average element rotation",
        "texts": [
            " 3. ELEMENT ROTATION AND DEFORMATION VECTORS An average rotation is defined for computational expediency. The definition is somewhat arbitrary. We consider two choices. In his discussion of incremental mechanics, Biot [6] suggested an average rotation for a particle in a deformable body. Consider a right triangular element OAB (OA = OB = 1). Subjected to motion, the element becomes (O'A'B'). An average rotation is calculated from the orientations of two coordinates (x, y) and (x, j>), shown in Fig. 1. (x, y) is oriented such that h and l2 are equal. Use linear distribution functions for the displacements: u = a11x + a12y From the geometry, it is found /j = a 2 1 c o s 9 - ( l + a1 1)sin\u03b8 la22 = (1 + 2) sin \u03b8 + a12 cos \u03b8 Setting h = l2 gives tan\u03b8 = - 2 + aa1122 (2) Thus, we may select three arbitrarily points in a given element and calculate the average rotation from the relative displacements. The second choice is simpler. If the change of orientation for a line connecting the node i and the centroid of element is cp,, the average rotation is assumed to be 1 n (3) where n is the total number of nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure3-30-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure3-30-1.png",
        "caption": "Figure 3-30 Displacement of a printer actuator as a function of time for different input frequencies showing loss of predictable output [from Hendriks (1983); Copyright 1983 by International Business Machines Corporation; reprinted with permission].",
        "texts": [
            " Hendriks uses an empirical law for the impact force versus relative displacement after impact; u is equal to the ratio of 104 A Survey of Systems with Chaotic Vibrations displacement to ribbon-paper thickness: = -AEPpun, u<0 (3-3.8) where A is the area of hammer-ribbon contact, EP acts like a ribbon-paper stiffness, and ft is a constant that depends on the maximum displacement. The point to be made is that this force is extremely nonlinear. When the print hammer is excited by a periodic voltage, it will respond periodically as long as the frequency is low. But as the frequency is increased, the hammer has little time to damp or settle out and the impact history becomes chaotic (see Figure 3-30). Thus, chaotic vibrations restrict the speed at which the printer can work. One potential solution which is under study is the addition of feedback control to suppress this chaos. Nonlinear Circuits Periodically Excited Circuits: Chaos in a Diode Circuit. The idealized diode is a circuit element that either conducts or does not. Such on-off behavior represents a strong nonlinearity. A number of experiments in Physical Experiments in Chaotic Systems 105 (a) (b) (c) Figure 3-31 (a) Model for a varactor diode circuit, (b) Circuit element when the diode is conducting, (c) Circuit element when the diode is off [from Rollins and Hunt (1982) with permission of The American Physical Society, copyright 1982]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure1.27-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure1.27-1.png",
        "caption": "Figure 1.27. (a) Noncontinuous and (b) continuous hysteresis loops. Both have memory effect.",
        "texts": [
            " Hysteresis also occurs in engineering. Thermostats are an example. Other examples are porous media filtration, granular motion, semiconductors, spin glasses, mechanical damage, and fatigue. Hysteresis also appears in redox chemical reaction, biology, economics, and even experimental psychology. From the mathematical point of view, nonconvexity is a source of bistability and leads to hysteresis in evolution. In general, hysteresis means a memory effect which could be rate-independent or rate-dependent. Figure 1.27a shows several rate independent hysteresis loops and Fig. 1.27b shows a continuous hysteresis loop, commonly seen in ferromagnetism and ferroelectrics. The following rules are observed. If a parameter u increases from Ul to U2, the function I moves along the curved path indicated by ABC; conversely, if U decreases from U2 to ul,Jmoves along the path CDA, where the ABC and CDA curves form an enclosed loop. Moreover, if u inverts its moving direction at a random moment when UI < u(t) < U2' I moves into the interior of the region S bounded by the loop ABCDA. The functionJ can attain any interior point of S by a suitable choice of the input function u(t)",
            " The memory effect makes these materials indispensable in modern technologies and development of smart materials. Computer memories require rate-independent hysteresis loop with the smallest S value. Different applications require different shapes of the hysteresis loops (Fig. 1.24). In solid materials, phase transitions with discontinuity of a physical parameter, for example magnetization, or polarization or dimension of its volume, will induce a discontinuous hysteresis effect, which occurs for instance in ferromagnetism, ferroelectricity, and solid redox reaction (Fig. 1.27a). 1.15.1.4. SELECTIVITY, SENSITIVITY, REPRODUCIBILITY, AND RECOVERABILITY. Functional materials with chemical sensitivity are mandatory for response to a specific change in its chemical environment, such as a specific type of molecules. An important characteristic of these compounds is their sensitivity to detect the species in small quantities. Selectivity is the ability to distinguish two or more similar chemical species, and specificity is the ability to quantitatively measure the same unique property for any case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003940_016003-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003940_016003-Figure7-1.png",
        "caption": "Figure 7. Stability diagram in the (\u03b5, \u03bb) plane where \u03b5 denotes the dimensionless control parameter in arbitrary units and \u03bb is the internal passive sliding resistance \u03bb in the axoneme. Displayed are the lines of instability which correspond to clockwise (solid line, red) and anticlockwise (dashed line, blue) twirling patterns. Parameter values are L = 3 \u00d7 10\u22126 m, \u03ba = 1.7 \u00d7 10\u221221 kg m3 s\u22122, \u03be\u22a5 = 2.5 \u00d7 10\u22123 kg m\u22121 s\u22121, K = 103 kg m\u22121, \u03c4 = 5 \u00d7 10\u22123 s, a = 90 \u00d7 10\u22129 m.",
        "texts": [
            " A typical example is given by \u03c7(\u03c9) = K + i\u03c9\u03bb \u2212 \u03c1k\u03b5 i\u03c9\u03c4\u0304 + (\u03c9\u03c4\u0304 )2 1 + (\u03c9\u03c4\u0304 )2 , (26) where k is a stiffness of a motor domain, \u03c1 the density of motors along the axoneme, K and \u03bb the internal elasticity and friction associated with microtubule sliding, \u03c4 the correlation time of motor attachments and detachments and \u03b5 denotes a dimensionless control parameter [18, 19]. For such a specific example, we can find the critical values of \u03b5 for which the modes \u0303\u00b1 i (s) become unstable. Using estimates for the values for the microscopic parameters [18, 19], we find that the clockwise (as seen from the distal end) twirling beat patterns corresponding to \u0303+ i (s) become unstable first. This is shown in figure 7 where for the purpose of the illustration we present a region of the stability diagram where the two lines of instability can be clearly distinguished. This region corresponds to small values of \u03bb and large values of the bifurcation frequency. As \u03bb increases, the frequency of the bifurcation decreases. Our estimates of the parameter values of cilia correspond to values of \u03bb 5 \u00d7 102 N s m\u22122 for which the frequency is \u03c9/2\u03c0 10 Hz. The motility of cilia and flagella lies at the heart of many biological processes, relevant to fields as diverse as the swimming of microorganisms, developmental biology and medicine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000690_j.rcim.2021.102138-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000690_j.rcim.2021.102138-Figure1-1.png",
        "caption": "Fig. 1. Mobile manipulator machining system for machining the sub-region of large complex components.",
        "texts": [
            " This is of great significance to the BP optimization of mobile manipulators. BP optimization is a complex nonlinear optimization problem with multiple constraints, and its goal is to improve the performance of the robot. More precisely, the goal of BP optimization is to improve the stiffness performance of the robot as much as possible under the premise of ensuring its kinematic performance. In order to describe this problem more clearly, this section will give a detailed explanation in conjunction with the scenario shown in Fig. 1. Fig. 1 shows the application scenario of mobile manipulator machining system in machining the LCC\u2019s sub-region. Meanwhile, some key frames and their transformation relations (X YT represents the 4 \u00d7 4 transformation matrix of frame {Y} w.r.t frame {X}) are also given. The definitions of these frames are given below. \u2022 {W} is the world frame, which is also the reference frame for other frames; \u2022 {Pi} is the frame corresponding to a point on the machining path of the sub-region. Assuming that the machining path is discretized into n points, and then the position vector ti = [xi, yi, zi]T , normal vector wi and tangent vector ui of any point Pi w",
            "t {W} can be defined as W BPT = [ I3\u00d73 bp 0 1 ] (10) where bp = [x, y, z0] T, and z0 is usually a constant, which is determined by the height of robot\u2019s base frame. \u2022 {6} is the end link frame of the robot; Q. Fan et al. Robotics and Computer-Integrated Manufacturing 70 (2021) 102138 \u2022 {tcp} is the TCP frame. And the transformation matrix of {tcp} w.r.t {6} and {Pi} is determined by the design parameters of the tool and the process parameters (mainly the cutting depth) respectively. Furthermore, according to the transformation relations between frames in Fig. 1, another expression of the transformation matrix of {BP} w.r.t {W} can be obtained as W BPT = W PiT\u22c5Pi tcpT\u22c56 tcpT\u2212 1\u22c5BP 6 T\u2212 1 (11) For a given machining task (i.e. machining path, process parameters, robot and tools are determined), W Pi T, Pi tcpT and 6 tcpT are usually known, which means that robot BP is the only factor determining the joint angle of the robot. Therefore, considering that the joint angle of the robot determines its kinematics and stiffness performance, the BP optimization problem of mobile manipulators can be defined as: Establishing an efficient optimization method under the conditions that the machining path, process parameters, robot and tool are determined, so as to accurately find the most suitable machining position for the mobile manipulator on the plane Z = z0 (z0 is the height of the robot\u2019s base frame), namely the robot\u2019s optimal BP",
            " The schematic diagram of this method is shown in Fig. 4. In Fig. 4, the search range of initial BP (denoted as bpint) is determined according to the robot\u2019s reachability and the boundary size parameters of the LCC\u2019s sub-region. Assume that the maximum reachable Q. Fan et al. Robotics and Computer-Integrated Manufacturing 70 (2021) 102138 distance of robot is dmax, and the boundary size parameters of LCC\u2019s subregion is Obound = [xO min,xO max,yO min, yO max,zO min, zO max]. Taking the scenario shown in Fig. 1 as an example, the search range of bpint can be defined as int bp = [int bpmin, int bpmax], and int bpmin = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 xO max \u2212 dmax yO min \u2212 dmax z0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 , int bpmax = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 xO min + dmax yO min z0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 (24) Then, the bpint can be obtained through Algorithm B2, where fix(\u22c5) is the function of rounding to zero in Matlab. Further, according to Fig. 4- b, the search range of optimal BP (denoted as bpopt) can be determined as opt bp = [opt bpmin,opt bpmax], and opt bpmin = bpint \u2212 \u23a1 \u23a3 a a 0 \u23a4 \u23a6, opt bpmax = bpint + \u23a1 \u23a3 a a 0 \u23a4 \u23a6 (25) where a is the side length or resolution of the grid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure6.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure6.3-1.png",
        "caption": "Figure 6.3. Addendum and dedendum, measured",
        "texts": [
            " The cutter offset for each gear is then equal to the required profile shift, and the dedendum values are as follows, (6.30) (6.31) where a r is the cutter addendum. Later in this chapter, we will give the corresponding equations for the case when the gears are to be cut by a pinion cutter. For the purpose of the gear pair design, we need the dedendum values bP1 and bp2 ' The dedendum bp in a gear is obviously related to bs ' since bp is the radial distance from the pitch circle to the root circle, while bs is the corresponding distance, measured from the standard pitch circle. The two lengths are shown in Figure 6.3, and we can use this diagram to express bP1 and bP2 in terms of bs 1 and bs2 ' (6.32) (6.33) We now choose the sizes of the two gear blanks, to give a sui table working depth for the gear pair, and adaquate clearances at each root circle. The working depth and the 158 Prof ile Shi ft from the pitch circle. clearances were defined by Equations (3.66 - 3.68), in terms of the addendum and dedendum values of each gear, measured from the pitch circles. In addition, recommended minimum values were given in Equations (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure10.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure10.9-1.png",
        "caption": "Fig. 10.9 Gough-Stewart platform (https://en.wikipedia. org/wiki/Stewart_platform)",
        "texts": [
            " A manipulator can only move in a pre-set path which can\u2019t be changed; thus, it is suitable for fixed automation of mass production. However, a robot\u2019s motion is programmable so that it is good for production of mixed products. The wide application of industrial robots in painting, material handling and welding was mainly driven by two opposite trends: the increase of labor cost and the decrease of robot\u2019s price. The change of the two factors since the 1990s is shown in Fig. 10.8 (Craig 2004). The origin of parallel robots is generally credited to the Steward Platform, as shown in Fig. 10.9, proposed by an English engineer, D. Stewart in 1965 (Stewart 1965) for the purpose of flight simulator. In fact, A Romanian-English scholar, V. Eric Gough, developed the same mechanism much earlier in 1956 for automotive tire tests (Gough 1956). Thus, in later literature, this mechanism was termed as Gough-Stewart Platform. Kenneth Hunt, an Australian scientist, started constructing robots on the basis of the Steward platform (Hunt 1990). To the mid. 1980s, theoretical investigations on the Steward platform started"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure1-1.png",
        "caption": "Fig. 1 Coordinate systems for the left handed",
        "texts": [
            " A cutter ead with two different rotation centers is termed a dual cutter ead. The center distance and orientation between the inner and he outer blade rotation centers is designed to achieve the necesary lengthwise crowning. In contrast, in other face hobbing proesses like Spiroflex\u00a9, the inner and outer blades rotate about one ingle rotation center, meaning that the lengthwise crowning is rimarily done by the cutter tilt on the cutting machine. The coordinate systems for dual cutter heads with a left-hand irection are shown in Fig. 1. During the cutting process, the inner nd outer cutter heads rotate separately at the same rotation speed bout two parallel axes. The origins oI and oA are the rotation enter of the inner and outer heads in the pitch plane of the cutter lade. Eccentricity Exz and orientation angle e of the dual head utter are used to describe the positional relationship between the wo origins. The inner blade radius r0I is generally equal to the ominal cutter radius r0, but, for proper contact ellipses, the outer lade radius r0A is increased to reduce the lengthwise curvature of he concave flanks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003459_robot.1996.503783-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003459_robot.1996.503783-Figure2-1.png",
        "caption": "Fig. 2 Link structure of WL-I2RVII",
        "texts": [
            " 2)[ 111 to acquirea relative position to the landing surface. The new version incorporated modifications that were required by the mounting ofthe newly developedfootunit WAF-3 (Waseda AnthropomorphicFootNo. 3)and was named WasedaLegNo. 12RefinedVII (WL-I 2RV11). Thetotal weight oftherobotis 109Kg theweightofthetrunkis30.0K;g.andthe height in a static straight standing trunk position is 1866 millimeters. An assemblydrawingofthismachine isillustrated in Fig. I . The linkstnictureand assignmentofactiveDOFs(degreesoffieedom) are illustrated in Fig. 2. The total active DOF ofthis machine is 9 DOF, which is the same as that of WE-] 2RV1, consisting of6 DOF for the pitch axes of the lowerlimbs, and 1 DOFforeach ofthe pitch axis. roll axis, and yaw axis ofthe trunk (3 DOF for the trunk). The actuators each employ an electric hydraulic servo system combining a hydraulic RA (rotary actuator) and a servo valve. The maximum torque ofthle actuator is 300 Nm and the maximum angular velocity about 150 degree per sec. Furthermore, thismachine hasthecapability ofautonomouslyexeclrting real-time controls, which require high-speed processing, with no external assistance because it is equipped with four units of I6 bit CPUsforcontrolling individual actuatorsandtwounitsof32 bit RISC processors for generating walking patterns on a real-time basis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000502_j.snb.2020.128452-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000502_j.snb.2020.128452-Figure1-1.png",
        "caption": "Fig. 1. (a) XPS survey spectrum of FeSe NR/CC; (b) High-resolution XPS spectra in the Fe 2p regions; (c) High-resolution XPS spectra in the Se 3d regions; (d) Low SEM image of bare CC; (e) Low and (f) high-magnification SEM images of FeSe NR/CC.",
        "texts": [
            " All electrochemical experiments were performed at room temperature. A traditional threeelectrode system was used to record electrochemical data, where a saturated calomel electrode (SCE) served as the reference electrode, the FeSe NR/CC and bare CC were used as working electrodes (0.5\u00d7 0.5 cm2), and a platinum wire was employed as the counter electrode. In order to study the chemical composition of the obtained product and the valence state of each element, X-ray photoemission spectroscopy (XPS) studies were carried out [25]. As shown in Fig. 1a, three elements (C, Fe, and Se) were detected on the surface of FeSe NR/CC. Three peaks centered at around 284.6 eV, 711.0 eV, and 58.0 eV refer to the C 1s, Fe 2p, and Se 3d, respectively [26]. Fig. 1b shows the XPS spectrum of the Fe 2p region. The binding energies of Fe 2p3/2 and Fe 2p1/2 are located at 711.4 eV and 725.28 eV, respectively, which is originated from Fe2+ [27,28]. Fig. 1c shows the Se 3d spectrum of FeSe. Two deconvoluted peaks can be observed for the material at banding energies between 52 and 56 eV, which correspond to the Se 3d5/2 and 3d3/2 orbitals [29]. Additionally, X-ray diffractogram of FeSe NR/CC was studied to further confirm the formation of the electrode, as shown in Fig. S1, the peaks at 22\u00b0 and 44\u00b0 (marked with \u201c*\u201d) belong to bare CC [30]. Moreover, the other peak positions at 29.5\u00b0 (101), 33.3\u00b0 (002), 34.3\u00b0 (110), 36.9\u00b0 (111), 53.3\u00b0 (103), and 58.1\u00b0 (211) are belong to FeSe/CC [31,32]. These results above confirm the successful formation of FeSe. Fig. 1d shows a typical FESEM image of the bare CC. It was constructed by numerous interdigitated carbon fiber beams and showed a smooth surface. After chemical modification, a large number of ferrous selenide nanorods were arrayed on the surface of CC substrate (FeSe NR/CC, Fig. 1e). The high-magnification SEM image (Fig. 1f) indicates that the surface of the FeSe NR/CC is rough, which will inevitably increase the specific surface area of the working electrode and improve the hydrophilicity of the electrode, allowing nitrite ion to enter the electrode/electrolyte interface effectively. To obtain the loading mass of FeSe nanorods on carbon cloth, A TGA analysis was performed for FeSe NR/CC and bare CC. As shown in Fig. S2, the weight loss of FeSe NR/CC and bare CC are 0.761 % and 0.601 %, respectively, Thus, the mass loading of FeSe nanorods on carbon cloth is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure6.27-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure6.27-1.png",
        "caption": "Figure 6.27. Single-lens ray diagram for calculating the electron phase shift introduced by spherical aberration.",
        "texts": [
            " If the lens were ideal, the light emitted from a point source located at the intersection of the front focal plane with the optic axis would be a plane wave propagating parallel to the optic axis. Thus, the back focal plane is the wave front. Due to the spherical aberration, the wave front of the spherical wave emitted from the point object is no longer a flat plane when it arrives at the back focal plane, so there is a relative phase shift which accounts for the spherical aberration. As shown in Fig. 6.27, the path length difference between the solid line and the dashed line is dL = dri'O = cse3'O = /82 \u2022 Thus 8 = drJ/, and dL = cse3 drJ/, where / is the focal length and e = rJ/. The phase difference is (6.49) Summing over the contributions made by the rays from the point source A gives (6.50) where E> is the considered up-limit of the scattering angle, which is related to the reciprocal space vector by E> = Alul. Thus the phase shift introduced by spherical aberration is (6.51) 6.3.3.2. DEFOCUS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure5-1.png",
        "caption": "Fig. 5. Complex open kinematic chain obtained by concatenating the loop A-B and the elementary open kinematic chain associated with the leg C of parallel Cartesian robotic manipulator: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " The motion parameter b2 is given by the number of independent motions between the extreme elements 1C and 0 in the serial open kinematic chain 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 -2C -1C associated with the second loop when no other loop is closed (Fig. 4). Five independent motions (vx, vy, vz,\u03c9x,\u03c9z) exist between the extreme elements 1C and 0 (Fig. 4). These velocities form the base of RF(2). The dimension of the range of the restriction of F2 to the kernel of F1 can also be obtained by inspection. dim(RF(2)/KF(1) ) is given by the number of independent motions between the extreme elements 1C and 0 in the complex open kinematic chain from Fig. 5 obtained by concatenating the closed loop A-B and the elementary open kinematic chain associated with the leg C. Only four independent motions (vx, vy, vz,\u03c9z) exists in this case between the extreme elements 1C and 0 (Fig. 5). These velocities form the base of RF(2)/KF(1) . Two other examples of parallel mechanisms with uncoupled translational motions and with decoupled Sch\u00f6nflies motions proposed by the author of this paper (Gogu, 2002) are presented to illustrate the applicability of Eq. (26). Fig. 6 presents a parallel robotic manipulator (Gogu, 2002) with three legs derived from the solution presented in Fig. 1 by eliminating the actuated prismatic joint from the leg C. In this case, leg C has just a guiding role by constraining the mobile platform to a planar motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000001_j.surfcoat.2019.02.009-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000001_j.surfcoat.2019.02.009-Figure12-1.png",
        "caption": "Fig. 12. Volumetric slice plot of the measured powder distribution for the large nozzle. Colors indicate the powder flow density \u03c1p.",
        "texts": [],
        "surrounding_texts": [
            "The purpose of the powder flow measurement is to improve the nozzle design and to predict any process behavior of DMD that originates from the powder distribution. Therefore, the calculated powder catchment efficiency \u03b7p derived from the measured powder flow density is analyzed in the following and is compared to the powder catchment efficiency \u03b7c measured from cladding tracks in order to evaluate the quality of the presented method. It is assumed to be accurate, if the calculated catchment efficiency shows good correlation to the actual catchment efficiency, for a broad range of standoff values and melt pool sizes. The powder flow density \u03c1p depends on all three spatial directions. Thus the catchment efficiency can be interpolated for arbitrary standoffs and melt pool sizes within the boundaries of the measurement. Similar to Haley et al. [4], the melt pool shape is modeled as an ellipse with the major axis as melt pool length lm and the minor axis as melt pool width wm. In polar coordinates, the radius of an ellipse is calculated as follows with the eccentricity \u03f5: = + r w \u03b8 w l \u03b8 ( , ) 2 (1 \u03f5 cos )m m m 2 (11) The powder catchment efficiency \u03b7p as a function of the melt pool width wm and the standoff S is the surface integral of the powder flow density \u03c1p within the melt pool area at a given standoff: \u222b \u222b=\u03b7 w S \u03c1 r \u03b8 S r dr d\u03b8( , ) ( , , )p m \u03c0 r w \u03b8 p0 2 0 ( , )m (12) \u03b7p should be equal to one when assuming an infinitely large melt pool, which verifies that the entire powder stream was covered by the measurement. The powder catchment efficiency was calculated numerically. Computed for each standoff range with a step size of 0.2mm, the powder catchment efficiency is plotted as a function of the standoff and for typical melt pool widths in Fig. 14 for the small nozzle and in Fig. 15 for the large nozzle. The catchment efficiency of the small nozzle rises slightly below the nozzle until S = \u22122.6 mm and drops continuously below. The overall efficiency is low, since the laser is only capable of creating a melt pool of wm = 0.8mm on average, which is too small for this type of nozzle. Even if all parameters are optimized once in order that the actual layer thickness equals the nominal one, the nozzle will create an unstable DMD process: Processing needs to take place at a standoff of S = \u22125mm or larger to prevent premature wear or destruction of the small nozzle tip by heat and fumes. When working with such standoff distances, any infinitesimal deviation from the planned build height will propagate itself, since an insufficient layer thickness leads to a further decrease of catchment efficiency in the next layer, and vice versa. This results in a wavy and impaired surface as shown by Zhu et al. [24] and Tan et al. [3]. In contrast, the large nozzle shows a pronounced maximum of the catchment efficiency and the process is able to stabilize itself with a standoff less or equal \u22129mm, which is a feasible distance without nozzle destruction: In case the deposited part becomes too high and the standoff gets smaller than the nominal one, the efficiency drops and creates a counter-effect; the buildup height decreases again and creates a passive stability as outlined by Haley et al. [4]. The overall efficiency of the large nozzle is relatively high, as the laser creates a bigger melt pool of wm = 2.2mm on average. For both nozzles, the efficiency decreases steeper above the focus than it decreases below the focus. This can be explained by three effects: First, gravity that forces particles to follow a parabolic trajectory; second, drag forces by the gas stream that merge below the focus; third, collision of two particles in radial direction with friction loss. All three effects cause a decreasing radial speed and constant or increasing axial speed of the particles with increasing standoff. This conclusion is also supported by the observations of Tabernero et al. [18] and Pinkerton and Li [15]. Validation is done with a direct comparison to cladding tracks. 28 tracks were deposited with the small nozzle and 60 tracks with the large nozzle, both with varying standoffs as listed in Table 3 on a structural steel S235 base material. The scanning path was in positive x-direction in machine coordinates, which corresponds to a turn angle of \u03b1 = 0\u00b0. Generally, the melt pool size differs significantly depending on the standoff, process parameters, and base material temperature and absorptivity. The different standoffs change the diameter of the laser spot on the base material, leading to a varying melt pool area. The laser focuses inside the nozzle, thus a higher standoff results in a bigger laser spot size. The influence of the process parameters and heat input on the melt pool size is further analyzed by Huang et al. [25]. Sections of cladding tracks were measured with a Leica DCM 3D surface metrology microscope. Surface roughness is removed with a low-pass filter and a cut-off length of 0.35mm. The resulting wavy track surface is shown in Fig. 16 for the large nozzle and standoffs between \u22125.2 and \u22124.0mm on the right side. The cross sectional area Am of each track is evaluated numerically on a length of 0.6mm. Knowing the total powder mass flow, the mean powder catchment efficiency \u03b7c from cladding tracks and the related standard deviation for this measurement length can be calculated. As shown on the left side, the melt pool length is approximated by analyzing the shape of the track end. Multiple measurements reveal that the melt pool length lm is 1.3-times the melt pool width wm on average for the applied process parameters, with the eccentricity \u03f5 = 0.8 as best fit for Eq. (11). The corresponding catchment efficiency \u03b7p from the powder flow measurement is calculated with the input of the powder flow density, standoff, melt pool area from the microscope measurements, scanning direction, and misalignment of laser and powder. Figs. 17 and 18 depict the correlation of the efficiency, with the catchment efficiency \u03b7p measured from the powder stream on the x-axis and the catchment efficiency \u03b7c measured from cladding tracks on the yaxis. The Figures show different scales due to the limited range of catchment efficiency of the small nozzle. Tracks made with the small nozzle have an irregular cross sectional area Am, leading to significant fluctuations of the actual catchment efficiency and to large error bars. However, the diagram shows a linear correlation for most data points, with a mean absolute error of 0.039 and the powder measurement slightly underestimating the actual catchment efficiency. The large nozzle deposits more uniform tracks with a broad range of catchment efficiency values. The comparison of prediction and cladding experiment results in a linear correlation with a mean absolute error of 0.049. Deviations arise from additional interactions of the powder stream with the melt pool. The effect of the hot melt pool on the gas stream cannot be considered for this powder measurement method. The fusing front and gradually solidifying tail of the melt pool may result in a bigger effective melt pool area than measured by surface metrology after processing, which could explain the underestimation of the prediction. The effect of misalignment of laser and powder as stated in Table 2 has been analyzed by depositing 18 tracks in all directions with a standoff of S = \u22129mm. The powder catchment efficiency measured from cladding tracks as a function of the turn angle \u03b1 is shown in Fig. 19. The catchment efficiency of the small nozzle does not show a clear direction dependency as expected from the adequate alignment of laser and powder. Cladding tracks made with the large nozzle are direction dependent, with a maximum catchment efficiency at 190\u00b0 and a low efficiency plateau between 250\u00b0 and 350\u00b0. As the catchment efficiency of the large nozzle varies by 15%, these fluctuations need to be considered when defining the tool path and process parameters based on a catchment efficiency prediction. Fig. 20 shows a 40mm high, 2.5D thin-walled blade that has been built with the large nozzle, considering both the spatial powder distribution and the focus misalignment. Based on the efficiency prediction, an initial standoff of S = \u22129mm has been applied for the highest efficiency. The parameters have been chosen in order that the process develops the self-stabilizing effect, making any layer height control unnecessary. The geometry of the top edge is accurate to 0.5mm relative to the predicted height. The demonstrator shows that the presented measurement methods are able to compensate certain machine and process deficiencies to achieve a high part accuracy. In the future, the powder measurement method shall be extended to inclined base materials and edges to study the deposition behavior that occurs during the fabrication of complex parts."
        ]
    },
    {
        "image_filename": "designv10_4_0003213_0094-114x(95)00089-h-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003213_0094-114x(95)00089-h-Figure1-1.png",
        "caption": "Fig. 1. Serial chain with consecutive links connected by helical pairs.",
        "texts": [
            " Firstly, an expression for the acceleration of a point in the end effector in terms of the direction and moment parts is obtained in Section 4. Section 5 shows how the acceleration of the end effector can be expressed as the sum of scalar multiples of the normalized screws representing the kinematic pairs, where the scalars are the corresponding relative angular accelerations, together with their Lie products, when the angular velocity of the end effector vanishes; i.e. when the end effector is instantaneously stationary or in pure translation. 2. ASSUMPTIONS AND NOTATION Consider the serial chain illustrated in Fig. 1. The base link will be labelled 1, while the end effector will be labelled m, where m > 1. The angular velocity and acceleration of a body k with respect to a body i will be denoted by i09k and i~_k respectively, and their magnitudes will be denoted by iCOk and ~tk. Similarly, the velocity and acceleration of a point P, fixed in a body k, with respect to a body or reference frame i, will be denoted by 'v_ k, and ~a k. It will be assumed that two adjacent links, k and l, are connected by a helical pair that passes through a point Bt, fixed in body l",
            " ~ - m - 2 ~ m - I ..}. m-- I~_,,n, (24) where Jg,. is the angular acceleration of the end effector with respect to the reference frame j, and ,~k+ l, for k = j , j + 1 . . . . . m - 1 is the relative angular acceleration of adjacent links. The next proposition shows that under the assumptions considered in this paper, it is possible to express :0: in terms of the relative angular velocities and accelerations of adjacent links of a serial chain. Proposition 7. Consider the serial chain shown in Fig. 1, where adjacent links are connected by helical pairs, as described in Section 2. Then . , . . . . m - 2 s m - I \u2022 m - I s , . Jo~m = j o g j + I Js-J+I \"-[-j+l( 'Oj+2 J + l S j + 2 \" d t - \" \"\" - l - m - 2 o g m - - I -- \" ~ - \" - l o g m -- \u2022 m - 2 S , . - I m - l sm ) \"~ ' j og j+ I JS j + l X ( j + l o g j + 2 J + l s J + 2 \" ] - ' ' ' ' - ~ r n _ 2 o g m _ l - - \"~-rn--logm - - - I - j + l g j + 2 j + I s J + 2 X ( j + 2ogj+ 3S+ 2s_. j + 3 --~ \u2022 ' \u2022 --~ m - 2 o g m - l m - 2S- m - I ..~ m - Io9, ",
            " Let k, 1, and m be three arbitrary r ind bodies; then the acceleration of a point O, fixed in m with respect to the reference frames associated with k and l are related by * _ a ~ ' = k - I - - L m 2 * ~ t \"-o. \"1- \"-o + _ x I vg ' , (31) where O* is a point fixed in body, or reference frame, I that, in the instant considered, coincides with point O. It is easy to recognize in (31) the presence of the Corioli's acceleration term. (28) Application of screw algebra in acceleration analysis 453 Proposit ion 9. Consider the serial chain s h o w n in Fig. 1, where adjacent links are jo ined by helical pairs. Then, if O is an arbitrary point fixed in body m, it fo l lows that \u2022 . _ \u2022 m-2sg, ~ cb m-~sg, J a ~ = j 0 ) j + l J S J o + l ' l - j + l ( ~ O j + 2 J + I s - J o + 2 + ' ' ' - J r ' m - 2 0 ) m - I - - + m - I -- - t , i JoJ+ 1 J_sJ+ 1 J- r., 2 j + [ e j + 2 X J+ I s~+2 j w j + I J_ X t j + l L Z ~ j + 2 o_ - ~ - ' ' ' 0)2 m - 2 s m - I m - 2 S r ~ - I 2 m - l s r a m IS~ Jl- m - 2 m - I - X _ \"lt- m _ 1 0 ) m - X - MI-2j0)j+ IJS j + l X ( j + 1 0 ) j + 2J+ ls_Jo +2 dl- \" \" \" -~-m_ 20) rn_ l m - 2 s _ ~ n - I d l - m _ 1 0 ) m m - I s ~ ) 0) m - l g*) \"{- 2 j + I 0 ) j + 2J+ Is_ j + 2 X ( j + 2(I",
            " Here, the coordinate system must have the arbitrary point chosen as the origin. This section shows that if the angular velocity of the end effector, with respect to the reference system, vanishes, then the acceleration of an arbitrary point in the end effector can be expressed in a simpler form. In fact, the acceleration state of the rigid body can be written in terms of the screws, representing the kinematic pairs which join the end effector to the reference frame, together with their Lie products. Proposition 10. Consider the serial chain shown in Fig. 1, where adjacent links are joined by helical pairs. If O is an arbitrary point fixed in the end effector, m, and the angular velocity of the end effector vanishes, then \u2022 - - ..-pj j + l o j + 2 \u2022 m - 2 s r ~ - I O)m r a - I sg l J~ .~r~=j(Oj+lJSJo+l J r j + i t ,~ j+ 2 o_. 0 \" J l - ' ' ' J r r a _ 2 O , ~ r a _ l _ 7 L m _ l _ (,tO [ m - 2 S i n - I - I sm ' t m - l s m ( m - 2 s . m - J I - m - 2 m - I t - X ( m _ l O ) m m _ O J - - m _ l ( , O m _ X I ) ] + . . . \" \" \" m - 2Sgl - I \"Jr j + l ( ",
            " Obviously, if the angular velocity of the rigid body m, with respect to body j, vanishes, then the acceleration state of body m, with respect to body j, is reduced to JAm = r'. -ml (48) - L J a L I \u2022 The following final proposition shows that if the angular velocity of the end effector of a serial chain vanishes, then the acceleration state of the end effeetor, with respect to any other link of the serial chain, has a very simple expression in terms of the screws representing the kinematic pairs that join the serial chain. Proposition 12. Considering the serial chain shown in Fig. 1, if the angular velocity of the end effector vanishes, then the acceleration state of the end effector m, with respect to link j, is given by j A m .~ . j~ .~ j+ i j ~ ] + 1 j c_ j+ l ~ j + 2 j + 1 5 / * 2 j f f . . . J r m -- 20)m - 1 m - - 2 $ m - - 1 J r m- - I ( ~ m m-- l s m +L~_2o~m_ m-2$m-I m_lO~m , , - 1 5 = ] + . . . + +[jco:+/$j+l /+~j+2/+J$j+2+. , .+._2ogm_~ r~-2$m-~ +m_~O~mm-~$.], (49) where [/$J+~ ,$,+~] is the Lie product of the screws inside the bracket [25]. Proof: Since JAm = rJ~ml [equation ( 4 8 ) ] - 456 Jos6 Maria Rico Martinez and Joseph Duffy where J ~__ m = j (~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003123_s0094-114x(03)00065-x-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003123_s0094-114x(03)00065-x-Figure1-1.png",
        "caption": "Fig. 1. 5-Bar 2-dof manipulator with prismatic actuations.",
        "texts": [
            " 1 By expressing the resultant force and moment at the platform in terms of the actuator forces, the input\u2013output force system can be written as 1 H R \u00bc HF: \u00f01\u00de Here, R denotes the vector of output forces and moments, F is the vector of actuator forces, andH is the force transformation matrix. In the following, some examples of this formulation for a few parallel manipulators are presented, which will be later used for path-planning studies. More detailed analysis of singularities can be found in earlier works [11,12]. Fig. 1 shows a 2-dof planar parallel manipulator with prismatic actuations. Denoting the base point of a leg by bi, the leg-vector can be written as Si \u00bc t bi; i \u00bc 1; 2: \u00f02\u00de From R \u00bc f1s1 \u00fe f2s2, we find the force-transformation matrix as H \u00bc \u00bd s1 s2 : \u00f03\u00de Fig. 2 shows a 3-dof planar parallel manipulator with prismatic actuations. In this case the legvectors are given by ere onwards, the subscript i is used to denote the ith leg. Si \u00bc t\u00fe qi bi; \u00f04\u00de where t \u00bc OO0, bi \u00bc OBi, and qi \u00bc O0Pi is the vector from the origin O0 of the platform frame to the platform connection-point (Pi) expressed in global reference frame, given by qi \u00bc Rpi; \u00f05\u00de where pi \u00bc O0Pi (in local frame) and R is the rotation matrix given by R \u00bc cos h sin h sin h cos h : \u00f06\u00de If R \u00bc \u00bd Fx Fy M T denotes the output forces and moment with respect to the frame at O0, the force-transformation matrix is given by H \u00bc s1 s2 s3 q1 s1 q2 s2 q3 s3 : \u00f07\u00de Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003288_1.2779889-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003288_1.2779889-Figure2-1.png",
        "caption": "Fig. 2 Coordinate systems between the cutter head and the generating gear",
        "texts": [
            " Assuming that the blade dge rl u is represented as a function of the variable u in the oordinate system Sl, the position vector of the cutter blade in the utter head of coordinate system St is represented by the following atrix equations: rt 0,rc, h, 0,r0, i;u = Mtp i \u00b7 Mpn r0 \u00b7 Mnm 0 \u00b7 Mml h \u00b7 rl 0,rc;u 1 here 0 is the profile angle, rc is the curvature radius of the pherical blade, h is the hook angle, 0 is the offset angle, r0 is he cutter radius, and i is the initial setting angle of the cutter ig. 1 Coordinate systems for the left-handed face-hobbing utter head ead. ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 Because the cutting process of bevel gears is often interpreted using a virtual, or imaginary, generating gear, Fig. 2 gives the coordinate systems between the cutter head and this imaginary gear, whose tooth is formed by the cutter blade locus moving in a circular or epicycloidal trace for face-milling or face-hobbing gears, respectively. The tilt center Q and the rotation center oI of the inner head coincide with each other, while point oA is a projection of the rotation center oA of the outer head on the machine plane. The related position between oI and oA is determined by the eccentricity ExZ and the orientation angle e see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003656_j.jfranklin.2008.06.003-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003656_j.jfranklin.2008.06.003-Figure2-1.png",
        "caption": "Fig. 2. Controllers u1 and u2.",
        "texts": [
            " According to Section 3 one first select Wg \u00bc 0:0666 0:0076 0:0102 0:7200 0:8879 0:1010 0:1360 0:0280 so thatWgB \u00bc 0. Then the pseudocontrol input, adaptive controller and the adaptive gains are designed in accordance with Eqs. (12), (16), (13) and (17), respectively, where y \u00bc 3, y0 \u00bc y1 \u00bc 0:2, r \u00bc 1, Z \u00bc 2 and r \u00bc 1. The results of simulation (with initial condition xT\u00f0t0\u00de \u00bc \u00bd2 2 1 1 \u00de are given in Fig. 1. The state trajectories x\u00f0t\u00de are shown in Fig. 1, one can see clearly that all the states are driven to the origin. Fig. 2 is the control efforts u. Due to the function r=krk in the control ARTICLE IN PRESS C.-C. Wen, C.-C. Cheng / Journal of the Franklin Institute 345 (2008) 926\u2013941 935 ARTICLE IN PRESS C.-C. Wen, C.-C. Cheng / Journal of the Franklin Institute 345 (2008) 926\u2013941936 uadp and us, the chattering phenomenon is inevitable. The adaptive gains b\u03020, b\u03021 and f\u03022 shown in Fig. 3 are all bounded. Fig. 4 presents the sliding surface functions, which all approach to zero in finite time. In order to alleviate the chattering phenomenon, one can use sat\u00f0r; \u00de \u00bc r=krk; krk4 ; r= ; krkp ; ( (20) to replace the function r=krk, where is a small positive constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000762_j.precisioneng.2021.01.002-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000762_j.precisioneng.2021.01.002-Figure1-1.png",
        "caption": "Fig. 1. (a) Front view and (b) rear view of the designed reference artefact. The black arrow indicates the building direction.",
        "texts": [
            " Therefore, the layers with a smaller melted section which require less energy during the melting, need to be compensated. The compensation is made by controlling the duration of the post-heating phase. This supplementary energy may have a detrimental effect on the surface roughness because it increases the sintering degree of the powders around the surface and affects the heat transfer. This point has never been addressed in the literature. Moreover, the artefact is hollowed out with edges that create internal surfaces parallel to the external ones. Fig. 1 shows the designed test artefact in which the black arrow indicates the build direction. Surfaces from 1 to 5 are the external upskin surfaces and are parallel to the external downskin surfaces from 6 to 10. The surface labelled with 1 is tilted by 35\u25e6 to the build platform. The other surfaces are tilted through increasing steps of 5\u25e6 up to 55\u25e6. The STL file of the artefact can be downloaded here [50]. From here, therefore, two series of surfaces are identified: internal and external. Internal surfaces are numbered identically to the corresponding external ones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003883_j.mechatronics.2006.05.002-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003883_j.mechatronics.2006.05.002-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the laser powder deposition (laser cladding by powder injection) process.",
        "texts": [
            " Keywords: Laser powder deposition; Rapid prototyping; Vision-based feedback device; CCD-based optical detector; Image processing Laser powder deposition (laser cladding by powder injection) has received significant attention in recent years due to its unique features and capabilities in various industries involved in metallic coating, high-value components repair, rapid prototyping, and low-volume manufacturing. This emerging laser material processing technique is an interdisciplinary technology utilizing laser, computer-aided design and manufacturing (CAD/CAM), robotics, sensors and control, and powder metallurgy. In this process, a laser beam melts powder particles and a thin layer of a moving substrate together to create a bulk layer on the substrate as shown in Fig. 1. A great variety of materials can be deposited on substrates to form a layer (which is known as \u2018\u2018clad\u2019\u2019) with a thickness of 0.1\u20132 mm. 0957-4158/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2006.05.002 * Corresponding author. Tel.: +1 519 888 4567x7560; fax: +1 519 888 4333. E-mail address: etoyserk@uwaterloo.ca (E. Toyserkani). This technique can produce much better coatings than other techniques such as arc welding and thermal spray, with the production of minimal dilution, minimal distortion, and good surface quality [1]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure1.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure1.9-1.png",
        "caption": "Figure 1.9. pitch point of a gear pair.",
        "texts": [
            " Law of Gearing for Two Gears It was shown in the previous section that a rack and pinion behave in the same manner as if the rack pitch line and the pinion pitch circle were to make rolling contact with no 20 The Law of Gearing slipping. We now investigate whether the same idea can be used for two gears. First, we find two pitch circles which, if they made rolling contact with each other, would provide the same angular velocity ratio as the gears. And then we will establish that the Law of Gearing also applies for a pair of gears, or in other words, that the common normal at the tooth contact point always passes through a fixed point. Figure 1.9 shows two gears, with point Al of gear 1 in contact with point A2 of gear 2. The distance C between the gear centers is called the center distance. Parts of the pitch circles have been drawn in, and their radii are shown as RPl and Rp2 . The point where they touch is the pitch point P. If the pitch circles are to make rolling contact with no slipping, their radii must satisfy the following equations, C (1.20) (1.21) The angular velocity ratio that we require was given in Equation (1.4), (1.22) Equations (1",
            "21 and 1.22) imply that the ratio of the pitch circle radii is equal to the ratio of the tooth numbers, ( 1. 23) We now solve Equations (1.20 and 1.23), to obtain the radii of the pi tch ci rc les, ( 1 .24 ) (1.25) The pitch point P, which is the point where the pitch circles touch, therefore lies on the line of centers and divides C1C2 in the ratio N1:N2 . We use this point as the origin of a fixed system of coordinates E, ~ and S, with axes Law of Gearing for Two Gears 21 in the directions shown in Figure 1.9. The position of the contact point relative to the pitch point is then given by the coordinates ~ and 1/. As we did in the case of the rack and pinion, we write down the velocities of points Al and A2 , and then equate their components along the common normal. The direction nn of the common normal, which is unknown at present, can be written in the following form, where s~ and s1/ are the components of nn in directions. Then the velocities of Al and components in the normal direction, are following four equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002785_s0951-8320(00)00106-x-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002785_s0951-8320(00)00106-x-Figure2-1.png",
        "caption": "Fig. 2. Stanford arm.",
        "texts": [
            " Four geometric parameters are associated with each link/ joint pair; the distance between the links di and the joint angle u i determine the relative position of neighboring links, and the link length ai and the twist angle a i determine the structure of links. For a revolute joint, di, ai, and a i are the arm parameters, and u i is the joint variable. For a prismatic joint, u i, ai and a i are the arm parameters, and di is the joint variable. The forward (or direct) kinematics problem, i.e. determination of the end-effector position and orientation from known arm parameters and joint variables, is solved using the Denavit\u00b1Hartenberg notation [10]. This technique uses the link-attached coordinate frames, shown in Fig. 2 for Stanform arm. The relative positions of two adjacent links can be described by a 4 \u00a3 4 homogeneous transformation matrix, known as D\u00b1H transformation matrix, given as Ai i21 C ui 2C aiS ui S aiS ui aiC ui S ui C aiC ui 2S aiC ui aiS ui 0 S ai C ai di 0 0 0 1 26666664 37777775 1 where C and S denote cosine and sine functions, respectively. Matrix Ai i21 relates the coordinate frame of the ith link tothe coordinate frame of the i 2 1 th link. The position and the orientation of the end-effector are computed as T A1 0A2 1;\u00bc;An n21 Yn i 1 Ai i21 n s a p 0 0 0 1 \" # 2 where n denotes the number of degrees of freedom, T is called the arm matrix and vectors n, s, a and p are called normal, sliding, approach and position vectors of the endeffector",
            " However, the variation in the SPDR is more than that in the CDR. The trajectories of the end-effector position for a speci\u00aec experiment in case 1 of Table 2 are shown in Fig. 7. Fig. 8 shows the deviation from the mean (error) in the x and y coordinates of the end-effector position. It is interesting to note that the deviation in the x-coordinate is larger than the deviation in the y-coordinate. Also, the deviation in the y-coordinate is very small at time zero, and it gradually increases with time. The Stanford arm, shown in Fig. 2, is a six degree-offreedom manipulator with all revolute joints except for the third joint which is a prismatic joint. The mean values and the standard deviations of various kinematic and dynamic parameters assumed in the analysis for this manipulator are given in Tables 3\u00b15. The kinematic reliabilities of the manipulator with u1 1208; u2 2308; d3 5 cm; u4 0; u5 458 and u6 908; for seven different sets of standard deviations are shown in Fig. 9. These results (Fig. 9) can be used to prescribe the manufacturing tolerances and actuator speci\u00aecations For the dynamic reliability, the random joint effort vector is represented by a six-dimensional \u00aerst-order autoregressive vector process (Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003387_robot.1987.1087795-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003387_robot.1987.1087795-Figure2-1.png",
        "caption": "Figure 2. Comparison of force ellipsoids for task compatibility,",
        "texts": [
            " Redundant manipulators have the extra degrees of freedom that may be utilized for aligning the optimal directions. However, the problem is really one of maximizing the compatibility of the manipulator with the task requirements, and the measure of Compatibility, as we shall see, cannot be based upon directional alignment alone. In fact, defining a suitable measure of task compatibility is the most elusive aspect of the problem. Alignment of the optimal directions is not a sufficient criterion for measuring task compatibility. Consider the grinding example shown in Fig. 2. We wish to control force along the vertical direction and velocity along the horizontal. The two ellipsoids shown are the force ellipsoids of a manipulator in two different postures. The transmission ratio along a particular direction is determined by the intersection of the directional vector with the surface of the ellipsoid. Although the optimal directions of ellipsoid A are aligned with the task directions, ellipsoid B is more \"task compatible\" because finer control of force and velocity can be achieved along the respective directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure2-1.png",
        "caption": "Figure 2 The 3-CRR mechanism.",
        "texts": [
            " The four key techniques are the important part of the methodology and very useful for successful application of the modified G-K criterion. Furthermore, they are easy to grasp. For a mechanism which contains passive freedoms, the final \u201cnominal mobility\u201d is available by subtracting the number of passive freedoms from the above result. In the following section, the mobility of six puzzling mechanisms is to be analyzed, which is expected to help understand the methodology. The 3-CRR mechanism, as shown in Figure 2, was proposed by Kong and Gosselin[45]. The mechanism has three identical limbs and each limb consists of a cylinder pair and two revolute joints. The three axes in the same limb are parallel. In addition, the axes of pairs on the base are orthogonal with each other. The coordinate system is shown in Figure 2. Take the first limb into consideration. The cylinder pair has two freedoms and can be regarded as the com- bination of a prismatic pair and a revolute joint. Then each limb has four single-DOF pairs. The limb twist screw system can be written as follows ( ) ( ) ( ) ( ) 1 1 1 2 1 3 3 3 1 4 4 4 0 0 0; 0 1 0 , 0 1 0; 0 0 0 , 0 1 0; 0 , 0 1 0; 0 , d f d f = = = = $ $ $ $ (9) where the four screws are linearly independent and they have two reciprocal screws. The constraint screw system of the first limb is ( ) ( ) 11 12 0 0 0; 1 0 0 , 0 0 0; 0 0 1 , r r = = $ $ (10) which denotes two constraint couples and constrains two revolutions",
            " So there are six constraint couples acting on the moving platform in total but no common constraint is produced, \u03bb=0. From eq. (8) we conclude that there are three parallel-redundant-constraints, \u03bd = 3. Then using the modified G-K criterion, we have ( ) 1 ( 1) 6 8 9 1 12 3 3. g i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + =\u2211 (11) Since the axes of pairs in each limb always keep parallel and the axes of the three pairs on the base are orthogonal with each other, eqs. (9) and (10) are invariable as long as we choose the same coordinate system as shown in Figure 2. Thus, the numbers of common constraints and redundant constraints always keep fixed. So the mobility is global. The Orthoglide mechanism[46] is shown in Figure 3. It has three limbs and each limb includes a four-bar paral- 1342 Huang Zhen et al. Sci China Ser E-Tech Sci | May 2009 | vol. 52 | no. 5 | 1337-1347 lelogram loop. Let us take the hinged parallelogram linkage into consideration firstly. It is shown in Figure 4 and can be regarded as having two limbs. Point A is chosen as the origin point, x\u2032-axis is along the link AD, y\u2032-axis locates on the plane ABCD and z\u2032-axis is along the direction of the revolute pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000411_tie.2021.3055170-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000411_tie.2021.3055170-Figure2-1.png",
        "caption": "Fig. 2: Quadcopter UAV axes definition. Rotation rates and local velocities referenced to Xb, Yb and Zb are designated [p,q,r] and [u,v,w] respectively as shown.",
        "texts": [
            " The dynamic equations of the quadcopter are developed with reasonable assumptions such as: 1) the quadcopter structure is rigid and symmetrical and the centre of gravity of the quadcopter coincides with the vehicle frame origin. 2) The position and velocities (derivative) of all the states are measurable and available. Our quadcopter is oriented such that the body Xb and Yb axes are at 45\u00b0 to the rotor arms and the Zb axis orthogonal to the other two axes to form a right-hand axis system as shown in Fig. 2. We also define inertial axes, where X and Y axes are aligned horizontally to point North and East respectively and the Z axis is aligned vertically to point down towards the centre of the earth. Euler angles are used to represent rotation from inertial to body-fixed axes in terms of roll (\u03c6), pitch (\u03b8) and yaw (\u03c8). The thrust and torque dynamics of the propeller are included to model a nonlinear QUAV system dynamics as Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on June 18,2021 at 21:19:52 UTC from IEEE Xplore"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000083_j.addma.2019.100935-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000083_j.addma.2019.100935-Figure2-1.png",
        "caption": "Fig. 2. Model description and problem statement (a) dimensions of the test model (b) fabricated component (c) widening deposited layer due to heat accumulation.",
        "texts": [
            "2 mm wire of ER4043 aluminum alloy, which is deposited on the substrate, a 5A06 aluminum plate with dimensions of 130 \u00d7 100 \u00d7 5 mm. The composition of the deposition wire and substrate are listed in Table 1. The shielding gas for the CMT torch was Ar (99.99 %) gas with a constant flow rate of 15 L/min. During the deposition, the wire was melted by the arc heat source and then solidified on the top surface of the previous layer, resulting in a layer-by-layer deposition of the part. The cylinder component is used as the typical model to study the thermal transfer behavior during the deposition process. As shown in Fig. 2(a), the dimensions of the test model were depicted. A total of 40 layers were deposited in sequence, from the bottom up. When a layer was deposited, the welding torch lifted and repeated the previous trajectory. It should be emphasized that the arc is kept burning and the welding torch is kept moving throughout the entire deposition period. This allows for the production of a continuously varied temperature field which shows a strong regularity and, therefore, makes the interlayer temperature of the following layers predictable. The K type thermocouple made with nickel-chromium and nickelsilicon materials is used to measure the temperature of the point A (seen in Fig. 2(a)) to provide confidence in the accuracy of the finite element model. The probing end of the wire was buried into the substrate plate. The sampling rate of the thermocouple was 10 Hz and the measurement range of temperatures was between 0 and 1300 \u00b0C. This system was depicted in detail in our previously published studies [19,20]. Fig. 2(b) shows the fabricated component with fine surface quality. However, the dimensional accuracy can not be guaranteed. As shown in Fig. 2(c), the layer width continues to widen due to the heat accumulation, especially for the last several layers. Fig. 3 shows the wall width variation from the 1th to the 40th layer. It can be seen that the wall width dramatically increased from 4.51 mm to 5.72 mm (approximately 26.8 % increased), which means that the redundant materials would be post machined and, therefore, result in lower production efficiency and higher cost. Thus, a controlled technique should be developed to deal with this problem, and the finite element model is first established to study the thermal behavior on the additively manufactured component. The Simufact.welding software (version 6.0.0) is used for thermal simulations. According to our previous study [21], it can provide the thermal distribution and the distortion prediction for the welding process with high accuracy. The geometric size of the FEM model is shown in Fig. 2(a). The wall thickness was set at 4.5 mm and the layer height was 1.5 mm. Fig. 4 shows the three-dimensional finite element mesh for the cylinder model. In the present model, linear brick elements with eight-node hexahedrons are used for thermal simulation. In addition, the software can automatically refine the elements for the area near the deposited layer from level 0 to 10. All the elements of the deposited layer were deactivated before deposition, and then activated sequentially following the heat source",
            " The voltage and amperage is obtained by measuring the waveform during deposition using Hall current and voltage sensor. The material properties were temperaturedependent which were obtained from Ref. [24]. A uniform coefficient of convection on all surfaces equal to 10 W (m2K)\u22121 and a radiation emissivity of 0.22 were assumed. Experimental validation was performed to prove the accuracy of the numerical simulation. It was verified by comparing the measured temperature cycling curves of point A (seen in Fig. 2(a)) with the corresponding simulated curves. The results are shown in Fig. 5, the dashed lines and solid lines are the experimental results and the simulated results, respectively. It is found that the trend in fluctuations of the simulated results approximately agrees with the actual measurements, indicating the effectiveness of the FE model. However, there are errors between the two curves, which are mainly due to the different heat dissipation conditions. In actual conditions, the heat prone to dissipation through the worktable is not considered in the FE model and, therefore, results in a lower actual temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003687_1.2745063-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003687_1.2745063-Figure1-1.png",
        "caption": "FIG. 1. a Orientation of an LCE film: the nematic director n is aligned with x and the sample is irradiated with light polarized in the x1 direction and b schematic of the bilayer film representation of the photostrain distribution.",
        "texts": [
            " Thus, if the light is polarized in a certain direction, only those azo molecules aligned in this direction will absorb photons and isomerize\u2014those in other [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: 202.28.191.34 On: Sat, 20 Dec 2014 14:00:43 directions will remain unaffected. While we only consider polarized light, the analysis can be readily extended to unpolarized light. Consider a monodomain LCE film lying in an x1\u2212x2 coordinate system. The nematic director is oriented along x, where the angle between x1 and x is as shown in Fig. 1 a . The sample is irradiated uniformly through the thickness by light of an appropriate wavelength. For simplicity it is assumed to be polarized in the x1 direction, but the results can be easily extended to arbitrary directions in the x1\u2212x2 plane. The azobenzene molecules photoisomerize as they absorb photons, resulting in uniform in-plane photostrains ij pm that are functions of the light intensity Io. In the x , y system the nonzero components are ij pm = x pm y pm xy pm = p Io \u2212 1 2 p Io 0 ",
            " Although a more rigorous micromechanics analysis that considers the interaction of internal stresses and strains among the domains could be undertaken, as we will describe in more detail later this simple averaging approach seems to adequately describe the behavior observed in the literature.2 To understand the behavior when irradiated nonuniformly through the thickness, particularly nonlinear geometric effects, we have to specify information regarding the size and shape of the film. We consider a monodomain square film of side length L, and thickness t, and use the same x , y and x1 , x2 coordinate systems as before; relevant dimensions are shown in Fig. 1 b . We assume the film is freely supported and is irradiated from the top at z=\u2212t /2 by light at a wavelength suitable to cause photostrains. Furthermore, we assume that photon absorption gives rise to an exponential attenuation of the optical intensity through the thickness of the film I z = Ioe\u2212 z+ t/2 /d. 3 Io is the light intensity at the top surface and d is an attenuation length.10 The photostrain that results from photoisomerization is assumed to be proportional to the light intensity, i",
            " The proportionality constant is taken to be such that ps Io is the strain that would occur if the film were uniformly irradiated through the thickness with intensity Io this would be physically realized if the attenuation length d was much greater than the film thickness t . As a result, the effect of Io is incorporated into the definition of ps and the remainder of our discussion will be cast in terms of the latter. An alternative way to model the effects of the photostrain on the film deformation is to treat the film of total thickness t as a bilayer with upper and lower layers of thickness t1 and t\u2212 t1 as shown in Fig. 1 b . The photostrain is taken to have a constant value in the upper layer and to vanish in the lower layer, i.e., p z = \u2212 pl z t1 = 0 t1 z t . 5 In both the exponential and layered representations, two parameters describe the photostrain. It turns out that the macroscopic deformation of the films can be characterized in terms of a uniform midplane strain and curvature. The variation of the photostrain through the thickness effects this deformation only in an integral sense, and so we can develop an equivalence between the two representations for their effect on the macroscopic deformation, and express pl and t1 in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002935_iros.1993.583168-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002935_iros.1993.583168-Figure5-1.png",
        "caption": "Fig. 5 Definition of vectors for walking system",
        "texts": [
            " (1) Modeling of the robot (2) Derivation of the equations of three-axis moment (3) Computation of the trunk motion The other is a program control for walking using preset walking patterns transformed from the motion of the lowerlimbs and the trunk. In this section, the algorithm to compute the balancing motion of the trunk is described. 3.1 Mod&ny of the IWmt On the basis of the problem mentioned in chapter 1, let the walking system be assumed as follows [41[61[81: (1) The robot is a system of particles. (2) The floor for walking is rigid and can not be moved by any forces and moments. (3) A Cartesian coordinate system 0-XYZ is set, where the Z-axis is vertical, the X-axis and Y-axis form a plane which is the same as that of the floor (Fig. 5) . (4) The contact region between the foot and the floor is a set of contact points. ( 5 ) The coefficient of friction for rotation around X , Y and Z-axis is zero at the contact point. In (l), the machine model is regarded as a model that has three particles in the hunk and n particles in the lower-limbs as shown in Fig. 6. On the 0 - X Y Z , let each vector to be established as shown in Fig. 5 and Fig. 7. An equation of the motion at an arbitrary point P is obtained by applying DAlembert's Principle as follows: n m,,r;'xf0'+~mi(ri -P)x(r i+G)+T=O ( 1 ) i=O P(xp, yp, ZJ i s defined as ZMP, so we denote P(x,, yp, z,,) as Pmp(x,p, y,, z-,). To consider the relative motion of each part, a translationally moving coordinate W(X, Y, 2) is established on the waist of the robot on a parallel with the fixed coordinate 0-XYZ ( shown in Fig. 6 ), Q(x,, y,. z,) is defined as the origin of W(X, Y, 2) on the 0 - X Y Z "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure5.20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure5.20-1.png",
        "caption": "Fig. 5.20 Jumo 004B turbojet engines in Me 262 jet fighter, the first jet aircraft (http://www. aircraftenginedesign.com/custom.html3.html)",
        "texts": [
            " In 1937, experiments of the engine failed due to a fuel leakage. Then the British government had no more interest in the engine. The theoretical and experimental research was mainly done by the British, but the practical work was left to the German. Hans von Ohain, a German engineer, designed a jet engine independently. Then he joined Heinkel Co., which was working on the design of jet engines. In August 1939, the first jet airplane in the world was created in Germany, and successfully tested in flight (Fig. 5.20). WWII provided a test field for various aircrafts. Aircrafts entered the jet age after the war. 164 5 Second Industrial Revolution Inventions of various machines, excluding power machines and machine tools, during the Second Industrial Revolution are shown in Table 5.4. After entering the era of steel, the fast growth of the machine industry dramatically increased the demand for steels, and further promoted the development of mining machinery. In 1863, a British, Thomas Harrison, made the first practical coal cutter (Singer et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.2-1.png",
        "caption": "Figure 2.2. Meshing diagram of a pinion and the basic rack.",
        "texts": [
            " the thi rd s equation shows that the circular pitch of the gear at its standard pitch circle is equal to the pitch of the basic rack, RS NPr (2.3) 21r Ps 211'Rs N (2.4) Ps Pr (2.5) Tooth Profile of an Involute Gear 27 The Involute Tooth Profile We will now determine the shape of gear tooth profiles which are conjugate to the basic rack in Figure 2.1. The word conjugate means, as we defined it in Chapter 1, that the gear teeth are shaped in such a manner that the Law of Gearing is satisfied, when the gear is meshed with the basic rack. In Figure 2.2, a pinion is shown meshing with the basic rack. The plnlon pitch circle radius is Rs' given by Equation (2.3), and the pitch line is the line in the basic rack which touches the pinion pitch circle at the pitch point P. The Law of Gearing states that the common normal at the contact point must pass through P. For any particular position of the rack, there is only one point Ar of the rack tooth profile whose normal passes through P, and this point must be the contact point. The pinion tooth must therefore be shaped so that its profile touches the rack tooth at Ar \u2022 28 Tooth Profile of an Involute Gear The point of the pinion tooth profile in Figure 2.2 which coincides with Ar is labelled A. The line joining the contadt point to the pitch point is called the line of action, since it coincides with the common normal at the contact point, and therefore in the absence of friction the contact force must act along this line. The angle between the line of action and the tangent to the pinion pitch circle at P is called the operating pressure angle ~ of the gear pair. Since the line of action is perpendicular to the tooth profile of the basic rack, it can be seen from the diagram that, when a gear is meshed with its basic rack, the operating pressure angle of the gear pair is equal to the pressure angle of the basic rack, (2",
            " This result is true for any position of the basic rack. Hence, the path of contact, which is the locus of all contact points, is a segment of the same straight line. And since the line of action is always the line joining the pitch point to the contact point, the direction of the line of action is fixed, and the line of action coincides with the line containing the path of contact. We now construct the perpendicular from the pinion center C to the line of action, and the foot of this perpendicular is labelled E, as shown in Figure 2.2. The pinion circle with center C and radius equal to CE is known as the base circle, and its radius is represented by the symbol Rb \u2022 Since the rack tooth profile and line CE are both perpendicular to the line of action, they must be parallel, and the angle ECP is equal to ~r' We can then use triangle ECP to express the base circle radius in terms of the standard pitch circle radius, (2.7) Alternative Definition of the Involute 29 The shape of the pinion tooth must be such that the normal to the tooth profile at point A passes through P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000812_j.matchar.2021.111020-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000812_j.matchar.2021.111020-Figure2-1.png",
        "caption": "Fig. 2. SLM process schematic diagram of gradient alloy steel.",
        "texts": [
            "5 mm were obtained. The substrate used in this research was 316 stainless steel plate with a size of 140 \u00d7 140 \u00d7 15 mm. The SLM equipment consisted of a fiber laser with the wavelength of 1070 nm and the beam diameter of the laser focal was 70 \u03bcm. The processing parameters used are optimized and adjusted based on the previous experiments of our team [10]. The constant deposition layer thickness was 50 \u03bcm. The other variable parameters list in Table 2. Schematic diagram of the SLM process are shown in Fig. 2. The prepared specimens were divided into four section according to the composition gradients by wire cutting. Prepared metallographic specimens according to the standard procedures, and the polished specimens of G1-G4 were etched via nitric acid alcohol solution (4 mL HNO3 + 96 mL C2H5OH) and aqua regia (1 mL HNO3 + 3 mL HCl), respectively. Phase analysis of SLMed samples were performed through X-ray diffraction (XRD, XRD-7000) with Cu-K\u03b1 radiation (\u03bb = 1.5406 \u00c5) at 4\u25e6/min over the range of 20\u25e6 - 100\u25e6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003459_robot.1996.503783-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003459_robot.1996.503783-Figure9-1.png",
        "caption": "Fig. 9 Control of landing motion",
        "texts": [
            " I) Latter Swing Phase: The robot walks with the standard walking pattem, until the preset swing-leg landing time in the standard walk- 11) Landing Phase: In thisstudy, wedefine the landing phase as the period between the time when the swing leg touches the path surface or the preset landing time ofthe foot plate has passed on the standard walking pattem and thie beginning of a double support phase on the standard walking pattem. During this phase foot lowering operation is performed using expression (2) so that the actual distance between the foot plates folk w the changes in the theoretical distance between the foot plates when walking on the horizontal, smooth path on the standard walking pattern. Fig. 9 shows the appearance ofthe correction of the lower-limb trajectories. (2) zd(R) = 'O*(#-,, *' ' d ( R > = Xd(#-l) -Hr(R-l> cosaR-,) (hri(#> sinas -H,(R-l) ZO'(,), XO'(,,: The Zmand theX\"coordinatesoftheoriginsofthe detection coordinates, in the detection of landing surfaces at \"n\" times. Thesimuhted distance between foot plates when walking on horizontal and flat surfaces with the standard walking pattems, in tke detection of landing surfaces at \"n\" times. HV(,): The actual distance between foot plates, in the detection of landing surfaces at \"n\" times"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000156_s11071-020-05481-1-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000156_s11071-020-05481-1-Figure1-1.png",
        "caption": "Fig. 1 Aircraft model and thrust vector diagram",
        "texts": [
            " 4 gives the simulation results and robustness verification; and the conclusions are provided in Sect. 5. The mathematical model of the aircraft comes from a benchmark mathematical model [12]. In order to avoid the singularity due to the high angle of attack, a mathematical model based on the track coordinate system is derived. In addition, the thrust vector technology needs to be adopted owing to the poor control effectiveness of aerodynamic actuators. Therefore, a mathematical model with thrust vector model is presented first. The aircraft and coordinate diagram is shown in Fig. 1. The meaning of nomenclature and variables can be found in \u201cAppendix.\u201d 2.1 Nonlinear dynamic model V\u0307 = 1 m [\u2212D + Y sin(\u03b2) \u2212 mgsin(\u03b3 )] + 1 m [Txcos(\u03b2) cos(\u03b1) + Tysin(\u03b2) + Tzcos(\u03b1)sin(\u03b2)] (1) \u03b1\u0307 =q \u2212 tan(\u03b2)[pcos(\u03b1) + rsin(\u03b1)] + 1 mV cos(\u03b2) [\u2212L + mgcos(\u03b3 )cos(\u03bc)] + 1 mV cos(\u03b2) [\u2212Tx sin(\u03b1) + Tzcos(\u03b1)] (2) \u03b2\u0307 = \u2212 rcos(\u03b1) + psin(\u03b1) + 1 mV [Y cos(\u03b2) + mgcos(\u03b3 )sin(\u03bc)] + 1 mV [\u2212Tx sin(\u03b2)cos(\u03b1) + Tycos(\u03b2) \u2212 Tzsin(\u03b2)sin(\u03b1)] (3) \u03b3\u0307 = 1 mV [Lcos(\u03bc) \u2212 Y sin(\u03bc)cos(\u03b2)] \u2212 Ty mV cos(\u03b2) + Tx mV [sin(\u03bc)sin(\u03b2)cos(\u03b1) + cos(\u03bc)sin(\u03b1)] + Tz sin(\u03b1) [sin(\u03bc)sin(\u03b2)sin(\u03b1) \u2212 cos(\u03bc)cos(\u03b1)] (4) \u03c7\u0307 = 1 mvcos(\u03b3 ) [Lsin(\u03bc) + Y cos(\u03bc)cos(\u03b2)] + Ty mvcos(\u03b3 ) cos(\u03bc)cos(\u03b2) + Tx mVcos(\u03b3 ) [sin(\u03bc) sin(\u03b1) \u2212 cos(\u03bc)sin(\u03b2)cos(\u03b1)] \u2212 Tz mV cos(\u03b3 ) [cos(\u03bc)sin(\u03b2)sin(\u03b1) + sin(\u03bc)cos(\u03b1)] (5) \u03bc\u0307 = 1 cos(\u03b2) [pcos(\u03b1) + rsin(\u03b1)] + L mV [tan(\u03b3 )sin(\u03bc) + tan(\u03b2)] + Y + Ty mV tan(\u03b3 )cos(\u03bc)cos(\u03b2) \u2212 g V (cos(\u03b3 )cos(\u03bc)tan(\u03b2)) + Tx sin(\u03b1) \u2212 Tzcos(\u03b1) mV [tan(\u03b3 )sin(\u03bc) + tan(\u03b2)] \u2212 Txcos(\u03b1) + Tzsin(\u03b1) mV [tan(\u03b3 )cos(\u03bc)sin(\u03b2)] (6) p\u0307 = Izz(la + lT ) + Ixz(na + nT ) Ixx Izz \u2212 I 2xz + Ixz(Ixx \u2212 Iyy + Izz) Ixx Izz \u2212 I 2xz pq + Izz(Iyy \u2212 Izz) \u2212 I 2xz Ixx Izz \u2212 I 2xz qr (7) q\u0307 = (ma + mT ) + (Izz \u2212 Ixx )pr + Ixz(r2 \u2212 p2) Iyy (8) r\u0307 = Ixz(la + lT ) + Ixx (na + nT ) Ixx Izz \u2212 I 2xz + Ixx (Ixx \u2212 Iyy) + I 2zz Ixx Izz \u2212 I 2xz pq \u2212 Ixz(Ixx \u2212 Iyy + Izz) Ixx Izz \u2212 I 2xz qr (9) x\u0307E =V cos(\u03b3 )cos(\u03c7) (10) y\u0307E = V cos(\u03b3 )sin(\u03c7) (11) z\u0307E = \u2212 V sin(\u03b3 ) (12) D,Y, L represent aerodynamic drag, lateral force and lift force, respectively, and can be obtained by \u23a1 \u23a3 D Y L \u23a4 \u23a6 = \u23a1 \u23a3 \u2212 cos\u03b1 cos\u03b2 \u2212 sin \u03b2 \u2212 sin \u03b1 cos\u03b2 \u2212 cos\u03b1 sin \u03b2 cos\u03b2 \u2212 sin \u03b1 sin \u03b2 sin \u03b1 0 \u2212 cos\u03b1 \u23a4 \u23a6 \u23a1 \u23a3 q\u0304 SCx_tot q\u0304 SCy_tot q\u0304 SCz_tot \u23a4 \u23a6 (13) and the aerodynamic torque can be obtained by\u23a1 \u23a3 la ma na \u23a4 \u23a6 = \u23a1 \u23a3 q\u0304 SbCl_tot q\u0304 ScCm_tot q\u0304 SbCn_tot \u23a4 \u23a6 (14) Ci_tot(i = x, y, z) and C j_tot( j = l,m, n) denote the total aerodynamic force and torque coefficients, respectively, which are nonlinear functions for \u03b1, \u03b2 and the aerodynamic control surfaces \u03b4i (i = e, a, r), and can be obtained by interpolation and calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.8-1.png",
        "caption": "Figure 12.8. positions for radial assembly.",
        "texts": [
            " The tooth shapes of the pinion and the internal gear will always allow axial assembly, provided the gear pair has been designed so that there is no interference or tip interference. In some gear boxes, however, axial movement of the pinion may be obstructed, and axial assembly is then 276 Internal Gears impossible. In this case, the gear pair must be assembled in the radial manner, and we must check that such assembly is feasible. The check can be made by the following simple, though long, procedure. Figure 12.8 shows an internal gear pair in position, so that a tooth of the pinion is lined up with a tooth space of the internal gear. We draw the ~ and ~ axes on the diagram, so that the ~ axis coincides wi th the center-line of the pinion tooth. The points AT2 , AT2 , AT2 , etc, shown on the internal gear, are the corner points of the teeth closest to the ~ axis. On the pinion, points A1, A;, Ai, etc, are the points of each tooth which are furthest from the ~ axis. For the teeth near to the ~ axis, these points lie at the intersection of the tooth profiles with the vertical tangent to the base circle, and their distance from the E axis is equal to half the span measurement 5, which was given by Axial and Radial Assembly 277 Equation (8",
            " For the remaining teeth, the point furthest from the ~ axis is the corner point of the tooth. In order to determine whether the gear pair can be assembled radially, we calculate the ~ coordinates of the labelled points on the pinion, and check that in each case they are less than the ~ coordinates of the corresponding points on the internal gear. If this condition is satisfied for each pair of points, then radial assembly can be carried out. In cases where radial assembly is not possible in the position of Figure 12.8, we can consider an alternative position, as shown in Figure 12.9. We place the gear pair so that a tooth space of the pinion is lined up with a tooth of the internal gear, and again we calculate the ~ coordinates of the various tooth points. As before, radial assembly is only possible if each point on the pinion is closer to the ~ axis than the corresponding point on the internal gear. The minimum value of (N2-N 1) for which radial assembly is possible depends primarily on the pressure angle. For 278 Internal Gears example, radial assembly of 20\u00b0 pressure angle gear pairs can generally be carried out when (N2-N 1) is 17 or larger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure2-14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure2-14-1.png",
        "caption": "Figure 2-14 Sketch of time evolution trajectories of a third-order system of equations and a typical Poincare plane.",
        "texts": [
            " In electrical systems or feedback control devices, self-excited oscillations can arise from negative resistance elements or negative feedback. One is then led to ask how to choose the sampling times in a Poincare map. Here the discussion gets a little abstract. Consider the lowest-order chaotic system governed by three first-order differential equations (e.g., the Lorenz equations of Chapter 1). In an electromechanical system, the variables x(t\\ y(t\\ and z ( t ) could represent displacement, velocity, and control force as in a feedback-controlled system. We then imagine the motion as a trajectory in a three-dimensional phase space (Figure 2-14). A Poincare map can be defined by constructing a two-dimensional oriented surface in this space and looking at the points (xw, yn, zn) where the trajectory pierces this surface. For example, we can 54 How to Identify Chaotic Vibrations choose a plane nxx + n2y + n3z = c with normal vector n = (nl9 n2, n3). As a special case, choose points where x = 0. Then the Poincare map consists of points that pierce this plane with the same sense; that is, if s(t) represents a unit vector along the trajectory, s(tn) \u2022 n must always have the same sign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000528_s11661-021-06211-x-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000528_s11661-021-06211-x-Figure10-1.png",
        "caption": "Fig. 10\u2014Schematic of cross section of the specimens, showing print layer at perimeters and related voids between perimeter walls, following section in Fig. 2: (a) the flat layout (Section AA), (b) the side layout (Section BB), (c) the vertical layout (Section CC), (d) shows the formation of rectangular void between perimeters walls, (e) the interactions of load direction and voids of the flat and side layouts and (f) the interactions of load direction and voids of the vertical layout.",
        "texts": [
            " This is attributed to the difference in the characteristics of voids between perimeter walls and of the porosity which were affected by the different specimen layouts, especially for vertical layout. For better understanding, the schematics of cross-sectional specimens and related voids between perimeter walls of specimens printed in the flat (section AA in Figure 2) and side layouts (section BB in Figure 2) are shown in Figures 10(a) and (b), respectively. For the vertical layout (section CC in Figure 2), the schematics, displaying cross sections of voids lines, are shown in Figure 10(c). These voids are commonly present in FDM processed material having different shapes due to differences in the printing strategy and parameters.[28] The formation of triangular-shaped voids, found in the flat and side layouts, is shown in Figure 10(d). During printing, the printing path is compressed, densified, and adhered to the previous adjacent layers but it still needs to maintain their shape, which cannot be fully dense. The retention of the triangular voids is therefore difficult to prevent in the perimeter region where there is no hatching in the perpendicular direction. In ductile metallic materials, failure usually occurs as a result of microscopic void nucleation and coalescence that is initiated by the presence of second phases such as carbides, non-metallic inclusions and by pre-existing voids within the microstructure",
            " Consequently, the tensile properties of the specimen printed in the vertical layout are significantly lower than those of the flat and side layouts, due to the existence of the very large size of defects, e.g., incomplete fusion and cross section of voids between perimeter walls that reduce the load-bearing area under stress. In addition, the interaction of load direction and voids also gives rise to the highest stress concentration at the corner of the voids, as expressed in schematic form in Figure 10(f). This causes high shear stress at that corner of the voids, leading to easier failure. These results are consistent with the tensile results of polymer and 316L fabricated by FDM process, in which the vertical layout exhibits significantly inferior tensile properties than the flat and side layout.[10,30] Layer delamination is the main failure in the vertical layout,[31] which is similar to this study that the fracture occurs at inter-layer positions. For the specimens printed in the side layout, which exhibits higher tensile properties with a slightly lower relative density than those printed in the vertical layout, this suggests that the layer delamination has greater influences on the tensile results than porosities in the vertical layout, where the printed layers are perpendicular to the loading direction",
            " Large variations can be expected when determining the circularity due to the wide range of void shapes in each specimen, i.e., many circular voids are included during measurements. It is interpreted that the shape of voids in the side layout has more acute angle and is more detrimental than that of the flat layout. This is consistent with fracture surfaces, where there are more fracture paths along the edge of triangular voids in side than in the flat layout. During tensile loading, due to the reduction in load-bearing area, cracks are initiated at corners of detrimentally shaped voids (Figure 10(e)), and cracks then propagate to the neighboring voids along the side of triangular void. This fracture model is in good agreement with a study, which proposed that, after microcracks and strain localizations are formed, final fracture follows a path to join up the microcracks.[38] This study has examined the effects of specimen layout on the as-sintered physical and mechanical properties of 17-4PH stainless steel fabricated by a metal-fused filament additive manufacturing process. The key results are the following: (1) The specimen layout affects the appearance of as-printed and as-sintered specimens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003223_tro.2006.882956-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003223_tro.2006.882956-Figure1-1.png",
        "caption": "Fig. 1. Tiltrotor-based rotorcraft.",
        "texts": [
            " Effectively, Gress proved in [4] that the total number of reactive devices, namely, propellers, could in fact be reduced to two by using their gyroscopic nature. He considered tilting rotors in order to obtain the three required moments (roll, pitch, yaw). However, this mechanism suffers from a weak pitching torque and some parasitic moments. In this paper, we propose an alternative configuration where the center of mass of the UAV is located below the tilting axes, resulting in a significant pitching moment. We have constructed two prototypes of a birotor rotorcraft, as shown in Fig. 1, inspired by Gress\u2019s mechanism. The experimental results showed that this aerodynamical configuration is very promising. The advantage of this design is that the reaction torque of the motors is cancelled, since the noncyclic propellers (propellers with a fixed blade angle) rotate in different directions. This configuration is also adapted for the miniaturization of the UAV, and it results in a simple mechanical realization. In addition, our main contribution is to provide a complete model of the birotor rotorcraft, and to develop a control algorithm for stabilization and trajectory tracking based on backstepping methodology [5]\u2013[8]",
            " Robustness against unmodeled inputs and external forces [see Fig. 4(b)] is also observed, even if a mathematical analysis of the controller robustness is not provided in this paper. The analysis presented here has shown that hover control of a two-propeller VTOL aircraft is possible using two tilting rotors. The pitch stability is increased by combining the OLT with the LT of the two rotors. The resulting oblique tilting appears to be effective and practical. Indeed, the experimental results obtained on prototypes constructed by our team [see Fig. 1(b)] are very promising. In this paper, we have also developed a 6-degree-of-freedom model of the birotor aircraft and synthesized a nonlinear controller which leads to a satisfactory control. To the authors\u2019 knowledge, no other control law has been derived for a small tiltrotor-based rotorcraft model. [1] G. K. Yamauchi, A. J. Wadcock, and M. R. Derby, \u201cMeasured aerodynamic interaction of two tiltrotors,\u201d in Proc. AHS 59th Annu. Forum, Phoenix, AZ, May 2003, pp. 1720\u20131731. [2] D. Wyatt, Bell Eagle Eye UAV Pocket Guide"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure8-6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure8-6-1.png",
        "caption": "Figure 8-6. Example of durometer mechanism",
        "texts": [],
        "surrounding_texts": [
            "For many years there was no move to produce an international standard for durometers but one was eventually published in 1986. ISO 7619 is now in two parts\"\u0302 \"\u0302 ' \u0302 ^, separating a meter calibrated in IRHD from the others. Part 1 now covers the Shore A and D type meters, a meter designated AO for soft materials and a micro Shore type meter designated AM. The Shore A scale corresponds approximately to the IRHD scale and the D scale can conveniently be used for hard rubbers above about 90 Shore A. The AO meter is suitable for rubbers less than 20 Shore A, whilst the AM meter covers the normal Shore A range. As expected from its name, the meter in Part 2 of the standard covers the IRHD range. The mechanism by which the spring pressure is applied and the indentation measured varies, but Figure 8.6 shows, as an example, the principle of the IRHD meter. The type A meter uses an indentor in the form of a truncated cone, types D and AM use a cone with a rounded end, whilst type AO and the IRHD meter use a hemispherical indentor. A clear advantage of the hemispherical geometry is the elimination of the problem of rapid wear on the Shore indentors. For the A, D, AO and AM meters, there is a defined relation between spring force and hardness, i.e. the spring Short term stress-strain properties 129 force varies with indentation. The IRHD meter is different in that the spring pressure is essentially constant over the whole range, varying by 0.15 N in a 2.65 N mean force as against between 550mN and 8050 mN in the Shore A, and it is this feature that enables it to mimic the standard IRHD scale. A significant change in the latest version of ISO 7619-1 (apart from the introduction of types AO and AM) was the tightening of the tolerances on the indentor and foot geometry and the spring force. For example, the tolerance on the truncated cone diameter for type A went from 0.03 to 0.01 mm and the spring force tolerance from 80 to 37.5 mN. These new tolerances are intended to improve the accuracy of measurements (see Section 4.4) but are likely to cause very considerable problems with existing instruments not complying and making the process of calibration more difficult. The tolerances for the IRHD meter were not changed although a good case could have been made to reduce the tolerance on the spring pressure. A minimum thickness of 1.5 mm for the type AM and 6 mm for the other instruments is specified. The standard time of application of the load is 3 sec for vulcanized rubber and 15 sec for thermoplastic rubbers, which is a change from the instantaneous reading specified previously. This is of course arbitrary and a compromise between \"instantaneous\", which is very uncertain, and long enough for equilibrium to be assured, which is time consuming. It is recognized that other times may be used and, in practice, there will be those who prefer instantaneous readings and those who use 30sec as for dead load methods. Also, when testing products, all manner of unreasonable test piece geometries are used, resulting in many instances in very large variabihty. The effect of time is considered further in Section 4.5. The use of durometers on a stand is supported in 7619-1, reflecting the practice of using them as an alternative to IRHD. In fact, type AM is specified as always being so used, which completely negates it being a portable instrument. When used on a stand, there are requirements for a timer, the load on the foot and speed of application. Also, the instruments can use any suitable transducer to measure indentation and be connected to a computer in the same way as for dead load testers. The standard does not consider the relation between the Shore scales and modulus but this has been investigated by Briscoe and Sebastian\"\u0302 ^ and Qi et The UK voted negatively on the ISO 7619 standards and at the time of writing the British standard, BS 903 Part A 57^^ is the same as the 1997 version of the ISO standard. This means it does not include the AO and AM types and does not have the reduced tolerances. Durometers are also covered in ASTM D2240'\u0302 ^ which specifies no less than eleven scales, A, B, C, D, DO, E, M, O, 0 0 , 0 0 0 and 000-S plus R referring to a particular foot geometry. A, D, E and M correspond to the ISO types A, D, AO and M, a significant difference being that ASTM has not"
        ]
    },
    {
        "image_filename": "designv10_4_0000958_tie.2021.3068674-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000958_tie.2021.3068674-Figure4-1.png",
        "caption": "Fig. 4 Signal flow of the modulation process of air-gap armature MMF.",
        "texts": [
            " Since the air-gap PM field was modeled in Part I, the modulation process of the air-gap armature magnetic field due to armature currents is analyzed here. According to MFMT, in the modulation process of the air-gap armature magnetic field, the three-phase windings injected with the following currents in (2) work as an excitation source to establish the primitive armature MMF Fw(\u03b8,t) [25-27]. Similar to the formation of the PM magnetic field, the stator and the rotating rotor provide static and dynamic modulation on the primitive armature MMF. Then, the air-gap armature magnetic field is formed as illustrated in Fig. 4.         )32sin()( )32sin()( )sin()( 0 0 0    ttIti ttIti ttIti eemC eemB eemA (2) where \u03c9et0 represents the initial current phase of phase A @t=0. The modulation process of the air-gap armature MMF of a 12s/10p FSPM machine is shown in Fig. 5, where the combined three-phase primitive armature MMF waveform is in blue, and the stator and rotor modulation functions are in green, and the modulated armature MMFs are in red respectively. Supposing that the stator and rotor are smooth and the wires are concentrated in the middle of slots, the waveform of the air-gap primitive armature MMF excited by single-phase current is an ideal square wave"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000094_j.jmapro.2020.03.018-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000094_j.jmapro.2020.03.018-Figure2-1.png",
        "caption": "Fig. 2. The trajectory of the molten droplets (a) in Free flight transfer and (b) in short arc transfer.",
        "texts": [
            " During Free Flight modes, the droplet trajectory from the wire tip to the weld pool is important. Norrish [17] describes the mechanism of metal transfer in terms of the balance of forces acting on the system, which includes gravitational force, aerodynamic drag, electromagnetic forces, vapour jet forces and surface tension. In positional free flight transfer, the gravitational force may be sufficient to exceed the axial forces which would normally project the droplet across the arc resulting in displacement of the material from the target position. This is illustrated in Fig. 2a. In addition, the common spray transfer mode only operates above a minimum transition current, a large molten weld pool is usually formed, which is undesirable for the multi-directional deposition process.. In short arc transfer, a droplet forms on the wire tip during the arcing phase, but material transfers when the wire tip contacts the base metal. Droplets transfer to the weld pool is influenced by the gravitational force less. Fig. 2b indicates that the molten metal normally transfers accurately on the target position when the correct welding parameters are used. For this reason, the short arc transfer has been used to deposit material in all positions. In addition, the positional performance of both free flight and shortcircuiting transfer may be improved by using dynamic control of transient welding current and wire feeding. These techniques are now known collectively as \u2018waveform controlled\u2019 in GMAW. Norrish [17] also argues in the case of spray transfer, the current may be pulsed to produce a strong axial transfer of droplets at low mean current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure8-1.png",
        "caption": "Fig. 8. Growth of the same cone as in Fig. 7, but viewed from axes fixed to the cone so that the growth surface moves to the left at velocity v 0",
        "texts": [
            " Also note that the cells on G move radially outward with radial velocity v 0 tanb, as time increases as indicated by Eqs. (43) and (44) and G must increase in area as time increases. If the range of h 1 , h 2 is terminated at some angle c 1 where c 1 (c, a hollow horn is generated as indicated by the stippled area in Fig. 7. Example 3.4. Axes fixed relative to the growing body Consider the same cone structure and growth as shown in Fig. 7, but viewed from axis x which are fixed to the growing body. In this case, the growth surface G moves to the left at velocity (!v 0 ) as shown in Fig. 8. The length of the cone is \u00b8\"v 0 t, the radius of G is a\"kt, and the cone half-angle is c where tan c\"(k/v 0 ), as in Fig. 7. Equation (1) describing the growth in Fig. 8 is obtained from Eqs. (38)\u2014(40) by replacing x 3 by (x 3 #v 0 t). Then x 1 and x 2 are again given by Eqs. (38) and (39), but Eq. (40) changes to x 3 \"!v 0 h 3 . It can be readily shown that g is again given by Eq. (34), but now x5 m\"0 and x5 G\"! g . The physical interpretation is now that the cells on G are moving along the cell tracks that they are generating and leaving the new material behind them at rest. It is noteworthy that in the Examples 3.3 and 3.4 that the vector growth velocity g is independent of the reference system x, as it should be when properly defined",
            " 9A at time t\"(n/2k) when the centerline is a quarter circle and the radius of G is a 0 . The coordinate h 3 is again taken to be h 3 \"q where q is the time at which a particular particle is initiated on G. Then h 3 \"constant, is a plane containing the x 3 axis. Several such planes are shown in Fig. 9B. In each such plane, the cross-section of the horn will be a circle. Example 3.6. A curvilinear horn of logarithmic spirals Consider producing a horn with the external form shown in Fig. 9, but with cell tracks which are at constant angles to the centerline, similar to Fig. 8, as compared to Fig. 6. This may be accomplished by the use of logarithmic spirals which are extensively discussed by D\u2019arcy Thompson (1942) in connection with the forms of shells, horns and other biological forms. Logarithmic spirals are plane curves (Fig. 10) described by r\"beh #05 a , (54) where r, h are polar coordinates and b and a are constants. The angle between the tangent to the spiral and the radius vector r is the constant angle a. This property is suggested in the alternate name of equiangular spiral",
            " 11 is a cross-section of a horn with the following logarithmic spirals as the cell tracks. The problem to be solved is to find the growth velocity g that produces this horn. From Table 1 it can be seen that the center-line curve C 0 is a circle. The curves C 1 and C 2 are logarithmic spirals which spiral outwards. The curves C 3 and C 4 are logarithmic curves spiraling inwards. The constants in Table 1 have been adjusted so that all curves meet at the point (50, 0) so C 0 is a quarter of a circle. The cross-section shown in Fig. 11 is the curved counterpart of Fig. 8 in the sense that along any radius in Fig. 11 the angle between tangents to the curves C 0 , C 1 , C 2 , C 3 , C 4 are constants independent of h. The same is true for the cell tracks in Fig. 8, for any line drawn parallel to the x 1 axis (which is the analogue of r as rPR). To complete the description of the 3-D horn, whose section is shown in Fig. 11, we assume that G is always a circle, and that as a result, sections h 3 \"constant, are planes containing the x 3 axis. The cross-sections on such planes are then also circles. Curves on which (h2 1 #h2 2 )\"constant, are also circles in the interior on h 3 \"constant planes. The stipulation that G is always a circle, together with the two cell tracks C 1 and C 4 , completely defined the external geometry of the horn"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000143_j.ijheatmasstransfer.2019.119187-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000143_j.ijheatmasstransfer.2019.119187-Figure4-1.png",
        "caption": "Fig. 4. Schematics of computational domains and boundary cond",
        "texts": [
            " (14) [43] . i j = 1 2 ( \u03b7i, j + \u03b7 j,i ) + \u03b1 T \u03b4i j (14) here \u03b5 is the strain tensor, \u03b7 is the displacement vector, and \u03b1 is he coefficient of thermal expansion. T denotes the temperature ariation in the solid domain. The stress tensor is given by Eq. (15) . The shear modulus and am\u00e9 constant are given by Eqs. (16) and (17) , respectively. i j = 2 G \u03b5 i j + \u03bb \u03b4i j (15) = E 2 ( 1 + \u03bd) (16) = \u03bdE ( 1 + \u03bd) ( 1 \u2212 2 \u03bd) (17) here E is Young\u2019s modulus, and \u03bd is Poisson\u2019s ratio. .4. Boundary conditions Fig. 4 shows the schematics of the computational domains and oundary conditions. In the thermal-fluid analysis, duct lengths of 0 mm were specified at the inlet and outlet for a fully develped water flow. The duct wall was set at no-slip and adiabatic onditions. In the model validation, adiabatic boundary conditions ere applied on both lateral outer walls, and the heat flux on the orking surface was set at 120 kW m \u22122 . In the simulation, peri- dic boundary conditions were applied on both lateral outer walls, nd the heat flux on the working surface was set at 500 kW m \u22122 onsidering actual operating conditions for hot stamping, metal inection, and die casting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000763_j.bbe.2020.12.010-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000763_j.bbe.2020.12.010-Figure2-1.png",
        "caption": "Fig. 2 \u2013 The front and side view of th",
        "texts": [
            " We will improve the structure design and choose lightweight materials so that the exoskeleton can continuously meet more movement requirements in the future. The rest of this paper is organized as follows. In Section 2, the overall mechanical structure, knee joint module, ratchet structure, ankle module design and static analysis are introduced in detail. Then, the human testing is described in Section 3. Next, the experimental results and analyses are presented in Section 4. A conclusion is drawn in Section 5. Finally, the conclusion is presented in Section 6. The overall prototype of the weight support exoskeleton is exhibited in Fig. 2. It consists of an ankle module, a knee module, and straps (waist straps, thigh straps, and shank straps). The exoskeleton will not interfere with normal activities of wearers, they can freely walk, squat, and climb stairs with the device. The hip joint is not included in the passive exoskeleton to optimize the overall mechanical structure; the knee joints have a passive flexion/extension degree of freedom; the ankle joints have a metatarsal flexion/ dorsal flexion and an abductor/adductor degree of freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure3-22-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure3-22-1.png",
        "caption": "Figure 3-22 Chaotic lateral motions of the levitated model.",
        "texts": [
            " is analogous to buckling of an elastic column. In our experiments, chaotic vibrations occurred when the system exhibited both divergence (multiple equilibrium states) and flutter. The flutter provides a mechanism to throw the model from one side of the guideway to another, similar to the buckled beam problem discussed in Chapter 2. The mathematical model for this instability, however, has two degrees of freedom. Lateral and roll dynamics 96 A Survey of Systems with Chaotic Vibrations were measured from films of the chaotic vibrations (Figure 3-22)). These vibrations were quite violent and if they occurred in an actual vehicle traveling at 400-500 km/h, the vehicle would probably derail and be destroyed. Many experiments on chaotic vibrations in elastic beams have been carried out by the author and coworkers (e.g., see Moon and Holmes, 1979, 1985; Moon 1980a,b, 1984; Moon and Shaw, 1983). Two types of problems have been investigated. In the first problem, the partial differential equation of motion for the beam is essentially linear, but the body forces or boundary conditions are nonlinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure2.25-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure2.25-1.png",
        "caption": "Fig. 2.25 Manual air bellow",
        "texts": [
            " A bag was made of horse or cow leather, and was pressed by the weight or limb strength to form air blast. This was the first significant improvement on blowers. There was a scene (Fig. 2.24) of using pedal leather bags on a relief in a tomb at Thebes in Egypt, dated 1500 BC (Huang and Qian 2013). Archaeology showed that simultaneous air supply with multi-bags appeared in the West-Zhou Dynasty of China. The leather bag could be driven by humans, animals and/or water power. A manual bag shown in Fig. 2.25 was the remote ancestor of modern air compressors, and still in use in some cases nowadays. Air supply could also be achieved through the reciprocating swing of a wooden fan, driven by humans or water power. In 31 AD, a Chinese officer Du Shi invented a water driven blower (Wang 1981; Lu 2012, 132\u2013134), as shown in Fig. 2.26. At that time, it was a very advanced water driven blower. From the point of view of modern mechanism analysis, it consists of a planar sheave mechanism, a spatial four-bar linkage and a planar four-bar linkage combined in series"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003275_s0022112096001632-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003275_s0022112096001632-Figure2-1.png",
        "caption": "FIGURE 2. Examples of typical domain deformations and the corresponding evolution of the mesh. The meshes shown correspond to the initial (a), intermediate ( b ) and final (c ) stages of a computation with Lo = 15 and Oh = 1.",
        "texts": [
            " It was found that generally only two steps in this iterative procedure were required in order to obtain the desired accuracy. These results justify our approach of assuming that the first approximation to fin+' is sufficiently accurate. As with the interpolation, the slightly increased accuracy obtained by applying the iterative procedure does not warrant the huge increase in the computational cost and hence the iterative procedure is not applied. As an example of the domain deformation we are capable of dealing with, figure 2 shows the initial (a) , intermediate (b ) and the final (c) mesh resulting from a simulation in which Oh = 1 and the initial half-length LO = 15. Note that only one quarter of the domain is plotted owing to the axial symmetry and the symmetry about the plane z = 0. 3.4. Numerical tests It is imperative to test our numerical implementation before we proceed with the liquid filament problem. We do this by considering a slightly extended drop which we allow to relax to its spherical shape. For sufficiently small values of the Ohnesorge number Oh the drop will oscillate and the amplitude of the oscillations decreases owing to the action of viscous forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000540_j.msea.2021.141985-Figure18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000540_j.msea.2021.141985-Figure18-1.png",
        "caption": "Fig. 18. (a) Diagrammatic sketches of cellular structure by side view of dendrite structure; (b) the microstructure perpendicular to the building direction of sample 21#.",
        "texts": [
            " The size of cellular crystals also corresponded to the local cooling rate mentioned above. Some reports [43] have attributed the formation of cellular crystals to the micro-segregation near the molten pool boundary driven by melt convection, the segregation provides heterogeneous nucleation particles for the growth of cellular crystals. But in this study, we judged the cellular crystals were simply the side view of dendrites whose directions were closely perpendicular to BD among other molten pool with 90\u25e6 rotated scanning direction, as shown in Fig. 18(a). The cellular crystals could not be found in a molten L. Zhang et al. Materials Science & Engineering A 826 (2021) 141985 pool with obvious boundary line; it arose between the adjacent molten pools, which was the previous or next layer with 90\u25e6 rotated scanning direction, as shown in Fig. 15(a). The area of cellular crystals increases with increasing energy input, as shown in Fig. 13\u201315. Cellular crystals were hardly found when energy input was low and an oval-shaped molten pool was formed. The area length was only about 15 \u03bcm, while a large number of cellular crystals were observed in semicircle- and wine cup-shaped molten pools when energy input increased, and the area lengths in them were 62 \u03bcm and 90 \u03bcm, respectively. In the case of oval-shaped molten pool, the dendrite growth direction was close to BD, L. Zhang et al. Materials Science & Engineering A 826 (2021) 141985 and dendrite, whose direction was closely perpendicular to BD was little. In the case of wine cup-shaped molten pool, the growth directions of large numbers of dendrites observed in horizontal section are perpendicular to BD, as shown in Fig. 18(b). Consequently, judging from its location, the cellular crystal was considered to be the side view of the dendrite, whose direction was closely perpendicular to BD. Fig. 19 shows EBSD micrographs of the microstructure of samples 9#, 13# and 21#. These as-fabricated samples were both dominated by columnar grains. From the grain boundary maps of Fig. 19(a)\u2013(c), we observed that the columnar crystals were irregular lamellar, large lath and regular lamellar in samples 9#, 13# and 21#, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000554_j.wear.2020.203201-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000554_j.wear.2020.203201-Figure1-1.png",
        "caption": "Fig. 1. Wear mechanism of ball\u2013raceway contact.",
        "texts": [
            " The traditional Archard wear model correlates the wear volume with some physical and geometrical properties of the sliding bodies, such as applied load, sliding distance and hardness, which is a simple and practical model to calculate the adhesive wear amount and wear depth of the ball-raceway contact. However, because of its limitations, the traditional Archard wear model cannot be used directly to analyze the wear of ball screws. Therefore, a new mathematical wear model needs to be introduced by considering the partial contact condition in ball screws. Fig. 1 shows the wear mechanism of the ball\u2013raceway contact relative to the ith ball. Qni and Qsi are respectively the normal contact forces of the ball\u2013nut and ball\u2013screw contacts, \u03b4ni and \u03b4si are respectively the normal contact deformations of the ball\u2013nut and ball\u2013screw contacts, Wni and Wsi are respectively the wear volumes of the ball\u2013nut and ball\u2013screw contacts, and \u0394\u03b4ni and \u0394\u03b4si are respectively the wear depths of the ball\u2013nut and ball\u2013screw contacts. According to Hertz contact theory, the area of contact between the ball and raceway is elliptical, which means the shape of the wear volume can be approximated as an elliptical cylinder, as shown in Fig. 1. According to traditional Archard wear theory, the wear volume is proportional to the normal contact force and sliding distance and is inversely proportional to the hardness of the material. Therefore, the wear volume, Wn\u2019 i\u00f0t\u00de, between the ith ball and the screw raceway (n\u2019 \u00bc s) or the nut raceway (n\u2019 \u00bc n) interface can be expressed as Wn\u2019i\u00f0t\u00de \u00bcK Qn\u2019i\u00f0t\u00de\u22c5Vn\u2019i\u00f0t\u00de\u22c5\u0394t 3H ; i \u00bc 1; 2:::M; (1) where Qn\u2019 i\u00f0t\u00de and Vn\u2019 i\u00f0t\u00de are respectively the normal contact force and velocity of sliding between the ith ball and the raceway, \u0394t is the working time, M is the effective number of balls, H is the hardness of the softer material (for ball screws, H is the hardness of the raceway), and K is a wear coefficient that is a dimensionless constant dependent on the material properties and lubricating condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003333_s0021-9797(03)00148-6-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003333_s0021-9797(03)00148-6-Figure5-1.png",
        "caption": "Fig. 5. Reversible cyclic voltammogram obtained for an ideal metallopolymer film under semi-infinite linear diffusion conditions.",
        "texts": [
            " Under these conditions, a thin section of the metallopolymer film is depleted of Os2+ centers and, in a manner reminiscent of solution phase reactants, semi-infinite linear diffusion controls the peak current. In contrast to the finite diffusion case discussed above, the peak current now increases as \u03c51/2. In order to propagate charge through these metallopolymers, electron self-exchange reactions occur between neighboring oxidized and reduced sites. In order to maintain electroneutrality, this electron hopping process is accompanied by the movement of charge compensating counterions that are mobile within the layer. As illustrated in Fig. 5, provided that the depletion layer remains well within the layer, and ohmic as well as migration effects are absent, the voltammetric response of an ideally responding film is reminiscent of that observed for a solution phase reactant. The effective diffusion coefficient, DCT, corresponding to \u201cdiffusion\u201d of either electrons or charge compensating counterions, can be estimated from the well-known Randles\u2013Sev\u00e7ik equation [23], (5)ip = ( 2.69 \u00d7 105)n3/2AD 1/2 CT C\u03c51/2, where C is the concentration of electroactive sites within the film"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002964_s0890-6955(98)00036-4-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002964_s0890-6955(98)00036-4-Figure13-1.png",
        "caption": "Fig. 13. First remeshing after heating by first laser pulse in finite element simulation.",
        "texts": [
            " The calculated weights of the solidified parts by several pulses of the laser beam agreed qualitatively well with the experimental ones. Remeshing in finite element simulation Finite element meshes are reconstructed after each heating by several laser pulses. Remeshing procedures consist of two processes: one in which the powder shape is changed and finite element meshes are remade after heating by the first laser pulse, and the other in which the shape of the molten ball and powders is changed and finite element meshes are remade after the second heating by the laser beam, as follows. First remeshing 1. As shown in Fig. 13, after the melted part of the powders is removed on the basis of the contour of the melting point in the temperature distribution, finite element meshes are remade in the powders. 2. The shape of the melted part removed from the powders is changed to a ball and finite element meshes are made in the ball. 3. The ball with the finite element mesh is put on the surface of the powders axi-symmetrically. 4. The node a0 of the powder surface is put on the node b0 of the ball surface on the axi- symmetric line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000871_j.ymssp.2021.107970-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000871_j.ymssp.2021.107970-Figure1-1.png",
        "caption": "Fig. 1. The simplified structure of spindle system.",
        "texts": [
            " The influences of spindle speed and the bearing parameters on the vibration behaviors and stability of the spindle system are analyzed by amplitude-frequency characteristic curve, bifurcation diagram, waterfall diagram, time domain waveform, spectrum diagram, trajectory and Poincar\u00e9. In addition, the influences of the eccentricity of the belt pulley, the extended length of the milling tool, as well as the position of the intermediate bearing set on the dynamic behaviors of the spindle are also analyzed. The research results can benefit the structural design of the spindle, optimize the bearings selection, as well as improve the machining accuracy and stability of the spindle. The simplified structure of the CNC vertical milling machine spindle system is shown in Fig. 1, which is mainly composed of tool, pre-tightening nut, tool holder, shaft, synchronous toothed belt pulley and angular contact ball bearings. The spindle shaft is supported by three pairs of angular contact ball bearings. The synchronous toothed belt wheel is driven by the motor, and then drives the spindle and the tool to rotate to complete the processing of the workpiece. In order to model and analyze the dynamic response of the spindle system, the following assumptions are made: (1) There are little effects of small parts such as nuts and the system lubrication on the dynamic behaviors of the spindle system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003426_iros.2003.1250608-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003426_iros.2003.1250608-Figure3-1.png",
        "caption": "Fig. 3. Explanation of the proposed method",
        "texts": [
            " Convex Hull For a humanoid robot whose hands do not touch an environment, the robot can keep the dynamical balance if the ZMP is included in the convex hull of the foot supporting area. By extending this idea, we define the convex hull of the supprting points including the contact points between the hands and the environment(Fig,3(a)). While there are many edges included in the convex hull, we extract the edges of the convex hull where a robot might fall down by the moment around the edge. As shown in Fig.3(a), we focus on three vertices j , X, and Y included in the convex hull. Since the vertex j can leave from the environment while it cannot go inside of the environment, the following inequality can be satisfied. d ~ y ) A q m , t 0, ( j = l , . . . J ) , (14) where plot, A&,,,, and nj denote the position vector of a point included in the edge formed by the vertices X and Y, the infinitesimal rotational displacement of the convex hull around pro[. and the unit normal vector of the environment where the vertex j contacts, respectively",
            " Then we consider the virtual floor above the real floor as shown in Fig.S(b). By using the force f, and moment mE at the GZMP on the virtual floor, we can formulate the moment around the edge including the vertices X and Y as where ez denotes the unit normal vector of the virtual floor. From eq.(19), wc can see that TL affects the moment around the edge when ( p x - py)Tez # 0. In this case, we cannot judge the moment around the edge by simply considering the relationship of position between the edge and the GZMP. Thus we redefine the GZMP as follows (Fig.3(c)): Definition 3 (GZMP(Modified)) The (modijied) generalized zem momem point pp) = [xy) y;') &p)]' is the point on the (virtual) floor at which the moment ZE generated by the reaction force and the reaction moment becomes normal to the edge of the convex hull satisfying the Proposition 2. By using this definition, we can consider the direction of moment around the edge by considering the position of the GZMP. Let the unit vector of the direction of TE be e!\"), and two unit vectors normal to e?' he e!xy' and e?'. The position of the GZMP modified in Definition 3 can be expressed as [O 0 l]T. Since the direction of moment around the edge satisfying Proposition 1 is limited by eq.(18), the region of the GZMP is also limited. To see the region of the GZMP, we considcr the combination of two edges sharing a common vertex as shown in Fig.3(d). We consider the GZMP on the plane including two edges sharing a common vertex. By using two edges, we can divide the plane into four regions. These regions can be identified by the direction of moment around the edge defined by eq.(19). The region of the GZMP is limited to one of the four regions by using eq.(18) if both of the edges satisfy Proposition 2. Fig.3(d) shows the region of the GZMP corresponding to m('\") > 0 and m(\") < 0. Also, Fig.3(e) shows four regions on the plane defined by the vertices X, Y, and Z. We Cuurther consider the change of moment when the robot begins to roll around the edge. Since the moment around the edge generated by the inertial force does not change even if the convex hull rotates around the edge, we only consider the moment generated by the gravity force. The change of moment is expressed as: where R-AB denotes the rotation matrix around the edge including the vertices X and Y whose amount of rotation is -AB, and 13 denotes the 3 x 3 identity matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000079_j.rcim.2019.101916-Figure21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000079_j.rcim.2019.101916-Figure21-1.png",
        "caption": "Fig. 21. (a) The 3D model of the part, (b) A humping free deposition, and (c) The overall appearance of the workpiece.",
        "texts": [
            " The welding process is more stable with a wider range of process parameter selection. ii) When the deposition path has multiple welding directions, for example, the contour path in strategy D in Fig. 20, it is necessary to use the travel speed with the strictest restriction (vertical-up) to guarantee a humping free deposition. The effectiveness of the proposed humping avoidance strategy outlined in this study is demonstrated through the fabrication of a thinwall workpiece with overhanging features. Fig. 21(a) presents the 3D model of the workpiece, the sub-volumes of the workpiece are numbered and the building direction of each sub-volume are also illustrated in Fig. 21(a). The key step for the fabrication of this workpiece is the deposition of the sub-volume two. According to the geometrical feature, a contour path is chosen to fabricate sub-volume two (Note that the start position of each deposition is designate to be different for mitigating the swellings at the connection point). Humping was observed at this situation using normal welding parameters for down-hand welding. Thus, the welding parameters must be carefully selected to avoid the occurrence of humping in the positional deposition. Firstly, the weld path consists of three directions (0\u00b0, 90\u00b0, and 180\u00b0), the welding travel speed should be determined with the most restricted condition (vertical-up) to guarantee a humping free deposition. Then, according to the humping map in Fig. 19, the welding travel speed is limited in the range from 0 to 200 mm/min. Finally, the wire feed speed is determined at 2 m /min to meet its cross-section dimensions. Fig. 21(b) demonstrates a humping free surface of sub-volume which proves the effectiveness of the proposed strategy. The overall appearance of the fabricated workpiece is presented in Fig. 21(c). The present research investigated the humping phenomenon for multi-layer multi-directional WAAM process. Firstly, the mechanism of humping formation was analysed for positional deposition using GMAW in the CMT process mode. It was found that the backward metal flow under the effect of gravity is responsible for the sagged humps in the positional deposition. Secondly, based on the observation of molten pool behaviour, the humping formation mechanism was confirmed. A molten pool dimensional ratio r is identified as an indicator for humping occurrence and can be used to help parameter selection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003605_0360-1285(90)90048-8-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003605_0360-1285(90)90048-8-Figure12-1.png",
        "caption": "FIG. 12. Cooled probe measurements of the rates of deposition of alkali metal sulfates in a coal-fired boiler) 7",
        "texts": [
            " The significance of the temperature gradient in the enrichment of the alkali metals is seen clearly in experimental results obtained by Bishop $7 who studied deposition in an experimental combustor. Bishop 57 observed that no alkali enrichment occurred in deposits formed on targets whose temperature was above a critical value. In contrast, deposits were enriched in sodium and potassium at lower target temperatures, with potassium preferred at surface temperatures below 640\u00b0C. Cutler and Raask 37 examined the deposition of alkali sulfates on cooled probes in a coal-fired boiler and found that the deposition rates increased nonlinearly with the sodium content of the coal (Fig. 12). The nonlinear behavior was attributed to the capture of volatile sodium by the alumino-silicate ash resulting in the release of potassium from the ash. The potassium was also deposited on the probe (Fig. 12). The presence of a thermal gradient may also cause liquid-phase migration of the fused salts. 58 As mentioned previously, Nelson and Cain 41 observed the migration of liquid trisulfates owing to a temperature gradient. However, the significance of thermal migration of liquid deposits in the corrosion process is not entirely clear, although some enrichment via this mechanism may occur. The presence of a temperature gradient between the hot flue gas and the cooler tube walls leads to the enrichment of alkali sulfates, required for liquidphase corrosion, on the tube surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000187_13621718.2019.1595925-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000187_13621718.2019.1595925-Figure2-1.png",
        "caption": "Figure 2. Schematic drawing of the forming process, (a) WAAM, (b) hybrid manufacturing.",
        "texts": [
            " The forming substrate was 12mmthick AA1060-H112 Al plate. The shielding gas of weld torch was 99.99% argon with a flow rate of 25 Lmin\u22121. Before depositing, the polished substrate was fixed on the experimental platform, and cleaned with acetone. The filler wire was dried for one hour in the furnace with 100\u00b0C. The arc mode for the deposition was CMT+Pulse (CMTP). The experimentwas carried out by alternating milling and depositing layer by layer. The experiment parameters were shown in Table 2, and the process was illustrated in Figure 2. For simplification, the distance from the highest point of as-fabricated thin wall to the Table 2. Deposition parameters of hybrid WAAM/Milling manufacturing. Parameters Values Wire filling speed, mmin\u22121 5.5 Scanning speed, mm s\u22121 8 Arc current, A 127 Arc voltage, V 17.5 Feed rate, mm s\u22121 25 Spindle speed, r min\u22121 12,000 Milling thickness, mm 0, 0.4, 0.8, 1.2, 1.6 final milling surface was named as t. The deposition width (w) and height (h) of the thin wall weremeasured by a vernier calliper at 50mm intervals per layer for three times"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000418_acsami.1c04597-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000418_acsami.1c04597-Figure6-1.png",
        "caption": "Figure 6. (A, B) Electrochemical reduction of 50 \u03bcM MTO at YIG/GCN/SPCE with a different pH range of 3.0\u221211.0 recorded at a scan rate of 50 mV s\u22121 (N2-saturated). (C) Schematic illustration of the electroreduction of MTO over the YIG/GCN/SPCE.",
        "texts": [
            " The results suggested that an accumulation time of 50 s showed the best performance. The optimized conditions, 50 s of accumulation time, 8.0 \u03bcL of https://doi.org/10.1021/acsami.1c04597 ACS Appl. Mater. Interfaces 2021, 13, 24865\u221224876 24870 nanocomposite loading amount, and 2.0 mg mL\u22121 concentration of nanocomposite were used for further studies. Next, the electrochemical behavior of MTO (50 \u03bcM) was tested by providing different pH environments in electrolytes (N2 saturated), ranging from 3.0 to 11.0 (Figure 6A). YIG/ GCN/SPCE was the working electrode. Initially, the reduction peak current followed a steady rise at acidic pH from 3.0 to 5.0 and reaches a maximum at 7.0. On gradually increasing the pH from 7.0 to 11.0, a decrease in the current value was observed. The peak potential was slightly shifted in the negative direction upon increasing pH from acidic to basic. Both these changes indicate that the electrocatalysis of MTO involving both electrons and protons and the voltammetric data are completely pH-dependent. As the maximum current was observed at pH 7.0, it was selected as an optimal condition to carry out further experiments and N2 was saturated in the reaction mixture due to the control of the oxygen reduction reaction. The overall chemical reaction of MTO is a fourelectron transfer reaction, which is consistent with previous reports (Figure 6C).27,28 Electrochemical Determination of MTO. The CV profiles of YIG/GCN/SPCE and controls were analyzed in the presence of 50 \u03bcM MTO (Figure 7A). A sharp cathodic peak was observed for all of the modified electrodes. The cathodic peak current was found to be \u22123.25 \u03bcA for bare SPCE, \u221212.41 \u03bcA for GCN, and \u221238.2 \u03bcA for YIG/GCN. The YIG/GCN-modified SPCE exhibits 11.7 times higher current response compared to unmodified SPCE, which indicates that YIG/GCN provides significant electrocatalytic activity, surface area, and signal amplification",
            " The limit of detection (LOD) was 950 pM, and the sensitivity was 29.83 \u03bcA \u03bcM\u22121 cm\u22122. The analytical performance of the YIG/GCN-modified sensor is either comparable to or better than the existing literature on MTO analysis (Table 1). This is the first report implementing a nanosized ternary metal oxide material for the reductive detection of MTO. Unlike single metal oxide catalysis, here two metals, i.e., yttrium and iron, are involved in the electrocatalysis, which significantly altered the electrocatalytic efficiency. As explained in Figure 6B, the MTO reduction process proceeds by the conversion of the \u2212NO2 functional group into \u2212NHOH. The electropositive Fe atom of the YIG naturally attracted the electronegative N atom of the MTO molecules, providing energetically favorable orientations that also facilitate the electrocatalysis of MTO. Remarkably, most of the previous methods used glassy carbon electrodes (GCE), whereas here we adopted SPCE, which has several advantages over GCE. In particular, portability, lowvolume consumption, and use and throw options of the SPECs are highly desirable for practical food testing purposes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003997_3-540-27969-5-Figure7.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003997_3-540-27969-5-Figure7.15-1.png",
        "caption": "Fig. 7.15. HopTuples self-maintain despite topology changes. (a) The tuple on the gray node must change its value to reflect the new hop distance from the source Px. (b) If the source detaches, all the tuples must auto-delete to reflect the new network situation",
        "texts": [
            " Note that if there are multiple paths going downhill, the tuple follows downhill each of them. This can be a limit, in some scenarios, because it wastes bandwidth. However, it improves robustness since it is able to cope with network link failures. Eventually, it would be very easy to base this tuple on the above UnicastTuple to avoid multipath propagation. HopTuple This kind of tuple inherits from StructureTuple to create distributed data structures that self-maintain their structure in an automatic way, to reflect changes in the network environment (see Fig. 7.15). Similarly to the previous NMGradient in Fig. 7.11, this class overloads the decideEnter method so as to allow the entrance not only if the tuple is not in the node yet \u2013 as in the base implementation \u2013 but also if there is a tuple with a higher value for the hop variable. This allows the tuple to enforce 7.3 TOTA Programming Model 139 the breadth-first propagation, assuring that the hop variable truly reflects the actual hop distance from the source. Moreover, this class overloads the empty makeSubscription method of the StructureTuple class, to let these tuples react to changes in the network topology, by adjusting their values to be consistent (after some delays) with the true hop distance from the source (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000251_rnc.4466-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000251_rnc.4466-Figure1-1.png",
        "caption": "FIGURE 1 Illustration of different controllability conditions [Colour figure can be viewed at wileyonlinelibrary.com]",
        "texts": [
            " Assumption 1. There exist continuous functions g i (xi, xi+1), gi(xi, xi+1), hi(xi) and hi(xi) for xi+1 \u2265 \ud835\udf00i+1 \u2265 0 and xi+1 \u2264 \ud835\udf00i+1 \u2264 0 such that { \ud835\udc53i ( xi, xi+1 ) \u2265 g i ( xi, xi+1 ) xi+1 + hi ( xi ) , xi+1 \u2265 \ud835\udf00i+1 \ud835\udc53i ( xi, xi+1 ) \u2264 gi ( xi, xi+1 ) xi+1 + hi ( xi ) , xi+1 \u2264 \ud835\udf00i+1, (3) where \ud835\udf00i+1 and \ud835\udf00i+1 are unknown constants. i = 1, 2, \u2026 , n. Furthermore, for |xi+1| \u2265 \ud835\udf00i+1 > max{|\ud835\udf00i+1|, |\ud835\udf00i+1|}, there exists an unknown positive constant gi, m satisfying min{g i (xi, xi+1), gi(xi, xi+1)} \u2265 gi,m. Remark 1. Figure 1A is an illustration of Assumption 1. It should be noted that the dotted lines are only special forms of boundary functions g i (xi, xi+1)xi+1 + hi(xi) and gi(xi, xi+1)xi+1 + hi(xi), where the continuous functions g i (xi, xi+1), gi(xi, xi+1), hi(xi), and hi(xi) are unknown. The inequality constraint (3) only depicts a general variation of \ud835\udc53i(xi, xi+1) with xi + 1, which has no special requirement for each specific point on the nonlinear curve. Figure 1B is an illustration of the common assumption utilized in other works.3-19 The conventional controllability condition of nonaffine functions is 0 < gi,m \u2264 \ud835\udf15\ud835\udc53i(xi, xi+1)\u2215\ud835\udf15xi+1 \u2264 gi,M, which requires the nonaffine function to be differentiable and its partial derivative to keep positive all the time. However, the bounds and signs of the derivatives of nonlinear functions for all the variables are difficult to be known in practical application. Remark 2. Assumption 1 guarantees the controllability of system (1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000903_j.asoc.2021.107226-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000903_j.asoc.2021.107226-Figure8-1.png",
        "caption": "Fig. 8. Control of three-dimensional model of lower-limb exoskeleton in imscape.",
        "texts": [
            " Case 2: Performance of three-dimensional 4-dof lower limb exoskeleton model with real-time gait data In this section, the performance results for the optimized FLC-PID and traditional PID controllers applied to hip and knee joints of the 4-dof lower-limb exoskeleton are presented. The rationale behind this case study is to provide an appropriate control approach for a 4-dof lower-limb exoskeleton that would efficiently mimic the bipedal human walking at different walking speeds. A three-dimensional lower-limb exoskeleton model, developed using the anthropomorphic data of healthy person having weight 55 kg and 1.72 cm height, and it is controlled in simscape/MATLAB version 2019 (MathWorks, USA, academic licence) is shown in Fig. 8. The hip joint trajectories for right and left legs obtained using experimental set-up at speed of 2.4 km/h are considered as inputs to the right and left hip joints of the 4-dof exoskeleton respectively. Similarly, the knee joint trajectories for right and left legs using experimental set-up, obtained at speed of 2.4 km/h, are provided as inputs to the right and left knee joints of the exoskeleton respectively. The optimized parameters and IAE values for all four joints for two control schemes, DFA-FLC-PID and DFA-PID, are listed in Table 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000097_j.addma.2020.101279-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000097_j.addma.2020.101279-Figure5-1.png",
        "caption": "Fig. 5. (a) Schematics represents resultant dendrites growth direction (RD) based on scanning direction (SD), deposition direction (DD). (b) Optical micrograph showing the parallel and inclined columnar dendrites.",
        "texts": [
            " A similar structure was observed in IN718 fabricated by Direct metal laser sintering (DMLS), Selective laser melting (SLM) and Laser solid form (LSF) process [17,28-30]. However, it is stated from the optical and SEM micrographs that the majority of the columnar grains (CG) were aligned perpendicular to the build direction preferably towards the top of the melt pool and in the scanning direction (SD) [29]. A sketch representing columnar dendrites aligned parallel and angular to the build direction based on the scanning and deposition direction is illustrated in Fig. 5a. re -p ro of In the L-PBF process, the bottom layers of a sample were subjected to repetitive thermal cycling compared to the top layers due to the heat transfer towards the bottom side. This also reduces the solidification rate of the depositions by minimizing the thermal gradient as it progresses towards upwards. The observation of relatively coarser columnar dendrites from the bottom to the top layers, as seen in Fig. 3c is attributed to the repetitive thermal cycling and decrease in the solidification rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003328_s0022-0728(96)04804-8-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003328_s0022-0728(96)04804-8-Figure5-1.png",
        "caption": "Fig. 5. Cyclic voltammograms of I mM 2,3-dihydroxybenzoic acid, (a) in the absence of, (b) in the presence of l mM 4HC at a glassy carbon electrode and at a scan rate of 2 0 0 m V s - ~; (c) as (b) at a scan rate of 100mVs -~ . Supporting electrolyte 0 .15M CH3COONa; T = 2 6 + I\u00b0C.",
        "texts": [
            " All anodic and cathodic peaks disappear when the charge consumption becomes about 4 e - per molecule of lb (Fig. 4, curve e). The reaction mechanism is similar to that of the previous case and, according to these results, it seems that the chemical reaction between 4HC and 3-methoxy-obenzoquinone is fast enough and leads presumably to the formation of product (Sb). OCH3 5b Similar to la , ~H NMR [26] and 13C NMR results indicate that 3-methoxy-o-benzoquinone (2b), produced from the oxidation of lb, is selectively attacked from C-5 by enolate anion 2, to produce the product 5b. Fig. 5 (curve a) shows the cyclic voltammogram of a 1 mM solution of lc in water, containing 0.15 M of sodium acetate. In this condition, the cyclic voltammogram exhibits a quasi-reversible two-electron process corresponding to the 2,3-dihydroxy-benzoic acid (lc)/o-quinone-3carboxylic acid (2c) couple. The cathodic counterpart of the anodic peak decreases when 1 mM of 4HC is added, and a second irreversible peak A 2 appears at more positive potentials (Fig. 5, curve b). This peak A 2 is related to the oxidation of 4HC. The multicyclic voltammogram of this solution shows a new anodic peak A 0 at 0.24V vs. SCE, which can be attributed to the oxidation of intermediate 3c, followed by a decrease in the height of peak A 2 (Fig. 5, curve c). Under these conditions, the peak current ratio lpal//Ipcl and the current f u n c t i o n Ipal/V I/2 decrease with increasing scan rate. As in the previous cases, controlledpotential coulometry for determination of the number of transferred electrons was performed at 0.50 V vs. SCE, and cyclic voltammetric analysis carried out during the electrolysis in order to elucidate the formation of intermediate(s) and other products, shows the formation of the new anodic peak A 0. All anodic and cathodic peaks disappear when the consumed charge reaches a limit of 4e - per molecule (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000220_s00170-020-05197-x-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000220_s00170-020-05197-x-Figure2-1.png",
        "caption": "Fig. 2 Main parts of GTE [18]",
        "texts": [
            " After that GE produced turbofan engine Advanced Turboprop (ATP), the first commercialized 3D printed engine (Fig. 1c). Thanks to additive technologies, the number of engines parts was reduce from 855 to 12, reduce a weight by 5%, that allowed to reduce the fuel consumption by 20% and increase a total engine performance by 10%. Russian Institute of Aviation Materials printed and tested small-size GTE for unmanned aircraft from Ni-Al-based alloy powder. The GTE consists of two main parts: hot and cold sections (Fig. 2) (cold section: air inlet, compressor, shaft, and diffuser section [9, 10]; hot section: combustion chamber, turbine, and exhaust). The main advantage of SLM is the ability to * A. V. Sotov SotovAnton@yandex.ru 1 Samara National Research University, Moskovskoe sh. 34, Samara, Russia 443086 2 A.A. Blagonravov Institute of Mechanical Engineering Research, Russian Academy of Sciences, M. Khariton\u2019evskij, 4, Moscow, Russia 101990 3 AO \u201cMetallist-Samara\u201d, Promyshlennosti St., 278, Samara, Russia 443023 4 OOO \u201cAN-TURBO\u201d, Aptekarskaya naberezhnaya, Saint Petersburg, Russia 197022 fabricate complex shape parts with thin walls and the same mechanical properties with the parts produced by traditional technologies methods [11\u201313]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure15-1.png",
        "caption": "Fig. 15. Half-size model under symmetrical constraint condition: (a) detailed thin-walled lattice structures and (b) homogenized solid model.",
        "texts": [
            " It took nearly one hour to finish the simulation based on the homogenized model on the same desktop computer. The significant reduction in computing time suggests the great advantage of employing the homogenized mechanical property and inherent strains in the simulation for lattice structures. In order to further accelerate the simulation, only half block needs to be considered given the symmetry in the problem. The half-size model is adopted in the simulation for the remaining cases for different volume densities as depicted in Fig. 15. Moreover, a coarser element mesh is used for half-size block model, while there are still five layers in the solid base. The total element number decreases to 45,000 for the half-size block representing the homogenized model, which saves nearly 84 % in the number of elements compared to the half-size model with lattice features. Generally, it took nearly half an hour to finish the layer-by-layer deposition and stress release simulation based on the half-size homogenized model. Especially for the case of volume density 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure8.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure8.2-1.png",
        "caption": "Figure 8.2. Measurement at the standard pitch circle.",
        "texts": [
            " The equation is also valid when the cutter is a hob, and although it is not exactly correct for the case of a pinion cutter, it can be used with negligible error, provided the required change in the cutter setting is small compared with the module. Gear-Tooth vernier Caliper The most direct method for measuring the tooth thickness of a gear makes use of an instrument called a gear-tooth caliper. This instrument, which is shown in Figure 8.1, is a vernier caliper, with an adjustable stop that determines the radius on the tooth at which the measurement is made. In order to make a measurement, the instrument is placed over one of the gear teeth, as shown in Figure 8.2. The two vernier scales on the caliper are used to measure the distance between the caliper jaws, and the depth of the jaw tips below the stop. Measurement by Gear-Tooth Vernier Caliper 193 On the gear, these lengths are known as the chordal tooth thickness and the chordal addendum. The tooth thickness measurement should be made with the jaw tips of the caliper touching the tooth faces near the middle of the tooth profile. For gears with zero profile shift, this would mean that the contact is at the standard pitch circle",
            " However, in a gear with profile shift e, the addendum as is extended by approximately e, so the middle of the profile lies at a radius approximately equal to (Rs+e). In practice, the measurement is normally made at the standard pitch circle for gears with small amounts of profile shift, and it is only for gears with large values of e that the alternative radius is used. The chordal tooth thickness and the chordal addendum are represented by the symbols t hand sc a sch ' when the measurement is made at the standard pitch circle, and we use t Rch and aRch when the measurement is made at radius R. The gear-tooth caliper is shown in Figure 8.2, adjusted so that the jaw tips touch the tooth faces at the standard pitch circle. The relations between the tooth thickness, the 194 Measurement of Tooth Thickness chordal tooth thickness and the chordal addendum can be read from the diagram, 8s ts (B.3) 2Rs tsch 2Rs sin 8s (B.4) asch RT - Rs cos 8s (B.5) These values of tsch and a sch are generally included in the specification of a gear. Figure B.3 shows the tooth thickness of a gear being measured, when the caliper jaws touch the tooth faces at radius R",
            " When a gear has an odd number of teeth, the pins are placed in tooth spaces which are as closely as possible opposite to each other, in the manner shown in Figure 8.8. The radii through the pin centers no longer form a straight line, and the angle between them is equal to [180\u00b0 - (180 0jN\u00bb). The relation between R' and M is then given by the following equation, M 2R' cos (9~0) + 2r (8.31) Apart from this change, the equations for finding the tooth thickness are exactly the same as those for a gear with an even number of teeth. Examples 205 Numerical Examples Example 8.1 The gear in Figure 8.2 has 36 teeth, a module of 8 mm, and a pressure angle of 20\u00b0. Calculate the correct settings for a gear-tooth caliper, if the tooth thickness is half the circular pi tch, and the addendum is one module. Example 8.2 RS = 144.000 mm ts = 12.566 0.043633 radians = 2.500\u00b0 tsch = 12.562 RT = 152.000 a sch = 8.137 mm (2.31) (8.3) (8.4) (2.40) (8.5) The gear shown in Figure 8.3 has 15 teeth, D.P. 2, and pressure angle 20\u00b0. It is cut from a blank with a diameter of 9.0 inches, and the specified profile shift is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure13.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure13.9-1.png",
        "caption": "Fig. 13.9 Metal belt CVT (www.quora.com)",
        "texts": [
            " However, the automotive industry in general did not realize the value of CVT then mainly because of two limiting factors. (1) The belt at that time was made from rubber and the power transmitted was thus very limited; (2) the clutch produced then had issues in stability and consistency. During the late 1960s, Hubert van Doorne, the co-founder of DAF, proposed to make the belt with steel, which greatly improved the power capacity, paving the way toward wider application in the automotive industry. In 1987, the Fuji Heavy Industries Ltd. (FHI) in Japan developed the steel belt CVT (Fig. 13.9), called Justy, which has been adopted in many vehicles manufactured in Japan and Italy. 478 13 Development of Theories in Mechanical Engineering of New Era Mechanical transmissions with fixed speed ratio were the main stream in the automotive industry before CVT. In this arrangement the transmission and engine are two separated units. CVT, however, integrates the engine and the transmission into one unit and the engine performance can be optimized through adjusting the speed ratio and the fuel supply"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.7-1.png",
        "caption": "Figure 13.7. Coordinate systems fixed in the gear.",
        "texts": [
            " The pitch plane can therefore be defined as the plane of the basic rack which is parallel to its reference plane, and which touches the standard pitch cylinder of the gear. In other words, it is the plane of the basic rack which lies at a distance Rs from the gear axis. 316 Tooth Surface of a Helical Involute Gear In order to describe the tooth surface of a helical gear, we use a set of Cartesian coordinates (x,y,z) fixed in the gear, with the z axis coinciding with the axis of the gear. This is the same system of coordinates that was used for spur gears in Part 1 of this book. In addition, we will use the cylindrical coordinates (R,e,z) shown in Figure 13.7, which are simply the polar coordinates used in Part 1, together with the axial coordinate z. We now consider two transverse sections through the gear, one at plane z=O and the other at plane z. As we showed earlier, the tooth profile in any transverse section must always be conjugate to the corresponding transverse section through the basic rack, so the tooth profiles in the two sections through the gear must each have a standard pitch circle and a base circle with radii given by Equations (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000958_tie.2021.3068674-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000958_tie.2021.3068674-Figure1-1.png",
        "caption": "Fig. 1 Distributions of flux line and flux density under on-load. (a) FSPM machine. (b) SR machine. (c) SynR machine. (d) PMsyn machine.",
        "texts": [
            " SynR machines follow the same torque generation mechanism as SR machines to produce reluctance torque [16-18]. For PMSyn machines the torque is only referring to the PM torque due to the interaction of armature field and PM field [19]. Besides, if the PMs are installed in a reluctance rotor, the output torque will contain both PM torque and reluctance torque [20-22]. Unlike the traditional machines, the PMs of FSPM machines are installed in the stator, resulting in the unipolarity of the stator cores, namely, the magnetic circuit direction of an arbitrary iron-core is fixed as shown in Fig. 1(a). In addition, FSPM machines have a unique stator slot/rotor salient pole combination mode, e.g. 12s/10p, 12s/11p, 12s/16p, 12s/17p, etc., where the odd rotor poles are difficult to achieve in traditional machines [23, 24]. The purpose of this paper (Part II) is to investigate the torque generation mechanism of FSPM machines from the perspective of the air-gap modulation magnetic field. Firstly, an analytical model of the air-gap armature field due to armature currents is derived, and its variations during the modulation process are analyzed in detail",
            "html for more information. machine. @\u03c9r=3.6deg/ms (mech.speed). (a) Amplitude versus rotor position. (b) Speed versus rotor position. V. ELECTROMAGNETIC TORQUE GENERATION In this section, according to the air-gap armature field (section III) and PM field (Part I), electromagnetic torque characteristics of FSPM machines are analyzed by the analytical method and verified by FE analysis. FSPM machines exhibit two unique features, namely, the magnetic circuit direction of two adjacent stator cores is opposite as shown in Fig. 1(a), and the rotor salient pole number can be odd, which are different from traditional machines. Considering the unipolarity of the stator core, the magnetic circuit function fmcs() on the stator side of FSPM machines is expressed by the Fourier series as       ...5,3,1 1 )2/(sin k skmcs kZmf  (10) where msk is the Fourier coefficient of fmcs(). Then, by the rotor dynamic modulation, the eigenfunction of the magnetic circuit fmc() in FSPM machines can be obtained   ])2/sin[( 2 1 ])2/sin[( 2 1 )2/cos( )(,),( 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000297_j.corsci.2020.108838-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000297_j.corsci.2020.108838-Figure1-1.png",
        "caption": "Fig. 1. L-PBF processed Al-6061 RAM2 and extruded Al-6061 T6 bars used in this study.",
        "texts": [
            "4 % fabricated through the L-PBF process (from Elementum 3D), and an extruded Al-6061 T6 (EXT) as a wrought alloy (provided by Alcoa) were used in this study.1 The Al6061 powder with a blend of B4C and Ti-rich reactive particles were used as feedstock to fabricate the AM bars. The printing parameters and metallurgical processing are the property of the material\u2019s vendor and may not be disclosed due to confidentiality. RAM bars were printed vertically with a length of 100mm and a diameter of 10mm. The EXT samples were chosen with the same size, as shown in Fig. 1. The bars were cut from cross-section into 10mm cylinders and mounted in cold epoxy. In L-PBF metal parts, anisotropic texture and microstructure have been reported in the periphery, beginning, and last deposited layers [11,33]. To eliminate this effect, all samples were chosen from the middle length of the bars. The backside of each mount was drilled up to the sample, and a wire was glued to establish the electrical connection required for the electrochemical test. Mounted samples were ground with SiC sandpapers, up to 1500 grit, then slightly polished with 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-26-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-26-1.png",
        "caption": "Figure 5-26 Sketch of the change in distance between two nearby orbits used to define the largest Lyapunov exponent.",
        "texts": [
            " 192 Criteria for Chaotic Vibrations An excellent review of Lyapunov exponents and their use in experiments to diagnose chaotic motion is given by Wolf et al. (1985). This review also contains two useful computer programs for calculating Lyapunov exponents. The divergence of chaotic orbits can only be locally exponential, since if the system is bounded, as most physical experiments are, d ( t ) cannot go to infinity. Thus, to define a measure of this divergence of orbits, we must average the exponential growth at many points along a trajectory, as shown in Figure 5-26. One begins with a reference trajectory [called a fuduciary by Wolf et al. (1985)] and a point on a nearby trajectory and measures d(t)/d0. When d ( t ) becomes too large (i.e., the growth departs from exponential behavior), one looks for a new \"nearby\" trajectory and defines a new d0(t). One can define the first Lyapunov exponent by the expression A = 1 - fn (5-4.3) Then the criterion for chaos becomes A > 0 chaotic X < 0 regular motion (5-4.4) The reader by now has surmised that this operation can only be done with the aid of a computer whether the data are from a numerical simulation or from a physical experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure6-1.png",
        "caption": "Fig. 6. Growth of a cone by normal growth velocities on an expanding growth surface G",
        "texts": [
            " Suppose the growth velocity is again given by Eq. (30). Then with the same choices of h i as in Example 3.1, Eqs. (31) and (32) also hold here. The only difference is that the domain in h space is now limited to (h2 1 #h2 2 )6k2h2 3 and 06h 3 6t. The solution implies that the cells on G are fixed in position once they are generated and new cells are added at the periphery of G as G grows. The solid generated is a cone with half angle c where tan c\"k/v 0 and all cell tracks and particle paths are lines parallel to x 3 as shown in Fig. 6. Example 3.3. Growth surface accreting with varying g Consider next a problem in which the external shape is given to be the same as the cone in Example 3.2, Fig. 6, but with the cell tracks as shown in Fig. 7. The cone in Fig. 7 grows exactly at the same rate as in Fig. 6 so \u00b8\"v 0 t and a\"kt in Fig. 7 and the cone half-angle is again c where tan c\"k/v 0 . The motivation for Fig. 7 is that cell tracks may be the direction of the final fiber structure and the fiber directions shown in Fig. 7 may produce a stronger structure than those in Fig. 6. The interior cell tracks in Fig. 7 form cones with half-angles b where 06b6c. The vector field g must also be such that g \u00b7 n\"v 0 on G to supply the mass required. At the same time there must be a radial velocity inwards at angle b to i 3 to produce the inclination of the cell tracks. The distribution of g on x 3 \"0 satisfying these conditions is g\"! x 3 t i 1 ! x 2 t i 2 #v 0 i 3 . (34) The results given by Eq. (34) is derived using the fact that the values of h 1 and h 2 are constant on cell tracks",
            " The coordinate h 3 is again taken to be h 3 \"q where q is the time at which a particular particle is initiated on G. Then h 3 \"constant, is a plane containing the x 3 axis. Several such planes are shown in Fig. 9B. In each such plane, the cross-section of the horn will be a circle. Example 3.6. A curvilinear horn of logarithmic spirals Consider producing a horn with the external form shown in Fig. 9, but with cell tracks which are at constant angles to the centerline, similar to Fig. 8, as compared to Fig. 6. This may be accomplished by the use of logarithmic spirals which are extensively discussed by D\u2019arcy Thompson (1942) in connection with the forms of shells, horns and other biological forms. Logarithmic spirals are plane curves (Fig. 10) described by r\"beh #05 a , (54) where r, h are polar coordinates and b and a are constants. The angle between the tangent to the spiral and the radius vector r is the constant angle a. This property is suggested in the alternate name of equiangular spiral. If a is (90\u00b0, then r increases with h",
            " The present paper does not provide any biological proof that the descriptions provided apply to any particular biological case. Rather, a rigorous vocabulary is presented and it remains to be seen by biological observations and experiments, where such theory does not provide a realistic description. Of course, in many cases there are observations recorded in the literature which assure that many of the aspects of the examples presented here are realistic. For example, it is known that the rhinoceros horn is matted hair, and hence, it has cell tracks more like Fig. 6 than Fig. 7. On the other hand, the structure of cows\u2019 horns is known to be more like Fig. 7. There are two points of the present vocabulary that particularly need to be confirmed or verified in each biological case. The first is the extent to which cell tracks (like the costa of Fig. 23) are, in fact, attributable to a single cell or to a group of cells, in which individual cells divide or die and are replaced by new cells. The second aspect which requires experimental information is the nature and degree of motion of generating cells"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000306_tmech.2020.3034640-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000306_tmech.2020.3034640-Figure5-1.png",
        "caption": "Fig. 5. The dimensions of the cross section of PneuNet in length direction.",
        "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. of the PneuNets is the elongation of the gap layer, so the calculation of the elongation of the gap layer is the key. The maximum displacement \u03b4 of the chamber lateral wall can be obtained, but since the gap layer is not at the pole of the deformed chamber lateral wall, it is difficult to obtain the displacement \u03b41 of the chamber lateral wall in the gap layer. As shown in Fig. 5, the approximate value of \u03b41 can be obtained by geometric relation. \u03b41 is given by 1 2s a s  = + (11) For the gap layer of the PneuNet ( ) ( )g 1(n 1) 2 1t bR t s nl l n + + = + \u2212 + \u2212 (12) where s is the gap height of the PneuNet, as shown in Fig. 3. Combining (11) and (12), the bending angle \u03b8 is given by ( ) 12 1 b n t s   \u2212 = + (13) According to (13), the bending angle \u03b8 of the PneuNet has no relation with the length lg of the gap between the chambers when the gap length is large enough. The bending angle \u03b8 is inversely proportional to the thickness tb of the inextensible layer at the bottom of the PneuNet and the height s of the gap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003927_tsmc.1984.6313236-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003927_tsmc.1984.6313236-Figure2-1.png",
        "caption": "Fig. 2. Impulsive force of 14.14 N . s acting on the biped. (a) Vertical component of 10 N . s downwards. (b) Vertical component of 10 N . s upwards.",
        "texts": [
            " The magnitudes of these impulsive forces depend on the magnitude of the impact force, but also on the position of all the links. This allows a quantita tive study of the internal and external forces of constraint. The effect of the impact on external constraint needs extra care. These constraints mayor may not be violated under the effect of the impact. If they are violated, the model must be accordingly modified by setting the corre sponding constraint force equal to zero. Suppose a five-link biped is standing on the ground with (J1 = 1.309 rad, (J2 = 1.047 rad, (J3 = 0, (J4 = 0, (Js = 0 (Fig. 2) with an impulse in two different directions. In the first case the vertical component of the impulsive force (10 N . s) is downwards. For the second case the vertical component is upwards. The four external constraint forces, two on the toe and two on the heel are listed in Table II. The y component of the ground reaction force shows that the impulsive force presses the biped against the ground in case a, and tends to lift the biped off the ground in case b. (14) (13) LlZ(O) = r1Q t:.tl)3 dt (10) where 2(0 + ) - 2(0 -) represent the velocities im mediately after and before the impact, and fo~t83 dt repre sents the magnitude of the impulsive force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.6-1.png",
        "caption": "Figure 7.6. position of point Ahc \u2022",
        "texts": [
            " If 9R is larger than 9R, the radius R is smaller than Ru' as we can see in Figure 7.5. The radius Ru of the undercut circle can be found by calculating 9R and 9R at a number of different radii, and eventually finding the value of R at which 9R and 9R are equal. The polar coordinate 9R of the point on the involute at radius R was given by Equation (2.35), (7. 7) The corresponding value of 9R depends on the type of cutter used, and we will deal first with the case when the gear is cut by a pinion cutter. Figure 7.6 represents the gear and the pinion cutter, in their positions when point Ahc of the cutter lies on the gear circle of radius R. In order to keep the diagram as simple as possible, the positions of the gear and cutter teeth are shown only by the tooth center-lines, which lie at angles P and P g c with the line of centers. The polar coordinates (Rhc ,9hc ) of point Ahc ' where 8hc is measured from the tooth center-line, were given by Equations (5.34 and 5.35). Our purpose is to find the polar coordinate 9R of point Ahc ' relative to the coordinate system fixed in the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.3-1.png",
        "caption": "Figure 5.3. positions of cutter, relative to gear blank.",
        "texts": [
            " The cutter is shaped exactly like a pinion, and is therefore called a pinion cutter. As before, the gear blank and the cutter are driven with constant angular velocities, as if they were a meshing gear pair. In addition, the cutter 114 Gear Cutting I, Spur Gears must have some other motion to provide the cutting action, and it is therefore given a reciprocating motion in the direction of its axis. This method of cutting gears is known as shaping, in common with other cutting processes in which the cutting tool has a reciprocating motion. Figure 5.3 shows the positions of the cutter, relative to the gear blank, as it makes a number of cutting strokes. The shape of the gear tooth, after the cutting has been completed, is the same as the envelope of the cutter positions. It can be seen that this shape is not exactly an involute, but consists of a series of arcs, whose sizes depend on the number of strokes that occur during the cutting of each tooth. The amount of material that can be removed with each cutting stroke is of course limited, and it is therefore impossible to cut the first tooth of the gear blank immediately to its full depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003148_00207170310001637147-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003148_00207170310001637147-Figure1-1.png",
        "caption": "Figure 1. The PVTOL aircraft (front view).",
        "texts": [
            " The proposed algorithm copes with (arbitrary) bounded inputs and takes into account the positive nature of the thrust. The stability proof is relatively simple. As far as we are aware, the previous works on the topic do not cover all these features simultaneously. The paper is organized as follows. In } 2, we recall the equations of motion for the PVTOL aircraft and state the control objective. In } 3, the proposed approach is presented. Simulations are shown in } 4 and conclusions are finally given in } 5. The PVTOL aircraft dynamics (see figure 1) are modelled by (Hauser et al. 1992) \u20acx \u00bc u1 sin \u00fe \"u2 cos \u20acy \u00bc u1 cos \u00fe \"u2 sin 1 \u20ac \u00bc u2 9>= >; \u00f01\u00de International Journal of Control ISSN 0020\u20137179 print/ISSN 1366\u20135820 online # 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00207170310001637147 Received 15 July 2002. Revised 8 October 2003. Accepted 17 October 2003. *Author for correspondence. e-mail: isabelle.fantoni@ hds.utc.fr y Instituto Potosino de Investigacio\u0301n Cient\u0131\u0301fica y Tecnolo\u0301gica, Apdo. Postal 2-66, 78216 San Luis Potos\u0131\u0301, S"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000480_j.automatica.2021.109708-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000480_j.automatica.2021.109708-Figure1-1.png",
        "caption": "Fig. 1. Relative position of target with respect to follower in NED reference frame.",
        "texts": [
            " Namely, the trajectory of x enters the invariant set given by x \u2208 { V \u03b1(x) \u2264 \u03b7 c(1 \u2212 \u03b2) } (8) for a finite time no greater than T \u2264 V 1\u2212\u03b1(x0) c\u03b2(1 \u2212 \u03b1) , (9) where 0 < \u03b2 < 1 is the parameter to specify the size of the invariant set and x0 is the initial value of x. Remark 1. The parameter \u03b2 in (8) and (9) indicates that the finite time T increases, if the trajectory of x reaches a smaller neighborhood of the origin. 2.2. Problem statement The motion equation of an aerial target is given by P\u0308Ta(t) = aTa(t), P\u0307Ta(0) = VTa0 , PT (0) = PTa0 , (10) here PTa = [ xTa(t) yTa(t) zTa(t) ]T and aTa = [ aTax (t) aTay (t) aTaz (t) ]T are, respectively, the position nd acceleration vector of the target\u2019s center of gravity in the orth-East-Down (NED) frame (Fig. 1). It is assumed that aTa is bounded. The motion equation of the following UAV is given by \u00a8F (t) = sat (aF (t)) , P\u0307F (0) = VF0 , PF (0) = PF0 , (11) here PF = [ xF (t) yF (t) zF (t) ]T denotes the follower\u2019s position, and aF = [ aFx (t) aFy (t) aFz (t) ]T is the follower\u2019s acceleration in the same NED frame (Fig. 1). sat(\u00b7) is a saturation function. Consequently, the relative position of the target with respect to the follower is given by R(t) = PTa(t) \u2212 PF (t), (12) hose dynamic equation in the NED frame is \u00a8(t) = aTa(t) \u2212 sat(aF (t)), R\u0307(0) = V0, R(0) = R0. (13) If the relative position is measurable, the objective of the inite-time tracking problem is formulated as lim \u2192T R(t) = 0, (14) here T is the finite chasing time dependent on design paramters and initial states and R(t) is the relative position measured y a vision-based sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003274_tcst.2003.815613-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003274_tcst.2003.815613-Figure4-1.png",
        "caption": "Fig. 4. The physically attainable thrust region (grid) for a propeller-rudder pair. An inscribed circular sector and the negative x-axis together serve as the feasible region D .",
        "texts": [
            " Unfortunately, a propeller-rudder device requires a nonconvex domain because these propulsive devices are unable to produce lateral forces without simultaneously generating significant longitudinal forces. It is reasonable to assume that the rudder is capable of producing lift for positive thrust force (forward). For negative longitudinal force the rudder can be regarded as inactive, thus the attainable set shrinks to a thin line. Typically the physically attainable thrust region resembles a twisted circular sector, represented by the grid in Fig. 4. Notice that the negative -axis is also a part of the attainable set. For convenience, the grid is approximated by an inscribed circular sector so that the feasible set is given by this sector element and the negative -axis. Even though a sequential QP (SQP) or a sequential linearly constrained (SLC) method does find a solution, careless utilization of any numerical method can lead to unintended results: 1) An SQP method solves a sequence of QP problems and is therefore more computationally demanding than a single QP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000498_j.automatica.2020.108921-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000498_j.automatica.2020.108921-Figure5-1.png",
        "caption": "Fig. 5. Laboratory setup consisting of dc-motor and load.",
        "texts": [
            " The latter is restricted to smaller perturbations in principle, due to the fact that the damping in (30b) limits the maximum amplitude and change rate of v. One can see that without anti-windup the state variable x exhibits a significant overshoot. The original STA prevents this overshoot, but exhibits a comparatively slow convergence to the reference instead. The saturated STA and the proposed approach, on the other hand, maintain a fast convergence speed. In order to demonstrate the applicability of the proposed algorithm in practice, the experimental setup shown in Fig. 5 is used. It consists of a dc-motor with input voltage u\u2217, to which a load is attached via a gear box. The control objective is for the load\u2019s angular velocity \u03c9 to track a given constant reference signal \u03c9d. A mathematical model of the setup is obtained by the application of the principle of angular momentum, i.e., I\u03c9\u0307 = \u2212 k2m\u03b72 g Rw \u03c9 + km\u03b7g Rw u\u2217, (35) where km, \u03b7g and Rw denote the dc-motor\u2019s torque constant, the gear ratio, and the resistance of the dc-motor\u2019s coil, respectively. The total moment of inertia I is given by I = \u03b72 g Im + Ia, (36) with Im and Ia being the motor and additional load inertia, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003056_s0094-114x(03)00003-x-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003056_s0094-114x(03)00003-x-Figure3-1.png",
        "caption": "Fig. 3. Slewing bearing section.",
        "texts": [
            " There are three types of relative displacements between the raceways in all loaded bearings (Fig. 2): \u2022 axial displacement dz, \u2022 radial displacement dr, \u2022 rotation h. These relative displacements define the position of the loci of the centres of curvature of the two raceways in reference to their initial positions, and they are shown in the following equation: s \u00bc f\u00f0dz; dr; h;A\u00de \u00f01\u00de where s is the relative distance between the centres of curvature of the raceways and A is the initial relative distance between the centres of curvature of the raceways (Fig. 3). The relative distance between the raceways determines the state of the deformations to which each of the ball bearings is subject, as its angular position (w) along the whole of the circumference is known (Fig. 4). \u2022 Cii represents the centre of curvature of the lower inner raceway. \u2022 Cis represents the centre of curvature of the upper inner raceway. \u2022 Cei represents the centre of curvature of the lower outer raceway. \u2022 Ces represents the centre of curvature of the upper outer raceway. \u2022 a and h are variables given by the design parameters, such as a0, ball bearing diameter and con- formity (radius of raceway curvature divided by diameter of ball bearing)",
            " As commented above, w is the angle determined by the position of the ball bearing within the bearing. Assuming that the radii of curvature of the raceways are equal, the initial coordinates (represented by 1) of the four centres of curvature, without taking the axial clearance into account, are: XCii1 \u00bc dm 2 \u00fe h cosw \u00f08\u00de YCii1 \u00bc dm 2 \u00fe h sinw \u00f09\u00de ZCii1 \u00bc a \u00f010\u00de XCis1 \u00bc dm 2 \u00fe h cosw \u00f011\u00de YCis1 \u00bc dm 2 \u00fe h sinw \u00f012\u00de ZCis1 \u00bc a \u00f013\u00de XCei1 \u00bc dm 2 h cosw \u00f014\u00de YCei1 \u00bc dm 2 h sinw \u00f015\u00de ZCei1 \u00bc a \u00f016\u00de XCes1 \u00bc dm 2 h cosw \u00f017\u00de YCes1 \u00bc dm 2 h sinw \u00f018\u00de ZCes1 \u00bc a \u00f019\u00de The initial distance (Fig. 3) between diagonally opposed centres of curvature is equal to A \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0a2 \u00fe h2\u00de p \u00f020\u00de However, the existing clearance modifies some of the coordinates of the centres of curvature of the Z axis. If Pr is defined as being the existing radial clearance, rc as the radius of curvature and d as the diameter of the ball bearing, we have the following relation (Fig. 5): 2\u00f0rc Pr\u00de A \u00bc d \u00f021\u00de Taking the inner ring as a reference, the outer ring will move down by an amount j, equal to the axial clearance, until contact exists between the sphere and the raceways"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.1-1.png",
        "caption": "Figure 3.1. A pinion meshed with a rack.",
        "texts": [
            " We now determine what conditions must be met by the rack parameters, if the rack is to mesh correctly with the pinion. In order to check whether the Law of Gearing is satisfied, we adopt the following procedure. We find a typical position of the contact point between the pinion and the rack, and we draw the common normal through this point. We also draw the perpendicular from the pinion center to the rack reference line, and the point where this line intersects the common normal is labelled P'. The Law of Gearing is satisfied if pI coincides with the pitch point P. Figure 3.1 shows the pinion base circle, and a pair of teeth in contact. The base circle radius is given by Equation (2.20), (3.1) A Pinion Meshed With a Rack 55 and by making use of Equation (2.30), which gives the standard pitch circle radius in terms of the module, we can express the base circle radius in terms of the module and the pressure angle, ~Nm cos 4lS (3.2) Since the module m and the pressure angle 4ls are part of the specification of the pinion, the base circle radius Rb is known, and its value is constant. Any normal to the rack tooth in Figure 3.1 must be perpendicular to the tooth profile, while any normal to the pinion tooth must touch the base circle. Hence, as shown in the diagram, the common normal must be the base circle tangent which is perpendicular to the rack tooth profile, and the contact point must lie on this line. If E is the point where the common normal touches the base circle, the radius CE is parallel to the rack tooth profile, and the length CP' can therefore be found from triangle ECP' , CP' cos 4l~ (3.3) To find the position of the pitch point, we use Equation (1.15), which gives the pitch circle radius of a pinion meshed with an arbitrary rack with pitch p, The rack in Figure 3.1 has a pitch p~, so in this case the pinion pitch circle radius is as follows, Np~ 271\" (3.4) Point P' in Figure 3.1 will coincide with the pitch point if the length CP' is equal to the pitch circle radius Rp' We equate the two expressions given in Equations (3.3 and 3.4), and rearrange the terms to put the condition in the following form., p~ cos 4l~ 271\"Rb N (3.5) 56 Gears in Mesh The base pitch Pb of the pinion is given by Equation (2.22), 211'Rb N (3.6) and the base pitch Pbr of the rack, defined as the distance between adjacent teeth measured along a common normal, can be expressed in terms of the pitch and the pressure angle with the help of Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000393_j.ejcon.2020.08.003-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000393_j.ejcon.2020.08.003-Figure2-1.png",
        "caption": "Fig. 2. Geometry description of two-dimensional path-following.",
        "texts": [
            " 1 , a typical pathollowing control system consists of path generation (waypoints), uidance law, controller and the marine craft. Here, several asumptions are given. First, the drift angle \u03b2 can be directly meaured. As discussed in [29] , the drift angle can be measured using global navigation satellite system an inertial navigation system nd inertial measurement unit. Second, the velocities of the ship an be measured correctly. This paper considers the straight path, where the path tangenial angle is constant. Fig. 2 shows the geometric information of wo-dimensional path-following control for a marine craft. The red ine is the predefined path. Two coordinate frames are defined in his figure. The straight path, which connects the predefined way oints ( x j , y j ) , j = 1 \u00b7 \u00b7 \u00b7 N, is defined in the North-East-Down (NED) oordinate frame. The body-fixed frame is a moving coordinate rame that is fixed to the craft. The ship motions, such as surge nd sway speed ( u,v ), are measured in the body-fixed frame. The ath-tangential frame is a moving coordinate frame, whose origin s the projection of the ship\u2019s centre of gravity ( x p , y p ) . \u03b3p is the ath tangential angle. The yaw angle and position are measured elative to the NED frame. daptive backstepping control for path-following of underactuated 16/j.ejcon.2020.08.003 H. Xu, P. Oliveira and C. Guedes Soares / European Journal of Control xxx (xxxx) xxx 3 2 p b t[ w i a R y c t 2 e a x y \u03c8 y r y w i b .1. Path-following control objective As presented in Fig. 2 , the path connects the N wayoints ( x j , y j ) for j = 1 , \u00b7 \u00b7 \u00b7 , N. The cross-track error y e is the distance etween the ship and the predefined path. From Fig. 2 , the equaions of cross-track error is given: 0 y e ] = R ( \u03b3p ) [ x (t) \u2212 x p (t) y (t) \u2212 y p (t) ] (1) here, ( x ( t) , y ( t) ) is the ship\u2019s location in real-time, ( x p (t) , y p (t) ) s the projection of the centre of the ship. \u03b3p is the path tangential ngle. R ( \u03b3p ) is the rotation matrix, and given as: ( \u03b3p ) = [ cos ( \u03b3p ) \u2212 sin ( \u03b3p ) sin ( \u03b3p ) cos ( \u03b3p ) ] \u2208 SO (2) (2) Expanding (1), leads to the cross-track error y e : e ( t ) = \u2212( x (t) \u2212 x p (t) ) sin ( \u03b3p ) + ( y (t) \u2212 y p (t) ) cos ( \u03b3p ) (3) Obviously, the control object of the path-following is to make ross-track error converge to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003798_ip-b.1983.0016-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003798_ip-b.1983.0016-Figure4-1.png",
        "caption": "Fig. 4 Possible operating points of induction generator in synchronous mode for three levels or remanent magnetism",
        "texts": [
            " 3, the magnetising currentIm can be determined: where cor is the synchronous electrical frequency proportional to the rotor speed, k = VOC/CJ0 (a constant proportional to the remanent magnetic flux density in the rotor) and Voc is the open-circuit voltage produced at rated system frequency co0. In this circuit, the normal response of a resonant circuit to a forcing function is modified by a nonlinear magnetising inductance and the variation in magnitude of the forcing function with rotor speed. Solving eqn. 1, using the values for the magnetising inductance and current from Fig. 2 and the machine parameters from Appendix 7, a set of possible synchronous operating points can be obtaind. Plotting these points produces curves of the form shown in Fig. 4, for values of remanent magnetism varying form an opencircuit voltage of 0.5 V to 0.1 V at 50 Hz. The curves rise gradually until increasing current causes a rapid rise in magnetising inductance (see Fig. 2), and an associated sudden decrease in synchronous resonant frequency which causes the curves to bend back upon themselves. If the machine speed is increased montonically from zero, the response will follow a curve of the form shown until the knee is reached (point X for instance), at which point, increasing rotor speed must cause the operating point to jump past synchronous resonance (to point Y)",
            " Point B, however, represents an unstable condition, in that any change in speed will cause the machine to drop out of resonance, an increase in speed tending to cause self excitation with resonance being regained at point A, whereas a decrease will cause the machine to drop back to the synchronous mode. It is point B which is of interest, and Fig. 7 shows the curves expanded about this area. IEEPROC, Vol. 130, Pt. B, No. 2, MARCH 1983 105 2.3 Interaction between modes The interaction between the synchronous and asynchronous modes can be seen by combining the contour a = 0, for asynchronous operation, with the curves for synchronous response as shown in Fig. 4. For a given value of remanent magnetism, a machine started from rest will have a capacitor current that follows the appropriate synchronous curve (A) up to a knee point (X). If the speed is further increased, the current must jump discontinuously to point Y, which is within the area where asynchronous operation is possible. Under these conditions, an asynchronous component will grow rapidly and the terminal voltage will increase to the appropriate value. The fixed rotor poles due to remanence are destroyed and the synchronous component of current decays to zero. If the synchronous operating point is close to point X, only a small disturbance is required to initiate self excitation. a Corresponding to point X in Fig. 4 for circuit shown in Fig. 3 b Corresponding to point Y The effect of this transition on the synchronous machine can be seen from the vector diagrams in Fig. 8 (for circuit, see Fig. 3). Below resonance, the load angle 6 is such that The MMF Fx produced by the current flowing, reinforces the remanent MMF F2 to produce the resultant MMF Fo. While above resonance, the current acts to reduce the remanent magnetism. The change in phase of the current between the two operating points is of the order of 150 degrees"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003743_j.ymssp.2006.05.010-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003743_j.ymssp.2006.05.010-Figure2-1.png",
        "caption": "Fig. 2. UH-60A transmission and sensor locations.",
        "texts": [
            " The analysis found success in distinguishing the faulted component data from the unfaulted component data, although the method required training data sets. ARTICLE IN PRESS D.M. Blunt, J.A. Keller / Mechanical Systems and Signal Processing 20 (2006) 2095\u20132111 2097 Wu et al. [3\u20135] reported that the crack could be detected using frequency and wavelet domain analyses of the raw vibration data, but the results depended on the sensor location and frequency band. The best results were obtained for the 5th harmonic (5 ) of the epicyclic mesh frequency for one sensor (3 in Fig. 2), and the 10th harmonic (10 ) for another sensor (5 in Fig. 2), although the reasons for this were not clear. The test-cell vibration data were also analysed by McInerny et al [6]. Like Keller and Grabill\u2019s analysis, a number of different metrics for the detection of faults in fixed-axis gears were modified and applied to the time synchronous averages of the planet carrier vibration. However, some statistics for the raw (non-averaged) vibration data were also presented, and a new metric measuring the ratio of the energy in the planet carrier average at multiples of the planet-pass frequency with the remainder of the energy in the average was ARTICLE IN PRESS D",
            " The vibration data for the onaircraft measurements were acquired using the VMEP system only. The test-cell measurements were made in the Helicopter Transmission Test Facility (HTTF) at the Patuxent River Naval Air Station, Maryland. The HTTF uses actual aircraft engines to provide power to all the aircraft drive systems except the rotors, which are replaced by water brakes. The transmission with the 82mm cracked planet carrier and an undamaged transmission were tested. The transmissions were instrumented with six accelerometers (Fig. 2 and Table 1), and two tachometers (1 pulse/ rev of the main rotor, and 92 pulses/rev of the accessory module hydraulic drive shaft). Raw time domain data were acquired from both transmissions for dual-engine torques of 20%, 30%, 50%, 70%, 90%, and 100% of the rated torque, which is 481Nm per engine (equivalent to 1054 kW per engine at 20,900 rpm). Because of the need for destructive material testing on the cracked carrier, only \u2018\u2018snapshots\u2019\u2019 of vibration data at each torque setting were measured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000554_j.wear.2020.203201-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000554_j.wear.2020.203201-Figure6-1.png",
        "caption": "Fig. 6. Running bench for ball screws.",
        "texts": [
            " When the axial load is applied in the opposite direction, the loading and unloading nuts are nuts B and A, respectively. Therefore, in a complete reciprocating process, both nuts can be regarded as bearing 1=2Fa, which is equivalent to the case of a double-nut ball screw with a preload Fp\u00fe 1=2Fa. The above analysis indicates that the running test of a ball screw under the preload is equivalent to a running test under the axial load; i.e., the mean preload (where the preload is always decreasing with running time) within a certain running time can be regarded as an axial load applied to the ball screw. Fig. 6 shows a wear test bench for ball screws, which mainly comprises a control cabinet, servo motor, headstock, work table, preload drag torque measuring configuration, and tailstock. The test bench can be described as a characteristic feed axis for machine tools using a preloaded double-nut ball screw, which means the worktable (connected with the nut) can move back and forth linearly with the rotation of the screw shaft. The maximum linear speed is 60 m/min. The measuring configuration of the preload drag torque mainly comprises a support unit, rod, and torque sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003684_j.triboint.2005.03.021-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003684_j.triboint.2005.03.021-Figure1-1.png",
        "caption": "Fig. 1. Schematic view of FZG gear test rig.",
        "texts": [
            " Standardised and internationally recognised test methods are available for determining the biodegradability (OECD 301B) and environmental toxicity (OECD 201, OECD 202) of lubricants and their components. The mineral oil did not match the minimum requirements of 60% biodegradability in 28 days, thus any toxicity test were performed for this lubricant. The ester based oil exceeded the minimum requirements of 60% biodegradability in 28 days and pass both toxicity tests, OECD 201 and OECD 202 as shows Table 1. Fig. 1 shows a schematic view of the FZG back-to-back spur gear test rig [5]. FZG type C gears, made of 20MnCr5 steel, carburised, quenched and oil annealed are used. Their characteristics are shown in Table 2. Both gears are run-in before Each lubricant is submitted to a set of gear tests performed in a wide range of speed and torque conditions, as well as input power, as shown in Table 3. The first 3 tests are performed at very low torque (no-load tests) corresponding to FZG load stage 1 (T2Z4.95 Nm) and three different speeds, in order to evaluate the influence of the oil on the churning losses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003134_s0076-6879(94)33032-8-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003134_s0076-6879(94)33032-8-Figure3-1.png",
        "caption": "FIG. 3. Apparatus used in the iodometric assay. G, Inert gas supply; PS, presaturator; P, pipettor; M, magnetic stirrer motor; SD, solvent delivery nozzle; FR, flow regulator valve; D, gas distributor; CT, connecting tube; V, vial; S, stopper with capillary opening; SV, sliding valve; ST, screw-top stopper holder; N, syringe needle. [Reproduced from J. M. Gebicki and J. Guille, Anal. Biochem. 176, 360 (1989), with permission.]",
        "texts": [
            " Two modifications to the basic assay allow processing of much larger numbers of samples; these are the use of elevated temperature (50 \u00b0 ) to increase the rate of reaction between I - and hydroperoxides and the addition of cadmium acetate after completion to complex unreacted iodide. 3,18 The latter allows measurements of absorbance to be made in open cuvettes. At the Cd/I- ratio 18 j . M. Gebicki and J. Guille, Anal. Biochem. 176, 360 (1989). described here, equilibrium (2) is not significantly affected. Like the previously described anaerobic assay, the limit of detection is approximately I nmol hydroperoxide. Apparatus. The apparatus required is shown in Fig. 3. A stream of inert gas (nitrogen or argon) is passed through a presaturator (PS) containing methanol-acetic acid (2 : 1) and then split: one line leads to a pipettor (P; Monoject Scientific) and the other through a flow regulator (FR) into a distributor (D) fitted with multiple outlets made of stainless steel tubing (Pierce Chemical Co., Rockford, IL) connected to 21-gauge syringe needles (N). The reaction vials are glass vials fitted with Mininert valves (both available from Pierce Chemical Co"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000224_taes.2020.2988836-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000224_taes.2020.2988836-Figure1-1.png",
        "caption": "Fig. 1: Schematic representation of MAVs with fixed single (a) or double (b) rotors.",
        "texts": [
            " The translation kinematics is simply modeled in SG by r\u0307B/G G = vB/G G , (6) where vB/G G \u2208 R3 denotes the SG representation of the velocity of SB w.r.t. SG. On the other hand, the translational dynamic model in SG is immediately obtained by the Newton\u2019s law as v\u0307B/G G = 1 m FcG \u2212 ge3 + 1 m FdG, (7) where m \u2208 R>0 is the vehicle\u2019s mass, g \u2208 R>0 is the gravity acceleration, and FcG \u2208 R3 and FdG \u2208 R3 are the SG representations of the control and disturbance forces. The disturbance force FdB is unknown, but we assume that it is bounded by \u2016FdB\u2016\u221e \u2264 \u03c1F , (8) where \u03c1F \u2208 R>0 is a known parameter. The control force FcG is detailed in II-C. Figure 1 illustrates the MAV configurations considered here. They are equipped with fixed (instead of vectorable) rotors, which can be either single or double. In general, each rotor produces two efforts on the MAV airframe, both along the z\u0302B axis: a thrust force and a reaction torque. Their magnitudes are usually modeled, respectively, by [25]: fi = kf\u03c9 2 i , (9) April 15, 2020 DRAFT Authorized licensed use limited to: University of Canberra. Downloaded on April 30,2020 at 06:37:39 UTC from IEEE Xplore",
            " Assume that fi, \u2200i, are bounded by the following range and rate admissible sets: fi \u2208 [fmin, fmax], (11) fi \u2212 f\u2212i \u2208 [\u2212\u03b4fmax, \u03b4fmax], (12) where f\u2212i \u2208 [fmin, fmax] is the thrust force of the ith rotor at the previous control update instant and fmin, fmax, and \u03b4fmax are known parameters. Note that there is no need for considering bounds on \u03c4i since it can be rewritten in terms of fi. Finally, the motor-driver dynamics can be modeled by \u03c9\u0307i = \u2212 1 T\u03c9 \u03c9i + k\u03c9 T\u03c9 \u03c9\u0304i, \u2200i = 1, . . . , nr, (13) where \u03c9\u0304i \u2208 R is the rotation speed command of the ith rotor, k\u03c9 is a DC gain and T\u03c9 is a time constant. Considering the configurations of Figure 1, this subsection provides general expressions for the control force FcB , DB/GFcG and torque TcB as a function of the thrust forces fi, \u2200i = 1, ..., nr. To start with, note that FcB has only one non-zero component (the z\u0302B one), given by F c = nr\u2211 i=1 fi, (14) which clearly coincides with the magnitude of FcB or FcG. April 15, 2020 DRAFT Authorized licensed use limited to: University of Canberra. Downloaded on April 30,2020 at 06:37:39 UTC from IEEE Xplore. Restrictions apply. 0018-9251 (c) 2020 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.20-1.png",
        "caption": "Figure 13.20. Normal section through point A.",
        "texts": [
            "53), if we substitute G and Rb in place of A and R. We then obtain an expression for the unit vector normal to the tooth surface at A, Normal Section at A We define the normal section at any point A as the section through the gear perpendicular to the helix tangent at A, or in other words, perpendicular to n~. Generally, we will consider the normal section through a point A which lies on the tooth surface, but the definition remains valid whether A lies on the tooth surface or not. Normal Profile Angle at Radius R Figure 13.20 shows the normal section through point A on the tooth surface at radius R. The shape of the tooth profile in a normal section is unknown at present, but we will describe later in this chapter how the shape can be calculated. If C is the centre of the transverse section through A, as shown in Figure 13.19, the line CA also lies in the normal section, since the unit vector n~ along CA is Normal Profile Angle at Radius R 339 perpendicular to n~. Earlier, we def ined the transverse profile angle ~tR as the angle between CA and the profile tangent in the transverse section. We now define the normal profile angle ~nR in a similar manner, as the angle between CA and the profile tangent in the normal section. The unit vector n~ in Figure 13.20 points in the direction of the normal to the tooth surface at A, and is therefore perpendicular to any line touching the surface at A. One such line is the helix tangent at A, so the vector n~ must be perpendicular to nA, which means that it lies in the JJ plane of the normal section. A second line touching the surface at A is the profile tangent in the normal section, so n~ is also perpendicular to this direction. The angle in Figure 13.20 between the unit vectors n~ and n~ is equal to ~nR' since one is perpendicular to the profile tangent, and the other is perpendicular to line CA. We can use this result to derive an expression for cos ~nR. cos ~nR 340 Tooth Surface of a Helical Involute Gear cos 'nR cos \"'b cos \"'R cos(BA-BG) + sin \"'b sin \"'R (13.79, 13.53) cos 'nR cos \"'b cos \"'R (13.68) cos 'nR cos \"'b cos \"'R (13.59) cos 'nR cos 'tR tan \"'b tan \"'R sin \"'b sin \"'R + sin \"'b sin \"'R + sin \"'b sin \"'R (13.80) Since there are quite a number of steps in the development just presented, no explanation has been given for each step, but at each line the number of the equation used to justify the step has been written in brackets under the equals sign. The same procedure will be used again later, wherever it is warranted by the number of steps in a proof. The angle between the vectors n~ and n~ in Figure 13.20 is ('1'/2 - 'nR)' so we can derive an expression for sin 'nR in a similar manner. sin 'nR sin 'nR cos \"'b sin(BA-BG) (13.79, 13.52) sin 'nR cos \"'b sin 'tR (13.81) (13.68) Finally, we combine Equations (13.80 and 13.81) to obtain an expression for tan 'nR' tan 'nR tan 'nR (13.82) Tooth Surface of a Helical Involute Gear 341 Normal Pressure Angle The normal profile angle of a gear at its standard pitch cylinder is called the normal pressure angle of the gear, and it is represented by the symbol ~ns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000072_s40192-019-00149-0-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000072_s40192-019-00149-0-Figure9-1.png",
        "caption": "Fig. 9 a Illustration of the CMM measurement points and the defined origin for the measurements. b Part deflection after the legs are separated from the baseplate via EDM",
        "texts": [
            " Before any measurements were performed, the tops of the 11 ridges were ground to provide smooth surfaces that could be accurately measured with a coordinate measuring machine (CMM) at NIST. The CMM used in this study has an International Organization for Standardization (ISO) 10360-2 maximum permissible error (MPE) of 5\u00a0\u03bcm. The height of the ground surfaces of each ridge relative to the top surface of the baseplate was calculated from three measurements made across the ridge and two measurements made on the baseplate, on either side of the part. Figure\u00a09a illustrates the locations of the 55 CMM measurements and the reference point for the CMM measurements. After the first CMM measurements, the 12 legs were then separated from the baseplate via EDM, allowing the part to deflect upward (positive Z direction) due to the release of residual stress, as shown in Fig.\u00a09b. The CMM measurements were performed a second time to measure the new relative height between the ridges and baseplate. Part deflection was calculated by the difference between these two sets of measurements. Inherently, diffraction techniques measure lattice spacings. Measured lattice spacings for samples that exhibit residual strains will be the strained plane spacings. The unstrained lattice spacing (d0) is often determined using a stress-free boundary condition, whether directly near a free surface on the sample being measured, or on a separate specimen extracted from the large sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000300_s11684-020-0781-x-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000300_s11684-020-0781-x-Figure5-1.png",
        "caption": "Fig. 5 Various wrist designs. (A) Cable-driven EndoWrist, reprinted with permission from John Wiley and Sons [21], (B) serial-linkage-actuated design, reprinted with permission from IEEE [51], (C) parallel-linkage-actuated design, reprinted with permission from IEEE [52], (D) bending wrist, reprinted with permission from SAGE [27], (E) concentric-tube wrist (rightmost) compared with EndoWrist (leftmost), reprinted with permission from IEEE [54], and (F) deformable wrist, reprinted with permission from IEEE [58].",
        "texts": [
            " Passive RCM technique is safer, but the instrument\u2019s accuracy is often affected by the compliance from the incision port in the abdominal wall under the pneumoperitoneum. While the RCM movements of an instrument are realized by an extracorporeal manipulator, a wrist is often integrated at the distal end for dexterity enhancement such that suturing and knot tying can be more conveniently conducted. Many wrists adopt serial-structured designs. The desire for design compactness and proximal actuator arrangement often leads to the choice of cable actuation [17,24,47,48], including the famous EndoWrist design shown in Fig. 5A. Shape memory alloy actuation is also a possible approach to realize compact wrist designs [49,50]. However, the motion responses are relatively slow. For example, the thermal exchange took approximately 8 s to complete in Reference [49]. To enhance the wrist\u2019s structural rigidity, serial and parallel linkages are also proposed. Representative examples using serially connected coupler actuation [51] and a 3-PRS structure [52] are shown in Fig. 5B and Fig. 5C, respectively. However, these linkage-actuated wrists may have limited motion ranges. For example, motion ranges of the pitch and yaw joints are only 40\u00b0 in Reference [51], whereas the parallel-linkage design in Reference [52] has a pitch motion from \u201350\u00b0 to 70\u00b0 and a yaw motion of 64\u00b0. In comparison, the EndoWrist in the da Vinci system has a pitch motion range of 70\u00b0 and a yaw motion range of 90\u00b0 [17]. The pulleys used in the cable-driven wrists and the pinned joints in the linkage-driven wrists have limited potentials in further miniaturization",
            " Continuum mechanisms, which are coined in Reference [53] and transmit forces and motions via the structures\u2019 continuous deformations, have been explored. Examples of continuum wrists for multi-port procedures using a 2-DoF bending segment are shown in Figs. 5D [27] and 5E [54], featuring a multibackbone design and a concentric-tube design, respectively. The structural and modeling simplicity makes the design popular in many surgical robotic systems for single-port and NOTES applications [55\u201357]. To further improve the structural simplicity, a deformable wrist design was recently proposed as shown in Fig. 5F [58]. The rigidity is also enhanced as elastic strips were used to replace elastic wires. In these continuum wrists, fatigue may seem a problem due to the repetitive bending. However, superelastic nitinol can easily undergo 105 cycles of deformation [59], which fulfill the requirement for a multiuse instrument. Besides stick-like instruments with an RCM manipulator, the patient-side surgical manipulator can also be designed to directly realize multi-DoF intracorporeal movements. In this case, only a lockable stand is required to hold these dexterous surgical manipulators to the entry ports of a patient\u2019s abdomen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.6-1.png",
        "caption": "Figure 3.6. Unit vectors associated with the rack tooth.",
        "texts": [
            " Sliding Velocity The sliding velocity at the contact point is defined as the difference between the velocities of the two points in contact. If point A of the pinion touches point Ar of the rack, then the sliding velocity is defined as follows, Sliding veloc i ty (3.30) In order to derive an expression for the sliding 64 Gears in Mesh velocity, we need to make use of the set of unit vectors nt, n~ and nS in the directions of the coordinate axes, and we also introduce the two unit vectors shown in Figure 3.6, which are associated with a rack tooth profile. These vectors are nnr' in the direction of the outward-pointing normal to the tooth profile, and nTr , in the tangential direction toward the tip of the tooth. If the rack velocity is vr ' this is of course the velocity of any point in the rack, and therefore in vector form the veloc i ty of Ar can be wri tten, (3.31) To obtain the velocity of point A, we form the vector product of the pinion angular velocity and the position vector from C to A. I f point A lies in posi tion s on the path of contact, the "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000509_j.ijimpeng.2020.103671-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000509_j.ijimpeng.2020.103671-Figure3-1.png",
        "caption": "Fig. 3. (a) Unit cell topology with finite element mesh of the shell lattice. (b) View of the untested uniaxial compression specimens (3 \u00d7 3 \u00d7 3 stacking of the unit cell) fabricated through selective laser melting with 316L. (For interpretation of the references to color in the text, the reader is referred to the web version of this article.)",
        "texts": [
            " The lattices investigated herein belong to an assembly of face-centered-cubic (FCC) shell lattices that are generated from smoothing the topology of tube lattices (also referred to as hollow truss lattices). The smooth shell lattice is obtained by minimizing the bending-energy based measure of the overall curvature. The curvature minimization technique is further tailored to obtain an elastically-isotropic shell-lattice. The geometry for a representative unit cell used in this study is shown in Fig. 3a. The cubic unit cells feature an edge length of 5.35 mm. Details on the mathematical formulation for the smooth FCC shell lattices are described in Bonatti and Mohr [5,6]. The applied curvature minimization method leads to a lattice with reduced stress concentration, which is usually the cause for failure in truss and plate lattices at large strains [34,37]. Elastically-isotropic FCC shell lattice specimens (assembly of 3 \u00d7 3 \u00d7 3 unit cells) with a relative density of 25% (ratio of solid material volume over unit cell volume) and a nominal edge length of 16.04mm are fabricated from stainless steel 316L through selective laser melting. A summary of the fabricated specimen geometries and weight properties are provided in Table 1. The specimen outer dimensions differ on average 1.3% from the target value. The relative density is on average 14% higher than the designed value. All specimens feature a target wall thickness of 0.32 mm. A photograph of a fabricated specimen is given in Fig. 3b. Due to limitations in the manufacturing process, all shell-lattice specimens are built along the [1 1 0] direction (diagonal on specimen surface). Consequently, the uniaxial compression tests conducted on the lattice's cubic surfaces compare to testing on 45\u00b0 and 90\u00b0, with respect to the building direction. Electron Back Scatter Diffraction (EBSD) images of the polycrystalline microstructure are obtained from three orthonormal surfaces of the parallel sheet structure (Fig. 4c). The extracted samples are processed by mechanical grinding with silicon carbide paper followed by final polishing using a 60 nm alumina colloid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000032_j.rcim.2020.101959-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000032_j.rcim.2020.101959-Figure11-1.png",
        "caption": "Fig. 11. Vector variations from the robot coordinate system origin to the sphere center.",
        "texts": [
            " The error mathematical expectation \u03bc is 0. The point constraint calibration errors are mainly focused on a2 and d4, and these errors are approximately proportional to their ideal value. If described as vectors, there are three main vectors from the robot basal coordinate system origin to the sphere center. Proportional variation of a2 and d4 to the nominal length leads to variation of the calculated sphere center, but the calculated camera optical axes at different poses will still converge at this sphere center, as shown in Fig. 11. 4.3. Distance constraint identification process Combined with the point constraint measurement, a distance constraint calibration is proposed as a supplement to improve the identification accuracy of joint length parameters (mainly for a2 and d4). The distance constraint calibration process is similar to the point constraint process. Eq. (9) is the distance constraint equation, which is transformed into Eq. (10) to facilitate iterative computation. The combined equation of point constraint and distance constraint is Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003982_j.apsusc.2008.09.039-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003982_j.apsusc.2008.09.039-Figure1-1.png",
        "caption": "Fig. 1. (a) The structure of the specimen, (b) the schematic diagram of the laser cladding affected region.",
        "texts": [
            " The cracks during laser cladding processes with five different laser cladding powder materials were online tested, respectively. The temperature ranges of crack generation and expansion were achieved using FEA. The factors that affect the amount of cracks were discussed, and main forms and extended forms of cracks were investigated finally by using optical microscope and ESEM. Cuboid specimen of 45 steel, 300 mm long, 40 mm wide and 40 mm thick was used as the base metal, and it is illustrated in Fig. 1(a). Two acoustic sensors were fixed on the side surfaces of the specimen. In order to control the temperature rise and protect the acoustic sensors during laser cladding process, two holes were made at the centre of the specimen for water cooling. Fig. 1(b) and (c) show the process of laser cladding. A laser beam moves in Xaxis direction with a constant speed, striking on a focused area of base metal surface while cladding powder is fed into a molten pool and finally cooled down to the clad layer. The thickness of coatings varies from 0.4 mm to 0.8 mm. The generation and expansion of the cracks were detected through tracking the sudden acoustic emission signals by using the two acoustic sensors. If both of the sensors receive acoustic emission signals at the same time, it can be judged that the crack has generated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure9.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure9.2-1.png",
        "caption": "Figure 9.2. Meshing diagram of a gear and basic rack.",
        "texts": [
            " The pitch is Pr' and the reference line is defined in the usual way, as the line along which the tooth thickness is equal to the space width. The rack coordinate system (xr'Yr) is chosen so that the Yr axis lies along the reference line, and the xr axis coincides with a tooth center-line. A typical point Ar of the tooth profile has coordinates (xr,y r ), and the profile angle at this point is ~Ar. Since the shape of the tooth profile is known, Y and A r ~ r are known functions of xr ' We now consider a gear meshed with the basic rack, as shown in Figure 9.2. The pitch circle radius of a plnlon meshed with a rack was given by Equation (1.15), and in Equation (1.19) we showed that the circular pitch of the pinion at its pitch circle is equal to the pitch of the rack. Since the gear in Figure 9.2 is meshed with its basic rack, we 208 Geometry of Non-Involute Gears use the symbol Rsg for the radius of the pitch circle, and the two equations take the following form, ( 9. 1 ) (9.2) The pitch point P is the point lying a distance Rsg from the center of the gear, on the line perpendicular to the reference line of the basic rack. We consider the basic rack when it is positioned with an offset e, so that its reference line lies a distance (Rsg+e) from the center of the gear. We will make use of the fixed (E,~) coordinate system, whose origin is at the pitch point, and the (x,y) coordinate system in the gear, where the x axis coincides with a tooth center-line",
            "5) For a gear being cut by a rack cutter, the relation between the position of the rack cutter and the angular 210 Geometry of Non-Involute Gears position of the gear was given by Equation (5.28), The same equation applies when we consider a gear meshed with its basic rack, and we can therefore find the angular position ~g of the gear, corresponding to the position ur of the basic rack, 1 (u _ lp ) R r 2 s sg (9.6) Since point Ar of the basic rack is the contact point, there is a point A of the gear which coincides with Ar , and its polar coordinates can be read from Figure 9.2, R (9.7) 1/ arctan (~) - ~g sg (9.8) Finally, the tangent to the gear tooth profile at A coincides with the tangent to the basic rack tooth profile at Ar , and therefore makes an angle ,Ar with the ~ axis. The angle YR, which is defined as the angle between the gear tooth tangent at A and the tooth center-line, is then given by the following expression, (9.9) Equations (9.3-9.9) can be used to find the polar coordinates (R,8R) of a point A on the gear tooth profile, and the angle YR, corresponding to any specified point Ar on the basic rack tooth profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003648_physrevlett.97.184302-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003648_physrevlett.97.184302-Figure1-1.png",
        "caption": "FIG. 1. (a) Blue bindweed (Ipomoea purpurea), a typical twining plant (illustration from von Sachs\u2019 physiology of plants [10]). The shoot apex spans from a to b. (b) Diagram of the apex region of a climbing twiner.",
        "texts": [
            " The filament is assumed to be clamped at its base (s 0), that is r 0 R; 0 , d3 0 0; 1 . The natural radius of the vine, R\u0302, corresponds to the radius of the vine when taken away from its support (see [4] for the experimental procedure that provides the value of R\u0302). The clamp models the constraint applied by the lower part of the plant on the shoot apex. The tip at s L lies on the disc and no moment is applied to it so that its curvature is equal to the intrinsic curvature u2 L u\u03022. We also require the external force at L to be radial (see Fig. 1). For each length L and ratio of radii R=R\u0302, these boundary conditions ensure the existence of a discrete set of solutions. Therefore solutions can be obtained numerically by traditional shooting methods for boundary-value problems: starting with the initial values at s 0 [r 0 R; 0 , d3 0 0; 1 , m 0 , and n 0 to be given by an initial guess], Eq. (1) is integrated with a Runge-Kutta alogrithm, up to s L where we check the end conditions. If they are not satisfied, we adjust the values for m 0 and n 0 until the computed solution satisfies the boundary conditions. Once a solution is known, the process of growth on the disk is carried out by finding solutions with increasing length, using parameter continuation. For each solution, we track the angle that the tip makes with the tangent to the disk (see Fig. 1). We refer to the portion of the filament off disk as the anchor. For small , a typical bifurcation diagram with distinct equilibria branches is shown in Fig. 2. On the first branch (continuous line) and for small enough L, we find stable solutions which can be continued up to a (fold) point where they first penetrate the disk. This is a bifurcation point where we identify another branch (the vertical line in Fig. 2) corresponding to solutions having a segment in continuous contact with the disk in addition to the anchor part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000371_tnnls.2020.2966914-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000371_tnnls.2020.2966914-Figure6-1.png",
        "caption": "Fig. 6. ECP model 210. Rectilinear electrical\u2013mechanical plant (massspring) used to implement the adaptive control algorithm based on the weights estimated by the application of a controlled BLF.",
        "texts": [
            " The system consisted of a mass-spring device with online measurement of the mass position (Servo Amplifiers 5-kHz current loop bandwidth). A high-resolution encoder measured the position of the mass connected with a spring of unknown stiffness (160 count/mm). The actuator was a brush-less dc servo motor (precision rack and pinion, 8-N output). The interface used for real-time controller implementation was MATLAB real-time windows target with a sample time of 0.001 s. No information on the mass or the spring was considered in the DNN identifier design. The plant is shown in Fig. 6. As the plant only can get the online measurement of the position, a model-free observer was also implemented to obtain the velocity. A comparison between the DNN identifier with and without the adaptive control gain restricted by the states constraints is presented. The following strategy was used in the implementation: 1) an observer based in sliding modes technique [32] to obtain state x2 from the position sensor measurements (state x1); 2) a control using learning laws obtained from a QLF; 3) a control using learning laws obtained from a BLF; and 4) the addition of an unknown mass-spring element as perturbation input for both systems, with QLF and BLF"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000824_j.biotechadv.2021.107785-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000824_j.biotechadv.2021.107785-Figure2-1.png",
        "caption": "Fig. 2. The link between complexity and scale of the features in 4D printed materials.",
        "texts": [
            " Self-assembled, multi-materials and designed materials are ideal for 4D printing, while conventional metals, ceramics, and thermoplastics are preferred in 3D printing (Gonza\u0301lez-Henr\u00edquez et al., 2019). The specificity of 4D printing technologies has its benefits and drawbacks. Smart materials exhibit timed and customized responses to humidity, light, heat, osmotic pressure, current, and presence of biomolecules (Mandon et al., 2017). Nonetheless, the materials are highly sophisticated; the complexity of the features was correlated with the scale, as shown in Fig. 2. From an engineering perspective, the drawbacks such as the complexity of the materials do not offset the tangible benefits associated with the application of self-programming materials, capable of responding to natural stimuli in farm environments; this worldview is supported by the nature of 4D printing technologies (Kim et al., 2020; Yu et al., 2020; Barletta et al., 2021), which are essentially a buildup of existing fabrication and characterization methods (particularly scanning probe microscope, focused ion beam, aerodynamically focused nanoparticle, and nanoparticle deposition system) (Gonza\u0301lez-Henr\u00edquez et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003734_j.actaastro.2008.04.009-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003734_j.actaastro.2008.04.009-Figure5-1.png",
        "caption": "Fig. 5. Forces applied to the aircraft.",
        "texts": [
            " This is barely at the threshold of detection of the semicircular canals, the vestibular organs that measure angular rotation of the head [6], and so this rotation is not typically perceived by the occupants. The control inputs required by the pilots of a parabolic flight aircraft are relatively simple, although precision is required to make the 0g phase as close to freefall as possible, and care is required not to exceed the load limits of the aircraft which at times flies near its maximum rated speed. The pilots modulate lift L with the elevators and wings, which indirectly changes pitch attitude , and thrust T with the engines (Fig. 5). Drag D varies with airspeed and other factors. Aircraft weight is defined as P = g \u00b7 mP , where mP is the mass of the aircraft. We assume that ax and az for the aircraft are the same as for the occupants, which is true when the occupants do not move relative to the aircraft. Table 1 Parabolic flight programs Organization Aircraft Location Comments U.S. Air Force F-94 (single jet) C-131B (twin propeller) Wright-Patterson Air Force Base, Ohio Early 1950s Late 1950s NASA Reduced Gravity Office \u201cWeightless Wonder\u201d Boeing KC-135A (four-engine jet) Houston, Texas Cleveland, Ohio Last flight in 2004 Douglas C-9B (twin-engine jet) Houston, Texas Cleveland, Ohio Current aircraft Russian Space Agency Ilyushin IL-76 (four-engine jet) Star City, Russia European Space Agency \u201cZero-G\u201d Airbus A300 (twin jet) Bordeaux, France Canadian Space Agency Dassault Falcon 20 (twin-engine business jet) Ottawa, Canada Since 1993 Zero Gravity Corporation Boeing 727 (twin-engine jet) Las Vegas KSC, Florida Space Adventures Ilyushin IL-76 (four-engine jet) Contracts to the Russian Space Agency For the 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003409_1.1899688-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003409_1.1899688-Figure1-1.png",
        "caption": "Fig. 1 Definition of the tooth",
        "texts": [
            " Accordingly, the most common way of defining modifications for helical gears is through a tip modification relief , a root modification, and a face crown. Another definition that has also been widely used considers an involute slope A, an involute crown B, and a face crown D. These modifications are obtained by removing material from the ideal involute surfaces or leaving additional material in the finishing process and, therefore, their magnitudes are defined as differences from the ideal perfect involute profile. By mapping the ideal involute profile to a rectangular plane, these modification parameters can be defined as shown in Fig. 1. With three modification parameters per gear, a total of six parameters p p p g g g A ,B ,D ,A ,B ,D determine the tooth surface modifications 05 by ASME Transactions of the ASME 5 Terms of Use: http://asme.org/terms sur Downloaded F of a pair formed by gears p and g. While other more contemporary modification schemes such as bias modification 10,11 are also use for helical gears, they are not common since they can only be achieved with costly hard gear finishing processes. Therefore, such modifications were excluded from this study"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure6-1.png",
        "caption": "Fig. 6. Translational robotic manipulator with two degrees of mobility: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " 5 obtained by concatenating the closed loop A-B and the elementary open kinematic chain associated with the leg C. Only four independent motions (vx, vy, vz,\u03c9z) exists in this case between the extreme elements 1C and 0 (Fig. 5). These velocities form the base of RF(2)/KF(1) . Two other examples of parallel mechanisms with uncoupled translational motions and with decoupled Sch\u00f6nflies motions proposed by the author of this paper (Gogu, 2002) are presented to illustrate the applicability of Eq. (26). Fig. 6 presents a parallel robotic manipulator (Gogu, 2002) with three legs derived from the solution presented in Fig. 1 by eliminating the actuated prismatic joint from the leg C. In this case, leg C has just a guiding role by constraining the mobile platform to a planar motion. This mechanism has p = 11 joints (2 prismatic and 9 revolute joints) and q = 2 independent loops. Each joint has one degree of mobility (fi = 1). The two independent loops have also the same motion parameter b1 = b2 = 5 whichever set of independent loops is chosen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure17.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure17.15-1.png",
        "caption": "Figure 17.15. Oblique line load on a cantilevered plate.",
        "texts": [
            " The angle between the generator and the helix tangent at radius R is the generator inclination angle vR' which was defined in Chapter 13. In order to use the equivalent spur gear to calculate the fillet stress in a helical gear, we must represent the real load on the helical gear, which acts along an oblique line at an angle with the tooth tip, by an equivalent load on the spur gear acting along a line parallel to the tooth tip. This equivalent load was studied by Wellauer and Tooth Load on the Equi valent Spur Gear 513 Seireg [8], who considered the cantilevered plate shown in Figure 17.15. The plate is loaded by a force of intensity w, acting along an oblique line at an angle v with the plate edge. They showed how to calculate the bending moment intensity at point A, which can then be expressed in the form (WH/Ch ), where H is the height of point Aw above point A. The quantity Ch is defined as the bending moment intensity if the plate were loaded along a line parallel with the plate edge, divided by the maximum bending moment intensity when the plate is loaded with the same force intensity along the oblique line",
            " They have therefore been recalculated [11], using essentially the original method, and they can be represented by the following expression, (17.61) The angle v must be expressed in degrees, as indicated by the notation, and the equation is valid for values of v between 0\u00b0 and 25\u00b0. In order to calculate the value of Ch required for a particular helical gear, we must choose the value of v to be used in Equation (17.61). On the helical gear, the generator inclination angle vR varies with the radius R. Hence, the load on the plate in Figure 17.15 should really lie along a curve, as shown in Figure 17.16, instead of a straight line. However, the bending-_moment intensity at A is determined primarily by the load in the immediate vicinity of point Aw' so it is sufficiently accurate to represent the load curve by a straight line at an angle v , where v is the generator w w inclination angle at point A \u2022 The value of v is given by w w Equation (13.87), in terms of the helix angle and the transverse profile angle of the helical gear at radius Rw' sin v w sin \"'w sin 9>tw (17"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000520_s11831-020-09511-4-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000520_s11831-020-09511-4-Figure9-1.png",
        "caption": "Fig. 9 Typical residual stress profile in WAAM deposition a clamped stress profile b out-of-plane distortion after unclamping c redistributed and balanced residual stress profile after unclamping [180, 181]",
        "texts": [
            " For the numerical prediction of residual stress and distortion in the component produced through WAAM, one has to perform mechanical simulation as the second part of thermo-mechanical analysis considering temperature distribution history obtained from the thermal simulation as an input. Warping, delamination, and loss of edge tolerance are the undesirable consequential effects of developed thermal stress [51, 52, 178, 179]. The residual stress can range from 60% to approximately 100% of the material\u2019s yield strength [4, 56, 119]. Tensile residual stresses are almost constant throughout the height but most substantial in the longitudinal direction, i.e., xx [180], as shown in Fig.\u00a09. The heat accumulated through the current layer deposition has a significant effect on the previously deposited layers. It surprisingly weakens the effect of final residual stress due to intermediate heat treatment [66, 67]. Mughal et\u00a0al. [170, 176] investigated the effect of distortion on base plate and substrate in weld based rapid prototyping method along with the studies on the deflection of the substrate in bolted and unbolted conditions. They found that the effect of bolting is dominant at the edges and the centre of deposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure8-1.png",
        "caption": "Fig. 8. Geometric model of the gravity compensator.",
        "texts": [
            " (16) results in \u03c1w, 2 = W T 2 ( $ w, 2 + $ w,c ) (17) where $ w, 2 = $ w,E + $ w, G E + $ w, G 5 + $ w, G 4 + $ w, G 3 + $ w, G 2 , $ w, G 2 = \u2212m 2 g [ \u02dc z ( r 3 + R 3 r 3 G 2 ) \u00d7\u02dc z ] , $ w,c = \u2212 [ R c \u03c1w,c, f (r 2 + R 3 r 2 c ) \u00d7 (R c \u03c1w,c, f ) ] , \u03c1w, 2 = [ \u03c1w, 2 , f \u03c1w, 2 ,\u03c4 ] , W 2 = [ R 2 \u02c6 r2 R 2 0 R 2 ] , r 2 = r 3 + R 3 r 3 2 , $ w, 2 is the resultant externally applied wrench imposed at point O E for joint 2, $ w, G 2 is the equivalent wrench due to the gravity force of link 2 applying on point O E , $ w,c is the equivalent wrench due to the balancing force imposing on point O E , \u03c1w, 2 is the reaction force of joint 2, \u02c6 r2 is the skew-matrix of the position vector r 2 . To calculate \u03c1w,c, f and R c in $ w,c , the detailed geometric model of the gravity compensator is shown in Fig. 8 . In such a structure, three key points O 2 , O c and O p form a triangle, whose shape is varied with \u03b82 . When \u03b82 = 0 \u00b0, it is noted that O c is located on the line of O p O 2 . The rod length L can be calculated as follow according to the law of cosines L 2 = a 2 + b 2 \u2212 2 ab cos \u03b82 (18) where a is the length of O p O 2 , and b is the length of O c O 2 . For the considered robot, the gravity compensator is a specifically designed hydro-pneumatic compensator. According to the ideal gas law, it always has P V = C (19) where P and V are the pressure and volume of the gas, and C is a constant at a certain temperature",
            " Then, the pulling force generated by the piston rod at L can be written as \u03c1w,c, f = P L A = P 0 V 0 A V 0 + A ( L \u2212 L 0 ) = CA V 0 + A ( L \u2212 L 0 ) (21) It is clear that L is changed with the rotation of joint 2, which means that the compensation force depends on the joint angle \u03b82 . Then, the force generated by the gravity compensator in { O c } can be expressed as \u03c1w,c, f = [ \u03c1w,c, f cos ( \u03c0 + \u03b3 ) 0 \u03c1w,c, f sin ( \u03c0 + \u03b3 ) ]T (22) where \u03b3 can be calculated according to the law of sines \u03b3 = arc sin ( a L sin \u03b82 ) . Besides, the rotation matrix R c at any configurations can be expressed as R c = R 2 Rot ( Y 2 , \u03b82 \u2212 \u03c8 ) (23) where \u03c8 is the structural parameter shown in Fig. 8 . Finally, to calculate the reaction force exerted on joint 1, a force diagram of substructure 1 is shown in Fig. 9 . The equation of static equilibrium at point O E can be written as \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 f E \u2212 m E g \u0303 z \u2212 m 5 g \u0303 z \u2212 m 4 g \u0303 z \u2212 m 3 g \u0303 z \u2212 m 2 g \u0303 z \u2212 m 1 g \u0303 z = \u03c1w, 1 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z \u2212 m 5 g ( R E r E 6 + R 6 r 6 G 5 ) \u00d7\u02dc z \u2212 m 4 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 G 4 ) \u00d7\u02dc z \u2212m 3 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 G 3 ) \u00d7\u02dc z \u2212 m 2 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 G 2 ) \u00d7\u02dc z \u2212m 1 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 2 + R 2 r 2 G 1 ) \u00d7\u02dc z = ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 2 + R 2 r 2 1 ) \u00d7 \u03c1w, 1 , f + \u03c1w, 1 ,\u03c4 (24) where \u03c1w, 1 , f = [ \u03c1w, 1 , f x \u03c1w, 1 , f y \u03c1w, 1 , f z ] T , \u03c1w, 1 ,\u03c4 = [ \u03c1w, 1 ,\u03c4x \u03c1w, 1 ,\u03c4y \u03c1w, 1 ,\u03c4 z ] T , \u03c1w, 1 , f and \u03c1w, 1 ,\u03c4 are the reaction force and torque of joint 1 acting at point O 1 , m 1 is the mass of link 1, G 1 is the mass center of link 1, r 2 G 1 is the position vector from point O 2 to point G 1 evaluated in { O 2 }, r 2 1 is the position vector from point O 2 to point O 1 evaluated in { O 2 }",
            " 12 that the link weights and the balancing force show no effects on the linear deflection along the Y -axis and the angular deflections around the X -axis and the Z -axis. However, the link weights cause significant linear deflection along the negative direction of the Z -axis and angular deflection around the positive direction of the Y -axis. These results are consistent with the intuitive deflection analysis. In this configuration, the direction of balancing force passes through the axis of joint 2 as demonstrated in Fig. 8 . As a result, rather than compensating the link weights to decrease the deflections, the balancing force adversely increases the total linear deflection along the Z -axis and the total angular deflections around the Y -axis. In fact, the deflections caused by the link weights illustrated in Fig. 12 are the sum of the gravity-induced deflections of each link. Fig. 13 shows the contribution of each link on the linear deflections and the angular deflections in each direction. As illustrated, it can be observed that the dominant factor is the in-line wrist (link 4, link 5 and link 6) and the end-effector (spindle) of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.17-1.png",
        "caption": "Figure 13.17. Transverse section at plane z=O.",
        "texts": [
            "15) we gave the base cylinder radius of the gear in terms of the standard pitch cylinder radius and the transverse pressure angle \"'tr of the basic rack, ( 13.61 ) When we compare Equations (13.60 and 13.61), it is evident that the transverse pressure angle of the gear is equal to the basic rack transverse pressure angle, (13.62) The Generator Through Point A The transverse section at plane z of a helical gear is shown in Figure 13.16, and as always in a transverse section, the tooth profile is an involute. The normal to the involute at a typical point A touches the base circle at E, and the involute meets the base circle at B. Figure 13.17 shows the transverse section through the same tooth at plane z=O, and in this section the involute meets the base circle at BO. The two points Band BO both lie on the curve forming the intersection of the base cylinder 332 Tooth Surface of a Helical Involute Gear with the tooth surface. Since this curve is a gear helix, BO can be identified as the point where the gear helix through B cuts the plane z=O. The profiles in the two sections are identical, except that the profile at plane z is rotated relative to the other by the angle tJ.8 given by Equation (13.18), (13.63) In Figure 13.16, B' is the point where the axial line through BO cuts plane z, so that line CB' is parallel to CaBo in Figure 13.17. B'CB is the angle through which the tooth profile has rotated between the two transverse sections, and is therefore equal to tJ.8. In Figure 13.17, E' is the point where the axial line through E cuts plane z=O, and A' is the point where the base circle tangent at E' cuts the tooth profile. We now use Equation (13.56) to derive an expression for the di fference between the lengths EA and E' A' \u2022 EA - E'A' arcEB - arcE'BO arc EB - arc EB' EA - E'A' arc B' B (13.64) The expression for tJ.8 in Equation (13.63) can be put into a different form by means of Equation (13.32), (13.65) and we substitute this expression into Equation (13.64). EA - E'A' (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure2-1.png",
        "caption": "Fig. 2 Coordinate systems for",
        "texts": [
            " Other parameters of the cutter heads include he profile angle 0 straight-lined edges , the hook angle h, the ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 offset angle 0, and the number of cutter starts z0. Coordinate systems Sl xl ,yl ,zl and St xt ,yt ,zt are rigidly connected to the cutting edge and the cutter head, respectively. And Sm, Sn, and Sp are auxiliary coordinate systems that describe the relative position of the cutter edge on the cutter head. Figure 2 shows the other type of face hobbing cutter head used in cutter tilting processes such as Oerlikon\u2019s Spirac\u00a9 and Spiroflex\u00a9 cutting systems. The outer and inner blades rotate about the same cutter axis, and all blades are mounted to the head cutter, with the cutting edge in the plane H. The plane T is tangent to the rolling circle small dashed circle in Fig. 2 and the plane H is rotated about common axis xl throught hook angle h. The tooth thickness is obtained by adjusting the radii of the inner and outer blade groups, r0I and r0A. In the modern face hobbing process, the hook angles hI and hA are used to finely adjust the bias condition of the tooth contact. Angle h is a function of the side rake angle, pressure angle and axial inclination angle 14 . The cutting edge of the cutter blade is generally straight lined with a circular-arc tip fillet. However, for better profile modification, a circular blade edge may be used instead of the straight line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000518_j.addma.2020.101604-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000518_j.addma.2020.101604-Figure1-1.png",
        "caption": "Fig. 1. Drawings of (a) round axial fatigue specimens with a uniform gage section, and (b) compact tension (CT) specimens following ASTM E647 standard [47].",
        "texts": [
            " To understand the effect of shield gas type, the same process parameters were used to fabricate parts under N2 shield gas. It is worth noting that the gas flow rate was the same for both shield gases, and the scan strategy utilized was a conventional parallel scan with a 67\u25e6 interlayer rotation. The design of experiment is detailed in Table 3. Two sets of 11.5 \u00d7 11.5 \u00d7 77 mm3 square bars were fabricated in the vertical direction and machined to the round axial fatigue specimens with a uniform gage section, shown in Fig. 1(a). All the machined specimens were further hand polished to remove the machining marks and make the surface mirror-finished. The surface roughness of the gage section was measured after polishing to be Ra = 0.93 \u00b1 0.24 \u03bcm using Keyence VHX6000, a digital optical microscope. It must be mentioned that the tensile tests were performed using the same geometry. Two sets of walls with the dimension of 65 \u00d7 6.5 \u00d7 65 mm3 were fabricated vertically and further machined by electrical discharge machining (EDM) into compact tension (CT) specimens in Fig. 1(b), following ASTM E647 standard [47]. For each type of specimens (i.e. axial fatigue and CT), one set was fabricated under Ar shield gas (dubbed \u201cAr specimens\u201d), and one set of specimens was fabricated under N2 shield gas (dubbed \u201cN2 specimens\u201d). All the axial fatigue and CT specimens were subjected to CAH1025 heat treatment procedure (solution heat treating at 1050 \u25e6C for 0.5 h followed by air cooling (Condition A, or CA), then aging at 552 \u25e6C for four hours followed by air cooling (H1025) [6]) utilizing a box furnace in an Ar atmosphere to prevent oxidation and surface decarburization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000735_j.jmapro.2021.04.016-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000735_j.jmapro.2021.04.016-Figure4-1.png",
        "caption": "Fig. 4. Finite element model(FEM). (a)Meshing results of FEM and (b) application of the life and death unit in the laser cladding process.",
        "texts": [
            " The heat flux density at one point in the ellipsoid along the front half of the x-axis: q(x, y, z) = 6 \u0305\u0305\u0305 3 \u221a f1\u03b7UI aba1\u03c03/2 exp( \u2212 3x2 a2 1 )exp( \u2212 3y2 b2 )exp( \u2212 3z2 c2 ) (10) The heat flux density at one point in the ellipsoid along the rear half of the x-axis: q(x, y, z) = 6 \u0305\u0305\u0305 3 \u221a f2\u03b7UI aba2\u03c03/2 exp( \u2212 3x2 a2 2 )exp( \u2212 3y2 b2 )exp( \u2212 3z2 c2 ) (11) Where, q is the heat flux density, a1, a2, b and c are shape parameters of double ellipsoid heat source functions, \u03b7 is the laser thermal efficiency, taking 0.3 in this article, U is voltage, I is the current, f1 and f2 are the energy distribution coefficients of the front and rear half of the heat source model, respectively, f1+ f2 = 2. The cladding process is simulated by dividing the finite element mesh and using the life and death element method [28], as shown in Fig. 4. The solidification process of molten pool was simulated by CA method. The flow chart of the process of CA is shown in Fig. 5. The temperature field of laser cladding is obtained through finite element analysis, and the local grid is selected as the interpolation domain. The temperature value of each node in the interpolation domain is derived, and the curve of the node temperature with time is fitted with Origin software. The temperature value of the microcell is obtained by bilinear interpolation [29], as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003056_s0094-114x(03)00003-x-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003056_s0094-114x(03)00003-x-Figure9-1.png",
        "caption": "Fig. 9. Projection of distances, angles and forces on the XY plane in the contact Cii\u2013Ces.",
        "texts": [
            " 8A), the distance between the centres of curvature will be A1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0XCii1 XCes2\u00de2 \u00fe \u00f0YCii1 YCes2\u00de2 \u00fe \u00f0ZCii1 ZCes2\u00de2 q \u00f039\u00de The relative displacement between the two centres of curvature will be equal to D1 \u00bc A1 A0 \u00f040\u00de The contact angle will be a1 \u00bc arcsin \u00f0ZCii1 ZCes2\u00de A1 \u00f041\u00de The reaction in the ball bearing will be q1 \u00bc KDn 1 \u00f042\u00de It is interesting to observe the relationship of angles in the contact (Fig. 9). A1 cos a1 is the projection on the XY plane of the distance between centres of curvature Cii and Ces cos b1 \u00bc XCii2 XCes2 A1 cos a1 \u00f043\u00de sin b1 \u00bc YCii2 YCes2 A1 cos a1 \u00f044\u00de The x; y; z components of the reaction will be q1x \u00bc q1 cos a1 cos b1 \u00f045\u00de q1y \u00bc q1 cos a1 sinb1 \u00f046\u00de q1z \u00bc q1 sin a1 \u00f047\u00de Substituting (43) in (45) and (44) in (46), we obtain the following: q1x \u00bc q1 XCii2 XCes2 A1 \u00f048\u00de q1y \u00bc q1 YCii2 YCes2 A1 \u00f049\u00de The vector position of the point of application of the reaction shows the following x; y; z components: R1x \u00bc XCii2 \u00fe \u00f0d A1\u00de 2 cos a1 cosb1 \u00f050\u00de R1y \u00bc YCii2 \u00fe \u00f0d A1\u00de 2 cos a1 sin b1 \u00f051\u00de R1z \u00bc ZCii2 \u00fe \u00f0d A1\u00de 2 sin a1 \u00f052\u00de where d \u00bc diameter of the ball bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000463_j.jallcom.2020.156722-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000463_j.jallcom.2020.156722-Figure1-1.png",
        "caption": "Fig. 1. (a) TiN/AlSi10Mg composite powder, (b) Schematic of the double laser scanning paths, (c) the stripe scanning strategy applied in SLM, (d) specimens manufactured by SLM; (e) dimensions of tensile test specimen based on ASTM E8 standard, and (f) photography of SLM-fabricated dog-bone specimens.",
        "texts": [
            " The microstructure-mechanical property relationship and the underlying strengthening mechanism are discussed. These findings can be a valuable reference for tuning the microstructure and mechanical properties of heat-treated AMCs. The near-spherical AlSi10Mg powder (D10 \u00bc 10.1 mm, D50 \u00bc 25.7 mm, and D90 \u00bc 65.6 mm) and TiN nanoparticles (99.9% purity, d50 \u00bc 80 nm) were supplied by MTI Co., Ltd., China. The chemical composition of AlSi10Mg powder is provided in Table 1. TiN/AlSi10Mg composite powder (4 wt% TiN and 96 wt% AlSi10Mg, Fig. 1a) was synthesized by ultrasonic vibration dispersion [16], the detailed mixing procedure can be seen in Fig. S1 (Supplementary Material). All specimens were fabricated using commercial SLM equipment (SLM solutions, 280 HL) equipped with double 400 W fiber lasers. The SLM parameters were optimized and set as follows: laser power \u00bc 200 W, laser scanning speed \u00bc 1200 mm/s, hatching distance \u00bc 0.09 mm, and layer thickness \u00bc 0.03 mm. A separate stripe scanning strategy and a zigzag pattern were used. The scanning direction alternated by 15 between each successive layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003798_ip-b.1983.0016-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003798_ip-b.1983.0016-Figure8-1.png",
        "caption": "Fig. 8 Vector diagrams",
        "texts": [
            " Under these conditions, an asynchronous component will grow rapidly and the terminal voltage will increase to the appropriate value. The fixed rotor poles due to remanence are destroyed and the synchronous component of current decays to zero. If the synchronous operating point is close to point X, only a small disturbance is required to initiate self excitation. a Corresponding to point X in Fig. 4 for circuit shown in Fig. 3 b Corresponding to point Y The effect of this transition on the synchronous machine can be seen from the vector diagrams in Fig. 8 (for circuit, see Fig. 3). Below resonance, the load angle 6 is such that The MMF Fx produced by the current flowing, reinforces the remanent MMF F2 to produce the resultant MMF Fo. While above resonance, the current acts to reduce the remanent magnetism. The change in phase of the current between the two operating points is of the order of 150 degrees. For the resonant-frequency line to be crossed and self excitation to occur, the synchronous machine must sustain this large change in phase \u2014 effectively a large loadangle swing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003347_anie.199105161-Figure20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003347_anie.199105161-Figure20-1.png",
        "caption": "Fig. 20. Schematic arrangement of an optical biosensor.",
        "texts": [
            " Urea can be determined by an analogous meth- These examples of optical sensors, which are summarized in Table 10, clearly illustrate that, like electrochemical biosensors, nearly all optical sensors depend on just a few basic principles, such as 1 ) the measurement of oxygen concentration by the fluorescence quenching of a dye (transducer: 0, optodes), 2 ) pH-measurements (transducers: pH optodes), and 3) the determination of NADH fluorescence using a bifurcated light-guide. Combining these measurement principles with different enzymes results in biosensors similar to those based on electrochemical transducers. There are no great differences in performance between them. Figure 20 shows the basic design features of an optical biosensor. od.\" 701 3.1.4. Mass-Sensitive Transducers A class of biosensors that have hitherto not been widely used are those based on piezoelectric crystals or surface acoustic wave (SAW) These provide a simple means of detecting changes in mass through the alteration in the resonance frequency of a crystal. If such a transducer is covered with a selectively adsorbing surface or absorbing film, the concentration of the ab- or adsorbed substance can be determined from the change in resonance frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000281_j.promfg.2020.04.215-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000281_j.promfg.2020.04.215-Figure5-1.png",
        "caption": "Fig. 5. Locations of extracted specimens",
        "texts": [
            " / Procedia Manufacturing 47 (2020) 261\u2013267 4 Author name / Procedia Manufacturing 00 (2019) 000\u2013000 Tensile testing was performed at room temperature with a constant crosshead displacement rate. The round tensile specimens M10, had a dog-bone shape with a gauge length of 25 mm and a diameter of 5 mm. To estimate the impact of the build direction on the mechanical behavior, tensile specimens were extracted from the deposited material parallel (upright), transverse (lying) and at 45\u00b0 to the build direction (see Fig. 5). Specimens were analyzed in their \u201cas-built\u201d, stress-relief annealed and \u03b2-heat-treated states. The most important microstructural parameters are the thickness of the \u03b1-platelets, the grain size of the primary \u03b2-phase, as well as the existence of grain boundary \u03b1-phase (i.e. continuous \u03b1-phase at \u03b2-grain boundaries). Moreover, the homogeneity vs. heterogeneity of the microstructure and texture are of interest. Fig. 6 shows the microstructure of a Ti-6Al-4V specimen, manufactured by pLMD, and the primary beta grain-size (a) as well as the single alpha-platelets (b) are indicated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002761_20.809140-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002761_20.809140-Figure6-1.png",
        "caption": "Fig. 6. The surface and its normal for computing the flux linked by the phase winding.",
        "texts": [
            " Anticipating the boundary conditions that the homogenous solution for the vector potential (not including the zeroth harmonic) must satisfy, the homogenous solution for the vector potential and the field are (23) (24) Applying the boundary condition at gives (25) Thus the final solution for the total vector potential is (26) and the field is (27a) (27b) At this point the magnetic flux density is known, both in the rotor and the stator slots, so that the total flux linked by a pole winding can be computed. To carry out this calculation Faraday\u2019s law requires that the flux density be integrated over a surface enclosed by the pole winding. The surface itself is arbitrary as long as the contour that encloses the surface (the surface edge) lies in the pole winding as required by Faraday\u2019s law. Here the surface in Fig. 6 will be used to simplify the surface integral that must be done. To do this integral, the usual approximations and approach for completing a flux integral are used. In particular, the edge of the surface located at is taken to be in one conductor and the flux integral is then done for each conductor. This leads to integrals. Then, within each conductor, the integral is done at each location within the conductor and the results are averaged to obtain the flux linked by that conductor (28) Defining (28) can be rewritten as (29) Equation (29) says that the flux linked by a pole winding is the number of turns around that pole times the average of the flux integral done at every location in the pole winding",
            " This result can be written alternately as (30) by re-labeling the locations of the surface\u2019s edge and defining the partial flux as (31) Next writing (30) as and letting go to infinity, to zero, and to zero while holding constant, at a value equal to the area of the winding, the sum in (29) can be taken over into an integral (32) Of course (32) still says that the flux linked by the pole winding is equal to the number of turns per pole times the average value of the flux linked at different points within the winding. To find the flux linked by the pole winding, the magnetic flux density must be integrated over the surface in Fig. 6 for fixed values of and to obtain the partial flux in (31). Then this result must be averaged over the winding. To compute the partial flux, the surface in Fig. 6 is broken into five parts as shown in Fig. 7. The partial flux is then found for each of these five surfaces and the results are added together to find the total partial flux. The integral over the surface labeled one is an integral over the pole face. This surface is exactly the same for any location of the total surface\u2019s edge. Thus the average in (32) for the surface labeled one just reduces to the flux linked by surface one. The field in this integral does not include any stator slot field, just rotor slot field",
            " The change in vector potential per line is 6.457 10 Webers/m for the analytical results and 6.176 10 Webers/meter for the FE results. Note the good agreement between the general flux paths as well as the total change in the value of the vector potential. The equal potentials of the vector potential in the stator slot of the 12/8 machine computed using FE analysis and using the analytical model are shown in Fig. 9. Now the stator is at the bottom of the figure and the rotor is at the top as in Fig. 6. The change in vector potential per line is 3.21 10 Webers/m for the analytical results and 3.10 10 Webers/meter for the FE results. Note the good agreement between the general flux paths as well as the total change in the value of the vector potential. For this machine the FE total change in the vector potential with 1A in the winding is 18.88 uWeber/m while the total analytical model change in the rotor slot and two stator slot vector potentials is 21.26 uWeber/meter, a 12.61% error. The computed unaligned phase inductances for the three different machines are summarized in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000249_admt.201800692-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000249_admt.201800692-Figure3-1.png",
        "caption": "Figure 3. Parallel 3D self-assembly of electronic components (e.g., capacitors) is an important strategy that will significantly reduce the number of sequential steps for fabrication as well as enhance electromagnetic performance per projected area footprint, leading the way to the miniaturization of the electronic systems.",
        "texts": [
            " These shapeable material technologies have already demonstrated (Figure 2b) the capability to self-assemble planar films into a number of different complex polygonal structures and tubular \u201cSwiss-rolls.\u201d[25\u201327,32\u201338] Being rather simple, the tubular \u201cSwiss-roll\u201d architecture possesses a continuous curvature of cylindrical and spiral shapes that affects the electrical and physical properties beneficial to the fabrication and performance of micro- and nanoelectronic components.[11,13\u201315,17,39] The initially planar structures are reshaped into 3D \u201cSwiss-rolls\u201d thereby enhancing the surface-per-footprint area, which affects parameters such as capacitance (Figure 3) and inductance areal footprint density. This method of fabrication paves the way toward the fully parallel self-assembly of 3D microelectronic components directly onto planar silicon chips and result in functional and novel devices ranging from the world\u2019s smallest jet propulsion engines[40] to energy storage devices, biosensors, ultracompact electronic components, and sensors which all benefit from the cylindrical 3D geometry.[11,12,41,14\u201319,26,39] If applied to the whole system containing passive components as well as active electronics, even more compact 3D devices with novel functionalities can be expected in the near future",
            " The global development in this direction resulted in the widespread use of electronics in many facets of human life, such as in consumer electronics and medical applications, and they are continually evolving to offer better performance, longer and more reliable operation, and smaller, lighter form factors. These improvements are directly related to the scale and weight of the electronic components whose performance and functionality are measured relative to their projected area or volume. Conventional technologies relying on 2D processes, namely those applied for the fabrication of semiconductor chips and main boards, face severe shortcomings in improving areal and volumetric performance (Figure 3), and as a result, 3D integration has been seen in the past decade as a potential solution within the electronics industry (Figure 1b).[7] Assembly of these 3D electronic systems is a demanding and quality sensitive process, but, advances during the last century resulted in a powerful portfolio of tools and processes that improved the overall efficiency of assembling complex systems\u2014for instance, industrial robots and automatic machines replaced the assembly line worker in state-of-the-art foundries manufacturing mesoscopic parts, resulting in the almost full automatization seen nowadays",
            " Due to the challenges associated with the manufacture and integration of the passive devices, electronic systems are mostly assembled from discrete components, including active and passive building blocks wired together through an interconnect board, a printed circuit board, or a set of wires. While there has been great progress toward enhanced integration density in the micro- and nanoscale silicon-based technologies, further miniaturization of these systems is limited mainly due to difficulties in integrating passive components into the overall manufacturing process. The development of 3D mesoscale selfassembly aims to provide a promising approach to tackle this issue (Figure 3) while maintaining compatibility with conventional lithography and printing based fabrication techniques. Initial interest in mesoscopic self-assembly was inspired by the structures and mechanisms observed in the chemical, materials, and biological sciences, and mainly focused on the self-assembly of atomic and molecular structures necessary for the synthesis of membranes, crystals, molecular monolayers, and polymeric ordered structures.[24,58\u201360] The chemomolecular self-assembly, being a one or two step process, provided strategies[21,60] for static and dynamic generation of nanostructures of diverse functionalities such as macromolecular and metal organic assemblies,[21,61\u201363] assembly of graphene sheets[64] and Adv",
            " As the cabling of power lines possess their own inductance and resistance, the capacitors should be placed close to the integrated circuit to avoid a sudden drop of the power line voltage due to a high load from the active integrated circuit side that would normally lead to a temporal interruption or malfunction in the entire circuit. Additionally, modern integrated circuits may have several power lines fed at various positions and thus require numerous decoupling capacitors connected through a PCB (Figure 3 or 9c) with an integrated circuit and power supply. This leads to a substantial use of the PCB area and requires newer small-scale devices with higher areal capacitance density for each new generation of the product. Swiss-roll architectures favor the fabrication of capacitors using a simple initially planar layout that corresponds to the double plate electrostatic capacitor (Figure 11a,b).[13,18] Selfassembly of this initially planar structure leads to a Swiss-roll (Figure 3) with several windings, where capacitance increases to almost twice its initial value due to overlapping of neighboring windings (Figure 11c) and as result increasing the effective area of the capacitor. This process is significantly simpler than the sequential layer by layer fabrication of capacitor plates used for conventional surface mounted device capacitors (Figure 3), and is performed in a parallel fashion on the wafer scale (Figure 11d). The demonstrated structures can possess more than 1 \u00b5F mm\u22122 with a footprint area of only 13 \u00d7 200 \u00b5m2 and more than 20 windings. If electrochemically active materials are used instead of simple metallic plates, more sophisticated energy storage devices can be realized, such as lithium ion batteries as outlined in a recent review.[129] The Swiss-roll architecture is useful in making soft electrical contacts with brittle or low modulus materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002886_s0921-5093(03)00435-0-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002886_s0921-5093(03)00435-0-Figure1-1.png",
        "caption": "Fig. 1. The diagrammatic sketch of the laser rapid forming system. 1. Laser beam; 2. focus length; 3. powder feeder; 4. prior passes; 5. working table; 6. Substrate; 7. resolidified metal; 8. melt pool.",
        "texts": [
            " on the forming characterizations, for instance the height of single layer and the width of single clad, were investigated systematically through laser rapid forming experiments. It was summarized how to control these parameters to improve the forming quality. Based on the research results, some metal components were fabricated. The experiments were carried out on a laser rapid forming system which consisted of a 5 kW continuous wave CO2 laser (RS850), a four-axis numerical control working table and a powder feeder with lateral nozzle. The working principle of the system is shown schematically in Fig. 1. The powders used in the experiment were 316L stainless steel and nickel-base alloy whose composition is listed in Table 1. Nickel-base alloy was mainly used to investigate the influences of processing parameters on forming characterizations, since it has better oxidation resistance and the stainless steel was used to study the influence of oxidation on surface quality. The substrate was 316L stainless steel sheets with dimension of 140 /30 /4 mm. In order to eliminate the moisture in the powder and clean the surface of the sheets, the powders were oven dried over 24 h in a vacuum drying furnace with 150 8C and the sheets were sandblasted before experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002838_s0167-6911(96)00082-5-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002838_s0167-6911(96)00082-5-Figure1-1.png",
        "caption": "Fig. 1. Qualitative description of the saturation function.",
        "texts": [
            " Here we have also, without loss of generality, assumed that all actuators have unity time constant. Definition 1. A function tr : ~m ____+ ~m is said to be a saturation function if, 1. tr(s) is decentralized, i.e., t r ( s ) = [a l ( s l ) , a2 ( s2 ) . . . . . ~Tm(Sm)] t, and for each i = 1 to m, 2. tri is locally Lipschitz, 3. there exists a Ai > 0, Ci 2 ~ Sit~i(Si)4 bi $2 Ciz~i ~ I~i(si)l ~ bilsil if [sil > A~, bi and \u00a2i, bi ~ ci > 0, such that if Isi] <<, A i Remark 1. (1) Graphically (see Fig. 1), each element of the vector-valued saturation function resides in the shaded area, and for some constants A > 0, and bi ~ c i > 0. For notational simplicity, but without loss of generality, we will assume throughout this paper that for each i, A i ---- A , b i z b~> 1 and ci = 1. (2) It follows from the above definition, a(s ) = s, arctan(s), tanh(s) and the standard saturation function or(s)--sign(s)min{Isl, 1} are all saturation functions. Definition 2. The set of all saturation functions with constant A and b is denoted by 6e(A,b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure6.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure6.1-1.png",
        "caption": "Figure 6.1. A gear with zero profile shift.",
        "texts": [
            "2 show two such gears, 150 Profile Shift each with the same number of teeth, and cut by the same cutter. Since both gears have the same standard pitch circle radius Rs and the same pressure angle ~s' they must have base circles of the same size, and therefore the tooth profiles of each gear are formed from parts of the same involute. However, the tooth thickness and the tip circle radius of the second gear are larger than those of the first. In Figure 6.2, the involutes forming the opposite faces of each tooth are further apart than those in Figure 6.1, so that the tooth profiles of one gear are shifted, relative to those of the other. Any gear whose tooth thickness ts is not equal to 0.5ps is said to be cut with profile shift. In this chapter, we will discuss how the amount of profile shift can be defined, and we will show how it is related to the tooth thickness. We will then describe a method by which the tooth thickness and the addendum values can be chosen, for a gear pair intended to mesh at any specified center distance C. And finally, we will present some of the most common reasons why gears are designed with profile shift"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003530_jsvi.2001.4152-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003530_jsvi.2001.4152-Figure3-1.png",
        "caption": "Figure 3. Model of the piston and the cylinder inner wall.",
        "texts": [
            " Based on the model, we estimated the impact forces of piston in cylinder. The engine block surface vibration response is predicted by convoluting the impact forces with measured impulse responses between the cylinder inner walls and engine block outer surfaces. Experimental veri\"cation on the predicted response has been also performed by experiment using a commercial 4-cylinder diesel engine. The errors in estimating the impact force and vibration response at engine block surface are also studied. We propose a two-dimensional lumped parameter model as shown in Figure 3. This \"gure describes the piston motion in translation along the x, and y-axis and the rotation around the piston pin axis. We neglected the motion in z-axis and angular motion other than the piston pin axis. This is simply because those e!ects on the impact are negligible compared with what we propose to consider. The piston impact on the cylinder inner wall occurs at the upper and lower ends of the piston skirt. The piston skirt sti!ness can be modelled on a linear spring located on those impact points",
            " If we de\"ne the piston position co-ordinates (x , y , ) at the piston pin position (P in Figures 3 and 4), the inertia force F in the horizontal direction (x-axis), the inertia force F in vertical direction ( y direction), and the inertia forceM in the rotational direction ( -axis) are readily obtained. That is F \"m x( \"m x( #s ( $ cos( # )! Q sin( # )) , (1) F \"m y( \"m y( !s ( $ sin( # )# Q cos( # )) , (2) M \"I $ \"I $ , (3) where m , I are mass and mass moment of inertia of piston respectively. s\" l #l is piston pin o!set distance. \"cos (l / l #l ) is piston pin o!set angle (Figure 3). Considering the applied external forces, we can obtain the equations of motion that describes the response of piston subjected to the external forces. Those are m x( #s ( $ cos( # )! Q sin( # )) \"A #F #F !F !F , (4) m y( !s ( $ sin( # )# Q cos( # )) \"!A !F !F !m g, (5) I $ \"F (x !x )#F l !F l !F l #F l #m g ) s sin( # )!\u00b9 #m xK l !m yK l , (6) where the F , F , F , F are the impact forces exerted on the piston skirts A, B, C, D, respectively. The F , F , \u00b9 , A , A are explosive force in the cylinder, friction force on piston wall, friction torque exerted on the piston pin, lateral and vertical direction reaction forces transmitted from connecting rod respectively",
            " In the equations of motion (equations (4)} (6)), the variables that we want to solve are accelerations (x( , y( , $ ) of the center of gravity of the piston in three directions, the impact forces (F , F , F , F ) exerted on the piston skirts, and lateral and vertical direction reaction forces (A , A ) transmitted from the connecting rod. We have three equations of motion but have nine unknown variables. Hence, six supplementary equations of motion or constraints must be needed. It is noteworthy that translational accelerations (x( , y( ) of the center of gravity of the piston are not independent unknown variables but a function of , Q and $ . In other words, we can \"nd the translational position, velocity, and acceleration of the piston from kinematics of crank-slider mechanism as shown in Figure 3. Therefore, we need four supplementary equations of motion. Those equations can be obtained from the proposed model that describes the mechanism at collision points. Next section addresses the model. 2.2.1. Basic concept of point mobility Mobility is de\"ned as the ratio of a velocity to a force. Mobility between di!erent input and output points is called &&transfer mobility'', and mobility at a point is often called &&(driving) point mobility''. This measure is sometimes used to estimate the mass, spring constant, and damping constant of lumped parameter system [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003734_j.actaastro.2008.04.009-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003734_j.actaastro.2008.04.009-Figure3-1.png",
        "caption": "Fig. 3. Coordinate system for the aircraft and free-body diagram of forces on the occupant (Aircraft image courtesy NASA JSC).",
        "texts": [
            " Additionally, any rotation of the aircraft should be minimal so that the occupants do not sense rotation relative to the aircraft; this is true for undesired roll and yaw rotations as well as pitch rotations which are unavoidable in flying a parabolic arc. The aircraft is flown along a precise trajectory so that, ideally, the forces on the occupants change along only one degree of freedom (vertical). Here we derive the motion required of the aircraft to meet this condition. We choose for our analysis a coordinate system fixed to the aircraft, where the x-axis is the longitudinal axis going from the front to the back of the aircraft, and the z-axis is the vertical axis. is the pitch angle of the aircraft with respect to the earth horizontal (Fig. 3). We define m as the mass of a person aboard the aircraft, and W = m \u00b7 g as the weight of the person due to the constant 1g of Earth\u2019s gravitational field. Wx and Wz are the projections of W along the x- and z-axes of the aircraft\u2019s coordinate system, respectively. The reaction forces between the person\u2019s feet and the aircraft are la- beled as Nx and Nz. The net accelerations of the person projected along the aircraft\u2019s longitudinal and vertical axes are labeled ax and az. Parabolic flight is designed to make Nz and az near zero during freefall (0g), while minimizing Nx and ax subject to aerodynamic constraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002751_s0043-1648(99)00143-x-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002751_s0043-1648(99)00143-x-Figure4-1.png",
        "caption": "Fig. 4. High-pressure concentric cylinder viscometer.",
        "texts": [
            " The inclination of the viscometer is 108 to ensure that the ball follows the wall of the bore giving a well-defined clearance between the ball and the bore. Balls of three different diameters were used to ensure laminar flow at all times in spite of changes in temperature and pressure. Influence of temperature and pressure on the width of the ballbore clearance was calculated and compensated for in the evaluation of viscosity. \u017d .The viscometer of concentric cylinder Couette type is w xshown in Fig. 4 19 . It is developed to measure the rheological properties of fluids at pressures up to 500 MPa. It has a shear-rate range of 0.5 to 20000 sy1 and can operate at up to 1008C at maximum pressure. Measurements can be made with constant shear strain or constant shear rate. The pressure vessel is designed as a compound cylinder with a titanium inner liner and a carbon fibre epoxy composite outer liner. A magnetic coupling is used to transmit torque into the pressure vessel. This has the advantage of eliminating the use of dynamic seals giving a very high reliability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000359_j.ijmecsci.2020.106150-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000359_j.ijmecsci.2020.106150-Figure1-1.png",
        "caption": "Fig. 1 The soft actuator structure and design: (a) 3D model and real object of the actuator. (b) Finite element simulation result. (c) Cross-sectional view and detailed size.",
        "texts": [
            " [21] investigated some key design parameters for the design of buckling actuators and soft machines and provided a constructive process of modeling soft machines driven by buckling actuators. Comparing with other types of actuators, soft pneumatic actuators have more application value. There are three main types of structural forms in soft pneumatic actuators including pleated structure [22\u201325], cylindrical form [26,27], and fiber-reinforced configuration [28,29]. Compared to the last two forms, the soft actuator with pleated multi-chamber structures (as shown in Fig. 1(a)) is a more promising candidate for applications in soft robots, because the input pressure of pleated actuators is smaller and actuators can be reversely bent under the action of negative pressure, which can effectively improve the bending range of soft robots [22]. Modeling of the bending angle and tip contact force of soft actuator generated by the pleated pneumatic actuators is challenging [30] due to the material nonlinearity, the mutual contact between adjacent chambers of pleated structure, and contact between the actuator tip and external object",
            " Compared with single-chamber soft actuators, the complex geometry of the pleated actuators improves the deformability of actuators but also increases the difficulty of analyzing their mechanical properties. Especially, when the adjacent chambers are squeezed under the input pressure, it greatly increased the difficulty of modeling the tip contact force of the actuator since it is difficult to estimate the unexpected deformations of the chambers\u2019 lateral walls. actuators with different pleated structures. This study investigates the behavioral characteristics of the soft actuator with pleated structures, as shown in Fig. 1(a). The bending and contact force modeling methods for pleated actuators are proposed. The main contributions of this paper are stated as follows: (1) a model is proposed considering the bending properties of materials by using the constant volume principle of the elastomer material and NeoHookean hyperelasticity theory. (2) Furthermore, an analytical model of tip contact force is obtained to capture the relationships of contact force, input pressure, and bending angle of the soft pleated actuator when its tip is in contact with the external environment. (3) A series of comparison experiments and FEM analysis are presented and discussed to verify the effectiveness of the proposed analytical model for pleated actuators with different specifications in working condition. This study focuses on the soft actuator, and the design is shown in Fig.1(b),(c), previously proposed in our earlier work [7], which consists of a connector, an extensible upper actuator, and an inextensible but flexible lower actuator. The upper actuator structure involves n-1 uniform chambers, the cross-section of which is combined by semicircle and rectangle, and one bigger end chamber. We design the dimensions of the upper actuator with pleated structures so that the two lateral walls of the chambers are thinner, and have a greater surface area than the other exterior walls",
            " The soft actuator is made by using silicone rubber material (Dragon skin 30), while the fiber paper is from inextensible material. When the soft actuator is pressurized, the expanding lateral walls of two neighboring chambers will push against each other, which results in a preferential elongation of the upper actuator. Meantime, the lower actuator has to bend to adapt this deformation because of the restraint of fiber paper. Therefore, the soft actuator could obtain smooth and continuous bending deformation. Fig. 2 Cross-sectional views of the soft actuator of Fig. 1(a). (1) Cross-section view of the actuator chamber. (2) Cross-section view of the actuator between adjacent chambers. The serial number i, i=1, 2 \u2026 n show the ith bending continuum unit of the actuator. As1 and As2 represent the solid cross-sectional area. Ac1 and Ac2 represent the cross-sectional area of air-flow area. 7 To accurately establish an analytical model of the pleated actuator, we divide the actuator into two different sub-modules as shown in Fig. 2(1) and Fig. 2(2). Among them, As (including As1 and As2) is the solid cross-sectional area, Ac (including Ac1 and Ac2) is the cross-sectional area of air-flow area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000245_ijvd.2019.109873-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000245_ijvd.2019.109873-Figure11-1.png",
        "caption": "Figure 11 Car side impact problem design (see online version for colours)",
        "texts": [
            " For this case study, the performance of NAMDE (shown in Table 13) is compared with evaporation rate water cycle algorithm (ER-WCA), WCA, salp swarm algorithm (SSA) (Yildiz et al., 2019a), NDE, Rank-iMDDE, MBA, TLBO and ABC algorithm. According to Table 13, NAMDE can get the lowest values of the best, average as well as worst solutions. Moreover, it can be seen that NAMDE is the most robust in solving this problem with standard deviation value of 1.1706E-12 followed by NDE and MBA. The car side impact design problem was introduced by Gu et al. (2001). The car (Figure 11) is exposed to a side impact on the foundation of the European Enhanced Vehicle-Safety Committee (EEVC) procedures. The aim is to minimise the total weight of the car using eleven mixed variables. The eighth and the ninth variables are discrete and the rest are continuous. There are ten inequality constraints. In this case NAMDE is compared with cohort intelligence (CI) (Kale and Kulkarni, 2018), \u03b5DE-LS, teaching-learning-based cuckoo search (TLCS), TLBO (Huang et al., 2015), cuckoo search (CS) algorithm (Gandomi et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002924_978-94-009-1718-7_36-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002924_978-94-009-1718-7_36-Figure9-1.png",
        "caption": "Fig. 9: Flattened positions: (I/J = 0 A lfI = 7r), ( I/J = 7r A lfI = 0)",
        "texts": [
            " (12) Point P with the given position vector Y = {Yl' Y2' Y3} in (Yl' Y2' Y3) is then moving with two degrees of freedoms in its workspace, an algebraic surface of order four: But with I{I:=} tfJ and tfJ:=} -tfJ (Fig. 7) formula (12) yields: X(tfJ) = a {O,l,O}+c {costfJ,costfJ,O}+ Y (14) and the workspace ofP reduces to a straight line in the plane X3 = Y3 \u2022 The two workspace are in contact at the singularity position ~ = 0 A l/f = 0 . The four accessible singularity positions of the queer square mechanism are shown in the Fig. 8 and Fig. 9. 368 Summary Some linkages show \"kinematotropy\", i.e., from a singularity position they can open up into regions with different global mobilities. In the paper three examples of such kinema totropic linkages are given, one of them is new. The question whether there exist many or only few kinematotropic linkages, can not be answered. [1] Griibler, M., Getriebelehre, Springer, Berlin 1917. [2] Kutzbach, K. Mechanische Leistungverzweigung, Maschinenbau, Der Betrieb, Band 8, S. 710, 1929. [3] Baker, J"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000954_j.cpc.2021.107956-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000954_j.cpc.2021.107956-Figure6-1.png",
        "caption": "Fig. 6. Evolution of the 3D volume (top row) and 2D contours (bottom row). The porous scaffold is composed of P-surface and G-surface unit structures. The red line denotes the 0.5 level of the middle slice of the composite scaffold. From (a) to (e), the iterations are 1, 4, 8, 12, and 18, respectively.",
        "texts": [
            " Experimental tests In this section, we focus on the continuous connection beween different unit scaffolds in biological tissue and obtaining superior mechanical properties of the structure. We will discuss different types of scaffolds based on TPMSs. We stop the evolution and regard the numerical results as the steady-state solution when relative error \u2225\u03c6n+1 \u2212 \u03c6n \u22252/\u2225\u03c6 n \u22252 is less than a tolerance tol. Unless otherwise stated, throughout this paper, we use h = 1, \u2206t = 0.5, and \u03f5 = 1. 4.1. Evolution of our proposed algorithm Fig. 6 displays the evolution of the proposed modified algorithm. Here, we use a composite scaffold consisting of P-surface and G-surface unit structures. In Fig. 6(a) to (e), the iterations are 1, 4, 8, 12, and 18, respectively. The tolerance is tol = 1e\u22124. Fidelity term parameter \u03b2 is set to 0.3. As can be observed, the surface of the composite structure becomes smooth under the influence of the mean curvature flow. To illustrate the details, we display the 0.5 level of the middle slice. The internal region is gradually connected under the mean curvature flow. To demonstrate the energy dissipation with the composite structure, we plot the discrete total energy curves with three different time steps: \u2206t = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure13.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure13.5-1.png",
        "caption": "Fig. 13.5 Path generation",
        "texts": [
            " Although the method is rarely used now, it was indeed a breakthrough at that time in cam design. It was the first cam design method based on dynamics, fundamentally changing the then popular static design method. The method was later adopted into the synthesis of cam mechanisms with single and two DOF (Erdman 1993). For linkages operating at high speed, the deflection of links become nonneglegible, and the real path described from one point would deviate from the one calculated based on rigid links. This is schematically illustrated in Fig. 13.5. The inertial load is more likely to excite resonance at high speed. Other potential issues related with high speed include vibration, noise and fatigue caused by cyclic stresses. 472 13 Development of Theories in Mechanical Engineering of New Era There are two conflicting requirements in modern machine design. First the machine is expected to be designed as light as possible. Second, the operation speed and accuracy required are getting higher and higher. Driven by these two factors, dynamics of mechanism became a research topic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003459_robot.1996.503783-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003459_robot.1996.503783-Figure7-1.png",
        "caption": "Fig. 7 Coordinate systems for adaptive walking",
        "texts": [
            " As for lower-limb trajectories used for that, the trajectory of the lower side of foot parts is set with constant leveling. A flow chart ofthis walking control method is shown in Fig. 6. A processing method of the information on the landing surface acquiredandthecontrol methods oflower-limbtrajectories: which are vital factors in the system, are described below. 4.1 Processing method of information on landing surfaces All kinds of information acquired by this mechanism for detectingalanding surface issenttothecomputer for controlling in realtime in walking, and arranged into the following information. Fig. 7 shows each system of coordinates set to the walking system. (1)The information on the groundingofthelower-foot plate: The grounding isjudged with ON/OFFofthe microswitches installed in the four corners ofthe lower side ofthe lower-foot plate. Basically, the leg wasjudged grounding when all microswitches in the four corners turn on. (2)Theinformation on the relativeangleand the relative distance of landing surfaces and upper-foot plates: With respect toobtainingtherelativeposition to thelanding surface, it is possible to determine aplane based on the measurement ofthe positions ofthree [Make a standard walking pattern) standard waking pattem [ the latter part of the swing phase ] I 1 points",
            " (3) IV) Former Swing Phase: The angle of ankle joints (foot plate) of which the retum to the standard walking pattem that does not complete is returned to the standard walking pattern, by the interpolation with the fifth polynomial. 4 3 Walking simulations Underthis walking control method. we performed adaptive walk- ing simulations to estimate the shape deviation ofthe path to which the machine model will adapt. Weassumedthat the machinemodel walking did not transform the walking path at all, the model is a system of particles as shown in Fig. 7, the structural members ofthe model did not ben4 and there was no delay in response ofthe actuators. As a result, the maximum walking speed was 1.28 dstep with a 0.3 m step length, and the adaptable deviation range was from -1 5 to +I 7 \"l step in the direction ofZ axis, and from -3 to +3 O in the tilt angle. 5 Walking experiments The authors conducted walking experiments using the proposed walking control method and the biped walkingrobot WL- 12RVII with WAF-3. The following a summary ofthe experimental results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000613_s11071-020-05764-7-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000613_s11071-020-05764-7-Figure4-1.png",
        "caption": "Fig. 4 Schematic diagram of the driving force distribution in the jth section of the mth segment",
        "texts": [
            " Then, the gravity of the entire SL-CDHRR can be expressed as: Fg \u00bc FT g;1; . . .;F T g;nJ h iT \u00f018\u00de where Fg;i \u00bc f g;i Ng;i \" # , Ng;i \u00bc 0; 0; 0\u00bd T. 3.2 Resolved the driving force and friction force The dynamic equation of the driving cable should be recursively inward through the end-effector. Take the driving cable in mth segment as an example, cables C m 1\u00f0 \u00dep\u00fej 3m 2 , C m 1\u00f0 \u00dep\u00fej 3m 1 , C m 1\u00f0 \u00dep\u00fej 3m pass through 2[(m - 1)p ? j] holes, and the force diagram of these driving cables acting on the jth section of the mth segment is shown in Fig. 4. As shown in Fig. 3, the direction of the cable tension between any two adjacent disks in the jth subsections of the mth segment can be expressed as: n~ p m 1\u00f0 \u00de\u00fej 3m 2 \u00bc 1\u00f0 \u00de j r O2 p m 1\u00f0 \u00de\u00fej\u00bd 1O2 p m 1\u00f0 \u00de\u00fej\u00bd 3m 2 r O2 p m 1\u00f0 \u00de\u00fej\u00bd 1O2 p m 1\u00f0 \u00de\u00fej\u00bd 3m 2 n~ p m 1\u00f0 \u00de\u00fej 3m 1 \u00bc 1\u00f0 \u00de j r O2 p m 1\u00f0 \u00de\u00fej\u00bd 1O2 p m 1\u00f0 \u00de\u00fej\u00bd 3m 1 r O2 p m 1\u00f0 \u00de\u00fej\u00bd 1O2 p m 1\u00f0 \u00de\u00fej\u00bd 3m 1 n~ p m 1\u00f0 \u00de\u00fej 3m \u00bc 1\u00f0 \u00de j r O2 p m 1\u00f0 \u00de\u00fej\u00bd 1O2 p m 1\u00f0 \u00de\u00fej\u00bd 3m r O2 p m 1\u00f0 \u00de\u00fej\u00bd 1O2 p m 1\u00f0 \u00de\u00fej\u00bd 3m 8 >>>>>>>< >>>>>>>: \u00f019\u00de where rOaOb c represents the position vector of the cth cable from Oa hole to Ob hole. As shown in Fig. 4, the tension forces on cable C m 1\u00f0 \u00dep\u00fej 3m 2 , C m 1\u00f0 \u00dep\u00fej 3m 1 and C m 1\u00f0 \u00dep\u00fej 3m in coordinate system no. 2[(m - 1)p ? j]- 1 are, respectively, f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m 2 ; f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m 1 and f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m , and the corresponding cables tension and hole positions can be expressed as: F 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m 2 \u00bc bR2 p m 1\u00f0 \u00de\u00fej\u00bd 1f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m 2 n~ p m 1\u00f0 \u00de\u00fej 3m 2 F 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m 1 \u00bc bR2 p m 1\u00f0 \u00de\u00fej\u00bd 1f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m 1 n~ p m 1\u00f0 \u00de\u00fej 3m 1 F 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m \u00bc bR2 p m 1\u00f0 \u00de\u00fej\u00bd 1f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 3m n~ p m 1\u00f0 \u00de\u00fej 3m 8 >< >: \u00f020\u00de r2 p m 1\u00f0 \u00de\u00fej\u00bd 1 q \u00bc bR2 p m 1\u00f0 \u00de\u00fej\u00bd 1 2 p m 1\u00f0 \u00de\u00fej\u00bd 1t~q \u00fe bt~2 p m 1\u00f0 \u00de\u00fej\u00bd 1 \u00f021\u00de where q is the number of cables,f 2 p m 1\u00f0 \u00de\u00fej\u00bd 1 q Fdr min, bR2 p m 1\u00f0 \u00de\u00fej\u00bd 1 and bt~2 p m 1\u00f0 \u00de\u00fej\u00bd 1, respectively, represent the rotation matrix and translation vector of the coordinate system no"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure4-1.png",
        "caption": "Fig. 4 The circle arc motion",
        "texts": [
            "org/about-asme/terms-of-use a c t a t h c t b c t t g w b n p i n g c 4 g g t i o J Downloaded Fr Mcb = \u2212 sin j \u2212 cos j 0 SR cos j \u2212 sin j 0 0 0 0 1 0 0 0 0 1 9 Mdc c1 = cos c \u2212 c1 sin c \u2212 c1 0 0 \u2212 sin c \u2212 c1 cos c \u2212 c1 0 0 0 0 1 0 0 0 0 1 10 re transformation matrices in which is the rotation angle of the utter head, i is the tilted angle, j is the swivel angle of the cutter ilting, SR is the radial distance of the cradle, c is the initial cradle ngle setting, and c1 is the first cradle rotation angle with respect o the epicycloidal motion. Typical imaginary generating gears for the face milling and face obbing processes are shown in Fig. 4. For the face hobbing proess, the pitch point B of the cutter blade is rigidly connected to he rolling circle, and the rolling circle rolls without slip on the ase circle. Point B also traces out an extended epicycloid in the oordinate system Sd of the imaginary generating gear. Therefore, he rotation of the cutter head itself is in a timed relationship with he rotation of the cutter axis about the axis of the imaginary enerating gear c1 = r b = z0 zp 11 here r is the radius of the rolling circle, b is the radius of the ase circle, z0 is the number of the cutter starts, and zp is the tooth umber of the imaginary generating gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000827_tie.2021.3088331-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000827_tie.2021.3088331-Figure1-1.png",
        "caption": "Fig. 1 Machine structure (a) proposed vernier machine; (b) regular vernier machine",
        "texts": [
            " model; in section III, electromagnetic performance of the proposed machine and the regular PMVM would be quantitatively analyzed by semi-analytical method and FEA. In section IV, influence of structure parameters on torque quality is analyzed by FEA. In section V, performance comparison between the optimized machines are carried out by FEA. In section VI, a prototype has been manufactured to verify all the analysis results. Finally, some conclusions will be drawn. II. STRUCTURE AND WORKING PRINCIPLE The proposed and the regular PMVM are shown in Fig. 1, which have the same surface-mounted PM rotor. The major difference lies in stator tooth. In the proposed machine, stator has teeth of irregular shape and distribution, whilst the regular PMVM has rectangular tooth and uniform distribution. Detailed structure of stator tooth is presented in Fig. 2. In both machines, the concentrated windings in opposite main tooth belong to one phase and are connected in series. TABLE I STRUCTURE PARAMETERS OF TWO MACHINES Parameters Quantity Main tooth number 6 Rotor pole pair number 13 Stator outer diameter Dso, mm 124 Rotor outer diameter Dro, mm 73 Magnet thickness hm, mm 2 Magnet pole arc, \u03b1pm 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.13-1.png",
        "caption": "Figure 3.13. Addendum and dedendum.",
        "texts": [
            " We did not, however, give any recommended values for the tooth thickness or the addendum in a gear. The reason for this omission is that suitable values depend on the operating conditions of a gear pair, and in particular, on the center distance. We defined the addendum as and the dedendum bs as the radial distances from the tip circle and the root circle to the standard pitch circle. The addendum and dedendum can also be measured from the pitch circle, in the manner shown in Recommended Tooth proportions 77 Figure 3.13, and in this case we use the symbols ap and bp to distinguish these quantities from as and bs \u2022 For a pair of gears, the working depth of the teeth is defined as the amount by which the teeth overlap when the gears are in operation, and it is therefore equal to the sum of the addendum values, measured f rom the pi tch eire les, Working depth (3.66) The clearance at the root circle of each gear is the amount by which the dedendum of that gear exceeds the addendum of the meshing gear. Hence, the clearance values c 1 and c 2 for the two gears of a pair are given by the following expressions, (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000316_j.ijfatigue.2019.01.004-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000316_j.ijfatigue.2019.01.004-Figure2-1.png",
        "caption": "Fig. 2. Initial and random position of a tooth pair in meshing simulation.",
        "texts": [
            " The contact points during this meshing process theoretically lie on the tangent line between two base circles, as shown by the black line in Fig. 1. However, when the gear deformation is larger than the backlash, advance engaging in and lagging engaging out will take place, leading to contact points that deviate from the theoretical line of action, as shown by the yellow line in Fig. 1. For this reason, double contacts and high contact pressure can be found in some areas of a tooth root, and the wear in these areas will thus be accelerated. Fig. 2 shows the meshing simulation for a tooth pair in a coordinate system. The origin of the coordinate system is at the rotational center of the pinion O1 and the rotational center of the wheel O2 is located at (0,a), where a is the center distance of the gear pair. Subscripts 1 and 2 denote the pinion and wheel, respectively, and rb is the radius of the base circle. P represents contact point and T1P is the path of contact respected to the pinion. It is assumed that the involute starts at the crossover point of the base circle and the y-axis with its coordinate (0,rb1) for the pinion tooth, and that for the wheel tooth starts with the coordinate (0,a+ rb1)",
            "P (2) When the gear rotates with an angle of \u0394\u03c6, the slope angle of point P becomes = \u2212\u223c\u03b1 \u03b1 \u03c6\u0394P P . Since P is the contact point of the pinion and the wheel, their contact planes must stay tangential to each other, implying that the slope angle relationship at the contact point satisfies = \u2212 =\u223c \u223c\u03b1 \u03b1 \u03b1 \u03c0\u0394 P P P1 2 . Supposing that the initial position of the contact tooth pair with a rotation angle of the pinon of zero, i.e., \u0394\u03c61ini = 0, the rotational angle of the tooth on the wheel can be obtained and hence defined as \u0394\u03c62ini, drawn as the dashed line in Fig. 2. Setting the initial position as the reference position, the rotational backlash with respect to the wheel can be obtained: \u239c \u239f= \u2212 \u239b \u239d \u2212 + \u239e \u23a0 j \u03c6 \u03c6 z z \u03c6\u0394 \u0394 \u00b7 \u0394 ,ini2 1 1 2 2 (3) where z is the tooth number of the gear. The angle between the radius of the contact point and its tangential line is \u03b3P= \u03b1P\u2212 \u03c6P, so the tangential velocity at the contact point P can be calculated as: =v \u03c9 r \u03b3\u00b7 \u00b7sin( ),t P P (4) where \u03c9 is the angular velocity and rP is the radius at point P. The rolling velocity vr and the sliding velocity vs can therefore be calculated as: = + = \u2212v v v v v v 2 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003309_095440605x32075-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003309_095440605x32075-Figure2-1.png",
        "caption": "Fig. 2 Rotation transformation",
        "texts": [
            " To describe the moving platform of the Stewart platform manipulator in detail, six coordinates are needed. Three of these coordinates are positional displacements, which describe the position of a fixed point in the moving platform with respect to the reference frame. The other three coordinates are angular displacements, which describe the orientation of the moving platform with respect to the reference frame. A set of Euler angles \u00bdf, u, c T is used to determine the orientation of a rigid body after the following rotational sequence, as shown in Fig. 2. 1. First rotating over an angle c around the Z-axis. Accordingly, the X-axis rotates to X0-axis, and the Y-axis to Y0-axis. Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science C04604 # IMechE 2006 2. Then rotating the resulted frame over an angle u around the intermediate Y0-axis. Accordingly, the Z-axis rotates to Z0-axis, and the X0-axis to X1-axis. 3. Finally rotating over an angle f around the X1axis. Accordingly, the Y0-axis rotates to Y1-axis, and the Z0-axis to Z1-axis. Then the frame X1 Y1 Z1 is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003768_rob.4620050502-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003768_rob.4620050502-Figure7-1.png",
        "caption": "Figure 7. 3-D redundant robot trajectory along AB - null space used to improve efficiency.",
        "texts": [
            " While moving the robot end-effector along this trajectory, the orientation of the end-effector was kept constant. Robot configurations along the trajectory AB are shown for four different cases in Figures 5 through 8. In Figure 5 , the desired end-effector trajectory is obtained by using only the rotational joints and the prismatic joint is kept locked. The pseudo-inverse solution is used in Figure 6 to determine the joint velocities along the trajectories. Efficiency of the robot is improved in Figure 7 by utilizing the redundancy to increase MVR in the direction of motion. In Figure 8, on the other hand, the redundancy is used to increase MMA in the direction of motion. Thus the robot\u2019s ability to apply force in the direction of motion is improved. MVR as a function of time is plotted in Figure 9 for the cases in Figures 5 through 7. Similarly a plot of MMA as a function of time is shown in Figure 10 for the cases in Figures 5 , 6 and 8. We note from Figure 9 that for the case in Figure 6, MVR in the direction of motion is consistently higher compared to the case in Figure 5",
            " This results in higher MVR along the trajectory as compared to the case in Figure 5 in which the prismatic joint is locked. Thus the addition of extra joint results in lower velocities at the other joints. This is particularly useful in the singularity re- Dubey and Luh: Redundant Robot Control 427 2 I Flgun 8. 3-D redundant robot trajectory along AB - null space used to improve mechanical advantage. Dubey and Luh: Redundant Robot Control 429 430 Journal of Robotic Systems-1988 gion where the joint velocities required are extremely high in the absence of redundancy. In Figure 7, as seen from Figure 3, MVR in the direction of motion is consistently much higher compared to the cases in Figures 5 and 6. The redundancy is utilized to improve MVR in Figure 7. This results in joint configurations requiring lower joint velocities for the desired end-effector motion. Thus more efficient motion is obtained in Figure 7 as compared to the cases in Figures 5 and 6. Improvement in MMA in Figure 8 as compared to Figures 5 and 6 can be noted from Figure 10. The redundancy is utilized in Figure 8 to improve MMA in the direction of motion. Thus robot's mechanical advantage or its ability to apply force in the direction of motion is improved as compared to the cases in Figures 5 and 6. We now have a control scheme for redundant robots which can be applied to improve either the efficiency or mechanical advantage depending on the type of task to be performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003015_s0167-9457(02)00176-8-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003015_s0167-9457(02)00176-8-Figure1-1.png",
        "caption": "Fig. 1. Clicker; a spring-loaded lever that produces an audible impetus to the archer that the arrow has been drawn to a fixed distance.",
        "texts": [
            " An archer pushes the bow with an extended arm, which is statically held in the direction of the target, while the other arm exerts a dynamic pulling of the bowstring from the beginning of the drawing phase, until the release is dynamically executed (Leroyer et al., 1993). The release phase must be well balanced and highly reproducible to achieve commendable results in a competition (Nishizono et al., 1987). The bowstring is released when an audible impulse is received from a device called \u2018\u2018clicker\u2019\u2019 that is used as a draw length check (Leroyer et al., 1993). Each arrow can be drawn to an exact distance and a standard release can be obtained using this device (Fig. 1). The clicker is reputed to improve the archer s score and used by all target archers. The archer should react to the clicker as quickly as possible. In particular, a repeated contraction and relaxation strategy in the forearm and pull finger muscles should be developed for this reason. The contraction and relaxation strategy in forearm muscle during the release of the bowstring is critical for accurate and reproducible scoring in archery. Two different approaches to this strategy were proposed in previous studies; however, they were not well defined (Clarys et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure17.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure17.1-1.png",
        "caption": "Figure 17.1. Tooth force component in the transverse plane.",
        "texts": [
            " The direction n~ of the normal to the tooth surface at A, when A is a point on the contact line, was given by Equation (14.94), n~ = cos \"'b [sin t/ltp nx(O) + cos t/ltp ny(O)] - sin \"'b nz(O) (17.2) In the absence of friction, the contact force acts in the direction opposite to n~, and its component parallel to the gear axis is therefore (w sin \"'b). Hence, the component perpendicular to the gear axis, which is the useful component, is equal to (W cos \"'b) \u2022 The base cylinder of gear 1 is shown in Figure 17.1, with Contact Length 491 the plane of action of the contact force touching the base cylinder. The diagram also shows the component of the contact force perpendicular to the gear axis. We take moments about the axis, to obtain a relation between the applied torque M1 and the contact force W, (17.3) and we use the same method to find the corresponding relation between the contact force and the torque M2 appl ied to gear 2, (17.4) The contact force is found from either of these equations. By combining the two equations, we obtain a relation between M1 and M2 , which is the same as Equation (11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure8.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure8.8-1.png",
        "caption": "Figure 8.8. Measurement over pins, for a gear wi th an odd number of teeth.",
        "texts": [
            " The order of the calculations is reversed when the tooth thickness is specified, and we want to find the corresponding value of M for inspection purposes. Equation (8.28) is used to 204 Measurement of Tooth Thickness give the value of (inv ~R')' and the angle ~R' is found by means of Equations (2.16 and 2.17). The values of R' and Mare then found from Equations (8.30 and 8.29). When a gear has an odd number of teeth, the pins are placed in tooth spaces which are as closely as possible opposite to each other, in the manner shown in Figure 8.8. The radii through the pin centers no longer form a straight line, and the angle between them is equal to [180\u00b0 - (180 0jN\u00bb). The relation between R' and M is then given by the following equation, M 2R' cos (9~0) + 2r (8.31) Apart from this change, the equations for finding the tooth thickness are exactly the same as those for a gear with an even number of teeth. Examples 205 Numerical Examples Example 8.1 The gear in Figure 8.2 has 36 teeth, a module of 8 mm, and a pressure angle of 20\u00b0. Calculate the correct settings for a gear-tooth caliper, if the tooth thickness is half the circular pi tch, and the addendum is one module",
            "2, the final tooth thickness is to be checked by a span measurement. Calculate the number of teeth over which the span should be measured, the corresponding value of the span, and the radius at which the caliper jaws will touch the faces of the teeth. N' = Integer closest to 2.7060 = 3 S 3.9662 inches R = 4.0435 inches (8.25) (8.18 ) (8.24) This radius is satisfactory, since the contact points are well below the tooth tips, and well above the fillet circle. Example 8.4 Calculate the measurement over pins for the 11-tooth gear shown in Figure 8.8, which has module 10 mm, pressure angle 20\u00b0, and profile shift 5.0 mm. The diameter of the measuring pins is 26 mm. N=ll, m=10, ~s=200, e=5.0, r=13.0 RS = 55.000 mm Rb 51. 683 ts = 19.348 inv~R' = 0.156726 ~R' = 41.227\u00b0 R' = 68.718 M = 162.038 mm (8.28) (2.16, 2.17) (8.30) (8.31) Chapter 9 Geometry of Non-Involute Gears Introduction In this chapter, we will first show how to calculate the tooth shape of a gear, when it is conjugate to a basic rack of arbitrary shape. This material is not required when the basic rack has straight-sided teeth, since we have already shown how to calculate the tooth profile shape of an involute gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002935_iros.1993.583168-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002935_iros.1993.583168-Figure2-1.png",
        "caption": "Fig. 2 Assembly drawing of wL-12RV",
        "texts": [
            "00 (C) 1993 IEEE Therefore, the objective of this study was to develop a biped walking robot which has an ability to compensate for the three-axis moment by trunk motion, to work out a control method of dynamic biped walking for the robot and to realize faster walking than before. 2.1 Machhe Model The biped walking robot WL-12RV (Waseda Leg-12 Refined v) is shown in Fig. 1. The total weight is 103.5 kg and the height is about 1.8 m. An assembly drawing and a link srructure of this robot are shown in Fig. 2 and Fig. 3. The assignment of DOF (Degrees Of Freedom) is shown in Fig. 3. As this diagram indicates, the lower-limbs have s ix rotational DOF on pitch-axis and the trunk has three rotational DOF on pitch-axis. roll-axis and yaw-axis. The total DOF is nine. . . . _ 2-2 Trunk M e d \" The trunk of this machine model is able to generate the three-axis moment by using three DOF link mechanisms. The weight of the trunk is 30.0 kg. A link smcture of the trunk is shown in Fig. 4. This trunk generates the three-axis moment as follows: The yaw-axis moment is generated by swinging two balance weights around the yaw-axis by a yaw-axis actuator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure4-6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure4-6-1.png",
        "caption": "Figure 4-6 Top: Poincare map sampling times at constant phase of forcing function. Bottom: Geometric interpretation of Poincare sections in the three-dimensional phase space.",
        "texts": [
            " We recall that the dynamics of a one-degree-of-freedom forced mechanical oscillator or Experimental Poincare Maps 131 L-R-C circuit may be described in a three-dimensional phase space. Thus, if jc(/) is the displacement, (x, x, <of ) represents a point in a cylindrical phase space where </> = <o/ represents the phase of the periodic forcing function. A Poincare map for this problem consists of digitally sampled points in this three-dimensional space, for example, (x(tn), x(tn), cotn = 27T\u00ab). As discussed in Chapter 2, this map can be thought of as slicing a torus (see Figure 4-6). Experimentally this can be done in several ways. If one has a storage oscilloscope, the Poincare map is obtained by intensifying the image on the screen at a certain phase of the forcing voltage (sometimes called z-axis modulation) (Figure 4-1). In our laboratory, we were able to generate a 5-10 V pulse of 1-2 jus duration when the forcing function reached a certain phase: (4-6.1) This pulse was then used to intensify a phase plane image, (*(/), x(t)\\ using two vertical amplifiers as in Figure 4-7",
            " A 132 Experimental Methods in Chaotic Vibrations similar technique can be employed using an analog-to-digital (A-D) signal converter by storing the sampled data in a computer for display at a later time. The important point here is that the sampling trigger signal must be exactly synchronous with the forcing function. Poincare Maps\u2014Change of Phase. As noted in Chapter 2, chaotic phase plane trajectories can often be unraveled using the Poincare map by taking Experimental Poincare Maps 133 a set of pictures for different phases </>0 in Eq. (4-6.1) (see Figure 4-8). This is tantamount to sweeping the Poincare plane in Figure 4-6. While one Poincare map can be used to expose the fractal nature of the attractor, a complete set of maps varying <f>0 from 0 to 2?r is sometimes needed to obtain a complete picture of the attractor on which the motion is riding. A series of pictures of various cross sections of a chaotic torus motion in a three-dimensional phase space is shown in Figure 4-8. Note the symmetry in the <p = 0\u00b0 and 180\u00b0 maps for the special case of the buckled beam (Figure 4-5). 134 Experimental Methods in Chaotic Vibrations Poincare Maps\u2014Effect of Damping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003749_robot.2006.1642140-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003749_robot.2006.1642140-Figure6-1.png",
        "caption": "Fig. 6. Spirals of Bellows Model",
        "texts": [
            " After all we proved that the set of (9), (10), (12) and (13) is the necessary and sufficient condition for making the 2 models draw a same backbone curve. (13) is just a initial condition, so the important condition is following 2 equations.( 0 \u03baFb ) = ( cos \u03c6 sin \u03c6 \u2212 sin \u03c6 cos \u03c6 ) ( \u03baBa \u03baBb ) (17) d\u03c6 ds = \u03c4 (18) As you know from (17) and (18), we can obtain \u03baBa and \u03baBb satisfying the condition as to any \u03c4 and \u03baFb. This prove that bellows model can draw any spatial curve as the backbone curve. Fig. 6 shows a bellows model drawing a spiral backbone curve. A spiral curve have constant curvature and torsion (\u03baF = const., \u03c4F = const.), so \u03baBa and \u03baBb are calculated from (17) and (18). The lines drawn on models in Fig. 6 means a certain direction of the dorsal reference frames; the line is straight when the backbone curve is straight. Comparing (3) and (6), we know that the lines are similar. This shows the dorsal reference frame expresses the posture of bellows sufficiently and bellows model (5) represents the characteristic of bellows. Fig. 7 shows the comparison of a spiral of a snake and that of a bellows model. The direction of the dorsal reference frame and that of the snake\u2019s body are alike, which confirm that snakes has the same characteristics as bellows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002771_s0924-0136(00)00850-5-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002771_s0924-0136(00)00850-5-Figure2-1.png",
        "caption": "Fig. 2. New modi\u00aeed water-cooled nozzle.",
        "texts": [
            " Once the cladding operation was completed, the focused lens of the laser was moved up and the workpiece was moved to the position beneath the milling head. Then, the surface of the workpiece with the clad pro\u00aele was machined to achieve the desired accuracy and a smooth surface, ready for the next cladding operation. During the operation of the cladding process, a lot of heat was generated, which affected the \u00afow of powder, as the workpiece was very close to the nozzle of the laser head. In order to remove the heat re\u00afected by the laser, a new watercooled nozzle was designed to increase the powder \u00afow, as shown in Fig. 2. Hence the over-heating problem of the nozzle and the powder \u00afow blockage were solved. The hybrid processes included SLC and milling. The substrate material of the cladding process was SS41, and the dimensions were 112 mm length, 40 mm width, and 13.5 mm thickness. The powder used in the cladding operation was mixed from Fe (72 wt.%), Ni (10 wt.%), and Cr (18 wt.%) powders. In order to make the minimum width of clad, the cladding parameters were laser power at 800 W, the focused lens at 7.5 in., the workpiece to the focused position at 8 mm, the distance of the nozzle to the workpiece at 5 mm, the powder \u00afow rate at 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003997_3-540-27969-5-Figure10.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003997_3-540-27969-5-Figure10.4-1.png",
        "caption": "Fig. 10.4. The invisible object",
        "texts": [
            " By assuming that one or multiple observers can move around the object and see all its sides, the IN and OUT devices described previously must be integrated together in a single device (or, from a different perspective, they must be both densely painted on the whole surface): in fact, there are no longer separated IN and OUT sides on the object. Moreover, if we want the object to show what is behind it independently of the position of the observers, each 10.2 STEP 2. The Invisible Object 213 portion of the surface should be able to retransmit different light configurations in different directions, so as to virtually extend all (a reasonable number of) the rays of light incident on the object (see Fig. 10.4). To this purpose, we can consider a device as a compound object capable of acquiring different light information (IN function) and of firing different light rays (OUT function) in different directions. Alternatively, we can consider a device as a unidirectional sensor or emitter. By distributing these unidirectional devices densely on the object surface (with a random orientation, as it would derive from painting), any portion of the surface will have, with high probability, sensor and emitters pointing in all directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003748_tie.2007.892635-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003748_tie.2007.892635-Figure6-1.png",
        "caption": "Fig. 6. XY -table used in experiments.",
        "texts": [
            " 5 clearly show that the output under the generalized CNF control almost perfectly tracks the transcendental signal, whereas the output under the normal CNF control always lags behind the target. In this section, we demonstrate the application of the proposed control technique in solving the trajectory tracking control problem in an XY -table. The likes of XY -tables, e.g., machine tools, are commonly used in the manufacturing industry. The precision control of an XY -table has been widely studied (see, e.g., [4], [6], [9], [11]\u2013[13], [17], and [18]). Fig. 6 is a photograph of the XY -table we are working with. In each axis of the XY -table, there is a brush-type dc servomotor (model MT22G2-10) that drives its load with a ball screw. The XY -table has a maximum speed of 5000 r/min and a maximum travel of 0.5 m (or 0.25 m in both directions) in each axis, and the displacement of each axis is measured by an optical encoder with 4000 pulse/revolution. A pulsewidthmodulation (PWM) power amplifier is used in the current mode to drive the two motors of the XY -table"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure7-1.png",
        "caption": "Fig. 7. Growth of a cone from an expanding surface G by growth velocities at variable angles to the growth surface to produce the cell tracks shown",
        "texts": [
            " The solution implies that the cells on G are fixed in position once they are generated and new cells are added at the periphery of G as G grows. The solid generated is a cone with half angle c where tan c\"k/v 0 and all cell tracks and particle paths are lines parallel to x 3 as shown in Fig. 6. Example 3.3. Growth surface accreting with varying g Consider next a problem in which the external shape is given to be the same as the cone in Example 3.2, Fig. 6, but with the cell tracks as shown in Fig. 7. The cone in Fig. 7 grows exactly at the same rate as in Fig. 6 so \u00b8\"v 0 t and a\"kt in Fig. 7 and the cone half-angle is again c where tan c\"k/v 0 . The motivation for Fig. 7 is that cell tracks may be the direction of the final fiber structure and the fiber directions shown in Fig. 7 may produce a stronger structure than those in Fig. 6. The interior cell tracks in Fig. 7 form cones with half-angles b where 06b6c. The vector field g must also be such that g \u00b7 n\"v 0 on G to supply the mass required. At the same time there must be a radial velocity inwards at angle b to i 3 to produce the inclination of the cell tracks. The distribution of g on x 3 \"0 satisfying these conditions is g\"! x 3 t i 1 ! x 2 t i 2 #v 0 i 3 . (34) The results given by Eq. (34) is derived using the fact that the values of h 1 and h 2 are constant on cell tracks. The values of h 1 and h 2 on the surface of the cone with half-angle b are assigned to be h 1 \"b cos/ and h 2 \"b sin/. From the geometry of Fig. 7, it can be shown that for any time, t, and position x that h 1 \"b x 1 r , (35) h 2 \"b x 2 r , (36) h 3 \"t! x 3 v 0 , (37) where b and r are given by b\"tan~1A r v 0 t!x 3 B (37a) and r\"[x2 1 #x2 2 ]1@2 (37b) so that Eqs. (35)\u2014(37) give h i in terms of x i and t. Equations (35)\u2014(37) can be inverted to give x 1 \"v 0 h 3 h 1 b tan b , (38) x 2 \"v 0 h 3 h 2 b tanb , (39) x 3 \"v 0 (t!h 3 ) , (40) where now b\"[h2 1 #h2 2 ]1@2 , (41) so that Eqs. (38)\u2014(40) give x i in terms of h i and t. It follows from Eqs. (38)\u2014(40) and Eqs. (10) that x5 m i \"0, x5 m 2 \"0, x5 m 3 \"v 0 . (42) Equation (42) shows that the particles move in straight lines parallel to i 3 , as expected. Note that in this case the particle paths are not the same as the cell tracks shown in Fig. 7. It also follows from Eqs. (38)\u2014(40) and Eq. (12) that x5 G 1 \" x 1 h 3 \" x 1 t , (43) x5 G 2 \" x 2 h 3 \" x 2 t , (44) x5 G 3 \"0 . (45) The result shown in Eqs. (43) and (44) is a result of the self-similarity of cones and is not expected to generalize to other shapes. Using Eqs. (43)\u2014(45) and (42) to compute g by substituting into Eq. (13) gives exactly the vector field of Eq. (34), which demonstrates the consistency of the solution. Also note that the cells on G move radially outward with radial velocity v 0 tanb, as time increases as indicated by Eqs. (43) and (44) and G must increase in area as time increases. If the range of h 1 , h 2 is terminated at some angle c 1 where c 1 (c, a hollow horn is generated as indicated by the stippled area in Fig. 7. Example 3.4. Axes fixed relative to the growing body Consider the same cone structure and growth as shown in Fig. 7, but viewed from axis x which are fixed to the growing body. In this case, the growth surface G moves to the left at velocity (!v 0 ) as shown in Fig. 8. The length of the cone is \u00b8\"v 0 t, the radius of G is a\"kt, and the cone half-angle is c where tan c\"(k/v 0 ), as in Fig. 7. Equation (1) describing the growth in Fig. 8 is obtained from Eqs. (38)\u2014(40) by replacing x 3 by (x 3 #v 0 t). Then x 1 and x 2 are again given by Eqs. (38) and (39), but Eq. (40) changes to x 3 \"!v 0 h 3 . It can be readily shown that g is again given by Eq. (34), but now x5 m\"0 and x5 G\"! g . The physical interpretation is now that the cells on G are moving along the cell tracks that they are generating and leaving the new material behind them at rest. It is noteworthy that in the Examples 3",
            " Example 3.8. Horns with 3-D spirals All of the examples shown in Figs. 5\u201415 have a plane of symmetry. In this example and in Example 3.9, horns with a three dimensional spiral component will be produced by introducing tangential and asymmetric components of the growth velocity distribution. Here we consider the simplest example of this type of horn or tusk, which is straight but has several screw-like threads similar to the horn of the narwhal. Consider the external form and coordinates shown in Fig. 7. In order to produce spiral cell tracks in the same external form, a rotational component is added to Eq. (34) representing rigid body rotation about the x 3 axis. Thus, g\"!A x 1 t #ux 2B i 1 !A x 2 t !ux 1B i 2 #v 0 i 3 , (55) where u is the angular velocity. To make the angle of the spiral a constant at the outer surface, u is varied in time so that u\"i v 0 a , (56) where i is a constant and a is the maximum radius of G at time t. An example of a tusk with 45\u00b0 spirals of cell tracks on the outer surface, generated by a computer program using Eq",
            " In summary, a compatibility rule for surface growth on an interior surface may be stated as follows: A vector field of surface growth g is compatible on an interior surface G if g is of the form of a Volterra dislocation, i.e. Eq. (21). In this case, the relative motion of the two parts of the body, either side of the growth surface, are rigid body motions. It is also possible to generate an incompatibility due to tangential components of g if cells on G and G itself are assumed to be fixed in location, but there are tangential components of g . For example, a radial outward component of g as given in Example 3.3 (Fig. 7) by Eq. (34) would be incompatible if xR G i were assumed to be zero instead of the result given by Eqs. (43) and (44). A general rule may be given in the case that it is assumed that G is fixed and the growth-producing cells are fixed in location on G. As already discussed in Sect. 2, the entire growth velocity field g on G must have the form of a Volterra dislocation, Eq. (21). Returning now to the possibility of residual stresses being produced by contraction or expansion of tissue after it is deposited on an external surface G of a growing body, it may be remarked first that this is not a surface growth phenomenon",
            " The present paper does not provide any biological proof that the descriptions provided apply to any particular biological case. Rather, a rigorous vocabulary is presented and it remains to be seen by biological observations and experiments, where such theory does not provide a realistic description. Of course, in many cases there are observations recorded in the literature which assure that many of the aspects of the examples presented here are realistic. For example, it is known that the rhinoceros horn is matted hair, and hence, it has cell tracks more like Fig. 6 than Fig. 7. On the other hand, the structure of cows\u2019 horns is known to be more like Fig. 7. There are two points of the present vocabulary that particularly need to be confirmed or verified in each biological case. The first is the extent to which cell tracks (like the costa of Fig. 23) are, in fact, attributable to a single cell or to a group of cells, in which individual cells divide or die and are replaced by new cells. The second aspect which requires experimental information is the nature and degree of motion of generating cells. (This is the velocity called x5 G in Eq. (12).) If the surface supporting the generating cells is bone and the growth of the supporting structure is the reason for the motion of the generating cells, one possibility is that there is an isotropic growth of the growth surface G and its supporting structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure3-1.png",
        "caption": "Fig. 3. Twist system and wrench system of an SP virtual chain.",
        "texts": [
            " Step 4: Generate SP-equivalent parallel mechanisms by selecting actuated joints in different ways for each SP-equivalent parallel kinematic chain (Section 6), obtained in Step 3. The procedure proposed above will be elaborated upon in the following sections. In any general configuration, an SP-equivalent parallel kinematic chain and its corresponding SP virtual chain have the same twist system and the same wrench system. Finding the wrench system of the SP-equivalent parallel kinematic chain is thus equivalent to finding the wrench system of the SP virtual chain (Fig. 3). The twist system of an SP-equivalent parallel kinematic chain is a 3-n0\u20131-n1-system. Here, n0, n1 and f0 denote, respectively, a twist of zero pitch, a twist of infinite pitch and a wrench of zero pitch. In the above 3-n0\u20131-n1 system, one set of its base is one n1 and three concurrent n0\u2019s. The intersection of the axes of the three n0\u2019s is referred to as the center of the 3-n0\u20131-n1-system. It can be found without difficulty that its wrench system is a 2-f0-system whose center is at the center of the 3-n0\u20131-n1-system (Fig. 3). As the wrench system, W, of a parallel kinematic chain is the linear combination of all of its leg-wrench systems, Wi, in any configuration [32], it is then concluded that the wrench system of any leg in an SP-equivalent parallel kinematic chain is a ci(0 6 ci 6 2)-f0-system in any general configuration. Since all the wrenches within a leg-wrench system are of the same pitch, the combination of leg-wrench systems can be simply represented by the combination of the orders, ci(i = 1,2, . . . ,m), of the leg-wrench systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002751_s0043-1648(99)00143-x-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002751_s0043-1648(99)00143-x-Figure3-1.png",
        "caption": "Fig. 3. Falling ball viscometer for determination of pressure\u2013viscosity coefficient.",
        "texts": [
            " The Roelands pressure\u2013 viscosity coefficient, a U , is a function of both p and T. T0 is a reference or ambient temperature. The Roelands equation can be compared to Barus equation and a relation between a and the dimensionless \u017d \u017d ..constant Z obtained Eq. 10 . a Zs 10\u017d .y95.1=10 lnh q9.67\u017d .0 To determine the influence of pressure on viscosity two different high pressure viscometers have been used, one falling ball type and one concentric cylinder. The falling ball viscometer can be seen in Fig. 3, from Hoglund et al.\u00a8 w x18 . The falling ball viscometer can be used at pressures up to 30 MPa. It consists of a pressure vessel with a 50 mm cylindrical bore. The viscosity of the lubricant is determined by the time it takes for a ball with a diameter slightly smaller than the bore to travel a predetermined distance, 100 mm. The bore is split in two parts, one for the test oil and one for the pressurizing hydraulic oil. The viscometer can be heated by a sleeve on the outside. The temperature range used in the tests was 20\u2013808C with an accuracy of \"0.18C, measured in the test oil. The pressure vessel is equipped with windows, not shown in Fig. 3, to allow the lubricant to be observed during a test and for measuring the falling speed of the ball. The latter is done using two light emitting diodes and two photo diodes mounted in the windows on opposite sides of the vessel. The inclination of the viscometer is 108 to ensure that the ball follows the wall of the bore giving a well-defined clearance between the ball and the bore. Balls of three different diameters were used to ensure laminar flow at all times in spite of changes in temperature and pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000833_j.cirpj.2021.06.022-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000833_j.cirpj.2021.06.022-Figure4-1.png",
        "caption": "Fig. 4. Process chain.",
        "texts": [
            " The wall width varied according to the welding parameters. The interpass temperature during the WAAM process was controlled using a FLIR A315 thermal IR camera (Fig. 3). Once the maximum temperature of the deposited upper layer had reached a specific value, the next pass was applied. The heat input during the WAAM process introduces significant distortion of the base plate leading to poor clamping and low alignment accuracy on the CNC machine. To overcome these problems, the substrate plate was pre-machined (as shown in Fig. 4) from the bottom before scanning using an ATOS Compact 3D scanner. Subsequently, the CAD model of the final part was fitted within the scanned WAAM part, using GOM software. By comparison with an actual surface, the machining allowance Table 1 Chemical composition of the filler wire (wt %). C Si Mn P S Cu Fe 0.088 0.9 1.510 0.012 0.012 0.190 Rest Fig. 3. Deposition of the WAAM sample. As a motion system for WAAM, a six-axis industrial robot arm CLOOS QRC320H was used. Samples were deposited using a Qineo pulse 450A welding power source with synergic control in w O r m F C a F W s a b o c w p f m t d d d F m 0 P as obtained, and part alignment was corrected when necessary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000595_j.ast.2021.106833-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000595_j.ast.2021.106833-Figure3-1.png",
        "caption": "Fig. 3. The diagram of control inputs on the UAV.",
        "texts": [
            " According to [35], the Newton-Euler equations of the dynamic model are given as follows\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u03c6\u0308(t) = \u03b8\u0307 (t)\u03c8\u0307(t) ( I y \u2212 Iz Ix ) \u2212 J R Ix \u03b8\u0307 (t) R(t) + l Ix u2(t) \u03b8\u0308 (t) = \u03c6\u0307(t)\u03c8\u0307(t) ( Iz \u2212 Ix I y ) + J R I y \u03c6\u0307(t) R(t) + l I y u3(t) \u03c8\u0308(t) = \u03c6\u0307(t)\u03b8\u0307(t) ( Ix \u2212 I y Iz ) + l I z u4(t) x\u0308(t) = 1 m [(cos\u03c6(t) cos\u03c8(t) sin \u03b8(t) + sin\u03c6(t) sin\u03c8(t))u1(t) \u2212 kt x\u0307(t) + dx(t)] y\u0308(t) = 1 m [(cos\u03c6(t) sin \u03b8(t) sin\u03c8(t) \u2212 cos\u03c8(t) sin\u03c6(t))u1(t) \u2212 kt y\u0307(t) + dy(t)] z\u0308(t) = 1 m [(cos \u03b8(t) cos \u03c6(t))u1(t) \u2212 kt z\u0307(t) \u2212 g] , (2) where \u03c6(t), \u03b8(t) and \u03c8(t) denote the roll, pitch and yaw angle, respectively, x(t), y(t) and z(t) denote the positions of the UAV, Ix , I y and Iz denote the moments of inertia around three axes of the UAV, J R denotes the rotational moments of inertia, R denotes a numerical computation on the angular velocities of the propeller blades, kt denotes the linear drag, g denotes the gravitational acceleration, u1(t), u2(t), u3(t) and u4(t) are the control inputs generated by four rotors of the UAV, u1(t) represents the total lift in z direction and u2(t), u3(t) and u4(t) denote the three rotational torques around different axes of the UAV. The diagram of the control inputs on the UAV is given in Fig. 3. Given xd(t) and yd(t) as the desired values generated by the pre-set desired trajectory ld(t), an error system is obtained as{ ex(t) = xd(t) \u2212 x(t) e y(t) = yd(t) \u2212 y(t) and{ e\u0307x(t) = x\u0307d(t) \u2212 x\u0307(t) e\u0307 y(t) = y\u0307d(t) \u2212 y\u0307(t) , where ex(t) and e y(t) are the tracking errors, e\u0307x(t) and e\u0307 y(t) are the derivatives of the tracking errors. It is obtained from the dynamic model (2) that\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 e\u0308x(t) = x\u0308d(t) \u2212 1 m [(cos\u03c6(t) cos\u03c8(t) sin \u03b8(t) + sin \u03c6(t) sin\u03c8(t))u1(t) \u2212 kt x\u0307(t) + dx(t)] e\u0308 y(t) = y\u0308d(t) \u2212 1 m [(cos \u03c6(t) sin \u03b8(t) sin \u03c8(t) \u2212 cos\u03c8(t) sin\u03c6(t))u1(t) \u2212 kt y\u0307(t) + dy(t)] (3) in which e\u0308x(t) and e\u0308 y(t) are the second order derivatives of ex(t) and e y(t), respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure2-12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure2-12-1.png",
        "caption": "Figure 2-12 Poincare map of chaotic vibration of a forced nonlinear oscillator showing self-similar structure at finer and finer scales.",
        "texts": [
            " Such motions are sometimes called stochas- How to Identify Chaotic Vibrations 53 TABLE 2-2 Classification of Poincare Maps Finite number of points: periodic or subharmonic oscillation Closed curve: quasiperiodic, two incommensurate frequencies present Open curve: suggest modeling as a one-dimensional map; try plotting x(t) versus x(t + T) Fractal collection of points: strange attractor in three phase space dimensions Fuzzy collection of points: (i) dynamical system with too much random or noisy input; (ii) strange attractor but system has very small dissipation\u2014use Lyapunov exponent test; (iii) strange attractor in phase space with more than three dimensions\u2014try multiple Poincare map; (iv) quasiperiodic motion with three or more dominant incommensurate frequencies. tic (e.g., see Lichtenberg and Lieberman, 1983). In damped systems, the Poincare map will sometimes appear as an infinite set of highly organized points arranged in what appear to be parallel lines, as shown in Figure 2-llfe,c. In numerical simulations, one can enlarge a portion of the Poincare map (see Figure 2-12) and observe further structure. If this structured set of points continues to exist after several enlargements, one says that the motion behaves as a strange attractor. This embedding of structure within structure is often referred to as a Cantor set (see Chapter 6). The appearance of Cantor set-like patterns in the Poincare map of a vibration history is a strong indicator of chaotic motions. The classes of patterns of Poincare maps are listed in Table 2-2. Poincare Maps in Autonomous Systems. Steady-state vibrations can also be generated without periodic or random inputs if the motion originates from a dynamic instability such as wind-induced flutter in an elastic structure (Figure 2-13) or a temperature-gradient-induced convection motion in a fluid or gas (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003004_1.1585087-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003004_1.1585087-Figure1-1.png",
        "caption": "FIG. 1. Schematic of the laser cladding process.",
        "texts": [
            " The effects of Marangoni phenomena and hydrodynamic of the liquid metal are considered in the material properties. The model also takes into account the power attenuation and Brewster effects to include the changes in absorption factor due to the clad geometry. A repetitive pulse laser beam is considered as a moving heat source in this modeling. In the following, the modeling approach is first discussed and then the assumptions for the numerical solution are presented. Finally, the numerical results are obtained at different powder feedrates and process velocities and compared with experimental data. Figure 1 shows the laser cladding process. A moving laser beam with a Guassian distribution intensity strikes on the substrate at t50. Due to additive material, the clad forms on the substrate as shown in the figure. The transient temperature distribution T(x ,y ,z ,t) is obtained from the threedimensional heat conduction in the substrate as11 ]~rcpT ! ]t 1\u00b9\u2022~rcpUT !2\u00b9\u2022~K\u00b9T !5Q , ~1! where Q is power generation per unit volume of the substrate (W/m3), K is thermal conductivity ~W/mK!, cp is specific heat capacity ~J/kg K"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000732_j.oceaneng.2021.108951-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000732_j.oceaneng.2021.108951-Figure1-1.png",
        "caption": "Fig. 1. AUV body-fixed and earth-fixed coordinate systems.",
        "texts": [
            " Section 3 presents the novel 3-D trajectory tracking control scheme, design of proposed nonlinear disturbance observer (NDO), and the detailed building and proving process of the kinematic and dynamic controller. In section 4, P.N. Nhut Thanh et al. Ocean Engineering 228 (2021) 108951 the proposed control scheme is verified via various numerical simulations with analysis. Eventually Section 5 delineates conclusions. 2. AUV implementation 2.1. Model of under-actuated AUV The model will be considered in this paper is the hybrid AUV2000 mentioned in Tran et al. (2021). At first, the earth-fixed frame {e} and the body-fixed frame {b} are defined, as illustrated in Fig. 1. Based on the previous study (Tran et al., 2021), the 6-DOF nonlinear kinematic and dynamic equations of motion of AUV can be expressed as follows: Kinematics: \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa\u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa\u23a9 x\u0307 = u cos \u03c8 cos \u03b8 + v( \u2212 sin \u03c8 cos \u03c6 + cos \u03c8 sin \u03b8 sin \u03c6) +w(sin \u03c8 sin \u03c6 + cos \u03c8 sin \u03b8 cos \u03c6) y\u0307 = u sin \u03c8 cos \u03b8 + v(cos \u03c8 cos \u03c6 + sin \u03c8 sin \u03b8 sin \u03c6) +w( \u2212 cos \u03c8 sin \u03c6 + sin \u03c8 sin \u03b8 cos \u03c6) z\u0307 = \u2212 u sin \u03b8 + v cos \u03b8 sin \u03c6 + w cos \u03b8 cos \u03c6 \u03c6\u0307 = p + q sin \u03c6 tan \u03b8 + r cos \u03c6 tan \u03b8 \u03b8\u0307 = q cos \u03c6 \u2212 r sin \u03c6 \u03c8\u0307 = q sin \u03c6 cos \u03b8 + r cos \u03c6 cos \u03b8 (1) Dynamics: ( m\u2212 Xu\u0307 ) u\u0307\u2212 myGr\u0307+mzGq\u0307 = ( Zw\u0307 \u2212 m ) wq+ ( Zq\u0307+mxG ) q2+ ( m\u2212 Yv\u0307 ) vr+ ( mxG \u2212 Yr\u0307 ) r2 \u2212 myGpq\u2212 mzGpr \u2212 (W \u2212 B)sin\u03b8+Xu|u|u|u|+Xprop+Xuu\u03b4\u03b4u2\u03b42 R+Xuv\u03b4uv\u03b4R+Xur\u03b4ur\u03b4R (2a) ( m\u2212 Yv\u0307 ) v\u0307\u2212 mzGp\u0307+ ( mxG \u2212 Yr\u0307 ) r\u0307 = ( Xu\u0307 \u2212 m ) ur+ ( m\u2212 Zw\u0307 ) wp\u2212 ( mxG+Zq\u0307 ) pq+myG ( p2+r2)\u2212 mzGqr+Yv|v|v|v| +Yr|r|r|r|+(W \u2212 B)cos\u03b8sin\u03c6+Yuvluv+Yuu\u03b4u2\u03b4R+Yuv\u03b4uv+Yur\u03b4ur (2b) ( m \u2212 Zw\u0307 ) w\u0307 \u2212 ( mxG +Zq\u0307 ) q\u0307+myGp\u0307 = ( m \u2212 Xu\u0307 +Zuqf ) uq+ ( Yv\u0307 \u2212 m ) vp \u2212 myGrq+mzG ( p2 +q2)+ ( Yr\u0307 \u2212 mxG ) rp +Zw|w|w|w|+(W \u2212 B)cos \u03b8 cos \u03c6+Zq|q|q|q|+ ( Zuwl +Zuwf ) uw (2c) ( Ixx \u2212 Kp\u0307 ) p\u0307+myGw\u0307 \u2212 mzGv\u0307 = ( Zw\u0307 \u2212 Yv\u0307 ) wv+ ( Zq\u0307+Yr\u0307 ) vq \u2212 ( Zq\u0307+Yr\u0307 ) wr+mzG(ur \u2212 wp)\u2212 myG(vp \u2212 uq) + ( Nr\u0307 \u2212 Mq\u0307 \u2212 Izz+Iyy ) qr+Kp|p|p|p|+(yGW \u2212 yBB)cos\u03b8cos\u03c6 \u2212 (zGW \u2212 zBB)cos\u03b8sin\u03c6+Kprop (2d) ( Iyy \u2212 Mq\u0307 ) q\u0307\u2212 ( mxG+Zq\u0307 ) w\u0307+mzGu\u0307 = ( Xu\u0307 \u2212 Zw\u0307+Muwl+Muwf ) uw+Mw|w|w|w|+ ( Kp\u0307 \u2212 Nr\u0307 \u2212 Ixx+Izz ) rp+Mq|q|q|q| + ( Muqf \u2212 mxG \u2212 Zq\u0307 ) uq\u2212 mzG(wq\u2212 vr)+ ( mxG \u2212 Yr\u0307 ) vp \u2212 (zGW \u2212 zBB)sin\u03b8\u2212 (xGW \u2212 xBB)cos\u03b8cos\u03c6 (2e) ( Izz \u2212 Nr\u0307 ) r\u0307+ ( mxG \u2212 Nv\u0307 ) v\u0307 \u2212 myGu\u0307 = ( Yv\u0307 \u2212 Xu\u0307 +Nuvl ) uv+ ( mxG +Zq\u0307 ) wp+ ( Mq\u0307 \u2212 Kp\u0307 + Ixx \u2212 Iyy ) pq+Nv|v|v|v| + ( Yr\u0307 \u2212 mxG ) ur+myG(wq \u2212 vr)+(xGW \u2212 xBB)cos \u03b8 sin \u03c6+Nr|r|r|r| +(yGW \u2212 yBB)sin \u03b8+Nuu\u03b4u2\u03b4R +Nuv\u03b4uv+Nur\u03b4ur (2f) where m is the AUV\u2019s mass, (xG, yG, zG) is the center of gravity, (xB, yB, zB) is the center of buoyancy, and Ixx, Iyy, Izz respectively are inertial moments about the x, y, and z axes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure15.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure15.8-1.png",
        "caption": "Figure 15.8. pitch cylinder of gear 1, viewed along the gear axis.",
        "texts": [
            " However, we can determine its position and direction, in a form that can be more easily understood, if we construct the vector from C01 to the contact point, Path of Contact 429 (15.73) We substitute the expression in Equation (15.50) for pPA1, and we use Equation (15.55) to express n~l in terms of nx1 (0), n y1 (0) and n z1 (0). We then obtain the following equation for the path of contact, P C01 A1 (Rp1 + sl sin I/Itp1) n x1 (0) + sl cos I/Itp1 ny 1 (0) + (tan ~C1 - sl tan 1/Ib1)nz1 (0) (15.74) I/I np sin 1/Ip1 This equation demonstrates a result which may be considered somewhat remarkable. If the gear is viewed in the axial direction, as shown in Figure 15.8, the path of contact appears exactly the same as the path of contact in a spur gear pair, and we can see that the straight line containing the path of contact touches the base cylinder of the gear. We can also use the diagram to obtain a relation between the radius R1 of the contact point, and the corresponding value of sl' 430 Crossed Helical Gears 2 2 v'(R 1-Rb1 ) - Rbl tan 4>tpl (15.75) Point POl was defined earlier as the point where line C01 C02 ' the common perpendicular to the gear axes, intersects the pitch cylinder of gear 1. When the gear is viewed in the axial direction, as in Figure 15.8, POl appears as the point where the radius in the nxl (O) direction meets the pitch cylinder. By setting sl equal to zero in Equation (15.74), we obtain the position vector to the point where the path of contact intersects the pitch cylinder. This point is labelled P l , and its position is given by the following expression, (15.76) It is clear that P l lies on the axial line through POl' so that in Figure 15.8 the two points appear to coincide, and the distance between the two points is equal to the coefficient of nzl (O) in Equation (15.76). An alternative form of Equation (15.74) can be found, simply by bringing together the terms containing the variable sl' (15.77) The terms in the square brackets represent a unit vector, giving the direction of the path of contact. Since the coefficient of nzl (O) has a magnitude of sin ~bl' the path of contact must make an angle C7r/2 - ~bl) with the gear axis. The coefficients of nx1 (0) and nyl (O) are in the ratio of tan 4>tpl : 1, which confirms that when the path of contact is viewed in the axial direction, it appears to make an angle 4>tpl with the nyl (O) direction, as we showed in Figure 15.8. By using the relations developed in Chapter 13 between the various angles, we can express the position vector from Co 1 to the contact point in yet another form, Path of Contact 431 (15.78) Once again, the terms in the square brackets represent a unit vector. Since the coefficient of n x1 {O) is sin ~np' the path of contact must make an angle (7r/2-~np) with the n x1 {O) direction. The coefficients of nz1 {O) and ny1 {O) are in the ratio of (- tan lPp1 ) : 1, so when the path of contact is viewed in the nx1 {O) direction, as shown in Figure 15",
            " The points where the line meets the two cylind~rs are again called the interference points E1 and E2 , exactly as they are in the case of a spur gear pair. The first condition for no interference is that the ends of the path of contact should lie between E1 and E2\u2022 The end point T2 of the path of contact is the point where line E1E2 intersects the tip cylinder of gear 2. The value of s2 at this point is given by Equation (15.79), (15.86) and the corresponding value of s1 at the same point can be found from Equation (15.59), (15.87) The interference point E1 is shown in Figure 15.8, and the value of s1 at this point can be read from the diagram, - Rb1 tan IP tp1 (15.88) For T2 to lie between E1 and E2 , the value of s~2 must be greater than s~1, and we therefore obtain the first Minimum Face Width 435 condition for no interference, > 0 (15.89) The limit circle of a gear was defined in Chapter 4 as the circle with radius RL, where RL is the minimum radius at which contact takes place. For gear 1, the minimum value of Rl occurs at point T2 , provided Equation (15.89) is satisfied, and the limit circle radius is then given by Equation (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure5-1.png",
        "caption": "Fig. 5. Variations in B i \u2013B i j chain.",
        "texts": [
            " 3 , a i \u2212 o = (R + \u03b4R i ) R z (\u03b7i + \u03b4\u03b7i ) j + \u03b4a zi k (4) where \u03b4R i and \u03b4\u03b7i are the variations in the nominal geometric parameters R and \u03b7i , respectively, and \u03b4a zi is the positioning error of A i along z-axis. According to Fig. 4 , b i \u2212 a i = (b i + \u03b4b i ) R Bi j (5) with R Bi = R z (\u03b7i + \u03b4\u03b7i )(I + [ \u03b4\u03c6i ]) R z (\u03b8i + \u03b4\u03b8i ) (6) where [ \u03b4\u03c6i ] represents the cross-product matrix (CPM) 2 of vector \u03b4\u03c6i = [ 0 \u03b4\u03c6yi \u03b4\u03c6zi ]T , and I is the 3 \u00d7 3 identity matrix. Moreover, \u03b4b i is the variation in b i , \u03b4\u03b8i is the error of input angle \u03b8i of the i th actuator and \u03b4\u03c6i represents the angular variations of manufacturing errors. According to Fig. 5 , b i j \u2212 b i = 1 2 \u03b5( j)(d i + \u03b4d i j ) R Bi (I + [ \u03b4\u03c8 i ]) i ; \u03b5( j) = { 1 , j = 1 \u22121 , j = 2 (7) where \u03b4\u03c8 i = [ 0 \u03b4\u03c8 yi \u03b4\u03c8 zi ]T is the orientation error of link B i 1 B i 2 with respect to the axis of rotation of the i th active revolute joint, and \u03b4d i is the variation of B i 1 B i 2 that is supposed to be equally shared by the connecting bar of the parallelogram. According to Fig. 6 , c i j \u2212 b i j = l i w i + \u03b4l i j w i + l i \u03b4w i j (8) where \u03b4l i is the variation in the length of link B i j C i j along the direction w i = [ w ix w iy w iz ]T = (c i \u2212 b i ) /l, and \u03b4w i j is the variation in the direction that is perpendicular to w i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000742_j.compositesb.2021.109202-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000742_j.compositesb.2021.109202-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagrams of (a) SLM-built samples and (b) stress rupture specimens (unit: mm).",
        "texts": [
            " The chemical composition of the powder is measured and shown in Table 1. The experiment was performed using a BLT-S600 SLM machine equipped with a 500W fiber laser. IN718 cylindrical specimens were fabricated on a forged 316L stainless steel substrate with a dimension of 600 \u00d7 600 \u00d7 80 mm3. The main process parameters are as follows: laser power of 305 W, scanning speed of 960 mm/s, layer thickness of 40 \u03bcm, laser spot diameter of 100 \u03bcm, hatch length of 100 \u03bcm, and interlayer scanning angle of 67\u25e6. Fig. 1(a) shows the schematic diagram of the SLM-built specimens. The as-built specimens were first treated by HIP at 1160 \u25e6C/100 MPa for 4 h with furnace cooling to improve density. The density of the samples was measured by Archimedes drainage method. It was found that the density of the specimens after HIP increased from 99.3 to 99.8%. Some spherical pores with size less than 20 \u03bcm cannot be completely eliminated. To analyze the precipitation behavior of \u03b4 phase, the HIP-treated specimens were further heat treated at 1050 \u25e6C for 1 h, and then heat-treated at the temperature of 900, 920, 940, 960, and 980 \u25e6C for 0",
            " Based on the precipitation behavior of \u03b4 phase, three different solution treatments were chosen to study the effect of \u03b4 phase on stress rupture properties of SLM-built IN718 alloy, as listed in Table 2. They were named as HSA-N, HSA- 980, and HSA-960, respectively. To obtain the strengthening phase with the suitable volume fraction, all specimens were aged at 720 \u25e6C for 8 h and then cooled at a rate of 50 \u25e6C/h to 620 \u25e6C for 8 h followed by air cooling according to the previous work. According to ASTM E139 (GB/T 2039), the specimens were machined according to the standard dimension of stress rupture specimen, as shown in Fig. 1(b). The loading direction of the specimen is perpendicular to the deposition direction. Stress rupture test under 690 MPa at 650 \u25e6C was performed on an RMTD10 electronic high temperature creep testing machine. Three specimens were tested for every heat treatment regime. For metallographic observation, all specimens were ground with 180\u20132500 grit waterproof abrasive papers and polished successively with the colloidal silicon solution for 10 min on a metallographic polisher. The specimens were etched in a solution of 8 ml HCl +20 ml CH3CH2OH + 14 g FeCl3 for 30 s before microstructure observation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure11.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure11.3-1.png",
        "caption": "Figure 11.3. Contact at the lowest point of single-tooth contact on gear 1.",
        "texts": [
            " It can be verified that we obtain the maximum value for Uc when the smaller radius of curvature is as small as possible. If the gears are numbered so that gear 1 is the pinion, then Rb1 is smaller than Rb2 , and we obtain the smallest value for P1 when s reaches its largest negative value. The contact point is then as far as possible below the pi tch point, and since we are considering only the period of single-tooth contact, the contact point must lie at the lowest point of single-tooth contact on the pinion. Figure 11.3 shows point Q on the path of contact, corresponding to the lowest point of single-tooth contact on the pinion, and the highest point of single-tooth contact on the gear. The value of P 1 can be read directly from the diagram, for the situation when the contact point coincides with Q, and the corresponding value of P2 is found from Equations (11.9 and 11.10), (11.11) (11.12) To calculate the maximum contact stress during the meshing Contact Stress 247 cycle, we substitute these values of Pl and P2 into Equation (11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure6-5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure6-5-1.png",
        "caption": "Figure 6-5 Horseshoe map.",
        "texts": [
            "2), one can easily see that for the Koch curve log 4 dc = - \u2014 - = 1. 26185 - \u2022 \u2022 (6-1.3) log 3 Similarly, one can show that for the Cantor set log 2 dc= -5- -0.63092-.. (6-1.4) log 3 Introduction 211 One way to interpret the fractal dimension of the Koch curve is that the distribution of points covers more than a line but less than an area. Two other examples of sets of which one can calculate the fractal dimension are the horseshoe map and the baker's transformation. The horseshoe map has been discussed in Chapters 1 and 5 and is shown graphically in Figure 6-5. It is perhaps the simplest example of an iterative dynamical process in the plane that leads to a loss of information and fractal properties. The calculation of the capacity fractal dimension for the horseshoe map is similar to that for the Cantor set except that the vertical direction leads to a contribution of \"one\" to the dimension. Using the definition (6-1.2), one can show that log 2 10g|\u20ac| + 1 (6-1.5) where c is the contraction parameter and 0 < e < 1/2. [See also Berge et al. (1985) for a discussion of this example.] Another example for which one can calculate the fractal properties is the baker's transformation two-dimensional map. This example may be found in Farmer et al. (1983) and is similar to the horseshoe map (Figure 6-5). Its name derives from the idea of a baker rolling, stretching, and cutting pastry dough as shown in Figure 6-6. In this example, one can write out the specific difference equation relating a piece of dough at position (xn, yn) to 0 Xfl J_ \\ Figure 6-6 Baker's transformation or map. 212 Introduction 213 it's new position in one iteration: 2 + Mn if yn > a if v < \u00ab (6-1-6) where 0 < xn < 1 and 0 < yn < 1. The article by Farmer et al. (1983) is very readable so we do not present the details but only quote the results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.8-1.png",
        "caption": "Fig. 7.8 Watt\u2019s linkage",
        "texts": [
            " Although linkages were already used in ancient times, systematic theoretical research, devising of more variations and application to real machines were not begun until the First Industrial Revolution. The golden age of linkages is the 19th century when progress in mathematics and manufacturing technology provided the capacity to create new linkages. However, the design theory of linkages became matured only after Reuleaux and Burmester. A linkage, seemingly very simple today, needed the most brilliant mind of that time to create it. J. Watt was an early user of linkage mechanisms. Initially, Watt empirically designed the Watt\u2019s linkage shown in Fig. 7.8 to guide the piston moving in a straight line. Although he abandoned this mechanism later, and turned to a slider-crank mechanism for this task (Gibson 1998), it stirred the interest to systematically analyze the characteristics of linkages in theory. The Watt linkage started the work to realize specific paths using coupler curves. Machining a plane is very easy today. However, in the second half of the 18th century, milling machines were not invented yet. It was not an easy job to make a prismatic pair of high quality with small clearance at that time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure11-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure11-2-1.png",
        "caption": "Figure 11-2. Arrangements for friction tests, (a) Linear track; (b) rotating shaft; (c) towed sled; (d) pin and rotating place (e) inclined plane. N = normal force, V = direction of motion,",
        "texts": [],
        "surrounding_texts": [
            "depend on the rigidity and damping of the testing system as well as on the properties of the surfaces. To minimise slip-stick it is necessary to construct the test apparatus, particularly the drive and force measuring elements, to be as stiff as possible. If slip-stick can occur in service, its presence can be more important, or rather troublesome, than the actual mean level of friction. It is fairly obvious that other factors such as lubricants, wear debris, ageing of the surfaces and humidity can also affect friction and, once again, test conditions must be chosen that resemble those found in service."
        ]
    },
    {
        "image_filename": "designv10_4_0000079_j.rcim.2019.101916-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000079_j.rcim.2019.101916-Figure14-1.png",
        "caption": "Fig. 14. (a) The definition of molten pool dimensions, and (b) the molten pool dimensions and molten pool dimensional ratio r of test 1 to 5 in group B.",
        "texts": [
            " Images of the weld pool are presented to assist the analysis of the molten pool behaviour (one representative image of each test is provided as the molten pool is analogous without humping). Note that molten pool geometry parameters (depth and length) are introduced here to help describe the molten pool geometry. The depth and the length of the molten pool are defined as the distance from the weld pool underneath wire electrode to the bottom and the tail of the molten pool, as illustrated schematically in Fig. 14(a). As illustrated in Fig. 13(a) to (f), the molten pool size increases in both depth and length with the increase in WFS. In GMAW welding, the welding current increase with the increase of WFS [56]. According to Eq. (1), the initial momentum of the metal flow increases, which may lead to humping. However, with a deeper weld pool, a portion of the metal flow momentum might be dissipated and thereby no humped weld bead forms. Based on the results, it is assumed that a long and shallow weld pool represents a high chance of humping occurrence while a short and deep weld pool means a low chance of humping occurrence. Thus, molten pool dimensional ratio r (defined as r=l/d) was introduced as an indicator representing the chance of humping occurrence. With different welding parameters. Fig. 14(b) presents the molten pool dimension and dimensional ratio r for each test in group B. It can be seen that r remains stable while the molten pool size increases in both depth and length with the increase in WFS. The impact of TS on humped weld bead was investigated in the test group C. A set of tests were conducted in which the TS was changed from 100 to 500 mm/min while the material deposition ratio rv (rv=WFS/TS) was set to a constant value 10. The material deposition rate rv determines the volume of the weld metal deposited in a unit time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.18-1.png",
        "caption": "Figure 13.18. The generator through point A.",
        "texts": [
            "17, E' is the point where the axial line through E cuts plane z=O, and A' is the point where the base circle tangent at E' cuts the tooth profile. We now use Equation (13.56) to derive an expression for the di fference between the lengths EA and E' A' \u2022 EA - E'A' arcEB - arcE'BO arc EB - arc EB' EA - E'A' arc B' B (13.64) The expression for tJ.8 in Equation (13.63) can be put into a different form by means of Equation (13.32), (13.65) and we substitute this expression into Equation (13.64). EA - E'A' (13.66) A three-dimensional view of the base cylinder is shown in Figure 13.18, and the lines EA and E'A' are drawn in on the diagram. In view of Equation (13.66), it is clear that the line AA' makes an angle ~b with the gear axis. In addition, every point on this line is a point on the gear tooth surface, since Equation (13.66) is satisfied at every point along the line. When a curved surface contains a family of straight lines, these lines are called generators of the surface, so The Generator Through Point A 333 the line AA' is known as the tooth surface generator through point A. Since lines EA and E'A' are both tangent to the base circles, the four points A, E, A', and E' lie in a plane which touches the base cylinder along line EE'. Hence, the generator through A must touch the base cylinder at a point on line EE', as shown in Figure 13.18, and this point is labelled G. It was stated in Chapter 2 that an involute can be thought of as the curve traced out by the end of a cable, when the cable is unwrapped from the base circle. In Figure 13.18, lines E'A' and EA would represent the cables corresponding to the transverse sections at plane z=Q and plane z. Since every point of line A'A lies on the tooth surface, it is possible to think of the plane E'A'AE as forming part of a flexible sheet, unwrapping from the base cylinder. We can therefore represent an involute helicoid in the following manner. We consider a flexible sheet, wrapped round the base cylinder, with its end cut off so that it makes an angle ~b with the gear axis. The involute helicoid is the surface swept out by the end of the sheet, when it is unwrapped from the base cylinder",
            " Coordinates of Point G For any point A of the tooth surface, there is a generator passing through the point, and this generator touches the base cylinder at some point G. Very often, we will want to find the position of G corresponding to a particular point A, and we can do this most conveniently by deriving expressions for the cylindrical coordinates (RG,eG,zG), in terms of the coordinates (R,eA,Z) of point A. Since G lies on the base cyl inder, the radi us RG is equal to the base cylinder radius Rb \u2022 And since G lies on the axial line through E, the angular coordinates of G and A differ by ~tR' as we can see from Figure 13.15. Finflly, length EA in Figure 13.18 is equal to (Rb tan ~tR)' as we stated in Equation (13.55), and the length GE is equal to EA divided by (tan ~b). Hence, the coordinates of point G are related to those of A in the following manner, eG eA - ~tR Properties of Point G Rb tan ~tR z - tan ~b ( 13.67) (13.68) (13.69) There are two important properties associated with point G, shown in Figure 13.18. First, point G lies on the Properties of Point G 335 gear helix through BO and B. And secondly, the generator GA is also the helix tangent at G. Before we prove the two properties, we will explain why they are significant. In the first place, if the generator through A coincides with the helix tangent at G, it is a very simple matter to find its direction. In addition, we know that the intersection of the tooth surface with any coaxial cylinder is a gear helix, and we know that the tooth profile in the transverse section at plane z meets the base circle at point B",
            "35), which gave the angular coordinate difference (eA_eAO ) between two points AO and A, lying on the same gear helix at plane z=O and plane z, (13.70) This equation can be adapted to give the angular difference ~e between any pair of points on the same gear helix, when nei ther point lies in the plane z=O, (13.71) where ~z is the difference between the z coordinates of the two points. We now determine whether points G and B satisfy this equation. Since point E lies on the axial line through G, as shown in Figure 13.18, the difference between the e coordinates of B and G is equal to the angle between the radii through Band E. This is the angle ECB, shown in Figure 13.15, and its value is given by Equation (13.57). angle ECB tan qJtR (13.72) 336 Tooth Surface of a Helical Involute Gear Point B lies in the transverse plane z, and the axial distance between Band G can therefore be found from Equation (13.69), Rb tan 9>tR tan 1/Ib (13.73) It is evident that the coordinate differences given by Equations (13.72 and 13",
            "77) Direction of the Normal to the Tooth Surface at A 337 This equation can be interpreted as stating that to get from Co to A, we can first go to G, and then move along the helix tangent at G. Since we know that line GA is the generator through A, we have proved that the helix tangent at G coincides with the generator through G and A. We can therefore use Equation (13.76) to give the direction of the generator through A. In moving from Co to A by the route just described, the distance that we would travel along the generator is equal to the coefficient of nG in Equation (13.77). This qu&ntity /.I is of course equal to the length GA, as we can see in Figure 13.18. Direction of the Normal to the Tooth Surface at A The simplest method for finding the normal to the tooth surface at A is to find the directions of any two tangents through A. The two tangents define the tangent plane, and the direction of the normal must be perpendicular to both of them. One line which touches the tooth surface at A is the generator through A, since the entire generator lies within the surface, and is therefore tangent to it. Hence, the normal to the tooth surface at A is perpendicular to the generator direction nG A second tangent direction can be seen in /"
        ],
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    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure2.40-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure2.40-1.png",
        "caption": "Fig. 2.40 A picture of Greek stone thrower \u201cBallista\u201d",
        "texts": [
            " Single bow appeared in the Neolithic. To the Bronze Age, metal arrows replaced stone ones. Around 1000 BC, bronze dagger appeared in many parts of the world. Around 2000 BC, the Nubian mercenaries in the 11th Dynasty of Egypt first used stone throwers, which work on the principle of lever. Thereafter, they were spread to Greece, Rome, Persia, India, Assyria, Macedonia and other countries. Archimedes made giant stone throwers in his later years to fight against Rome\u2019s military invasion of Syracuse. Figure 2.40 shows a Greek stone thrower \u201cBallista\u201d (Gurstelle 2004). At the end of the 14th century BC, Egypt and the Hittites kingdom set out about 2000 war chariots in the battle of Syria, which was the earliest written record of war chariots. The earliest archaeological evidence of repeating crossbow was from a tomb at Qinjiazui in Hubei Province, China. It was dated back to the 4th century BC, the Spring-Autumn Period (Lin 1993). To the Three-Kingdoms Period, a type of repeating crossbow which shoot ten arrows successively (Fig"
        ],
        "surrounding_texts": []
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    {
        "image_filename": "designv10_4_0002876_s0022-460x(02)01213-0-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002876_s0022-460x(02)01213-0-Figure12-1.png",
        "caption": "Fig. 12. Driven shaft with gear and bearing shown.",
        "texts": [
            " In this section, the effects of integrating the gear inertia and boundary conditions are described. To account for the gear inertia, additional elements were added to the transfer function chain of the periodic shaft. Waves are assumed to propagate through the gear elements as if they were part of the same material as the shaft. The element material properties and geometry were made to reflect those of the steel gears available in the lab. The actual configuration for the transverse vibration testing is shown in Fig. 12. The model must also consider the added inertia of the bearings at either end of the shaft in order to accurately predict the propagation parameter. The analysis considers the bearings to be effectively pinned boundary conditions (see Fig. 13). The shaft was tested in two orientations (see Fig. 14). The propagation parameter for the periodic shaft in both configurations are shown in Figs. 15 and 16. Note that there are attenuation regions at lower frequencies for the periodic shaft including the bearing and gear inertias than for the shaft without their inclusion (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002845_978-94-015-9064-8-FigureI-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002845_978-94-015-9064-8-FigureI-1.png",
        "caption": "Figure I shows the four configurations corresponding to this type of singularity for a five-bar planar closed-loop linkage. The configuration space manifold of the five-bar is given implicitly by",
        "texts": [
            " This article presents a numerical method which systematically changes the parameters of a given Stewart-Gough platform with the goal to increase the number of real postures and ultimately to obtain an example which possesses 40 real postures. The proposed method is exemplified by way of one particular example of a Stewart-Gough platform for which we obtained 40 real postures. In this paper we will deal with a structure which consists of two rigid bodies which are held in relative position to each other by means of six rigid rods. The end points of these Fig. 1: A general Stewart-Gough platform with local coordi nate frames attached to base and platform. 7 rods are attached to the bodies via spherical joints (see Fig. I). If the length of the rods can be changed (by actuators) one body can be moved relative to the other. Such a mechanical design is then in the literature usually referred to as a Stew art-Gough platform (Gough, 1956; Stewart 1965). For our investigation we assume that the relative positions between each of the two sets of six points of each body (Ai' Bi, i = 1, . . . ,6) are defined and that the lengths of the connect ing rods ( Li ) are given. There fore the relative positions of the two bodies are also defined",
            " Depending on the complexity of the kinematic structure of the legs both problems may provide many solutions since both involve non-linear equations. In most cases the equations are difficult to solve in closed form. This paper focuses attention on fully parallel mechanisms with pure translational motion. In a previous paper (Parenti-Castelli et aI, 1998) the three dof parallel manipulator presented in (Tsai, 1996), henceforth called Tsai manipulator, was analyzed for evaluating the sensitivity of the mechanism to geometric parameter variation and manufacturing tolerances. Fig. I shows the schematic of the Tsai manipulator that features three independent legs whose endings are joined respectively to the base and to the platform by universal joints. Each leg comprises an actuated prismatic pair, between the two universal joints, that controls the leg length. The Tsai manipulator provides the platform with a pure translational motion with respect to the base. The model presented in (Parenti-Castelli et aI, 1998) retained only the topology of the Tsai manipulator taking into account a quite general geometry",
            " In this paper, a closed-form solution for the forward kinematics of a kind of parallel manipulator is obtained. An approach is developed to formulate the basic kinematic equations. Using this approach, the derived solution is neither nwnerical nor polynomial, but a simple closed-form solution, i.e., there is no need of iterative nwnerical procedure. Four possible solutions to the forward displacement problem for this manipulator are obtained. 2. Geometry and Coordinate Systems The considered three-legged parallel manipulator is shown in Fig.I. Two of the legs have SPS structure. The third leg has R\\-LR2-LP3-LR3 structure (the R\\ revolute joint is attached to the base and R3 revolute joint - to the moving platform, respectively). The active (actuated) joints are: i) the three prismatic joints of the legs; and ii) the revolute joint R\\ of the third leg which is connected to the base platform. The manipulator has four degrees of freedom. The axis of the revolute joint R3, which is attached to the moving platform, is perpendicular to the leg 3 (020 3) and coincident 149 with the line B3B2 ",
            " This paper presents a new type of a parallel robot that is a modification of and an extension to six-Degrees-Of-Freedom (DOF) of the three-DOF planar parallel robot presented by Mohammadi, Zsombor-Murray and Angeles,[1993]. The structure presented in the above mentioned paper is of two triangles, one stationary and one moveable, connected at three points, one at each side, by a combination of revolute and prismatic joints. The prismatic joints are actuated while the revolute joints are passive. This constitutes three-DOF of planar motion - two translational and one rotational - of the movable triangle (see Fig. I). Fig. 1: Double-Triangular planar manipulator Observing the work envelope of this structure, it seems that the area covered by the moveable triangle's center (output link), especially when a combination of translational and rotational motion is required, is relatively small. Fig. 2 depicts the work volume of the Double-Triangular manipulator for a translational motion and for a combination of translational and rotational motion. If, for example, a rotational motion of 55\u00b0 is required, then the useful work envelope becomes too small",
            " There were several attempts to generalize this structure (Wohlhart, 1993, 1995), the most successful of it was presented in a recently published paper (Roschel, 1996). Fig.1 gives a three dimensional picture of the Roschel Octahedron, which we are going to analyze below. The octahedron has five fundamental loops (L = 5) and the number of relative degrees of freedom provided by the joints is I-J; =24. Therefore, its internal degree of freedom should be I-J; -6L=-6, which means that it should be stiffer than simply stiff. As Fig. I shows, there is neither plane- 277 \u00a9 1998 Kluwer Academic Publishers. 278 Fig. I: 3D-picture of the Roschel Octahedron symmetry nor line-sym metry, the eight link bodies are different in size and the angles between the rotary joints in the gussets are differ ent although the octahe dron is movable with one degree of freedom. The well-covered secret of its movability is that in all positions each prismatic link-body tangentially touches an inscribed sphere. Let us have two bars ( a, f3) with intersecting axes fixed in space. The unit vectors na and n p in their axes determine positive directions",
            " (8, 181= 1, is the unit line of the Mozzi-Chasles screw-axis and 0= 0+\u00a3 a is the dual half-angle of the dis placement.) This paper shows that screws of a tan-screw form, T= tan 0 8, characterised by pitch PT= 20'/ sin 20, enjoy the same properties of linear combination. Screws of a particular sin-screw form S= sin 0 8, characterised by pitch Ps= a/tan 0, have found recent use in representing finite displacements of a rigid body. (8, 181= 1, is the unit line of the screw-axis and 0= 0+\u00a3 a is the dual half-angle of the displacement.) It is found, when a body with spa tial symmetries of figure is relocated - or, equivalently, when a displacement is incompletely specified - that the (possibly infinite) set of screws available to the body in achieving the relocation is described by linear combination of a small basis set, if the screws have that sin-screw form. This result has been established for a number of particular kinematic situations (Parkin, 1992; Huang et.al., 1994; Hunt et.al., 1995). More re cently, by observing that the symmetry sin-screws of a body - screws of displacements that leave the body invariant - themselves constitute a lin early combined set, it has been shown that the result applies generally, and extends to the corresponding biquaternions (Parkin, 1995; Parkin, 1997)",
            "(12) by forward substitution because of the lower-triangular structure of UT . Now, with y known, w can be found as w=HTy. (13) Substituting eq.(13) into eq.(6) yields iJ = HTy+h. (14) The RR problem being solved by integrating eq.(14) to obtain 8. The whole process from planning the trajectory until implementing it on the robot is outlined in Figure 1, where RVS stands for the Robot Visualization System, a software package developed at CIM for robot design and control (Wu et al., 1997). The robot of that figure is the C3 Arm, a four-axis isotropic robot for three-dimensional positioning tasks. Before applying the OP to the C3 Arm, the desired trajectory in the Carte sian space has to be defined. This trajectory must be generated in such a Produce a data file containing the joint angles of the robot trajectory in the Produce a data file containing the joint angles of the robot Figure 1. A flowchart of the RR process. 429 Produce a data file containing the trajectory in the Cartesian space, as a result from forward kinematics, performed way that the resulting joint-space trajectory obtained from the RR process will be smooth",
            " Here, the geometric way is the use of linear mani folds of correlations and quadratic transformations. By these methods we show that the anchor points have to be conjugate points with respect to 3-dimensional linear manifolds of correlations. This result is used to give all possible configurations of anchor points of architecturally shaky SGP. The paper is sequel to paper [Mick -Roschel 98]. Therefore references to it are prefixed \"I\". It deals with six legged SGPs given by six pairs of an chor points Xi and Yi (i = 1, ... ,6), each set on a plane c and t.p, resp. (see Fig. I.1). In theorem I.4.1 we gave a characterization of architecturally shaky platforms of this type. Now we discuss these results in a geometric context: Linear manifolds of correlations are used to give a geometric char acterization of the six pairs of anchor points Xi and Yi(i = 1, ... ,6). It is shown the theory of n-fold conjugate pairs of points illuminates Karger's characterisation of architecturally shaky SGP [Karger 97]. The paper is organized as follows: In the second chapter well known geo metric results on linear manifolds of correlations between planes are used",
            " Thus all points on this conic section kl = k2 with equation XlX2(/1l,O - /LO,2) + XOXl(/LO,2 - /Ll,2) + XOX2(/1l,2 - /Lo,d = 0 (13) and their images under Ql,2 (4) are four-fold conjugate points with respect to K 3. As kl contains two singular points of Ql,2 the images are on a conic section again. Moreover, the restriction of Ql,2 to kl determines a projectivity from kl to Ql,2 (kd\u00b7 We consider a given platform with anchor points {Xi, Yi} E f X rp with coordinates (XO,i, XI,i, XZ,i)(YO,i, YI,i, Y2,;) (14) (i = 1, ... ,6) as in (1.16) (see Fig. I.l). As stated in I, chapter 4, archi tecturally shaky platforms have anchor points with coordinates satisfying (1.19). This is a system of 6 homogeneous linear equations for the 9 elements ajk of the matrix (ajk). We have T(aoo, aOl, a02, alD, all, a12, a20, a21, a22)t = (0, ... , O)t (15) with coefficient matrix T given by T~( YO,IXO,1 YO,IXI,1 YO,lXZ,1 YI,IXO,1 YI,IXI,1 YO,6 XO,6 YO,6 XI,6 YO,6 X2,6 YI,6 XO,6 YI,6 X I,6 YI,IXZ,1 YZ,IXO,1 YZ,IXI,1 y\",x\", ) (16) Yl,6 XZ,6 Y2,6 XO,6 YZ,6 XI,6 YZ,6 X2,6 The elements of T depend of the coordinates of the six anchor points {Xi, Y,;}",
            " where Xi denotes the i-th joint variable (the joints are numbered consecu tively from I to 5 in the clockwise direction, starting with the left-most base joint), Li is the i-th link length, Cij = COS(Xi + Xj), 8ij = sin (Xi + Xj), etc. At the four configurations shown, the rank of \\7 x <1} is less than 3, indicating a configuration space singularity. Figures 3 and 4 depict the configuration space manifold (front and rear views) for the five-bar linkage, projected onto the X1-X2-X5 subspace. In the other half of the configuration space manifold not depicted, the ellipsoid containing points A and B eventually converges to a single point, which we label H. The configuration space singularity of Figure Ia is indicated in Figures 3 and 4 by points C and D, which actually correspond to the same physi cal configuration: the joint configuration manifold \"wraps around\" at this point. Figure Ic corresponds to point E, while Figure Id corresponds to point G and F. The configuration space singularity of Figure I b corresponds to the point H (not shown in the Figure). As expected, the tangent space at all these configuration space singularities is no longer two-dimensional. 489 Case 2: Actuator Singularity This case corresponds to the metric in the joint space losing rank, i. e., rank G < m, so that G -1 will not exist. Recall that G is obtained by projecting the ambient space metric E onto M, where the choice of E reflects which joints of the mechanism are actuated. The rank of G therefore reflects the number of actuators that can be moved independently",
            " The base So is supposed to be J -XJ -YJ -ZJ J -XJ OJ rigid. The beams are connected by rigid joints noted LI, L2 , .. LD from the base to the tip. These joints have non null spatial extension. Each joint Lj has only one degree of freedom between S j_1 and S j parameterized by q'j and supported by the unit vector ~j' The joints are either prismatic or rotational. We identify the nature of the joint by a Boolean variable 0' j : if 0' j = 1 , the joint is prismatic, otherwise, the joint is rotational. Each joint Lj is composed oftwo rigid bodies (cf fig. I): the first one is attached to S j_1 and noted LI,j' the second one L2.j is attached to S j' We define two sets of points Aj=l..D and Bj=l..D such that Aj and Bj coincides respectively with the first and last point of the neutral line of Sj. We also define a third set of points Pj=l..n such that Pj can be considered as \" the geometric center\" of the joint. At last we complete for each joint, the vector ~j with two other unit vectors so as to define a joint frame denoted by Raj' centered in Pj , and on whose axis are attached to L1,j ",
            " As p :::;; (n-k), the system (5) can always be solved. During the process, when the rank of K drops, we repeat the method by designing a new basis of CWK. If rank(K) :::;; k-n+5, the joint configuration is singular. In the example given before of an anthropomorphic arm, we have chosen the set K as the joining of the six shoulder and wrist axis. The CWK basis was constituted of one wrench (p = 1), and the reciprocity condition was a 1 x 1 matrix. Let us consider a 7-DOF manipulator with nonzero offsets at shoulder and elbow (Fig.I). Joint variables and axis are called respectively qi and Li. In order to get reduced polynomial expressions, we opt for the variable change Yj = tan(q;f2). This change is valid as long as joint angles belong to }-1t,1t[ interval. Let us denote Si = sin(qi) and Tgi = tan(qi)\u00b7 537 Because axis pairs (L1, L3), (L3, L5) and (L5, L7) are respectively passing through a same point, let us opt for the set K={L1,L3,L5,L7}. We distinguish several cases according to the dimension of the manifold generated by set K"
        ],
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    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.7-1.png",
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        "caption": "Figure 16.7. Right-handed hob and spur gear.",
        "texts": [],
        "surrounding_texts": [
            "The most commonly used method for cutting helical gears is by hobbing. As always in generating cutting, one gear is used to cut another. A typical hob is shown in Figure 16.3, and it can be seen that, apart from the gashes forming the cutting faces, the hob is simply a helical gear, in which each tooth is referred to as a thread. A hob. 458 Gear Cutting II, Helical Gears Since the hob is similar in shape to a screw, its helix angle \"'sh is always large, particularly when there is only one thread. It is cust~mary to specify the shape of a hob by means of its lead angle, rather than its helix angle. For a right-handed hob, the lead angle Ash is defined as the complement of the helix angle, (16.13) where Ash and \"'sh are measured in degrees. For a left-handed hob, whose helix angle is negative, the lead angle can be def ined as follows, - 90 0 - '\" sh ( 16.14) so that we obtain a negative lead angle for a left-handed hob. In practice, it is generally the magnitude of the lead angle which is given in the specification, together with a statement to indicate whether the hob is right or left-handed. It is clear that the lead angle can be determined from the helix angle, and vice versa. In describing the geometry of the hobbing process, we will specify the shape of the hob by means of its helix angle, since the symbols will then agree with the notation used in Chapter 15, where we described the geometry of crossed helical gears. Figure 16.4 shows a hob in position to cut a gear blank, and since their axes are not parallel, it is clear that they form a crossed helical gear pair. During the cutting process, the hob and the gear blank are rotated about their axes with angular veloci ties wh and wg ' I n order to cut the teeth of the gear across the entire face-width, the hob is moved slowly in the direction of the gear axis, and the velocity of the hob center is called the feed velocity vh . The values required for the three variables wh ' Wg and vh are achieved by means of change gears or stepping motors in the hobbing machine. There are two additional settings which must be made when the hobbing machine is being set up. These are the shaft angle ~, which is the angle between the axes of the hob and the gear blank, and the cutting center Hobbing 459 distance CC, which is the distance between the two axes. In the remainder of this section, we will determine the values required for the machine parameters wh ' wg ' vh ' E and CC, if the hob is to cut a gear with Ng teeth, normal module mn , normal pressure angle ~ns' helix angle ~sg' and normal tooth thickness t nsg Before we discuss the details of the cutting process, we will first prove that, as usual, the gear will have the same normal module and normal pressure angle as those of the hob. We showed in Chapter 15 that the minimum condition for correct meshing of two crossed helical gears is that their normal base pitches should be equal. The corresponding result, when we consider a gear being cut by a hob, is that the normal base pitch of the gear will always be equal to that of the hob. Since the normal base pitch of the hob is equal to that of the basic rack, we can conclude that the normal base pitches of the gear and the basic rack are equal, and the gear can therefore mesh correctly with the basic rack. As always, the standard pitch cylinder of the gear is defined as its pitch cylinder when it is meshed with the basic rack. The normal pitch Pns and the normal pressure angle ~ns of the gear must 460 Gear Cutting II, Helical Gears then be equal to those of the basic rack, and hence equal to those of the hob. This result remains true, whether or not the cutting pitch cylinders of the gear and the hob coincide with the i r standard pi tch cylinders. In order to cut the gear described earlier, we must therefore use a hob with the same normal module and normal pressure angle as those specified for the gear. We consider next how to cut the required number of teeth, and the correct helix angle. When a rack cutter is used to cut a gear, the helix angle of the gear depends on the angle at which the cutter is set, so it might be expected that the helix angle of a gear being hobbed would be determined by the value of the shaft angle ~. This is not the case, however, and we will now show that the number of teeth cut in the gear blank, and the helix angle at which they are cut, depend only on the values chosen for wh ' Wg and vh \u2022 In Chapter 5, we defined the cutting point as the point where the cutter makes a cut on the final tooth surface, and we showed that this point corresponds to the contact point when the gear blank and the cutter are regarded as a pair of meshing gears. The situation is no different when the cutter is a hob. We described in Chapter 15 how to find the position of the contact point in a crossed helical gear pair, and this point becomes the cutting point when we consider a hob cutting a gear. As in any metal-cutting process, the shape of each tooth cut in a gear blank is the envelope of positions through which the hob moves, relative to the gear blank. For the purpose of determining this shape, it is helpful to neglect the gashes in the hob thread, so that the threads are regarded as continuous, and we can imagine that the teeth are formed in the gear blank by grinding, rather than by cutting. If the hob and the gear blank were a pair of crossed helical gears, there would always be at least one thread of the hob making contact with the gear. Hence, for the hob and the gear blank, there is always at least one thread which is in contact with the final tooth surface of the gear. We label the points in contact AOh on the hob, and AOg on the gear. After the hob turns through exactly one angular pitch, the position of the thread containing point AOh is occupied by the Hobbing 461 next thread, and the corresponding point Alh on this thread will now be the cutting point, touching a point A1g on the gear tooth adjacent to the tooth containing AOg. As the hob rotates, we can identify a sequence of points such as AOh and Alh on the hob threads, and AOg and A1g on the gear teeth. The points on the hob lie in the same transverse section and are evenly spaced, at angular intervals equal to the angular pitch. Of course, if the hob has only one thread, the angular pitch is 360 0 , and the points all coincide. On the other hand, the gear points do not lie in one transverse section, due to the feed of the hob in the direction of the gear axis, and each point is displaced axially a small amount relative to the next point. We now consider the position on the gear of point ANg , the cutting point when the hob has turned through Ng angular pitches. Since the gear is to have Ng teeth, points AOg and ANg must be on the same tooth. Hence, if the gear is a spur gear, ANg must lie on the axial line through AOg' while if the gear is a helical gear, ANg must lie on the gear helix through AOg. The distance through which the hob is fed during one revolution of the gear blank is called the feed rate f. Since the magnitude of f is small compared with the tooth dimensions, point ANg always lies close to the axial line through AOg. The gear blank must therefore turn through approximately one revolution while the hob turns through Ng angular pitches, which is a rotation equal to (Ng/Nh ) revolutions. In order to meet this requirement, the angular velocity ratio (wh/wg ) must be approximately equal to (Ng/Nh ), or exactly equal, when a spur gear is being cut. In the case of a helical gear, the small difference between the two ratios is one of the factors which determine the helix angle of the gear, as we will show later in this section. Once the settings are chosen for the hobbing machine, the value of (wh/wg ) is established, and the number of teeth that will be cut in the gear is then given by the following expression, NhWh Integer closest to (--) Wg (16.15) 462 Gear Cutting II, Helical Gears Having found how the value of Ng depends on the hobbing machine angular velocities wh and wg ' we now consider the helix angle. If points AOg and A1g lie at radius R, the positions of these points at various times can be plotted on a developed cylinder of radius R, as shown in Figure 16.5. The times at which the hob touches points AOg and A1g are called T and T', and the diagram shows the positions of AOg at time T, and A1g at time T'. Since the feed of the hob is in the direction of the gear axis, the line in the diagram joining AOg and A1g is in the same direction. The diagram also shows the gear helices through these points, which appear as straight lines making an angle ~Rg with the gear axis, and these are labelled helix 0 and helix 1. The point on helix 0 in the transverse section through A1g is labelled Ag \u2022 The position of helix 0 at time T' is shown by the dotted line, and the positions of Aog and Ag at this time are shown as AOg and Ag \u2022 In Figure 16.5, the length AOgA1g represents the hob feed between the times T and T', and AgAg represents the arc Hobbing 463 length moved by point Ag in the same time interval. Since helix 0 and helix 1 are gear helices on adjacent teeth at the same radius, their positions at any instant are exactly one tooth pitch apart. A1g and Ag lie on the two helices in their positions at time T', so the distance between these points is equal to the transverse pitch. We therefore obtain the following expressions for the three lengths, A A' 9 9 A A' 19 9 The time interval required for the hob to rotate through one angular pitch can be expressed in terms of the hob angular velocity, T' - T We now use triangle AOgA1gAg to relate the three lengths, A A' - A A' 19 9 9 9 and when their values are substituted, we obtain the following relation between wh ' Wg and vh ' 211' vh -N-- tan l/IR hWh 9 ( 16.16) The feed rate f of the hob was defined earlier as the distance moved by the hob during one revolution of the gear blank. It is customary to express the feed velocity vh in terms of f, _f_ (211') Wg (16.17) and with this substitution, Equation (16.16) takes the following form, tan l/IRg 211'R ( 16.18) 464 Gear Cutting II, Helical Gears The helix angle of the gear at radius R is expressed in terms of the lead Lg by Equation (13.31), tan IPRg and Equation (16.18) then becomes a relation giving the lead that will be cut in the gear, l(NhWh ) f - Ng Wg ( 16.19) The quantity (Ng/Lg) is equal to the reciprocal of the axial pitch, as we showed in Equation (13.36), and this can be expressed in terms of the helix angle IPsg by means of Equation (13.42), _1_ Pzg sin IPSg Pns (16.20) Hence, Equation (16.19) can be put into two alternative forms, giving either the axial pitch or the helix angle of the gear, _1_ Pzg l(NhWh ) f - Ng Wg (16.21 ) (16.22) It is an interesting result that, as we pointed out earlier, the helix angle cut in a gear is not affected by the shaft angle ~ of the hobbing machine. This angle is generally set equal to the standard shaft angle ~s' or in other words, equal to the sum of the helix angles of the gear and the hob, ~s (16.23) We showed in Chapter 15 that a pair of crossed helical gears can mesh correctly, even when the shaft angle is not equal to the standard shaft angle. It therefore follows that a hob can cut an accurate involute gear, even when ~ is not exactly equal to ~s. However, for the remainder of this section, we will assume that the shaft angle is set equal to ~s' and in a Hobbing 465 later section of the chapter we will discuss the consequences of a small change in this value. The last setting of the hobbing machine to be considered is the cutting center distance CC , and its effect on the tooth thickness of the gear. As we discussed earlier, the cutting process can be considered as equivalent to meshing with zero backlash. An expression for the normal backlash in a crossed helical gear pair was given in Equation (15.96), The length ~Cp Equation (15.47), in this expression (16.24) was defined by (16.25) and all the other quanti ties are defined on the pitch cylinders, as indicated by the notation. We are considering, at present, a hob cutting a gear blank when the shaft angle ~ is set equal to the standard value ~s. In this case the cutting pitch cylinders coincide with the standard pitch cylinders, as we proved in Chapter 15. If we replace RP1 and Rp2 in Equation (16.25) by Rsg and Rsh ' and set the backlash in Equation (16.24) equal to zero, these two equations give an expression for the normal tooth thickness cut in the gear, (16.26) The expression in brackets in this relation represents the hob offset. When the normal tooth thickness t h of the hob is ns equal to O.5Pns' Equation (16.26) has exactly the same form as Equation (16.12), which gave the normal tooth thickness of a gear cut by a rack cutter. If the normal tooth thickness of the hob is greater than O.5Pns' the normal tooth thickness of the gear is reduced by the same amount. Whatever the value of t nsh ' the effect of a change in the hob offset on the tooth thickness of the gear is identical to the corresponding effect caused by a change in the offset of a rack cutter. In Chapter 5, we stated that the tooth thickness of a gear cut by 466 Gear Cutting II, Helical Gears a hob is generally calculated as if the gear were cut by a rac k cutter. We have now shown that thi s procedure is essentially correct, prpvided the hobbing machine is set with its shaft angle ~ equal to the standard value ~s' There is a second manner in which the cutting action of a hob resembles that of a rack cutter. In the discussion following Equations (15.74 and 15.77), we showed that the path of contact in a crossed helical gear pair touches each base cylinder, and makes an angle (~- 'tp1) with the line of centers, when viewed in the direction of the axis of gear 1. Hence, in the case of a hob cutting a gear, the path followed by the cutting point touches the base cylinders of the gear and the hob, and makes an angle (~- 'tpg) with the line of centers, when viewed in the direction of the gear axis. If the shaft angle is set at the standard value, this angle becomes (1[2 - 't ), as shown in Figure 16.6, and the path of the sg . cutting point then appears identical with the corresponding path when the gear is cut by a rack cutter. It is for this reason that, when we check for undercutting in a gear, we can regard the hob as equivalent to a rack cutter. We check that Swivel Angle 467 there would be no undercutting if the gear was cut by the rack cutter, and this implies that there will also be no undercutting when in fact the hob is used. Swi vel Angle Earlier in this chapter, we stated that it is common practice to specify the lead angle of a hob, instead of its helix angle. It is also customary to specify the angular setting of the hobbing machine by means of the swivel angle, rather than by the shaft angle. Since a hob is shaped like a screw, its helix angle is always large, particularly in the case of a single-thread hob, for which the helix angle is typically about 85\u00b0. The helix angle of the gear being cut may of course have any value, but in the majority of gears, the magnitude of the helix angle is between 0\u00b0 and 30\u00b0. In general, right-handed hobs are used to cut right-handed gears, and left-handed hobs are used for left-handed gears. In most cases, therefore, the shaft angle is approximately equal to a right angle, and the swivel angle is defined as the amount by which the shaft angle differs from a right angle. For example, if the axis of the gear is vertical during the cutting process, the swivel angle a is defined as the angle which the hob axis makes with the 468 Gear Cutting II, Helical Gears horizontal. The standard shaft angle was defined by Equation (16.23), as the sum of the gear and the hob helix angles. We express the helix angle of the hob in terms of its lead angle, by means of Equation (16.13 or 16.14), and we obtain the following expression for the standard shaft angle, ,f, + 90\u00b0 - A \"'sg - sh (16.27) where the plus and minus signs refer to a right or Hobbing Machine Gear Train Layout 469 left-handed hob. We now define the standard swivel angle os' so that it differs by a right angle from the standard shaft angle, (16.28) As discussed earlier, the hobbing machine is generally set so that the shaft angle is equal to the standard shaft angle, and it then follows that the swivel angle is equal to the standard swivel angle. Figures 16.7 and 16.8 show the relations between the shaft angles and the swivel angles when a right-handed hob is used to cut a spur gear or a right-handed helical gear, while Figures 16.9 and 16.10 show the corresponding relations when a left-handed hob is used to cut a spur gear or a left-handed helical gear. Hobbing Machine Gear Train Layout We showed in Equations (16.15 and 16.22) that the number of teeth and the helix angle cut in a gear depend on the feed rate f and the angular velocity ratio (wh/wg ) in the hobbing machine, NhWh Integer closest to (----) Wg (16.29) 470 Gear Cutting II, Helical Gears sin I/I sg l(NhWh ) f - Ng Wg (16.30) It is helpful to examine how the gear trains in some typical hobbing machines are arranged, in order to achieve the values of Ng and I/I sg required in the gear. One type of hobbing machine is shown schematically in Figure 16.11. The rectangular boxes in the diagram represent gear pairs or gear trains, with the output-input ratio in each case given by the constant k. The symbol ki stands for the ratio of the index change gears, kf is the ratio of the feed change gears, and the other k values represent the gear trains built into the machine, whose ratios cannot be altered by the user. The values of wh and wg , and of the hob feed velocity vh ' can be read from the diagram in terms of the input angular velocity w 1 ' (16.31) (16.32) Hobbing Machine Gear Train Layout 471 (16.33) The feed rate f was given by Equation (16.17), in terms of Wg and vh ' and when these are expressed by means of Equations (16.32 and 16.33), we obtain a relation between the feed rate and some of the gear ratios in the hobbing machine, f The terms in brackets are combined into a single constant, known as the machine feed constant Cf , whose value is provided by the manufacturer of the hobbing machine. The feed rate is then expressed solely as a function of the ratio kf of the feed change gears, f (16.34) To obtain the ratio (wh/wg ) in terms of the hobbing machine gear ratios, we express wh and Wg by means of Equations (16.31 and 16.32), As before, the terms in brackets are combined into another constant, the machine index constant Ci , whose value is also provided by the manufacturer, and the angular velocity ratio is then given by the following expression, C\u00b7 1 k.\" 1 (16.35) We substitute this expression into Equations (16.29 and 16.30), and we obtain the number of teeth that will be cut in the gear, and its helix angle, in terms of the hobbing machine gear ratios, NhC. Integer closest to ( __ l) k i (16.36) {16.37l We now determine how the machine ratios should be 472 Gear Cutting I I, Helical Gears chosen, in order to cut a gear with the number of teeth and helix angle required. The feed rate f and the hob angular velocity wh are chosen to obtain good metal-cutting characteristics. The values depend on the size of the hob, the hardness of the material being cut, and the surface finish required. For more details, the reader should consult references such as the Gear Handbook [2]. Once a value for f is. chosen, the required ratio kf for the feed change gears is found from Equation (16.34), f Cf (16.38) The value chosen for wh is obtained by setting the input speed change, shown in Figure 16.11, to a suitable value. With the feed change gear ratio already selected, the index change gear ratio is used to determine both the number of teeth cut in the gear, and its helix angle. We choose the ratio ki so that it satisfies Equation (16.37), in order to obtain the required helix angle, NhCi ki f sin ~Sg (16.39) (1rm + N ) n g When this value for ki is substituted into Equation (16.36), we find that we also obtain the correct number of teeth, because the magnitude of the term (f sin ~Sg/1rmn) in the expression for ki is always very much less than 0.5. It is sometimes difficult to find change gears which provide exactly the value of ki given by Equation (16.39). Once the change gears have been chosen, their actual ratio ki should be calculated, and this value is substituted into Equation (16.37), to give the helix angle that will in fact be cut in the gear. Use of a Differential in the Hobbing Machine There is one major problem associated with hobbing machines, when they are designed in the manner shown in Figure 16.11. If a second cut is required, as is often the case, it is necessary to disconnect the feed drive, in order Use of a Differential in the Hobbing Machine 473 to return the hob quickly to its starting position. It is then very difficult to reset the machine, with the work table and the hob in exactly the correct positions. This problem can be overcome if a differential is incorporated into the hobbing machine. In order to determine the relation that must be maintained between the hob feed, the work table rotation and the hob rotation, we once again consider Equation (16.30), We use Equation (16.17) to express the hob feed rate f in terms of the feed velocity vh ' and we obtain the relation which must be maintained throughout the cutting process between the hob feed velocity, the table angular velocity, and the hob angular veloci ty, (16.40) A gear train with one degree of freedom can always be represented by a linear equation relating the angular velocities of the input and the output shafts. A differential is a gear train with two degrees of freedom, and it has three shafts, either two input and one output, or one input and two output. The angular velocities of the three shafts are always related by a single linear equation. Hence, as we can see from Equation (16.40), if the hob feed, the work table drive and the hob drive were all connected to the three shafts of a suitable differential, they would then always maintain the correct relative positions. The differential may be a simple planetary gear train, or one which is constructed of bevel gears. In either case, the output angular velocity w3 is a linear combination of the input angular velocities w1 and w2 ' and can therefore be represented by the following equation, (16.41) The constants k7 and ka of the differential depend on the design of the gear train, and need not concern us here. 474 Gear Cutting II, Helical Gears The complete layout of the hobbing machine is shown in Figure 16.12, where the differential is represented as a simple planetary gear train. The hob drive is connected to the sun gear of the differential, the table drive is connected to the planet carrier, and the feed is connected to the internal gear. As before, the index change gears and the feed change gears are represented by symbols ki and kf , and now there is a third set of change gears, the differential change gears, represented by the symbol kd \u2022 The constants k1 to k6 are the fixed ratios of the gear trains in the hobbing machine. The constant k6 represents the ratio of a worm and gear, connecting the differential change gears to the internal gear of the differential. This ratio is shown with a minus sign, since the hand of the helix in the worm is chosen so that a positive angular velocity in the worm produces a negative angular veloci ty in the gear. We pointed out earlier that the number of teeth and the helix angle cut in the gear depend on the feed rate f and the Use of a Differential in the Hobbing Machine 475 angular velocity ratio (wh/wg ). We therefore need to express these two quantities in terms of the hobbing machine gear ratios. We start by writing down a number of relations between the angular velocities, Wh k1w1 (16.42) Wg k2ki k3w3 (16.43) vh k2kik4kfw3 (16.44) w 2 k2kik4kfkd(-k6)w3 (16.45) The feed rate f, which was given by Equation (16.17), can now be expressed in terms of the gear ratios, f As before, the terms in brackets are combined into a single quantity, the machine feed constant Cf , and the feed rate is then given simply in terms of the feed change gear ratio, f (16.46) When Equations (16.42 and 16.43) are used to express wh and wg ' the angular velocity ratio takes the following form, wh k1w1 Wg k2k3kiw3 and the relation between w 1 and w3 is found from Equations (16.41 and 16.45), The last two equations are combined to give the angular velocity ratio in terms of the gear ratios, and we use Equation (16.46) to express the ratio kf in terms of the feed rate f, (16.47) 476 Gear Cutting II, Helical Gears We now define the machine index constant Ci and the machine di fferent ial constant Cd as follows, C. 1 k1 k2 k3k7 k3 k7Cf k1k4 k6kS As usual, the values of the machine constants Cf ' Ci and Cd are all provided by the manufacturer of the hobbing machine. Ci is a ratio, but Cf and Cd are lengths, since they are defined in terms of the feed rate f, which is the distance moved by the hob during one revolution of the work table. When the constants are substituted into Equation (16.47), we obtain the final expression for the angular velocity ratio, (16.4S) This expression is substituted into Equations (16.29 and 16.30), and we obtain the number of teeth and the helix angle that will be cut in the gear, corresponding to the feed rate f and the change gear ratios ki and kd in the hobbing machine, C\u00b7 fkd Integer closest to [Nh(k: + c)] 1 d (16.49) (16.50) Once again, we must determine how the change gear ratios kf , k i and kd should be chosen, in order to cut a gear with Ng teeth and helix angle ~sg' As before, we choose the feed rate f from metal-cutting considerations, and the ratio kf is then given by Equation (16.46), (16.51) If we are cutting a spur gear, or in other words a gear with zero helix angle, we can satisfy Equation (16.50) by setting the value of kd equal to zero, and choosing the value of ki as follows, Use of a Differential in the Hobbing Machine k. 1 477 (16.52) The conventional method for cutting a helical gear is to use the same value for ki , and to choose kd in a manner which then satisfies Equation (16.50), Cd sin IPsg Nh '/I'mn (16.53) An alternative expression for the required differential change gear ratio is found by combining Equations (16.20 and 16.53), (16.54) When we compare the last two equations, it is clear that it is much easier to select suitable change gears, giving the correct value for kd , if we design the gear so that its axial pitch Pzg is a round number, rather than its helix angle IPsg. There are times when it is difficult, or even impossible, to find change gears which provide the exact values for ki and kd , given by Equations (16.52 and 16.53). For example, when the value required for Ng is a large prime number, we cannot obtain the exact value for ki , since most sets of change gears do not contain gears with more than 120 teeth. Also, when the helix angle ~sg is very small, it may be difficult to obtain a sufficiently accurate value for kd \u2022 When these situations occur, we can choose the index gears so that their ratio ki differs slightly from the value given by Equation (16.52), and the differential change gears are then used to ensure that Equation (16.50) is still satisfied with sufficient accuracy. Since the index change gear ratio is close to the value given by Equation (16.52), it can be represented by an expression with the following form, k. 1 (16.55) where the quantity ~ may be either positive or negative. This expression for ki is substituted into Equation (16.50), and we obtain the corresponding value of the differential change gear ratio required to cut the correct helix angle, 478 Gear Cutting II, Helical Gears (16.56) We have determined the values of ki and kd in a manner that satisfies Equation (16.50), so we know that the correct helix angle will be cut. It is now necessary to substitute the values of ki and kd into Equation (16.49), in order to confirm that the gear will also be cut with the correct number of teeth. The expressions for ki and kd given by Equations (16.55 and 16.56) are substituted into the right-hand side of Equation (16.49), with the following result, (16.57) As we pointed earlier, the magni tude of the term (f sin ~sg/wmn) is always less than 0.5, so with these values of ki and kd , the number of teeth cut in the gear will indeed be equal to the number required. The change gear ratios given be Equations (16.55 and 16.56) can be used for cutting either helical or spur gears, whenever it is difficult to obtain the values given by Equations (16.52 and 16.53). It is interesting that the quantity a has cancelled out from the expression in Equation (16.57). This means that there is no theoretical limit to the value of a which can be used, and the ratio ki may therefore differ considerably from the value given by Equation (16.52). In practice, however, it is usually easier to select the differential change gears to obtain an accurate value for kd , if the index gears are chosen so that their ratio is close to the value given by Equation (16.52), and the magnitude of a is therefore small compared wi th 1. It is evident that a differential is useful in the design of a hobbing machine, since it facilitates the selection of the necessary change gears. However, the original purpose for which the differential was introduced, as we discussed earlier in the chapter, was to maintain the correct relation between the hob feed, the work table rotation and the hob rotation, during a rapid return of the hob to its starting position. Figure 16.13 shows how this purpose is achieved. The drive is disconnected, by means of a dog clutch, between the feed change gears and the feed drive. An auxiliary motor, Theoretically Correct Shape for the Hob Thread 479 known as the hob rapid traverse motor, is then used to drive the hob feed. The drive passes through the di fferent ial, causing the work table to turn at exactly the correct speed, so that the helical teeth in the gear mesh continuously with the threads of the hob. During the entire return motion of the hob, only a very small rotation of the table is required, compared with the many revolutions that take place while the gear is being cut. Hence, the return of the hob can be carried out quite quickly, without damage to the gearing driving the work table. Theoretically Correct Shape for the Hob Thread We stated in Chapter 5 that a hob whose thread profile is straight-s;ded in the normal section will not cut exact involute tooth profiles. We are now in a position to estimate the amount of error, and to determine the correct normal 480 Gear Cutting II, Helical Gears profile in the hob thread. In Chapter 15, we proved that two involute helical gears can mesh with crossed axes, and maintain a constant angular velocity ratio. The hobbing process is essentially the same as the meshing of a pair of crossed helical gears. It therefore follows that, in order to cut correct involute profiles in the gear, the thread of the hob must also have the shape of an involute helicoid. In other words, the thread has an involute profile in the transverse section. The corresponding profile in the normal section is a convex curve, and not a straight line. However, because the helix angle of a hob is so large, the profile in the normal section is extremely close to the straight line. Hence, when a straight-sided hob is used to cut gears, the resulting error in the gear tooth profiles is generally small. We can estimate this error in the following manner. We described a method in Chapter 13 for calculating the profile of the normal section through a helicoid. We now use this method to find the profile of the normal section through the hob thread. We calculate the distances, at the thread tip and at the top of the fillet, between this profile and its tangent at the standard pitch cylinder, as shown in Figure 16.14. The profile of a straight-sided hob would coincide with this tangent, and a hob of that type would therefore cut too deeply into the teeth of the gear, in the regions near the fillet and near the tip. Figure 16.15 shows the normal section through an Effect of a Non-Standard Shaft Angle 481 exact involute helicoid tooth, and it also shows the profile we obtain when the gear is cut by a straight-sided hob. The maximum differences between the two profiles are approximately equal to the distances described earlier, by which the normal section profile of the involute hob deviates from the straight line. As we can see in Figure 16.15, the tooth shape cut by a straight-sided hob is similar to the shape of a tooth cut with tip and root relief. The errors caused by the use of a straight-sided hob are therefore sometimes beneficial, and this is one of the reasons for the continued use of straight-sided hobs, when true involute hobs are also readily obtainable. There are times, however, when the errors caused by straight-sided hobs may be excessive. This is often the case for gears cut by multi-thread hobs, or by single-thread hobs of large module, whose helix angles are usually less than 85\u00b0. Whenever there is a possibility that a straight-sided hob may cut too much tip and root relief in a gear, the procedure just described can be used to determine whether a true involute hob should be used. Effect of a Non-Standard Shaft Angle In an earlier section of this chapter, we described how to calculate the tooth thickness cut in a gear, when the shaft angle ~ of the hobbing machine is set equal to the standard value ~s. We stated at that time that we would still obtain a 482 Gear Cutting II, Helical Gears correct involute profile in the gear tooth, even if the values of E and Es wer~ not the same. The only effect of the altered shaft angle is a change in the tooth thickness, and we will now discuss briefly how the new tooth thickness can be found. Since it is not generally necessary to make this calculation, we will simply outline the steps, without presenting all the equations. When the shaft angle is not equal to its standard value, the cutting pitch cylinders of the gear and the hob do not coincide with their standard pitch cylinders. The first step is therefore to calculate the cutting pitch cylinder radii R~g and R~h. Knowing the normal thread thickness t nsh of the hob at its standard pitch cylinder, we then calculate its normal thread thickness t nph at the cutting pitch cylinder. To find the normal tooth thickness cut in the gear, we regard the hobbing process as the meshing of a crossed helical gear pair with zero backlash. An expression was given in Equation (15.96) for the normal backlash in a crossed helical gear pair, The length ~cp in this equation was defined by Equation (15.47), as the difference between the center distance and the sum of the pitch cylinder radii. For the situation of a hob cutting a gear, ~cp would represent the difference between the cutting center distance and the sum of the cutting pitch cylinder radii, We combine these equations, and set the backlash Bn equal to zero, to obtain the normal tooth thickness t npg cut in the gear. The final step is to calculate the corresponding normal tooth thickness t nsg of the gear at its standard pi tch cylinder. If we carry out this calculation, we will find that the normal tooth thickness t nsg cut in the gear is almost independent of the shaft angle E. In other words, the tooth thickness is hardly affected by a small change in the shaft Geometric Design of a Helical Gear Pair 483 angle, provided of course that the cutting center distance is left unchanged. However, the radii of the cutting pitch cylinders are very sensitive to the shaft angle value. In particular, a small change in the value of ~ can move the cutting pitch cylinder of the hob right off the surface of the hob thread. In the absence of experimental evidence, it is not certain what effect this may have on the tooth surface quality. Therefore, although the shaft angle need not theoretically be set equal to its standard value, it is nevertheless recommended that in practice this value should continue to be used. Geometric Design of a Helical Gear Pair In the final section of this chapter, we outline a procedure by which we can choose the helix angle, the profile shift values and the gear blank diameters, for a pair of helical gears intended to mesh on parallel shafts at an arbi trary center di stance C. Since the standard center distance depends on the helix angle, (16.58) it would appear that we can always choose the helix angle so that the standard center distance Cs is equal to the center distance C. In this case, the pitch cylinder of each gear would coincide with its standard pitch cylinder. However, as we will show, it is not always practical to choose the helix angle in this manner, and there is no particular advantage in doing so. When the gears are cut by a pinion cutter, the helix angle of each gear is equal to that of the cutter, so the choice of ~s is limited by the cutters that are available. When a rack cutter is used to cut the gears, the cutter veloci ty v r and the gear blank angular veloci ty must be related by Equation (16.11), 484 Gear Cutting II, Helical Gears This equation must be satisfied exactly, because an incorrect value for vr would result in uneven spacing of the teeth on the gear. However, when ~s is chosen so that Cs is equal to C, it may be impossible to find change gears giving the exact relation between vr and wg \u2022 In general, it is probably easiest to obtain the required helix angle when the gear is cut by a hob, and the differential change gear ratio is given by either Equation (16.53) or Equation (16.56). Even in this case, it may be difficult to find a set of change gears giving a sufficiently small error. The effort required is seldom justified, because a gear pair can be designed quite satisfactorily, assuming only that Cs is approximately equal to C. The procedure is essentially the same as the one described in Chapter 6, for the design of a spur gear pair. For the reasons just outlined, it is generally best to choose the helix angle ~s so that the gears can be cut wi thout difficulty, and at the same time the standard center distance Cs is slightly less than the center distance C. The value of Cs should lie within the range given by Equation (6.14), C (16.59) The design procedure now consists in the choice of suitable profile shift values, and the gear blank diameters, in order to obtain the backlash required, and adaquate values for the working depth and the clearances at each root cylinder. We consider the meshing geometry in a transverse plane, and the design steps are then identical to those used in the design of a spur gear pair. For a helical gear pair, it is customary to specify the normal backlash Bn' rather than the circular backlash B. It is therefore necessary to calculate a number of the gear parameters in the transverse plane, before we can consider the transverse plane geometry. The values of mt' Rs1 ' ~ts' Rb1 , Rp1 ' ~p' ~tP' Ptp' and Bare found from Equations (13.148, 13.150, 13.151, 13.152, 14.28, 14.7, 14.8, 14. 10 and 14.72). (16.60) (16.61) Geometric Design of a Helical Gear Pair B tan tl>ns cos \"'s Rp1 tan \"'s Rs1 Rb1 Rp1 21TC 485 (16.62) (16.63) (16.64) (16.65) (16.66) (16.67) (16.68) The design of a helical gear pair with parameters mn and tl>ns' and normal backlash Bn' has now been effectively replaced by the design of a spur gear pair with parameters mt and tl>ts' and circular backlash B. We use the method described in Chapter 6, and in particular Equations (6.45 - 6.53), to carry out the necessary steps. Since the procedure was explained in Chapter 6, the equations will be presented here with very little explanation. We start by writing down the transverse tooth thicknesses at the pi tch cylinders, 1 2\"(Ptp-B) + tlttp (16.69) 1 2\"(Ptp -B) - tlttp (16.70) where tlttp is a quantity chosen by the designer, to increase the tooth thickness in one gear, and reduce it in the other. The next four equations are given for gear 1 only, since the corresponding equations for gear 2 are found by interchanging the subscripts 1 and 2. t ttsl R [.:..!E..!. + 2(inv tP tp - invtl>ts\u00bb) (16.71) s 1 Rpl 1 tI> (tts11 (16.72) e 1 2 tan 2\"1Tmt ) ts bs1 a r - e 1 (16.73) 486 Gear Cutting II, Helical Gears b + R - R sl p1 sl (16.74) The addendum values ap1 and ap2 are chosen to give a working depth of 2.0mn , and equal clearances at each root cylinder, mn - ~(bp1 - bp2 ) 1 mn + 2(bp1 - bp2 ) (16.75) (16.76) And finally, we obtain the diameters of the two gear blanks, (16.77) (16.78) Once the dimensions of the gear pair are all chosen, the designer should of course check, as in the design of a spur gear pair, that there is no interference or undercutting, and that the contact ratio, the root cylinder clearances, and the tip cylinder tooth thicknesses are all adaquate. Gear Cutting II, Helical Gears 487 Numerical Examples Example 16. 1 A 55-tooth helical gear with normal module 4 mm, normal pressure angle 20 0 and helix angle 30 0, is to be cut with a normal tooth thickness of 6.915 mm. Calculate the cutting center distance, and the radius of the root cylinder in the gear, if it is cut by a 32-tooth pinion cutter with a normal tooth thickness of 6.40 mm, and a tip cylinder diameter of 158.12mm. mn=4, ~ns=200, ~s=300, Ng=55, t nsg=6.915 Nc =32, t nsc =6.40, RTc =79.06 Example 16.2 Rsg = 127.017 mm ~ts 22.796 0 Rbg = 117.096 ttsg = 7.985 73.901 68. 129 7.390 inv ~~p = 0.024565 ~~p = 23.471 0 201.932 mm 122.872 mm (13.113) (13.113) (16.6) (2.16,2.17) (16.7) (16.8) A hobbing machine has an index constant C. of 24, and a 1 differential constant Cd of 25 mm. Calculate the change gear ratios required to cut a 49-tooth gear with a normal module of 5 mm and a l)elix angle of 23 0, using a 2-thread hob. C.=24, Cd=25, N =49, Nh=2, m =5, ~ =23 0 1 g n s 488 Gear Cutting II, Helical Gears k. = (48/49) 1 kd = 0.3109340 40.201 mm (16.52) (16.53) (16.20) The index change ratio can obviously be provided by a single gear pair. The differential ratio can be achieved with good accuracy by two gear pairs, having ratios of (24/66) and (59/69). It is not always easy, however, to find change gears which give the required ratio. In the case described in this example, it would have been simpler if the gear pair had been designed with an axial pitch of 40 mm, in which case the required differential change gear ratio would have been exactly (25/80). Example 16.3 When lead screws and other transfer mechanisms are converted from inches to mms, it is sometimes necessary to introduce a factor of 25.4 into their drives. This factor requires a gear with 127 teeth, which is difficult to cut using conventional change gear ratios, because 127 is a prime number, and most sets of change gears do not contain gears with more than 120 teeth. Use Equations (16.55 and 16.56) to choose the ratios to cut a 127-tooth spur gear wi th a single-thread hob, when the hobbing machine has a feed rate of 0.020 inches, and the machine constants Ci and Cd are 24 and 0.5 inches. Required ki = 0.1889764 (16.52) Choose index change gears with ratios (24/41) and (31/96). (24/41) x (31/96) - (1/31) 0.8064516 (16.55) (16.56) The differential ratio can be provided by a single gear pair with a ratio of (25/31). Chapter 17 Tooth Stresses in Helical Gears Introduction The calculation of the tooth stresses in a helical gear is considerably more complicated than the corresponding calculat ion for a spur gear. The contact stress and the fillet stress in each tooth depend on the intensity of the load, and on its position. Since the load intensity varies, as the position of the contact line moves up or down the tooth face, it is not easy to decide when the maximum stresses will occur. As we pointed out in Chapter 11, we consider in this book only the static stresses that would occur if the gears were not rotating. The actual stresses that exist in normal operation are found by multiplying the static stresses by various factors, to account for dynamic effects, type of loading, and so on. Values for these factors are given in the AGMA Standard referred to in Chapter 11 [6]. The method described in this chapter for calculating the static stresses is based on the AGMA method, but differs from it in certain respects. A summary of the differences will be presented at the end of the chapter. Tooth Contact Force In a helical gear pair, there are generally several tooth pairs which are simultaneously in contact. The contact in each tooth pair takes place along a straight line, which coincides with one of the generators in each tooth. In order to calculate the tooth stresses, we assume that the load intensity w is constant along all the contact lines. The value 490 Tooth Stresses in Helical Gears of w at any instant is then equal to the total contact force W, divid.d by the total contact length Lc' w (17.1) In this section of the chapter, we determine the value of W, corresponding to any specified value of the applied torque. And in the following section, we will describe how to calculate the contact length Lc. The direction n~ of the normal to the tooth surface at A, when A is a point on the contact line, was given by Equation (14.94), n~ = cos \"'b [sin t/ltp nx(O) + cos t/ltp ny(O)] - sin \"'b nz(O) (17.2) In the absence of friction, the contact force acts in the direction opposite to n~, and its component parallel to the gear axis is therefore (w sin \"'b). Hence, the component perpendicular to the gear axis, which is the useful component, is equal to (W cos \"'b) \u2022 The base cylinder of gear 1 is shown in Figure 17.1, with Contact Length 491 the plane of action of the contact force touching the base cylinder. The diagram also shows the component of the contact force perpendicular to the gear axis. We take moments about the axis, to obtain a relation between the applied torque M1 and the contact force W, (17.3) and we use the same method to find the corresponding relation between the contact force and the torque M2 appl ied to gear 2, (17.4) The contact force is found from either of these equations. By combining the two equations, we obtain a relation between M1 and M2 , which is the same as Equation (11.3), the corresponding relation between the torques applied to a pair of spur gears. (17.5) Contact Length As we stated earlier, there generally several tooth pairs in contact at any instant, and the contact length Lc is the sum of the contact lengths on each of these tooth pairs. In this section, we will derive a general expression for Lc' It turns out that we do not often need to make use of the general expression, since the cases required for the stress analysis are always special, and therefore simpler. However, it is a matter of interest to have the general result, and it also helps to determine when the maximum and minimum values of Lc occur. A transverse section through the gear pair is shown in Figure 17.2, with the plane of action touching the two base cylinders. As usual, the ends T1 and T2 of the path of contact are the points where the tip cylinders intersect the plane of action. Figure 17.3 shows the plane of action, with the axial lines through T1 and T2 meeting the transverse plane z=O at T10 and T20 , and meeting the transverse plane z=F at T1F and T2F \u2022 The region of contact is the rectangle T10T20T2FT1F. We stated in Chapter 14 that the lines of contact on the different contacting tooth pairs can be represented by a set of diagonal lines in the region of contact, each making an angle \"'b with the gear axis, and with a vertical spacing equal to the transverse base pi tch Ptb. To find the length of the contact lines in the rectangle, it is helpful to construct two additional triangles T'T 10T1F and T10T\"T20 , as shown in Figure 17.3. The value of Lc is then found as the length of the diagonal lines in triangle T' T\"T 2F' minus the lengths in triangles T'T 10T1F and T10T\"T20 \u2022 We proved in Chapter 14 that the lengths T' T 1 F and T 1 F T 2F are equal to mFPtb and mpptb' where mF and mp are the face contact ratio and the profile contact ratio, given by Equations (14.68 and 14.64), _1_ Ptb F tan \"'b (17.6) Contact Length 493 The plane of action. In addition, the length T'T2F is equal to mcptb' where mc is the total contact ratio, equal to the sum of mF and mp , (17.8) In order to find the value of Lc' we first consider a general triangle of height mPtb' where m can represent any of the contact ratios me' mF or mp. This triangle is shown in Figure 17.4, and the upper contact line is shown in a typical position, lying a vertical distance ePtb below the top corner of the triangle, where e is any number between 0 and 1. The number of contact lines in the triangle is equal to 494 Tooth Stresses in Hel ical Gears (n +1), where n represents the integral part of the number e e (m-e). If e is greater than m, there are no contact lines in the triangle, and the value required for ne is -1. We therefore define a function, n int(f) (17.9) where f is any number, and n is the largest integer which is less than or equal to f. If, for example, f has the values 2.2, 1.0 and -0.3, the corresponding values of n are 2, 1 and -1. The val ue of n e can then be expressed by the funct ion, n e int(m-e) (17.10) In the triangle shown in Figure 17.4, the upper contact line has a length (m-w)ptb/sin ~b' The next contact line is shorter than the first by Ptb/sin ~b' and so on. The total contact length Le can therefore be expressed as an arithmetic series, whose sum is given by the following expression, (17.11) We now apply this result to the three triangles in If we use this method to calculate the contact length Lc for various values of e, we will find the following results. Minimum and Maximum Values for Lc 495 The value of L is always a minimum when e is zero, and a c contact line passes through the upper corner T10 of the region of contact. And the value of L is a maximum when e is equal to c [mF - int(mF)], and a contact line passes through the other upper corner T1F of the contact region. Minimum and Maximum Values of Lc For the purpose of the stress analysis, we would expect to be most interested in the minimum value of Lc' since this corresponds to the maximum load intensity. Now that we know that the contact length is a minimum when a contact line passes through T10 , it is possible to find simpler expressions for the value Lcmin \u2022 We can simplify the expressions further, if we consider only gear pairs in which every transverse section has either one or two contact points. This condition means that the profile contact ratio lies between the following limits, < 2 (17.16) and this range includes all gear pairs of normal design. In the transverse section shown in Figure 17.2, there are two points Q and Q' marked on the plane of action. Point Q lies a distance Ptb below T l' and Q' lies a distance Ptb above T2\u2022 If the diagram represented a spur gear pair, Q and Q' would be the points on the path of contact corresponding to the ends of the period of single-tooth contact. In a helical gear pair, there is generally no period of single-tooth contact, because the total contact ratio mc is usually larger than 2. However, Q and Q' would represent the ends of the period of single-tooth contact in any particular transverse section, and it is therefore still customary to refer to these points as the end points of single-tooth contact. The region of contact is shown again in Figure 17.5, with the axial lines through Q and Q' cutting the transverse plane z=O a~ QO and QQ' and cutting the transverse plane z=F at QF and Qp.. We have stated that the value of Lc is a minimum when a contact line passes through point T 10. There must simultaneously be a second contact line through QO' since the distance between T10 and QO is equal to the transverse base pitch Ptb' Due to the symmetry of the rectangle, we can also argue that Lc is again a minimum when there are contact lines through T 2F and QF' We now consider a particular gear pair, with the contact lines shown in Figure 17.5. One contact line passes through point T10 , while a second line starts at QO' and intersects the plane z=F at point AF , somewhere between QF and QF' For this situation to be possible, the length mFPtb must be less than (2-mp)ptb' as we can see from the diagram. Such a gear pair is therefore defined by the condition, (17.17) and will be referred to as a very low face contact ratio (VLFCR) gear pair. A spur gear pair, in which the face contact ratio is zero, would fit into this category. The condition given by Equation (17.17) is equivalent to the statement that the total contact ratio mc is less than 2. This means that there are periods of the meshing cycle when only one tooth pair is in contact, which is the situation shown in Figure 17.5. The contact length Lcmin for this case can be read directly from the diagram, L . cmln F cos \"'b (17.18) Minimum and Maximum Values for Lc 497 The same region of contact is shown in Figure 17.6, but the contact line has moved up, so that it now passes through point Qp., and a new contact line is about to enter the region at T2F \u2022 During the period when the contact line moves between the positions of Figures 17.5 and 17.6, there is only one tooth pair in contact, and the contact length Lc remains constant, with the value equal to Lcmin given by Equation (17.18). The region of contact for a second gear pair is shown in Figure 17.7. The contact line which starts at QO now intersects the plane z=F at a point between QF and T1F \u2022 The face contact ratio must lie wi thin the following range, 498 Tooth Stresses in Helical Gears < (17.19) and this type of gear pair will be described as a low face contact ratio (LFCR) gear pair. We know that the contact length is at its minimum value, since one contact line passes through T10 \u2022 To calculate the value of Lcmin ' we take the length of the contact line through QO' and we add the length of the short contact line near T2F , L . cmln F cos 1/Ib + Ptb (m +m -2) sin 1/Ib F P The expression is simplified if we use Equation (17.6) to express Ptb in terms of F, L . cmln (17.20) Lastly, we consider gear pairs in which the face contact ratio is greater than 1, > (17.21) Gear pairs that fall within this category are known as normal helical gear pairs, since most helical gear pairs are designed with a face contact ratio larger than 1. The region of contact for a gear pair of this type is shown in Figure 17.8, with the contact lines in the positions Minimum and Maximum Values for Lc 499 corresponding to the minimum contact length. Starting from the left, there is one contact line passing through QQ' then there are a number of complete contact lines stretching from the bottom edge to the top edge of the region, and finally there are either one or two lines which intersect the right-hand edge. To find the value of Lcmin' we consider in turn each of the three groups of contact lines just described. We start by defining two new quantities nc and nF , as the integer parts of mc and mF , (17.22) (17.23) The number of contact lines crossing the upper edge of the region is nF , which means that the number of complete lines is (nF-1). The total number of contact lines is nc ' so the number crossing the right-hand edge is (nc-nF). Hence, the contact length Lcmin is found as follows, L . cmln Ptb \u2022\u2022 1. [1 + mp (nF-1) + (m -n ) + (m -n +l)(n -nF-1)] sIn \"'b c c c c c The result is then simplified, and expressed in terms of the face-width F, L . cmln 500 Tooth Stresses in Helical Gears We pointed out earlier that the maximum load intensity on a gear tooth corresponds to the minimum contact length, and for this reason we derived expressions for Lcmin ' However, as we will show later in this chapter, the fillet stress is often a maximum when the contact line passes through the corner T1F of the contact region, and this occurs when the load intensity is a minimum. We therefore also need expressions for Lcmax ' the maximum contact length. Minimum and Maximum Values for Lc lie in the following range, < The contact length is again the sum of the two lengths, and, as usual, we express the result in terms of F, 5{)1 (17.27) 502 Tooth Stresses in Helical Gears lower edge of the region is then equal to (nFP+2), and the total number of contact lines in the region is (nF+2). Hence, the number of complete contact lines is (nFP+1), and the number of lines crossing the left-hand edge of the region is (nF-nFP)' By considering the three groups of contact lines described earlier, we-obtain the following expression for the contact length, As before, we simplify this result, and express Lcmax in terms of F, Contact Stress In the last section of Chapter 14, we proved that when A is a contact point between a rack and a pinion, the line of contact through A and the common normal at A both, lie in the plane of action. The same is true when A is a contact point between a pair of helical gears. To prove this statement, we need only consider the imaginary rack between the gears, and make use of the result just stated, first for one gear and the imaginary rack, and then for the second gear and the imaginary rack. The plane of action for a gear pair is shown in Figure 17.12, with the contact line GA making an angle..pb with the n direction, as we proved in Equation (14.93). Near z point A, the tooth surfaces can be represented by two circular cylinders in contact, with their axes lying in the plane of action. Their radi i are shown as Pc 1 and Pc2' with the subscript c indicating that these are the radii of curvature when we make a section through the cylinders perpendicular to the line of contact. If we make a transverse section, as shown in the diagram, the cylinders appear as ellipses. For gear 1, the semi-minor axis of the ellipse is Pc1 ' while the semi-major axis is equal to (pc 1/cOS ..pb)' The radius of Contact Stress 503 curvature Pt 1 at point A in the transverse section through the tooth profile is then equal to the radius of curvature at the corresponding point of the ellipse, 2 Pc l (17.31) The corresponding equation for gear 2 can be written down immediately, (17.32) The maximum contact stress 0c between two cylinders of radii Pc1 and Pc2 was given by Equation (11.5),"
        ]
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure13.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure13.2-1.png",
        "caption": "Fig. 13.2 Approximate synthesis of path generation",
        "texts": [
            " Due to this reason, Freudenstein and Levitsky were both credited as the pioneers in modern kinematics of mechanisms (Angeles 1997). With regard to mechanism synthesis, the 1960s saw intensive research on precision point synthesis. However, this method has two critical drawbacks, namely limitation on the number of precision points, and the inability in handling some constraints. This fact motivated some researchers to explore alternative synthesis methods, such as the approximate point synthesis (Fig. 13.2) developed in the late 1960s. 13.1 Mechanism and Machine Science 467 Around the mid. 1960s, nonlinear programming was introduced to mechanism synthesis, becoming one of the most commonly used tools in approximate point synthesis. This optimum method was widely accepted in later MMS study, and found successful application in the design of flying shears, harbor cranes and hydraulic excavators (Erdman 1993; Chen and Yu 2014). Historically, invention of new mechanisms has heavily relied on intuition and inspiration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000061_physrevfluids.4.043102-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000061_physrevfluids.4.043102-Figure3-1.png",
        "caption": "FIG. 3. Schematic of the simplified two-dimensional projection of the axoneme. In this model, the axoneme is composed of two polar filaments x+ and x\u2212 and has centerline x. Nexin links are shown as elastic springs that resist sliding . Mechanical loads exerted by bound dynein motors result in an internal shear force density \u00b1 f (s, t ) that acts in the opposite direction on the two filaments, generating an active internal moment.",
        "texts": [
            " Without loss of generality, we will assume that t\u0302(0, t ) = e\u0302x, and therefore \u03c6(0, t ) = 0. (20) We have yet to specify the nature of the active internal forces and induced moments that drive the filament dynamics. Next, we present the model for internal axoneme mechanics and for the kinematics of molecular motors that are responsible for spontaneous oscillations. As a simplified model for the cross-linked flagellar bundle that composes the axoneme, we resort to a two-dimensional projection of the three-dimensional structure as illustrated in Fig. 3. In the complete \u201c9+2\u201d structure, the molecular motors connecting pairs of doublets lead to sliding forces that result in deformations. The structure of the axenomal cross-section, as depicted in Fig. 1, involves a cyclic arrangement of the dyneins, and therefore motors on opposite sides of the axoneme operate antagonistically, as in a \u201ctug-of-war.\u201d To capture this process within a minimal framework, we follow previous models [5,6] and idealize the axoneme as a pair of two polar elastic filaments (+) and (\u2212) separated by a constant distance a that are able to deform in tandem in the plane of motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000554_j.wear.2020.203201-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000554_j.wear.2020.203201-Figure4-1.png",
        "caption": "Fig. 4. Position of the ball in space and the coordinate systems.",
        "texts": [
            " Under dynamic working conditions, the contact load and sliding speed of each ball are different, mainly owing to the effect of the gyroscopic torque, centrifugal force, and contact angle. The modeling of the complete coordinate systems is explained in the following section. Accordingly, the analysis of the contact load on the ball\u2013raceway contacts and the analysis of the sliding velocities on the ball\u2013raceway contacts are introduced on the basis of various coordinate systems. Four coordinate systems [2] are established as shown in Fig. 4: the global coordinate system, rotating coordinate system, Frenet coordinate system, and contact coordinate system. The global coordinate system, (X,Y,Z), is fixed in space with the Z axis aligned with the axis of the screw. The rotating coordinate system, (xr  yr  zr), rotates with the same angle as the screw. The Frenet coordinate system, (t, n, b), is introduced to describe the motion of the ball center. (xm\u2019n\u2019  ym\u2019n\u2019  zm\u2019n\u2019 ) denotes the contact coordinate system. Subscript m\u2019 \u00bc A or B respectively denotes that the information applies to a ball in nut A or B",
            " According to Hertz theory, the relationship between the deformation and the normal contact force can be modeled by \ufffd \u03b4m\u2019si \u03b4m\u2019ni \ufffd \u00bc c2 E\u22c5 \" Ys\u22c5 ffiffiffiffiffiffiffiffiffiffiffiffiX \u03c1s 3 q 0 0 Yn\u22c5 ffiffiffiffiffiffiffiffiffiffiffiffiX \u03c1n 3 q 3 5 2 4 Q2=3 m\u2019si Q2=3 m\u2019ni 3 5; (29) where P \u03c1s and P \u03c1n are respectively the sums of the principal curvature of the ball\u2013screw track and ball\u2013nut track while Ys and Yn are respectively the auxiliary values of the elliptical integral for the ball\u2013screw track and ball\u2013nut track. When the axial force is applied, the axial displacements of nuts A and B are equal, which means \u0394\u03b4A \u00bc \u0394\u03b4B. Accordingly, combining Eqs. 26\u201329, 4 M \u00fe 2 nonlinear equations are obtained. Thus, under a certain axial load, normal contact loads of the 2 M balls and the axial forces acting on the two nuts can be obtained numerically using MATLAB software. This section describes the analysis of the speed difference between the ball and raceway. As shown in Fig. 4, the position vector OOAi \ufffd\ufffd! in the (X, Y, Z) coordinate system can be expressed as OOAi \ufffd\ufffd! \u00bc 2 4 rm cos\u00f0\u03b7\u00fe \u03b2A\u00de rm sin \u03b7\u00fe \u03b2A\u00de rm\u03b2A tan \u03b3 3 5 T X: (30) Taking the first-order derivative of Eq. (30) with respect to time, the velocity of the center of the ball is obtained as VOOAi \ufffd\ufffd! \u00bcOOAi \ufffd\ufffd! : : \u00bc 2 4 rm sin\u00f0\u03b7\u00fe \u03b2A\u00de\u22c5\u00f0\u03b7 : \u00fe \u03b2A : \u00de rm cos\u00f0\u03b7\u00fe \u03b2A\u00de\u22c5\u00f0\u03b7 : \u00fe \u03b2A : \u00de rm\u03b2A : tan \u03b3 3 5 T X: (31) The revolution velocity of the ball in nut A \u03c9mA, is obtained by taking the time derivative of \u00f0\u03b2A \u00fe \u03b7\u00de: \u03c9mA\u00bc \u03b2A : \u00fe \u03b7: \u00bc \u03b2A : \u00fe \u03c9 (32) where \u03c9 is the rotational speed of the screw"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000109_j.jallcom.2020.156866-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000109_j.jallcom.2020.156866-Figure5-1.png",
        "caption": "Fig. 5. The interaction process: (a) The initial stage; (b) the temperature gradient.",
        "texts": [
            " The temperature profiles over the time of the monitoring point located at the center of the scanning track with and without laser re-melting are shown in Fig. 4. The calculated temperature of the process with and without laser re-melting reached the maximum at the same time Subsequently, the temperature curves exhibited another peak due to the thermal conditions of the laser in situ remelting. The maximum temperature or first peak (T) was 2953 K; the second peak was defined as Tr. The temperature of the second peak was considerably higher and increased from 2174 K to 2770 K as the scanning speed decreased from 400 mm/s to 200 mm/s. As shown in Fig. 5b, at the track start, high laser energy and low powder conductivity led to a high transient temperature and an extremely large temperature gradient [40], causing a molten pool when the temperature exceeded the melting point of Tie6Ale4V (1933 K), as shown in Fig. 5a. As the moving distance increased, the heat diffusion and updated material properties resulted in a reduction in the maximum temperature and temperature stabilization. The temperature of the monitoring point decreased, but the temperature gradient was less than that during heating. As a result, the heat was also transferred from the heat source to this point. After the track ended, the laser re-melting was performed. The second peak occurred at the monitoring point. The temperature was lower than at the first peak (2690 K), although the scanning speed was the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000275_s00170-019-04851-3-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000275_s00170-019-04851-3-Figure3-1.png",
        "caption": "Fig. 3 Schematic illustration of the additive/subtractive hybrid manufacturing process (Du, Bai, and Zhang 2016)",
        "texts": [
            " The process of pairing additive manufacturing and traditional subtractive techniques is one of the recent hybrid manufacturing technologies. Additive/subtractive hybrid manufacturing incorporates directly injected powder or selected regions of a powder bed by scanning an energy source which results in melting then solidification of materials forming a part while simultaneous machining is done to remove traces of unwanted materials for enhanced precision. This alternating process is carried out repeatedly until the required geometry is achieved as illustrated in Fig. 3 [34]. Alternatively, this technology is employed for repair purposes whereby material powder is added layer by layer fitting to the defect geometry creating a metallurgical bond between new material and the damaged surface area of a part [4]. This reduces cost and extends service life of parts whether traditionally manufactured or 3D printed. Laser additive manufacturing technique is increasingly becoming established in a wide range of industrial applications. It is best suited for rapid manufacturing, refurbishment, and surface coating mainly in the demanding industries such as aerospace, automotive, tool making, and biomedical applications [7, 32, 35]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure3-29-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure3-29-1.png",
        "caption": "Figure 3-29 Sketch of pin-actuator for a printer mechanism.",
        "texts": [
            " In fact, we have shown that chaotic motions of very thin sheets of paper generate a broad spectrum of acoustic noise in the surrounding air. Impact Print Hammer Impact-type problems have emerged as an obvious class of mechanical examples of chaotic vibrations. The bouncing ball (3-2.9), the Fermi accel- Physical Experiments in Chaotic Systems 103 erator model (3-2.8), and the beam with nonlinear boundary conditions all fall into this category. A practical realization of impact-induced chaotic vibrations is the impact print hammer experiment studied by Hendriks (1983) (Figure 3-29). In this printing device, a hammer head is accelerated by a magnetic force and the kinetic energy is absorbed in pushing ink from a ribbon onto paper. Hendriks uses an empirical law for the impact force versus relative displacement after impact; u is equal to the ratio of 104 A Survey of Systems with Chaotic Vibrations displacement to ribbon-paper thickness: = -AEPpun, u<0 (3-3.8) where A is the area of hammer-ribbon contact, EP acts like a ribbon-paper stiffness, and ft is a constant that depends on the maximum displacement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000180_j.matdes.2020.109410-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000180_j.matdes.2020.109410-Figure6-1.png",
        "caption": "Fig. 6. Schematics of layer-wise scan strategy for (a) ML-Z: unidirectional scanning without layer-wise rotation, (b) ML-S: unidirectional scanning with 180 layer-wise rotation, and (c) ML-RT90: unidirectional scanning with 90 layer-wise rotation.",
        "texts": [
            " While the final case is the most representative of the AM process, insights gained from the simpler cases will provide important context to understand the results shown for the final case. In the first set, single-track simulationswere carried out to study the grain structure evolution within the melt pool. In the second set, multiple-track simulationswere carried out to reveal the grain structure formed within the overlap region between two neighboring tracks. In the third set, multiple-track and multiple-layer simulations were carried out to identify the features of grain structure formed in consecutive layers with several different scan strategies, as shown in Fig. 6. In this study, small scale simulations were conducted to advance the understanding of solidification behavior and subsequent as-built grain structures that are likely present regardless of the scale of the process, because the melt pool and heat effected zones are localized within the scale of the simulation shown in this study. In addition, the powderscale thermo-fluid flow simulation and the grain structure simulation are extremely time-consuming and thus limited to small scale problems. In all the simulations, the cell spacing used in the CA mesh is set to 1",
            " This is representative under the simplifying assumption that additional layers or trackswill result in a repeated pattern similar to how the second layer or track interacts with the first layer or track, i.e. that each subsequent layer interacts only with the powder and one previously deposited layer, meaning the remelting depth is less than the layer height. Based on the two-track simulation result presented in Section 3.2, a second powder layer is spread on the solidified tracks, and then another two tracks (labeled Track 3 and Track 4) are scanned as shown in Fig. 6 (a). This case is referred to as \u201cML-Z\u201d (multiple-track, multiple-layer with Z-shaped tracks). The melt pool sizes for Track 3 and Track 4 are listed in Table 4. The width and depth of the overlap region between the two tracks are 41.25 \u03bcm and 25.9 \u03bcm, respectively, with the overlap region of the first layer partially remelted. Although the remelted depth between layers depends on location across the tracks, the mean remelt depth is 31.25 \u03bcm. In addition, Fig. 17 plots surface temperature versus location along the centerline of the melt pools of the 2-track-by-2-layer case",
            " The scan strategy used for this multiple-layer simulation promoted gradual texture strengthening track-by-track and layer-by-layer by directing the preferential growth direction, i.e. the thermal gradient direction, consistently in approximately the same direction. As a consequence, the mechanical behavior of the build will likely be anisotropic, which is one of the main performance concerns for additive manufacturing [2]. To provide insight into the microstructure development and resulting texture in various layer-wise scan strategies, another two layer-wise scan strategies are considered: ML-S shown in Fig. 6(b) and ML-RT90 shown in Fig. 6(c). These two scan strategies have the same raster pattern for the first layer as ML-Z, but a different scan direction on the second layer. The ML-S case (Fig. 6(b)) has a counterdirectional scan direction compared with the first layer, while the MLRT90 (Fig. 6(c)) has a 90\u00b0 layer-wise rotation angle. Different layer-wise scan strategies lead to the different alignment of melt tracks and thermal profiles along the build direction, which, based on the understanding obtained in the previous sections can significantly change the microstructure, as illustrated in Fig. 19. The simulated grain structure after deposition with the ML-S strategy is shown in Fig. 20 (a1). Although still columnar, the grains are more complex than those made with the ML-Z strategy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003511_j.matchar.2005.12.005-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003511_j.matchar.2005.12.005-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagrams of (a) shell and (b) block LENS builds.",
        "texts": [
            " While LENS processing parameters such as laser power, travel speed, and powder feed rate may have significant influence on void formation, characterization and careful choice of starting powders may also be an important means to control porosity. Two types of stainless steel powders and deposits were investigated: 304L and 17-4PH. Five lots of atomized powder \u2013 one lot of 17-4PH and four lots of 304L (denoted as 304L-1, 2, 3 and 4) \u2013 were characterized and then used to produce LENS builds. The nominal powder sizes, reported by the manufacturers, were \u2212100/+270 mesh (approximately 50 to 150 \u03bcm diameter). Thin-wall \u2018shell\u2019 and three-dimensional \u2018block\u2019 builds (Fig. 1) were deposited on stainless steel substrates with the following process parameters: laser power 520 to 700 W, powder feed rate 30 to 36 g/ min, travel speed 50, 100, and 200 cm/min. For the shell builds, the laser moved in a single direction (clockwise or anticlockwise) around the structure. For the block builds, the laser direction alternated from layer to layer, as shown schematically in Fig. 1b. Fig. 1a shows a partial shell build and Fig. 1b shows an entire block build (note that Fig. 1a and b are not drawn to scale and the dimensions are indicated for information only). Note also that the typical shell layer thickness was 250 \u03bcm and the typical block layer thickness was about 750 \u03bcm. In general, the block geometry could be deposited with thicker layers and, therefore, faster build times. The major process variables in this study included starting powder characteristics, laser travel speed, and build geometry. To deposit material with faster travel speeds, the laser power and/or powder feed rate must also be increased to maintain similar heat inputs. The starting powder morphology was characterized by quantitative image analysis (200 times magnification) to determine powder size and distribution, amount of porosity, and pore size and distribution. Thin-wall deposits were prepared in vertical cross- sections (Fig. 1) to show all layers from the substrate to the top of the deposit. Block deposits were sectioned in the x\u2013z plane to show individual layers in both longitudinal and transverse orientations. Image analysis was performed on as-polished deposits (50 times magnification) to characterize the amount of porosity, pore size, and distribution. Since relatively low magnification was needed to obtain statistically meaningful bulk porosity measurements, very small pores (1\u20132 \u03bcm in diameter) were not included in the analyses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.8-1.png",
        "caption": "Figure 7.8: PPR robot",
        "texts": [
            " In fact, a peculiar feature of nonholonomic systems is the nonzero drift (also called holonomy or phase angle) that occurs in n - m generalized coordinates when the remaining m perform a cyclic motion [50]. The kinematic control system (7.36) is underactuated. Depending on the choice of the generalized inverse G, i.e., on the chosen inversion strategy, system (7.36) may or may not be controllable. Correspondingly, the robot motion is subject to a kinematic constraint that is nonholonomic or holonomic. Below, we shall study in detail one simple redundant manipulator. PPR Robot Let us consider the planar PPR robot shown in Fig. 7.8, having two prismatic and one revolute joints. This robot is redundant for the task of positioning the tip of the end effector in the plane with unspecified orientation of the end-effector (n = 3, m = 2). Denoting by P the length of the third link, the direct kinematic equations are P:r Q1 + f'c3 Py q2 + f.s3, where S3=sinq3 and c3=cosq3. The differential kinematics is expressedas eq. (7.35), where the analytic .Jacobian matrix J(q) = [ 01 o -f.s3 J 1 f.c3 is always of full rank. The k subscript in the ",
            " In case I, the system starts from q0 = ( -1, 3, Jr/3), while, in case II, from q0 = (1,3,7r/3). The simulation results in Figs. 7.9-7.11 show the planned Cartesian paths. t\\ote that the sinusoidal steering method requires larger motions, due to its two-phase structure, while the other two controllers behave similarly. Moreover, the presence of cusps in the path corresponds to motion inversions with zero velocity, similarly to whCI.t occurs in the parking maneuvers of a car. PPR robot Consider again the kinematic model of the PPR robot of Fig. 7.8 under weighted pseudoinversion, as expressed by eq. (7.37). A particular dass of reconfiguration tasks is the one in which the initial and final configurations provide the same end-effector position, that is k(qf) = k(qo). (7.48) Correspondingly, as the robot moves under the task control input u, the end-effector will trace a dosed path. Let T be the desired duration of a reconfiguration cyde. One way to find suitable open-loop commands is to transform system (7.37) into chained form, which is certainly possible for a nonholonomic system with m = 2 and n = 3, and use one of the previous methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000245_ijvd.2019.109873-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000245_ijvd.2019.109873-Figure5-1.png",
        "caption": "Figure 5 Welded beam design (see online version for colours)",
        "texts": [
            " For the speed reducer problem NAMDE algorithm is compared with UFA, SSBSA, passing vehicle search (PVS) (Savsani and Savsani, 2016), \u03b5DE-LS, \u03b5DE-PCGA, IAPSO, crossoverbased artificial bee colony (CB-ABC) (Brajevic, 2015), Rank-iMDDE, UABC, COMDE, MVDE, DELC and PSO-DE. The results of the compared methods are presented in Table 7. From Table 7 it is clear that all methods obtained the optimal results in terms of best solution except PSO-DE. Besides, Rank-iMDDE is the most robust among the used methods in solving this problem. NAMDE is slightly worse than COMDE, DELC, \u03b5DE-LS in terms of standard deviation. The goal is to minimise the manufacturing cost of the welded beam (Sandgren, 1990), as shown in Figure 5. The design is subject to constraints on shear stress, bending stress in the beam, buckling load and beam deflection. In addition to this, there are four continuous variables:h, l, t. For the welded beam design problem NAMDE algorithm is compared with UFA, IGMM, MCEO, SSBSA, IAPSO, Rank-iMDDE, COMDE, DELC, WCA, social-spider algorithm (SSO-C) (Cuevas and Cienfuegos, 2014), hybrid technique (HTDEA) (Yildiz, 2013a), hybrid robust particle swam optimisation algorithm (HRPSO) (Yildiz, 2012) and multiple trial vector based DE (MDDE) (Mezura-Montes et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000736_j.compstruct.2021.113822-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000736_j.compstruct.2021.113822-Figure12-1.png",
        "caption": "Fig. 12. The deformations of the HMS beam with x0-y0-plane sinusoidal magnet direction of axis z0, i.e. \u03b8a = \u03c0/2, with different magnetic forces P for (a) n = 1,",
        "texts": [
            " It can be observed that the HMS beam bends in the x0\u2010y0 plane with large deflection. Compared to the uniform magnetized beam in Section 5.1, the deformed shapes of the present nonuniform HMS beam are more complex. 5.2.2. Out-of-plane applied magnetic field The deformations of a planar magnetized beam under an in\u2010plane external magnetic field are two\u2010dimensional, as shown in Figs. 10 and 11. To generate complex 3D configurations, out\u2010of\u2010plane magnetic fields are required. The results of the beam\u2019s deformations under an applied magnetic field with \u03b8a = \u03c0/2 are given in Fig. 12 and the counterparts for \u03b8a = \u2013\u03c0/4, \u03c8a = \u03c0/4 are displayed in Fig. 13. As shown in these figures, when an out\u2010of\u2010plane magnetic field is applied, the HMS beam with planar nonuniform magnetization will tend to align the direction of residual magnetic flux density with the direction of Ba by 3D bending and twisting deformations. The twisting angle of the 3D large\u2010deformation beam is large, and thus the twisting deformation can play a significant role. By changing Br 0 or Ba, various 3D configurations of the HMS beam can be obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000508_soro.2020.0006-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000508_soro.2020.0006-Figure2-1.png",
        "caption": "FIG. 2. Molding, degassing, curing, and assembly steps for prototyping the flexible catheter MiFlex.",
        "texts": [
            " Afterward, the theoretical workspace of the catheter based on the constant bending radius assumption is obtained and its validity is investigated by experimental comparison. Furthermore, the proposed learning-based forward and inverse kinematic model of the catheter is described and the accuracy of those is investigated. In the end, the experimental test procedures and setups for studying the performance of the proposed trajectory tracking are described. The prototyped catheter in this study, named as MiFlex, is a tendon-driven catheter with four inextensible tendons. Figure 2 shows the fabrication steps and finally the size and assembly of the catheter. The selected dimensions for the catheter prototype were 6 mm in diameter and 40 mm in length. The selected diameter was to replicate an 18-Fr (1Fr = 1/3 mm) catheter, and a 40 mm length was according to Refs.46,47 for the average transversal diameter of the right atrium in adults diagnosed with AFib. For the fabrication, a cylindrical mold was rapid prototyped with a 3D printer (Replicator+; MakerBot, NY). Also, a square platform (16 \u00b7 16 \u00b7 8 mm), housing four through holes, was 3D printed to provide a platform for the fixed end of the catheter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure15.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure15.7-1.png",
        "caption": "Figure 15.7. View of the pitch cylinders in the direction along the ,teeth of the imaginary rack.",
        "texts": [
            " A rotation AP1 of gear 1 causes a change AS 1 in the value of sl' which can be found from Equation (15.67), AS 1 (15.70) The corresponding displacement of the contact point is then given by Equation (15.69), (15.71) It can be seen that the displacement is always in the direction of nnr' or in other words, perpendicular to the plane of the imaginary rack tooth face. Since the direction is always the same, it means that the path of contact is a 428 Crossed Helical Gears straight line, and it makes an angle ~np with the n~ direction, as shown in Figure 15.7. The common normal at the contact point is also perpendicular to the tooth face of the imaginary rack, so the path of contact coincides with the line of action, exactly as it does in the case of a spur gear pair. In order to find the relation between the gear rotation and the distance moved by the contact point along the path of contact, we combine Equations (15.70 and 15.71), and then use Equation (13.95) to simplify the resulting expression, flp (15.72) It is not easy to visualize the path of contact, when it is given by Equation (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003030_1.1767815-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003030_1.1767815-Figure6-1.png",
        "caption": "Fig. 6 Active surface of the teeth and fluid circulation",
        "texts": [
            " For a rotating disk, the solution of a simplified form of the Navier-Stokes equations for a Newtonian fluid @10#, leads to the following dimensionless moment coefficient: Cl5 4pmbR2v 1 2 rv2R5 5 8p Re S b R D (9) The situation is more complex in the case of a gear. Following Akin @11#, it is assumed that the gas flow on one tooth is deflected by the preceding tooth ~in the sense of the rotation!, such that the active tooth surface is approximately limited by a line from the tooth profile to the tip corner of the preceding tooth ~Fig. 6!. Applying an averaged form of the Newton equation, it gives: F5QU>rxbv2S Ra2 x 2 D 2 (10) with: Ra : tip radius x as defined in Fig. 6. For a gear with Z teeth, the total resisting moment reads: M>Zrxbv2S Ra2 x 2 D 3 (11) SEPTEMBER 2004, Vol. 126 \u00d5 905 13 Terms of Use: http://asme.org/terms Downloaded F The contributions of deflectors, flanges, etc. are introduced via the reduction factor j which represents the influence of obstacles on the fluid aspiration by the teeth. Its definition is: j5j11j2 where j1 accounts for an obstacle on one side of the tested gear and j2 for the other side with j1,25(h/R)0.56 if there is a deflector, flange, etc",
            "org/terms Downloaded F the gear is sound, with rather good agreement between the experimental and theoretical findings for all gears. For both kinds of approach, the maximum relative deviation between the theoretical and experimental findings does not exceed 14% as shown in Table 5. Comparisons have been extended to the case of a gear with flanges in order to assess the model based upon the simulation of fluid flows. Simple experiments with smoke have revealed that the air was aspired in the inter-tooth spaces by the sides and ejected as shown in Fig. 6. Introducing obstacles such as flanges can therefore reduce the air aspiration and ejection by the rotating teeth and modify the corresponding power loss. The curves in Fig. 14 show rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 04/15/20 that the theoretical results by air flow modeling look satisfactory and stress the crucial influence of the teeth on windage losses since they generate approximately half of the total loss at 10,000 rpm ~curves for gear 4 in Figs. 13 and 14!. This observation is SEPTEMBER 2004, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003768_rob.4620050502-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003768_rob.4620050502-Figure1-1.png",
        "caption": "Figure 1.",
        "texts": [
            " The non-zero elements of E, are the singular values ofJ, and their number is equal to the rank of J , , As assumed, if the rank of J , is equal to m, then it can be shown that r , , the manipulator velocity ratio will lie in the following rangeI9: The actual value of rv depends not only on the robot configuration and the weighing matrices W, and W B , but also on the direction of the end-effector velocity vector. The surface (or curve form = 2) formed by the end points of vectors rvu, for a given robot configuration can be represented by an ellipsoid with principal axes U ~ U I , ~ 2 1 ~ 2 , --- urnurn, where u#Rm is the ith column vector of U in Eq. (26). We will call this surface the manipulator-velocity-ratio ellipsoid (MVRE) (Fig. 1). This ellipsoid Dubey and Luh: Redundant Robot Control 41 7 is equivalent to the manipulability ellipsoid described by Yoshikawa,8 if the weighing W , and W B are identify matrices. The shape and size of the ellipsoid will depend on the configuration of the robot. If the rank of J , is r < m, then ui ,for i equal to r 4- 1 to m, will be zero. The least norm solutionJ:x, for x, in the direction(s) of vector(s) ui corresponding to ui equal to zero, can be shown to be zero. This means that the robot is unable to move in that particular direction(s)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure4-1.png",
        "caption": "Fig. 4. A Y-shaped unit as Y1 of Fig. 2.",
        "texts": [
            " The intersection between two perpendicular circular loop-chains is made of an elementary four-legged platform with four pairs of scissors structure as its legs to connect the platform to the radially movable base as in Fig. 3. These elementary four-legged platforms are uniformly distributed on the three circular loopchains. They fold and unfold radially and contribute to the mechanism folding. In each of the eight octants separated by three co-orthogonal circular chains, a Y-shaped mechanism unit spans the space and connects to the three circular chains. Eight Y-shaped units from Y1 to Y8 are provided as in Fig. 2. Each of the Y-shaped unit has an elementary three-legged platform in the middle as in Fig. 4. This platform is provided in each octant to strengthen the ball by associating each of the legs with one circular loop-chain via a four-legged platform on the loop-chain. Thus, the four-legged platform acts as another function of connecting a three-legged platform to a circular kinematic loop-chain. The suspended kinematic pairs of the three-legged elementary platform move radially in an octant and make the elementary platform to fold towards or unfold outwards the center of the ball. Thus, the ball mechanism can be decomposed into an equatorial kinematic loop-chain, four supplementary chains disintegrated from the other two loop-chains and eight Y-shaped units"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003859_detc2007-34210-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003859_detc2007-34210-Figure7-1.png",
        "caption": "Figure 7: Original error surfaces before correction",
        "texts": [
            " Table 3: Design Data (in metric) Pinion (Left Hand) Gear (Right Hand) Number of Teeth 13 47 Module 4.681 Face Width 42.92 38.00 Pinion Offset 30.00 Shaft Angle 90\u02da Outer Cone Distance 123.12 116.50 Mean Cone Distance 101.61 97.40 Outside Diameter 91.80 221.30 Cutter Radius 95.25 Mean Spiral Angles 45\u00b030\u201d 27\u00b039\u201d Pitch Angle 18\u00b022\u201d 70\u00b046\u201d Copyright \u00a9 2007 by ASME Copyright \u00a9 2007 by The Gleason Works erms of Use: http://www.asme.org/about-asme/terms-of-use The original error surfaces of the concave and convex tooth flanks are shown in Figure 7. Figure 8 and 9 respectively show the error surfaces after second order correction and after higher order correction where universal motion coefficients of the 3rd and 4th orders of ratio of roll, cutter tilt, radial setting, offset, and sliding base are selected for the correction. The correction result is conventionally evaluated by the Sum of Squared Errors (SSE) of both flanks and the Root MeanSquared Error (RMSE) of each flank. Downloaded From: http://proceedings.asmedigitalcollection.asme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003388_70.704238-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003388_70.704238-Figure4-1.png",
        "caption": "Fig. 4. Two-link manipulator.",
        "texts": [
            " We first write the motion equations of link 1 and link 2 separately, and then join them together with two holonomic constraints. Even though this example is simple, the methodology is equally applicable to more complex systems. Dynamic Equations: Since link 1 is hinged to the ground, it has one degree of freedom. Its motion equation is given by I1 1 = 1 m1glc1 cos 1 (46) where 1 is the joint angle, m1 is the mass, I1 is the moment of inertia, and 1 is the joint torque. All other notations are illustrated in Fig. 4. Before link 2 is connected to link 1, it is free to move in the plane and has three degrees of freedom. Its equations of motion are given by m2 x2 = 0 (47) m2 y2 = m2g (48) I2 2 = 0 (49) where (x2; y2) is the coordinates of the center of gravity of link 2, m2 is the mass, and I2 is the moment of inertia. These equations can be written in the matrix form as: M(q) q + V (q; _q) +G(q) = E(q)u with q = 1 x2 y2 2 ; M = I1 0 0 0 0 m2 0 0 0 0 m2 0 0 0 0 I2 ; G(q) = m1glc1 cos 1 0 m2g 0 V = 0 0 0 0 ; E = 1 0 0 0 ; u = 1: Constraint Equations: The two links are now connected by a revolute joint going through point A on link 1 and point B on link 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000614_j.addma.2021.101847-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000614_j.addma.2021.101847-Figure1-1.png",
        "caption": "Fig. 1. Schematic of cube and rod fabricated samples in the LPBF process.",
        "texts": [
            " Cubic and rod samples were additively manufactured using an EOS M290 additive machine at Additive Metal Manufacturing Inc. (AMM) in Concord, ON. The same process parameters recommended by EOS GmbH [35] to achieve the minimum porosity volume fraction were used (listed in Table 2). Stripe scanning strategy by rotating the laser beam 67\u25e6 between the successive layers was utilized during the process. Sample cube (a = 15 mm) and the rods (D = 12 mm, L/D = 10) were printed on the top of a build plate preheated at 40 \u25e6C. Fig. 1 shows the schematic of the cubes and rods that were fabricated. A Calvin 1543 heat treatment chamber was used to perform the heat treatment procedure. The heat treatment schedule recommended by EOS GmbH [35] for the C300 maraging steel consists of heating the sample at 490 \u25e6C for 6 h, followed by furnace cooling. Phase analysis was implemented using the X-ray diffraction (XRD) technique using a Bruker D8 DISCOVER instrument Located at McMaster Analytical X-Ray Diffraction (MAX) facility. This instrument, equipped with DAVINCI"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure1-14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure1-14-1.png",
        "caption": "Figure 1-14 Classical phase plane portraits near four different types of equilibrium points for a system of two time-independent differential equations.",
        "texts": [
            " 20 Introduction: A New Age of Dynamics Some authors use the notation V F or Z)F, where F = (/, g), to represent the matrix of partial derivatives in Eq. (1-2.17). The nature of the motion about each equilibrium point is determined by looking for eigensolutions (1-2.18) where a and ft are constants. The motion is classified according to the nature of the two eigenvalues of DF [i.e., whether s is real or complex and whether Real (s) > 0 or < 0.] Sketches of trajectories in the phase plane for different eigenvalues are shown in Figure 1-14. For example, the saddle point is obtained when both eigenvalues s are real, but sl < 0 and s2 > 0. A spiral occurs when sl and s2 are complex conjugates. The stability of the linearized system (1-2.17) depends on the sign of Real (s). When one of the real parts of sl and s2 is positive, the motion about the equilibrium point is unstable. If the roots are not pure imaginary numbers, then theorems exist to show that the local motion of the linearized Classical Nonlinear Vibration Theory: A Brief Review 21 system is qualitatively similar to the original nonlinear system (1-2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003976_j.matdes.2008.05.024-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003976_j.matdes.2008.05.024-Figure4-1.png",
        "caption": "Fig. 4. Deformed shape of the hybrid shaft, [\u00b145]3.",
        "texts": [
            " The distributed forces were calculated by converting the applied torque to tangential force by multiplying with outside diameter and dividing the same by number of nodes on the side of the fixture of the shaft ons of torsion test specimen. model. To restrict the movement of the nodes in the radial direction at the end at which the force is applied, the DOF in r-direction was arrested. The nodes are to be rotated along cylindrical coordinate system so that the applied forces in nodal h-direction are tangential to the perimeter of the shaft. No cantilever effect will be formed since the forces will deform the shaft about its axis by pure twisting. Fig. 4 shows the deform shape of the hybrid shaft under static torsion load. The failure indices of the aluminum tube wound externally by four layers of carbon and glass fiber/epoxy composite at different winding angles are shown in Fig. 5. It can be seen that 45 angle can withstand more torque than that for 90 in all cases. Moreover, at a lower torsion load, the failure indices are close to each other this is because the aluminum tube is still within the elastic limit. When the failure index is one, the failure torque is 131 N m and 195 N m for aluminum tube wound externally by four layers of glass and carbon fibers at winding angle of 45 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002964_s0890-6955(98)00036-4-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002964_s0890-6955(98)00036-4-Figure3-1.png",
        "caption": "Fig. 3. Experimental equipment in laser rapid prototyping using metallic powders.",
        "texts": [
            " The thermal conductivity of powders is measured and expressed as a function of relative density of powders, b [12] (see Appendix B). Once the temperature of the powders becomes higher than the melting point, the thermal conductivity of the solid state is used. Density, specific heat and thermal conductivity are assumed to be independent of temperature. The time step in the calculation is 0.1 ms during heating and 1.0\u20132.0 ms on cooling, one hundredth of the cooling time. The distribution of laser intensity across the laser beam diameter is assumed to be homogeneous. The finite element simulation was tested experimentally. Fig. 3 illustrates the outline of the experimental equipment. A pulsed Nd:YAG laser (Lumonics Laxstar) with maximum output power of 3 kW is used. The laser beam is transmitted to the powder surface by a fibre optics cable. The diameter of the laser beam is 0.8 mm at the powder surface. Cu powders are spread in a container with a uniform thickness and compressed to increase the density. The total thickness of the powder is 10 mm. The powder container is attached to the x\u2013y table although the x\u2013y table is not moved in this experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003976_j.matdes.2008.05.024-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003976_j.matdes.2008.05.024-Figure1-1.png",
        "caption": "Fig. 1. Configuration and dimensi",
        "texts": [
            " They found that the torque capacity was increased about 12-fold for the aluminum tube wound with six layers of carbon fiber and a winding angle of 45 compared with an ordinary aluminum tube. In this paper, a finite element method was used to investigate maximum torsion capacity of a hybrid aluminum/composite drive shaft. The hybrid shaft is consisting from aluminum tube wounded outside by E-glass and carbon fibers/epoxy composite and their hybrids at different winding angle, number of layers and stacking sequences. A full length FE model was constructed for the 175 mm long hybrid shaft under static torsion load. Fig. 1 shows the configuration and dimensions of the hybrid specimen. Each layer on the hybrid shaft was modeled as a separate volume and meshed using solid46 element. The layered element solid46 allows for up to 100 different material layers with different orientations and orthotropic material properties in each layer. The element has three degrees of freedom at each node and translations in the nodal x, y, and z directions. The layers were assumed perfectly bonded with the surface of aluminum tube. An eight-node solid element, solid45, was used for the aluminum tube"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003089_s1727719100003348-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003089_s1727719100003348-Figure2-1.png",
        "caption": "Fig. 2 Rigid body rotation",
        "texts": [
            " Use linear distribution functions for the displacements: u = a11x + a12y From the geometry, it is found /j = a 2 1 c o s 9 - ( l + a1 1)sin\u03b8 la22 = (1 + 2) sin \u03b8 + a12 cos \u03b8 Setting h = l2 gives tan\u03b8 = - 2 + aa1122 (2) Thus, we may select three arbitrarily points in a given element and calculate the average rotation from the relative displacements. The second choice is simpler. If the change of orientation for a line connecting the node i and the centroid of element is cp,, the average rotation is assumed to be 1 n (3) where n is the total number of nodes. Consider a right triangle OAB, as shown in Fig. 2. The position of points O and B are (x, y) and (x + dx,y + dy). If the triangle is rotated about point O for an angle \u03b8, the rotational displacements are = (R T R -I) dx cos \u03b8 sinBl -sin \u03b8 cosBj (4) For element analysis, we choose a reference point C in the element and define the rigid body translation as the displacement of C. Then, duu = u - = \\-\\r are the relative displacement vector and relative position vector. A deformation vector is defined as dduud =du-dur (5) If for each element a set of deformation coordinates are defined with the origin located at point C, the deformation vector in deformation coordinates is u = dd = \u00a3 2 [ ( u - u c ) - ( R r I (6) Deformation coordinates are defined according to the shape functions selected for the element analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure13.12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure13.12-1.png",
        "caption": "Fig. 13.12 A flexible robot",
        "texts": [
            " However, over-sized parts and links consume more materials and power. More importantly the large inertial of the links makes it difficult for trajectory tracking. In view of the negative effect of over-sizing, light weight became an important criterion in robot design. In this case, the elasticity of links and the flexibility of joints have to be considered. Light weight design has a series of benefits, such as lower cost, higher speed, high payload/weight ratio, lower energy consumption and easier operation etc. (Fig. 13.12). In addition, elastic robots are especially important for some applications requiring soft and gentle touch. Examples include robots in surgery, deburring, grinding, painting and drawing. The spatial manipulators on space stations for retrieving satellites are made very slender and required to be light weight. Light weight is critical to control the launching cost. The slender design of the manipulator leads to larger deflection, making it a challenge to track the trajectory. The flexible multi-body-dynamics was developed during the early 1970s mainly for this challenge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure9-1.png",
        "caption": "Fig. 9. Force analysis of substructure 1.",
        "texts": [
            " Then, the force generated by the gravity compensator in { O c } can be expressed as \u03c1w,c, f = [ \u03c1w,c, f cos ( \u03c0 + \u03b3 ) 0 \u03c1w,c, f sin ( \u03c0 + \u03b3 ) ]T (22) where \u03b3 can be calculated according to the law of sines \u03b3 = arc sin ( a L sin \u03b82 ) . Besides, the rotation matrix R c at any configurations can be expressed as R c = R 2 Rot ( Y 2 , \u03b82 \u2212 \u03c8 ) (23) where \u03c8 is the structural parameter shown in Fig. 8 . Finally, to calculate the reaction force exerted on joint 1, a force diagram of substructure 1 is shown in Fig. 9 . The equation of static equilibrium at point O E can be written as \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 f E \u2212 m E g \u0303 z \u2212 m 5 g \u0303 z \u2212 m 4 g \u0303 z \u2212 m 3 g \u0303 z \u2212 m 2 g \u0303 z \u2212 m 1 g \u0303 z = \u03c1w, 1 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z \u2212 m 5 g ( R E r E 6 + R 6 r 6 G 5 ) \u00d7\u02dc z \u2212 m 4 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 G 4 ) \u00d7\u02dc z \u2212m 3 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 G 3 ) \u00d7\u02dc z \u2212 m 2 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 G 2 ) \u00d7\u02dc z \u2212m 1 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 2 + R 2 r 2 G 1 ) \u00d7\u02dc z = ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 2 + R 2 r 2 1 ) \u00d7 \u03c1w, 1 , f + \u03c1w, 1 ,\u03c4 (24) where \u03c1w, 1 , f = [ \u03c1w, 1 , f x \u03c1w, 1 , f y \u03c1w, 1 , f z ] T , \u03c1w, 1 ,\u03c4 = [ \u03c1w, 1 ,\u03c4x \u03c1w, 1 ,\u03c4y \u03c1w, 1 ,\u03c4 z ] T , \u03c1w, 1 , f and \u03c1w, 1 ,\u03c4 are the reaction force and torque of joint 1 acting at point O 1 , m 1 is the mass of link 1, G 1 is the mass center of link 1, r 2 G 1 is the position vector from point O 2 to point G 1 evaluated in { O 2 }, r 2 1 is the position vector from point O 2 to point O 1 evaluated in { O 2 }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003515_j.compstruc.2007.01.015-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003515_j.compstruc.2007.01.015-Figure2-1.png",
        "caption": "Fig. 2. (a) Curved beam element. At nodes i, j a local coordinate system is defined based on the Frenet triad. Six displacements, three forces and three moments are defined at each node. (b) Transverse section of cilium model. Microtubules are modeled as thin-walled beams. They are connected by elastic springs modeling nexin and dynein links. The entire structure is enclosed in an elastic outer membrane. An inner membrane surrounds the two central microtubules. It is linked by elastic springs to each microtubule; the springs model the radial spokes of real cilia.",
        "texts": [
            " The shape of the cross-section of a microtubule is given as a polar curve r \u00bc r\u00f0h\u00de: \u00f03\u00de An elastic spring element is described in a local coordinate system with the s-axis along the spring length. The element has two nodes i and j with nodal displacements Ue \u00bc \u00bd ui uj T and nodal forces oriented along the s-axis F e \u00bc \u00bd fi fj Tj : The rigidity matrix Ke of the element specifies the linear dependence of forces upon displacements, F = KU and is given by Ke \u00bc k k k k \u00f04\u00de with k the element\u2019s spring constant. Each microtubule or microtubule doublet is modeled as a thin-walled beam (Fig. 2). A total Lagrangian Timoshenko beam element is used [2,16]. For details on derivation see [11,7]. The curved beam element has 6 degrees of freedom per node and two nodes per element. The 6 displacements defined at each node are 3 linear displacements (u,v,w) along the \u00f0~T ; ~N ;~B\u00de directions and 3 rotations (a,b,c) around the \u00f0~T ; ~N ;~B\u00de axes. The angular displacement a specifies the section twist, while b, c give the section\u2019s rotation. The displacements produce forces (VT, VN, VB) and moments (MT, MN, MB) within the cross-section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003181_1.2833896-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003181_1.2833896-Figure1-1.png",
        "caption": "Fig. 1 Calculation of the central roller race deformation",
        "texts": [
            " It will therefore be possible for bearing users, willing to study for themselves a complete statically indeterminate system including shafts, housing, and bearings, to do such calculations using accurate nonlinear bearing force-displacements relation ships suggested in this paper and to predict easily the perfor mances of bearings and other system components. This ap proach, easy to implement in any non-linear F.E.A. package, describes any bearing element and completes the F.E.A. library of elements. 2 The Rolling Element-Race Deformation S as a Function of the Five Race Displacements 2;1 For Roller Bearings Figure 1 shows a tapered roller bearing whose cone and cup centers are represented by the Journal of Tribology OCTOBER 1997, Vol. 1 1 9 / 8 5 1 Copyright \u00a9 1997 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use points / and O respectively. The half included cup angle is a, half included cone angle is P, the half included center line angle is 7 and the roller angle is 2v. These three angles are negative in Fig. 1 and are positive if the roller apex is on the left. Cone and cup radius can be represented by Ri and Ro respec tively, while the roller has an effective length L and a mean diameter D. The two sketches show the relative position of the cone and cup, before and after displacements of the point / relative to O. Using the previously described 5 displacements of / relative to O, the local roller-race deformation 6 (i//) at the roller race contact center must first be calculated at any orbital roller location tp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000035_j.triboint.2020.106496-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000035_j.triboint.2020.106496-Figure6-1.png",
        "caption": "Fig. 6. PIV (top row) and CFD (bottom row) velocity fields for three angular gear velocities. From left to right: 10 rad/s (tangential velocity of 0.55 m/s), 20 rad/s (tangential velocity of 1.1 m/s), and 30 rad/s (tangential velocity of 1.6 m/s).",
        "texts": [
            " The PIV raw images were taken every rotation of the gear. One hundred image pairs were taken, analyzed, averaged, and then reported. The torque measurements, in opposite to the PIV, were performed at higher velocity range since at low velocities the small torque values were resulting in a large uncertainty of the results. Table 2 reports the configurations that were numerically reproduced. Low tangential velocities were exploited to check the validity of the numerical model to predict the oil distribution. In Fig. 6 a side-by-side comparison of experimental and numerical velocity fields for three angular velocities is shown. The velocity fields shown are at the midplane of the gearbox. As seen, at the lowest rotational speed the oil splashing was minimal and was characterized by the oil lifting on the left side of the gear and on the right side of the pinion. This phenomenon was captured by the CFD very well. At increased rotational speed the amount of splashed oil increased and current CFD simulations captured the splashed oil distribution remarkably well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000954_j.cpc.2021.107956-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000954_j.cpc.2021.107956-Figure3-1.png",
        "caption": "Fig. 3. Schematic of merging tiles in the 3D domain. (a) Before merging volume. (b) After merging volume.",
        "texts": [
            " This process functions in the same l x l \u03c8 Table 1 Model demonstration and mathematical expression of TPMSs. Type Surface Implicit equation P \u03c8P (x, y, z) = cos(2\u03c0x) + cos(2\u03c0y) + cos(2\u03c0z) = 0 D \u03c8D(x, y, z) = cos(2\u03c0x) cos(2\u03c0y) cos(2\u03c0z) \u2212 sin(2\u03c0x) sin(2\u03c0y) sin(2\u03c0z) = 0 G \u03c8G(x, y, z) = sin(2\u03c0x) cos(2\u03c0y) + sin(2\u03c0z) cos(2\u03c0x)+sin(2\u03c0y) cos(2\u03c0z) = 0 I \u03c8I\u2212WP (x, y, z) = 2[cos(2\u03c0x) cos(2\u03c0y) + cos(2\u03c0y) cos(2\u03c0z) + cos(2\u03c0z) cos(2\u03c0x)]\u2212cos(4\u03c0x)\u2212cos(4\u03c0y)\u2212cos(4\u03c0z) = 0 manner in a 3D domain. Figs. 3(a) and (b) illustrate the initial and final structure in a 3D domain, respectively. The schematic diagram in Fig. 3(b) describes the interpolation in a 3D domain. In the level set framework, the calculated \u03c8\u0303 uses the zero level as the interface to distinguish between the inside and the outside of the composite scaffold. The volume can be determined and denoted by a discrete function \u03c8\u0303(x), where \u03c8\u0303(x) > 0 if the voxel is determined to be a volume voxel; otherwise, \u03c8\u0303(x) < 0. To ink with Section 2.2, we define (x) := \u23a7\u23a8\u23a9 1 if \u03c8\u0303(x) > \u03b1(\u03c8\u0303max \u2212 \u03c8\u0303min), 0 if \u03c8\u0303(x) < \u2212\u03b1(\u03c8\u0303max \u2212 \u03c8\u0303min), 0.5\u03c8\u0303(x) + 0.5 otherwise, \u03b1(\u03c8\u0303max\u2212\u03c8\u0303min) where \u03c8\u0303max and \u03c8\u0303min are the maximum and minimum of \u03c8\u0303 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000954_j.cpc.2021.107956-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000954_j.cpc.2021.107956-Figure13-1.png",
        "caption": "Fig. 13. Parameter sensitivity analysis for \u03b2 in fidelity term. The complex scaffold is composed of a P-surface and I-WP-surface unit structures. From (a) to (d), \u03b2 is 0.01, 0.1, 1, and 10, respectively. Stop condition tol is the same for the four results as in 1e\u22124. (e) 0.5 contour lines of slices from (a) to (d). Red, green, blue, and magenta represent lines with \u03b2 of 0.01, 0.1, 1, and 10, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " Observing he numerical results, the proposed method can effectively design ifferent porous scaffolds with high-quality external anatomical one surfaces. .4. Parameter sensitivity analysis We conducted a parameter sensitivity analysis for model paameters tol and \u03b2 . The last term in Eq. (6) is the fidelity term o ensure that \u03c6 remains close to \u03c8 . Parameter \u03b2 balances the idelity term and motion by mean curvature flow, which means hat it can control the convergent mean curvature of the strucure. As can be seen in Fig. 13, different \u03b2 values can lead to ifferent results. From Fig. 13(a) to (d), we choose \u03b2 as 0.01, .1, 1, and 10, respectively, leading to mean curvatures of 0.022, 0.012, \u22120.05, and \u22120.032, respectively. To demonstrate the nfluence of \u03b2 further, we plotted 0.5 contour lines in Fig. 13(e). u i a r m s w t s t t i t i e 1 4 o L s s f{ U Here, the red, green, blue, and magenta colors represent isolines with \u03b2 values of 0.01, 0.1, 1, and 10, respectively. From the closep view, we can see that the surface of the composite scaffold s smoother with smaller values of \u03b2 . Therefore, considering lgorithm efficiency, we suggest using 0.1 \u2264 \u03b2 \u2264 1. Eq. (6) ensures that the total energy, E(\u03c6), decreases with espect to time, which implies that the solution of the proposed ethod is stable. Therefore, we can stop the evolution and asume that the computational result is a steady-state solution hen relative error \u2225\u03c6n+1 \u2212 \u03c6n \u22252/\u2225\u03c6 n \u22252 is less than tolerance ol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000827_tie.2021.3088331-Figure20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000827_tie.2021.3088331-Figure20-1.png",
        "caption": "Fig. 20 Countour plots of two machines under overload condition(Im=28A). (a)Optimized regular vernier machine; (b) Optimized proposed vernier machine",
        "texts": [
            "1Nm, respectively. Thus, the average torque increases by 30%. The torque ripple is 2.7% and 7.5%, respectively. (6th torque ripple is caused mainly by 5th back EMF harmonic) The optimized machine has 62% lower torque ripple than its counterpart. Fig. 19 shows the FEA-predicted average torque versus phase current peak values. It is shown that the proposed machine has better linearity than its counterpart which can be explained by the contour plot of two machines under over-loaded condition (Im=28A) shown in Fig.20. It is observed that in the regular split-tooth vernier machine, saturation is severer in both rotor and stator yoke, which is due to larger armature reaction caused by 1st flux harmonic at higher current. Thus, the proposed machine has better overload capability. Power factor PF can be calculated as (20):   2 11/ 1 /e m mPF \u03c9 L I E        (20) where Lm is phase winding synchronous inductance. The Lm in two machines at rated load are calculated as 3.7mH and 2.7mH, respectively. Based on calculated E1 in section A, PF of the proposed machine and the regular vernier machine can be obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001029_j.mechmachtheory.2021.104357-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001029_j.mechmachtheory.2021.104357-Figure3-1.png",
        "caption": "Fig. 3. Fillet-foundation effect on gear tooth with crack [9] .",
        "texts": [
            " The stiffness for a slice of gear tooth along the width ( z-axis) is given as; K t (z) = 1 1 K b + 1 K s + 1 K a (14) For the complete tooth width b, the tooth mesh stiffness, K T is given as; K T = \u222b b 0 K t (z) dz (15) The presence of tooth fillet affects the dynamics of gear tooth loading. Its effect can be further observed in the mesh stiffness, as reported by Sainsot et al. [9] . The deflection ( \u03b4 f ) by considering the linear stress variation at the root of gear tooth can be computed as; \u03b4 f = F cos 2 (\u03b11 ) bE { L \u2217 ( d S f ) 2 + M \u2217 ( d S f ) + P \u2217(1 + Q \u2217tan 2 (\u03b11 )) } (16) where b is tooth width; d, and S f are shown in Fig. 3 . The coefficients L \u2217, M \u2217, P \u2217, and Q \u2217 can be obtained from the polynomial function as follows [9] ; X \u2217 i (h f i , \u03b8 f ) = A i /\u03b8 2 f + B i .h 2 f i + C i .h f i /\u03b8 f + D i /\u03b8 f + E i .h f i + F i (17) X \u2217 i shows the coefficients L \u2217, M \u2217, P \u2217, and Q \u2217. The coefficients A i , B i , C i , D i , E i , and F i are given in Table 1 [9] , and h f i = r f /r int , where r f , r int , and \u03b8 f are shown in Fig. 3 . The stiffness due to gear tooth fillet foundation is given as; 1 K f = \u03b4 f F (18) The effect of the Hertzian contact along the line of action leads to Hertzian contact stiffness K h , which is given as [40] ; 1 K h = 4(1 \u2212 \u03bd2 ) \u03c0Eb (19) The total mesh stiffness of a gear pair (p-pinion, g-gear) accounts for the tooth stiffness ( K T p , K Tg ), stiffness due to the tooth fillet foundation ( K f p , K f g ), and the Hertzian stiffness. The expression for total mesh stiffness, K is given as [38] ; K = 1 1 K T p + 1 K f p + 1 K Tg + 1 K f g + 1 K h = K 1 (20) The above expression is valid for a gear system with a single pair of teeth in contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure17.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure17.13-1.png",
        "caption": "Figure 17.13. Radii of curvature in the transverse section.",
        "texts": [
            "5), p Pc l Pc2 (17.33) where w is the load intensity, and Cp is the elastic coefficient given by Equation (11.6), w(1-v 2 ) w(1-v 2 ) v[ 1 + 2 ] El E2 = (17.34) 504 Tooth Stresses in Helical Gears The radii Pc1 and Pc2 are expressed by means of Equations (17.31 and 17.32) in terms of Pt1 and Pt2' the radii of curvature of the tooth profiles in the transverse section through A. We proved in Equation (10.1) that Pt1 and Pt2 are equal to the lengths E1A and AE2 in the transverse section, which is shown in Figure 17.13. We can see from the diagram that the sum (P t1 +Pt2 ) is equal to (C sin ~t)' where C is the center distance, and ~t is the operating transverse pressure angle of the gear pair. The contact stress is then given by the following expression, (17.35) We showed in Equation (14.34) that ~t is equal to ~tP' the operating transverse pressure angle of either gear. And, as we proved in Equation (13.92), the product (sin ~tP cos l/Ib) is equal to sin, \u2022 We can therefore simplify the expression for np 0c to its final form, C sin 'np Cp v' [ w ( P P ) ] t 1 t2 (17.36) Contact Stress 505 The values of Pt1 and Pt2 depend on the position s of point A on the path of contact in the transverse section. We now have to determine at which point the contact stress should be calculated. We use Figure 17.13 to express Pt1 and Pt2 in terms of s, Rb1 tan 4>t + s (17.37) (17.38) We showed in Chapter 11 that the minimum value of the product (P t1 Pt2 ) is obtained when the smaller of the two radii of curvature is as small as possible. In other words, if gear 1 is the pinion, (P t1 Pt 2) is a minimum when s reaches its largest negative value, which occurs at the lowest possible posi tion in the region of contact. However, the contact stress also depends on the load intensity w, and we therefore need consider only the contact lines for which the load intensity is a maximum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000695_j.jmapro.2021.03.003-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000695_j.jmapro.2021.03.003-Figure1-1.png",
        "caption": "Fig. 1. Proposed ECMP process for the SLM internal hole.",
        "texts": [
            " The polishing principle, electrochemical tests, details of sample preparation, simulations for the electrochemical and mechanical effects, experimental setup and conditions are introduced. The polishing results are obtained under various electrochemical parameters. According to the results, a qualitative model is established to schematically describe the polishing process through the superposition of the electrochemical and mechanical effects. The principle of the ECMP process of an internal hole is shown in Fig. 1. The cathode tool is shown in Fig. 2 in which a metallic twisted pair was used as the cathode electrode and a large number of nylon filaments (made by DuPont Company), which functioned as flexible abrasive, were fixed on the cathode. During the ECMP process, C. Zhao et al. Journal of Manufacturing Processes 64 (2021) 1544\u20131562 electrochemical reactions took place on the surface of the internal hole to enable material dissolution. Meanwhile, the cathode tool moved to drag the flexible abrasive to mechanically scratch the internal surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000431_s00170-020-05065-8-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000431_s00170-020-05065-8-Figure4-1.png",
        "caption": "Fig. 4 a Schematic drawing of the twin-cantilever part with a saw-tooth support structure. x, y, z denotes the Cartesian coordinate. b Part dimension and scan strategy. PL, PW, and PH denote part length, part width, and part height respectively. Red arrows denote a unidirectional scan strategy",
        "texts": [
            " The temperature profile, thermal stress, and residual stress were calculated as intermediate variables. The presented model has significant computational advantages without resorting to finite element analysis (FEA) or any iterationbased calculations. The presented model was validated with distortion prediction of a twin-cantilever part produced by PBMAM with Ti6Al4V powders. The twin-cantilever part has been favored in the investigation due to the easily measurable distortion. The part geometry with saw tooth support structure is illustrated in Fig. 4. The process parameters and part dimensions are given in Table 1. The saw tooth structure was designed with dimensions of 1 mm in thickness (x-direction), 5 mm in height (z-direction), and 5 mm in width (y-direction). The space between two adjacent teeth was 1 mm. The twincantilever part was printed by GPI Prototype (Lake Bluff, IL) with the EOS machine under standard atmosphere (atm). The statistical power size distribution of the Ti6AL4V powders was analyzed by laser size diffraction as per ASTM B822 as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure3-1.png",
        "caption": "Fig. 3. An elementary four-legged platform and parallelogram links.",
        "texts": [
            " Each loop-chain is constructed by a number of parallelograms with scissors structure. The three loop-chains are perpendicular to each other and are on three perpendicular planes, x\u2013z, y\u2013z and x\u2013z as in Fig. 2. These circular loop-chains thus separate the ball space into eight octants from Y1 to Y8. The intersection between two perpendicular circular loop-chains is made of an elementary four-legged platform with four pairs of scissors structure as its legs to connect the platform to the radially movable base as in Fig. 3. These elementary four-legged platforms are uniformly distributed on the three circular loopchains. They fold and unfold radially and contribute to the mechanism folding. In each of the eight octants separated by three co-orthogonal circular chains, a Y-shaped mechanism unit spans the space and connects to the three circular chains. Eight Y-shaped units from Y1 to Y8 are provided as in Fig. 2. Each of the Y-shaped unit has an elementary three-legged platform in the middle as in Fig. 4. This platform is provided in each octant to strengthen the ball by associating each of the legs with one circular loop-chain via a four-legged platform on the loop-chain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003385_mcs.2002.1077786-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003385_mcs.2002.1077786-Figure4-1.png",
        "caption": "Figure 4. Spherical pendulum.",
        "texts": [
            " Now, since ( , , , )V x x x x1 2 3 4 0= , it follows from ii) of Theorem 1 that (4), (5) is Lyapunov stable with respect to x 1, x 2, and x 4 uniformly in x 3. Furthermore, since the system involves a nonlinear coupling of an undamped oscillator with a rotaional rigid-body mode, it follows that x t3( ) \u2192 \u221e as t \u2192 \u221e. Example 2. In this example, we apply Theorem 1 to a Lagrange-Dirichlet problem involving a conservative Euler-Lagrange system with a nonnegative-definite kinetic energy function T and a positive-definite potential function U . Specifically, we consider the motion of the spherical pendulum shown in Fig. 4, where \u03b8denotes the angular position of the pendulum with respect to the vertical z-axis and \u03c6 denotes the angular position of the pendulum in the x-y plane, m denotes the mass of the pendulum, L denotes the length of the pendulum, k denotes the torsional spring stiffness, and g denotes the gravitational acceleration. Definingq = \u03c6 [ ]\u03b8 T to be the generalized system positions and [ ]q = \u03c6 \u03b8 T to be the generalized system velocities, it follows that governing equations of motion are given by the Euler-Lagrange equation d dt q q t q t q q t q t \u2202 \u2202       \u2212 \u2202 \u2202     ( ( ), ( )) ( ( ), ( ))   = = = \u2265 0 0 0 00 0 , ( ) , ( ) ,,q q q q t (26) December 2002 IEEE Control Systems Magazine 71 where ( , ) ( , ) ( )q q T q q U q= \u2212 denotes the system Lagrangian, T q q m L L( , ) ( / ) [( ) ( sin ) ]= + \u03c6 1 2 2 2\u03b8 \u03b8 denotes the system kinetic energy, andU q mgL cos k( ) ( ) ( / )= \u2212 + \u03c6 1 1 2 2\u03b8 denotes the system potential energy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000691_j.ast.2021.106573-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000691_j.ast.2021.106573-Figure4-1.png",
        "caption": "Fig. 4. Two different configurations of the manipulator\u2019s arms depending on the distance of the first joint from the desired position of the end-effector.",
        "texts": [
            " For this purpose, consider again the defined system output in (46). If we generate a mapping between the position of the end-effector and the joint angles of the manipulator, then the proposed formulation in Section 3.2.1 can be used for the simultaneous control of the system trajectory and the end-effector position. Due to the redundancy of the manipulator used in the current study, various configurations of the manipulator\u2019s arms can be found for a specific position of the end-effector. A possible configuration is illustrated in Fig. 4. Indeed, depending on the distance between the desired position of the end-effector and the first joint of the manipulator, two different configurations are proposed for the manipulator\u2019s arms. To be more precise, if we define \u03be = \u2223\u2223Ptarget \u2212 P0 \u2223\u2223 , (52) where Ptarget and P0 represent respectively, the desired position of the end-effector and the position of the first joint of the manipulator in the inertial reference frame (and | | denotes the Euclidean norm), then the desired configuration of the manipulator\u2019s arms are defined as follows (see Fig. 4): Configuration = { a, \u03be \u2265 d1 + d2 \u2212 d3 b, \u03be < d1 + d2 \u2212 d3 (53) Accordingly, in the first configuration (Fig. 4a), the first joint angle is equal to the angle between Ptarget \u2212 P0 and the xb axis. Besides, the second and third joint angles can be determined in such a way that d2, d3, and \u2223\u2223Ptarget \u2212 P1 \u2223\u2223 form a triangle (P1 denotes the position of the second joint of the manipulator in the inertial frame). Using such a configuration, the second joint angle can also compensate for the tracking error of the first joint angle. On the other hand, in the second configuration (Fig. 4b), the first and second joint angles are determined such that d1, d2 + d3, and \u03be form a triangle, and the third joint angle is set to zero. In a similar manner to Section 3.2.1, a multi-stage MPC will be employed to perform the simultaneous trajectory tracking and aerial grasping mission. The multi-stage MPC is introduced in the following subsection. It is obvious that the pose of the manipulator\u2019s links is directly affected by the generalized force of the actuators embedded in the manipulator\u2019s joints, not the thrust forces of the rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002841_1.1623761-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002841_1.1623761-Figure6-1.png",
        "caption": "Fig. 6 \u201ea\u2026 Position of ball center and raceway groove curvature centers with and without applied load \u201eb\u2026 the detailed graph to describe the u8 angle shown in Fig. 6\u201ea\u2026",
        "texts": [
            " Similarly, the slip angle C i at the screw, as shown in Fig. 5, is C i5tan21S VY i VXi D1p (36a) For the contact point formed at the screw, the relationship between VXi and VYi is @9# VYi VXi 5 d~vm2v!2rb@~vb2v cos a!cos a i2vn sin a i# rb~v t2v sin a! (36b) where VXi ,VYi 5 the components of the ball\u2019s sliding velocity relative to the screw in the Xi- and Y i-directions, respectively. The slip angles are applied to evaluate the frictional forces and frictional moments created at the contact surfaces of the nut and the screw. 2.5 Contact Angle. Figure 6~a!, shows the positions of the ball center and the raceway groove curvature centers with and without applied load. BD is the distance between two centers, oo and oi1 , before applying the load. So we can get: BD5~ro1ri2D !5DS ro D 1 ri D 21 D (37) where D denotes the diameter of a ball. Under a static axial load, the distance BD between these two centers will be changed by the amounts of the two contact deformations, dr and da , in the radial and axial directions respectively, as shown in Fig. 6~b!. In the present study, the curvature center of the nut is assumed to be fixed in a position such that do and d i are defined to be the total elastic deformations created at the contact points of the nut and the screw respectively. Geometric analyses for Fig. 6~a! give @11# A15BD sin ao1da1u8Ri* (38a) rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/31/20 A25BD cos ao1dr (38b) cos ao5 X2 ~ f o20.5!D1do (39a) sin ao5 X1 ~ f o20.5!D1do (39b) cos a i5 A22X2 ~ f i20.5!D1d i (39c) sin a i5 A12X1 ~ f i20.5!D1d i (39d) Ri*5 1 2 dm1~ f i20.5!D cos ao (39e) where f o : dimensionless radius of curvature of the nut; ( f o5ro /D) f i : dimensionless radius of curvature of the screw; ( f i5ri /D) da ,dr : the elastic deformations created in the radial and the axial directions respectively due to the loads applying in these two directions. u8 : the angular displacement of the b-axis due to the applications of the axial and radial loads ~see Fig. 6~b!!. DECEMBER 2003, Vol. 125 \u00d5 723 13 Terms of Use: http://asme.org/terms Downloaded F ao : the initial contact angle of ao and a i prior to loading. Using the pythagorean theorem in Fig. 6~a!, it can be found that ~A12X1!21~A22X2!22@~ f i20.5!D1d i# 250 (40a) X1 21X2 22@~ f 020.5!D1do#250 (40b) The solutions for X1 and X2 can be obtained from the solutions of the above two equations if the solutions of do and d i are available. The flow chart of the numerical analyses achieving these two parameters will be discussed later. These solutions are used in Eq. ~39! to obtain the contact angles, ao and a i , formed at the nut and the screw respectively. 2.6 Frictional Force and Moment. The shear stress tn8 (n85i or o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000736_j.compstruct.2021.113822-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000736_j.compstruct.2021.113822-Figure14-1.png",
        "caption": "Fig. 14. The deformations of the HMS beam with 3D sinusoidal magnetization, i.e. \u03b8r = n\u03c0\u03be/2, \u03c8r = n\u03c0\u03be/2, actuated by the magnetic field in the reverse direction of axis z0, i.e. \u03b8a = \u03c0/2, with different magnetic forces P, for (a) n = 1, (b) n = 2, (c) n = 3 and (d) n = 4.",
        "texts": [
            "2, the 3D large\u2010deformation behaviors of the HMS beam with both uniform and nonuniform planar magnetizations are studied. In order to show the deformations of the general HMS beam, the 3D nonuniform magnetizations are considered by assuming \u03b8r = n\u03c0\u03be/2 and \u03c8r = n\u03c0\u03be/2. In these cases, Br 0 is varied in a 3D sinusoidal form along the beam length direction. Two types of applied magnetic fields, i.e. \u03b8a = \u03c0/2 and \u03b8a = \u2013\u03c0/4, \u03c8a = \u03c0/4, will be considered. The deformed shapes of the centerline and the twisting deformation of the cross section are given for various P and half\u2010wave numbers n. As shown in Fig. 14, the initially straight HMS beam transforms into a complicated 3D curved line after applying a magnetic field. Again, the twisting deformation is significant for such 3D deformation. Since the residual magnetic flux density is 3D nonuniform, the deformations of the HMS beam may be nonplanar. Various half\u2010wave numbers n and magnetic loads P are considered in Fig. 14 for the case of \u03b8a = \u03c0/2. Another type of the applied magnetic field with \u03b8a = \u2013\u03c0/4 and \u03c8a = \u03c0/4 is considered and the results are shown in Fig. 15. The deformations of the HMS beam with different magnetic loads P and half\u2010 wave numbers n are provided. As shown in the figures, the 3D large\u2010 deformation responses consisting of large bending and twisting deformations occur. The deformations are extremely large when the dimensionless displacements approach to 1 and the twisting angle exceeds 2.5. Therefore, the developed theoretical model is capable of predicting the 3D large\u2010deformation behaviors of HMS beams"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.7-1.png",
        "caption": "Figure 2.7. Base pitch.",
        "texts": [
            "23) and as a special case of this equation, we set R equal to Rs' and we obtain the corresponding relation between the base pitch and the circular pitch at the standard pitch circle, (2.24) There is a property of involute curves which we will make use of in the chapters that follow. The normal to a tooth profile at any point A is also normal to any other involute of the base circle, and if it cuts the next tooth profile at point A', the length AA' is equal to the base pitch Pb' Thus, the distance between adjacent tooth profiles, measured along a common normal, is equal to Pb' These results can be proved Gear Parameters 37 with the help of Figure 2.7. The normal to the involute at A must touch the base circle at some point E, since this is the defining property of the involute. If line EA cuts the next tooth profile at A', the normal to the second tooth profile at A' must also touch the base circle, and therefore coincides with line EAA'. Hence, a line which is normal to one involute is also normal to other involutes of the same base circle. To prove that the length AA' is equal to the base pitch, we make use of Equation (2.8), which states that EA is equal to arc EB. Referring again to Figure 2.7, we have the following relations, AA' EA' - EA arc EB' - arc EB arc BB' Since the involutes shown in Figure 2.7 are the profiles of adjacent teeth, arc BB' is by definition equal to the base pitch, and the equation can be written, AA' (2.25) We have therefore proved the statement made earlier, that the distance between adjacent tooth profiles, measured along a common normal, is equal to the base pitch. The definition of the base pitch given in Equation (2.22) would not apply in the case of a rack, because both the base circle radius and the number of teeth are infinite. However, earlier in the chapter we gave a definition for the base pitch of a rack, as the distance between adjacent tooth prof i les, measured along a common normal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000946_s11548-020-02300-1-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000946_s11548-020-02300-1-Figure2-1.png",
        "caption": "Fig. 2 Details of the puncture robot",
        "texts": [
            " The proposed robotic system comprises a 6-DOF passive arm, 3-DOF US-guided puncture robot, and puncture planning software, as shown in Fig.\u00a01. The passive arm fixed at the edge of an operation bed is used to hold the puncture robot and provide stable support. It has two states: lock and release. In the release state, it has good compliance and can be easily dragged. In the lock state, it has sufficient stiffness to provide stable support for the robotic system. The puncture robot integrates a US probe, a needle, and a driving mechanism, as shown in Fig.\u00a02. A Terason uSmart 3200T NexGen US system (Terason Division of Teratech Corporation, Burlington, MA, USA) with a linear array probe is used for 2D US image acquisitions. The frequency and depth are set to 14\u00a0MHz and 55\u00a0mm, respectively. A 22G hypodermic needle with a length of 80\u00a0mm is mounted at the end of the driving mechanism with a quick-release device and can move with the mechanism. In addition, a needle guide is used to support the needle in close proximity to the skin entry point. This effectively increases the resistance of the needle to deformation",
            " To analyze the puncture error caused by the needle 1 3 deformation, the robot-assisted puncture experiments in water phantom without needle guide were performed as the third group experiments. The needle will not deform in water, and the experimental results show that the puncture accuracy (mean positioning and orientation accuracies of 0.81 \u00b1 0.16\u00a0mm and 0.31 \u00b1 0.24\u00b0, respectively) is significantly higher than those for the first group of puncture experiments performed in the pork phantom, as shown in Fig.\u00a09a. The deformation of the needle leads to a larger puncture error in our robotic system. Therefore, we used a needle guide (Fig.\u00a02) to support the needle in close proximity to the skin entry point and improve the resistance to deformation of the needle. With the needle guide, the robot-assisted puncture experiments were performed in the pork phantom as the fourth group of experiments. Compared with the first group of experiments without needle guide, the puncture accuracy (mean positioning and orientation accuracies of 0.9 \u00b1 0.29\u00a0mm and 0.76 \u00b1 0.34\u00b0, respectively), and especially the orientation accuracy, were significantly improved, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003195_tmag.2004.824127-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003195_tmag.2004.824127-Figure14-1.png",
        "caption": "Fig. 14. Squirrel cage induction motor with broken bars.",
        "texts": [
            " Then, these terminal resistors are subsequently set to zero to model the terminal fault. Fig. 13 gives the waveforms of stator phase currents. Based on the computed stator phase currents, the parameters of transient reactance , subtransient reactance , transient time constant , and subtransient time constant can be further extracted by the procedures specified in [16]. C. Induction Motor With Broken Bars In this example, the performance of a three-phase induction motor with the ratings of 220 V, connection, four poles, 50 Hz (Fig. 14) is simulated at the rated speed of 1410 rpm. If the broken bars exist, generally the symmetry cannot be used to reduce the solution domain. Figs. 15 and 16 show the computed stator currents when broken bars exist. The computed results show that the broken rotor bars will lead to the change of the magnitude of the stator current with the frequency of ( is the slip and is the source frequency). Power electronic inverter-fed motors have become commonly used in variable speed drives. Because the high , fast switching, and possible long feeder cable, the repetitive steep-fronted voltage is becoming a source of premature winding insulation failures [17], [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.12-1.png",
        "caption": "Figure 2.12. Tooth profile, N=36, ~s=14.5\u00b0.",
        "texts": [],
        "surrounding_texts": [
            "Of all the many types of machine elements which exist today, gears are among the most commonly used. The basic idea of a wheel with teeth is extremely simple, and dates back several thousand years. It is obvious to any observer that one gear drives another by means of the meshing teeth, and to the person who has never studied gears, it might seem that no further explanation is required. It may therefore come as a surprise to discover the large quantity of geometric theory that exists on the subject of gears, and to find that there is probably no branch of mechanical engineering where theory and practice are more closely linked. Enormous improvements have been made in the performance of gears during the last two hundred years or so, and this has been due principally to the careful attention given to the shape of the teeth. The theoretical shape of the tooth profile used in most modern gears is an involute. When precision gears are cut by modern gear-cutting machines, the accuracy with which the actual teeth conform to their theoretical shape is quite remarkable, and far exceeds the accuracy which is attained in the manufacture of most other types of machine elements. The first part of this book deals with spur gears, which are gears with teeth that are parallel to the gear axis. The second part describes helical gears, whose teeth form helices about the gear axis. The book is primarily about involute gears, since this type of gear is by far the most commonly used. However, the first chapter introduces the Law of Gearing, which must be satisfied by any pair of gears, and the statements made apply not only to involute gears, but are also true for non-involute types of gear. There is one other chapter of the book which also deals with non-involute gears. Chapter 9 is on the general theory of gear tooth geometry, and 2 Introduction is included in the book simply because the tooth profiles of involute gears contain sections which are not involute. In particular, the part of each tooth near its root, known as the fillet, is not an involute, but its shape can be found from the general theory of gears. And in some gears, small alterations from the involute shape, known as profile modifications, are made in the teeth, and again the final shape of the teeth can be found by means of the general theory. In helical gears, the angle between the helix tangent and the gear axis is known as the helix angle. Spur gears can be regarded as helical gears, in which the helix angle is zero. Since a spur gear is therefore simply a special case of a helical gear, it might be asked why the two types should be dealt with separately. However, the geometry of spur gears is considerably simpler than that of helical gears, and it is therefore convenient to describe it first. The cross-section of a helical gear perpendicular to its axis, known as its transverse section, is the same as the cross-section of a spur gear, so a knowledge of spur gear geometry makes a good starting point for the study of helical gears. The treatment of spur gear theory in this book is fairly conventional, except in one respect. No distinction is made between a gear pair meshed at the standard center distance, and one at extended centers. The terminology and the notation are the same for both cases. In conformity with this principle, the name \"pitch circle\" is always used for the circle of a gear which passes through the pitch point, and its radius is always represented by the symbol Rp' whatever its value. It is important to make a clear distinction between the pitch circle when a gear is in operation, and the pitch circle when it is meshed with its basic rack, which is used as a reference circle. For this reason, the pitch circle when the gear is meshed with its basic rack is called the standard pitch circle, and its radius is labelled Rs' where the subscript s is used to indicate the word \"standard\". Apart from this change, the definitions and notation in this book have been chosen to conform as closely as possible with those used in current North American practice. However, a few additional alterations have been made, in cases where Introduction 3 the existing terminology is confusing. For example, the phrase \"pre'ssure angle\" is used at present for several different angles. Its original meaning is the angle between the line of action and the common tangent to the pitch circles, but it is used also for the angle between the tooth profile and the tooth center-line of a rack, and the angle between the radius and the profile tangent of a gear tooth at either the standard pitch circle or the pitch circle. In addi t ion, the angle between the radi us and the prof i Ie tangent at a typical radius R of the tooth profile is also commonly known as the pressure angle. In current usage, all these angles are called either the pressure angle or the operating pressure angle, and they are all represented by the symbol ~ when they are equal to the pressure angle of the basic rack, and ~' when they are not. Over the years, several attempts have been made to rename some of these angles, but the proposed alternative names have not been widely accepted, so in this book the name \"pressure angle\" has generally been retained, while the notation has been altered to help identify the particular angle that is referred to. The angle between the radius and the profile tangent at a typical point of the gear tooth profile is referred to as the profile angle at radius R, and it is represented by the symbol ~R' The profile angles of a gear at the standard pitch circle and the pitch circle are called the pressure angle and the operating pressure angle of the gear, with the symbols ~s and ~P' and the pressure angle of the basic rack is represented by the symbol ~r' Finally, the angle between the line of action and the common tangent to the pitch circles is called the operating pressure angle of the gear pair, and this is the only angle for which the customary symbol ~ is still used. The symbols for the different pressure angles are distinguished by their subscripts, and the same convention is used for all quantities, such as the circular pitch and the tooth thickness, whose values are functions of the radius. The subscripts R, s, p, or b are used whenever a quantity is measured on a gear tooth at a general radius R, at the standard pitch circle, at the pitch circle, or at the base circle, and the subscript r applies to the corresponding quantity measured on a rack tooth. 4 Introduction The second part of the book deals with the geometry of helical gears, and the treatment differs substantially from the traditional approach. The sUbject is essentially three-dimensional, and in the past the geometr ic theorems have usually been proved with the help of projective geometry. In other fields of mechanics, projective geometry has been largely superseded by vector methods, and in the author's opinion, most of the theorems relating to helical gears can be proved far more easily using vector algebra than using projective geometry. The entire description of helical gears in this book is therefore given with the help of vector theory. I t is believed that most younger engineers, and today's engineering grounding in vector students, receive a more thorough theory than they do in projective geometry, and should therefore find thi s new approach to helical gear geometry easier to understand. The word \"pitch\" is used in this book in a manner which differs slightly from the customary North American usage, and is in fact based on current European practice. In North America, the phrase \"circular pitch\" describes a particular length on a spur gear, while \"diametral pitch\" is a quantity used to indicate the tooth size, defined as the number of teeth divided by the diameter of the standard pitch circle. The original meaning of the word \"pitch\" is the distance between similar objects that are repeated at regular intervals. In this book, the word is only used in a manner which conforms with the original meaning. The of a spur gear is defined in the usual circular pi tch way, and the corresponding lengths in a helical gear are called the transverse pitch, the normal pitch, and the axial pitch. In general, the diametral pitch is not referred to in this book, since it is not a pitch in the sense described above. In order to specify the tooth size of a gear we use the module, which is the method used throughout Europe and Japan. However, since the diametral pitch is still in common use in North America, the relation between the module and the diametral pitch is described in the text, and the diametral pitch is used in some of the examples at the end of each chapter. A list of references is provided, and this consists of a number of books and articles which the author has found Introduction 5 particularly helpful in his own study of gear geometry. In addition, several articles are listed because they describe, in considerable detail, certain topics which are only outlined in this book. The list is not intended to include all possible references, and no attempt has been made in the text to identify a source for each idea or theorem. In some cases, it would probably be very di ff icult to di scover where a particular idea originated. When any reference is quoted in the text, it is identified by a number in square brackets, which refers to the number in the list of references at the end of the book. In the diagrams throughout the book, the gear tooth profiles were drawn by a computer-driven plotter. The remaining parts of the diagrams were drawn by Mr. Hiroshi Yokota, of the University of Alberta. The author would like to thank him for his excellent work. The author also wishes to express his appreciation to the University of Alberta, and to the Natural Sciences and Engineering Research Council of Canada, both of whom provided support for the project. This book is about the theoretical geometry of involute gears, and is not intended to replace the many books and manuals that exist on the design of gears. However, the full potential of the involute as a tooth profile can only be used by a designer who has a good understanding of its fundamental geometric properties. It is hoped that the book will contribute to that understanding. PART 1 SPUR GEARS Chapter 1 The Law of Gearing External and Internal Gears A spur gear is a gear cut from a cylindrical blank, with teeth which are parallel to the gear axis, as shown in Figure 1.1. If the teeth face outwards, the gear is called an external gear, and if they face inwards, like those of the gear shown in Figure 1.2, the gear is known as an internal gear. Much of the geometric theory of gears applies equally to both external and internal gears. However, for the sake of clarity, this book is restricted to the subject of external gears, except for a single chapter. The exception is Chapter 12, where we will show which parts of the theory of external gears are valid for internal gears, and we will discuss the special features that apply only to internal gears. The Requirement for a Constant Angular Veloci ty Ratio When two gears rotate together, as shown in Figure 1.3, the teeth of each gear pass in and out of mesh with those of the other gear, and this occurs in an area that lies somewhere between the gear centers C1 and C2 . The teeth from the two gears pass through the meshing area alternately, first one from gear 1, then one from gear 2, and so on. Hence, if the gears have N1 and N2 teeth, and during a certain time interval T the number of teeth from each gear passing through the meshing area is n, then the gears will make respectively (n/N 1) and (n/N2) revolutions. By expressing the number of '0 The Law of Gearing Figure'. ,. An external gear. revolutions in radians and dividing by the time taken, we obtain average- values for the gear angular velocities w, and w2 , (w, ) average (w2 )average (...!l.)211' N, T _ (...!l.) 211' N2 T Figure '.2. An internal gear. ( 1.1) (1. 2) Constant Angular Veloci ty Ratio 11 where the minus sign indicates that the direction of rotation for gear 2 must be opposite to that of gear 1. From Equations (1.1 and 1.2), we can immediately obtain a relation between the average angular veloc i ties, - N (w ) 2 2 average ( 1. 3) Equation (1.3) is true for all gears, whatever the shape of the teeth. However, if the tooth shape is arbitrary, the gears will not run smoothly. Suppose gear 1 is driving, and turns at a constant angular velocity. In general, the angular veloci ty of gear 2 wi 11 not be constant, but wi 11 be a periodic function, repeating itself as each pair of teeth are meshed, with an average value given by Equation (1.3). The variation in angular veloci ty of gear 2 leads to vibrations in the gear train, and will generally cause fatigue cracks to form in the teeth, resulting in early failure of the gears. Theoretical studies of gear tooth profiles date back to the 16th Century, but for many years the craftsmen who cut gears made no use of the knowledge that was available. Most machinery was quite slow-moving, and vibration was not considered important. Toward the end of the 18th Century, 12 The Law of Gearing machine designers began to make greater demands on the gears in the machines they bui It. The gears turned faster than before, and were more heavily loaded. Tooth breakage then developed into a serious problem, and it became necessary to choose tooth profiles which would allow the driven gear to maintain a constant angular velocity, whenever the driving gear angular velocity was constant. To achieve this end, the angular velocity ratio (w 1/w2 ) must remain constant at all times, and not simply on average, as described by Equation (1.3). The new requirement for the angular veloci ties can be expressed by the equation, ( 1 .4) The purpose of this chapter is to determine the condition that must be satisfied by the meshing tooth prof i les, if the gears are to have the constant angular velocity ratio given in Equation (1.4). However, before looking at the case of two gears meshing together, we will consider that of a gear meshing with a rack. Rack and Pinion Rack and Pinion 13 A rack is a segment of a gear whose radius is infinite. I f the number of teeth N2 of gear 2 in Figure 1.3 were extremely large, the radius of the gear would also be large, relative to the tooth size, and the teeth near the meshing area would lie almost on a straight line. In the limit, as N2 becomes infinite, the teeth would lie exactly on a straight line, as shown in Figure 1.4. When two gears mesh, the smaller of the two is called the pinion, and the larger is usually referred to as the gear. Any gear meshed with a rack is considered smaller than the rack, since the rack is part of a gear with an infinite number of teeth. Hence, it is common to speak of a rack and pinion. Whereas a gear pair is used to transmit rotary motion between shafts, a rack and pinion are used to convert rotary motion into linear, or vice-versa. One well-known application is the rack and pinion steering of many automobiles. Part of a rack is shown in Figure 1.5. The pitch p is the distance between corresponding points of adjacent teeth. If we draw any line along the rack parallel to the line of teeth, 14 The Law of Gearing the intersection of this line with the tooth profiles will determine the tooth thickness and the space width, measured along that particular line. We define the rack reference line as the line along which the tooth thickness and the space width are equal, and since their sum is equal to the pitch p, the tooth thickness and the space width measured along the rack reference line must each be equal to (p/2). We now introduce coordinates xr and Yr fixed in the rack, with their origin on the rack reference line. The xr axis lies along a tooth center-line, and the Yr axis coincides with the rack reference line, as shown in Figure 1.5. A typical point of the rack tooth profile is labelled Ar' and the tangent to the tooth profile at this point makes an angle ~Ar with the x axis. The angle ~Ar is called the rack profile angle a~ point Ar \u2022 In relating the rack velocity to the pinion angular velocity, the reasoning is identical to that used earlier for two gears. During any time interval T, the number n of rack teeth passing through the meshing area is equal to the number of pinion teeth which pass through. Thus, average values for the rack velocity vr and the pinion angular velocity ware given by the following expressions, (W)average !!E T ( 1. 5) ( 1. 6) where vr is defined as positive in the upward direction, and W is defined as positive when the angular velocity is counter-clockwise. The relation we require is obtained by eliminating (niT) from Equations (1.5 and 1.6). N 21r(w)average ( 1. 7) Equation (1.7) is exactly analogous to Equation (1.3). As with a pair of gears, the satisfactory operation of a rack and pinion requires that the relation between vr and w should remain constant. Hence, the tooth shapes must be such that vr and w satisfy the following equation, . Ar Ar - 51n IP n - cos IP n t ~ ( 1. 9) Since Ar is the contact point, the unit vector nnr lies in the direction of the common normal. The velocity of Ar' and its component along the common normal, are given by the following two equations, 16 The Law of Gearing A - cos ~ r v r (1.10) (1.11) where the dot indicates the scalar product between two vectors. If the vector from the pinion center C to point A is (xnE+Yn~), then the velocity of point A and its component along the common normal can be expressed as follows, VA wnS x (xnE+Yn~) - wYne + wxn~ (1.12) A nnr vA . Ar Ar (1.13) vn wY Sln ~ - wX cos ~ where the symbol x in Equation (1.12) indicates the vector product. We now equate the normal velocity components of Ar and A, given by Equations (1.11 and 1.13), and use Equation (1.8) to express the relation we require between vr and w. We then obtain the following equation that must be satisfied by X and Y, the coordinates of the contact point. Rack and Pinion y (x - ~) 211\" A cot 1/1 r 17 (1.14) Equation (1.14) can be interpreted in the following manner. There is a fixed point P, at a distance (Np/211\") from C on the line through C perpendicular to the rack reference line, such that the slope of line PA is equal to cot I/IAr \u2022 This means that line PA makes an angle (11\"/2 _I/iAq with the n~ direction, and it is therefore the common normal at the contact point A, since the common tangent makes an angle I/IA r with the n~ direction. The position of point P is shown in Figure 1.7. The result just proved is known as the Law of Gearing, as it relates to a rack and pinion. It may be stated in the following way. The condition that must be satisfied by the tooth profiles of a rack and pinion, in order that the relation between rack velocity and pinion angular velocity should remain constant, is that the common normal at the contact point should at all times pass through a fixed point P. The position of P is at a distance (Np/211\") from the pinion center C, on the perpendicular from C towards the rack reference line. The point P is called the pitch point. The circle passing through P whose center is at C is called the pinion pitch circle, and its radius Rp is equal to the length CP, (1.15) In Equation (1.8), we gave the relation that we require between the rack velocity and the pinion angular velocity. We used that relation to prove the Law of Gearing, which lead us to define the pitch point and the pinion pitch circle. Having now derived an expression in Equation (1.15) for the pitch circle radius, we can combine Equations (1.8 and 1.15), and we obtain a simpler form for the relation between the rack velocity and the pinion angular velocity, (1.16) The line in the rack which touches the pinion pitch circle at P, as shown in Figure 1.7, is known as the rack 18 The Law of Gearing pitch line. When the pinion and rack are in motion, the velocity of any point on the pinion pitch circle is equal to RpW, and the velocity of any point on the rack pitch line is equal to vr ' Since these velocities are equal, as we can see from Equation (1.16), the motion of a rack and pinion is identical to the motion that would be obtained if the rack pitch line and the pinio~ pitch circle were to make rolling contact with no slipping. Ci rcular pi tch The circular pitch of the pinion teeth at any radius R is defined as the distance between corresponding points of adjacent teeth, measured around the circumference of the circle of radius R. Thus, the circular pitch PR at radius R, which is shown in Figure 1.8, is given by the following expression, 211'R N (1.17) In the case when the circular pitch is measured on the pitch Circular pitch. Law of Gearing for Two Gears circle, we use the symbol Pp' and its value can substituting Rp in place of R in Equation (1.17). 211'Rp Pp N 19 be found by (1.18) When we replace the pitch circle radius Rp in this equation by the expression given in Equation (1.15), it is clear that the circular pitch of the gear at its pitch circle is equal to the pitch p of the rack, p (1.19) This result can be used to provide an alternative definition of the pitch circle of a pinion, when it is meshed with a rack. The pitch circle can be defined as the circle on which the pinion circular pitch is equal to the rack pitch p. Law of Gearing for Two Gears It was shown in the previous section that a rack and pinion behave in the same manner as if the rack pitch line and the pinion pitch circle were to make rolling contact with no 20 The Law of Gearing slipping. We now investigate whether the same idea can be used for two gears. First, we find two pitch circles which, if they made rolling contact with each other, would provide the same angular velocity ratio as the gears. And then we will establish that the Law of Gearing also applies for a pair of gears, or in other words, that the common normal at the tooth contact point always passes through a fixed point. Figure 1.9 shows two gears, with point Al of gear 1 in contact with point A2 of gear 2. The distance C between the gear centers is called the center distance. Parts of the pitch circles have been drawn in, and their radii are shown as RPl and Rp2 . The point where they touch is the pitch point P. If the pitch circles are to make rolling contact with no slipping, their radii must satisfy the following equations, C (1.20) (1.21) The angular velocity ratio that we require was given in Equation (1.4), (1.22) Equations (1.21 and 1.22) imply that the ratio of the pitch circle radii is equal to the ratio of the tooth numbers, ( 1. 23) We now solve Equations (1.20 and 1.23), to obtain the radii of the pi tch ci rc les, ( 1 .24 ) (1.25) The pitch point P, which is the point where the pitch circles touch, therefore lies on the line of centers and divides C1C2 in the ratio N1:N2 . We use this point as the origin of a fixed system of coordinates E, ~ and S, with axes Law of Gearing for Two Gears 21 in the directions shown in Figure 1.9. The position of the contact point relative to the pitch point is then given by the coordinates ~ and 1/. As we did in the case of the rack and pinion, we write down the velocities of points Al and A2 , and then equate their components along the common normal. The direction nn of the common normal, which is unknown at present, can be written in the following form, where s~ and s1/ are the components of nn in directions. Then the velocities of Al and components in the normal direction, are following four equations. Al v = w 1nS x [(Rpl+~)n~+1/n1/] A2 v (1.26) the coordinate A2 , and their given by the ( 1. 29) ( 1 .30) A A Equating the expressions for vn 1 and vn 2 , we obtain a relation which must be satisfied by the vector components s~ and s1/' o (1.31) The expression between the square brackets is zero, as we can see from Equation (1.21). The angular velocities w1 and w2 can never be equal, because for a pair of external gears the angular velocities must be of opposite sign, and for a pinion meshed with an internal gear, the pinion angular velocity must be greater than that of the internal gear. Hence, the term (w 1-w2 ) cannot be zero, and it follows that the remaining term is zero. The condition given by Equation (1.31) therefore reduces to the following form, 22 The Law of Gearing ( 1. 32) Equation (1.32) can be interpreted as showing that the unit vector nn along the common normal is parallel to line PA 1. In other words, the common normal at the contact point must always pass through the pitch point, which is the point that divides the line of centers C1C2 in the ratio N1 :N2 \u2022 This is the statement of the Law of Gearing, as it applies to a pair of gears. We proved in Equation (1.19) that when a pinion is meshed with a rack, the circular pitch of the pinion at its pitch circle is equal to the pitch of the rack. A similar result is also true for a pair of gears. The circular pitch of each gear at its pitch circle is given by Equation (1.18), Pp1 211'Rp1 N1 ( 1. 33) Pp2 211'Rp2 N2 (1.34) When we use Equations (1.24 and 1.25) to express the pitch circle radii RP1 and Rp2 ' it is immediately clear that the circular pitches of the two gears must be equal, (1.35) Path of Contact The locus of successive contact points between a pair of teeth is called the path of contact. One consequence of the Law of Gearing is that the path of contact must pass through the pitch point. To prove this statement, we need only consider the situation if it were not true. If the path of contact were to cross the line of centers at any point P' which is not the pitch point, then when the contact point was at P', the common normal at the contact point would not pass through the pitch point, and the gear pair would not satisfy the Law of Gearing. The Basic Rack 23 Conjugate Profiles and the Basic Rack Any pair of tooth profiles that satisfy the Law of Gearing are said to be conjugate. If the tooth profile of one gear is chosen arbitrarily, it is possible to find a tooth profile for the other gear, such that the two profiles are conjugate. In particular, we can specify a rack tooth profile, and then define a system of gears as having tooth profiles which are conjugate to the chosen rack. This is the method generally used by various organisations, such as the American Gear Manufacturers Association (AGMA) and the International Organisation for Standardization (ISO), to define the tooth profiles for a system of gears. The rack tooth profile is then known as the basic rack for the system of gears. In the next chapter, we will consider a particular basic rack, which is the one used to define the tooth profile of an involute gear, and we will then describe the geometry of the gear teeth. Chapter 2 Tooth Profile of an Involute Gear Basic Involute Rack In general, the tooth profile of a rack may be curved, and the profile angle ~Ar would then vary from one point of the tooth to another. We now consider a particular rack, in which the teeth are straight-sided. This is the basic rack which we use to define the tooth shape of an involute gear. The profile angle for this rack is constant, and the value of the constant will be represented by the symbol ~r' which is called the pressure angle of the basic rack. Thus, for the basic rack used to define involute tooth profiles, constant (2.1) In some cases the profile angle ~Ar may vary near the tips and the roots of the basic rack teeth. For example, the teeth may be rounded at the tips. The rack is still called an involute rack, provided a substantial part of its tooth profile is straight-sided. For the purpose of finding the shape of the gear tooth, we will start by assuming that the basic rack has teeth which are entirely straight-sided, as shown in Figure 2.1. The pressure angle is ~r' and we use the symbol Pr to represent the pitch of the basic rack. Base Pi tch of the Basic Rack The dimensions of the basic rack are determined by the values of Pr and ~r' In addition, there is a third quantity shown in Figure 2.1 called the rack base pitch, which is Standard pitch Circle 25 defined as the distance between adjacent teeth, measured along a common normal. The reason why this particular length on a rack is called the base pitch will be made clear later in this chapter. For the moment, we will simply use Figure 2.1 to express the base pitch Pbr of the basic rack in terms of its pi tch and pressure angle, (2.2) The three quantities Pr' Pbr and 4J r are the parameters used to describe the basic rack. Since they are related by Equation (2.2), it is clear that only two of the quantities are independent. We can choose any two, and then use Equation (2.2) to find the third. Standard Pi~ch Circle For any tooth profile, there are a number of quantities whose values are functions of the radius R. These include the circular pitch PR' which was introduced in Chapter 1, and the profile angle and the tooth thickness, which will be 26 Tooth Profile of an Involute Gear discussed later in this chapter. As part of the description of a gear, it is necessary to provide the values of each of these quantities at some specified radius. An obvious choice for this radius is the pitch circle radius of the gear when it is meshed with its basic rack. In Chapter 1 we defined the pitch circle of a gear as the circle through the pi tch point, and we used the symbol Rp to represent its radius. We showed there that the value of Rp depends on the pitch of the rack, when the gear is meshed with a rack, and on the center distance when the gear is meshed with another gear. In order, therefore, to identify the particular pitch circle of a gear when it is meshed with its basic rack, we will call it the standard pitch circle, and we will represent its radius by the symbol Rs' In Equations (1.15 and 1.18), we gave expressions for the pitch circle radius of a gear when it is meshed with an arbitrary rack, and for the circular pitch measured at the pitch circle, We also showed, in Equation (1.19), that the circular pitch at the pitch circle is equal to the pitch p of the rack, When we replace the rack pitch p in these equations by Pr' the pitch of the basic rack, the first two equations give the standard pitch circle radius Rs of a gear, and its circular pi tch p at the standard pi tch ci rcle, while. the thi rd s equation shows that the circular pitch of the gear at its standard pitch circle is equal to the pitch of the basic rack, RS NPr (2.3) 21r Ps 211'Rs N (2.4) Ps Pr (2.5) Tooth Profile of an Involute Gear 27 The Involute Tooth Profile We will now determine the shape of gear tooth profiles which are conjugate to the basic rack in Figure 2.1. The word conjugate means, as we defined it in Chapter 1, that the gear teeth are shaped in such a manner that the Law of Gearing is satisfied, when the gear is meshed with the basic rack. In Figure 2.2, a pinion is shown meshing with the basic rack. The plnlon pitch circle radius is Rs' given by Equation (2.3), and the pitch line is the line in the basic rack which touches the pinion pitch circle at the pitch point P. The Law of Gearing states that the common normal at the contact point must pass through P. For any particular position of the rack, there is only one point Ar of the rack tooth profile whose normal passes through P, and this point must be the contact point. The pinion tooth must therefore be shaped so that its profile touches the rack tooth at Ar \u2022 28 Tooth Profile of an Involute Gear The point of the pinion tooth profile in Figure 2.2 which coincides with Ar is labelled A. The line joining the contadt point to the pitch point is called the line of action, since it coincides with the common normal at the contact point, and therefore in the absence of friction the contact force must act along this line. The angle between the line of action and the tangent to the pinion pitch circle at P is called the operating pressure angle ~ of the gear pair. Since the line of action is perpendicular to the tooth profile of the basic rack, it can be seen from the diagram that, when a gear is meshed with its basic rack, the operating pressure angle of the gear pair is equal to the pressure angle of the basic rack, (2.6) If we were to consider the basic rack in a new position, the description of the meshing geometry would be essentially a repetition of the last paragraph. The new contact point would again lie on the line which passes through the pitch point in a direction perpendicular to the tooth profile of the basic rack. This result is true for any position of the basic rack. Hence, the path of contact, which is the locus of all contact points, is a segment of the same straight line. And since the line of action is always the line joining the pitch point to the contact point, the direction of the line of action is fixed, and the line of action coincides with the line containing the path of contact. We now construct the perpendicular from the pinion center C to the line of action, and the foot of this perpendicular is labelled E, as shown in Figure 2.2. The pinion circle with center C and radius equal to CE is known as the base circle, and its radius is represented by the symbol Rb \u2022 Since the rack tooth profile and line CE are both perpendicular to the line of action, they must be parallel, and the angle ECP is equal to ~r' We can then use triangle ECP to express the base circle radius in terms of the standard pitch circle radius, (2.7) Alternative Definition of the Involute 29 The shape of the pinion tooth must be such that the normal to the tooth profile at point A passes through P. This is a direct statement of the Law of Gearing. using the base circle just defined, we can restate the property of the tooth shape a little differently. The shape of the tooth profile must be such that the normal at the contact point touches the base circle. As the pinion rotates, the contact point moves along the pinion tooth, and therefore at each point of the profile the normal to the profile must touch the base circle. A curve with this property is known as an involute of the base circle, and this is the origin of the name \"involute gear\". Alternative Definition of the Involute There is another manner in which the involute can be defined. If the base circle is fixed, and a rigid bar AD rolls without slipping on the base circle, as shown in Figure 2.3, then the path followed by point A is an involute. It is easy to prove that the two definitions are equivalent. If point E is the contact point between the base circle and bar, then E is also the instantaneous center of the bar as it rolls. The 30 Tooth Profile of an Involute Gear velocity of point A is therefore perpendicular to EA. This means that the tangent to the involute at A is perpendicular to EA, and therefore the normal is along EA, which is the property by which the involute was originally defined. The Involute Function The alternative definition is useful in helping to derive some of the fundamental geometric equations of the involute. The point in Figure 2.3 where the involute curve meets the base circle is labelled B. This is the point where the end A of the bar would meet the base circle, if the bar rolled to the position where A was the contact point. Due to the fact that the bar rolls without slipping, we can say that the length of arc EB on the base circle must be equal to the length EA on the bar. In symbolic form, this can be written, arc EB EA (2.8) We now need to define a number of new symbols, and to derive the relations between them. Figure 2.4 shows the base Profile angle and roll angle. The Involute Function 31 circle, and an involute curve starting at point B, with a typical point A at radius R. The normal to the involute at A touches the base circle at E. We define an angle ~R' called the profile angle at radius R, as the angle between the radius through A and the involute tangent at A. The radius CE is perpendicular to EA, since EA touches the base circle, and CE is therefore parallel to the involute tangent at A. Hence, the angle ECA is equal to the profile angle, angle ECA (2.9) Referring to triangle ECA, we obtain two immediate results, (2.10) EA (2.11) Next, we define an angle ER, called the roll angle at radius R, as the angle between the radius through B and the involute tangent at A. Since CE is parallel to the involute tangent at A, the angle ECB is equal to the roll angle, angle ECB (2.12) and the length of arc EB is therefore given by the following equation, arc EB (2.13) where ER must of course be expressed in radians. We now combine Equations (2.8, 2.11 and 2.13), in order to obtain a relation between ER and ~R' (2.14 ) The angle between the radii CA and CB is clearly a function of ~R' and the name inv ~R (short for involute function of ~R) has been chosen for this function. We express the angle ACB as the difference between angles ECB and ECA, and since angle ECB is given by Equation (2.14) in radians, 32 Tooth Prof i Ie of an I nvol ute Gear the angles in the following equation are all expressed in radians. inv I/>R angle ACB (2.15) The function inv I/>R is used throughout the geometry of involute gears. Since, as we have shown, it represents an angle measured in radians, it is generally convenient to express other angles also in radians. For this reason, the following convention will be used in this book. Unless it is explicitly stated that an angle is given in degrees, it will be understood that the value is expressed in radians. For example, the polar coordinate 9R of a point on the tooth profile is given by Equation (2.35). The units are not given, so it is understood that the equation gives the value of 9R in radians. When I/>R is known, the value of inv I/>R is given by Equation (2.15). It is also sometimes necessary to find I/>R' when the value of inv I/>R is known, and this can be carried out by means of the following two steps, q (inv If> ) 2/3 R 1.0 + 1.04004q + 0.32451q2 - 0.00321q3 - 0.00894q4 + 0.00319q5 - 0.00048q6 (2.16) (2.17) The maximum error given by the procedure is 0.0001\u00b0, for values of I/>R between 0\u00b0 and 65\u00b0, and this range of I/>R values is sufficient for most practical purposes. The coefficients in Equation (2.17) are a simplified version of a set of ceofficients developed by Polder [9]. For the purpose of describing the geometry of a tooth, we generally use the radius R to specify any point A on the tooth profile. The profile angle at A is then given by Equa t i on (2. 1 0 ) , Rb R (2.18) and the angle between line CA and the fixed line CB is expressed by the involute function, Pressure Angle of a Gear angle ACB inv /fiR 33 (2.19) Another common description of the involute is based on the same idea as the alternative definition given earlier. We consider a cable wrapped round a fixed cylinder of radius Rb , with one end of the cable attached to the cylinder. If the other end of the cable is partly unwound, the path followed by that end will be an involute. If Figure 2.5 were to represent the cable and cylinder, then EA would be the section of cable unwound from the cylinder, and it is obvious that the length of this part of the cable is equal to the arc EB, where the cable was originally wrapped round the cylinder. Pressure Angle of a Gear The pressure angle /fI s of a gear is defined as the gear profile angle /fiR at the standard pitch circle. The profile angle at radius R was given by Equation (2.10), and the pressure angle can be found by setting R equal to Rs in this relation, (2.20) 34 Tooth Profile of an Involute Gear When Equation (2.20) is compared with Equation (2.7), it is clear that the pressure angle of the gear is equal to that of the basic rack, \"'r (2.21) There is a more direct proof that the two pressure angles are equal. Figure 2.6 shows the gear meshed with its basic rack, in positions such that the contact point coincides with the pitch point. If As is the point on the gear tooth profile at radius Rs' the pressure angle of the gear is defined as the angle between the radius CAs and the tooth profile tangent at As. Since As is also the contact point, when the gear and the basic rack are in the positions shown, the tangent to the gear tooth profile lies along the rack tooth profile, and the pressure angle \"'s of the gear is therefore equal to the basic rack pressure angle \"'r. It is evident that the name \"pressure angle\" is used for several angles, each defined in a different manner. The pressure angle \"'r of the basic rack is the angle between the Base pi tch 35 tooth profile and the tooth center-line, while the pressure angle ~ of a gear is the profile angle at its standard pitch s circle. Each of these two angles is a constant quantity associated with a particular gear, and in principle it can be measured on the gear. On the other hand, the operating pressure angle ~ of a gear pair only exists when the two gears are meshed. For a rack and pinion, it is defined as the angle between the line of action and the tangent to the pinion pitch circle at P, while for a pair of gears it is the angle between the line of action and the common tangent to the two pitch circles. We have shown, in Equations (2.6 and 2.21), that for a pinion meshed with its basic rack, the three pressure angles are all equal in value. In Chapter 3 we will show that, in general, the operating pressure angle ~ of a gear pair may differ from the other two pressure angles. However, even when the values are equal, it is important to know which angle is referred to when the name \"pressure angle\" is used, and for this reason the symbols ~r' ~s and ~ will be used throughout this book to distinguish the three angles. Base pitch The circular pitch at radius R was defined in Chapter 1 as the distance between corresponding points of adjacent teeth, measured around the circle of radius R. An expression for the circular pitch at radius R was given by Equation (1.17), 211\"R N The base pitch Pb of a gear is defined in a similar manner, as the distance between corresponding points of adjacent teeth, measured around the base circle. In other words, the base pitch is the circular pitch at the base circle, 211\"Rb N (2.22) In Equation (2.10), we gave an expression for the base circle radius in terms of a typical radius R and the corresponding 36 Tooth Profile of an Involute Gear profile angle /fiR' We combine the last three equations to derive a relation between the base pitch and the circular pitch at radius R, (2.23) and as a special case of this equation, we set R equal to Rs' and we obtain the corresponding relation between the base pitch and the circular pitch at the standard pitch circle, (2.24) There is a property of involute curves which we will make use of in the chapters that follow. The normal to a tooth profile at any point A is also normal to any other involute of the base circle, and if it cuts the next tooth profile at point A', the length AA' is equal to the base pitch Pb' Thus, the distance between adjacent tooth profiles, measured along a common normal, is equal to Pb' These results can be proved Gear Parameters 37 with the help of Figure 2.7. The normal to the involute at A must touch the base circle at some point E, since this is the defining property of the involute. If line EA cuts the next tooth profile at A', the normal to the second tooth profile at A' must also touch the base circle, and therefore coincides with line EAA'. Hence, a line which is normal to one involute is also normal to other involutes of the same base circle. To prove that the length AA' is equal to the base pitch, we make use of Equation (2.8), which states that EA is equal to arc EB. Referring again to Figure 2.7, we have the following relations, AA' EA' - EA arc EB' - arc EB arc BB' Since the involutes shown in Figure 2.7 are the profiles of adjacent teeth, arc BB' is by definition equal to the base pitch, and the equation can be written, AA' (2.25) We have therefore proved the statement made earlier, that the distance between adjacent tooth profiles, measured along a common normal, is equal to the base pitch. The definition of the base pitch given in Equation (2.22) would not apply in the case of a rack, because both the base circle radius and the number of teeth are infinite. However, earlier in the chapter we gave a definition for the base pitch of a rack, as the distance between adjacent tooth prof i les, measured along a common normal. In view of the result given by Equation (2.25), it is now possible to see that there is no essential difference between the two definitions. Relations Between the Gear Parameters and Those of the Basic Rack We pointed out earlier that the parameters Pr' Pbr and 'r can be used to describe the basic rack, and for gears we introduced three corresponding quantities, the circular 38 Tooth Profile of an Involute Gear pitch Ps at the standard pitch circle, the base pitch Pb' and the pressure angle 41 s \u2022 We have already shown in Equations (2.5 and 2.21) that the two pi tches and the two pressure angles are equal, The two base pitches were expressed in terms of the remaining quantities by means of Equations (2.2 and 2.24), When we compare these equations, bearing in mind that the pitches and pressure angles are equal, it is clear that the two base pi tches are also equal, = (2.26) We stated in Chapter 1 that we can define a system of gears, simply by specifying the shape of the teeth in the basic rack. The teeth of each gear in the system must be shaped so that they are conjugate to the basic rack. We have now shown that, for any gear in an involute system, the circular pitch at the standard pitch circle, the base pitch and the pressure angle must each be equal to the corresponding quantity in the basic rack. When the geometry of a gear is described, it is necessary to refer repeatedly to the circular pitch at the standard pitch circle. Since this phrase is so cumbersome, it is common practice to describe Ps simply as the \"circular pitch\". There is no danger of confusion, provided the circular pitch at any other radius is clearly identified, and therefore from now on in the book we will adopt this convention. The same convention will be used for the names of several other gear tooth quantities, whose values depend on the radius, and these will be pointed out as they occur. Tooth Profile of an Involute Gear 39 Module and Diametral pitch When we introduced the standard pitch circle of a gear, we stated that a number of the gear parameters are defined on the standard pitch circle. As part of the specification of a gear, we must therefore give the radius of the standard pitch circle, or alternatively some quantity from which the radius can be calculated. The standard pitch circle radius Rs was given originally by Equation (2.3) in terms of the basic rack pitch Pr' NPr \"\"\"21r (2.27) and since the pitch of the basic rack is equal to the circular pitch of the gear, the radius of the standard pitch circle can be expressed directly in terms of the circular pi tch, (2.28) For a system of gears conjugate to a particular basic rack, it would therefore be necessary to specify only the value of the circular pitch Ps' which is the same for every gear in the system, and we would then use Equation (2.28) to calculate the standard pitch circle radius of each gear. This method of specification was in fact used in the past, and gears in which the circular pi tch is specified as a convenient length are known as \"circular pitch gears\". However, they are seldom made today, as they have one slight disadvantage. If the value of the circular pitch is chosen as a round number, the standard pitch circle radius is always an inconvenient size, due to the presence of the factor w in Equation (2.28). It has been found more practical to design gears in which the standard pitch circle radius is a round number. With this consideration in mind, we introduce a quantity called the module m, defined in terms of the basic rack pitch, m (2.29) We now combine Equations (2.27 and 2.29), in order to express the standard pitch circle radius in terms of the module, 40 Tooth Profile of an Involute Gear (2.30) and, since once again the circular pitch of the gear is equal to the basic rack pitch, a relation between the circular pitch and the module can be found immediately from Equation (2.29), (2.31) The module, which we have shown is proportional to the circular pitch, is used not only in the calculation of the standard pitch circle radius, but also as a measure of the tooth size. When two gears are meshed together, they must clearly have teeth of approximately the same size, and in prac t ice they are des i gned with the same module m and the same pressure angle ~s. In other words, the two gears are both conjugate to the same basic rack. We will show in Chapter 3 that these conditions ensure correct meshing of the gears. The module can be measured in either mms or inches. In practice, it is most commonly measured in mms, since the module is generally used in countries which have adopted the metric system. In North America, the quantity used at present to specify the tooth size of a gear is known as the diametral pitch Pd. This is defined as the number of teeth in the gear, divided by the diameter of the standard pitch circle, N 2Rs (2.32) A relation between the diametral pitch and the circular pitch can be found from Equations (2.28 and 2.32), ..JL Ps (2.33) and when we use Equation (2.31) to express the circular pitch in terms of the module, it is clear that the diametral pitch is equal to the rec iprocal of the module, 1 m (2.34) Since the diametral pitch is expressed in teeth per inch, Equation (2.34) requires that the module be given in inches. Tooth Thickness 41 It seems probable that the use of the diametral pitch will eventually be abandoned in favour of the module. The gear geometry in this book is therefore described in terms of the module, and the module is also used in most of the examples at the end of each chapter. However, since the diametral pi tch is still widely used in North America, a number of examples are also included in which the tooth size is specified by means of the diametral pitch. For these problems, the module will first be found, using Equation (2.34), and the remaining calculations will then be carried out in terms of the module. Tooth Thickness The tooth thickness at radius R is defined as the arc length between opposite faces of a tooth, measured around the circumference of the circle of radius R. We will show in this section that when we know the tooth thickness at one radius, we can calculate it at any other. Thus, it is only necessary to specify the tooth thickness at one particular radius, and for this purpose we generally choose the standard pitch circle. The symbol ts is used to designate the tooth thickness at the standard pitch circle, and tR is used for the tooth thickness at radius R. The tooth thickness ts at the standard 42 Tooth Profile of an Involute Gear pitch circle is described simply as \"the tooth thickness\", in the same way that the circular pitch at the standard pitch circle is called the circular pitch. The gap between the teeth, measured around the circle of radius R, is called the space width at radius R, and like the tooth thickness, the space width is generally measured on the standard pi tch circle. Since the tooth thickness, the space width and the circular pitch are all defined as arc lengths, as shown in Figure 2.8, it is clear that the sum of the tooth thickness and the space width at any radius R is equal to the circular pi tch at radius R. A gear tooth is shown in Figure 2.9, with points B, As and A on the tooth profile at radii Rb , Rs and R. We will derive an expression for the tooth thickness tR at radius R, assuming the tooth thickness ts is known, and we start by finding the polar coordinate 9R of point A, angle xCA angle xCAs + angle AsCB - angle ACB Tooth Thickness 43 The angle ACB is given by the involute function inv 'R' as we showed in Equation (2.19), and since the profile angle at the standard pitch circle is equal to the pressure angle 's' the angle AsCB is equal to inv,s. Hence, the expression for 8R can be written, = (2.35) Having found the polar coordinate 8R of point A, we can immediately write down an expression for the tooth thickness at radius R, In order to find a relation between the thicknesses at any two radii R1 and R2, we use Equation twice to write down the tooth thicknesses tR and tR ' h 1 \" b h ,1 2 t en e lmlnate ts etween t e two expressIons, tR tR = R2[r + 2(inv 'R - inv'R )] 2 1 1 2 (2.36) tooth (2.36) and we (2.37) where 'R and /fiR are the prof ile angles at the two radi i. 1 2 44 Tooth Profi Ie of an I nvol ute Gear There is another quantity which will be useful in the description of a gear tooth profile, in particular in Chapter 11, where we discuss the tooth strength of a gear. We define an angle YR, as shown in Figure 2.10, as the angle between the profile tangent at point A and the tooth center-line, which coincides with the x axis. Since line CE in Figure 2.10 is parallel to the profile tangen~ at A, the angle between CE and the x axis is equal to YR' and we can therefore express YR as follows, (2.38) We replace 8R by the expression given in Equation (2.35), and the equation for YR then takes the following form, Standard Basic Rack Forms 45 and bs between these circles and the standard pi tch circle are called the addendum and the dedendum, and for this reason the tip and root circles are also called the addendum and dedendum circles. The sum of the addendum and the dedendum is known as the whole depth of the gear teeth. Finally, we use Figure 2.11 to express the addendum and the dedendum in terms of RT, Rs and Rroot ' Standard Basic Rack Forms R - R T s (2.40) (2.41) Although it is possible to choose arbitrary values for the module m and the pressure angle ~r of a basic rack, there are a number of standard values which are most frequently used. As we have shown, the module and pressure angle ~s of a gear are equal to the module and pressure angle ~r of its 46 Tooth Profile of an Involute Gear basic rack, so by choosing standard values for the basic rack parameters, we are also choosing the same values for the parameters of the gear. These standard values are recommended by organisations such as the ISO and the AGMA, first because they have been found in practice to give satisfactory results, and secondly for economic reasons. The tools used for cutting gears have dimensions which depend on the module and the pressure angle of the gear to be cut. A gear manufacturer will normally keep in stock the tools necessary for cutting gears with standard values of module and pressure angle, but when di fferent values are required, the cutting tool must be made specially, and the cost of the gear is therefore increased. Preferred values for the module, measured in mms, are as follows, 1, 1.25, 1.5, 8, 10, 12, 2, 2.5, 3, 16, 20, 25, 4, 5, 6, 32, 40, 50, and the preferred values for the diametral pitch, measured in Standard Basic Rack Forms 47 teeth per inch, are given below."
        ]
    },
    {
        "image_filename": "designv10_4_0003427_978-94-017-0657-5_48-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003427_978-94-017-0657-5_48-Figure4-1.png",
        "caption": "Figure 4. The intersection of three Figure 5. The CAD Model of a 3-CRR othorgonal planes. TPM, from (Kong and Gosselin, 2001c).",
        "texts": [
            " An 1-0 decoupled linear TPM refers to a linear TPM for which three translations along three orthogonal directions can be controlled inde pendently by three actuators. In this case, the forward displacement analysis of linear TPMs can be further simplified. Recalling the geometric interpretation of the forward displacement analysis of TPMs, the forward displacement analysis of linear TPMs Linear TPMs. consists in finding the intersection of three planar leg-surfaces. When the three planar leg-surfaces are perpendicular (see planes PABC, PADE and PCFE in Fig. 4), the translation of the moving platform along the intersection of any two of the three planar leg-surfaces is controlled by the position of the other planar leg-surface. For example, the translation of the moving platform along PC, i.e., the intersection of planes PABC and PCFE, is controlled by the position of plane PADE. We can thus conclude that for a TPM to be 1-0 decoupled, its three planar leg surfaces should be perpendicular. Among the linear TPMs, the 3-PPP, 3-PPRR, 3-PRPR, 3-PRRP, 3- PRRR, 3-RRPP, 3-RRPil:R, 3-RRRPR, 3-RRRRP and 3-RRRRR linear TPMs are TPMs with constant-orientation planar leg-surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000509_j.ijimpeng.2020.103671-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000509_j.ijimpeng.2020.103671-Figure1-1.png",
        "caption": "Fig. 1. (a) Design for a parallel sheet structure of 170 mm height, 210 mm width and 1 mm wall thickness for each sheet. The 0\u00b0-direction aligns with the printing direction. (b) An inclined close-up view of the printed rectangular block from the top.",
        "texts": [
            " Finite element simulations with the obtained material model are then validated through low and high rate compression experiments on additively-manufactured shell-lattices. All additively manufactured parts are produced through selective laser melting (SLM) on a Concept Laser M2 system with stainless steel 316L powder featuring a particle size distribution in the range of 20- 50\u00b5m. According to our manufacturing partner, the same machine settings have been used for all additively-manufactured structures. The specimens for the characterization of the base material are obtained from a special rectangular box featuring multiple parallel walls of 1mm thickness (Fig. 1). The parallel-sheet design of this structure enables the convenient extraction of sheet metal specimens for material characterization through water-jet cutting. Overall 6 different types of flat specimens are machined: \u2022 Uniaxial tension (UT) specimens featuring a 40mm long and 10mm wide gage section for low and intermediate strain rate testing (Fig. 2a). \u2022 Short uniaxial tension specimens (D-UT) featuring a 15mm long and 5mm wide gage section. This specimen is solely used for high strain rate testing (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000230_j.matchemphys.2020.123487-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000230_j.matchemphys.2020.123487-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of hardness measurement.",
        "texts": [
            " The polished samples were etched in aqua regia (the volume ratio of concentrated hydrochloric acid and concentrated nitric acid is 3:1) for 10s, and then the microstructures of the top, section and front sides of the etched SLM 316L were observed by optical microscope. The Vickers hardness tests were carried out on the top, section and front of the SLM 316L and rolled 316L samples by Vickers hardness equipment. Under a load of 100 g and a dwell time of 15 s, the distance between measuring points is 0.5 mm. As shown in Fig. 2, for the top surface, the hardness values were measured along the direction parallel to the x-axis and y-axis (Tx and Ty), respectively. For sections, the hardness value were measured along the direction parallel to the x-axis and z-axis (Cx and Cz). For the front face, the hardness values were measured along the direction parallel to the y-axis and z-axis (Fy and Fz). The hardness tests of worn samples were measured along the wear track, and the results of hardness were compared before and after wear test",
            " Materials Chemistry and Physics 254 (2020) 123487 boundary of the molten pool to the center of the molten pool. The laser heat source is mainly concentrated in the molten pool, and the edge of the molten pool is small, so that it can be seen from Fig. 3a, b and 3c that there are pores or poor fusion at the junction of the molten pool (in the yellow box). Unlike the rolled 316L, SLM 316L also has specific substructure, which is related to Marangoni convection. Fig. 4 shows the hardness test results along the specific plane and direction as shown in Fig. 2 before the wear test. From Fig. 4a and b, it can be seen that the hardness values in different directions of different forming surfaces are basically not very different. The hardness values of any formed surface is higher than that of rolled 316L. This is because in SLM forming process, the laser scanning speed is very fast, the cooling rate of each molten pool is very high [18] (103 K/s-108 K/s) and there are very large thermal gradients in the molten pool, the internal atoms of the formed parts move violently, resulting in crystal defects such as vacancy, generating a large number of dislocations in the structure, accumulating large residual stress, forming a large number of fine grains, hindering the passage of dislocations, and making that SLM 316L has a large number of high-density dislocations [21,22]\u3002 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003783_38.55154-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003783_38.55154-Figure2-1.png",
        "caption": "Figure 2. A physical interpretation of the columns of the Jacobian matrix that describes the kinematic transformation between the joint velocities and the velocity of the hand.",
        "texts": [
            "g., a hand), and the controllable variables are the joints in the limb. The relationship between these trajectories can be specified as positions, velocities, accelerations, or even higher order deriva- 64 IEEE Computer Graphics & Applications tives. Using velocities is particularly convenient, because we can avoid the typically nonlinear relationship between positions. Consider once again the motion of the human arm in the sagittal plane, where desired trajectories are given for the hand (see Figure 2). The relationship between the velocity of the hand, denoted by the 2D vector x, and the joint velocities, denoted by the 3D vector 6, is given by X = J0 (1) where J is known as the Jacobian matrix and is conveniently represented by its columns as The columns of J have a simple physical interpretation, because they are the resulting hand velocities for a unit rotational velocity at each of the respective joints. They can be easily calculated by noting that they are closely related to the vector defined from a joint\u2019s axis to the hand, denoted by pi (pl, p z , and p3 in Figure 2). In particular, the magnitudes of the ji\u2019s and pi\u2019s are equal, and their directions are perpendicular. This relation is easily extended to three dimensions using the cross product of a unit vector along the axis of rotation with the vector pi to obtain ji.\u201d The above description shows that the velocity produced at the hand by a given joint velocity will vary, depending on the configuration of the arm. This fact is sometimes emphasized by explicitly denoting the Jacobian\u2019s dependence on the joint angles by writing J(0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000187_13621718.2019.1595925-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000187_13621718.2019.1595925-Figure8-1.png",
        "caption": "Figure 8. Al5Si inter-ring shell segment deposited by hybrid WAAM/Milling manufacturing, (a) as-deposited, (b) milled shape on side surface, (c) overall shape of the shell, (d) milled shape on top surface, (e) section view of design drawing.",
        "texts": [
            " The spreading time to the sides is so long that the liquid metal was solidified before it spreads fully at the edge. It enhances the surface accuracy by increasing the fluctuation of side wall profile. Figure 7. Schematic diagram of the forces acting on liquid metal and melt flow, (a) WAAM, (b) hybrid manufacturing (t < 1.2mm), (c) hybrid manufacturing (t > 1.2mm). Where \u03b8 is liquid\u2013solid contact angle, \u03c3 is surface tension, Ff is buoyancy, f is friction, Farc is arc force, G is gravity and F is the resultant. Figure 8 shows an Al5Si hybridWAAM/Milling manufactured inter-ring shell segment with some stiffeners in the inner wall. The height is 210mm, the bottom diameter is 190mm, and the top diameter is 150mm (Figure 8(e)). Using WAAM, it is difficult and costly to the secondary machining of the shell arm and reinforcing bar because of the ring top cover. However, it can be fabricated effectively by hybrid WAAM/Milling manufacturing. First, a layer is created by the WAAM (Figure 8(a)), then the upper surface is milled by 0.8mm (Figure 8(d)). After repeating the two steps for 10 layers, the surface of the deposited shell and reinforcement is milled to satisfy the design requirement (Figure 8(b)). Subsequently, this processing cycle is repeated until the part is completed (Figure 8(c)). (1) When the milling thickness (t) is at the range of 0.4\u20131.2mm, the surface roughness and machining allowance of hybrid WAAM/Milling manufacturing are smaller than those of the WAAM by 22.9 and 31.6%, respectively. When the t increases to 1.6mm, they increase to be 71.5 and 22.5% higher than those of the WAAM, respectively. (2) An empirical formula was derived to predict the total deposition height of this hybrid manufacturing, which is linear with the t and the deposition layers. (3) The accuracy improvement was achieved by the change of melt flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000011_jsen.2019.2918018-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000011_jsen.2019.2918018-Figure8-1.png",
        "caption": "Fig. 8. Flux vector distribution showing the existence of stray magnetic flux (cross-sectional view).",
        "texts": [
            " The test motor with parallel-connected distributed windings was fed by the three-phase voltage source in the simulation, as shown in Fig. 7. Two winding short-circuit faults at different locations were alternatively set by controlling the switches S1 and S2. When the switch S1 is turned on, the winding a1 is shorted by a fault resistor Rf. Similarly, when the switch S2 is turned on, the winding a7 is shorted by the fault resistor Rf. The winding a1 and a7 are located at two different places with a 180-degree difference, as illustrated in Fig. 6(a). The resistance of the fault resistor Rf in the simulation is 0.02 \u03a9. Fig. 8 shows the simulated flux vector distribution of the test motor which rotated at 1500 rpm. It can be observed that the stray magnetic flux \u03a6st originated from the windings in stator slots and leaks outside the stator yoke. Hence, the changes in the phase currents and winding healthy conditions led to the change of \u03a6st. Fig. 9 shows the simulation results of winding currents (i.e., ia1, ia2 and ia3), fault resistor current (iRf), radial components (Brad) and tangential components (Btan) of stray magnetic field at the four sensing points (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003541_s0263574700009358-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003541_s0263574700009358-Figure2-1.png",
        "caption": "Fig. 2. A six-freedom arm at a special configuration: axes $2 and $3 are coplanar with and parallel to one that is linearly dependent on three others ($4, $5, and $6).",
        "texts": [
            "j (8) These four linear conditions define a general two-system (ref. 1, Section 12.5) that contains a second screw of zero pitch directed along the line AB (Figure 1). Since equations (8) have been obtained independently of $5 it follows that we may give $5 any coordinates whatever and there will be one screw of the two-system reciprocal to it. This can easily be checked, as can the facts that $',$\" (equations (5) and (7)), and the zero-pitch screw along AB all satisfy equations (8) and so belong to the two-system. The arm of Figure 2 resembles that of Figure 1 except that $5 and $6 (concurrent in C with $4) are now given general directions, and the orientation of $, (normal to the y-axis) is not specified. The arm is at a special configuration because all six actuator-screws have a common transversal along AC, this being a zero-pitch reciprocal screw $' = (2a, - 1 , 0 ; 0,0, -2a), see Appendix, Section 8. (If the distance a is \\/5 it is consistent with Figure 1). We have http://journals.cambridge.org Downloaded: 31 Mar 2015 IP address: 130",
            ") Then rank of 0 0 0 0 0 0 0 0 -la la - 1 0 0 0 -la la - 1 0 0 0 -la la - 1 0 0 0 -la la - 1 0 0 0 -la la - 1 0 from which we see that the special configuration arises through the linear dependence of $2, $3, $4, $5, and $6, which must all belong to the same four-system, in fact that first special four-system (ref. 1, Section 12.9.1). Accordingly we might expect that any one of the three actuators associated with $3, $4, and $5 could effect an escape. But this is not so; $3 is the only possible one, a conclusion that is evident from inspection of Figure 2. But we need a better-founded explanation of this phenomenon so that a general Theorem may be stated. The four-system of screws $2 to $6 can here be broken down into two sub-systems that are not independent. The first is a second special two-system (ref. 1, Section 12.5.2) defined by $2 and $3; the second is a second special three-system (ref. 1, Section 12.7.2) comprising all the zero-pitch screws on the \u00b0\u00b02 lines of the bundle centred on C, defined by $4, $5, and $6. One of the screws of the two-system is linearly dependent on $4, $5, and $6, and so belongs to the three-system; this screw $ (zero-pitch) passes through C and lies parallel to the y-axis, having coordinates $- (0 ,1 ,0 ; 0,0,2a)",
            " The following general Theorem can now be stated: Theorem 2: 'If an n-system listed in Table I is, at any general arm-configuration, defined by a group of n sequentially-joined actuator-screws, 0 < n < 5 , and if, at a certain (special) configuration, this n-system also contains another screw that is either (i) an actuator-screw or (ii) a screw linearly dependent on two or more other actuator screws, then no actuator-screw belonging to this rt-system can effect an escape from the special configuration.' In the Example of Figure 2 the n -system of Theorem 2 (second special three-system) is defined by $4, $5, and $6. Theorem 2(ii) applies when the point C lies in the plane of $2 and $3. $2 and $6 cannot, in any case, effect an escape, since actuation at either does not alter the relative positions of all five affected screws. Theorem 2 rules out $4 and $5, leaving $3. Theorem 2(i) applies in the even more elementary Example of Figure 1, the n-system (one-system, the first entry in Table I) being simply $6 (or $4), the special configuration arising when $4 (or $6) belongs to the one-system",
            " The only logical strategy seems to be to use equation (1) to find the conditions that define a reciprocal system, and then use the knowledge of this system and of the system(s) to which the actuator-screws belong to assist in determining how to effect an escape. Embodiment of this approach in any control algorithm may not be an attractive or even a feasible proposition. However, systematic avoidance of or an escape from configurations at which one freedom is lost could prevent any larger number of freedoms ever being lost. Of the many possible two- and three-freedom-loss configurations that can be identified, a few are now chosen and dealt with briefly. (a) Loss of two freedoms (i) In Figure 2 let $5 and $6 remain generally-orientated, and let $, lie in the ry-plane; then $, = (1,0,0; 0,0, -1) . From equation (1) the reciprocal screw system is defined by the four conditions 2aM'-R*' = 0, this being a first special two-system (ref. 1, Section http://journals.cambridge.org Downloaded: 31 Mar 2015 IP address: 130.159.70.209 178 Jacobian and its cofactors 12.5.1) comprising a pencil of zero-pitch screws in the xy-plane, centre C, all of them intersecting all six actuator-screws. All six actuator-screws belong to a first special four-system (ref. 1, Section 12.9.1) which contains (as subsets) not only the two sub-systems of Section 5 but also the fourth special three-system (ref. 1, Section 12.7.4) that contains the four linearly dependent screws $1; $2, $3, and $4. Actuation at $3 on its own destroys linear dependence within all the screw systems and restores the full six freedoms to the end-effector. (ii) In Figure 2 let $6 and $4 be coaxial (as in Figure 1), and let $5 be parallel to $2 and $3 and coplanar with them. Another first special two-system of zero-pitch reciprocal screws comprising a planar pencil in the xy-plane, centre A, applies, and is defined by L' + R*' = 0, Since the one-system to which $4 and $6 belong is in Table I, $5 must be actuated; but $3 needs to be actuated too to restore the sixth freedom. (iii) In Figure 4 let $5 be turned through 90\u00b0 to bring $2, $3, and $6 coplanar in the xy-plane, and let $t be directed along the z-axis"
        ],
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    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.9-1.png",
        "caption": "Fig. 7.9 Roberts-Chebyshev theorem",
        "texts": [
            " Alternatively, a linkage containing only revolute pairs was often used to generate a coupler curve to approximate a needed straight line. Besides Watt, a Russian scholar, Chebyshev, also put forward a linkage which could generate an approximately straight line (Ap\u0442o\u0431o\u043be\u0432c\u043a\u0438\u0439 1953). In addition to straight lines, linkages could also realize approximately circular curves and other shaped curves. Before CNC machine tools appeared, specially designed coupler curves were used to machine parts with irregular shapes. This situation called for the establishment of a theory. As shown in Fig. 7.9, a coupler curve generated by the point P could be attached in three different four-bar linkages O1A1A2O2,O1C1C2O3, andO2B1B2O3. This conclusion was proved independently by a British scholar, Samuel Roberts, in 1875, and a Russian mathematician, P.Chebyshev, in 1878, thus, knownasRoberts-Chebyshev theorem (Verstraten 2012). 7.2 Development of Modern Mechanism Subject 229 230 7 Birth and Development of Modern Mechanical Engineering Discipline Linkages were widely applied in many machines during the two industrial revolutions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003859_detc2007-34210-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003859_detc2007-34210-Figure3-1.png",
        "caption": "Figure 3: Definition of a local coordinate system",
        "texts": [
            "org/about-asme/terms-of-use \u23aa \u23aa \u23a9 \u23aa\u23aa \u23a8 \u23a7 = = =+ 0),,( ),,( ),,(),,( 22 quf Lquz Rquyqux \u03b8 \u03b8 \u03b8\u03b8 (3) Consequently, the coordinates ( x , y , z ) and the unit normal components ( xn , yn , zn ) of the corresponding surface point can be obtained, which are called the tooth surface nominal data representing the theoretical target tooth surfaces. In case of inverse engineering, the target tooth flank form may be numerically represented by the measured coordinates of a group of grid points of a master hypoid pinion or gear. In order to visually represent the tooth flank form error, a local coordinate system S(X, Y,\u03b4 ) is defined for each side of tooth flank and shown in Figure 3. We assume that the positive direction of axis \u03b4 is the same as that of the tooth surface normals whose positive directions are defined as pointing out of the tooth from inside to outside. Under such assumption, a positive error indicates a thicker tooth than the target one, and a negative error indicates a thinner tooth. Each side of tooth surfaces is rotated at an angle 1\u03b1 and 2\u03b1 respectively so that at the reference point coordinate 0=y . The nominal data of the grid points of the convex and concave tooth surfaces are then transformed into the same coordinate system as that of the Coordinate Measuring Machine (CMM) and can be numerically represented by the position vectors and unit normals as, Downloaded From: http://proceedings",
            " Using a regression method, the error surfaces can be represented by polynomials of two variables (up to 6th order) as, \u23aa\u23a9 \u23aa \u23a8 \u23a7 ++++++= ++++++= 6 27 2 54 2 3212 6 27 2 54 2 3211 ... ... YbYbXYbXbYbXb YaYaXYaXaYaXa \u03b4 \u03b4 (7) Here, 1\u03b4 and 2\u03b4 are errors of concave and convex side tooth surfaces respectively. The goal of the correction process is to compensate for error surfaces 1\u03b4 and 2\u03b4 by an appropriate correction of the 3 Copyright \u00a9 2007 by ASME Copyright \u00a9 2007 by The Gleason Works Terms of Use: http://www.asme.org/about-asme/terms-of-use universal motion coefficients. Since coordinates X and Y correspond to the tooth profile and lengthwise directions respectively (Figure 3), the coefficients in Equation (7) indicate specific geometric meanings. For instance, 1a and 2a are first order errors or pressure angle and spiral angle errors respectively; 3a , 4a and 5a are second order errors in profile, warping, and lengthwise curvatures; and so on. Using the universal motions represented by Equation (1), we may minimize the higher order components of the error surfaces 1\u03b4 and 2\u03b4 . For a face-mill single-side process, the correction calculation is conducted separately on each tooth side and the tooth thickness error is corrected to the nominal thickness directly using the machine stock divider"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000915_j.addma.2021.102045-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000915_j.addma.2021.102045-Figure1-1.png",
        "caption": "Fig. 1. The orientation of the tensile samples machined from the components are shown: Transverse and Longitudinal.",
        "texts": [
            " The morphologies at the top and middle positions of the three depositions were observed through the Electron Backscatter Diffraction (EBSD). The grain size of the depositions were obtained from EBSD data processed by HKL Channel 5, Tango. Dog-bone-shaped tensile samples were separately cut from the component, along the directions perpendicular and parallel to the deposition direction, with the gauge length of 6 mm and the cross section of 2 (width) \u00d7 2 (thickness) mm2. The schematic diagram of sampling is displayed in Fig. 1. According to the D1708 standard of American Society for Testing of Materials (ASTM), the tensile test with displacement control was conducted at the nominal rate of 0.005 mm/s. During LAMW\uff0cY2O3 particles move with the flowing liquid metal, causing the temperature of the particles to change as the ambient temperature changes. In order to study the influence of melt pool flowing and heat distribution on the evolution of Y2O3 particle morphology, a CFD model of single-pass LAMW was established to calculate the temperature distribution on the deposited bead and the molten metal flow path inside the bead"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003751_s0263574708004748-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003751_s0263574708004748-Figure1-1.png",
        "caption": "Fig. 1. Construction of the spherical robot.",
        "texts": [
            " In Section 3, the kinematic model of the system is derived. Section 4 describes the path planning algorithm proposed. In Section 5, the equations of motion are derived using Lagrange\u2013D\u2019Alembert principle and torque equations are obtained for execution of the motion. In Section 6, simulation results for the algorithm are reported. Section 7 provides concluding remarks. The spherical robot consists of a spherical aluminium shell within which four D.C. motors are mounted symmetrically on the inner surface as shown in Fig. 1. On one axis (z-axis), two diametrically opposite motors B1 and B2 are mechanically coupled to rotors. Both the motors are controlled by common reversible electronic speed controller and are actuated in tandem. Similarly, on the perpendicular axis, (x-axis), two motors A1 and A2 are attached to identical separate rotors. Both these motors are controlled by one electronic speed controller and are actuated in tandem. When both the motors on one of the axes are actuated, the corresponding rotors start rotating in one direction and the spherical shell starts rolling in the opposite direction due to conservation of angular momentum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003030_1.1767815-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003030_1.1767815-Figure5-1.png",
        "caption": "Fig. 5 Turbulent and laminar zones",
        "texts": [],
        "surrounding_texts": [
            "Following Dawson @8#, the power loss is divided into the windage loss at the front and rear faces of the gear ~or disk!, and the windage loss at the teeth ~or side of the disk!. 4.1 Front\u00d5Rear Faces. The friction force on any elemental annulus ~Fig. 4! can be expressed as: dF5 1 2 Cxrv2r2ds5pCxrv2r3dr (6) with: r: fluid density (kg/m3) Cx5n/(rvr2/m)m , according to @9,10# ~see Table 4!, where n and m are 2 coefficients depending on the nature of the flow. The dimensionless moment coefficient C f is deduced by integrating the elemental moments over the total surface (S) as: C f5 M 1 2 rv2R5 5 2p R5 n S rv m D m E (S) r422mdr (7) Table 3 Constants in Eq. \u201e5\u2026 a b g d c 60 20.25 0.8 20.4 0.56"
        ]
    },
    {
        "image_filename": "designv10_4_0002816_ip-cta:19951613-Figure20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002816_ip-cta:19951613-Figure20-1.png",
        "caption": "Fig. 20",
        "texts": [
            " Likewise, BTT control complicates the calculation of missile position as a highly nonlinear axes transformation is now required. Applying the basic laws of aerodynamics while making assumptions such as constant mass, small attack angle a and small sideslip angle b. the nonlinear model shown in Section 9.2 can be developed [31]. This includes many of the important nonlinear aspects of BTT-CLOS guidance, such as the axes transformation and nonlinear 1EE Proc.-Control Theory Appl., Val 142, No. I , January 1995 cross-coupling. The various parameters of this model are assumed constant and are as given in Section 9.3. Fig. 20 shows the axis system and the sign convention used 60 40 20- - - and highlights the roll, yaw and pitch motions of the missile. Here r#J represents the role angle, q is the pitch rate with r the yaw rate, respectively. Within the BTT framework, the system inputs used for control are the aileron angle and the elevator angle 6. The complete BTT-CLOS missile under closed-loop control is shown in Fig. 21. Here z, and y, represent the position of the line of sight in the plane of the missile. Axis system and sign congention In practice there are many nonlinearities present within the missile control system, such as axis transformation, actuator saturation, nonlinear cross-coupling between pitch and yaw dynamics and nonlinear variations of aerodynamic derivatives [32]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.15-1.png",
        "caption": "Figure 5.15. Meshing diagram of a gear and rack cutter.",
        "texts": [
            " The path followed by Ahc is a circle of radius Rhc ' and the point where this circle intersects the common tangent to the base circles is labelled Hc. Since point Af of the gear coincides with point Ahc of the cutter when the cutting point is at Hc' the fillet circle of the gear must Radius of the Fillet Circle 139 pass through point Hc' and its radius Rfg is given by the following expression, (5.47) The radius Rhc in this equation can of course be replaced by the tip circle radius RTc , for pinion cutters with no rounding at the tooth tips. The meshing diagram is shown in Figure 5.15, for the case when a rack cutter is used to cut the gear. We consider the rack cutter when it is offset a distance e from its standard position, so that its reference line lies a distance (Rsg+e) from the center of the gear blank. The distance between point Ahr and the rack cutter pitch line is then equal to (h-e). The involute section of the gear tooth profile is cut by the straight-sided part of the cutter tooth, and the end point Af of the gear tooth involute is therefore cut by point Ahr on the cutter",
            " When we check to see whether undercutting will take place, we can 142 Gear Cutting I, Spur Gears therefore treat the cutter tooth as if it ~nded at point Ahc ' We make the check, simply by determining the position of point Hc on the path of contact. For no undercutting, Hc must lie between the pitch point and the interference point E \u2022 In g other words, the length HcEc in Figure 5.14 must be less than or equal to EgEc' and the condition for no undercutting can be expressed as follows, (5.49) The same considerations on undercutting apply when a gear is cut by a rack cutter or a hob. The path of contact in Figure 5.15 must end between the pitch point and the interference point, so the length HrP must be less than EgP, and we obtain the following condition for no undercutting, Rbg tan tPs (5.50) It can be seen that, for any particular value of the cutter offset e, there is a lower limit to the base circle radius in the gear being cut, if there is to be no undercutting. This means, in effect, that there is a lower limit to the number of teeth in the gear. For example, if a 20\u00b0 rack cutter is used with a value of h given by Equation (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure3-20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure3-20-1.png",
        "caption": "Figure 3-20 Magnetic dipole rotor in a rotating magnetic field.",
        "texts": [
            "1) where / is the rotational inertia of the rotor, c is a viscous damping constant, M is the magnetic dipole strength of the rotor dipole, and Bs and Bd are the intensities of the steady and dynamic magnetic fields, respectively. Figure 3-19 shows a comparison of periodic and chaotic rotor speeds under periodic excitation. Additional discussion of this experiment may be found in Chapters 4 and 6. Chaos theory has also been used to excite Physical Experiments in Chaotic Systems 93 nonperiodic vibrations in a multi-pendulum mobile sculpture by Viet et al. (1983). Magnetic Compass Needle Another magnetomechanical device with stochastic dynamics is a compass needle in an oscillatory or rotating magnetic field (Figure 3-20). The rotating magnetic field can be created by two Helmholtz coils with sinusoidal currents applied with different phases to each coil. Croquette and Poitou (1981) have performed experiments on this problem. They have modeled this problem with the following equation and observed period-doubling bifurcations. sin(0 (3-3.2) Here damping is very small (y//<o \u00ab 10 2). This system is an example of a problem with near zero dissipation (y = 0) and is referred to as a Hamiltonian system. As discussed in the example of the Fermi accelerator model, chaos in systems without dissipation is often referred to as stochasticity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000691_j.ast.2021.106573-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000691_j.ast.2021.106573-Figure3-1.png",
        "caption": "Fig. 3. The schematic view of the manipulator\u2019s arms.",
        "texts": [
            " To calculate the linear and angular velocities of the end-effector in the inertial frame, we have [42]: P\u0307e = P\u0307b \u2212 Skew ( RbPb eb ) \u03c9 + RbP\u0307b eb, (3) \u03c9e = \u03c9 + Rb\u03c9 b eb, (4) where \u03c9 and \u03c9b eb represent the angular velocity of the UAV and the relative angular velocity of the end-effector expressed in the O b . To derive the relative linear and angular velocities of the endeffector with respect to O b , we have vb eb = [ P\u0307b eb \u03c9b eb ] = [ JP JO ] \u03b7\u0307 = Jb eb\u03b7\u0307, (5) where \u03b7 = [ \u03b71 \u03b72 \u03b73 ]T is the vector of joint angles for a 3-DOF manipulator (Fig. 3). In addition, Jb eb is the Jacobian matrix, which can be computed using the Denavit-Hartenberg (DH) parametrization [5]. Also, the angular velocity \u03c9 can be obtained using the rates of the Euler angles as follows: \u03c9 = T\u0307 (6) where = [ \u03d5 \u03b8 \u03c8 ]T is the vector of the Euler angels and T = Rb \u239b \u239d 1 0 \u2212 sin \u03b8 0 cos\u03d5 sin\u03d5 cos \u03b8 0 sin\u03d5 cos\u03d5 cos \u03b8 \u239e \u23a0 = RbQ. (7) Finally, if the generalized state variables of the aerial manipulator are defined as: q = [ PT b T \u03b7T ]T , (8) then the equations of the linear and angular velocities of the endeffector can be summarized as follows: ve = [ P\u0307e \u03c9e ] = [ BP BO ] q\u0307 = ( I3 \u2212Skew ( RbPb eb ) T RbJP 03 T RbJO ) q\u0307"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003123_s0094-114x(03)00065-x-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003123_s0094-114x(03)00065-x-Figure2-1.png",
        "caption": "Fig. 2. 8-Bar 3-dof manipulator with prismatic actuations.",
        "texts": [
            " 1 By expressing the resultant force and moment at the platform in terms of the actuator forces, the input\u2013output force system can be written as 1 H R \u00bc HF: \u00f01\u00de Here, R denotes the vector of output forces and moments, F is the vector of actuator forces, andH is the force transformation matrix. In the following, some examples of this formulation for a few parallel manipulators are presented, which will be later used for path-planning studies. More detailed analysis of singularities can be found in earlier works [11,12]. Fig. 1 shows a 2-dof planar parallel manipulator with prismatic actuations. Denoting the base point of a leg by bi, the leg-vector can be written as Si \u00bc t bi; i \u00bc 1; 2: \u00f02\u00de From R \u00bc f1s1 \u00fe f2s2, we find the force-transformation matrix as H \u00bc \u00bd s1 s2 : \u00f03\u00de Fig. 2 shows a 3-dof planar parallel manipulator with prismatic actuations. In this case the legvectors are given by ere onwards, the subscript i is used to denote the ith leg. Si \u00bc t\u00fe qi bi; \u00f04\u00de where t \u00bc OO0, bi \u00bc OBi, and qi \u00bc O0Pi is the vector from the origin O0 of the platform frame to the platform connection-point (Pi) expressed in global reference frame, given by qi \u00bc Rpi; \u00f05\u00de where pi \u00bc O0Pi (in local frame) and R is the rotation matrix given by R \u00bc cos h sin h sin h cos h : \u00f06\u00de If R \u00bc \u00bd Fx Fy M T denotes the output forces and moment with respect to the frame at O0, the force-transformation matrix is given by H \u00bc s1 s2 s3 q1 s1 q2 s2 q3 s3 : \u00f07\u00de Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003733_s10846-008-9263-0-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003733_s10846-008-9263-0-Figure1-1.png",
        "caption": "Fig. 1 Aerosonde UAV",
        "texts": [
            " Three fuzzy modules are designed for autonomous control, one module is used for adjusting the roll angle value to control UAV\u2019s flight heading, and the other two are used for adjusting elevator and throttle controls to obtain the desired altitude and speed values. The performance of the proposed system is evaluated by simulating a number of test flights, using the standard configuration of MATLAB and the Aerosim Aeronautical Simulation Block Set [11], which provides a complete set of tools for rapid development of detailed six-degree-of-freedom nonlinear generic manned/unmanned aerial vehicle models. As a test air vehicle a model which is called Aerosonde UAV [10] is utilized (shown in Fig. 1). Basic characteristics of Aerosonde UAV are shown in Table 1. The great flexibility of the Aerosonde, combined with a sophisticated command and control system, enables deployment and command from virtually any location. GMS aircraft instruments are deployed in order to get visual outputs that aid the designer in the evaluation of the controllers. The paper is organized as follows. Section 2 starts with the basic flight pattern definition for a UAV and then explain a sample mission plan which includes SID (Standard Instrument Departure) and TACAN (Tactical Air Navigation) procedures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure7-1.png",
        "caption": "Fig. 7. RVE model and directional inherent strains for thin-walled lattice support structures.",
        "texts": [
            " Table 1 gives the volume densities of the various lattice support structures related to the lattice unit size. The height of the RVE model is 0.4mm for all the four cases in Table 1, and hence represents the height of ten physical thin layers. The number of lumped thin layers in the RVE is determined for simplicity since in the trials no significant influence is shown in the homogenization results by varying the height of the RVE model. Take the first case in Table 1 as the example. According to those geometrical size parameters, the RVE model is built as shown in Fig. 7, and a reasonable mesh is adopted for further analysis. Note the wall thickness of the RVE is 0.05mm as elucidated in Fig. 4(c). The directional inherent strain vectors including = \u2212 \u2212\u03b5 ( 0.010, 0.003, 0.009)1 * and = \u2212 \u2212\u03b5 ( 0.003, 0.010, 0.009)2 * are assigned to the four walls with respect to their span-wise direction accordingly as shown in Fig. 5. For the four corners, the two in-plane components in the directional inherent strain vector are averaged, and the simple inherent strain vector = \u2212 \u2212\u03b5 ( 0",
            " By averaging the variation, a 10 um variation is applied to the wall thickness in the RVE-based homogenization analysis. Based on this variation, an analysis can be performed to evaluate the error bar of homogenized inherent strains. The homogenized CTE vector, i.e., the effective inherent strain vector ( =\u03b5 \u03b5 \u03b5 \u03b5( , , )H xx h yy h zz h* ), is shown in Fig. 9 corresponding to different volume densities. The in-plane inherent strains are normalized in Fig. 9 with respect to = \u2212\u03b5 0.0065xx 0 , which indicates averaged inherent strains for corner regions (see Fig. 7). Note that the vertical component of the effective inherent strain vector is independent of the relative density and thus remains constant for different volume densities ( =\u03b5 0.009,zz h see Fig. 9). The error bars are also plotted and centered by homogenized results using wall thickness of 0.1mm in Fig. 9. From Fig. 9, it can be observed that when the volume density is unity, the homogenized in-plane inherent strain is = \u2212\u03b5 0.0065xx 0 . This result makes physical sense because the inherent strains should assume the values at the corner regions",
            " For the solid base, it was deposited using the default EOS process parameters including laser power of 285W and rotational laser scanning strategy for solid components. As a result, a different inherent strain vector should be assigned to the elements in the solid base. According to Ref. [24], the mean inherent strain vector of = \u2212 \u2212\u03b5 ( 0.015, 0.015, 0.02)s * is adopted for the five layers in the solid base of the full-scale model. For the thin-walled lattice support structures, three different inherent strain vectors as mentioned in Section 4.1 (see Fig. 7) are assigned to those thin walls and cross regions, respectively. After the layer-by-layer inherent strain simulation, the elements in the intersection of the lattice support structure and the solid base are killed to simulate the stress release. Due to the large number of elements and many load steps in the nonlinear analysis, it took around 9.5 h on a desktop computer (Intel Xeon E5, 8-core, RAM 32.0 GB) to finish the full-scale simulation even though the layer-wise inherent strain method has been employed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002857_1.1613366-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002857_1.1613366-Figure1-1.png",
        "caption": "FIG. 1. Schematic representation of a cylindrically rolled sheet with radial direction r , tangential direction t , and direction along the cylinder axis y .",
        "texts": [
            " We predict that the scroll strain energy and radius depend on the winding direction due to the cubic symmetry of the semiconductors, ^100& being the preferred winding direction. The inclusion of nonlinear strain does not lead to significant differences. The inclusion of anharmonic strain ~third order elastic coefficients! leads to a small decrease of the scroll radius. Strain in curved structures has been treated previously, e.g., Refs. 7\u201310, due to the importance to measurement techniques employing film bending and to applications such as thin foil, foldable electronics. We assume here cylindrically rolled structures ~Fig. 1!. The stress in the radial direction is relaxed and zero ~Refs. 9 and 10!. We show later that in first order there is no impact on the radius of curvature whether the strain along the cylinder axis y is relaxed or not. First we treat the problem with linear strain theory. The in-plane lattice constant in the tangential direction is denoted with at , the in-plane lattice constant along the cylinder axis with ay , and the lattice constant in radial direction shall be ar . The according strains are \u00ab t , \u00aby , and \u00abr , e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.16-1.png",
        "caption": "Figure 13.16. Transverse section at plane z.",
        "texts": [
            "54), if we substitute Rs in place of R, (13.60) The Generator Through Point A 331 In Equation (13.15) we gave the base cylinder radius of the gear in terms of the standard pitch cylinder radius and the transverse pressure angle \"'tr of the basic rack, ( 13.61 ) When we compare Equations (13.60 and 13.61), it is evident that the transverse pressure angle of the gear is equal to the basic rack transverse pressure angle, (13.62) The Generator Through Point A The transverse section at plane z of a helical gear is shown in Figure 13.16, and as always in a transverse section, the tooth profile is an involute. The normal to the involute at a typical point A touches the base circle at E, and the involute meets the base circle at B. Figure 13.17 shows the transverse section through the same tooth at plane z=O, and in this section the involute meets the base circle at BO. The two points Band BO both lie on the curve forming the intersection of the base cylinder 332 Tooth Surface of a Helical Involute Gear with the tooth surface. Since this curve is a gear helix, BO can be identified as the point where the gear helix through B cuts the plane z=O. The profiles in the two sections are identical, except that the profile at plane z is rotated relative to the other by the angle tJ.8 given by Equation (13.18), (13.63) In Figure 13.16, B' is the point where the axial line through BO cuts plane z, so that line CB' is parallel to CaBo in Figure 13.17. B'CB is the angle through which the tooth profile has rotated between the two transverse sections, and is therefore equal to tJ.8. In Figure 13.17, E' is the point where the axial line through E cuts plane z=O, and A' is the point where the base circle tangent at E' cuts the tooth profile. We now use Equation (13.56) to derive an expression for the di fference between the lengths EA and E' A' \u2022 EA - E'A' arcEB - arcE'BO arc EB - arc EB' EA - E'A' arc B' B (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002985_tcst.2004.839563-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002985_tcst.2004.839563-Figure1-1.png",
        "caption": "Fig. 1. Three-DOF model helicopter.",
        "texts": [
            " There are significant nonlinearities in the system due to friction and the aerodynamics of the propellers. Only the angular position of the helicopter is used for feedback. The paper is organized as follows. In Section II, we describe the experiment setup. Section III formulates the problem and briefly describes the controller design. Experimental results are presented in Section IV. Section V summarizes the paper. The laboratory model helicopter used to evaluate the adaptive output feedback control method is shown in Fig. 1. It consists 1063-6536/$20.00 \u00a9 2005 IEEE of a rectangular frame and two propellers mounted at its two ends with axes normal to the frame. The helicopter frame is free to roll about its center where it is connected to the end of a long arm, which is free to rotate in pitch and yaw. The system has a total of three DOF with two control inputs as the voltages applied to the electric motors driving the propellers. Control voltage is applied equally to both motors, keeping the helicopter frame horizontal",
            " For , it is not possible to make SPR, so a stable low-pass filter is introduced in (16) so that can be made SPR (17) The adaptive signal is the output of a linearly parameterized NN, represented by (18) where is the NN weight vector, is a suitably chosen vector of radial basis functions filtered through , and is the input vector composed of current and past input\u2013output data. NN weights are initialized as zero and updated using (19) where the positive\u2013definite matrix and are the adaptation gains. In this section, we present experimental results obtained using the laboratory helicopter model depicted in Fig. 1. The arm carrying the helicopter is balanced so that it remains horizontal when the propellers are not actuated, and this position is defined as zero pitch angle. Positive and negative commands in the following results correspond to positions above and below the horizontal, respectively. The PCH loop contains an actuator model that includes the characteristics that are desired to be hedged from the adaptive system. The most important characteristic that can destabilize the system is saturation of the control voltage introduced to protect the control hardware"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure15-1.png",
        "caption": "Fig. 15. AIPM machine rotor topology with asymmetric V-shape PMs and outside flux barrier [56]. (a) Rotor topology. (b) PM magnetization directions.",
        "texts": [
            " Compared with the conventional V-shape IPM machine using the same volume of PMs, significant torque enhancement, torque ripple reduction, and CPSR extension can be achieved simultaneously. Similar demagnetization withstand capability to the V-shape IPM benchmark is also proved for the proposed AIPM machine, with slightly complicated rib structures. In [56], an AIPM rotor topology with asymmetric V-shape PMs and extra flux barriers outside the PMs is proposed for IPM synchronous machines as shown in Fig. 15. The outer and inner ends of flux barrier are located near the rotor surface between adjacent V-shape PMs and near the bottom of asymmetric PM cavity, respectively. The proposed AIPM machine with outer flux barrier [56], Fig.15, and the AIPM machine with inner flux barrier [38]-[39], Fig. 8(d), are designed with the same stator, rotor diameter and PM usage to the conventional V-shape IPM machine for Toyota Prius 2010 and final optimal machines are compared. It confirms the proposed AIPM machine with outer flux barriers shows inherently higher torque density than the AIPM machine with inner flux barrier structure, as will be further described in Section IV.B. Compared with the IPM machine benchmark, significant torque enhancement is achieved by employing the proposed AIPM topology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.6-1.png",
        "caption": "Figure 5.6. Gear blank and rack cutter.",
        "texts": [
            " It should therefore be measured each time, so that the correct value can be used in Equation (5.18), when the cutting center distance is calculated. Shaping wi th a Rack Cutter The principle underlying the use of the pinion cutter, and indeed all methods of generating cutting, is that we use one gear to cut another. The same principle is valid, of course, when the cutter has the shape of a rack. A cutter of this type is called a rack cutter, and it has some advantages and some disadvantages, compared with the pinion cutter. Figure 5.6 shows a partly finished gear blank, being cut by a rack cutter. During the cutting process the gear blank is rotated, and the cutter is moved in the direction of its reference line, exactly as if the two were meshed together. In addition, the cutter is given a reciprocating motion parallel to the gear axis, which provides the cutting action. We showed in Chapter 3 that a pinion can mesh correctly with any rack whose base pitch is equal to that of the gear. Hence, in theory the cutter could be designed with any values of pitch and pressure angle, provided its base pitch is equal to the required base pitch of the gear being cut"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000812_j.matchar.2021.111020-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000812_j.matchar.2021.111020-Figure15-1.png",
        "caption": "Fig. 15. Schematic diagram of the micro-wear mechanism of SLMed samples.",
        "texts": [
            " Consequently, the wear mechanism of G4 sample is oxidative wear and abrasive wear. Based on the analysis mentioned above, the mechanisms of wear text in this experimental state for the first three gradients of gradient alloy steel are oxidative wear, abrasive wear and adhesive wear. In contrast, G4 is mainly oxidative wear and abrasive wear. Combined with the microstructure analysis of SLMed gradient alloy steel in Fig. 5 and Fig. 6, a micro-wear model is established to intuitively clarify the micro-wear mechanism under the actual working condition (Fig. 15). During the sliding process, the force acting on the unit molten pool can be divided into tangential force (Ft) and normal force (Fn). Fn mainly causes the material to deform downward under the load, and Ft can be defined as the adhesion force between materials in contact with each other. The COF \u03b7 can be calculated as follows [50]: \u03b7 = Fn + Ft P (3) where P is a reasonable load. Based on the classic friction and adhesion theory, Ft can be calculated as follows: where Ar is the actual contact area, a material with better plasticity will increase the actual friction area, \u03c4a is the average shear stress during wear text, which is related to the strength of the material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000499_tvt.2020.2983546-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000499_tvt.2020.2983546-Figure1-1.png",
        "caption": "Fig. 1. The established EV SynRM drive.",
        "texts": [
            " Then an adaptive commutation scheme is proposed to determine the proper commutation instant with total loss minimization. The fitted core loss resistance and d- and q-axis inductances are all used for determining the commutation angle. The driving characteristics of the established EV SynRM drive are verified experimentally, including acceleration/deceleration, reversible operation and regenerative braking. II. SYSTEM CONFIGURATION AND PROBLEM STATEMENTS The established battery powered EV SynRM drive is shown in Fig. 1. A bidirectional DC/DC interface converter is used to establish a 550V DC-link from the battery bank (160V) in boost converter mode by ),,( LDT AA  . And a three-phase inverter is used to drive the SynRM coupled with a PMSG dynamic load. A flywheel is added on the shaft of M-G set to increase the kinetic stored energy for facilitating the regenerative braking test. The photo of the constructed M-G set is also depicted in Fig. 1. The proper commutation is arranged to yield the improved driving characteristics. In addition, a dynamic brake leg is equipped to avoid the DC-link overvoltage due to the failure of regenerative braking. The control schemes of SynRM drive, DC/DC interface converter and dynamic brake are shown in Figs. 2(a) to 2(c). In regenerative braking, the buck converter is formed by ),,( LDT AA  to let the recovered energy charge the battery. The maximum battery charging current * bm i is set by the limited inductor current command * Lmi ",
            " To yield the dL and qL under various current levels, the step current response method is applied at the d-axis and q-axis directed positions to measure their values. The fitted incremental dL and qL are shown in Figs. 8(a) and 8(b), and also listed as follows:       A3 ),H()( A3 ),H(0766.0 )(\u02c6 21 dsds ds dsd ii i iL  (20) where -0.0041  and 0.08862  . And,          A6 0.0113(H), A60.6A (H),)ln( A6.0),H(0334.0 )(\u02c6 21 qs qsqs qs qsq i ii i iL  (21) -0.0095981  and 284960.02  . (e) Core loss resistance The iron loss is estimated from the measured SynRM terminal variables as follows: (1) The load PMSG shown in Fig. 1 is removed, and the SynRM is driven under various speeds with commutation shift angle of  45 . The motor input power min PP  is measured and the copper loss cuP is calculated from (16). Hence the iron loss cP can be yielded as: cuinc PPP  (22) (2) The steady-state d-axis and q-axis voltages and currents ),( qsds VV and ),( qsds II of the SynRM are obtained from the DSP control scheme depicted in Fig. 2. Then the voltages across the iron loss resistances shown in Fig. 6 can be calculated as: sqsqscqsdsdscd RIVVRIVV  , (23) (3) Then the equivalent resistance cR can be obtained from (16) as:   c cqcd c P VV R 22 2 3   (24) The results are fitted as: )\u03a9( )()(\u02c6 baR rrc   , 0",
            "org/publications_standards/publications/rights/index.html for more information. 8 0V,55( dcV )rpm2000,45 '  r  are shown in Fig. 12(b). The dynamic response improvement by applying the robust control can be aware from the results. Accordingly, the robust control weighting factor 9.0W is set. Having good current and speed control characteristics, the EV driving operating performances are then assessed. V. EXPERIMENTAL EVALUATION A. Energy Conversion Efficiency Assessment Let the whole developed battery-powered EV SynRM drive shown in Fig. 1 be operated under ( 'r 2000rpm, V)550dcV and two load resistances ( \u03a925LR and \u03a967.16 ) with various commutation angles being manually set, Table 1 lists the measured steady-state characteristics at \u03a9.67.16LR And the composite efficiencies gmmg   at \u03a925LR and \u03a967.16 are plotted in Fig. 13. The related power components are labeled in Fig. 1, and the efficiencies are defined as follows:  gLdcmbdc PPPPPP / ,/ ,/ 321    gmmgmg PP   / , mgm   Comments: To estimate the efficiency of the driven SynRM, it is assumed that: (i) without faithful eddy current brake and accurate torque meter for making the motor loading test, two three-phase power analyzers are employed to measure the armature powers of the studied SynRM and the PMSG; (ii) the SynRM and the load PMSG possess the almost identical efficiencies, although the latter may have slightly higher efficiency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000416_j.isatra.2021.04.046-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000416_j.isatra.2021.04.046-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor model.",
        "texts": [
            " Finally, the summary f this article and future work are discusses in Section 5. . Dynamic modeling In this section, the attitude dynamic model of quadrotor with ncertainties and disturbances is introduced. In our research, the ttitude model is based on the following assumptions [7,27]: (a) The quadrotor structure is rigid and symmetrical. (b) The center of gravity of the quadrotor is assumed to coin- cide with the geometric center. (c) The pitch angle is assumed to satisfy the constraint |\u03b8 | < \u03c0/2. eferring to Fig. 1, this article studies the \u2018\u2018x\u2019\u2019-type configuration uadrotor. Define E = {xe, ye.ze} as the fixed coordinate system f the earth and B = {xb, yb, zb} as the fixed coordinate system f the quadrotor body. Based on assumptions (a)\u2013(c), quadrotor ttitude model can be described by (see [27,28]) \u0398\u0307 = W\u2126 = [1 sin\u03c6 sin \u03b8/cos \u03b8 cos\u03c6 sin \u03b8/cos \u03b8 0 cos\u03c6 \u2212 sin\u03c6 0 sin\u03c6/cos \u03b8 cos\u03c6/cos \u03b8 ] \u2126, (1) \u2126\u0307 = \u2212J\u22121\u2126 \u00d7 (J\u2126) + J\u22121\u03c4 + d, (2) where \u0398 = [\u03c6, \u03b8, \u03c8] T and \u2126 = [\u03c9xb , \u03c9yb , \u03c9zb ] T represent he Euler angles in the frame E and the angular velocity in the rame B, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.1-1.png",
        "caption": "Figure 13.1. A stepped gear.",
        "texts": [
            " During part of each meshing cycle there is a single pair of teeth in contact, while during the remainder of the cycle there are two. For each tooth pair in contact, the length of the contact line is equal to the gear face-width F. Hence, the total length of the contact line is either F or 2F, depending on the number of pairs of teeth in contact. And each time a tooth pair comes into contact or loses contact, the total length of the contact line either increases or decreases by F. These large and abrupt changes in the length of the contact line result in noisy operation of the gears. The gear shown in Figure 13.1 is called a stepped gear. It is formed by two spur gears side by side, each with a face-width of (F/2), so that the total face-width is F. When a tooth pair comes into contact or loses contact, the change in the total length of the contact line is now only (F/2), compared with F for a conventional pair of spur gears, and the resulting operation is smoother. We could improve the performance further by increasing the number of gears in the stepped gear, keeping the total face-width constant, and if the number were increased to infinity, we would obtain a helical gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000107_j.oceaneng.2020.108158-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000107_j.oceaneng.2020.108158-Figure1-1.png",
        "caption": "Fig. 1. Definition of the earth-fixed \ud835\udc42\ud835\udc4b0\ud835\udc4c0 and the body-fixed \ud835\udc34\ud835\udc4b\ud835\udc4c coordinate frames.",
        "texts": [
            " Suppose that there is a Lyapunov function \ud835\udc49 (\ud835\udc65) and scalars \ud835\udefc, \ud835\udefd, \ud835\udc5d, \ud835\udc5e, \ud835\udc58 \u2208 \u211c+, \ud835\udc5d\ud835\udc58 < 1, \ud835\udc54\ud835\udc58 > 1, and 0 < \ud835\udf17 <\u221e, such that ?\u0307? (\ud835\udc65) \u2264 \u2212(\ud835\udefc\ud835\udc49 (\ud835\udc65)\ud835\udc5d + \ud835\udefd\ud835\udc49 (\ud835\udc65)\ud835\udc54)\ud835\udc58 + \ud835\udf17. Then the trajectory of this system is practical fixed-time stable. Also, the residual set is given by { lim \ud835\udc61\u2192\ud835\udc47 \ud835\udc65|\ud835\udc49 (\ud835\udc65) \u2264 min { \ud835\udefc\u22121\u2215\ud835\udc5d( \ud835\udf17 1 \u2212 \ud835\udf03\ud835\udc58 ) 1 \ud835\udc58\ud835\udc5d , \ud835\udefd\u22121\u2215\ud835\udc5d( \ud835\udf17 1 \u2212 \ud835\udf03\ud835\udc58 ) 1 \ud835\udc58\ud835\udc54 }} where \ud835\udf03 is a scalar and satisfies 0 < \ud835\udf03 \u2264 1. The time \ud835\udc47 is bounded by \ud835\udc47 \u2264 1 \ud835\udefc\ud835\udc58\ud835\udf03\ud835\udc58(1 \u2212 \ud835\udc5d\ud835\udc58) + 1 \ud835\udefd\ud835\udc58\ud835\udf03\ud835\udc58(\ud835\udc54\ud835\udc58 \u2212 1) Lemma 3 (Zhang et al., 2020). If { \ud835\udc651, \ud835\udc652,\u2026 , \ud835\udc65\ud835\udc5b } \u2208 \u211c and \ud835\udc5d > 0, then (| | \ud835\udc651|| + | | \ud835\udc652|| +\u22ef + | | \ud835\udc65\ud835\udc5b||)\ud835\udc5d \u2264 max(\ud835\udc5b\ud835\udc5d\u22121, 1)(| | \ud835\udc651|| \ud835\udc5d + | | \ud835\udc652|| \ud835\udc5d +\u22ef + | | \ud835\udc65\ud835\udc5b|| \ud835\udc5d). Fig. 1 illustrates the reference frames, i.e., the earth-fixed \ud835\udc42\ud835\udc4b0\ud835\udc4c0 and the body-fixed \ud835\udc34\ud835\udc4b\ud835\udc4c . The MSV models including kinematics and dynamics can be modeled as follows ?\u0307?=\ud835\udc45(\ud835\udf13)\ud835\udc63 (1) \ud835\udc40?\u0307? + \ud835\udc36(\ud835\udc63)\ud835\udc63 +\ud835\udc37(\ud835\udc63)\ud835\udc63 = \ud835\udf0f + \ud835\udc4f (2) here the vectors \ud835\udf02 = [\ud835\udc65, \ud835\udc66, \ud835\udf13]T \u2208 \u211c3 and \ud835\udc63 = [\ud835\udc62, \ud835\udf10, \ud835\udc5f]T \u2208 \u211c3 are respectively position and velocity. The vectors \ud835\udf0f = [\ud835\udf0f1, \ud835\udf0f2, \ud835\udf0f3]T \u2208 \u211c3 and \ud835\udc4f(\ud835\udc61) = [\ud835\udc4f1(\ud835\udc61), \ud835\udc4f2(\ud835\udc61), \ud835\udc4f3(\ud835\udc61)]T \u2208 \u211c3 are respectively the control inputs and environmental unknown disturbances, and \ud835\udc45(\ud835\udf13) = \u23a1 \u23a2 \u23a2 cos(\ud835\udf13) \u2212 sin(\ud835\udf13) 0 sin(\ud835\udf13) cos(\ud835\udf13) 0 \u23a4 \u23a5 \u23a5 (3) \u23a3 0 0 1 \u23a6 \ud835\udc45 \ud835\udc45 A l t r t 4 4 f \ud835\udc64 w t \ud835\udc64 \ud835\udf12 w s \ud835\udc4f T w a \ud835\udc58 c P \ud835\udf02 w is a rotation matrix with the following properties (Wang et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000566_tie.2020.3009563-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000566_tie.2020.3009563-Figure2-1.png",
        "caption": "Fig. 2. PMSM with fault in phase A. (a) Inter-turn short-circuit; (b) Resistive unbalance.",
        "texts": [
            " In literature [15], the case of machine with delta-connected winding is also mentioned where the neutral point is not accessible. Then the zero-sequence current component (ZSCC) might be used as an alternative signal other than the ZSVC, which has the similar principle as that of the method with the ZSVC. Two main incipient faults in stator windings, namely inter-turn short-circuit or resistive unbalance are considered in this paper. Inter-turn short-circuit fault can be modeled by adding a new current path within the faulty phase winding, as shown in Fig. 2(a). The inter-turn degraded insulation is modeled with resistance Rf and fault turn ratio \u03bc. if is the fault circulating current within short-circuited turns. The resistive unbalance fault can be modeled by adding an additional resistance Radd, as shown in Fig. 2(b). According to [15], the ZSVC of the PMSM with inter-turn short-circuit fault in phase A can be expressed as dt d dt di MLiRv f fs 0,PM ZS_ISF )2( 3 1 3 1    (1) where Rf is the equivalent resistance of degraded insulation between the short-circuit turns and \u03bc is the ratio between the number of short-circuited turns and the total number of turns in a certain phase. Rs is the resistance of stator phase winding, L and M are the self-inductance and mutual-inductance in one phase, respectively, \u03bbPM,0 is zero sequence flux and can be expressed as )( 3 1 PMPMPM0,PM cba   (2) where \u03bbPMa, \u03bbPMb and \u03bbPMc are the phase flux generated by the PMs",
            " By using the HF transformation, the injected HF current will be transformed into a dc component. And the fundamental current will be transformed into harmonic component, which is easy to be filtered by low-pass filters. In the HF current regulator, PI controllers are used to regulate the d-axis and q-axis current, respectively, and two low-pass (LP) filters are used to extract the dc component from the transformation results. Supposing an inter-turn short-circuit occurs in the PMSM phase A as shown in Fig. 2(a), the voltage equation of the shorted circuit loop can be expressed as 0)( )( 2   dt di LiRR dt d dt di MLiR f ffs PMaa as    (8) Considering that the back-EMF is zero and voltage drop on phase resistance is negligible at high frequency, the voltage equation of the short-circuit loop with HF signal injection can be obtained according to (8), it is dt di LiRR dt di ML hf hffs ha ,2 , , )()(   (9) where ia,h and if,h are the injected HF current in phase A and the HF fault circulating current, respectively, which can be expressed as      )(sin )(sin hf,hhf,hf, ha,hhha, tIi tIi   (10) whereh is the angular velocity of injected HF current and satisfies h = ht, Ih and a,h are the amplitude and initial phase angle of the HF injected current in phase A, If,h and f,h are the amplitude and initial phase angle of the HF fault circulating current within short-circuited turns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000039_j.addma.2020.101437-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000039_j.addma.2020.101437-Figure4-1.png",
        "caption": "Figure 4 \u2013 Schematic representation of the surface laser relation in spherical coordinates",
        "texts": [
            "6) In the special case where the azimuthal angles of the surface normal \ud835\udf09 and the laser incidence \ud835\udf12 are identical, the surface laser relation angle \ud835\udf01 can also be calculated solely by the polar angles of the surface normal \ud835\udefc and the laser incidence \ud835\udf13, as represented in equation (2.7). In this situation the plane \ud835\udc46\ud835\udc5b created by the surface normal ?\u20d7? and the plane \ud835\udc46\ud835\udc59 created by the laser incidence \ud835\udc59 are concurrent. \ud835\udf01(\ud835\udf09 = \ud835\udf12) = |\ud835\udefc \u2212 \ud835\udf13| (2.7) Jo ur na l P re - ro of The surface laser relation angle \ud835\udf01 between laser incidence and surface normal can vary between 0\u00b0 and 180\u00b0. The resulting plane \ud835\udc46\ud835\udc5f of both vectors can also be tilted. For illustration of the parameter \ud835\udf01, the surface normal ?\u20d7? and the laser incidence \ud835\udc59 are represented on an additive demonstrator in Figure 4 as well as the surface laser relation angle \ud835\udf01. For the position dependent characterization of additive surface roughness, two build jobs are built and analyzed. Both build jobs consist of 25 specimens each, which are arranged in an equally distributed 5\u00d75-array. The specimens are built with the default EOS parameter set \u201cIN718_PerformanceM291 2.11\u201d for Inconel 718 comprising different settings for volume, upskin, downskin and contour exposure as well as a build layer thickness of 40 \u00b5m. An adaptation of this parameter set was not conducted, since the aim in this work is the analyzation of the position dependency and not the influence of energy input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.7-1.png",
        "caption": "Figure 4.7. Meshing diagram of a gear pair.",
        "texts": [
            " We can show now, however, that in general the fillet circle is larger than the base circle, for the following reason. The involute was defined in Chapter 2 as a curve for which the normal at any point touches the base circle. With this definition, it is impossible for the involute to extend inside the base circle. Since the fillet circle passes through Af , the point where the fillet joins the involute, the radius Rf is in general greater than the base circle radius Rb \u2022 In exceptional cases, Rf may be equal to Rb , but it is never smaller. First Condi tion For No Interference Figure 4.7 shows the meshing diagram for a typical gear pair. As usual, the path of contact lies along the common tangent to the base circles, which touches the two base circles at El and E2\u2022 The ends of the path of contact are at Tl and T2 , the points where the tip circles intersect line E1E2 \u2022 When the gears are in the positions shown, point Al of gear 1 is in contact with point A2 of gear 2. Hence, the contact on the tooth of gear 1 takes place at a radius equal to C1Al . When the contact point is closer to El , the radius C1Al is reduced, and if the contact point were to coincide with El the radius C1Al would be equal to Rbl \u2022 We have stated that interference will occur if there is contact at the tooth fillet",
            " This means that the contact on gear 1 must only take place on the involute section of the tooth profile, or in other words, at radii greater than the fillet circle radius Rfl \u2022 We have also pointed out that the Condi tions For No Interference 93 fillet circle radius is generally larger than the base circle radius. If, therefore, the contact point is allowed to move down the tooth profile of gear 1 as far as the base circle, there will def inately be interference. Hence, in order to prevent the interference, it is first necessary that the path of contact should end at a point on line E1E2 lying above E1\u2022 The length T2E2 in Figure 4.7 must therefore be less than E1E2 , and the necessary condition for no interference can be expressed in the following form, < (4.18 ) The meshing diagram of a rack and pinion is shown in Figure 4.8. The line containing the path of contact touches the pinion base circle at E, and the end of the path of contact is shown as Tr \u2022 As before, interference would take place at the tooth fillets of the pinion if the contact point were to move down the tooth profile as far as the base circle, so point Tr must lie above point E",
            " However, even when these conditions are satisfied, they are not always sufficient to prevent interference. We stated earlier that the tooth fillet of a gear extends to point Af , which generally lies a certain distance outside the base circle. We must now ensure that the top of the fillet, between the base circle and the fillet circle, does not come into contact with the teeth of the meshing gear. We therefore calculate the minimum radius at which contact takes place, and compare thi s wi th the radius of the fillet ci rcle. Limi t Ci rcle In Figure 4.7, the lower end of the path of contact is point T2 , and the radius C1T2 is therefore the minimum radius in gear 1 where contact occurs. The circle in gear 1 which passes through T2 is called the limit circle or the contact circle of gear 1, and its radius is labelled RL1 \u2022 The length Conditions For No Interference 95 E,T2 in Figure 4.7 is expressed as the difference between E,E 2 and T2E2, and we then use triangle C,E,T2 to derive an expression for the radius RL\" (4.20) In the case of the rack and pinion, the limit circle of the pinion is the circle passing through point Tr , the lower end of the path of contact. The radius RL of this circle can be read immediately from Figure 4.8, 2 ~2 Rb + [Rb tan 41 - sin 41] (4.21) Second Condi tion For No Interference Since the lowest contact point on a gear tooth is at the limit circle, and contact below the fillet circle must be prevented, it is clear that any gear pair must be designed so that the fillet circle of each gear is smaller than the corresponding limit circle, < (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure10-1.png",
        "caption": "Fig. 10. Four-legged SP-equivalent parallel mechanisms with identical type of legs. (a) 4 R\u0302R\u0302R\u0302\u00f0RR\u00dekE and (b) 4 R\u0302R\u0302\u00f0PRR\u00dekE.",
        "texts": [
            " (2) The actuated joints should preferably be on the base or close to the base. (3) No unactuated P joint exists. Using the above criteria and the validity condition of actuated joints, a large number of the m(m P 2)-legged SP-equivalent parallel mechanisms corresponding to each SP-equivalent parallel kinematic chain can be generated. Due to the large number of SP-equivalent parallel mechanisms, only 4-legged SP-equivalent parallel mechanisms with all legs of the same type satisfying the above criteria are shown in Fig. 10. The type synthesis of SP-equivalent parallel mechanisms has been well solved using the virtual chain approach to the type synthesis of parallel mechanisms proposed in [9\u201313]. SP-equivalent parallel kinematic chains with inactive joints as well as SP-equivalent parallel kinematic chains without inactive joints have been obtained. The validity condition of actuated joints of SP-equivalent parallel mechanisms has been reduced to the calculation of a 4 \u00b7 4 determinant. The SP-equivalent parallel kinematic chains obtained include some new SP-equivalent parallel kinematic chains as well as all the known SP-equivalent parallel kinematic chains"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure7-1.png",
        "caption": "Fig. 7. Force analysis of substructure 2.",
        "texts": [
            " Different from other joints, a hydro-pneumatic gravity compensator consisting of two diaphragm accumulators and a hydraulic cylinder is installed between the link arm (link 2) and the rotating column (link 1). As a passive mechanism, the volume of gas in the accumulator can be adjusted by the hydraulic oil. Using a piston rod to pull the link arm, this assembly can significantly decrease the driving torques of joint 2 in either a moving or a stationary configuration. Considering the effects of the gravity compensator, a force diagram of substructure 2 is shown in Fig. 7 . A coordinate system { O c } is established, where the direction of the X c -axis always points from point O c to point O 2 and the direction of the Y c -axis parallels to the Y 2 -axis. To calculate the reaction force exerted on joint 2, the equation of static equilibrium at point O E can be written as \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 f E \u2212 m E g \u0303 z \u2212 m 5 g \u0303 z \u2212 m 4 g \u0303 z \u2212 m 3 g \u0303 z \u2212 m 2 g \u0303 z \u2212 R c \u03c1w,c, f = R 2 \u03c1w, 2 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z \u2212 m 5 g ( R E r E 6 + R 6 r 6 G 5 ) \u00d7\u02dc z \u2212 m 4 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 G 4 ) \u00d7\u02dc z \u2212m 3 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 G 3 ) \u00d7\u02dc z \u2212 m 2 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 G 2 ) \u00d7\u02dc z \u2212 ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 2 + R 3 r 2 c ) \u00d7 ( R c \u03c1w,c, f ) = ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 + R 3 r 3 2 ) \u00d7 ( R 2 \u03c1w, 2 , f ) + R 2 \u03c1w, 2 ,\u03c4 (16) where \u03c1w, 2 , f = [ \u03c1w, 2 , f x \u03c1w, 2 , f y \u03c1w, 2 , f z ] T , \u03c1w, 2 ,\u03c4 = [ \u03c1w, 2 ,\u03c4x \u03c1w, 2 ,\u03c4y \u03c1w, 2 ,\u03c4 z ] T , \u03c1w,c, f = [ \u03c1w,c, f x 0 \u03c1w,c, f z ] T , \u03c1w, 2 , f and \u03c1w, 2 ,\u03c4 are the reaction force and torque of joint 2 acting at point O 2 , \u03c1w,c, f is the pulling force exerted by piston rod on link 2 at point O c , R c is the orientation matrix of { O c } with respect to { O 1 }, m 2 is the mass of link 2, G 2 is the mass center of link 2, r 3 G 2 is the position vector from point O 3 to point G 2 evaluated in { O 3 }, r 3 2 is the position vector from point O 3 to point O 2 evaluated in { O 3 }, and r 2 c is the position vector from point O 2 to point O c evaluated in { O 3 }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001014_j.jmapro.2021.02.033-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001014_j.jmapro.2021.02.033-Figure2-1.png",
        "caption": "Fig. 2. Double ellipsoidal heat source.",
        "texts": [
            " Journal of Manufacturing Processes 64 (2021) 960\u2013971 However, when welding path is complex or the size of heat source model differs greatly from the size of the unit, the above discretize method will fail. In this work, the deposition process is discretized into simulation steps with the specified time interval \u0394t, and the unit activation judgment is made for each simulation step. Firstly, the double ellipsoid heat source model [32] is selected due to the influence of arc movement on the heat distribution of molten pool, and the shape parameters a, b, cf and cr are shown in Fig. 2. Then, based on the units that are obtained by discretizing the part geometry, the unit activation judgment can be performed as follows. For each simulation step, the intersection area of the envelope areas that are formed by the movement of the front ellipsoid and the rear ellipsoid in the current simulation step respectively is calculated firstly. Then, those unactivated units whose center point is covered by the intersection area will be the activated units of this simulation step. Fig. 3 shows the process of unit activation judgment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure12-1.png",
        "caption": "Fig. 12. Deployed shape of the semi-circular chain.",
        "texts": [
            " The mechanism decomposition results in supplementary kinematic chains with the same mobility as the equatorial loop-chain. The first type of supplementary chains are semi-circular chains formed by elementary fourlegged platforms. Similar to the analysis in the previous sections, the legs containing four links and six joints, which are perpendicular to the semi-circular chain, are removed from every elementary platforms in the chain. The mechanism hence left is a semi-circular chain joined by parallelogram mechanisms and planar two-legged platform mechanisms and can be illustrated in Fig. 12. Decomposing the above, a quarter-circular chain is obtained in Fig. 13. From the previous analysis, the mobility of this mechanism is one. The second type of supplementary kinematic chains consists of three-legged elementary platforms. The analysis of this type results in mobility one from the similar mobility analysis as before. Hence the ball mechanism is completely decomposed and the mobility analysis is concluded. This paper revealed the multi-loop mechanism of a complex and articulated ball, characterized the mechanism with three-legged elementary platforms and four-legged elementary platforms and developed mechanism decomposition in the mobility analysis of the ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000245_ijvd.2019.109873-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000245_ijvd.2019.109873-Figure1-1.png",
        "caption": "Figure 1 Three bar truss design (see online version for colours)",
        "texts": [
            " In the first step, the results achieved by the proposed NAMDE, for the 11 design problems, are compared with other results reported in the literature using different algorithms. After several experiments, the initial parameters of the developed algorithm used are: F1 = 0.8, F2 = 0.5, Cr = 0.95, \u03c41 = 0.5, \u03c42 = 0.2. Below the description and the results of each problem are detailed. The three bar truss problem is designed for minimum volume and subjected to three nonlinear constraints (Nowacki, 1974). It comprises two design variables consisting of the cross-sectional areas of the two members, as shown in Figure 1. The problem has been optimised in the literature utilising different methods, NAMDE is compared with eleven optimisers (listed in Table 4): upgraded firefly algorithm (UFA) (Brajevic\u0301 and Ignjatovic\u0301, 2018), modified backtracking search optimisation algorithm (SSBSA) (Wang et al., 2018), \u03b5DE-LS (Yi et al., 2016), pre-estimate comparison gradient based approximation \u03b5constrained differential evolution (\u03b5DE-PCGA) (Yi et al., 2018), Rank-iMDDE (Gong et al., 2014), upgraded artificial bee colony (UABC) (Brajevic and Tuba, 2013), constrained optimisation based on a modified DE (COMDE) (Mohamed and Sabry, 2012), water cycle algorithm (WCA) (Eskandar et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.23-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.23-1.png",
        "caption": "Fig. 7.23 Radial piston pump",
        "texts": [
            " The standardization of hydraulic elements greatly speed up the application of hydraulic drive after WWI. To the 1920s, a booming period appeared, hydraulic power was widely applied to machine tools and various construction machines. Large machines, including vehicles, aircrafts and ships, required large capacity transmission units. To meet this requirement, high power density and good controllable characteristics are necessary for hydraulic elements. In 1922, a Swiss engineer, Hans Thoma, invented the radial piston pump (Fig. 7.23) which can 252 7 Birth and Development of Modern Mechanical Engineering Discipline provide especially high pressure and relatively small flows. Subsequently, other types of piston pumps and hydraulic motors appeared. These new progresses made the performance of hydraulic transmissions further improved (Li 2011). In 1925, Harry Vickers, an American industrialist, invented the pressure balanced vane pump. All of these laid the foundation for the establishment of the modern hydraulic elements industry and hydraulic technology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.3-1.png",
        "caption": "Figure 12.3. Tooth thickness at radius R.",
        "texts": [
            "1), ts ~7I'm + 2e tan \"'s For an internal gear, the tooth shape is the same as the tooth space of an external gear, so the tooth thickness of the internal gear is equal to the space width of the external gear. Hence, the tooth thickness of an internal gear is related to its profile shift in the following manner, ~7I'm - 2e tan \"'s (12.16) To locate the position of point A at a typical radius R on the tooth profile, we again use a coordinate system in which the x axis coincides with a tooth center-line, as shown in Figure 12.3. The points on the involute at radii Rb , Rs and R are labelled B, As and A. The angle ACB is equal to inv \"'R' as we proved in Equation (2.19), and angle AsCB is equal to inv \"'5' The polar coordinate 6R of point A is therefore found as the angle xCAs ' minus angle AsCB, plus angle ACB, ts 2Rs - inv \"'s + inv \"'R ( 12.17) We can use this result, to write down the tooth thickness tR at radius R, ( 12.18) It can be seen in Figure 12.3 that the tip circle of an 266 Internal Gears internal gear lies inside the standard pitch circle, while the root circle lies outside it. The addendum as and the dedendum bs are still defined in the usual way, as the radial distances from the standard pitch circle to the tip circle and the root circle. Hence, as and bs are related to the various radi i in the following manner, ( 12.19) (12.20) Meshing Geometry of an Internal Gear Pair The meshing diagram of an internal gear pair is shown in Figure 12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure11-1.png",
        "caption": "Fig. 11. (a) The decomposed symmetrical mechanism. (b) The corresponding graph.",
        "texts": [
            " Thus, in order to simplify the calculation of the mobility of the magic ball mechanism, all two scissorstyped legs perpendicular to the loop-chain in Fig. 10 of all four-legged elementary platforms are removed. The remaining mechanism forms a circular loop-chain in Fig. 10. It is a kinematic chain joined by parallelograms and planar two-legged platform on the x\u2013y plane. The mobility of the loop chain does not change. In this kinematic loop-chain, the symmetrical mechanism is composed of basic units each of which consisting of a planar two-legged platform and two parallelogram mechanisms as in Fig. 11a. Fig. 11b is the corresponding topological graph [22]. From the similar analysis in Fig. 8 and the constraints mentioned in Section 4, the mobility of the basic unit is one. From the above result that the basic unit has mobility one, calculating the mobility of the circular loop-chain, the topological graph of the chain can be simplified. Similar to the analysis of the basic unit, the mobility of this kinematic chain is one. Thus, the mobility of the equatorial circular loop-chain is one and that indicates that the mobility of the ball mechanism is one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003330_j.jpba.2005.03.014-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003330_j.jpba.2005.03.014-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the electrochemical microflow cell (I) and screen-printed gold electrode (II) used in the voltammetric and amperometric measurements.",
        "texts": [
            "65 mm of thick. On to this surface the working (W), reference (R) and the auxiliary (A) electrodes were applied. The working and auxiliary electrodes were made of Au/Pd (98:2%) and the reference of Ag/AgCl (60:40%). At the end of the sensor was a contacting field, connected with the active part by the silver conducting parts that are covered by a dielectric protection layer. The sensor was connected with a cable to the potentiostat. The arrangement of the microflow cell system is illustrated in Fig. 1I. A driving shaft (2) was located in the center of a conventional electrochemical vessel (1) carrying the body of the microflow insert (7). The driving shaft was connected to a pump rotor (3). The chamber located above the rotor (4) was connected to the electrode cell containing the three electrodes (8) via a capillary (6). The thin capillary was located in the bulk solution guided the fluid coming from the rotor to the electrode cell (7) where the screen-printed electrode was positioned. The capillary fulfilled the function of stabilizing the flow of liquid before it entered the electrode cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003307_1.2791809-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003307_1.2791809-Figure2-1.png",
        "caption": "Fig. 2 Free-body diagram of the fih body",
        "texts": [
            " The results of the algorithms with respect to two examples are provided in Section 6. 2 Some Definitions Referring to Fig. l, it is assumed that a serial multibody system, namely, the serial manipulator, has a fixed \"base\" and n moving rigid bodies, numbered # 1 . . . . . #n, coupled by n one-degree-offreedom kinematic pairs or joints, say, a prismatic or a revolute, which are indicated in Fig. 1 as 1 . . . . . n. The ith joint couples the ith body with that of the (i - 1)st. Now, referring to the motion of the ith body, Fig. 2, the following terms are defined: t~ and n~: the six-dimensional vectors of twist and wrench of the ith link, i.e., ti-~\" and wi--= fs (1) Vi where 0~ and v~ are the three-dimensional vectors of angular velocity and the linear velocity of the mass center of the ith link, C~, as shown in Fig. 2, respectively, whereas ni and fi are the three-dimensional vectors of the moment about Ci and the force at Ci, respectively. Journal of Applied Mechanics DECEMBER 1999, Vol. 66 / 987 Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ~i and M~: the 6 \u00d7 6 matrices of angular velocity and mass of the ith body, respectively, namely, o I o 1 O toi \u00d7 1 and Mi ~ O mil (2) where o~ \u00d7 1 is the 3 \u00d7 3 cross-product tensor associated with vector ooi, which when operates on any three-dimensional Cartesian vector, x, results in a cross-product vector, i",
            " n, are given in Eq. (2). //: the n-dimensional independent vector of joint rates, i.e., O ~- [0 , . . . . . 0 , ] ~ (5) where 0~ is the displacement of the ith joint, as shown in Fig. 3. 3 Dynamic Model ing Using the DeNOC For a serial-chain mechanical system shown in Fig. l, the steps to obtain the dynamic equations of motion using the DeNOC matrices are given below: 1 Derivation of the Unconstrained Newton-Euler (NE) Equations of Motion: (a) From the free-body diagram of the ith rigid body, Fig. 2, write the Newton-Euler equations of motion as Iigo i -I- 0.) i X I io0 i = n i (6a) mi~ri : f i (6b) where ni and f~ are the resultant moment about and force applied at the mass center, C~, respectively. Using the definitions given in Eqs. (1) and (2), the above six scalar equations can be put in a compact form as M i t i -I- [Wilt i = w i (7) (b) (a) where the six-dimensional twist-rate vector, ti, and the 6 X 6 mass-rate matrix, 19Ii, are, respectively, the time derivative of t~ and M~, which are defined as Write Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure9-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure9-2-1.png",
        "caption": "Figure 9-2. Sinusoidal stain and stress cycles. I strain, amplitude a; II in-phase stress, amplitude b; III out-of-phase stress, amplitude c; IV total stress (resultant of II and III, ampHtude d. a is the loss angle",
        "texts": [],
        "surrounding_texts": [
            "There is an international standard, ISO 4664^ which is written as a guide to dynamic testing and which can be referred to for definitions of terms used and also includes classifications of test machines, preferred conditions, recommended test piece shapes and a bibliography. The British standard is identical (BS ISO 4664). ASTM has taken the same approach but the equivalent^ is more like a small text book and includes some rather unnecessary definitions (e.g. lubricated and relative). Whilst it is some ways a valuable reference, in other respects it is \"over the top\" for many peoples testing needs. The static tests considered in Chapter 8 treat the rubber as being essentially an elastic, or rather 'high elastic', material whereas it is in fact viscoelastic and, hence, its response to dynamic stressing is a combination of an elastic response and a viscous response and energy is lost in each cycle. This behaviour can be conveniently envisaged by a simple empirical model of a spring and dashpot in parallel (Voigt-Kelvin model). For sinusoidal strain the motion is described by: Dynamic stress and strain properties 175 Y = YQ sin Q)t where: y= strain, yo = maximum strain amplitude, co = angular frequency, and t = time. If the rubber were a perfect spring the stress (x) would be similarly sinusoidal and in phase with the strain. However, because the rubber is viscoelastic the stress will not be in phase with the strain but can be considered to precede it by the phase angle (5) so that: T = Tr, s m {(Dt + 5) This is the same as saying that the deformation lags behind the force by the angle 5. It is convenient to consider the stress as a vector having two components, one in phase with the displacement (x') and one 90\u00b0 out of phase (x\") and to define corresponding in-phase, out-of-phase and the resultant moduli. The sinusoidal motion is illustrated in Figure 9.2 and the vector in Figure 9.3."
        ]
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.20-1.png",
        "caption": "Fig. 7.20 Lanchester balancer",
        "texts": [
            " A large quantity of works on this topic were published (Arakelian and Smith 2005). In this method, the unbalanced inertia force is decomposed into a Fourier series. Reduction of the inertia effect is achieved by installing a counterweight on the crank to balance the first order harmonic of the inertia force. This method, as illustrated in Fig. 7.19, was widely used. To balance the shaking force of the second order harmonic, Frederick Lanchester, a British automobile engineer, designed the Lanchester balancer (Lanchester 1914) (Fig. 7.20) which still finds application nowadays. In modern automobiles, balance shafts are installed to balance the inertia force in four stroke engines. These shafts are driven by the crank through the gears or a synchronous toothed belt with a 2:1 transmission ratio. Counterweights on balance shafts balance the second-order shaking force. The design is the same with the original Lanchester balancer in principle. As a theoretical problem, complete balancing of both shaking force and shaking moment of linkages, was solved in the 1960s (Arakelian and Smith 2005)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000457_j.addma.2020.101467-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000457_j.addma.2020.101467-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of (a) laser head, deposited sample geometry, and (b) dog bone-shaped tensile samples.",
        "texts": [
            " Four successive batches of blended powder were collected from the nozzle of the DED equipment. The theoretical density, \u03c1, was calculated using a rule of mixture (\u03c1 = w1\u03c11 + w2\u03c12), where wX is the weight fraction of component X with \u03c1X. Rectangular shaped samples (13 mm \u00d7 13 mm \u00d7 120 mm) were fabricated using a DED (MX-3, Insstek) machine at a laser scan speed of 850 mm/min, a laser power of 400 W, hatch spacing of 500 \u03bcm, layer thickness of 250 \u03bcm, and dwell time of 3.5 s between each layer (Fig. 1a). Neither lack of fusion defects nor unmelted powders were observed in the as-deposited samples for the initially used process parameters, and thus, the process parameters were kept constant. Argon shielding gas was purged into the melt pool to prevent oxidation. Each layer was continuously deposited via a zigzag pattern, followed by 90\u00b0 rotation for the successive layer, resulting in a crosshatched scan pattern. The bulk density of as-deposited samples was also measured using a He gas pycnometer with cut samples (4 mm x 4 mm x 4 mm). X-ray diffraction (XRD, PANalytical) was performed on a PANalytical's X\u2032pert PRO with Cu K\u03b11 radiation (\u03bb =0.1540 nm) at a voltage of 45 kV and, current of 200 mA, and 2\u03b8 scan rate of 5\u00b0/min. Electron backscattered diffraction (EBSD, QUANTAX EBSD, Bruker) analyses were done using a FEI Quattro ESEM operated at an acceleration voltage of 20 kV, a step size of 0.12 \u03bcm, and a working distance of 19.5 mm, respectively. Dog bone-shaped tensile samples were machined from as-deposited samples (Fig. 1b). The gauge section was \u223c1.4 mm in thickness, 40 mm in width, and 15 mm in length. Tensile tests were performed at a strain rate of 10\u22124 s at room temperature using a universal testing machine (MINOS-100S, MTDI). Five tensile tests for each direction were performed. The representative SEM/EDS maps for Ti64 and CCM powders exhibited spherical powder shapes (see Fig. 2a) and average powder sizes of 103\u00b1 36.9 \u03bcm and 84\u00b1 38.5 \u03bcm, respectively. EDS maps of Ti (Fig. 2b) and Co (Fig. 2c) revealed CCM powder particles well dispersed in Ti64",
            " This peak shift could be related to the precipitation of the \u03b1 phase in the 5Co alloy, which causes slightly enhanced partitioning of Co, Cr, and V to \u03b2 (see Fig. S1 in Supplementary material) as compared to the 10Co alloy. As expected, no intermetallic phases were formed owing to the high solubility of Co in the \u03b2-Ti phase and thus, we can exclude intermetallic phases from the following discussion on the observed microstructure and tensile properties. Fig. 4 shows representative engineering stress-strain curves of the reference Ti64 sample as well as the 5Co and 10Co samples along X, Y, and Z directions (compare Fig. 1b). The tensile properties of the investigated samples are summarized in Table 3. The reference Ti64 sample showed 0.2 % offset yield stress values ranging from 1051 to 1180 MPa, which were comparable to previously reported data [20]. A strong anisotropy in total elongation was measured in Ti64 samples, where the ductility along X and Y directions was significantly lower (2.7\u00b1 0.9 % and 2.5\u00b1 1.5 %, respectively) than along Z, the build direction (10.7\u00b1 1.1 %). Blending of Ti64 with CCM significantly changed the tensile mechanical properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000193_j.ijfatigue.2019.06.025-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000193_j.ijfatigue.2019.06.025-Figure2-1.png",
        "caption": "Fig. 2. Scan strategy.",
        "texts": [
            " Both chemical compositions were evaluated via spark emission spectroscopy for bulk as well as SLM samples, and can be found in Table 1. The SLM samples were fabricated using an SLM Solution 280HL (SLM Solutions GmbH) utilizing two Yb:YAG fiber lasers (wavelength 1030 nm) with a focus diameter of 80 \u03bcm, a maximum power of 400W and a Gaussian distribution. Production took place under inert atmosphere using argon gas to prevent oxidation of the alloy. The base plate was preheated to \u00b0100 C and a contour-hatch scanning strategy was applied, as shown in Fig. 2. Starting with a contour scan of two lines, the inner part of the samples was scanned with a bidirectional hatch pattern. The scan orientation of every pattern was subsequently rotated by \u00b067 for each layer with a layer thickness of 30 \u03bcm. Cylindrical samples with a diameter of 12 mm and a length of 105 mm were built in two different build directions as vertical and horizontal build for mechanical testing. Cylinders built with their longitudinal axis along the building direction (vertically build) are denoted SLM-v, while cylinders with their longitudinal axis orthogonal to the building direction (horizontally build) are labeled SLM-h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure1-15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure1-15-1.png",
        "caption": "Figure 1-15 Phase plane trajectories for an oscillator with a nonlinear restoring force [Duffing's equation (1-2.19)]: (a) Hard spring problem; a, ft > 0. (b) Soft spring problem; a > 0, 0 < 0. (c) Two-well potential; a < 0, ft > 0.",
        "texts": [
            " The study of these changes in nonlinear problems as system parameters are varied is the subject of bifurcation theory. Values of these parameters at which the qualitative or topological nature of motion changes are known as critical or bifurcation values. As an example, consider the solutions to the undamped Duffing oscillator Jc + ax + fix3 = 0 (1-2.19) One can first plot the equilibrium points as a function of a. As a changes from positive to negative, one equilibrium point splits into three points. Dynamically, one center is transformed into a saddle point at the origin and two centers (Figure 1-15). This kind of bifurcation is known as a pitchfork. Physically, the force \u2014(ax + /?x3) can be derived from a potential energy function. When a becomes negative, a one-well potential changes into a double-well potential problem. This represents a qualitative change in the dynamics and thus a = 0 is a critical bifurcation value. Another example of a bifurcation is the emergence of limit cycles in physical systems. In this case, as some control parameter is varied, a pair of complex conjugate eigenvalues sl9 s2= + /<o + y cross from the left-hand plane (y < 0, a stable spiral) into the right-hand plane (y > 0, an unstable spiral) and a periodic motion emerges known as a limit cycle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.22-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.22-1.png",
        "caption": "Fig. 7.22 Axial piston pump",
        "texts": [
            " Mineral oil in general is more viscous, thus, has good lubricating and better anti-corrosion properties. In 1905, Reynolds Janney, an American engineer, started using oil to replace water as the working medium of the presses. This greatly improved the working quality of the presses (Li 2011). After oil was used as the working medium of hydraulic power, it was needed to develop a variety of oil pumps for use in different conditions. In 1907, two American engineers, Harvey Williams and Reynolds Janney, developed the first axial piston devices (Fig. 7.22), which could be used as either a pump or a turbine. This device was used in 1906 in warships to drive the turret (Li 2011). Its application in machine tools came, however, much later. At the turn of the 19th and 20th centuries, hydraulic planers were made in Germany, and hydraulic turret lathe and grinding machines in the U.S. (Zhou and Yu 2008). Hydrodynamic transmission, involving one or more torque converters, is another type of fluid transmission. Fluid couplings originated from the work of a German engineer, Hermann F\u00f6ttinger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure10.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure10.4-1.png",
        "caption": "Figure 10.4. Envelope 01 formed by a curve 02 in gear 2.",
        "texts": [],
        "surrounding_texts": [
            "Example 9.1 A hob has a module of 6 mm and a pressure angle of 20\u00b0. Its addendum is 7.5 mm, and the tooth tip radius is 1.8 mm. The hob is used to cut a 24-tooth gear, with a profile shift of 1.5 mm. Calculate the polar coordinates in the gear of the point where the fillet meets the involute, and of the point where the fillet meets the root circle. Rsg = 72.000 mm Ps = 18.850 We start by finding the coordinates (x~,y~) of the center of the circular section at the tip of the hob tooth. h = 6.316 (5.40) x~ - 5.700 (5.43) y~ = - 0.722 (5.44) Note that y~ is negative, which is essential in a correctly des i gned hob. A t the top of the fi llet , ur - 10.817 ~'= -4.200 1'/' - 11.539 s' = - 12.280 s = - 14.080 ~=-4.816 7j = - 13.231 13g - 0.281138 radians = - 16.108\u00b0 R = 68.475 mm, 8R = 4.967\u00b0 At the root circle, Ur = 0.722 ~' = - 4.200 7j' = 0 s' = - 4.200 (9.20) (9.10) (9.11) (9.12) (9.13) (9.14) (9.15) (9.16) (9.17,9.18) (9.21) (9.10) (9.11) (9.12) 226 Geometry of Non-Involute Gears s = -6.000 - 6.000 11 = 0 - 0.120869 radians = - 6.925\u00b0 R = 66.000, 9R = 6.925\u00b0 (9.13) (9.14) (9.15) (9.16) (9.17,9.18) It should be noted that this point is not on the center-line of the tooth space, where the value of 9R is 7.5\u00b0. The tooth profile contains a very small circular section, coinciding with the root circle, which is generated by the flat section at the tip of the hob tooth. Example 9.2 A hob with D.P. 2.5 and pressure angle 20\u00b0 is designed to cut gears with tip relief. The tooth profile of the hob is shaped like Figure 9.8, with the values of q and r being 0.16 . q and 4.8 inches. Determine the reduction in the tip tooth thickness of a 40-tooth gear, compared with a gear cut by a conventional hob, if the gear has zero profile shift and an addendum of 0.4 inches. m = 0.4000 inches Rsg 8.0000 RTg = 8.4000 The value of xr on the hob which generates the tip of the tooth on the gear must be found by trial and error. We will use the correct value immediately, and proceed with the remaining calculations. xr 0.3560 tJ>A r = 22.5110 (9.23) Yr = - 0.4486 (9.24) ~ 0.3560 (9.3) 11 = 0.8590 (9.4) u = r 1.3076 (9.5) f3g 0.084916 radians 4.865\u00b0 (9.6) R = 8.4000 (9.7) Examples 8R = 1.004\u00b0 = 0.017526 radians tR = 2R8R = 0.2944 inches For a gear with no tip relief, Rb = 7.5175 41T = 26.499\u00b0 tT = 0.3043 inches Reduction in tooth thickness = 0.0098 inches Example 9.3 227 (9.8) (2.36) Repeat the calculations of Example 9.1, assuming that the gear is cut by a 16-tooth pinion cutter with a tip circle diameter of 113.4 mm, a profile shift of 1.8 mm, and rounding at the tooth tips with a radius of 1.5 mm. This is the cutter shown in Figure 5.12. m=6, 41 s =200, Nc =16, RTc =56.7, ec =1.8, r CT=1.5 Ng=24, eg=1.5 We must first find the polar coordinates (R~,8~) of the center of the circular section at the tip of the cutter tooth. Rsc = 48.000 mm Rbc = 45.105 R~ 55.200 41hc = 36.454\u00b0 Rhc = 56.078 tsc = 10.735 0.024246 radians 35.065\u00b0 x' c 55.200 y~ = 0.132 8' = 0 137\u00b0 c \u2022 (5.32) (5.33) (5.34) (6.1) (5.35) (5.36) (5.37) (5.38) (5.39) Next, we determine the center distance at which the cutter wi 11 cut the requi red tooth thickness in the gear. Rsg = 72.000 Rbg = 67.658 Ps = 18.850 t sg = 1 0 \u2022 5 1 7 ( 6. 1 ) 228 Geometry of Non-Involute Gears CC = s 120.000 inv ~~ = 0.024914 (5.18) ~c p 23.577\u00b0 (2.16,2.17) ~c 23.577\u00b0 (5.19) CC 123.033 (5.20) RC pg 73.820 (5.8) RC pc = 49.213 (5.9) Lastly, we find the coordinates in the gear of the end points of the fillet. At the top of the fillet, a = 11.626\u00b0 ~'=-4.854 71' - 11 \u2022 124 s' - 12.137 s = -13.637 e - 5.454 71 = - 12.498 ~c = 11.489\u00b0 = 0.200516 radians ~g = - 0.264577 radians = - 15.159\u00b0 R = 69.499 mm, 9R = 4.799\u00b0 At the root circle, a = 0 ~' = - 5.987 71' = 0 s' = - 5.987 s = - 7.487 ~ = - 7.487 71 = 0 ~c - 0.137\u00b0 = - 0.002388 radians ~g - 0.129308 radians = - 7.409\u00b0 R = 66.333 mm, 9R = 7.409\u00b0 (9.35) (9.25) (9.26) (9.27) (9.28) (9.29) (9.30) (9.31) (9.32) (9.33, 9.34) (9.36) (9.25) (9.26) (9.27) (9.28) (9.29 ) (9.30) (9.31) (9.32) (9.33, 9.34) Chapter 10 Curvature of Tooth Profiles Involute Radius of Curvature The radius of curvature at any point of an involute is found most easily, by making use of one of the special propert ies of the curve. We pointed out in Chapter 2 that the involute can be represented as the path followed by point A of a rigid bar, while the bar rolls without slipping on a circle of radius Rb \u2022 The bar and the circle are shown in Figure 10.1, and the contact point is labelled E. Since E is also the instantaneous center of the bar, the path of A coincides momentarily with the circle whose center is E, and the radius of curvature p of the involute at point A is therefore equal to the length EA, p EA ( 10. 1) If A is the point of the involute at radius R, as shown in Figure 10.2, the angle ECA is equal to the profile angle ~R' as we proved in Equation (2.9), and the radius of curvature can therefore be expressed as follows, p (10.2) Euler-Savary Equation The equation just derived gives a very simple method for calculating the radius of curvature, at any point on the involute section of a gear tooth profile. However, the equation is of course not suitable for finding the radius of 230 Curvature of Tooth Profiles curvature in the fillet. For this purpose, we make use of the Euler-Savary equation, which gives a relation between the radii of curvature of two conjugate profiles. The fillet of a gear tooth is conjugate to the circular section at the tip of the cutter tooth, whose radius is known. We can therefore use the Euler-Savary equation to find the radius of curvature at any point on the fillet. Before we make use of the Euler-Savary equation, we will show how the equation is derived. We consider a pair of meshing gears, as shown in Figure 10.3, and we first discuss the motion of gear 2 relative to gear 1. We regard gear 1 as fixed, so that the motion of gear 2 can be represented by the motion of its pitch circle, rolling without slipping on the pitch circle of gear 1. If the angular velocity of gear 2 relative to gear 1 is w radians/second counter-clockwise, then the velocity of the gear center C2 is (Rp2w), and the angular velocity of the line of centers is equal to the velocity of C2, divided by the center distance. The velocity of P, the point at which the pitch circles touch each other, is then given by the following expression, Euler-Savary Equation 23' R c Figure '0.2. Radius of curvature of the involute. ('0.3) We now consider the motion of a 'particular curve in gear 2, which we will call curve 02. As gear 2 rolls on the pitch circle of gear \" the various positions occupied by curve 02 form an envelope, and this envelope is called curve 0,. Figure '0.4 shows the positions of gear 2 at two distinct times l' and 1\" \u2022 At time 1', the center of gear 2 is C2 ' and the point where the pitch circles touch is P. The corresponding points at time 1\" are shown as C2 and P'. The two positions of the curve in gear 2 are shown as 02 and 02' and these curves touch the envelope 0, at points A and A' \u2022 The instantaneous center of gear 2 at time l' is P. Hence, the point of gear 2 which coincides with A has a velocity that is perpendicular to PA. The tangent to the envelope 0, must lie in the same direction, and the normal therefore coincides with PA. The two lines PA and P'A' are each normal to curve 0, at adjacent points, so the point 0, where these lines meet is the center of curvature of curve 0, at A, and the length O,A is the radius of curvature Pl. The velocity of A can be related to the velocity of P. If PA makes an angle ~ with the tangent to the pitch circles at P, the velocity of P has a component perpendicular to PA of 232 Curvature of Tooth Profiles (vp sin 1/1), and the velocity vAil can be expressed as follows, (10.4) In this expression, s is the distance from P to A. The symbol vAil is used to represent the velocity of A, to indicate that the velocity is measured relative to gear 1. We next determine the velocity of A, measured relative to gear 2. Figure 10.5 shows the system with gear 2 at rest, and gear 1 rolling on the pitch circle of gear 2 with a clockwise angular velocity w. As before, the positions of the moving gear at the two times T and T' are indicated by the unprimed and the primed symbols. Curve 02 is now the envelope of curve 01' and the two positions shown of curve 01 touch curve 02 at A and A'. The lines PA and P'A' are normal to curve 02' so the point 02 where they meet is the center of curvature, and the length 02A is the radius of curvature P2. If we calculate the velocity of P, we will find that it Euler-Savary Equation 233 is the same as before. In other words, it is still given by the expression in Equation (10.3). Its component perpendicular to PA is also unchanged, and we can now write down the veloc i ty of A, (10.5) The velocity of any point A, measured relative to gear 1, is equal to the velocity of A measured relative to gear 2, plus the velocity relative to gear 1 of the point in gear 2 which coincides with A. This is a standard theorem of dynamics, and for the case we are considering, it can be written as follows, vA/ 2 + ws (10.6) We now combine Equations (10.3 - 10.6), and we obtain a relation between the radii of curvature Pl and P2 of curves 01 and \u00b02 , Pl P2 (Pl- s ) - (P2+ s ) _, s_ (_1_ + _1_) Sln ~ Rpl RP2 (10.7) 234 Curvature of Tooth Profiles Finally, the left-hand side of this equation is simplified, and the relation takes the following form, which is known as the Euler-Savary equation for envelopes, _1_ (_1_ + _1_) sin q, Rpl Rp2 (10.8) In the derivation of this equation, we have used exactly the same notation used throughout the rest of this book. The two curves 01 and 02 represent the tooth profiles, A is the contact point between the teeth, and P is the pitch point. The angle q, is the operating pressure angle of the gear pair, which, as we have shown, is not constant when we are dealing with non-involute profiles. Finally, s is the coordinate giving the position of A on the line of action, and it is positive when A lies above P. In Figures 10.4 and 10.5, the two curves 01 and 02 are shown as convex, and we assumed in the derivation that Pl and P2 are positive. The equation remains valid if either curve is concave, but the corresponding radius of curvature is then negative. Curvature of Tooth Profiles 235 Gear Tooth Fillet Radius of Curvature We can use Equation (10.8) to obtain the radius of curvature at any point on a gear tooth profile, when the gear is cut by a non-involute cutter. If gear 1 represents the gear being cut, and gear 2 the cutter, it is convenient to replace the subscripts 1 and 2 by g and c. In Equation (10.8), the radii RP1 and Rp2 of the pitch circles are then replaced by the cutting pitch circle radii R~g and R~c. We simplify the equation by introducing a length RO' defined as follows, _1_ + 1 RC RC pg pc (10.9) so that the quantity (1/RO) represents the relative curvature of the two cutting pitch circles. We then solve Equation (10.8) for Pg ' obtaining the following expression, (p +s)2 c (10.10) In order to calculate the radius of curvature Pg at a point on the gear tooth profile, we use the methods described in Chapter 9 to find the coordinates (~,~) of the cutting point, corresponding to any specified point on the cutter tooth. The radius of curvature of the cutter tooth profile at this point gives the value of Pc to be used in Equation (10.10), and expressions for If> and s can be read from Figure 9.9, which shows the meshing diagram during the cutting process, tan If> s \u00a3. ~ -~ sin If> (10.11) (10.12) These values for P, If> and s are substituted into c Equation (10.10), and we obtain the radius of curvature Pg at the corresponding point on the gear tooth profile. We first use this method to find the radius of curvature at points on a gear tooth fillet, for the case when the gear is cut by a rack cutter. The cutting pitch circle radius of the rack cutter is infinite, and the cutting pitch circle of 236 Curvature of Tooth Profiles the gear coincides with its standard pitch circle, so the length RO defined by Equation (10.9) is equal to the standard pitch circle radius of the gear, ( 10.13) The radius of curvature of the circular tip of the rack cutter tooth is rrT' and the values of ~ and ~ are given by Equations (9.14 and 9.15). The profile radius of curvature at a point on the gear tooth fillet can then be found from Equation (10.10). However, since the fillet is concave, the radius of curvature given by this equation would always be negative. It is rather more convenient to change the sign in the equation, so that we obtain an expression for Pf' the magnitude of the fillet radius of curvature, (10.14) A point of particular interest is the point where the fillet meets the root circle, since the radius of curvature at this point is required for the calculation of the maximum fillet stress in the tooth. The position of the cutting point is given by Equations (9.10 - 9.15). To find the position corresponding to the point where the fillet meets the root circle, we choose the cutter position ur equal to (-y~), as we proved in Equation (9.21). We then obtain the following values, '11 0 These values are substituted into Equation (10.14), glvlng an expression for r f , the magnitude of the fillet radius of curvature, at the point where the fillet meets the root circle, Gear Tooth Fillet Radius of Curvature 237 (a r -e-r rT }2 ( 10.15) The fillet radius of curvature is found by the same procedure, for a gear which is cut by a pinion cutter. The radii of the cutting pitch circles were given by Equations (5.8 and 5.9), When these values are substituted into Equation (10.9), we obtain the following expression for the length RO' NgNCCC (N +N }2 g c (10.16) The gear tooth fillet is cut by the circular section at the tip of the cutter tooth, whose radius is r cT ' If there is no rounding at the cutter tooth tip, so that there is a sharp corner where the tooth profile meets the tip circle, then the value of r cT is zero. We use Equations (9.25 - 9.30) to find the coordinates (~,~) of the cutting point, corresponding to any specified point on the cutter tooth profile. The values of ~ and s are found, as before, from Equations (10.11 and 10.12). The radius of curvature at the corresponding point of the gear tooth fillet is given by Equation (10.10), and again we change the sign so that we obtain the magnitude P f of the radius of curvature, (rCT+s)2 P r + f cT RO sin ~ - (rCT+s) (10.17) To find the magnitude r f of the fillet radius of curvature, at the point where the fillet meets the root circle, we must determine the corresponding values of ~ and s. When we described in Chapter 9 how the shape of the gear tooth fillet is calculated, we specified the position of the cutter by the angle a between the line of centers, and the line C A' c c in the cutter. We showed in Equation (9.36) that, when a is zero, the cutter is in the correct position to cut the point on the gear tooth where the fillet meets the root circle. With 238 Curvature of Tooth Profiles this value of a, the coordinates (~,~) of the cutting point are found from Equations (9.25 - 9.30), and the values of , and s are then given by Equations (10.11 and 10.12), t RC pc - R Tc ~ 0 , 90 0 s RC pc - R Tc We substitute these values into Equation (10.17), and we obtain an expression for r f , (RTC-Rpc-rCT)2 r f r cT + c ( 10. 18) RO + (RTC-Rpc-rCT) Examples 239"
        ]
    },
    {
        "image_filename": "designv10_4_0003967_ichr.2005.1573536-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003967_ichr.2005.1573536-Figure4-1.png",
        "caption": "Fig. 4. Humanoid modeled by rectangle box with a bar",
        "texts": [
            " The global scheme is based on two motion planners benefiting from the respective advantages of both sampling and diffusion probabilistic approaches. The first one plans a global path while the second one is dedicated to path re-shaping. As task planning is concerned, the objective is to compute a motion plan guarantying collision-freeness for both the robot and the object. We use here a functional decomposition of the robot body already experienced in motion planning for virtual mannequins [14]. At this level the robot is modeled as a geometric parallelepiped bounding box (see Fig. 4). Only that box and the object to be manipulated are considered with respect to collision avoidance. The configuration space to be searched is then 9-dimensionated (3 dimensions for the box, 6 dimensions for the object). To explore such a space we use a sampling approach as in [14]. The novelty here is to consider an additional constraint for the locomotion of the humanoid. We want the robot walking in a \u201cnatural\u201d manner: it should walk sideway only if it is necessary. This constraint is taken into account by considering two different steering methods (or local methods) to build the roadmap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003832_0094-5765(88)90189-0-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003832_0094-5765(88)90189-0-Figure3-1.png",
        "caption": "Fig. 3. Equilibrium configurations.",
        "texts": [
            " After some simplification, one obtains, sin 01o[COS 010 + al cos 020] = 0, (20) sin 0z0[cos 020 + a2 cos 0t0] = 0, (21) where a I = 1~212/(1 -- t~, ) Ii = [1~2/(t~ 2 + 1~3)](12/11 ), a 2 = / ~ , l , / ( 1 - / t 2 ) l 2 = [/~/(U, + Us)](/,/6), (22) and 0~0 and 020 are the equilibrium values of 0~ and 02, respectively. Note that a I and a 2 are positive. Equations (20) and (21) have four possible solutions: (i) 010 = 020 = 0; (ii) 010 = 020 = ~/2; (iii) 010=0, 020=cos l [ - a 2 ] , if a 2 < l ; this implies z 2 = 0; (iv) 020=0, 010=cos l [ - a l ] , if a l < l ; this implies z~ = 0. The four equilibrium configurations are shown in Fig. 3. The first two equilibrium configurations correspond to the three bodies aligned along the local vertical and the direction of flight, respectively. The last two equilibrium configurations are intuitively less obvious, in which one tether is parallel to the local vertical, while the other is inclined. The odd body in three, that is not connected to the vertical tether, has the same altitude as the system centre of mass. Considering small oscillations around the vertical equilibrium configuration, one has 0 1 = 0 1 o + 0 1 = 0 1 , 0 2 = 0 2 o + 0 : = 0 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003824_physreve.74.031915-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003824_physreve.74.031915-Figure1-1.png",
        "caption": "FIG. 1. a Sketch of motor-mediated two-rod interaction for fully inelastic collision =1/2 and b integration regions C1,2 for Eq. 2 .",
        "texts": [
            " We model the motor-mediated inelastic interaction by an instantaneous collision in which two rods change their orientations according to the following collision rule: 1 a 2 a = 1 \u2212 1 \u2212 1 b 2 b , 1 where 1,2 b are the two rods\u2019 orientations before and 1,2 a after the collision, and the constant characterizes inelasticity of collisions analog of restitution coefficient in granular media . The angle between two rods is reduced after the collision by an \u201cinelasticity\u201d factor =2 \u22121. Totally elastic collision corresponds to =0 or =\u22121 the rods exchange their angles , and a totally inelastic collision corresponds to =1/2 or =0: rods acquire identical orientation 1,2 a = 1 b + 2 b /2 see Fig. 1 a . Here we assume that two rods only interact if the angle between them before collision is less than some cutoff angle 0, 2 b\u2212 1 b 0 . Because of 2 periodicity, we have to add the rule of collision between two rods with 2 \u2212 0 2 b\u2212 1 b 2 . In this case, we have to replace 1 b,a\u2192 1 b,a+ , 2 b,a\u2192 2 b,a\u2212 in Eq. 1 . In the following, we will only consider the case of totally inelastic rods =1/2 and 0= , the generalization for arbitrary and 0 is straightforward see 19 . The probability distribution of orientation angles P obeys the following master equation: 031915-2 tP = Dr 2 P + g C1 d 1d 2P 1 P 2 \u2212 1/2 \u2212 2/2 \u2212 \u2212 2 + g C2 d 1d 2 P 1 P 2 \u2212 1/2 \u2212 2 2 \u2212 \u2212 \u2212 2 , 2 where g is the \u201ccollision rate,\u201d or a probability of two tubules to interact via a motor, the diffusion term Dr describes thermal fluctuations of the rod orientation, and the integration domains C1 ,C2 are shown in Fig. 1 b . The collision rate is proportional to the concentration of molecular motors m, and from the dimensional analysis one finds that g is of the order of mDrl 2, since 1/Dr is the only time scale in Eq. 2 , and the effective interaction cross section of microtubules is of the order of l2. Rescaling time scale ts=Drt, probability Ps=gP /Dr, and defining angle difference w= 2\u2212 1, one obtains tPs = 2 Ps + \u2212 dw Ps + w 2 P \u2212 w 2 \u2212 Ps Ps \u2212 w 3 we dropped the subscript s at time t for brevity . The rescaled number density = 0 2 Ps , t d now is proportional to the density of rods multiplied by the density of motors"
        ],
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    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.22-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.22-1.png",
        "caption": "Figure 13.22. Coincident normals to the tooth surfaces at points A and A' \u2022",
        "texts": [
            "107) and when we use Equation (13.79) to express the vectors n~ and n~', the condition becomes: 348 Tooth Surface of a Helical Involute Gear - cos \"'b sin eG n + cos \"'b cos eG n G' x G' Y sin \"'b n z - cos \"'b sin e nx + cos \"'b cos e ny sin \"'b n z (13.108) The solution to this equation can be seen by inspection, G' e (13.109) G G' For the polar coordinates e and e to be equal, the two points G and G' must lie on the same axial line. The two generators and the axial line GG' then form a plane, as shown in Figure 13.22, and this plane is perpendicular to nGR\u2022 The G G' unit vectors n# and n# must be equal, in view of Equation (13.109), and the two generators are therefore parallel. The plane containing these generators is called a base tangent plane, since it touches the base cylinder along line GG' \u2022 The unit vector n~ normal to the tooth surface at A is parallel to n~, as we showed in Equation (13.78), and is therefore perpendicular to n~ and to n~. It must then lie in the base tangent plane, in the direction perpendicular to the generators. The same is true of the uni t vector n~' , normal to the second tooth surface at A'. Hence, if we choose A and A' so that the line joining them is perpendicular to the Normal Base pi tch 349 generators, the normals at A and A' will coincide, and we have found a common normal. The length AA' can then be read from Figure 13.22, AA' Pz sin \"'b (13.110) We showed in Equation (13.45) that the axial pitch is related to the normal base pi tch as follows, and when the last two equations are combined, it is clear that the length AA' in Figure 13.22 is equal to the normal base pitch, AA' (13.111) We have therefore proved the statement made at the beginning of this section, that the normal base pitch is equal to the distance between adjacent tooth surfaces, measured along a common normal. We can also use Figure 13.22 to prove another important result. The generators AG and A'G' are the lines where the base tangent plane intersects the tooth surfaces containing A and A'. The same plane would intersect the other teeth of the gear in a set of parallel lines, each a distance Pnb apart, and each making an angle \"'b with the z axis. Hence, the section formed by a base tangent plane looks the same as the developed base cylinder, in which the teeth also appear as straight lines, a distance Pnb apart, making an angle \"'b with the z axis"
        ],
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    },
    {
        "image_filename": "designv10_4_0003751_s0263574708004748-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003751_s0263574708004748-Figure6-1.png",
        "caption": "Fig. 6. Rolling about the axis z\u2032 b in Step 1.",
        "texts": [
            " Substituting in the equations of motion (16)\u2013(20), we get Iz\u03c6\u0308 + J z zz(\u03c6\u0308 + \u03c8\u03082) = \u2212mr2 sin2 \u03b80\u03c6\u0308, J z zz(\u03c6\u0308 + \u03c8\u03082) = \u03c4z yielding (Iz + mr2 sin2 \u03b80)\u03c6\u0308 = \u2212\u03c4z. (21) In this maneuver the sphere rolls along a latitude circle of radius sin \u03b8 . Using the parallel axis theorem, the moment of inertia about the axis z\u2032 b passing through the point of contact I is (Iz + mr2 sin2 \u03b80) where Iz is the moment of inertia of the system about the zb-axis. The rolling motion is instantaneous rotation of the sphere about the axis z\u2032 b as shown in Fig. 6. The angular acceleration being \u03c6\u0308, the torque obtained in (21) can be physically interpreted. We similarly obtain the dynamic equations for the remaining paths as follows. Step 2: In this step, only the Euler angle \u03b8 changes and \u03b1\u0307 = 0 and \u03c6\u0307 = 0. The angle \u03c6 is changed to \u00b1\u03c0/2 in Step 1 and only X motor actuated resulting in \u03c8\u03071 = 0 and \u03c8\u03072 = 0. Applying all these conditions in the equations of motion, a torque equation for execution of this maneuver is obtained as \u2212\u03c4x = (Ix + mr2)\u03b8\u0308 . http://journals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-FigureC-4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-FigureC-4-1.png",
        "caption": "Figure C-4 Double pendulum and \"Space ball\" chaotic toys.",
        "texts": [
            " A simple way to do this is to put double-sided sticky cellophane tape along the beam and to put a thin shim-type metal layer (0.1 mm) on top of this. When constrained layer damping is placed on each side of the beam, a significant increase in damping can be achieved and some very beautiful fractal-looking Poincare maps can be obtained. The reader should see Chapter 4 for other suggestions about experiments in chaotic vibrations. 284 Chaotic Toys C.3 A CHAOTIC DOUBLE PENDULUM OR \"SPACE BALL\" This toy has several variations, two of which are shown in Figure C-4. The commercial versions are well made (from Taiwan) but I could not find the name of any manufacturer (nor for that matter any patent numbers) on the devices. The basic principles involve the forced motion of a pendulum that interacts with a magnetic circuit in the base. Attached to the primary pendulum is another rotating arm. Several configurations are possible as shown in Figure C-4. In all caes, the pivot point of the second arm is forced by the motion of the driven pendulum. In some versions of this toy, small magnets on both arms interact when the second arm rotates past the primary arm. Neon Bulb Chaotic Toy 285 A simple but clever driving circuit is used to provide current impulses to a driving magnet as shown in Figure C-5. When the lower pendulum oscillates, the magnetic field in the attached magnet generates a voltage in a coil in the base circuit. This voltage is applied to a transistor which begins to conduct when this motion-induced voltage reaches a critical value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000392_j.addma.2020.101494-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000392_j.addma.2020.101494-Figure10-1.png",
        "caption": "Fig. 10. Resulting productivity increase of 24.5 % through high-speed printing at \u03c1>95 % on a demonstrator build job consisting of three scaled A380 fuel connectors.",
        "texts": [
            " higher robustness against local or global process parameter deviations and thus higher quality. Also, the required laser power may be reduced. The most obvious, however, is the potential to increase the productivity by increasing the scan speed during L-PBF. Within the investigations presented here, the allowable scan speed increase was 60\u201370 % when compared to the reference. To evaluate the effect of increasing scan speed on actual productivity, a demonstrator build job consisting of three Airbus A380 fuel connector parts was considered (cf. Fig. 10, for more information on the A380 fuel connector case study, please cf. to [45]). The parts were scaled to a build height of approximately 220mm for this comparison, resulting in n=3674 layers of l= 60 \u03bcm. Firstly, the reference parameter set (v= 100 %) was attributed to the demonstrator build job and transferred to the SLM 500 H L L-PBF machine. The predicted build time is t =24 h and 8min. Secondly, the high-speed parameter set (v= 167 %) was attributed to the build job. Again, the job was transferred to the L-PBF system, resulting in a predicted build time of t =17 h and 51min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003350_j.1460-2687.2002.00109.x-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003350_j.1460-2687.2002.00109.x-Figure5-1.png",
        "caption": "Figure 5 A schematic diagram of the forces acting on a football.",
        "texts": [
            " Once the quadratic coefficients, a, b, c and d had been found for each test, these fitted trajectories could be compared with a simulation of a ball in flight to determine the lift and drag coefficients for the ball. A step-by-step model, similar to that used by Mehta (1985) was designed for the simulation of a football in flight. The model assumed that the ball is subjected to two forces, Fd and Fl, caused by drag and lift as well as mg caused by its weight. A force 194 Sports Engineering (2002) 5, 193\u2013200 \u2022 2002 Blackwell Science Ltd diagram of a ball travelling with a velocity v at an angle h to the ground under these conditions is shown in Fig. 5. The equations of motion can be derived by resolving the resulting accelerations vertically and horizontally to give m d dt \u00f0v sin h\u00de \u00bc mg Fd sin h F1 cos h \u00f03\u00de m d dt \u00f0v cos h\u00de \u00bc Fd cos h F1 sin h \u00f04\u00de These equations can then be re-written to deal with finite differences using md\u00f0v sin h\u00de \u00bc dt\u00bdmg Fd sin h F1 cos h \u00f05\u00de md\u00f0v cos h\u00de \u00bc dt\u00bd Fd sin h F1 cos h \u00f06\u00de The forces Fd and Fl were assumed to vary with velocity squared according to the following equations Fd \u00bc 1 2CdqAv2 \u00f07\u00de F1 \u00bc 1 2C1qAv2 \u00f08\u00de (where, q is density of air, A is projected area of ball, Cd is the drag coefficient and Cl is the lift coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure11-1.png",
        "caption": "Fig. 11. Isocontours of the mean sensitivity indices of all the variations on different workspace cross-sections: (a) z = 201 mm ; (b) z = 287 mm .",
        "texts": [
            " Both robots have the same sensitivity indices with regard to the same type of variations, except the ones that relate to the parallelogram structure, with smaller indices of Delta-RU than those of original one. The major reason lies in that the Delta-RU robot has fewer parameters in the RUU linkage compared to the traditional Delta with the parallelogram structure in all the three linkages. The isocontours of mean of the indices \u03bdp and \u03bd\u03c6 defined by Eq. (28) over the different workspace cross-sections of the Delta-RU robot are displayed in Fig. 11 . It is noteworthy that the closer end-effector location to the central region of the workspace, the smaller the sensitivity indices of the end-effector posture to variations in the geometric parameters. Moreover, both the positional and orientational sensitivity indices at most workspace points decrease with the increasing z-coordinates, except the maximums in each sectional workspace appearing at the boundaries. The maximum \u03bd\u03c6 in each sectional workspace reduces to 0.06 at z = 373 mm from 1.39 at z = 201 mm , while the maximum \u03bdp in each sectional workspace decreases to the global minimum at a certain z-coordinate (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000695_j.jmapro.2021.03.003-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000695_j.jmapro.2021.03.003-Figure9-1.png",
        "caption": "Fig. 9. Contact stress distribution under the mechanical effect.",
        "texts": [
            " Journal of Manufacturing Processes 64 (2021) 1544\u20131562 was dissolved to have a deformation on the profile. The surface asperity was decreased in height and other regions of the anode surface were simultaneously broken. However, the most intensive current density still existed on the highest fraction of the attacked partially melted powder, which indicated the most protruding area of the surface asperity was preferentially removed and the SLM internal surface gradually became leveled and smooth. Fig. 9 shows the simulated contact stress distribution between the surface asperity and the flexible abrasive filament. It was observed that the surface asperity was pressed with the movement of the flexible abrasive filament and consequently the deformation of the flexible abrasive filament. The large contact stress existed on the contacting area of them, which indicates the most protruding area of the partially melted powder was prone to be chopped off under the mechanical effect. What\u2019s more, the large pressure was also seen in the fixed side of the surface asperity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure3-1.png",
        "caption": "Fig. 3. Force analysis of substructure 6.",
        "texts": [
            " The total deflection of the robot is $ t = l \u2211 i =1 $ t,i = l \u2211 i =1 C i $ w = C$ w , C = l \u2211 i =1 W i C i W T i (7) where C is the conventional compliance matrix without considering the effects of link weights and gravity compensator. This section conducts the static reaction force analysis of the Kuka KR 500 industrial robot to establish a linear map between the forces. For the considered robot, the reaction force bear by each joint is influenced by the external wrench imposed upon the end-effector, the gravity force of the movable links and the balancing force of the gravity compensator. To calculate the force exerted by substructure 6 on joint 6, a force diagram of substructure 6 is shown in Fig. 3 . The static force/torque equilibrium equations of the system at point O E can be written as { f E \u2212 m E g \u0303 z = R 6 \u03c1w, 6 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z = ( R E r E 6 ) \u00d7 ( R 6 \u03c1w, 6 , f )+ R 6 \u03c1w, 6 ,\u03c4 (8) where m E = m 6 + m S , \u0303 z = [ 0 0 1 ] T , \u03c1w, 6 , f = [ \u03c1w, 6 , f x \u03c1w, 6 , f y \u03c1w, 6 , f z ] T , \u03c1w, 6 ,\u03c4 = [ \u03c1w, 6 ,\u03c4x \u03c1w, 6 ,\u03c4y \u03c1w, 6 ,\u03c4 z ] T , f E and \u03c4E represent the equivalent external force and torque imposed at point O E , \u03c1w, 6 , f and \u03c1w, 6 ,\u03c4 are the reaction force and torque of joint 6 acting at point O 6 , m E is the mass of the end-effector which includes the mass of link 6 m 6 and mass of spindle m S , G E is the mass center of the end-effector, r E G E denotes the position vector from point O E to point G E expressed in { O E }, r E 6 is the position vector from point O E to point O 6 expressed in { O E }, and \u0303 z is the unit vector vertically upward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003001_s0005-1098(99)00037-0-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003001_s0005-1098(99)00037-0-Figure1-1.png",
        "caption": "Fig. 1. Example of a non-IS stable robot.",
        "texts": [
            " Notice that < 1 is not a suitable ISS-Lyapunov function for the considered system because the expression of <Q 1 is only negative semi-de\"nite: <Q 1 \"!qR TK D qR #qR TK P q d 4!a 1 DqR D2#a 2 Dq d D2, (18) where a 1 (a 2 ) is a su$ciently small (large) constant. Nevertheless, < 1 is a qISS-Lyapunov function, provided that we de\"ne the system output y as qR . Simulations showed that robots controlled via a PD action are not necessarily input-to-state stable. Hereafter, we illustrate an example of a non-input-to-state stable robot and then prove ISS for a signi\"cant class of manipulators. Example 1. Consider the manipulator shown in Fig. 1. A simple model is obtained modeling the arm as a segment with mass M and length \u00b8, and the hand as a material point with mass m. If we denote with r the position of the hand and with h the angle of the arm, the equations for such a system are (mr2#M\u00b82/3) hG#2mrrR hQ \"q, mrK!mrhQ 2\"F. (19) With the matrix notation introduced in Eq. (14) and de\"ning q\"[h, r]T we have: H\"C mr2#M\u00b82/3 0 0 mD , C\"C mrrR mrhQ !mrhQ 0 D. The closed-loop system, obtained choosing q and F as q\"!k d1 hQ !k p1 (h!h d ), F\""
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002924_978-94-009-1718-7_36-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002924_978-94-009-1718-7_36-Figure6-1.png",
        "caption": "Fig. 6: Workspace of point P (F = 2).",
        "texts": [
            " The local mobility of the mechanism in the flattened position turns out to be in the first configuration F = 5, in the second and the third F = 2, and in the fourth configuration F = 1. 6. Workspaces of poiot P Three plates of the Queer Square mechanism are moving translatorially if the plate which carries the coordinate system (XI' x2' x3) is held fixed on ground (Fig. 3). To find the regions in which the point P is possibly moving we introduce a second coordinate system (YI' Y2' Y3) fixed on one of this three plates (see Fig. 6 and 7). By actuating both angles <P and lfI simultaneously we get for the relation between the position vectors X and y: x = a {O, 1,0} + c {costfJ,cos l{I,sintfJ + sin I{I} + Y. (12) Point P with the given position vector Y = {Yl' Y2' Y3} in (Yl' Y2' Y3) is then moving with two degrees of freedoms in its workspace, an algebraic surface of order four: But with I{I:=} tfJ and tfJ:=} -tfJ (Fig. 7) formula (12) yields: X(tfJ) = a {O,l,O}+c {costfJ,costfJ,O}+ Y (14) and the workspace ofP reduces to a straight line in the plane X3 = Y3 \u2022 The two workspace are in contact at the singularity position ~ = 0 A l/f = 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003503_s0022-460x(03)00127-5-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003503_s0022-460x(03)00127-5-Figure2-1.png",
        "caption": "Fig. 2. Position of ball center and raceway curvature centers.",
        "texts": [
            " The position vectors of the groove radius center of the inner and outer race in contact with the jth ball, ~Rij and ~Roj; can be determined from the mass center of the rotor as shown in In the above equations, Ri; Ro; ai and ao are the radial and axial components of the position vectors of the groove radius center of the inner and outer race, and they can be expressed in terms of the pitch diameter dm; the distance between the groove radius centers of inner and outer race d; and contact angle a: Also, cj is the azimuth angle of the jth ball in the x2y plane, and it can be expressed in terms of the cage rotating frequency [8,9]. When a ball bearing operates at high speed, the centrifugal force and gyroscopic moment of the ball are not negligible, so that the contact angles of the inner and outer race are dissimilar and that the groove radius center of the inner race is not collinear with that of the outer race. Fig. 2 shows the position of the ball center and the race curvature center with and without including the centrifugal force and gyroscopic moment of the ball with respect to the same outer race curvature center. In Fig. 2, Xzj; Xrj; aij ; aoj;, lij and loj are the axial and radial components of the position of the ball center, the contact angles of the inner and outer race, and the distances between the ball center and the groove radius centers of the inner and outer race, respectively. Considering the effect of ball waviness in contact with the inner and outer race, wij and woj; and ball oversize, hj; the following equations determine lij and loj: lij \u00bc ri \u00f0D \u00fe hj\u00de=2 wij ; loj \u00bc ro \u00f0D \u00fe hj\u00de=2 woj; \u00f09\u00de where ri and ro are the groove radius of the inner and outer race",
            " (1)\u2013(4) to the position vectors of the groove radius centers of the inner and outer race, the distance between the two position vectors can be expressed as follows [6]: Drj \u00bc\u00f0Ri Ro\u00de \u00fe ai\u00f0yy coscj yx sin cj\u00de \u00fe x coscj \u00fe y sin cj \u00fe \u00f0pij poj\u00de \u00fe qij\u00f0yy coscj yx sin cj\u00de; Dzj \u00bc\u00f0ai ao\u00de \u00fe Ri\u00f0yx sin cj yy coscj\u00de \u00fe z \u00fe \u00f0qij qoj\u00de \u00fe pij\u00f0yx sin cj yy coscj\u00de; \u00f010\u00de where Drj and Dzj are the radial and axial component of the distance between the groove radius centers of the inner and outer race. In the case of the outer-race rotating type of ball bearing, the outer race has translational and angular motion and the inner race is stationary during the rotation of the ball bearing. Similar expressions can be derived to determine the distance between the position vectors of the groove radius center of the inner and outer race. Applying the Pythagorean theorem to Fig. 2, the following equations can be obtained [7,9]: Dzj Xzj 2\u00fe Drj Xrj 2 lij \u00fe dij 2\u00bc 0; X 2 zj \u00fe X 2 rj loj \u00fe doj 2\u00bc 0; \u00f011\u00de where dij and doj are the elastic deformation of the contact point between the ball and each race. Fig. 3 shows the free-body diagram of the ball acted by the contact forces of the inner and outer race, fij and foj and the centrifugal force and gyroscopic moment of a ball, Fcj and MGj: In Fig. 3, D and z are the ball diameter and the angle between the spinning axis of the ball and the bearing centerline, and lij and loj are the constants determined by the race control theory [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure9-1.png",
        "caption": "Figure 9.B. A rack cutter with profile modification.",
        "texts": [
            "31) Chapter 9 Geometry of Non-Involute Gears Introduction In this chapter, we will first show how to calculate the tooth shape of a gear, when it is conjugate to a basic rack of arbitrary shape. This material is not required when the basic rack has straight-sided teeth, since we have already shown how to calculate the tooth profile shape of an involute gear. However, the method described will useful for finding the shapes of gear tooth fillets, which are conjugate to the circular tips of the cutter teeth. General Theory We consider a basic rack with a curved tooth profile, as shown in Figure 9.1. The pitch is Pr' and the reference line is defined in the usual way, as the line along which the tooth thickness is equal to the space width. The rack coordinate system (xr'Yr) is chosen so that the Yr axis lies along the reference line, and the xr axis coincides with a tooth center-line. A typical point Ar of the tooth profile has coordinates (xr,y r ), and the profile angle at this point is ~Ar. Since the shape of the tooth profile is known, Y and A r ~ r are known functions of xr ' We now consider a gear meshed with the basic rack, as shown in Figure 9.2. The pitch circle radius of a plnlon meshed with a rack was given by Equation (1.15), and in Equation (1.19) we showed that the circular pitch of the pinion at its pitch circle is equal to the pitch of the rack. Since the gear in Figure 9.2 is meshed with its basic rack, we 208 Geometry of Non-Involute Gears use the symbol Rsg for the radius of the pitch circle, and the two equations take the following form, ( 9. 1 ) (9.2) The pitch point P is the point lying a distance Rsg from the center of the gear, on the line perpendicular to the reference line of the basic rack. We consider the basic rack when it is positioned with an offset e, so that its reference line lies a distance (Rsg+e) from the center of the gear. We will make use of the fixed (E,~) coordinate system, whose origin is at the pitch point, and the (x,y) coordinate system in the gear, where the x axis coincides with a tooth center-line",
            "5) For a gear being cut by a rack cutter, the relation between the position of the rack cutter and the angular 210 Geometry of Non-Involute Gears position of the gear was given by Equation (5.28), The same equation applies when we consider a gear meshed with its basic rack, and we can therefore find the angular position ~g of the gear, corresponding to the position ur of the basic rack, 1 (u _ lp ) R r 2 s sg (9.6) Since point Ar of the basic rack is the contact point, there is a point A of the gear which coincides with Ar , and its polar coordinates can be read from Figure 9.2, R (9.7) 1/ arctan (~) - ~g sg (9.8) Finally, the tangent to the gear tooth profile at A coincides with the tangent to the basic rack tooth profile at Ar , and therefore makes an angle ,Ar with the ~ axis. The angle YR, which is defined as the angle between the gear tooth tangent at A and the tooth center-line, is then given by the following expression, (9.9) Equations (9.3-9.9) can be used to find the polar coordinates (R,8R) of a point A on the gear tooth profile, and the angle YR, corresponding to any specified point Ar on the basic rack tooth profile",
            " By taking a number of points on the basic rack, we can construct the entire profile of the gear tooth. The general theory just described is helpful for clarifying some of the definitions used in gearing. If we use Equations (9.3 and 9.4) to calculate the position of the contact points, corresponding to a number of points on the basic rack tooth profile, we obtain a series of points on the path of contact. When the basic rack tooth profile is curved, General Theory 211 the path of contact is also curved, as we can see in Figure 9.3. The line of action, which is the line along which the contact force acts in the absence of friction, coincides with the common normal at the contact point. The Law of Gearing states that this line passes through the pitch point, so the line of action is always the line from P to the contact point. The operating pressure angle ~ of the gear pair is the angle between the line of action and the tangent at P to the pitch circle. It is evident that, when the path of contact is not straight, the value of ~ varies as the contact point moves along the path of contact. Two basic racks that fit together exactly, in the manner shown in Figure 9.4, are said to be complementary. If each of these basic racks is used to define the tooth profile of a gear, then these two gears can mesh together correctly, and the Law of Gearing will be satisfied. However, the gears can only operate at the standard center distance Cs ' equal to the sum of the standard pitch circle radii. If the center distance is altered, the common normal at the contact point will no 212 Geometry of Non-Involute Gears longer intersect the line of centers at a fixed point, and the Law of Gearing is not satisfied",
            " Fillet Shape Cut by a Rack Cutter The general theory just described, which gives the shape of tooth profiles conjugate to an arbitrary basic rack, can also be used to find the shape of gear tooth profiles, when they are cut by a rack cutter with curved teeth. In particular, when we consider involute gears, we will use the Fillet Shape Cut by a Rac k Cutter 213 method to find the shape of the tooth fillet, which is cut by the circular section at the tooth tip of the rack cutter. The tooth profile of the rack cutter is shown in Figure 9.5. The circular section of the profile extends from point Ahr to point ATr \u2022 The radius of this section is rrT' and its center is at point A~, whose coordinates (x~,y~) are given by Equations (5.43 and 5.44). In the general theory described in the previous section, we chose a point Ar of the cutter tooth profile, and determined the position ur of the cutter, at which Ar would be the cutting point. For the special case when the cut ter tooth profi Ie is circular, it is sl ightly more convenient to reverse this order. We choose the position of the cutter, and we then determine which point Ar of the circular profile is the cutting point. We therefore consider the cutter in the position shown in Figure 9.5, with an offset e and with the x axis lying a r distance (-ur ) below line CPo In this position of the cutter, the center A~ of the tooth profile circular section has coordinates (~' ,~'), which are given by the following equations, ~ I e + x' r (9.10) 214 Geometry of Non-Involute Gears 1/' (9.11) If the line from the pitch point to A~ intersects the tooth profile at Ar' and Ar is a point on the circular part of the profile, then the normal to the profile at Ar passes through P, and Ar must be the cutting point. The line ArP is the line of action, when the cutter is in the position shown in Figure 9.5. We now reintroduce the coordinate s, measured from the pitch point along the line of action, with points above P being positive. The positions s' and s of points A' r and Ar on the line of action can be expressed as follows, s' s s' - r rT (9.12) (9.13) and we then write down the position of the cutting point Ar' (9.14) ( ...\u00a7...) ., \u2022 s' 'f (9.15) It is evident that the negative signs of s\u00b7 and s cancel out, and it would have been simpler to have used positive values. However, we will make use of these equations again in Chapter 10, when we discuss the fillet curvature, and for that purpose it is important to retain the correct sign fors",
            "21) To construct the entire fillet of the gear tooth, we consider a number of positions of the cutter, starting with the ur value given by Equation (9.20) and ending with the value given by Equation (9.21). We then use Equations (9.10 - 9.18) to calculate the positions of the corresponding points on the fi llet. Fillet Shape of an Undercut Gear The method described in the previous section for finding the shape of a gear tooth fillet can still be used when the gear is undercut. The meshing diagram for the gear and the cutter is shown in Figure 9.6. Since the gear is undercut, we are considering a situation in which the end point Hr of the path of contact lies below the interference point Eg \u2022 The point of the cutter tooth profile which passes through Eg is labelled AEr \u2022 The tooth profile of the undercut gear is shown in Figure 9.7. Although the shape of the involute part of the profile is already known, and it is therefore unnecessary to use the general theory described at the beginning of this chapter, it is nevertheless helpful to consider the results we would obtain if we were to do so. A typical point of the cutter tooth profile is shown as Ar in Figure 9.6. In order to use the general method, we need a relation between the coordinates xr and Yr of point Ar' and this relation can be Fillet Shape of an Undercut Gear 217 read from the diagram, - 11Tm - x t .. 4 r an \"'r (9.22) Equations (9.3-9.8) can then be used to find the position of the corresponding point A on the gear tooth profile, which is shown in Figure 9.7. We consider a sequence of points on the rack cutter tooth, starting near the root and moving towards the tip. As we move along the profile to AEr , the cutting point moves down the path of contact to Eg , and on the gear tooth the corresponding points lie on the involute, down to point B where the involute meets the base circle. We next consider a number of points on the cutter tooth between AEr and Ahr \u2022 The positions of the cutting point, given by E and 77 in Equations (9.3 and 9.4), lie between Eg and Hr on the path of contact. The corresponding points on the gear, found by means of Equations (9.5 - 9.8), lie on the curve shown in Figure 9.7, joining point B to point Af \u2022 It can be seen that the straight section of the cutter tooth generates a curve on the gear which has a cusp at the base circle. This is a characteristic sign of a gear which is undercut. Finally, we consider points on the curved section of the 218 Geometry of Non-Involute Gears cutter tooth, lying between Ahr and ATr \u2022 We use Equations (9.10 - 9.18) to find the corresponding points on the gear, and we obtain the curve in' Figure 9.7 which starts at point Af , and ends at the root circle. From a physical point of view, it is clear that the final shape of the gear tooth is given by the shaded profile in Figure 9~ 7, and that parts of the curve followed by the cutting point have no effect on the final shape of the tooth. Since we do not need to know the path of the cutting point between Band Af , it is not necessary to use Equations (9.3 - 9.8) to find this path. We know the shape of the involute part of the tooth prof ile, and the shape of the fillet curve is given by Equations (9.10 - 9.18). To complete the description of the tooth shape, it is only necessary to find the position of point Au' where the fillet curve intersects the involute",
            " The profile is not altered between the highest and the 220 Geometry of Non-Involute Gears lowest points of single-tooth contact. This procedure is called tip and root relief, or profile modification. The extra material is removed from the tooth face of each gear by means of a rack cutter or a hob whose teeth are not straight-sided along their entire profile. The purpose of this section of the chapter is to show how the tooth profile of the gear is calculated, when the cutter tooth profile is modified in this way. The tooth profile of the rack cutter is shown in Figure 9.B. Near the root of the tooth, the tooth thickness is increased, compared to that of a conventional cutter, so that the gear will be cut with tip relief. The straight section of the tooth profile ends at point Aqr' a distance q from the Yr axis, and beyond this point the profile is formed by a circular arc of radius rq \u2022 The values of q and rq are chosen by the tool designer, but there are some recommended limits on the values that should be used. For example, in the basic rack recommended by the ISO for general and heavy engineering, the minimum value of q is 0",
            " Since we have now expressed Yr as a function of xr for all points on the cutter tooth profile below Ahr , we can use Equations (9.3 - 9.8) to calculate the corresponding section of the gear tooth profile. We could, of course, also express Yr as a function of xr for the tip section of the cutter tooth, but the method described earlier is generally more convenient. Fillet Shape Cut by a Pinion Cutter To find the fillet shape of a gear cut by a pinion cutter, we use a procedure which is essentially the same as the method described earlier, for the case when the gear was cut by a rack cutter. Figure 9.9 shows the pinion cutter, in position to cut a point on the tooth fillet of the gear. The circular section of the cutter tooth profile starts at point Ahc ' and ends at ATc \u2022 The radius of the section is r cT ' and its center A~ has polar coordinates (R~,8~) given by Equations (5.32 and 5.39). We consider the posi tion of the cutter when the line C A' c c makes an angle a with the line of centers. The coordinates 222 Geometry of Non-Involute Gears (E' ,1/') of point A~ are then given by the following equations, ~ , RC - R' cos a pc C (9",
            "34) The last step required before we can calculate the shape of the gear tooth fillet is to determine the initial and final values of a, corresponding to the upper and lower ends of the fillet. The upper end is cut by point Ahc ' the end of the involute section of the cutter tooth profile. When Ahc is the cutting point, the cutting pressure angle is equal to ~c, the same value as the cutting pressure angle when the involute part of the gear tooth profile is being cut. The corresponding position of A' is shown in Figure 9.10, and the angle E C A' c c c c c is then equal to (~ +a). We can therefore express a in terms of R~ and the base circle radius Rbc ' a R arccos (R~c) _ ~c c (9.35) 224 Geometry of Non-Involute Gears The other end of the fillet, where it meets the root circle, is cut by point ATc on the cutter. ATc will be the cutting point when the line from P to A~ passes through ATc \u2022 Since ATc ' A~ and Cc are collinear, ATc will be the cutting point when the line through the three points coincides with the line of centers",
            "120869 radians = - 6.925\u00b0 R = 66.000, 9R = 6.925\u00b0 (9.13) (9.14) (9.15) (9.16) (9.17,9.18) It should be noted that this point is not on the center-line of the tooth space, where the value of 9R is 7.5\u00b0. The tooth profile contains a very small circular section, coinciding with the root circle, which is generated by the flat section at the tip of the hob tooth. Example 9.2 A hob with D.P. 2.5 and pressure angle 20\u00b0 is designed to cut gears with tip relief. The tooth profile of the hob is shaped like Figure 9.8, with the values of q and r being 0.16 . q and 4.8 inches. Determine the reduction in the tip tooth thickness of a 40-tooth gear, compared with a gear cut by a conventional hob, if the gear has zero profile shift and an addendum of 0.4 inches. m = 0.4000 inches Rsg 8.0000 RTg = 8.4000 The value of xr on the hob which generates the tip of the tooth on the gear must be found by trial and error. We will use the correct value immediately, and proceed with the remaining calculations. xr 0.3560 tJ>A r = 22",
            " We then solve Equation (10.8) for Pg ' obtaining the following expression, (p +s)2 c (10.10) In order to calculate the radius of curvature Pg at a point on the gear tooth profile, we use the methods described in Chapter 9 to find the coordinates (~,~) of the cutting point, corresponding to any specified point on the cutter tooth. The radius of curvature of the cutter tooth profile at this point gives the value of Pc to be used in Equation (10.10), and expressions for If> and s can be read from Figure 9.9, which shows the meshing diagram during the cutting process, tan If> s \u00a3. ~ -~ sin If> (10.11) (10.12) These values for P, If> and s are substituted into c Equation (10.10), and we obtain the radius of curvature Pg at the corresponding point on the gear tooth profile. We first use this method to find the radius of curvature at points on a gear tooth fillet, for the case when the gear is cut by a rack cutter. The cutting pitch circle radius of the rack cutter is infinite, and the cutting pitch circle of 236 Curvature of Tooth Profiles the gear coincides with its standard pitch circle, so the length RO defined by Equation (10"
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        "caption": "Fig. 10. Construction of a gas sensor of the SnO, thick-film type",
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            "The essential principle of a chemo- or biosensor is described in terms of three basic components (Fig. 1). The most important component is the receptor (the recognition system), where in general an energetic interaction specific to the substance in question (the analyte) enables it to be recognized. The development of new recognition principles, or the improvement of known processes for this purpose, is a task for the chemist or physical chemist. Campared with this challenge the next stage is less difficult; the function of this second component of any chemo- or biosensor is to \"relay\" the substance-specific signal, in other words to transform an energy quantity into an electrical signal proportional to it. Karl Cammann, born in i939 in Diisseldorf, studied Chemistry at the Technical University of Munich after obtaining a degree in chemical engineering and working in industry (Beckman Instruments) for several years. His scientific advisor for the Diplom thesis was H. Gerischer; his Ph.D. advisor was G. Ertl (University of Munich). After postdoctoral positions with G. A. Rechnitz (State University of New York at Buffalo) and S. Mazur (University of Chicago) he accepted an assistant professorship for Analytical Chemistry at the University of Ulm. In 1986 he became an Associate Professor of Analytical Chemistry at the Technical University of Munich and shortly thereafter (i987) Full Professor of Analytical Chemistry at the Westfiilische Wilhelms University of Miinster (chair of Prof. E: Umland). His research interests lie in the field of selective chemical detectors and monitors. In 1987 he received two awards for the development of a new plasma-emission-spectroscopic GC-detector (OcP van der Grinten Pollution Control Award: Technology Transfer Award of the German Ministry for Education and Science). Angew. Chem. Inr. Ed. Engl. 30 (1991) 516-539 517 Receptor Transducer (recognition sys tem) e.g. semiconductor surface. ion-selective membrane. biomolecule. reagent layer Electronics Output e.g. e.g. change in electrode. potential,current, omplifier, photodiode -light guide/ l ight in,ensity, A-D converteretc. n pen recorder, data-processing system This task is usually performed by one of a wide choice of familiar physical transducers. Often a third component, consisting of a further electronic unit (a preamplifier, impedance converter, multiplexer, analogue-to-digital converter, etc.) is placed directly after the transducer, to suppress as far as possible external influences caused by interfering electric or magnetic fields, or to feed the separate signals from several recognition systems simultaneously to the data processing unit through a single electrical connection. Chemo- and biosensors can be classified according to the type of sensor element used for molecular recognition, or according to the type of transducer. If the emphasis is on analytical selectivity, the most important component is the recognition system. If on the other hand the limit of detectability or the signal-to-noise ratio is crucial, the critical component may be the physical or electronic transducer (see Table 2). All chemo- and biosensors can be used directly for analyzing gases and liquids (the latter also includes suspensions or pastes) for specific ions or molecules, in concentrations varying from the ppb range to the percent range. As the sample preparation required for chemo- or biosensors of adequate selectivity is minimal, and the sensors are available at low cost, high rates of growth are forecast by all the market studies that have been carried out. For sensors that are less selective, it is still possible in many cases to design a comparatively inexpensive measuring instrument, by incorporating automatic sample preparation based on a chemical reaction which is selective, or on separation techniques. Flow injection analysis is especially valuable in this respect.[241 2. Chemosensors 2.1. Electrochemical Sensors 2.1.1. Ion-Selective Electrodes Till a few years ago ion-selective electrodes (including the glass pH electrode) were the most important class of chemosensors in economic terms, since at that time the \u201clambdaprobe\u201d for controlling three-way catalytic converters for automobiles was not yet produced in today\u2019s numbers because of the absence of legal requirements. In ion-selective potentiometry the data are processed using an extension of the Nernst equation derived empirically by N i ~ o l s k y . ~ ~ ~ ] This extended equation (a) relates the activity of the ion species to be determined and the measured voltage when an ISE halfcell is connected to a common reference electrode, taking into account the effects of all interfering components. RT U = U o +7 In [ a M + x K M - -MF I Li = potential of the cell R = universal gas constant T = absolute temperature F = Faraday constant Uo = standard potential of the cell aM = activity of the ion being measured zM = charge of the ion being measured (with appropriate sign) KM-, = selectivity coefficient (measured ion vs. interfering ion) a, = activity of the interfering ion z , = charge of the interfering ion (with appropriate sign) The selectivity is described by the selectivity coefficient K M - , , which unfortunately is not a constant, since it depends on the method used for the determination and on the concentrations of all the interfering species and the ion to be measured. For good ISEs it is of the order of which means that a 104-fold excess of the interfering ion would change the reading by a factor of 2 (i.e. an error of 100%). A new theoretical model of the mechanism for the selectivity in the potential generated at the phase boundary between the ionselective membrane and the measured medium has been developed in the last few years.[26-301 This is based on the studies of Koryta13 l1 and others on electrochemical phenomena at the interface between two immiscible electrolytes, and also on results from studies on corrosion involving competing electrode reactions. The basic principle of ion-selective potentiometry is the observation of an ion-selective change in the potential at the phase boundary. This in turn depends on the ion-selective change (or shift) of charge (or charge distribution) at this boundary, i.e., a significant transfer between the phases occurs only for the ion species in question. This requires that 518 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 certain energetic and geometrical variables be optimally matched. If an uncharged ion-selective membrane electrode which satisfies the electrical neutrality condition is immersed in an electrolyte solution, a transfer of charge carriers occurs between the phases. The direction of this (membrane + solution or the reverse) is determined by the gradient of the chemical potential. When only one species of ion can selectively cross the boundary (this selectivity results, for example, from specific complex formation in liquid or PVC membranes, or from the dimensions of lattice sites in polycrystalline or semicrystalline materials), this selective transfer of charge carriers leads to a redistribution and an accumulation of charge at the phase boundary. This generates an electric field, thus counteracting the ion transfer which was at first energetically favored, so that eventually, under the combined influence of the electrostatic repulsion between similarly charged particles and the attractive forces due to the oppositely charged carriers left behind, the transfer of charge carriers ceases and the reverse reaction is favored. In the equilibrium state the microscopic ion currents passing in both directions through the phase boundary are equal, and the ion-selective potential difference that is thereby established is constant and can be measured. Externally the condition is one of zero current (a requirement for potentiometric measurement). In terms of electrochemical kinetics the transport of charge carriers (measured ions) across the phase boundary between the electrode or ion-selective membrane and the solution corresponds to a directed electric current i'or i(depending on whether the direction is from membrane to solution or the reverse). In the equilibrium state i'= i= i,. The current density j , (= &/A, A = area) is called the exchange current density (see Fig. 2). The two opposing current densities :and Jmaintain the ion-selective charge distribution at the phase boundary at a constant value. Furthermore, these microscopic ion-currents actually make it possible to measure the charge distribution at this interface, since in practice one cannot avoid drawing a current of lo-'' to A in i [ pAlcmZ] Fig. 2. Schematic representation of the forward and reverse currents iand i passing through the phase boundary; the selectivity is given by the ratio of the (equilibrium) charges qH and q, for the measured and interfering ions respectively (see text). the measuring circuit, depending on the amplifier used, which corresponds to a net flow of lo9 to lo5 elementary charges per second. The ion-selective electrical potential generated at the phase boundary of such an ion sensor by selective charge separation is, of course, dependent on the concentration of the ionic species which can cross the boundary. The relationship between ion concentration and interfacial potential was derived theoretically by Nernst as long ago as 1889, in the brilliant work leading to the equation named after him. From the ion-exchange current density j,, which can be determined experimentally, the recent theory predicts the selectivity of a potentiometric sensor. The potential in each case is determined by the ionic species that has the greatest exchange current density. Other reactions may take place at the phase boundary in parallel with the process described (because real solutions usually contain interfering ions in addition to those being measured). The thermodynamic equilibrium potentials for the individual electrode reactions (in this case, the parallel processes in which the measured and interfering ions cross the phase boundary between two ionic conductors), as in the case of corroding metal electrodes, may not be fully achieved. This results in deviations from the theoretical Nernst behavior. In order to achieve a high ion-exchange current density and thereby obtain the desired selectivity, appropriate changes can be made in the thermodynamic and kinetic variables. For example, introducing into the membrane an ionophore for a particular ion species causes an increase in the exchange current density, and therefore in the selectivity for that ion. The selectivity obtained in this way is probably due to a long-range ion-dipole interaction between this particular ion species in the solution and the ionophore in the membrane surface. It is conceivable that, specifically for the potential-determining ion species, an overlap of the energy barriers involved (desolvation and decomplexation activation-energy profiles) occurs, which results in the lowering of the effective activation energy for ion transfer over the entire phase boundary. This activation energy can also be expressed in electrochemical terms as an ion-transfer resistance. This in turn is inversely proportional to the exchange current density, and can be obtained, for instance, from impedance spectra.r32* 331 The selectivity of all types of ion-selective membranes, the rapid establishment of the potential, even for thick membranes, and the abnormally large graph slopes in the U vs. log a diagram that are occasionally found (steeper than predicted by the Nernst factor preceding the logarithm of the activity of the measured ion, see Eq. (a)), can all be satisfactorily explained by this novel theoretical approach which also considers kinetic parameters. Numerous fundamental studies have been carried out in our research group since 1975 to determine the conditions that must be fulfilled for a particular ion to be potential-determining (and therefore able to be measured selectively). For every type of electrode the critical factor was the ratio of the exchange current density for the measured ion to that for the relevant interfering ion. In every case this ratio was equal to the potentiometrically measured selectivity coeficient in the extended form of the Nernst equation [Eq. (a)]. A comparison of good ion-selective electrodes reveals several common features. Firstly, they have a rather high poten- Angew. Chem. Ini. Ed. Engl. 30 (1991) 516-539 519 tial-determining exchange current density for the measured ion at the phase boundary between the ion-selective membrane and the solution. Secondly, for solid membranes, there is a preferential ionic conductivity in regions near the surface (e.g., Ag,S is a good conductor for Ag@ ions, and LaF, doped with EuZ0 is a good conductor for F' ions). In PVC membranes with selective ionic charge carriers the preferred method is to use only iondipole interactions, as is evident from a glance at the list of so-called electroactive compounds that are available.[341 Apparently the course of the activation energy threshold for the transfer of ions from the membrane phase to the solution, together with the course of activation energy for the desolvation process, determines the intersection point (i.e., the effective energy of activation for the phase transition of the relevant ion). The existence of a purely kinetic effect in favor of the ion being measured is a necessary, but not a sufficient, condition for a selective Nernst sensor which performs well and above all is stable over long periods. In addition there must be a certain degree of nonpolarizability. This quantity, as electrochemists use it, is, in simple terms, a measure of the ability of an electrochemical half-cell to maintain a constant potential regardless of the instantaneous current density at the interface. Good ion-selective electrodes, like good reference electrodes, have a relatively steep characteristic curve in the current vs. voltage diagram (C-V curve) for the ion being measured. Viewed from this standpoint, the interfering ions have characteristic C-V curves that are less steep than that for the ion being measured. If these ions are present in a solution together with the measured ions, according to our present state of knowledge a mixed potential is established, as is the case for corroding metal electrodes. This is determined predominantly by the equilibrium potential for that electrode reaction (transfer of ions between phases) which has the steepest C-V characteristic. To obtain a favorable C-V characteristic over as large a range of overpotential as possible, it is also necessary to take concentration polarization effects into account. Here higher concentrations of the measured ions in the membrane phase turn out to be beneficial; their diffusion from there into the solution, which has an unfavorable effect on the limits of detection, is hindered by complexation and by the charges of appropriately chosen counterions. This also has the advantage of increasing the buffer capacity for the chemical potential of the measured ions in the membrane phase. A detailed treatment of these aspects has been Ion-selective electrodes can be used as electrochemical half-cells in combination with suitable constant-potential reference electrodes for the quantitative determination of a wide range of substances (see Table 1). They can be classified according to the type of membrane, viz., glass, solid, liquid, or PVC membrane electrodes.[36q 371 Glass and solid membrane electrodes are robust and have a typical lifetime of several years, much longer than liquid or PVC membrane electrodes, which only remain effective for about six months, depending on the application, unless one is prepared to accept large sacrifices in sensitivity and selectivity. However, for the latter types of electrodes some manufacturers have introduced a modular design which allows the easy and rapid renewal of sensitive electrode elements. The most important types of ionophores required to make one's own selective PVC membranes are available commercially,[381 and are supplied complete with instructions; these were developed mainly by Simon's research group in Zurich. 2.1.2 Ion-Selective Field Effect Transistors (ISFETs) It was believed for a long time that in ion-selective field effect transistors, first described by Bergveldt3'* 401 in 1970, we at last had a new generation of sensors which met all the requirements of miniaturizability, compatibility with microelectronics, and the capability for being mass-produced, with attendant cost savings. The now familiar production techniques of microelectronics seemed to offer prospects for developing chemosensors in the form of disposable mass-produced articles. Since then the initial euphoria has given way to a more realistic assessment, since these sensors still pose difficulties with regard to long-term stability and integration with miniaturized reference electrodes. Nevertheless, it is of interest to examine this class of sensors in a little more detail in the following discussion, since they bring together the disciplines of chemistry, electronics, and thin film technology, and they provide the basis for biochips. An ISFET can be generally regarded as a very miniaturized version of an ion-selective half-cell with an in-built impedance converter. It can be used to determine the activity of not only individual ion species, for which ion-selective macro-electrodes are also available, but also-in the form of an enzyme-coated ISFET (b iochip ta wide variety of substrates. The transistors that are used can in most cases be made as very small devices, allowing the accommodation of several sensitive surfaces for detecting different ions or substrates on a single chip with an area of only a few mm2. The entire electronic control circuit, including temperature compensation, can also be fitted on the same chip. The basic building block of all ISFETs is a field effect transistor (FET), in which the metallic gate of a conventional transistor is replaced by an insulating layer, above which is an ion-selective layer. The value at any instant of the gating potential, which controls the current between the source and the drain, is determined by the activity of the ion species being measured, through the presence of the ion-selective surface film. Figure 3 shows the basic construction of an ISFET in a form which has certain advantages. Often, however, instead of measuring the variation of the source-todrain current as a function of the activity of the measured ion 520 Angew. Chem. Int. Ed. EngI. 30 (1991) 516-539 species, one measures the control voltage that must be applied via a reference electrode to hold this current at a constant value; this makes it possible to maintain an optimal working point, chosen to reduce temperature effects. In an ISFET the ion-selective PVC membrane, which is applied to the gate surface mainly by spin-coating, forms the sensor element, which recognizes specific substances. By using known electroactive compounds, all types of ion-selective PVC membrane electrodes can also be incorporated into ISFETs. However, problems with the adhesion of the plastic membrane to the gate surface result in contact difficulties, since the membrane which gives the selectivity becomes detached, usually after a few weeks. In a pH-ISFET[41-44] protons produce a field, whose intensity depends on the H@ concentration, at a thin film of SiO,, Si,N,, A1,0, or Ta,O, . A serious disadvantage of these materials is that in many cases they still have some sensitivity to light and redox systems. Also, the diffusion of impurities into the lower layers of the semiconductor, which are known to be sensitive to this, usually results in a slow drift of the measuring signal, of the order of a few mV per day. The disadvantages mentioned, together with the fundamental problem of leakage-path formation in the insulation of the remaining transistor surfaces, which again causes drift in the readings before the device finally ceases to function, has so far prevented ISFETs from achieving a larger commercial success. However, recent developments in the area of electrolytic glazing offer some hope of improvements.[451 In the development of ISFETs work is already in progress on multisensor arrays146. 471 in which several different ion-selective sensor elements controlling separate gates are integrated on a single chip. Here, however, one is approaching the limits of miniaturization technology. The spin-coating technique cannot lay down closely spaced regions of different selectivity less than 1 mm2 in area. Experiments in which a common plasticized PVC membrane is laid down to cover all the gates before local regions above individual gate surfaces are doped with different electroactive compounds have also encountered problems, because diffusion of ionic carriers within the membrane smears out the ion selectivities. It is also necessary to integrate into the ISFET a miniaturized reference electrode with long-term stability, in order to exploit fully the advantages of the device as a miniaturized chemosensor. If the dimensions of the salt-bridge elements are too small, resulting in only short-term resistance of the integrated reference electrode to invasion by potentialfalsifying substances, it will only be possible to make disposable sensors. Here, however, it is important to investigate the possibility of using a conventional thick-film design for the electrodes, which might also be cheaper. In this connection an interesting alternative to ISFETs are film electrodes produced using planar technology.[481 These too offer the advantages of miniaturized sensors which can be economically mass-produced. One commercially available 501 is based on the principle of zero-point potentiometry. In this one-shot disposable sensor, the measuring and reference systems are identical, and as the pair are made under identical conditions from the same materials the potential difference with the relevant membranes in contact with the same solution is zero. If one now deposits on one of the sensor surfaces a reference solution of known concentra- tion, and on the other the solution to be tested (see Fig. 4), according to the Nernst equation the observed potential difference gives a direct measure of the concentration difference between the two solutions for the relevant measured ion species (concentration meter design). The errors that are pos sible in difference methods of this sort (where no transport of samples is involved) are very small, as the problems with conventional reference electrodes (variations in potential due to diffusion), ageing effects, and electrode poisoning effects are avoided. However, continuous measurements are not possible with this device. 2.1.3. Ion-Conducting Solid Electrolyte Sensors The lambda-probe, which has become familiar because of the three-way catalytic converter, is currently the most widely used of all electrochemical sensors. It enables the measurement of the residual oxygen content in the exhaust from internal combustion engines, making use of the selective ionic conductivity of the 02@ ion in yttrium-doped ZrO, at temperatures above 400\u00b0C. A potentiometer device for measuring 0, concentrations can be designed as a concentration cell, which allows the gaseous oxygen to be in equilibrium with the lattice oxygen in the solid electrolyte [reaction (l)]. If there is a higher oxygen concentration on one side of the ZrO, membrane than on the other (i.e. on one side an oxygen partial pressure p r f , for example, of the outside atmosphere or of a reference gas, and on the other side a partial pressure pgImPle, for example, of the exhaust gas or other medium being analyzed), according to the Nernst equation a potential difference proportional to the logarithm of the ratio of the two oxygen pressures is set up [Eq. (b)]. RT pgf U=-ln4 F pgTPle The selectivity of this sensor results from the fact that in ZrO, there is a selective conductivity for OZe ions (similar to that for Fe ions in single crystals of LaF,), which also determines the surface reaction. Figure 5 shows schematically the construction of a lambda-probe working on the potentio- Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 521 metric prin~iple.[~\u2019~ With regard to the other analytical properties of the device, the same arguments as for ion-selective membrane electrodes apply here. The range of concentrations that can be measured is enormous ( > 10 decades), provided that the current in the measuring circuit is considerably less than the exchange current for the redox reaction (a) at the platinum contact electrodes. The precision in this case also is limited to 0.1 mV, and at constant temperature this gives a relative precision of about 2 YO in the measured concentration. This accuracy is sufficient for the typical use in a three-way catalyst for automobiles; due to the logarithmic dependence of the signal according to the Nernst equation an immense potential difference results. LaF, , which has an appreciable ionic conductivity even at room temperature, has been found to be a suitable solid electrolyte for the determination of 0, at room temperature.[\u201d] In this material a change in potential is produced by OHe and HOF ions formed as intermediates, and this allows an indirect measurement of the 0, High temperature solid electrolytes with Oze conductivity can also be used at a constant oxygen concentration for detecting oxidizable substances, by making use of a second reaction that takes place at the electrodes. An example where this occurs is in the catalytic oxidation of NH, and the determination of chromium in molten steel,[5s1 by reaction (2) . 3OZe(SIC) + 2Cr(metal) --t Cr,03(2nd phase) + be-(metal) (SIC = solid ionic conductor) (2) Here the OZe ions moving in the solid electrolyte oxidize the chromium with the release of electrons, which can be measured as a change in potential. It has also been shown that silicon can be determined by a similar method when ZrSiO, is the solid ionic A very compact sensor suitable for applications at these high temperatures (above 1600\u00b0C) has recently been developed; this can be used for up to 10 h in molten Special sensors have also been developed for determining oxygen in liquid sodium, which is used in fast breeder reactor^.^^^*^^^ In addition to withstanding high temperatures and mechanical loading, these sensors must also be resistant to radiation and corrosion by sodium. Solid electrolyte sensors that have been developed for determining substances other than oxygen include especially those for SO,/SO, and C0,.[601 These consist for example, of Li,SO, + Ag,S0,[57~6*-641 and have a working temperature of about 400 \u201cC. The sensitivity of such sensors is in the range of 3 to lo4 ppm of SO,, and they are currently being tested for use in monitoring exhaust gases. The measurement of CI, is also possible with surface-modified solid electrolytes, e.g. the ionic conductor LiAICI, with its surface covered by a thin film of LiCl or AlCl,. The cell voltage is determined by the partial pressure of chlorine, and obeys the Nernst equation.t65* 2.1.4. Amperometric Sensors To avoid the requirements for temperature constancy in the lambda-probe, and obtain a linear instead of a logarithmic relationship between signal and concentration with higher accuracy, which is essential in engines working with I > 1 .O, the sensor can alternatively be designed as a limiting current probe.t67. 681 This configuration, which can also be operated at temperatures below 400\u00b0C, differs from the potentiometric form of a lambda-probe in that a current flows through the 0, concentration cell as a result of an externally applied voltage (\u201cpumping voltage\u201d), thereby transporting oxygen from one side of the ZrO, membrane to the other (an \u201coxygen pump\u201d). In front of the cathode there is a diffusion barrier (e.g. a porous ceramic layer), which the oxygen must traverse before being reduced and transported through the ZrO, to the anode (Fig. 6). If the applied voltage is chosen so that each oxygen molecule that arrives is immediately reduced at the cathode, a voltage-independent limiting current region is obtained, as in polarography. The current then flowing is directly proportional to the 0, concentration to be measured, and the temperature coefficient is no longer given by the Nernst factor, but is determined by the properties of the diffusion barrier.t691 The amperometric measuring principle has largely been used to advantage in industrial chemosensors for gases. The classic example of this is the Clark oxygen The oxygen whose concentration is to be measured diffuses through a gas-permeable membrane 10 to 50pm thick, which is made of polytetrafluoroethylene (Teflon) or a fluorinated ethylene-propylene copolymer (FEP) with a very high permeability to oxygen. Behind this membrane is an electrolyte solution containing chloride ions, in which are immersed a platinum or gold cathode as the working electrode 522 Angew. Chem. In!. Ed. Engl. 30 (199!) 516-539 and an anode of Ag/AgCl as the constant potential counterelectrode (cf. Fig. 14). The reduction of the oxygen takes place at a working electrode potential of approximately - 0.8 V relative to the Ag/AgCl electrode. The rate-limiting step is the diffusion of the oxygen through the gas-permeable membrane, and the rate of this depends on the gradient of the 0, partial pressure across the membrane. The current is therefore determined primarily by the 0, partial pressure. As the membrane is impermeable to liquids and electrolytes, the sensor can also be used to determine dissolved oxygen in liquids; in this case the dependence on the partial pressure must be noted. The sensor gives the same reading for air and for a liquid that is saturated with air! To obtain a reading which indicates the dissolved oxygen in mgL-' it is necessary to calibrate the sensor. A disadvantage of most 0, sensors based on this principle is that oxygen is consumed. When they are used in stationary liquids there may not be a sufficient flow of oxygen to the electrode (resulting in an oxygen-deficient layer in the liquid whose growth follows a I/i law), which gives readings that are too low. The solution being measured must therefore be stirred, but this leads to some extent to a dependence of the observed signal on the convection flow. The effects of this disadvantage (especially in biomedical applications) can be minimized by reducing the area of the working electrode, which in turn causes difficulties because the current then becomes very small. Efforts are now in progress to overcome this problem by using an array of ultramicroelectrodes (Fig. 7). The use individual electrodes as small as 1 pm in diameter, has led to such low reaction rates that the Brownian motion of the molecules together with the radial diffusion sphere ensures a sufficient oxygen supply. However, sensor technologies of this sort can only be put into effect with the most modern microelectronics manufacturing processes. Amperometric oxygen electrodes are widely used as transducers for many types of biosensors (see Table 7). Many gas sensors for SO,, CO and NO function on a similar principle. The measurement is based on the electro- chemical oxidation of the relevant gas in the space separated off by the gas-permeable membrane. The selectivity of amperometric sensors can be tailored to suit particular needs. Up to now the main technological use for amperometric chemosensors has been for measurements on gases, even though amperometry is also suitable for analyzing liquids, because of their limited selectivity. In the most commonly used aqueous electrolytic media, the usable voltage range extends over about 2 V. All substances that can be altered electrochemically, i.e. those that can be oxidized or reduced, which number many tens of thousands, are converted at voltages within this range. In the ideal case one can expect to distinguish ten substances at best in a voltammetric diagram by virtue of their different half-wave potential^.^'^] The separation capacity achieved by the proper choice of a working electrode potential within the limiting current region for the substance to be determined is in general inadequate for the analysis of unknown liquids. However, if a gas-permeable membrane is interposed, the interfering substances are limited to gases that can permeate the membrane equally well, and also undergo electrochemical reactions under these conditions. In the case of the Clark 0, sensor, for example, these are chlorine and some haloforms (CHX,). These interferences can be even further reduced by a careful choice of the membrane material and the electrolyte. Occasionally a difference in electrochemical reversibility coupled with pulse techniques is also exploited to increase selectivity. The limit of detectability for amperometric gas sensors is determined by the noise level of the background current. Nevertheless, chemosensors for environmental applications (measurement of NO,, SO, etc.) can be employed in the low ppm region without special signal-processing techniques. 2.1.5. Galvanic Sensors Amperometric measurements are also possible without an external current source, if a galvanic circuit is formed. The Angew. Chem. Int. Ed. Engl. 30 (199f) 516-539 523 best known example is the so-called internal electrolysis, in which Cu2@ ions are reductively deposited on a platinum wire mesh when this is connected to a zinc rod immersed in a zinc sulfate solution which is separated by a diaphragm from the solution containing the copper ions. Here again the driving force for the current which arises when zinc dissolves and copper ions are deposited on the platinum surface is the difference between the chemical potentials, or the energy difference between the two redox reactions in the electrochemical series. If in this example one connects a galvanometer externally between the zinc electrode and the platinum mesh, the current vs. time diagram obtained during the electrolysis has an exponential shape. The quantitative deposition of the Cu2@ ions on the platinum mesh is complete when the current has fallen to about 0.1 YO of its initial value. In this case, instead of using the gravimetric method, the amount of copper deposited can be calculated by Faraday\u2019s law from the total charge that has flowed (the integral of the current vs. time curve) as long as interference from side-reactions is absent. This coulometric procedure is one of the most precise absolute determination methods available, and requires no calibration. Coulometry is still an elegant method with exciting new possibilities for the development of intelligent sensors, and regrettably is too little used. Over 25 years ago a coulometric measurement cell for SO, was proposed.[\u201d] Subsequent advances in miniature electrochemical cells based on thin-film and thick-film technologies allow the easy application of such a cell as a chemosensor (Fig. 8). If the reaction is quantitative, a current of the order of 1 PA, which is easily measurable, corresponds to an analyte reaction rate of only lo-\u2019\u2019 mols-\u2019 ! Here the selectivity is achieved by a preceding chemical reaction or membrane separation stage, either of which can nowadays easily be realized by means of a suitable layered structure. An \u201canalytical fuel cell\u201d of this kind has recently also appeared on the market in the form of an alcohol meter (for analysis of breath samples). As well as using the catalytic activity of noble metal electrodes, it is also possible, of course, to use enzymes to give increased selectivity. The H,O,, which is then often produced in quantities proportional to the amount of analyte, can also be easily determined coulometrically. A galvanic measuring cell for the determination of oxygen in solutions has been well-known since the rnid-1960~.[\u2019~1 In contrast to the Clark sensor, the Mackereth oxygen sensor uses lead instead of silver as the anode material, and silver instead of platinum as the cathode material. This has the important advantage that a calibration in a blank solution (such as a saturated sulfide solution) is no longer necessary, since the electrodes produce no current in the absence of oxygen. For the internal electrolyte either sodium hydroxide or potassium hydrogen carbonate can be used. 2.2. Semiconductor Gas Sensors Sensors based on semiconductors are often used in gas alarm devices. The underlying principle here depends on a transfer of electrons between a semiconductor surface and adsorbed gas molecules. This charge transfer results in an increase or decrease in the number of free charge carriers at the semiconductor surface, causing a change in conductivity which can be measured and is proportional to the number of reacting gas molecules present. Oxidizable gases such as hydrogen, hydrogen sulfide, carbon monoxide, and alkanes of low molecular mass reduce the surface conductivity of certain n-type semiconductors (SnO,, ZnO etc.), which are used at temperatures between 100 and 600\u00b0C. Reducible gases such as chlorine, oxygen, or ozone have an analogous effect on p-type semiconductors (NiO, CuO etc.). The mechanism of the electron transfer is still under intensive study and one possible model shown in Figure 9. When a gas molecule of the analyte approaches the surface of the semiconductor it first undergoes a weak physisorption. In the following step it can be either desorbed or chemisorbed with the transfer of an electron. The latter process causes a distortion of the valence 524 Angew. Chem. I n f . Ed. Engl. 30 (1991) 516-539 and conduction bands, and alters the electronic work function. Depending on the composition and the structure of the surface and on the interactions between the molecules and the surface, certain types of molecules can act preferentially. The selectivity of simple sensors of this kind, which can be easily and cheaply produced with thick film techniques (see Fig. lo), can be altered within certain limits using existing knowledge of heterogeneous catalysis. To obtain improved sensitivities and selectivities for particular applications, however, mechanistic studies of the kind used in heterogeneous catalysis research, requiring sophisticated and expensive equipment, are necessary, rather than the time-consuming trial-and-error methods of nonspecialists. Often the semiconductor surface is modified by introducing metals such as palladium, silver, or platinum, whose purpose is to weaken the 0, double bond. The selectivity can be further increased to a certain extent by choosing the best operating temperature (Fig. 11) . Nevertheless, the selectivities of these types of b) a) aK[%] 6ol A K [%] 6ol 4017p 20 , . ::p+ '\\ 200 400 600 800 T[\"C] 200 400 600 800 T[\"C] Fig. 11. Effects of temperature and of the presence of platinum on the selectivity of an SnO, gas sensor. a) Pure SnO, sensor, b) SnO, sensor with 1 % platinum. sensors based on semiconductors are often insufficient.[731 The surface composition, density of charge carriers, Fermi energy level, number of reactive centers at the surface, and even the extent of distortion of the bands, can be affected by the presence of other species (interfering molecules such as water, catalyst poisons etc.). This can cause changes in selectivity. These effects must be taken into account during calibration. A change in the selectivity, sensitivity (signal per unit concentration in the analyte) or zero point of the calibration line between carrying out the calibration and the analysis is inadmissable. As it is a simple matter to modify the sensitivity, experiments are now in progress to use a sensor array in which each miniaturized individual sensor has a different sensitivity profile. Samples which contain interfering substances cause each individual sensor to give a different signal. By carrying out calibration measurements with different concentrations of the various interfering components, it should be possible, by a pattern recognition analysis, to use a special algorithm for the calculation of the true sample content. A simultaneous analysis on a mixture using such a sensor array should in principle enable the determination of every substance which has an effect on the signal, if more sensors than components to be analyzed are used. This has in fact been achieved for simple and well-defined Nevertheless, the analytical chemist with experience of industrial practice will harbour doubts about the feasibility of this method for real samples whose composition is generally unknown and continually changing. Taking the simplest form of an analytical function (c) is it possible to keep the parameters a and e constant between the calibration and the measurement? How can the algorithm take into account situations where interfering substances poison the sensors to differentor cause different drift phenomena? What are the consequences of \"matrix effects\" which cause the sensitivity e to vary from sample to sample? Table 3. Materials for selective chemosensor elements. Sensor Examples Species Refs. materials detected ~~ ~ glasses Li,O-BaO-SO, H@ (5.61 synthetic PVC, silicone and PMMA mem- e.g. K\", Na@, [14-16, suitable carriers NHF, NO? PTFE membranes for gas sensors NH,, CO,, SO, [37] solid LaF, F e (371 Na,O-AI,O,-SO, Na@ [71 polymers branes[a] with plasticizers and Gaze, Mg'\", 34.36-381 0, [53,541 ZrO, (lambda probe) 0, [5l. 521 Cr (551 TiO,, Nb,O, 0, Nasicon [b] Na [651 Na@ [661 ZrSiO, Si ~561 Na,SO, + Ag,SO, SO,/SO, [57,60-641 semi-con- Si, GaAs, Sic, SnO,, ZnO, CuO Oxidizing or [73.109- 1 1 11 ductors reducing gases metal oxide AI,O,, Si,N,, SO,, TiO, as HO, H,, 0, [73,109-1111 or nitride insulators, electronic conductors films and electroactive materials [a] Polylmethylmethacrylate. [b] Na, ..Zr,Si,P,.,O,,. 2.3. Fiber-optic Sensors (Optodes) Chemical information can also be translated into measurable signals through the interaction of electromagnetic radiation with the analyte. Spectroscopic analysis, spectrophoto- Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 525 metry, fluorimetry, and luminescence measurements are well-established and proven techniques. Their adaptation for performing in situ analyses with miniaturized probes that can be employed in the same way as chemosensors has come about through the application of modern light-guide technology. For use in conjunction with fiber optics a new class of sensors was developed, known as optodes (also as opt r o d e ~ ) . [ ~ ~ - ~ ~ ] These optical sensors make use of changes in fluorescence, absorption, chemiluminescence, light scattering, polarization, Raman scattering, refractive index, or reflection, which at present are still detected by conventional optical or spectroscopic instruments. The light input is fed into the sample by a light-guide. The return path for the fluorescence emission or reflected light from the sample to the detector can be through the same light-guide or through a second branch (in a Y-branched light-guide). Figure 12 shows as an example the layout of a fiber-optic analytical system as commonly used for fluorescence measurements. The AC signal produced by a chopper is amplified frequency- and phase-selectively by a lock-in amplifier. This procedure makes it possible to measure delayed fluorescence as well (by the phase shift). Fluorescence and luminescence measurements give high sensitivity compared with other optical measurement methods and are therefore preferable for trace analysis. , 1 Fig. 12. Fiber-optic system for analysis by fluorescence measurements; the excitation unit (2) contains the light source (xenon or halogen lamp or laser) producing a beam which is passed through a monochromator (3), a chopper (4). and an optical coupler (5) into the light guide (6). The fluorescence radiation passes through a second light guide branch, coupler (7). and monochromator (8) to the detector (9), which consists of a photodiode or photomultiplier. (1) is the base plate. Chemiluminescence measurements have an additional advantage, as they do not require an external light source. However, because chemiluminescence is a comparatively rare phenomenon, the method is mainly limited to systems such as H,O,/luminol. The great advantage of fiber-optic sensors is that the measurements do not require a reference system, apart from comparison of the light intensities in the beam before and after it passes through the sample compartment (i.e. measuring Zo/l), or the use of a dual beam arrangement to compensate for fluctuations in the intensity of the light source. With the electrochemical sensors described earlier a second electrode giving a constant potential is always needed. Optodes can easily be miniaturized, as light-guides of suitably small diameter (e.g. 0.1 mm) are commercially available, although increasing miniaturization makes good coupling of the input radiation more difficult. Optodes can also be used in complex media such as blood. They are less susceptible to disturbance by electromagnetic fields and temperature changes than are potentiometric electrodes and semiconductor sensors. On the other hand, problems can arise from scattered and background light falling on optodes. In many cases these sensors can only be used within a small range of concentrations, like the spectroscopic analytical cuvette techniques on which they are usually based, and their selectivity is similar to that of those techniques. The detection limit also leaves room for future improvements, as it is restricted at present by the thinness of the optical films generally used for the measurements (see Table 4). Despite all this, fiber-optic sensors are expected to emerge from their present status as research devices and find a place in industrial use in future; the flow-through cuvettes will probably be abandoned first. The types most studied are pH-optodes. The technique is based on the immobilization of an indicator dye at the end of the light-guide, which allows pH values to be determined by measuring fluorescence or absorption. Indicators that have been used include 8-hydroxypyrene-I ,3,6-trisulfonate (HPTS) as well as conventional dyes such as eosin or phenyl orange.1791 Such pH-optodes also form the basis for a range of gas sensors. For example, CO, and NH, optodes contain a pH optode immersed in a suitable internal solution behind a gas-permeable membrane, as in the analogous potentiometric sensors. The acidity or basicity of the above gases alters the pH of the internal solution by an amount related to the gas concentration to be measured. Such sensors are of particular interest for in vivo applications (blood, body fluids, etc.), since unlike electrochemical sensors they do not have electrical connections to voltage-carrying components. The fields of application are similar for 0, optodes, which work on the principle of direct fluorescence quenching. The mathematical basis of this type of sensor is given by the Stern-Volmer equation.[\"] The fluorescence of an indicator such as decacyclene or perylene, which is immobilized on the tip of the light-guide, is partially quenched by oxygen. This effect can be used, after calibration, for the determination of Some new developments are based on applying knowledge of the selectivity mechanism of ion-selective electrodes to fiber-optic systems. For example, valinomycin as a selective K@ carrier can be immobilized in a suitable matrix, together with a pH-sensitive indicator in its protonated form, so as to produce a membrane which can be attached to the tip of a light-guide. If this sensor is immersed in a solution containing K@ ions, these ions will preferentially enter the membrane phase, with the formation of a potassium-valinomycin complex. To maintain electrical neutrality H@ ions (as the most readily mobile ion species) move out of the membrane phase, causing a change in the absorption or fluorescence of the pH indicator in the membrane, which can easily be measured.Is l ] In conclusion it should be noted that at present there are only a few manufacturers of optodes, and it will certainly take several more years before such fiber-optic analytical systems become as widely used as electrochemical sensors. 0 2 . 2.4. Mass-Sensitive Transducers Chemosensors based on mass-sensitive transducers have been less thoroughly investigated, and their use has so far been restricted to special applications. The measuring prin- 526 Angew. Chem. Int. Ed. Engl. 30 (1991) S16-S39 ciple depends on the shift Af in the characteristic frequency of a quartz oscillator due to a mass change Am, which occurs when a layer of foreign material is deposited on its surface. The oscillation frequency is usually in the 9 to 14 MHz range, and the selectivity is obtained by coating the surface with an appropriate adsorbent. By using phthalocyanine, for example, planar-conjugated molecules and higher alcohols can be determined; in this case mass changes as small as g can be d e t e ~ t e d . ~ ~ ~ * * ~ ] When working in vacuum the relationship between A f and Am is linear for small values of Am and is given by the Sauerbrey equation [Eq. (d)].[s41 f, = resonance frequency in the unloaded condition m = mass of the quartz crystal in the unloaded condition The suitability of quartz oscillators for gas analysis has been demonstrated beyond doubt. Difficulties arise, however, in the search for selective ab- or adsorbents for particular analytes, and in compensation for the effects of moisture and other interfering deposits. Also it must be noted that the surface adsorption or film absorption are not usually reversible. Transducers of this type are potentially important for biosensors for gas phase use. At present, however, their high cost inhibits the development of practicable oneshot disposable sensors. When quartz oscillator detectors are used directly in liqu i d ~ [ ~ \u2019 * 861 without a drying stage before the mass-change measurement, the damping of the oscillations must also be taken into account [Eq. (e)]. q = viscosity of the liquid p = density of the liquid pQ = shear modulus of the quartz pQ = density of the quartz The latest st~dies,\u2019~\u2019] which are based on an exact coulometric calibration, show that a 0.41m thick layer of the surrounding liquid moves with the quartz crystal surface during its oscillation. This makes exacting demands on the constancy of all the effects that shift the frequency. The layer of liquid that moves with the surface reduces the mass resolution (i.e. the ability to measure very small mass changes). It should also be mentioned here that a similar device is marketed for determining the densities of liquids ; density changes of the order of a few parts per million can be detected. Surface acoustic wave (SAW) detectors are devices in which acoustic waves are produced at the surface of a suitable material, by setting up appropriate resonance conditions between two surfaces. The resonance frequency is typically a few hundred MHz, and according to the Sauerbrey equation (d) this should result in greater sensitivity. However, this cannot be fully exploited, as it is only possible to measure the change in mass within a very thin layer between the two specially shaped electrodes. The selectivity is governed by the same considerations as above. 2.5. Applications of Chemosensors The use of chemosensors in technology has grown enormously during the past decade. R & D in the field of chemosensors is being energetically pursued worldwide, but especially in Japan. The range of uses of conventional chemosensors extends from chemical process control technology through applications in clinical chemistry to municipal services. A field of special importance for chemosensors is environmental protection, where increased public awareness and ever stricter legislation make it increasingly necessary to set up on-line monitoring systems for environmentally significant gases such as NO, SO,, NH,, CO, or C0,.t88-931 The wide variety of chemosensors that have so far been developed means that in many cases the most suitable one for a particular application can be chosen from a number of alternative constructions. As an example Table 4 lists the various methods of measurement available for determining a single substance, in this case oxygen. The largest market for chemosensors at present is the automobile industry, which even in 1987 required over ten million oxygen sensors (lambda-probes) throughout the world for controlling the operating conditions of the threeway catalytic converter. A similarly large market exists for semiconductor sensors based on SnO, for detecting oxidizable gases such as CO, NO, and CH,, which are used mainly in monitoring instruments (alarm devices) in underground garages, tunnels, and coal mines, and for measuring emissions in industry. Here the poor selectivity is not a serious disadvantage; on the contrary it gives extra safety. Conventional electrochemical sensors too are widely used in measurement and control technology, especially glass pH electrodes, of which about a million are produced every year throughout the The largest areas of use for conventional potentiometric sensors are in medicine and environmental technology. In clinical chemistry, for example, ion-selective sensors have many uses for measurements in biological media.[95 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 527 They have been used successfully for some years to measure concentrations of individual ion species such as NaO, KO, CaZO, and Mg20 in blood. Unlike other methods of analysis such as atomic absorption spectroscopy (AAS), which always measure the total concentration of the ion species (both free and bound ions), ion-selective sensors allow a direct measurement of the activity of the free ion, which is the effective concentration and the only component that is relevant for medical diagnostic purposes.r1001 Fluoride in urine and blood can be determined by, for example, a LaF, single crystal electrode, which gives an extremely high selectivity for Fe. A knowledge of the fluoride concentration is important in the chemotherapeutic treatment of osteoporosis and kidney disease, and in the determination of the Fe content of the blood after the use of narcotic^.^^'] The detection of traces of cyanide in blood is necessary during treatment of hypertonia with sodium pentacyanonitrosylferrate(i1) (sodium nitroprusside), and this too can be carried out with an ion-selective electrode. Iodide- and bromide-selective sensors are of interest in clinical toxicology, in connection with radioimmunological investigations into the functioning of the thyroid gland (using the iodine-I31 isotope) and the administration of the bromine-containing sleeping drugs, ureides. Use of the latter often causes toxic effects due to metabolic dehalogenation and a dangerous build-up of Bre ions. In treating manic-depressive patients a control of the lithium content is of particular importance; this can be determined using ion-selective membrane electrodes which consist of PVC and a lithium ionophore such as ETH 1810 (N, N-dicyclohexyl-N', Nf-diisobutyl-cis-cyclohexane-1,2-dicarboxamide). The non-invasive measurement of the transcutaneous blood CO, partial pressure is a technique that can be used to advantage in operations, in amputational surgery and in sport related medical practice. Here the sensor works on a principle analogous to that of other potentiometric gas sensors such as NH, or SO, detectors. It is essentially a pH probe consisting of a glass electrode and an Ag/AgCl reference electrode. The gas diffuses through a semipermeable membrane into an intermediate electrolyte, whose pH changes according to the gas partial pressure and is measured by the pH electrode. Figure 13 shows a sketch of the sensor. The sensors that have been described are still used mainly for in vitro measurements, but the main research objective is to develop catheter needle electrodes for in vivo measure- cover glass electrode housing electrolyte rese electrolyte gas membrane Fig. 13. Gas sensor for measuring CO, partial pressures in medical applications[95]; the sensor allows transcutaneous measurement of C0,. ments. Figure 14 shows an example of an amperometric catheter electrode for measuring 0, partial ISFETs have proved successful mainly in medical technology. Up to now pH-ISFETs have become commercially available and are used for determining acidity in blood and serum (whose normal pH value is 7.41) and other body fluids. Another technological application is in the photographic industry; here ISFETs are used in process control, to maintain important parameters such as the concentrations of H@ and Ag@ ions at constant levels.[102] The Ektachem film electrodes mentioned earlier (cf. Fig. 4) can be used as one-shot disposable sensors in medical applications. The Kodak Ektachem DT 60 is a commercially available 50 . and can be used for the determination of KO, NaO, Cle and other substances. Figure 15 shows a film sensor of this type for potassium. Potentiometric sensors can be used for environmental protection both in laboratory investigations and on-line applications. One task that they can perform is the continuous monitoring of NO: and NHT concentrations in groundwater and drinking water. This gives early warning of excessive concentrations in the water, allowing the necessary corrective measures to be applied quickly. Figure 16 is an example of a recorder trace obtained with a sensor used to monitor nitrate in drinking water. The trace shows immediately if the maximum legally permitted nitrate concentration of 50 mg L-' (50 ppm) is exceeded. Here the technique of flow injection analysis (FIA) can be used, since the selectivity of the sensor makes a preliminary chromatographic separation unnecessary.\" 041 528 Angew. Chem. Inr. Ed. Engl. 30 (1991) 516-539 100 Table 6. Summary of commercially available sensors - - A 3 min Fig. 16. Recorder trace obtained during the FIA monitoring ofNO? in drinking water; carrier electrolyte: 50 ppm NO? in 0.01 M NaH,PO, ' H,O; flow rate: 3.0 mLmin-'; sample quantity: 0.3 mL in 0.01 M NaH,PO, H,O. The numbers represent the concentration of nitrate in mgL- ' ; A: doubly distilled water: B: drinking water. In process engineering, ion-selective sensors for Ca2@, Na@, NHF, or CIo can monitor the purity of boiler feed water in steam with a glass electrode for Na@, ppb concentrations are detectable. Monitoring these concentrations is critically important in relation to boiler scale formation and turbine corrosion. Table 5 lists important characteristics of the various types of sensors described here, such as the range of measurement, useful life and detection limits. ISEs that do not incorporate PVC membranes can also be used to a limited extent in nonaqueous media. For example, it is well known in the oil industry that impurities in crude oil feedstocks can adversely affect the refining process, and it is therefore essential to carry out continuous anaIyses.[lo6] Table 6 gives a summary of some commercially available sensors.\" \"1 2.6. Development Trends One should not overlook the fact that the majority of development work on sensors proceeds by methods that are still more or less empirical. Recently the most up-to-date research techniques, e.g., electrochemical impedance spec- Supplier detector Species Range Applications detected AEG NO, monitor NO, 0-600 ppm vehicle exhausts. flue gases gas analyzing CO 0- 1500 ppm NO 0-1000 ppm 0- IS00 ppm flue gases 0-200 ppm I MSI (Drager) 0, 0-20.9% computer so, NO, Unitronic (Figaro) CH, gas monitor C,H, C4HlO CO NH3 H,S H 2 0 Transducer NO2 Research, Inc. H2S gas monitor CO 500- 10.000 ppm 50- 1000 p p i 30-300 ppm tunnels) 5 - 100 ppm 0-100 ppm humidity gas alarms (garages, gas alarms I 10ppb-50ppm 0-1000 ppm Bran & Liibbe Na@ 0-20 ppb Ionometer S'O troscopy,[' OS1 tracer methods, and surface analytical techniques[\"'- '\"1 such as secondary ion mass spectrometry (SIMS), Auger electron spectroscopy (AES), or X-ray photoelectron spectroscopy (XPS, also known as ESCA), have been applied to optimize performance parameters such as selectivity, stability, dynamic behavior, reproducibility and sensitivity. These methods will at the same time provide a deeper insight into the mechanisms of functioning of the selective sensor elements. A changing trend can now be seen in the technology of chemosensors, away from the hitherto conventional sensor design principle based on electrode-like structures, towards miniaturization with recognition systems and signal processing integrated in a single device.\" 12, ' l31 These developments can benefit from the existing technology of microelectronics. Besides savings in materials, this technology can also lead to considerable cost reductions through mass production, and may sometimes even result in sensors with improved proper- ties. Physical sensors for a wide variety of variables are produced by these methods and are already well-known, while chemical sensors made in this way are just appearing on the market. Thick-film technology offers an alternative way of integrating sensor recognition systems and subsequent signal processing on a single chip, and is within the financial budgets of medium-sized industrial concerns. A potentiometric hydrogen sensor based on thick-film technology and developed by the Battelle Institute is shown in Figure 37. The sensitive material is Nasicon (Na, +xZr,Si,P,-,O,,), a solid ionic conductor which responds to hydrogen at elevated temperatures, but is a good Na@ sensor at room temperature and in solutions. This sensor based on Nasicon is at present one of only a few commercially available sensors made by thick-film technology. 3. Biosensors A biosensor combines in a single sensor element the sensitivity of a chemosensor with the selectivity of a biological recognition mechanism. The great promise offered by such a combination has been the subject of increasing research efforts in the last few years, as is evident from the rapid growth in the number ofpublications in this area and the appearance of the first monographs on the A number of different biosensors with biological or biochemical recognition systems coupled to various types of chemosensors have been demonstrated. Although to date biosensors have commercial importance only in medical technology, their use in future in other fields such as environmental monitoring and process engineering is likely. For this reason some relevant developments are described below. Biosensors functioning on enzymic principles belong to the oldest generation of sensors in this category; they employ selective chemical reactions catalyzed by selected enzymes. The most effective method is to immobilize the relevant enzymes in or on the sensor element, which allows the device to be used repeatedly. Unfortunately the stability of enzymes immobilized in this way is at present rather limited, and consequently the lifetime at room temperature under working conditions varies between only a few days and several months, depending on the enzyme used and the immobilizing technique. However, if it is refrigerated and freeze-dried, an immobilized enzyme retains its activity almost indefinitely. Another class of biosensors are immunosensors. These operate on a different principle, namely the selective association between antigens and antibodies. This specific biocomplex formation can be exploited in a number of ways as a means of analysis for one of the two partners. The methods that are of importance for the development of these sensors differ from those involved in radio immuno-assay (RIA), and are based either on enzymic immuno-assay (EIA) in combination with various detection methods (photometry, amperometry, or surface plasmon resonance), or on direct potentiometry . Some of the systems under development function without isolation of biomolecules. In other words, these are enzymic biosensors in which biological materials such as intact cell cultures, tissue sections or microorganisms are used directly without purification; for immunosensors one uses intact receptors, receptor structures or reconstituted units. As the development of biosensors follows on that of transducers or chemosensors, biosensors are not yet at such an advanced stage, and only a few types are commercially available at present. Nevertheless, some important advances have been achieved in each class of biosensors. 3.1. Monoenzyme Sensors Monoenzyme sensors were the first biosensors to be developed, and are the best known. Here an enzyme is coupled to an optical or electrochemical chemosensor, which selectively detects one of the reaction partners of the substrate, or a reaction product. As early as the 1960s with the first enzyme electrodes, immobilization of the enzyme was a development goal. Although the immobilization technique is crucial to the behavior of the biosensor, it will not be considered in detail here. The situation is basically similar to that in bioreactors, where the aim is to achieve a high surface activity combined with a high durability; accordingly, the immobilization techniques used in biosensors are similar to those for bioreactors.[116-'201 However, it must be said that many of the techniques are still far from giving reproducible results. Many preparative procedures evolved by trial and error, and if a breakthrough could be achieved in immobilization without loss of activity, many of the present disadvantages of biosensors would be overcome. The modification of the coenzyme nicotinamide adenine dinucleotide (NAD@) can also be regarded as a type of immobilization.t121. 1221 If the effective molecular mass of NAD@ is increased by reaction with polyethylene glycol (PEG) to give PEG-NAD@, the coenzyme can be immobilized behind a dialysis membrane, so that it can be used repeatedly after a recycling procedure. Chemically preactivated membrane filters for simple and rapid immobilization of enzymes have recently become commercially available (Immunodyne, Gelman Sciences). The simplification of the procedure brought about by them could lead to a breakthrough in extending the storage life of biosensors. If a filter membrane freshly coated with the enzyme could be fitted to the sensor shortly before making a measurement, the cost of the biomaterial would be worthwhile in view of the great advantages of a rapid but selective measurement. 3.1 .I . Electrochemical Biosensors In the past the development of monoenzyme biosensors with different transducers was mainly limited to electro- 530 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 chemical sensors. This situation has now changed to some extent through the development of new optodes and of the technique of surface plasmon resonance. Biosensors with electrochemical transducers are still essentially restricted, owing to the nature of the products from enzymic reactions, to two methods of measurement, namely amperometry and potentiometry . Amperometric Biosensors: The majority of biosensors used in research are of the amperometric type. Table7 gives a short summary, which is by no means exhaustive, of the many different types of biosensors using conventional amperometry. Table 7. Amperometric biosensors. Substrate Enzyme Product(s) Range Refs. detected deh ydrogenase choline oxydase alcohol oxidase alcohol malate formiate choline ethanol formaldehyde formaldehyde dehydrogenase glucose glucose oxidase glutamine glutaminase, glutamate oxidase glycerol glycerol dehydrogenase hypoxanthine xanthine oxidase lactate lactate oxidase oligosaccharides glycoamylase, glucose oxidase phenol polyphenol oxidase inorganic nucleoside phosphorus phosphorylase 10-150mmolL-' NADH ( 5 - 1 0 0 ) ~ 1 0 - ~ m o l L - ' [121,124] H,O, 500 mmolL-' [a] [125] NADH mol L-' [a] [126] H,O, 10 mgL-' [a] I1 141 H,02 0-7gL-I [127-1351 H,O, 0-25 mmolL-' ~1361 NADH, O2 11371 H20, 4 - 1 8 0 ~ 1 0 ~ ~ m o l L - ' [138,139] H,O, 0.1-2.5mmolL-' [140] H20, 1-4011Un0lL-' 11141 quinone - 11251 [a] Only the upper limit is known In amperometric transducers, reaction partners or products of the enzymic reaction are directly reduced or oxidized at the working electrode, and the resulting current is measured. From this, on the basis of the stoichiometry, the quantity of the substrate that has reacted can be determined. As is evident from Table 7, the most commonly used transducers are based on the oxygen/hydrogen peroxide electrodes described in Section 2.1.4, since many enzymic reactions (e.g. those of the oxygenases) involve the consumption or production of oxygen. This consumption of 0, or production of H,O, is measured by an 0, electrode. In this area of development considerable time has been invested in the glucose sensor, which is based on reaction ( 3 ) (3) GOD B-D-glucose + 0, -+ H,O -gluconic acid + H,O, catalyzed by the enzyme glucose oxidase (GOD). In this selective reaction three concentration changes can be and have been used to determine the amount of material reacted: 1) the reduction in concentration of the cosubstrate (reduction in O,), 2) the increase in H,O, concentration, or 3) the concentration of the He ions generated by the disso- ciation of the gluconic acid. Greater progress has been made in the area of in-vitro glucose measurements than in any other, which is not surprising in view of the large amount of research effort on this topic (about half of all the papers on biosensors are concerned with glucose measurements). Despite this, however, an implantable glucose sensor, which would be desirable in medical technology, is still not within sight. Implants need to have a lifetime of several years, because if it is shorter the added trauma for the patient as a result of more frequent operations is unacceptable. Up to now the lifetime of the enzyme GOD in synthetic glucose solutions has been at best about 100 days.['231 Among the problems which hinder applications are those arising from the nature of the cosubstrate (the quantity of 0, available for reaction ( 3 ) limit the measurement range), from product inhibition, from the possibility of the enzyme being attacked by proteases, and from diffusion difficulties caused by encapsulation of the implant. Other types of amperometric biosensors are those based on the detection of a coenzyme. Well over 100 enzymic reactions are known in which nicotinamide adenine dinucleotide (NAD@) functions as a coenzyme. The direct electrochemical reduction of NAD@ or oxidation of the reduced form NADH have both been successfully demonstrated,['42' 1431 but owing to the very large overvoltage that must be applied (+ 0.7 to + 1.0 V vs. Ag/AgCl), the determination of both species is instead carried out with electron carriers (mediators), which work on the principle shown in Figure 18.[144-1471 A similar situation exists for the coenzyme N A D P ~ . The compounds used as mediators are reversible redox systems with high exchange current densities, often redox dyes such as methylene blue or thionine, or sometimes modified ferrocenes or hexacyanoferrates. The advantages of such a mediator are well-known: it reacts with the coenzyme NAD@ in a homogeneous solution without significant inhibition by kinetic factors, the mediator itself is electrochemically reversible, and it reacts at the electrode at a significantly lower potential than NAD@. Because of the lower working potential fewer interfering effects from other electrolyzable substances in the sample are expected. Ferrocenes have also been used to effect the direct transfer of electrons between the enzyme and the electrode. A modified ferrocene serves as mediator between immobilized glucose oxidase and a graphite e l e c t r ~ d e . ~ ' ~ ~ ~ This glucose sensor, developed at the Cranfield Institute of Technology (UK), is unaffected by O,, as the ferrocene replaces oxygen as the cosubstrate. The sensor can therefore also be used in anaerobic media (e.g. in fermenters). In general the immobi- Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 531 lization of mediators presents difficulties. An immobilization effective enough to prevent loss of the mediator from the transducer with time is usually accompanied by severe deactivation of that mediator. Potentiometric Biosensors: Biosensors with potentiometric transducers can be used in any situation where protons are either generated or removed in the course of the enzymic reaction. Most types are based on a pH electrode, as can be seen from Table 8, which gives a short summary of potentiometric biosensors. A pH measurement is an alternative way of following the glucose conversion reaction (eq. (3)) already described under amperometric biosensors. In this case the change in pH caused by the formation of gluconic acid is measured. Fats may be determined by measuring the change in pH caused by the formation of fatty acids, as listed in Table 8. Though still at the development this method seems to offer great promise, especially in view of the numerous potential applications in food technology. Recently stable lipases which even allow the determination of fats in organic solutions have been isolated. The performance of all biosensors that work by means of a pH measurement is greatly affected by the buffer capacity of the sample solution. A lipophilic layer or membrane between the reaction zone and the buffer system decreases this dependence. Whereas with amperometric sensors, which consume some of the substance being determined during the course of the measurement, deposits of proteins formed on their surface attenuate the signal, with potentiometric sensors only the response time and not the magnitude of the signal is affected, since here the measurement does not consume the substance. This can be a crucial factor in the case of implants. The conversion of aspartam by the enzyme L-aspartase is of interest in connection with the production and use of artificial sweeteners. The NH, generated in the reaction can be determined by the well-known NH, gas electrode. This type of electrode has also been used successfully for some time to determine urea in urine by means of the enzyme urease. The enzymic hydrolysis of urea [reaction (4)], like the oxidation of glucose, allows the use of various chemosensors as transducer. CO(NH,), + 2 H,O 2 NHY + C0:O (4) In aqueous solution the reaction products give the pHdependent equilibria (5) and (6), which provide further spe- NHF + OHe ZII? NH,+H,O (5) C O i e + H @ ZII? HCOF z=? C O , + H , O (6) He -Ha cies for which transducers are available. Potentiometric ISEs are available for two of the reaction products, the ammonium and carbonate ions. Furthermore, the gases NH, and CO, which may be produced depending on the pH in the reaction zone can be detected by means of the appropriate gas electrodes mentioned above.[1601 A urea sensor as described here can be made in the form of a simple triple-membrane configuration as shown in Figure 19. Conductometry is another electrochemical transducer principle which can be applied to biosensors, since the progress of an enzymic reaction can also be measured by the change in the resistivity of the solution. However, as well as lacking selectivity, this method suffers from the fundamental difficulty that only the total resistivity can be measured and the change in resistivity is caused not only by the reaction, but also by the introduction of an ion-containing medium. A difference method has been proposed by Wut~on.['~'' Con- 532 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 ductometric biosensors for urea and for D-amino acids are described by Rechnitz et a1.['621 3.1.2. Biochips The new microelectronic transducers are becoming increasingly important, as they make it possible to produce one-shot disposable biosensors. This offers a possible solution to the ever-present problems of poor storage properties and short lifetimes of biosensors. Even the problem of sterilization could be solved by sterile sensor elements which are introduced immediately before the measurement. Special mention must be made here of ion-selective field effect transistors (ISFETs), whose small size, particularly, warrants their application as transducers in biosensors, as this factor is of great importance for catheter sensors in medical technology. Enzyme-modified ISFETs, known as ENFETs, consist in many cases of pH-sensitive ISFETs with an enzyme immobilized on their surface; this catalyzes the reaction of a substrate which generates or removes protons. Examples of the use of ENFETs are the determination of glucose)'52* 1631 urea, and penicillins,\" 5 8 * 1651 in which the appropriate enzymes were immobilized on the pH-sensitive surface of the ISFET with glutaraldehyde and bovine serum albumin, or in membranes. To compensate for errors caused by temperature fluctuations or by pH changes from effects other than the enzymic reaction, a differential measurement can be performed with two pH-ISFETs, one coated with the enzyme and one bare, as described in the first German patent for a b i o ~ h i p . [ ' ~ ~ ] The determination of triglycerides has also been performed by a differential measurement, with lipase immobilized in a polyvinylpyrrolidone membrane on the pH-sensitive surface of a pH-ISFET.['661 Table 9 gives a summary of the ENFETs that have been reported. 3.1.3. Optical Transducers In addition to the well-proven electrochemical transducers, optical sensors have recently been exploited to an increasing extent for substrate recognition by enzymic reactions, since fiber-optic spectrophotometers and fluorimeters are now commercially available. The way in which these optical biosensors function will be described here with the help of a few examples. Wolfbeis and T r e f f n ~ k \" ~ ~ ~ have developed a biosensor for glucose determination using the reaction described in Eq. ( 3 ) ; this sensor contains as its transducer an oxygen optode which has already been described in Section 2.3. The glucose oxidase was bound to a nylon membrane by activated carboxyl groups (Immunodyne) and the membrane was attached to the surface of the optode. Another approach of Wolfbeis et al.['68] is based on the intrinsic fluorescence of the enzyme concerned. Enzymes with FAD (flavine adenine dinucleotide) as prosthetic group change their fluorescence properties during the reaction with the substrate, because flavoproteins have different properties in their oxidized and reduced states. This change can be measured with optical fibers that have the enzyme held at their ends by a dialysis membrane. Experiments have been carried out on this system with glucose oxidase, lactate monooxygenase and cholesterol oxidase as enzymes. An optical biosensor has been developed for controlling the biotechnological manufacture of penicillin. This sensor monitors the change in pH caused by the enzymic conversion of penicillin to penicillic acid; the measurement can be performed either electrochemically or optically.['691 For the latter the enzyme penicillinase was immobilized in a polymer together with a pH-indicator, as described in Section 2.3 for pH-optodes. Urea can be determined by an analogous meth- These examples of optical sensors, which are summarized in Table 10, clearly illustrate that, like electrochemical biosensors, nearly all optical sensors depend on just a few basic principles, such as 1 ) the measurement of oxygen concentration by the fluorescence quenching of a dye (transducer: 0, optodes), 2 ) pH-measurements (transducers: pH optodes), and 3) the determination of NADH fluorescence using a bifurcated light-guide. Combining these measurement principles with different enzymes results in biosensors similar to those based on electrochemical transducers. There are no great differences in performance between them. Figure 20 shows the basic design features of an optical biosensor. od.\" 701 3.1.4. Mass-Sensitive Transducers A class of biosensors that have hitherto not been widely used are those based on piezoelectric crystals or surface acoustic wave (SAW) These provide a simple means of detecting changes in mass through the alteration in the resonance frequency of a crystal. If such a transducer is covered with a selectively adsorbing surface or absorbing film, the concentration of the ab- or adsorbed substance can be determined from the change in resonance frequency. Using a 9 MHz piezoelectric quartz crystal, for example, it is theoretically possible to measure mass changes as small as lo-' g. Guilbault et al. describe sensors based on piezoelectric crystals coated with enzymes. The selectivity is provided by the formation of an enzyme-substrate complex, and the sensitivity is given by the stoichiometric mass increase given by the equation of the reaction. With immobilized formaldehyde dehydrogenase,[' \"1 atmospheric formaldehyde concentrations in the range from 1 to 100 ppm can be detected, with choline esterase,\" 731 pesticides in the ppb range. Measurements in liquid media cause greater problems and are controversial. To maintain the theoretical sensitivity described in Equation (d), piezoelectric sensors should be subjected to a reproducible drying step in air before use. 3.2. Multienzyme Sensors The repeated use of expensive coenzymes is possible if they are regenerated by a second enzyme. The recycling method described by Schepers et al.\" 7 4 1 could be applied to many analytes. The fluorescence of the reduced coenzyme nicotinamide adenine dinucleotide (NADH) is measured in a flow-through cell using a fiber-optic device. The molecular mass of the NAD@ is increased by binding it onto polyethyleneglycol in order to trap it within the cell, together with an enzyme such as alcohol dehydrogenase, behind a dialysis membrane. When a second enzyme, e.g. lactate dehydrogenase, is also included behind this membrane, it becomes possible to regenerate the NADH by adding pyruvate. However, the need to add this reagent means that the device is no longer a sensor in the narrow sense, because a sensor should work without addition of reagents. Several enzymes, or even a whole enzyme series, could be necessary in cases where a single enzymic reaction step does not yield a substance which can be detected by a transducer.[' 14, 3.3. Biosensors Based on Tissue Sections or Cell Cultures Not only isolated enzymes but also entire groups of intact cells can be used as the basis for biosensors. Compared with the isolated enzymes, these often have the advantage of being active for longer periods, as the enzymes are kept in their natural environment. In this case an additional immobilization step for the coenzymes or cofactors is not necessary. However, such cell groups are often less selective, as they contain mixtures of enzymes. Arnold and R e ~ h n i t z \" ~ ~ ] published a table listing biosensors based on tissues and related materials. NH, or 0, chemosensors are often used as transducers. The principle of these devices will be explained by taking as an example a biosensor for hydrogen peroxide. As bovine liver contains relatively high concentrations of the enzyme catalase, a section of fresh tissue only 0.1 mm thick is immobilized with nylon mesh on the surface of a membrane-covered 0, electrode. The hydrogen peroxide whose concentration is to be determined undergoes enzymic decomposition to oxygen and water, and the oxygen thus produced is measured amperometrically. This sensor is less sensitive to fluctuations in temperature and pH, and has a longer lifetime than a biosensor containing an isolated enzyme.['76] Another device of this kind which is frequently cited is the \"bananatrode\" which has been described by Rechnitz et al.['77] Here a thin slice of banana in front of an 0, sensor is used as a detector for dopamine, which undergoes oxidation by the enzyme polyphenol oxidase present in bananas. The consumption of oxygen is then measured. 3.4. Microbial Biosensors The majority of biosensors based on immobilized microorganisms function with amperometric oxygen sensors as transducers.[' 'I Biosensors for the determination of phosphate, nitrate, nitrite, sulfite, methane, and phenol have recently been described, but none has yet achieved a commercial breakthrough. The determination of phosphate was performed with a sensor based on the microorganism Chlorella vulgaris in immobilized form. An 0, optrode was used to measure the increase in the photocurrent on introducing phosphate. The photocurrent was found to be a function of the phosphate concentration in the range from 8 to 70 mmol L- .I1 791 Karube, Kitagawa et al.\" have developed a microbiological sensor for alcohol using a pH ISFET as a transducer. For this the acetic acid bacterium Gluconobacter suboxydans was immobilized on the ISFET behind a gas-permeable membrane. Ethanol which diffuses in through the membrane is converted to acetic acid by the bacteria. This biosensor can be used for the determination of ethanol in the range from 3 to 70 mmol L-I. 3.5. Immunosensors Antibodies (Ab) and antigens (Ag) (or haptenes) bind specifically and strongly to each other. Techniques for following such reactions in order to determine one of the reac- 534 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 tion partners have up to now relied mainly on labeling one of the immunoreactands. This is the principle used in immunoassays, which are now indispensable in biochemical analysis. Immune reactions are subject to the limitations imposed by the law of mass action. In the equilibrium reaction between the free antigen (Ag) and the antibody (Ab) to form the antigen-antibody complex, the equilibrium ratio between the concentrations of the complex and of the free reaction partners is determined by the affinity constant K [Eq. (f)l. In immunoassays quantitative determinations can be carried out by means of competitive binding tests or sandwich tests. In competitive tests labeled antigens are used. If radioactive labeling is used, the procedure is called a radioimmunoassay (RIA). If instead, an enzyme is covalently bound to the antigen (horseradish peroxidase or alkaline phosphatase are often used), the procedure is called enzyme immunoassay (EIA). The labeled antigen and the antigen to be assayed compete for the binding of the immobilized antibody, and the concentration of the antigen can be determined by comparison with a reaction of a known concentration of the pure antigen. Sandwich tests are carried out with labeled antibodies. When radioactive labeling is used the measurement is described as an immunoradiometric assay (IRMA), whereas if the antibody is attached to an enzyme it is called an enzyme-linked immunosorption assay (ELISA). The antigen which is to be determined binds to an antibody which is immobilized on a support, and is quantitatively determined by means of a second labeled antibody. Both systems have important disadvantages. Purified antibodies and antigens are required. The calibration curves are only linear over a small concentration range. With radioactive labeling there are problems of waste management. Although an immunoassay is simple to perform, it involves a succession of stages, and often a separation step, requiring several hours of work. In the last few years several immunosensors have been developed in which the immunological reaction is measured directly. These sensors use electrochemical, optical, or piezoelectric transducers or capacitance bridges. It should eventually be possible to perform the most important types of immunochemical analysis with disposable sensors.[' ' I Enzyme immunoelectrodes comprise the transducer (electrode), the immune reaction system, and an enzyme indicator and are based on the usual EIA phnciples, except that the product of the enzyme-catalyzed reaction (often H,O,) is detected electrochemically and not by photometry.[182, 1831 Ion-selective membrane electrodes have also been used for the determination of antibodies. The method is described by Rechniiz et al./1841 in which the corresponding antigen is covalently bound to an ionophore of the benzo-crown-ether group and immobilized in a PVC membrane to give an electrode sensitive to alkali metal ions. The change in the potential of the electrode which occurs on adding the appropriate antibody is caused by the alteration of the properties of the ionophore when the antibody binds to the antigen-ionophore complex. Another type of immunosensor is based on the antigen-induced change in the potential of a chemically modified semiconductor surface (TiO,), the mechanism of which is still not understood.t1851 Based on early fundamental studies on potentiometric immunosensors during the period 1978 - 89, the interdisciplinary research center for chemoand biosensors at the Westfaelische Wilhelms University (FRG) has just elucidated the general mechanism of immunologically-induced changes in electrode potential.\" 86* 1871 There are in principle many different antibodies for a particular antigen or haptene, so that a large variety of organic molecules can be selectively determined. If the remaining problems of standardization and storage life can be solved, this analytical technique should revolutionize at least molecular analysis, since a potentiometric immunoassay is fast, sensitive, and extremely economic. Immunosensors based on mass-sensitive transducers (piezoelectric crystals and SAW devices) exploit the mass increase which results from the immune reaction.\" 881 Here again measurements in liquids present problems. Immune reactions at surfaces also alter certain optical properties, on which optical sensors are based. One optical effect that can be used to determine antigens with immobilized antibodies is the change the resonance angle in surface plasmon resonance (SPR) spectroscopy[' 891 when immunocomplexation forms a film on a silicon or metal oxide base layer. Others are the change in light scattering from a coated glass surface when an immunocomplex is formed,\"901 and changes in the reflection and absorption of a light beam (evanescent wave te~hnique).['~'] A strict definition classifies immunosensors not as true sensors, but as dosimeters, because the immune reactions are not reversible. Under suitable conditions (e.g. by altering the pH) it is possible to break down the biocomplex to recover the antibody and the antigen, allowing a quasi-continuous measurement sequence.['86, l E 7 1 A continuously operating type of immunosensor based on competitive reactions has been developed ; here the analyte and a heterobifunctional complex compete for binding sites on an immobilized antibody!'921 Nonspecific binding is a difficulty which limits the sensitivity of immunosensors in many applications. This problem has been investigated in detail by Cullen and L ~ w e . ~ ' ~ ~ ] 3.6. Biosensors Based on Receptors A very promising approach is the development of biosensors in which individual receptors or receptor structures from living organisms are immobilized on transducers.\" 94] The advantages of receptors over enzymes, for example, lie in very high sensitivities and short response times. It is known, for example, that some marine species can recognize substances at concentrations as low as mol L-' , However, the problems of isolating receptor molecules and of their instability when immobilized are still so great, that this idea must be regarded at present as an interesting approach with potential for future developments. A sensor for the determination of glucose which is based on a receptor protein has been developed by Schultz and Meadows.\"951 This makes use of the competition between glucose and a glucose analogue, a dextran labeled with fluorescein isothiocyanate (FITC-dextran), for binding sites on Angew. Chem. Int . Ed. Engl. 30 (1991) 514-539 535 the glucose receptor protein concanavalin A labeled with rhodamine (Rh-Con A). FITC-dextran and Rh-Con A are sealed in a length of dialysis tube at the end of a bifurcated light guide with a diameter of 100 pm (Fig. 21). Light of a suitable wavelength excites FITC, which fluoresces. If the FITC is connected via the dextran to the Rh-Con A, the energy absorbed by the FITC is transmitted to the rhodamine, which then also fluoresces. If glucose diffuses through the dialysis membrane into the measuring cell, the dextran is partly displaced from its binding sites by the glucose and the measured FITC fluorescence increases, because less energy is transferred from FITC to rhodamine. From increase in fluorescence intensity the glucose concentration can be determined. 3.7. Applications of Biosensors An important technological application of biosensors is the control of fermentation processes. Here it is desirable to measure continuously as far as possible, to ensure optimization of the fermentation process and to minimize the consumption of expensive nutrients. It is particularly important to monitor glucose, ethanol, lactate, cephalosphorins and penicillins. Another area in which biosensors are used, is food technology and food testing. Of interest is the glucose content of wine and fruit drinks,[1961 lactate production during milk processing,[1971 and the freshness of fish, which is measured with a hypoxanthin sensor.[19s1 An area of growing importance is monitoring the quality of water and effluents. Most of the sensors developed so far are based on the combination of microorganisms and transducers. Some sensors serve to determine individual constituents of water, such as phosphate, nitrite, and nitrate,\" '] while others measure composite parameters through their inhibiting effects on microorganisms or enzymes. However, the latter are more like simple early warning systems (screening) than true sensors, as an alarm indication needs to be followed by a more precise analysis. Moreover, these systems work irreversibly. Such warning systems are used in particular to monitor pesticide contents or concentrations of heavy metal ions and the inhibition of the microorganisms is mea- sured by the reduction in CO, production.['991 To obtain a quantity which can be related to the biological oxygen demand (BOD), changes in the respiratory rate of E-ichosporon cutaneum are measured with an oxygen electrode.[z00] A sensor of this type is already in routine operation in Japan. A final example of a field in which biosensors are finding application is medical technology. The most frequently performed analyses are of glucose and lactate, and it is therefore in this area that the most intensive research is being undertaken. The desirability of in-vivo measurements, for example, to control an insulin pump, is giving impetus to the development of miniaturized biosensors. Here of utmost importance is the requirement that the reagents are biocompatible and physiologically harmless. Already a few biosensors, based on electrochemical or optical transducers or on piezoelectric crystal measurements in the gas phase, are commercially available. Analytical instruments have been developed to avoid some problems of biosensors. Here pretreatment of the samples can prolong the life of the sensor. The early commercially available analytical instruments for medical technology are usually based on an oxygen or hydrogen peroxide electrode as a transducer, with an oxidase as the biochemical component. They permit analyses on whole blood for glucose content in the range from 0 to 30 mmolL-' or lactate content from 0 to 15 mmol L-l. A BOD-measuring instrument based on the BOD sensor described earlier is now also available. A list of commercially available analytical instruments based on biosensors can be found in the article by Owen.[201] 4. Outlook This article aimed to give a concise overview of the present state of development of chemical sensors that are already or might become important for chemical, medical, and environmental applications. However it does not claim to be exhaustive. In the field of biosensors alone there are, according to recent CAS on-line searches, over 3000 publications and over 300 patents, although there are at present barely a dozen types of commercially available sensors, of which more than a half are for glucose. One of the main reasons for this striking imbalance with regard to marketing success may be found in the low degree of interdisciplinary cooperation among scientists. Many of the publications go no further than demonstrating a reproducible effect observed for a single chemical substance. Often there is no investigation into the effects of interfering substances, nor an answer to the central analytical question: how accurately and reliably does the sensor measure the substance for which one is analyzing? Reports which only give information on reproducibility, measured on pure synthetic samples containing no interfering constituents, should be avoided in view of the present wealth of knowledge about sources of systematic errors. To an analytical chemist a report on the development of a new analytical method which tells one nothing about matrix effects, and therefore about its absolute accuracy (defined as coincidence with the true content in the sample) is like a report on a synthetic method for a new compound which was identified by elemental analysis alone (i.e. without 536 Angew. Chem. in[ . Ed. Engl. 30 (1991) 516-539 Confirmation by universally recognized and indeed prescribed methods of modern structural analysis). In the field of chemosensor development, as in that of ultra-trace analysis, there is a growing tendency to play down the importance of interfering effects. The disproportionately large amount of research effort devoted to the microelectronic aspects of modern transducers is pointless if not accompanied by a deeper understanding of the mechanisms by which substances are specifically recognized. The fundamental mechanisms of the molecular interactions taking place in these devices cannot be planned and optimized on purely engineering considerations; they depend on natural laws that one can use but cannot alter! In summary it may be concluded that the development of sensors will advances further simply because there is a strong demand for it. The more research effort concentrated on the central problem of a selective molecular recognition, the quicker such advances will be achieved. Our present knowledge of mechanisms indicates that it is necessary to involve chemists from a wide variety of disciplines: theoretical, inorganic, organic, biochemical, analytical, and physico-chemical. The development of new sensors can only progress by an interdisciplinary approach, which must also include the collaboration of biologists, physicists, and medical scientists. At this stage improvement in the transducer properties has a lower priority than improvement in the selectivity of chemosensors and the lifetime of biosensors. The transducers now available have adequate stability and sensitivity, and their full exploitation is prevented only by the laws of physicalchemistry or by shortcomings in the properties of the sensor elements. The basic ideas ofthe novel approach to the theory of ion-selective electrodes described here were developed in 1975 by K. Cammann in his Ph.D. thesis. He would like to thank his academic teachers, Prof. Dr. G. Ertl and Prof. Dr. H . Gerischer, for many discussions and helpful suggestions. During a Humboldt-Fellowship, for which the Alexander von Humboldt Foundation is sincerely thanked, Prof. Dr. S. L. Xie could verifv this far-reaching theory completely by means of the most modern experimental equipment. The basic research in this field during recent years was generously funded by the Deutsche Forschungsgemeinschaft (DFG) and the Fonds der Chemischen Industrie, which we have much appreciated. Grateful acknowledgement is also given to the Bundesministerium fur Forschung und Technologie (BMFT) for its generous financial help to research in the field of biosensors at Miinster. Last but not least, we owe a debt of gratitude to the State of Nordrhein- Westfalen, which is establishing a research institute for chemical sensors and biosensors (attached to the University of Miinster) in cooperation with the FraunhoferManagement-Gesellschaft (FhM) . 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        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.15-1.png",
        "caption": "Figure 12.15. Checking for undercutting by the cut ter tooth fillet.",
        "texts": [
            " The correct involute profile in a tooth of the gear is cut by the involute part of the cutter tooth. The profile of the cutter tooth can only coincide with the involute down to the base circle, and the tooth may be designed so that the fillet starts slightly outside the base circle, since the involute radius of curvature becomes zero at the base circle. The involute part of the tooth, therefore, ends at the fillet circle, which is either larger than the base circle, or the same size. On any particular cutter, the radius Rfc of the fillet circle can be measured. In Figure 12.15, the fillet circle of the cutter is shown, intersecting the line of action at Fc. The involute section of the cutter tooth profile lies outside the fillet Undercutting 289 circle, so the cutting of the involute part of the gear tooth profile can only take place outside this circle. This means that the path of contact must end at a point somewhere above Fc ' and we obtain the following condition that must be satisfied if there is to be no undercutting, (12.81) If the tip circle radius RTg required for the gear is smaller than the minimum value given by this condition, then it is necessary to use a cutter wi th more teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003003_1.1320821-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003003_1.1320821-Figure3-1.png",
        "caption": "Fig. 3 Photograph of the test rig \u201espur gears\u2026 and sketch of the geared unit \u201ewith bearing labels\u2026",
        "texts": [
            " that there is Transactions of the ASME 15 Terms of Use: http://asme.org/terms Downloaded F no interference outside the contact area and finally, iii! that convergence on normal and friction force is achieved ~Eqs. ~11! and ~12!!. The complete procedure is summarized in Table 1. Comparisons between numerical and experimental results are carried out at low speeds in order to emphazise the influence of tooth friction ~lubricant film thickness is minimum and probably cannot prevent from some asperity contacts!. The test rig shown in Fig. 3 was used to measure bearing forces which were expected to be particularly sensitive to tooth friction excitations. Power is supplied by a 220 kW motor equipped with programmable electronic speed control which can operate the test stand from 0 to 6000 rpm on pinion ~from 50 to 500 rpm in the present experiments!. The load is imposed by an electric torque-regulated generator on the gear shaft. Spur and helical gears have been mounted between hydrostatic bearings which are housed in rigid pedestals",
            " The test gears were ground with lead and involute deviations less than 5 mm and cumulative pitch errors within 20 mm. Both spur and helical gears have symmetrical short tip reliefs of approximately 20 mm ~spur gears! and 13 mm ~helical gears! amplitude over 20 percent of the active profile. The test gears were lubricated by jet and the temperature of the oil ~ISO VG 100! in the sump was kept at 55\u00b0C. Gear, shaft and lubricant data are listed in rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 04/13/20 Table 2 and a sketch of the test rig is given in Fig. 3. Bearing forces were sensed by four three-dimensional piezoelectric transducers mounted between the test stand base and the bearing pedestals ~Fig. 4!. Figures 5, 6 and 7 show the measured and simulated bearing forces on the input and output shafts for spur and helical gears ~bearing labels are given in Fig. 3!. Simulations were performed in the following conditions: i! no friction, ii! a constant friction coefficient of 0.1, iii! using the formula of Benedict and Kelley @6# and iv! the formula proposed by Kelley and Lemanski @20#. A number of significant observations can be made: ~a! the influence of tooth friction on bearing forces at low speeds is certainly non negligible particularly in the s\u0304 direction ~horizontal! where important alternating components at the mesh period are observed. Note that the simulated forces with no tooth friction are nearly constant because the total normal tooth load is itself nearly constant in the absence of dynamic effects",
            " The phenomenon probably caused by the significant moments of rocking is correctly reproduced by the model. It is also observed that the average measured and calculated bearing forces do not correspond to no-friction forces. Experimental results over 500 rpm are found to be perturbed by dynamic effects and the frequency range of the force sensors is not sufficient for measurements over 2000 rpm. The results in this section are therefore kept limited to simulated dynamic forces and transmission errors. For each kind of gear ~spur or helical!, peakto-peak bearing force ~see Fig. 3 for bearing labels! and peak-topeak T.E. have been computed in the range 0-800 rad/s on pinion. 520 \u00d5 Vol. 122, DECEMBER 2000 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 04/13/20 Simulations have been performed in the following conditions: ~i! all bearings were supposed to be isotropic with a radial stiffness of 108 N/m, ii! a unique modal damping factor of 0.01 has been used throughout and iii! a constant friction coefficient of 0.1 has been considered. Results in Figs. 7\u201311 confirm the qualitative indications of Bo\u0308rner and Houser @14#, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002750_s0043-1648(00)00384-7-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002750_s0043-1648(00)00384-7-Figure1-1.png",
        "caption": "Fig. 1. Helical gear wheels with global coordinate system.",
        "texts": [
            " The simulation is an initial value problem since a complete mesh cycle is repeated a number of times with gradually changing surfaces due to the wear, which is being integrated over each time step. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Simulation; Wear; Helical gears The aim of this paper is to investigate the process of wear between two teeth flanks running continuously under what can be considered as high load and low running speed. Since the authors have previously investigated the w xwear of involute spur gears 1\u20133 , this paper focuses on \u017d .how to simulate wear of involute helix gears see Fig. 1 . The overall aim is to predict the time dependent wear development with a computer simulation of the surface interaction of a general set of gear wheels. This will predict how a worn gear surface will affect the wear and pressure distribution. The findings can be used to increase the resistance against mild wear, thus prolonging the life of a gear and also increasing its performance. Helical gear wheels differ from spur gear wheels both in geometry and working behaviour. Spur gears will ideally have a contact situation where the load is axially aligned and distributed evenly across the width of the \u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure10-1.png",
        "caption": "Fig. 10. AIPM machine rotor topologies with asymmetric inset PMs and symmetrical rotor core. (a) Asymmetric inset PMs [43]-[45]. (b) Hybrid pole topology with asymmetric inset PMs and symmetrical V-shape PMs [46]-[47].",
        "texts": [
            " However, the enhancement of torque density is generally relatively small and flux barrier designs especially for topologies with thin ribs may raise mechanical stress issues. Except for employing asymmetric rotor core to shift the reluctance axis, MFS effect can also be utilized by using asymmetric PM configuration as it can adjust the relative position between PM field and reluctance axes. Various AIPM machine rotor topologies with asymmetric PMs and symmetrical rotor cores have been proposed in literature. The AIPM machine rotor topology with asymmetric PM configuration was firstly introduced by using inset PMs in [43], Fig. 10 (a), as the axis of PM field can be easily shifted by asymmetric PM position. Compared with an SPM machine, the AIPM machine with shifted inset PM position in [43]-[45] shows increased torque density, improved CPSR, and reduced losses. A similar topology with hybrid pole configurations, i.e. adjacent poles using asymmetric inset PMs and symmetrical V-shape PMs alternatively, has been proposed and employed in an IPM machine in [46] and [47] as shown in Fig. 10 (b). The hybrid pole AIPM machine shows torque enhancement and torque ripple reduction compared with a V-shape IPM benchmark, although the torque density is slightly smaller than the symmetrical inset IPM benchmark. Besides, compared with IPM machines whose PMs are buried inside the rotor core, the AIPM machine with inset PMs may require mechanical retaining such as rotor sleeve for high speed operation. Hybrid PM configuration combining NdFeB and ferrite PMs is also employed [48] as shown in Fig",
            " Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (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. BA-05 8 To illustrate the MFS effect for torque density enhancement in various AIPM machine topologies, six typical AIPM rotor topologies in four categories, including AIPM-SS [23] in Figs. 6 (a)-(c), AIPM-SA [22] in Fig. 8 (a), AIPM-AS [46]-[47] in Fig. 10 (b), as well as AIPM-AA1 [25], AIPM-AA2 [56], and AIPM-AA3 [57] that are shown in Figs. 14-15 and Fig. 16 (b) respectively, are redesigned with the same stator, rotor diameter, and PM usage to the conventional V-shape IPM machine in Toyota Prius 2010 [60]. Some key parameters of selected AIPM machines and IPM benchmark machine for Prius 2010 are given in Table II. The torque performance of these machines is calculated by using finite element (FE) analysis. The phase back electromotive forces (EMFs) of AIPM machines and the Prius 2010 benchmark are compared in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure17-1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure17-1-1.png",
        "caption": "Figure 17-1. Basis of manometric gas permeability apparatus",
        "texts": [],
        "surrounding_texts": [
            "The test piece is a disc, suitable dimensions being between 50 mm and 65 mm diameter and thickness between 0.25 mm and 3 mm. The lower the permeability of the rubber the more advantageous it is to use a thin test piece. It is essential that the means of clamping the test piece in the cell is such that there is no leakage of gas. After the cell and test piece have been assembled and the high pressure side filled with gas at the test pressure, the increase in pressure on the low pressure side is measured as a function of time. The standard suggests a conditioning period of at least 16 h to reach steady state conditions unless an approximate value of the diffusion coefficient is known, when the minimum conditioning time can be estimated from: t = 2D where: d = test piece thickness, and D = diffusion coefficient. In the steady state, a plot of pressure change against time should be linear. Any departure from linearity in the direction of increasing slope with time indicates that the steady state has not been reached. Leakage around the edges of the test piece will only result in an unexpectedly high rate of Permeability 353 pressure rise. Any tendency for the slope to decrease with time is an indication of a leak from the low pressure side. When a manometer system is used to measure pressure, the reservoir height is adjusted to bring the liquid level above a datum mark with the by pass valve open so that the pressure in the low pressure side is atmospheric. The bypass valve is then closed. As the gas diffuses through the test piece the increase in pressure causes the liquid level to fall and as the meniscus passes the datum line a clock is started (i.e. at zero time). The reservoir is then raised to bring the meniscus above the datum line and both time and the manometer reading are noted when again the meniscus passes the datum line. This process is repeated to give a series of readings. In this way the pressure reading (manometer reading) is always taken at constant volume of the low pressure side of the cell. The apparatus and procedure described require great care in setting up and in operation. The effort is eased considerably if an automatic pressure measuring device operating at effectively constant volume is used instead of the manometer^. Probably, all apparatus now has some form of pressure transducer. Improvements as regards accuracy and sensitivity can also be obtained by, for example, having a vacuum instead of atmospheric pressure on the low pressure side. Using a capillary, the permeability of the test piece can be calculated from: dhVxdx273x9Slxl0^xp dt AxPxTxlOUOQ where: dh/dt = rate of manometer rise (m/s), V = effective volume of low pressure side of the cell (m), d = test piece thickness (m), p = density of manometer liquid (Mg/m^), A = effective test piece area (m^), P = pressure difference across the test piece (Pa) and T = test temperature (K). 273 and 101300 are the standard temperature and pressure respectively. The factor 10\u0302 is due to the density being in MgW."
        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.14-1.png",
        "caption": "Figure 14.14. Transverse section through the pinion and rack.",
        "texts": [
            " However, it is not practical, at this stage of the book, to include each step of every proof. The results can always be verified by the method described earlier, in which all the angles are expressed in terms of <l>np and .pb. The expressions for n~ and nnr given by Equations (14.89 and 14.90) are substituted into Equation (14.87), and the value of 8G which satisfies the equation can then be seen by inspection, - fJ - <l>tp (14.91) This expression for 8G can be given a physical interpretation. Figure 14.14 shows a typical transverse section through the pinion, with the line of action in that section touching the base cylinder at E. If point A of the tooth profile is in contact with the rack tooth, it must lie position and Orientation of the Contact Line 399 in the plane of action, and the generator through A must touch the base cylinder at a point on the line where the plane of action touches the base cylinder. This means that G lies on the axial line through E, and its angular coordinate eG is given by the expression in Equation (14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000132_j.jallcom.2019.151792-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000132_j.jallcom.2019.151792-Figure2-1.png",
        "caption": "Fig. 2. Schematic illustration of (a) LMD system, (b) tensile samples cut from deposited sample, (c) schematic of 90 alternating scanning strategy.",
        "texts": [
            " The chemical composition of PREPed powder and deposited sample was analyzed by Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES, Agilent 725). Table 1 lists the chemical composition of PREPed powder and deposited sample, which is very close to the nominal chemical compositionwith a low oxygen concentration. The home-made LMD equipment consists of a 4 kW continuous fiber laser, a 5-axis numerical control manipulator, a coaxial powder delivery system and a deposition chamber kept constant with an oxygen level under 10 ppm. Fig. 2a shows the schematic diagram of the deposition system. All Ti-55531 samples were deposited on as-forged Ti-55531 alloy substrates and an alternating scanning strategy was employed with the schematic shown in Fig. 3. For the parameters optimization, cubic samples with a size of 15mm 15mm 15mm were fabricated with different parameters, as list in Table 2. The Z axis steps in all samples were set as 0.3mm. After selecting the useful parameter, tall walls with size of 50mm 20mm 50mm were fabricated for heat treatment and subsequent tensile tests",
            " For EBSD analysis, the accelerating voltage is 20 kV, current 2.4 is mA, step size is 3.5 mm (NordlysMax3, Oxford). The phase information was investigated by X-ray diffraction (XRD, D8 Advance, Bruker). The tensile test was performed by using an INSTRON 3382 machine with strain rate of 10 3s 1 and an extensometer was used. The tensile samples are of the gauge section with 10.0mm in length, 3mm in width and 1.5mm in thickness. Samples were cut parallel and perpendicular to the building direction, as shown in Fig. 2b. For each direction, five testing specimens were extracted and tested to obtain an average value of ultimate tensile strength (UTS) and yield strength (YS). The Vickers microhardness was performed with a load of 200 g for 10 s (WILSON-VH1150, BUEHLER). Previous studies have indicated that processing parameters of LMD significantly influenced the density and geometry integrity of as-deposited Ti-alloy parts. Thus, this section investigates the effects of processing parameters on the density and geometry integrity of processed Ti-55531 alloy, so as to work out the best preparation parameter for subsequent heat treatment and tensile tests"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000083_j.addma.2019.100935-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000083_j.addma.2019.100935-Figure6-1.png",
        "caption": "Fig. 6. Temperature distribution of the cylinder part when the heat source moves to the midpoint of (a); 1th layer (b); 5th layer (c); 10th layer(d); 20th layer(e); 30th layer(f); 40th layer.",
        "texts": [
            "3 \u00b0C, which occurred on the first layer. This error tends to decrease layer by layer. The minimum peak temperature error that appeared on the 20th layer is 10.6 \u00b0C. The average error of the simulated and experimental curves is 4.4 \u00b0C. Although the simulation results lack some accuracy, they can provide the temperature variation trends for the deposition process. This still allows the thermal transfer behavior to be studied on the manufactured part as well as for the development of the dimensional control technique. Fig. 6 depicts the temperature distribution on the cylinder part with the number of layers at 1, 5, 10, 20, 30, and 40, respectively. The welding current was 60 A, welding voltage was 12.9 V, and the travel speed was 8 mm/s. It was shown that both the maximum temperature and the high-temperature region increase along with the layer number, and the temperature gradient also shows a downward trend. This is expected because the heat dissipation condition becomes poorer with the increase in layers. When the workpiece height is relatively low, the heat is prone to dissipation through the substrate plate (seen in Fig. 6 (a), (b) and (c)), and as a consequence the high-temperature area on the substrate plate becomes larger [25\u201327]. As the workpiece was \u2018growing tall\u2019, the heat accumulated on the workpiece (seen in Fig. 6 (d), (e) and (f)), and the high-temperature area on the substrate plate became smaller until it dropped to room temperature. The simulation results of a 40-layer cylinder component gives a clear understanding of the overall thermal transfer behavior during deposition process [28]. To analyze the thermal behavior for planning process parameters, the thermal cycle should be divided into different stages and discussed separately [29,30]. Fig. 7 shows the peak temperature and interlayer temperature of the midpoint in the different layers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002890_j.wear.2004.10.012-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002890_j.wear.2004.10.012-Figure1-1.png",
        "caption": "Fig. 1. The disc machine (a) and the configuration of the disc housing (b).",
        "texts": [
            " The decay of martensite gives rise to preferential ites for crack nucleation and propagation. The micropitting echanisms suggested previously are explained in terms of ubricant pressure effects inside the crack [30,31] or slip line eld theory [32,33] but with no reference to the steel mirostructure. re designed to work either with two rollers [29,34,35] or our rollers [33,36,37]. In this work, the experimental study f micropitting was carried out using a two-disc machine deigned at the University of Newcastle, which is schematically hown in Fig. 1a. A three-phase motor drives a lower shaft which is conected to the upper shaft via a pair of gears and two pairs of bearings. The disc samples are fitted at the other ends of the two shafts. Different loads can be applied at the extremity of the hanger which incorporates a spring to minimise dynamic loads and the load is transmitted via a pivot to the upper shaft and consequently from the upper shaft to the discs. The discs are enclosed in the disc housing, which contains lubricant and is cooled by water (see Fig. 1b). The lubricant is sprayed in-between the rolling discs by the means of a tube that comes down from the lubricant reservoir. The temperature of the sprayed lubricant is controlled by a cartridge heater situated at the entrance in the disc housing. The temperature of the lubricant in the disc housing is controlled by the water flow through the walls of the disc housing. The disc housing has an orifice where the lubricant can exit the system and flows into a heat exchanger where it is cooled. From the heat exchanger, the lubricant flows into a basin from where it is pumped back to the reservoir"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.1-1.png",
        "caption": "Figure 14.1. A helical rack.",
        "texts": [
            "16) A Pinion Meshed wi th a Rack 369 Due to the helical rotation of the gear teeth between the two transverse sections, the rack tooth profile at plane z must be displaced relative to that at plane z=O. The rack displacement ~ur corresponding to a gear rotation ~f3 was given by Equation (3.24), (14.17) If we choose the value of ~f3 in this relation equal to the helical rotation ~e given by Equation (14.16), we obtain the required relative displacement between the transverse rack sections at plane z=O and plane z, z tan I/Ip (14.18) For a rack with helix angle I/I~, the value of this relative displacement is equal to (z tan I/I~), as we can see in Figure 14.1. We therefore substitute this expression for ~ur in Equation (14.18), and it is immediately clear that the rack helix angle must be equal to the operating helix angle of the gear, 1/1' r (14.19) 370 Hel ical Gears in Mesh A relation between the operating pressure angles and the operating helix angle of the gear was given by Equa t i on (14. 9) , tan I/Itp cos \"'p and in Equation (14.2) we gave the corresponding relation between the angles in the rack, tan I/I~r tan I/Itr cos \"'~ Since we have just proved that I/Itp and \"'p are equal to I/I tr and \",~, it is clear that the two normal pressure angles must also be equal, (14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000012_s11431-019-9506-5-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000012_s11431-019-9506-5-Figure8-1.png",
        "caption": "Figure 8 (Color online) Finite element model in ANSYS software.",
        "texts": [
            " Based on the proposed model, the meshing characteristics of the spur gear pair with tip relief and surface wear are analyzed. The finite element method is used to verify the meshing characteristics obtained from the proposed method. The finite element model is established in ANSYS software and the gear pair is meshed using Plane182. Conta174 and Targe170 are used to simulate the contact relationship among tooth flanks. The tooth profile information is imported into ANSYS to establish irregular worn tooth profiles (Figure 8). The mesh stiffness obtained from the proposed method and the finite element method is shown in Figure 9. The mesh stiffness decreases at moment A due to the severe wear at the tooth root of the pinion. The mesh stiffness obtained from the two methods is coincident (Figure 9) and the maximum error is 8.68% (Table 2). It is remarkable that the efficiency of the proposed method is much higher than the finite element method. The proposed method costs 4 s to calculate the mesh stiffness for a mesh cycle, while the finite element method costs 2 h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.13-1.png",
        "caption": "Figure 13.13. Unit vectors at point A.",
        "texts": [
            "42) The axial pitch in this equation is still represented by the same symbol Pz' since it is independent of the radius. Lastly, we introduce the transverse base pitch Ptb and the normal base pitch Pnb' defined on the developed base cylinder, with similar relations existing between them and the axial pitch. Ptb 211'Rb (13.43) N Pnb Ptb cos \"'b (13.44) Pz Pnb (13.45) sin \"'b Unit Vectors Associated with the Gear Helix at A The point at radius R on the tooth profile in the transverse section at plane z=O is labelled AO' as shown in Figure 13.13, and a typical point on the gear helix through AO is labelled A. We will now derive expressions for a set of unit vectors associated with the gear helix at A. These vectors are in the directions of the tangent, the principal normal, and the binormal to the helix. The first step is to calculate the position vector from the coordinate origin to point A, whose position is determined by the position of AO' and the value of the angular coordinate eA. The x and y coordinates of A can be written down immediately in terms of R and eA, and since A lies on the gear helix through AO' the z coordinate is given by Equation (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure7-1.png",
        "caption": "Fig. 7. Variations in C i j \u2013C i \u2013P chain.",
        "texts": [
            " 5 , b i j \u2212 b i = 1 2 \u03b5( j)(d i + \u03b4d i j ) R Bi (I + [ \u03b4\u03c8 i ]) i ; \u03b5( j) = { 1 , j = 1 \u22121 , j = 2 (7) where \u03b4\u03c8 i = [ 0 \u03b4\u03c8 yi \u03b4\u03c8 zi ]T is the orientation error of link B i 1 B i 2 with respect to the axis of rotation of the i th active revolute joint, and \u03b4d i is the variation of B i 1 B i 2 that is supposed to be equally shared by the connecting bar of the parallelogram. According to Fig. 6 , c i j \u2212 b i j = l i w i + \u03b4l i j w i + l i \u03b4w i j (8) where \u03b4l i is the variation in the length of link B i j C i j along the direction w i = [ w ix w iy w iz ]T = (c i \u2212 b i ) /l, and \u03b4w i j is the variation in the direction that is perpendicular to w i . According to Fig. 7 , c i \u2212 p = (I + [ \u03b4\u03c9 ])(r + \u03b4r i ) R z (\u03b7i + \u03b4\u03bei ) j (9) 2 Throughout this paper, [ \u00b7] = CPM (\u00b7) denotes the cross-product matrix (CPM) where \u03b4\u03c9 = [ \u03b4\u03b1 \u03b4\u03b2 \u03b4\u03b3 ]T represents the small-amplitude angular displacements of the end-effector with respect to the reference frame, and \u03b4r i , \u03b4\u03bei are the variations of the manufacturing errors of the mobile platform. Moreover, c i j \u2212 c i = 1 2 \u03b5( j)(I + [ \u03b4\u03c9 ])(d i + \u03b4c i ) R z (\u03b7i + \u03b4\u03bei )(I + [ \u03b4\u03b6i ]) i ; \u03b5( j) = { 1 , j = 1 \u22121 , j = 2 (10) where \u03b4\u03b6i = [ 0 \u03b4\u03b6yi \u03b4\u03b6zi ]T is the orientation error of link C i C i j with respect to unit vector R z (\u03b7i ) i in terms of manufacturing errors, and \u03b4c i is the variation of C i 1 C i 2 that is supposed to be equally shared by the connecting bar of the parallelogram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.9-1.png",
        "caption": "Figure 13.9. Helix through point AO'",
        "texts": [
            "17) In our study of the tooth shape of a helical gear, we are not considering a ro~ation of the gear, but a rotation of the tooth profile as we move axially along the gear. We therefore replace I),,~ by the prof i Ie rota t i on 1),,9, and for I)\"u we r substitute the expression (z tan ~r)' which is the relative displacement between the rack tooth profiles in the two transverse sections. We then obtain the following expression for the angle 1),,9, z tan 1),,9 Rs \"'r (13.18 ) 318 Tooth Surface of a Helical Involute Gear The Helix and the Involute Helicoid A helix is a spatial curve which can be defined in the following manner. If a rigid bar CA, as shown in Figure 13.9, moves so that one end C travels along a fixed line, while the bar remains perpendicular to the line and rotates through an angle proportional to the distance travelled by C, the path followed by the other end A is a helix. The motion can be described by the following equation, kz (13.19) where OA is the angle the bar makes with a fixed direction, OAO is the initial angle, z is the distance travelled by point C, and k is a constant. The value of z at which the bar has made a complete revolution is known as the helix lead L"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003815_tmag.2008.922782-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003815_tmag.2008.922782-Figure1-1.png",
        "caption": "Fig. 1. Halbach array PM spherical motor. (a) Working principle. (b) Distribution of Halbach array PM.",
        "texts": [
            " In order to further improve the performance of PM spherical motors, a Halbach array permanent-magnet spherical motor is proposed in this paper, since the Halbach array magnetic structures have inherently sinusoidal air gap magnetic field distribution, higher air gap flux density, and good self-shielding in a single DOF motor [9], [10]. Three-dimensional (3-D) magnetic field produced by the ball-shaped Halbach array rotor is analyzed. The Halbach array PM spherical motor and conventional magnet array spherical motor are compared in terms of spherical harmonic component and amplitude of air-gap flux density and of the torque. The influence of radial-magnetized position of magnetic poles on air-gap flux density is also discussed in this paper. Fig. 1(a) shows the structure of the Halbach array PM spherical motor. The Halbach array spherical magnets are attached to the equator of the rotor, which is shown in Fig. 1(b). The Halbach spherical magnets can be realized from discrete premagnetized segments fabricated from sintered NdFeB and SmCo segment. The rotor structure parameters of the Halbach array PM spherical motor include latitudinal angle , inner radius of magnet , and outer radius of magnet . Digital Object Identifier 10.1109/TMAG.2008.922782 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. The air-gap flux density of the Halbach array PM spherical motor can be expressed as [11] B1= B1r B1 B1' = / n=2;4;"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002921_s0165-0114(03)00135-0-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002921_s0165-0114(03)00135-0-Figure1-1.png",
        "caption": "Fig. 1. The ball and plate system.",
        "texts": [
            " Simulation results have shown that the hierarchical fuzzy control scheme can control the ball from a point to another without hitting the obstacles and in the least time. c\u00a9 2003 Elsevier B.V. All rights reserved. Keywords: Trajectory tracking; Trajectory planning; Fuzzy control; Genetic algorithm; Ball and plate system A ball moving on a beam is a typical nonlinear dynamic system, which is often adopted to prooftest diverse control schemes [1,3,5,6,7]. Ball and plate system is the extension of the traditional ball and beam problem that moves a metal ball on a rigid plate as shown in Fig. 1 [4]. The slope of the plate can be manipulated in two perpendicular directions, so that the tilting of the plate will make the ball move on the plate. In this paper, a trajectory planning and tracking problem is Supported by the National Natural Science Foundation of China (No. 60174015) and the Basic Research Foundation of Information Science College of Tsinghua University. \u2217 Corresponding author. E-mail address: zlh@mail.tsinghua.edu.cn (N. Zhang). 0165-0114/$ - see front matter c\u00a9 2003 Elsevier B",
            " Section 2 gives the control requirements, system parameters, and mathematical model of the ball and plate system in detail. Section 3 introduces the hierarchical fuzzy control scheme and the detailed design steps of the fuzzy controllers in planning, supervision and tracking levels, respectively. Section 4 presents how to use the genetic algorithm to optimize the parameters of the fuzzy planning controller and shows the simulation result. Finally, Section 5 concludes the paper. The ball and plate system is shown in Fig. 1, where a metal ball stays on a rigid square plate with each side length of 1 m. The slope of the plate can be manipulated by two perpendicularly installed step motors, so that the tilting of the plate will make the ball moving. The ball\u2019s position is measured using a CCD camera. It is required to control the ball from point A (0, 0.33) to point G (0.84, 1) without hitting the obstacles and take as little time as possible. The path must be A \u2192 B \u2192 C \u2192 D \u2192 E \u2192 F \u2192 G as shown in Fig. 2. In order to compare diFerent control schemes easily, all concerned parameter values are listed in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003081_j.jmatprotec.2004.04.220-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003081_j.jmatprotec.2004.04.220-Figure2-1.png",
        "caption": "Fig. 2. Design of cutting surfaced specimens prior to precipitation annealing and design of microhardness measurement of surfaced layer after precipitation annealing.",
        "texts": [
            "1 obtained in the surfaced layers after precipitation annealing was chosen as a response (y). For each experimental design nine specimens were required, that is four specimens to perform precipitation annealing under the conditions (T, t) defined by factorial points, i.e., corners of a square, and five specimens for five replicates of precipitation annealing under the condition (T, t) defined by a center point, i.e., the square center. The arc surfaced specimens were first cut to obtain three parts as shown in Fig. 2. The second act of cutting was performed at the smaller central part with 39 mm in length because it was assumed that this section of the surfaced layer was homogeneous. The central section was cut in the direction transverse to the direction of the surfaced weld to obtain ten slices each with 3 mm in thickness. From the pieces obtained side sections were cut off to obtain central sections with 23 mm in width. The central section was then cut along the central line of the surfaced layer. Thus twenty specimens, ten of them were \u201cleft\u201d and ten \u201cright\u201d, each with 11 mm in width were obtained",
            " The specimens required for the performance of the experimental design were chosen at random from the set of the left and right specimens available. The specimens were precipitation annealed in a laboratory tubular furnace in Ar shielding atmosphere under the temperature/time conditions specified in the experimental designs for the alloy given (Fig. 1). After precipitation annealing, the response (y), i.e., the microhardness HV0.1 of the surfaced layers, was measured at three measuring points as shown in Fig. 2. As a reference measurement result, i.e., a response (y), at the individual point of the experimental design, that is under individual temperature/time conditions of precipitation annealing, an average of three measurements was taken into account. The results obtained in the microhardness measurements in the surfaced layers after precipitation annealing under different conditions are given in Fig. 3. The results of the microhardness measurements given in Fig. 3a and d indicate that the AL-1 and AL-4 alloys achieved the highest microhardness at the center points of the experimental designs, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000061_physrevfluids.4.043102-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000061_physrevfluids.4.043102-Figure2-1.png",
        "caption": "FIG. 2. Schematic of an elastic rod of length L and arclength s that is clamped at s = 0. The rod is represented as a space curve in the (x, y) plane, which we parametrize by the tangent angle \u03c6(s, t ).",
        "texts": [
            " These representations could provide a basis for studying hydrodynamic interactions between spontaneously beating filaments and potential mechanisms for synchronization. We summarize and conclude in Sec. VI. A. Viscous dynamics of an elastic filament We idealize a beating flagellum or cilium as an inextensible unshearable planar elastic rod submerged in a fluid with viscosity \u03bd. Its motion is described by a set of geometrically nonlinear equations following Euler\u2019s elastica theory [28], with viscous stresses captured by nonlocal slenderbody hydrodynamics as we explain in Sec. II A 2. As shown in Fig. 2, we consider a filament with length L and diameter a such that \u03b5 = a/L 1, where \u03b5 is the slenderness ratio. We impose that one end of the filament is fixed, as in the case of a cilium attached to a wall or a flagellum affixed to a sperm head, and we assume clamped boundary conditions at that end. We parametrize the filament centerline with arc-length s \u2208 [0, L], and in the case of planar deformations conformations are fully described by the tangent angle \u03c6(s, t ). Expressions for the tangent and normal vectors to the curve follow as t\u0302 = cos \u03c6 e\u0302x + sin \u03c6 e\u0302y, (1) n\u0302 = \u2212 sin \u03c6 e\u0302x + cos \u03c6 e\u0302y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002996_s0022-0728(00)00114-5-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002996_s0022-0728(00)00114-5-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms of a CoHCF/GC electrode in phosphate buffer solution (pH 7.0) containing (a) 0.01, (b) 0.1 and (c) 1.0 mol dm\u22123 KNO3 as supporting electrolyte at a scan rate of 5 mV s\u22121.",
        "texts": [
            " The currents remained at 90% of that for the first cycle after 50 min continuous scanning (about 125 cycles), then, almost no changes in height and separation of cyclic voltammetric peaks were observed after 110 min repetitive scans (about 275 cycles). In addition, the CoHCF/GC electrode can withstand being exposed in air or being stored in solution for a period of time (at least one week) and the peak height and the separation of the peak potentials remain unchanged. The voltammetric responses of a CoHCF/GC electrode were also affected by the concentrations of supporting electrolyte. Fig. 2 shows the cyclic voltammograms of a CoHCF/GC electrode in three different concentrations of KNO3 (pH 7.0). With a decrease of the concentration of electrolyte, the redox peak potentials shifted in the negative direction. The dependence of the peak potential (Ep), the separation of the peaks potential (DEp) and the formal potential (E\u00b0%) on the concentration of supporting electrolyte are shown in Table 1. Fig. 3 shows the effects of alkali metal cations on the voltammetric behaviour of a CoHCF/GC electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000116_tcyb.2020.3035779-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000116_tcyb.2020.3035779-Figure7-1.png",
        "caption": "Fig. 7. One-link manipulator.",
        "texts": [
            " 6, we can obtain the number of event-triggered under the designed parameters is 618 in 30 s. From Figs. 1\u20135, we can obtain that all the signals of the system are bounded. The system output signal y can track yd and the tracking error converges to a small neighborhood of the origin in a fixed time. Meanwhile, we choose K11 = K12 = K21 = K22 = 20 to get good convergence performance and guarantee the boundedness of control signal. Example 2: This article consider a one-link manipulator with dynamics (see Fig. 7). Then, the dynamic model of the Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 29,2021 at 07:14:48 UTC from IEEE Xplore. Restrictions apply. system is given as follows: Mq\u0308 + Cq\u0307 + G sin(q) = \u03c4 B\u03c4\u0307 + H\u03c4 = u \u2212 Kmq\u0307 (75) where q, q\u0307, and q\u0308 represent the position, velocity, and acceleration of the angular, respectively. u denotes the input of the system. M denotes the inertia of the mechanical drive system, C denotes the viscous friction coefficient, G denotes the positive number related to the load mass and gravity coefficient, and \u03c4 is the torque of the dynamic subsystem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000959_j.apm.2021.03.051-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000959_j.apm.2021.03.051-Figure1-1.png",
        "caption": "Fig. 1. Quasi-static loading process of spur gear-pair.",
        "texts": [
            " The model presented in [65] is suitable for any length and shape of profile modification, but the amount of modification should be equal to the teeth deflection at the inner point of contact, in such a way that the effective start of contact is shifted to the theoretical location. However, as the teeth deflection depends on the transmitted load, such adjusted amount of modification is not possible when gears operate under non-nominal load conditions, or under variable load. In this paper, the analytic model of the MS, LSR, and QSTE presented in [65] is extended to consider non-nominal loads, which will also be valid for non-adjusted amount of modification. Fig. 1 depicts the quasi-static loading process of the spur tooth-pairs. It is assumed that output gear is fixed -i.e., points 1, 2, 3, and 4 in Fig. 1 do not move-, while the input gear rotates clockwise. If the gear is unloaded, the input gear can rotate up to position ( a ), corresponding to the tooth-pair j = 1 being in contact at point a 1 on the pressure line. At this position, the tooth-pair j = 0 is not in contact. As the load increases, due to the elastic deflections of the teeth, the input gear rotates and the input-gear tooth j = 0 approaches the corresponding mating tooth. This occurs up to position ( b ), in which tooth-pair j = 0 contacts at point i , outside the pressure line",
            " 2 , the \u03be parameters corresponding to different tooth pairs in simultaneous contact are related by: \u03be( i + j ) = \u03be( i ) + j (2) while the difference between the \u03be parameters corresponding to the theoretical inner and outer points of contact, \u03be inn and \u03be o respectively, is equal to the theoretical contact ratio, \u03b5\u03b1: \u03beo = \u03beinn + \u03b5 \u03b1 (3) Accordingly, the theoretical contact interval is described by \u03be inn \u2264 \u03be \u2264 \u03be o . But the teeth deflections under load induces an earlier start of contact and a delayed end of contact, resulting in a slightly longer effective contact interval -also named extended contact interval-, in which three different sub-intervals can be distinguished: premature contact ( \u03bemin \u2264 \u03be \u2264 \u03be inn ), theoretical contact ( \u03be inn \u2264 \u03be \u2264 \u03be o ), and delayed contact ( \u03be o \u2264 \u03be \u2264 \u03bemax ). The premature contact interval can be described from Fig. 1 . If assumed the total load induces a rotation on the input gear just to reach the position ( b ) -in such a way that positions ( b ) and ( c ) are coincident-, the point i (denoted by I for this specific case in [50 , 51] ) corresponds to the mesh-in impact point, the effective inner point of contact is located at point b 0 , and the premature contact interval is represented by interval b 0 e . As described in [64 , 65] , the limits of the extended contact interval, \u03bemin and \u03bemax , can be computed from: \u03bemin = \u03beinn \u2212 2 \u03c0 z 1 \u221a r b2 \u03d5 2 ( \u03beinn ) r b1 C p\u2212inn (4a) \u03bemax = \u03beo + 2 \u03c0 z 1 \u221a r b2 \u03d5 2 ( \u03beo ) r b1 C p\u2212o (4b) where \u03d52 ( \u03be ) is the QSTE -which is a function of \u03be - and C p \u2212 inn and C p \u2212 o can be computed as described in [64 , 65] ",
            " For any other SMS approach, numerical results may be slightly different, but the shape of the curves presented herein will be identical, and conclusions perfectly valid. As proved in [11 , 64 , 65] , the delay of the driven tooth respect to the driving tooth is equal for all the tooth pairs in simultaneous contact. This delay is different at any contact position, and therefore the LTE is not uniform along the meshing cycle; but for a given contact position, the delay is the same for all the tooth pairs in contact. In Fig. 1 , the length of the interval a 0 b 0 is equal to the length of the interval a 1 b 1 , the length of the interval b 0 c 0 is equal to the length of the interval b 1 c 1 , etc. Nevertheless, the above does not allow to conclude that the deflection is equal for all the pairs in contact. In fact, inside the additional contact intervals, part of the delay is covered to approach the driving tooth to the mating tooth to contact it. As shown in Fig. 1 , the delay interval (namely, the interval in the pressure line corresponding to the angle of delay) is represented by a 1 c 1 , whose length is equal to that of interval a 0 c 0 , which represents the delay interval as well. On the contrary, the deflection of tooth-pair j = 0 is represented by the interval b 0 c 0 , while the deflection of tooth-pair j = 1 is represented by the interval a 1 c 1 , which is longer. The difference between them is the approach distance, which is represented by interval a 0 b 0 in Fig. 1 . The approach distance \u03b4G can be expressed as [65] : \u03b4G ( \u03be ) = ( 2 \u03c0 z 1 )2 C p\u2212inn r b1 ( \u03beinn \u2212 \u03be ) 2 for \u03bemin \u2264 \u03be \u2264 \u03beinn \u03b4G ( \u03be ) = 0 for \u03beinn \u2264 \u03be \u2264 \u03beo \u03b4G ( \u03be ) = ( 2 \u03c0 z 1 )2 C p\u2212o r b1 ( \u03be \u2212 \u03beo ) 2 for \u03beo \u2264 \u03be \u2264 \u03bemax (7) Profile reliefs induce a new no-deflection sub-interval of the interval of delay. The profile modification can be expressed as [65] : \u03b4R ( \u03be ) = R \u2212inn \u03b4R \u2212inn ( \u03be ) for \u03beinn \u2264 \u03be \u2264 \u03beinn + \u03ber\u2212inn \u03b4R ( \u03be ) = 0 for \u03beinn + \u03ber\u2212inn \u2264 \u03be \u2264 \u03beo \u2212 \u03ber\u2212o \u03b4R ( \u03be ) = R \u2212o \u03b4R \u2212o ( \u03be ) for \u03beo \u2212 \u03ber\u2212o \u2264 \u03be \u2264 \u03beo (8) where R \u2212 inn and R \u2212 o are the amount of modification at the driven and driving tooth tips (or driving and driven tooth roots), respectively, \u03b4R \u2212 inn ( \u03be ) and \u03b4R \u2212 o ( \u03be ) the unitary functions describing the shape of modifications, and \u03be r \u2212 inn and \u03be r \u2212 o the lengths of modification",
            " For usual reliefs, as linear or parabolic, \u03b4R \u2212 inn ( \u03be ) and \u03b4R \u2212 o ( \u03be ) are expressed as: \u03b4R \u2212inn ( \u03be ) = ( 1 \u2212 \u03be \u2212 \u03beinn \u03ber\u2212inn )n (9a) \u03b4R \u2212o ( \u03be ) = ( 1 \u2212 \u03beo \u2212 \u03be \u03ber\u2212o )n (9b) with n = 1 for linear relief and n = 2 for parabolic relief. Finally, in order to ensure at least one tooth pair in contact at points of the unmodified involute profile at any contact position, the lengths of modification should verify: \u03b5 \u03b1 \u2212 ( \u03ber\u2212inn + \u03ber\u2212o ) \u2265 1 (10) The QSTE is the difference between the theoretical rotation of the driven gear and the actual one, for a given rotation of the input gear. In Fig. 1 , the actual position of the tooth j = 1 of the driven gear is described by point 3, while the theoretical position would correspond to contact at point c 1 , and therefore the output-gear tooth would be located at position described by point 3 \u2032 . The QSTE is represented by angle \u03d52 in Fig. 1 . If \u03b4( \u03be ) denotes the length of the delay interval when a given tooth pair (denoted by j = 0) is in contact at the contact point described by \u03be , the load at any tooth pair j is given by: F j ( \u03be ) = K M j ( \u03be ) ( \u03b4( \u03be ) \u2212 \u03b4G j ( \u03be ) \u2212 \u03b4R j ( \u03be ) ) (11) Accounting Eq. (2) and doing K M = 0 and \u03b4G = 0 outside the extended contact interval, and \u03b4R \u2212 inn = \u03b4R \u2212 o = 1 outside the theoretical contact interval, Eq. (11) can be expressed as: F j ( \u03be ) = K M ( \u03be + j ) ( \u03b4( \u03be ) \u2212 \u03b4G ( \u03be + j ) \u2212 \u03b4R ( \u03be + j ) ) (12) Applying Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003623_tmag.2006.892301-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003623_tmag.2006.892301-Figure2-1.png",
        "caption": "Fig. 2. Winding arrangement and structure of a 2-hp, 6-pole, 36-slot PM motor.",
        "texts": [
            " Therefore, the parameters in (1) including the inductances and back EMFs can be calculated using the solutions of transient FE-circuit-coupled computation. The inductances of each winding branch ( , , , and ) are calculated based on the energy perturbation method [4]. Note that the parameters obtained from the FE-circuit coupling contains the information of the fault location and the number of turns involved. As an example, a 2-hp, 6-pole, 36-slot PM motor is studied. The winding arrangement and geometry of this machine are shown in Fig. 2. Some of the inductance and back EMF profiles are shown in Fig. 3, which are obtained from the steady-state solutions of nonlinear transient FE computation covering a complete ac cycle. The dependency of rotor position and effect of saturation are considered. In Fig. 3(a), the self inductance of the shorted turn(s) (subwinding ) is given. The number of turns being shorted is varied between 1 and 3. In Fig. 3(b)\u2013(d), three mutual inductance profiles are given. They are the mutual inductance between the shorted turn(s) in phase (subwinding ) and the rest of the turns in the same phase (subwinding ), the phase winding, and the phase winding, respectively",
            " The reason is because the magnetic field of PM machines is dominated by permanent magnets not the winding currents. Therefore, the inductances obtained from nonlinear FE computation includes the effect of saturation and also keeps their relation with the number of turns in case of linear magnetic behaviors. Fig. 3(e) shows the self inductance profile of the shorted turns locating in slot A1 and slot B5, respectively. One can see that can be easily obtained by simply shifting the profile of using the angle between slot A1 and slot B5, seen in Fig. 2. The curve in Fig. 3(f) shows the back EMF of a single shorted turn located in slot A1, the back EMF of a single shorted turn located in slot B5, and the back EMF of two shorted turns located in slot A2. It can be observed that the back EMF is proportional to the number of turns shorted and its profile is associated with the fault location. From these results, one can conclude that if the FE-based phase variable model parameters are available for one fault case, the parameters for other fault cases can be easily obtained by shifting horizontally according to spatial location of the short circuit faults and vertically according to the number of turns being shorted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure8-14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure8-14-1.png",
        "caption": "Figure 8-14. Ways of producing biaxial extension. Top equibiaxial straining jig; bottom inflation method",
        "texts": [],
        "surrounding_texts": [
            "A compression stress/strain test is in many ways easier to carry out than a tensile test, and in view of the large number of appUcations of rubber in compression, should be more often used. Frequently, it would be logical for the 'test piece' to be the complete product and a compressive force applied as it would be in service. Usually a constant rate of deformation would be appropriate and the force and corresponding deformation recorded without attempts at calculating the resultant stresses and strains. Specially prepared test pieces for measuring material properties are usually in the form of a disc or short cylinder, the compressive force being"
        ]
    },
    {
        "image_filename": "designv10_4_0002841_1.1623761-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002841_1.1623761-Figure5-1.png",
        "caption": "Fig. 5 Sliding velocities and slip angles formed at the ballscrew and ball-nut contacts",
        "texts": [
            " (32) The substitution of Eq. ~26a! into Eq. ~23! to replace vo by vm yields vR vm 5 2~11g8 cos ao!cos a g8~cos b cos ao1sin b sin ao! (33) The angular velocities of ball\u2019s revolution and spinning, vm and vR , can be obtained by Eq. ~32! and Eq. ~33!. Now define a new coordinate system, (X j ,Y j ,Z j), ( j5i or o! such that its origin is positioned at the center of the contact ellipse of the screw or the nut. The X j-axis is defined to be tangential to the ball\u2019s circle formed on the b-n plane ~see Fig. 5!. The Y j-axis is defined to be parallel to the t-axis, and the Z j-axis is normal to the contact surface at the contact point, and thus points outward of the ball center. The slip angle formed at the nut between the Xo-axis and the opposite direction of the slip velocity (VY SA), as Fig. 5 shows, is defined as Co5tan21S VYo VXo D1p (34) For the contact point at the nut, the relationship between VXo and VYo is given as @9# Transactions of the ASME 13 Terms of Use: http://asme.org/terms Downloaded F VYo VXo 5 dvm1rb~vb cos ao2vn sin ao! 2rbv t (35) where VXo ,VYo 5 the components of the ball\u2019s sliding velocity relative to the nut in the Xo- and Y o-directions, respectively. Similarly, the slip angle C i at the screw, as shown in Fig. 5, is C i5tan21S VY i VXi D1p (36a) For the contact point formed at the screw, the relationship between VXi and VYi is @9# VYi VXi 5 d~vm2v!2rb@~vb2v cos a!cos a i2vn sin a i# rb~v t2v sin a! (36b) where VXi ,VYi 5 the components of the ball\u2019s sliding velocity relative to the screw in the Xi- and Y i-directions, respectively. The slip angles are applied to evaluate the frictional forces and frictional moments created at the contact surfaces of the nut and the screw. 2.5 Contact Angle. Figure 6~a!, shows the positions of the ball center and the raceway groove curvature centers with and without applied load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure8.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure8.4-1.png",
        "caption": "Figure 8.4. Span measurement over 3 teeth.",
        "texts": [
            " The tip circle of the gear is used as a datum, so any error in the value used for RT causes an error in the calculated value of ts' The tips of the caliper jaws are subject to wear, which of course alters the measured values. And lastly, for correct measurement, the caliper must be held so that it is symmetrical with respect to the tooth center-line, and the jaws touch each face of the tooth at the same height. The other two methods described in this chapter for measuring the tooth thickness of a gear are not subject to these objections. 196 Measurement of Tooth Thickness By measuring over several teeth, as shown in Figure 8.4, it is possible to make the measurement using the parallel faces of the caliper jaws, instead of the tips. This procedure is known as span measurement. An ordinary caliper can be used, without the adjustable stop of the gear-tooth caliper. We measure the length AA' over N' teeth, and from this measured length S, it is possible to calculate the tooth thickness ts of each tooth. Since line AA'is normal to the tooth profiles at A and at A', the line must touch the base circle at some point E. The involutes through A and A' meet the base circle at B and B', and we know that AE and A'E are equal to arc BE and arc B'E",
            "lS) In order to find the tooth thickness ts of a gear, we measure the length S, and ts is then found from Equation (S.lS), - (N'-ll1rm - Nm inv ~ cos ~s s S (S. 19) We have pointed already that, in the span measurement, the contact between the gear teeth and the caliper jaws takes place on the flat faces of the jaws. These faces are less subject to wear than the tips of the jaws, so the span 198 Measurement of Tooth Thickness measurement is generally more accurate than the measurement made with a gear-tooth caliper. In addition, there is no need for exact symmetry in the span measurement. If the caliper in Figure 8.4 is held so that the lengths AE and A'E are not qui te equal, there is no change in the measured length S. Number of Teeth in the Span We have not yet considered the number N' of teeth over which the span measurement should be made. Ideally, the caliper jaws should touch the tooth faces near the middle of their profiles. This means, as we pointed out earlier, that the contact should take place at a radius of approximately (Rs+e). The value of N' must therefore be chosen with this consideration in mind"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003734_j.actaastro.2008.04.009-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003734_j.actaastro.2008.04.009-Figure4-1.png",
        "caption": "Fig. 4. Relative acceleration of the otolith organs compared to the head of the occupant.",
        "texts": [
            " The semicircular canals sense angular velocity, while the otolith organs sense GIA (g level) due to either gravity or linear acceleration. While the otoliths have the dominant role, the body also contains other non-vestibular GIA sensors (graviceptors) that function analogously, such as proprioception. In this section we derive the accelerations and angular velocities sensed by these organs during parabolic flight, which lead to subjective sensations of orientation and motion. The otolith organ can be modeled as a simple springdamper-mass system (Fig. 4). A mass, the otoconia, embedded in a gelatinous membrane, is attached to the end of a set of lever arms, known as hair cells. The other ends of the hair cells are attached to the temporal bone of the head. Any acceleration of the head causes the hair cells to deflect relative to the temporal bone. (This describes a simplified and idealized set of hair cells, since there are many of them, with a wide range of directional sensitivities.) The hair cells transduce acceleration by measuring the relative movement of the otoconia, and send this information to the brain via the vestibular nerve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.8-1.png",
        "caption": "Figure 4.8. Meshing diagram of a rack and pinion.",
        "texts": [
            " If, therefore, the contact point is allowed to move down the tooth profile of gear 1 as far as the base circle, there will def inately be interference. Hence, in order to prevent the interference, it is first necessary that the path of contact should end at a point on line E1E2 lying above E1\u2022 The length T2E2 in Figure 4.7 must therefore be less than E1E2 , and the necessary condition for no interference can be expressed in the following form, < (4.18 ) The meshing diagram of a rack and pinion is shown in Figure 4.8. The line containing the path of contact touches the pinion base circle at E, and the end of the path of contact is shown as Tr \u2022 As before, interference would take place at the tooth fillets of the pinion if the contact point were to move down the tooth profile as far as the base circle, so point Tr must lie above point E. The length TrP must therefore be less than EP, and we obtain the following condition for no interference, ~ sin t/J < (4.19 ) 94 Contact Ratio, Interference and Backlash where apr is the rack addendum, measured from its pitch line",
            " The circle in gear 1 which passes through T2 is called the limit circle or the contact circle of gear 1, and its radius is labelled RL1 \u2022 The length Conditions For No Interference 95 E,T2 in Figure 4.7 is expressed as the difference between E,E 2 and T2E2, and we then use triangle C,E,T2 to derive an expression for the radius RL\" (4.20) In the case of the rack and pinion, the limit circle of the pinion is the circle passing through point Tr , the lower end of the path of contact. The radius RL of this circle can be read immediately from Figure 4.8, 2 ~2 Rb + [Rb tan 41 - sin 41] (4.21) Second Condi tion For No Interference Since the lowest contact point on a gear tooth is at the limit circle, and contact below the fillet circle must be prevented, it is clear that any gear pair must be designed so that the fillet circle of each gear is smaller than the corresponding limit circle, < (4.22) In order to allow for small errors in the center distance, it is advisable to design a gear pair so that the fillet circle of each gear is smaller than the limit circle by a definate margin"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003235_amc.2004.1297665-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003235_amc.2004.1297665-Figure2-1.png",
        "caption": "Fig. 2. Camber angle and turning radius",
        "texts": [
            " Assuming that the turning radius R is much bigger than the wheel base L, the turning radius R is represented as follows approximately. R = Lcot(@ - a1 +a*) (2) 0-7803-8300-1/04/$20.00 82004 IEEE. 193 AMC 2004 - Kawasaki, Japan If the side slip doesn't occur, the turning radius R is written as follows. R = L c o t p (3) The angle formed by vertical axis and a bicycle is named camber angle. When camber angle of bicycle is 6' degrees, the turning radius R can be represented by using the cylinder and the oval. In Fig.2, the soleplate of the cylinder means the circular orbit of bicycle at the camber angle 0 is 0 degrees. When the cylinder leans 0 degree, the shape of soleplate become an oval. In this case, the turning radius is assumed that the length between the focus of oval and the nearest point on the circumference geometrically. Using this relationship and approximation, turning radius R is represented as follows. ~ = ~ ~ ~ ~ a ~ ~ t p (4) Assuming that the direction angle is relatively small, the turning radius R is represented as follows approximately (5) R = -cosa L P Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000958_tie.2021.3068674-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000958_tie.2021.3068674-Figure9-1.png",
        "caption": "Fig. 9 The harmonics phase relationship of the 12s/10p machine at different operation states. (a) Motor operation. (b) Generator operation.",
        "texts": [
            " Namely, the phase difference between the forward rotating and static harmonics in the air-gap armature and PM flux densities are equal to \u03c9et0. At the same time, the phase difference of the backward rotating harmonics is equal to -\u03c9et0. Furthermore, the same phase difference characteristics exist between the air-gap armature flux density harmonics and the corresponding FMR rotors. The phase relationships of the dominant harmonics of the 12s/10p FSPM machine in different operation states are shown in Fig. 9. As shown in Fig. 9(a), when \u03c9et0>0, the 4 th , 6 th , 16 th , 18 th , and 28 th harmonics of air-gap armature flux density lead the corresponding harmonics of PM flux density and FMR rotors to generate positive PM and reluctance torques. However, the 8 th harmonic lags that of the PM flux density and generates negative PM and reluctance torques. At present, because the positive torque is greater than the negative one, the 12s/10p machine is in the motoring state at \u03c9et0>0. From Fig. 9(b), the phase relationships of harmonics are the opposite at \u03c9et0<0, which corresponds to the generator operation of the machine. The harmonics torque-angle curves and their PM and reluctance torque components are calculated by Maxwell stress tensor as shown in Fig. 10. As revealed by the following equation, the electromagnetic torque Tem(t) and the v th harmonic torque component Tem-v(t) can be calculated based on the obtained air-gap synthetic flux density and its v th radial and tangential harmonics respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.9-1.png",
        "caption": "Figure 7.9. A pinion with moderate undercut.",
        "texts": [
            "12 ) 184 Miscellaneous Circles We now write down a second relation from the triangle in undercut circle by calculating 8R and 8R at a number of radii, starting with the base circle radius Rbg , and gradually increasing the value of R until 8R is larger than 8R\u2022 Contact Ratio When One Gear Is Undercut We consider the case when gear 1 is undercut, and we first calculate the radii Ru1 and RL1 of the undercut and limit circles of gear 1, in order to determine which circle is larger. The meshing diagram is shown in Figure 7.9, for the case when the undercut ci rc Ie is smaller than the limi t Contact Ratio When One Gear Is Undercut 185 circle. The two circles are nearly equal in size, and to avoid complicating the diagram, the limit circle is not shown. However, it is possible to verify that the limit circle is larger than the undercut circle, by the following argument. The point where the undercut circle intersects line E1E2 , the common tangent to the base circles, is labelled U1\u2022 The lower end T2 of the path of contact lies between U1 and the pitch point, so T2 lies outside the undercut circle",
            " The radius of the undercut circle is found by trial and error, using Equations (7.11-7.13). In order to save space, only the final set of calculations is given below. Choose R = 56.555 mm ur - 23.378 - 0.651431 radians = - 37.324\u00b0 9' 8.345\u00b0 R tsg = 15.708 4>R = 4.488\u00b0 9R = 0.145643 radians = 8.345\u00b0 (7.11) (7.12) (7.13) (5.31) (2.18) (7.7) Since 9R is equal to 9R, we have chosen the correct value of R, and the undercut circle radius Ru is equal to 56.555 mm. This particular gear is shown in Figure 5.16. Example 7.3 The gear pair shown in Figure 7.9 has the following specification. Gear 1 is the gear which was described in Example 7.2, with a tip circle diameter of 140 mm, and the radius of its undercut circle was calculated in that example. Gear 2 has 25 teeth, and the diameter of its tip circle is 285 mm. The center distance is 195 mm. Show that the form circle of gear 1 is larger than its undercut circle, and then calculate the contact ratio. m=10, 4>5=20\u00b0, N1=12, N2=25 RT1 =70.0, RT2 =142.5, C=195.0 Rbl = 56.382 mm Rb2 = 117.462 4> = 26"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000850_j.addma.2021.101851-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000850_j.addma.2021.101851-Figure5-1.png",
        "caption": "Fig. 5. (a) Build layout and (b) image of completed build. The build plate is 252 mm \u00d7 252 mm for reference. (c) stack of five oversized tensile bars, (d) machined dimensions of tensile bars, (e) stack of three witness blocks and schematic of cross-sectioning for hardness, density, and microstructure (\u03bc-structure) characterization of the Z and Y planes. Dimensions are in millimeters.",
        "texts": [
            " A dynamic state is generated by a rotating blade that is forced downward through a cylinder of powder. Lastly, a qualitative assessment of the spreadability of the powder was made using the layer-wise imaging on the commercial LPBF machine. An image is recorded before and after each powder layer is spread. Regions with poor powder coverage and raking (streaks in the powder layer) are noted. A single build for each customized batch of powder (Fine, Medium, and Coarse) was carried out on a commercial laser powder bed fusion machine (EOS M2901). The build layout is shown in Fig. 5, which contains many extra parts not included in this study. Tensile bars with the loading axis along the X-direction (recoating direction) and corresponding witness blocks for hardness and microstructure (directly before or after tensile bars) in positions 1, 4, 5, and 8 are included in this study. The process parameters used in this study are listed in Table 3, which were used for each customized powder. Additionally, a ceramic recoating blade was used in line with the OEM recommendation. The PSDs indicate there is a fraction of powder greater than the prescribed layer thickness of 40 \u00b5m for the medium, coarse, and OEM powders",
            " Note that the process parameters are optimized for OEM powder (OEM 1) and not necessarily the optimal parameters for each of the three powder types. LPBF metals often exhibit location specific and directionally dependent microstructures and properties (i. e., heterogenous and anisotropic) [59]. These aspects were not studied; however, we compared and tested the same locations and sample direction (X direction) whenever comparing parts produced by the three powders. The geometry of the tensile bars and witness blocks are described next. The tensile bars were built oversized in stacks of five bars as shown in Fig. 5c. Witness blocks were 20 mm \u00d7 20 mm x 36 mm with a curved edge facing the recoating blade as shown in Fig. 5e. Tensile bars and witness blocks were stress-relieved on the build plate at 650 \u25e6C for 1 h in an argon atmosphere followed by furnace cooling. After stress-relieving, parts were wire-electrical discharge machined (EDM) from the build 1 Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose. J.S. Weaver et al. Additive Manufacturing 39 (2021) 101851 plate. Tensile bar stacks were wire-EDM into five separate bars. Tensile bars were machined and ground to the specified final dimensions in Fig. 5d. Only bars S2, S3, and S5, denoted in Fig. 5c, were tested. The actual cross-sectional dimensions of the gage section were measured with calipers on each specimen. Tensile tests were carried out according to ASTM E8 [60] on a MTS hydraulic load frame with a 50 kN load cell. A 25.4 mm clip gage was attached to the sample to measure strain. The sample was strained at a rate of 0.015 min\u2212 1 up to a strain of 0.05. The strain gage was removed, and the sample was further strained to failure at an increased strain rate of 0.05 min\u2212 1. Stress-strain curves were calculated up to a strain of 0",
            " The ultimate tensile strength (UTS) was determined from the maximum force and initial cross-sectional area. Elongation after failure (as opposed to elongation at failure) was measured by scribing lines spaced 25 mm apart prior to testing and pushing together broken specimens after testing to measure final distance between the scribed lines. The distance was measured using an optical microscope with a digital stage. Witness blocks were sectioned with a precision saw approximately 17 mm from the top of the build, Fig. 5e. The top half was reserved for Rockwell hardness (HRC and HRA) measurements following ASTM E18 J.S. Weaver et al. Additive Manufacturing 39 (2021) 101851 [61] on the cross-sectioned plane. The top and bottom surfaces were ground to a final step with 1200 grit paper. The bottom half of the witness block was sectioned further with a second cut to produce an approximately 5 mm thick slice, Fig. 5e. This 5 mm slice was quartered into samples for scanning electron microscopy and He pycnometer density measurements. All electron microscopy measurements were made on the witness block in position 4 of the build layout. Samples for electron microscopy were polished with a final step of 0.02 \u00b5m colloidal silica in a vibratory polisher. Electron backscatter diffraction (EBSD) was performed on a JOEL JSM7100F field-emission scanning electron microscope (SEM) in combination with an Oxford NordlysMax2 detector using a beam voltage of 20 keV, working distance of 15\u201317 mm, spot size setting of 12, and 4 \u00d7 4 camera binning",
            " X-ray diffraction (XRD) was performed on the same Z-axis samples with a Rigaku SmartLab system. Density measurements were made using a He pycnometer. One sample per witness block was measured 10 times each. This was completed for all four positions: 1, 4, 5, and 8. Prior to density measurements, samples were ground to remove burs from sectioning as well as the as-built surfaces that were present on two faces. Porosity was estimated using a solid density of 7.8 g cm\u2212 1. The porosity was also estimated from optical microscopy. Additional sectioning of witness blocks not shown in Fig. 5e was made for these measurements. After hardness testing, the top and bottom halves of witness blocks were sectioned to reveal the X-plane in the approximate middle of the witness block. This was done on all four witness blocks: positions 1, 4, 5, and 8. These samples were metallographically prepared similar to SEM samples; however, the final step of 0.02 \u00b5m colloidal silica was performed with an automatic wheel polisher instead of a vibratory polisher. Images were taken with a 5x objective and pixel size 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000625_j.msea.2021.141264-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000625_j.msea.2021.141264-Figure1-1.png",
        "caption": "Fig. 1. The detailed scan strategy diagram during LMD processing.",
        "texts": [
            " LMD experiments was carried out at a RC-LDM8060 facility (Zhongkeyuchen, China) equipped with a 2000 W diode fiber laser system, and the laser spot diameter of was 2.5 mm. During LMD processing, HEA samples were prepared at 45# steel substrate, and the oxygen content in working chamber was controlled below 50 ppm at N2 atmosphere. The deposition parameters of LMD are as follow: laser power (P) was 1000 W, scanning speed (V) was 800 mm/min, the hatch spacing (h) was 1 mm and the deposition layer thickness (t) was 0.3 mm. The scanning strategy was set to rotate 0\u25e6 between two continuous layers, as shown in Fig. 1. The dimension of LMD samples was 50 \u00d7 30 \u00d7 40 mm3. The phase analysis was carried out by X-ray diffraction (XRD) with a Cu-K\u03b1 radiation (\u03bb = 0.15406 nm, D/max2550, Japan). The microstructure of LMD samples were characterized by an Optical Microscope (OM, Leica/MeF3A), a field emission scanning electron microscopy (SEM, TESCAN, MIRA3) equipped with an energy dispersive spectrometer (EDS) and a transmission electron microscopy (TEM, JEOL 2100F. SEM observations were conducted through both back scattered electron imaging (BSE) and electron channeling contrast imaging (ECCI) modes. The crystal orientation and grain size were observed using electron backscatter diffraction (EBSD, FEI NanoLAB, 600i). TEM samples were prepared by electrolytic double injection technique, and an automatic twin-jet electro-polisher (Tenupol-5, Denmark) was used in a 10% HClO4+C2H5OH solution (238 K, 25 V). The tensile tests were conducted at a MST Alliance RT machine (MTS systems, Eden Prairie, MN, USA) at three different directions (see in Fig. 1) at room temperature (initial strain rate 1.0 \u00d7 10-3 s-1), and the thickness of the tensile samples is 1.5 mm, and for reproducibility, the samples in each direction were P. Niu et al. Materials Science & Engineering A 814 (2021) 141264 tested three times. Engineering strain during tensile deformation of LMD samples was analyzed via digital image correlation (DIC) method (Aramis system, GOM ARAMIS 5 M). Fig. 2 shows the XRD patterns of the LMDed Fe50Mn30Co10Cr10 HEA specimens at different direction, and both HCP \u03b5 and FCC \u03b3 phases are observed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000091_s10853-020-04566-x-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000091_s10853-020-04566-x-Figure4-1.png",
        "caption": "Figure 4 Main elements distribution of the as-built part in Fig. 3d: a region 1; b region 2. Figure 5 Microstructure evolution process of the as-built part.",
        "texts": [
            " Consequently, the proportion of the coarser microstructure in the XZ plane caused by the temper softening effect was larger than that in the XY plane, while the volume fraction of the finer microstructure in the XZ plane because of the remelting phenomenon is smaller than that in the XY plane. In order to further explore the microstructure evolution of the as-built sample after laser irradiation and rapid solidification, EDS analyses of the different microstructure (as revealed in Fig. 3d) are shown in Fig. 4. Compared to the blocky structures (region 1), the relative content of Cr element is much higher in the cell structure or the cellular dendritic grain (region 2), while the relative content of Fe element is interestingly lower. According to the characterization results of the SEM and the EDS, the evolution process of the microstructure within the as-built sample can be illustrated as follows. Upon the basis of the constitutional supercooling theory [30, 31] and the Mullins\u2013 Sekerka (MS) instability of the planar interface [32, 33], the solid/liquid interface stability is determined by the thermal gradient, interface energy and the solute-enriched layer (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-27-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-27-1.png",
        "caption": "Figure 5-27 Chaotic orbit for the Bernoulli map, Xn + l = 2Xn (mod 1).",
        "texts": [
            " To examine one such case, consider the extension of the concept of Lyapunov Lyapunov Exponents 193 exponents to a one-dimensional map *\u201e+!=/(*\u00bb) (5-4.5) In regions where /(*) is smooth and differentiable, the stretch between neighboring orbits is measured by \\df/dx\\. To see this, suppose we consider two initial conditions JCQ and x0 4- c. Then in Eq. (5-4.2) (5-4.6) \u20ac '0 Following Eq. (5-4.3), we define the Lyapunov or characteristic exponent as 1 N A = lim \u2014 \u00a3 log: AT-oo N k = Q (5-4.7) dx An illustrative example is the Bernoulli map xn+1 = 2xn (modi) (5-4.8) as shown in Figure 5-27. Here (mod 1) means jc(mod 1) = x - Integer(x) This map is multivalued and is known to be chaotic. Except for the switching value at x = \\, \\ f ' \\ = 2. Applying the definition (5-4.7), we find A = 1. Thus, on the average, the distance between nearby points grows as dn = d02\u00bb The units of A are one bit per iteration. One interpretation of A is that one bit of information about the initial state is lost every time the map is iterated. To see this, write xn in binary notation. For example, xn = (| + J + u + T2s) = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure17.17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure17.17-1.png",
        "caption": "Figure 17.17. Transverse section at plane z=F.",
        "texts": [
            "15) to calculate the load intensity at a number of different positions of the contact line, and then finding the corresponding fillet stress by means of Equation (17.64). We now consider the three types of gear pair defined earlier, and for each type we will determine the contact length Lc and the radius Rw for the critical position of the contact line. For VLFCR gear pairs, the highest point reached by a contact line with maximum load intensity is QF' shown in Figure 17.6, which is the highest point of single-tooth contact. The transverse section z=F is shown in Figure 17.17, with QF lying a distance (mp-1)ptb below the upper end of the path of contact. When the contact line is in this position, the contact length is equal to Lcmin ' and the radius Rw of point Aw can be read from Figure 17.17. When mF :!> 2-mp L L . F (17.65) c cmln cos .,pb R2 R2 + [v'(R2_R2) 2 (17.66) - (mp-1)ptb1 w b T b Equations (17.65 and 17.66) were derived from a consideration of gear 1. If we considered gear 2 instead, the cri tical position of the contact line would pass through point QO in the region of contact, and the contact length would be unchanged, due to the symmetry of the contact region. The equations are therefore valid for either gear, and this is why there are no subscripts 1 or 2 in the equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000763_j.bbe.2020.12.010-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000763_j.bbe.2020.12.010-Figure4-1.png",
        "caption": "Fig. 4 \u2013 The mechanical",
        "texts": [
            " The device uses torsion spring to store energy and act as a buffer during workers squatting. The stored energy is released to assist workers when standing up. The thigh support rod made of high strength material is connected to a fixed base. The shank support rod is connected to the load-bearing outer bezel and rotates freely within a certain range relative to the fixed base, which can meet the e overall mechanical structure. normal requirement of some activities such as walking, ascending and descending stair. The locking mechanism is presented in Fig. 4. The active disc is fixedly connected with pawl disc; it rotates relative to positioning disc and realize one-way positioning by engagement of ratchet and pawl. The active disc and pawl disc can be reversely rotated by manually operating a change-over switch to ensure workers adjust the device to any position according to the actual work requirements. Six compressed springs and six shaped springs were mounted on the pawl disc. The compressed springs were used to make sure the switch returns to the original position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000131_j.msea.2019.138230-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000131_j.msea.2019.138230-Figure6-1.png",
        "caption": "Figure 6: Cylindrical tensile specimens were built with a 10 mm diameter, 40 mm gauge length, and a 1% taper to the middle. Specimens were built in the vertical (90\u25e6) and diagonal (45\u25e6) orientations.",
        "texts": [
            " The 10 specimens of each orientation and scan strategy were split evenly between the two solution treatments. Solution treatments and aging were performed in a vacuum furnace at Winston Heat Treating (Dayton, OH, USA). Following the split solution treatment, all specimens were aged using the double-aging treatment per AMS 5663 [14] for IN718 employment in high-temperature applications. The parameters for the solution and aging treatments are shown in Table 3. After the final heat treatment, the parts were machined to their final dimensions as shown in Figure 6a. The cylindrical dog-bone specimens have a 10 mm diameter with a 40 mm gauge length. The gauge section included a 1% taper to improve strain measurements. Tests were performed with an extensometer at a strain rate of 0.0005-0.0006 strain per minute. Microstructural characterization was performed by collecting EBSD maps on each specimen. Five maps were collected on the core section for each scan strategy and annealing time in order to generate statistical data. Each map covered an area of approximately 920 \u03bcm by 730 \u03bcm (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure2-1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure2-1-1.png",
        "caption": "Figure 2-1. Choices for compression testing an engine mount",
        "texts": [],
        "surrounding_texts": [
            "If our knowledge of the properties and behaviour of rubbers, and hence our design rules, were such that we could predict the performance of the product accurately from tests on laboratory test pieces, then perhaps product testing would be rarely needed. The serious problem of the changes which the manufacturing process introduces can be overcome by obtaining test pieces from the product as discussed in chapter 4. However, the fact is that our understanding of the properties of rubber is simply not good enough to make performance predictions reliably in a great many cases, even if the test pieces come from the product. Hence, there will often be need to test the whole product to be sure that it will perform satisfactorily.\nIn the case of a new design it can be more expedient, and certainly effective, to subject prototypes to real service rather than to develop simulation tests. However, there are many cases when this is simply not sensible for time, cost or safety reasons. So, when real service trials have to be ruled out and prediction from laboratory material tests cannot be relied upon then there must be whole product testing.\nIt can be extremely difficult and/or expensive to devise tests to simulate service adequately and the justification for investment will be in proportion to the importance of the product in risk and/or sales terms. There is clearly much skill in designing rigs and test schedules which maximise information gained at minimum cost. In practice, there is danger of spending very large amounts and still not getting the simulation accurate enough, but most commonly the pressure is to under design the apparatus and to curtail the test programme to cut costs. By far the most difficult factor is when assessing durability and there are a number of degradative agents and some form of acceleration is required to reduce the time scale.\nThe same principle applies to quality control testing, but here there is much greater probability that the experience gained from proving the product initially will allow the quality of subsequent production to be reliably judged on the basis of tests on test pieces or the product test procedure can be simplified.\nSometimes a product test will give more valuable assessment of quahty for the same testing cost as needed for test pieces. This would be true, for example, for compression testing of a simple engine mounting (Figure 2.1) because the cost of moulding test pieces would be little different from the value of the mounting and the testing costs would be equal. It would be pretty pointless to go to the trouble of cutting test pieces from the mounting. When the value of the product is high, it is again a matter of judging whether control on test pieces gives sufficient confidence to reject the costly",
            "General considerations 25\nalternative of product tests. In this situation, non-destructive tests become particularly attractive.\nFor both quality control and design or performance evaluation purposes, it is relatively clear when whole product testing is desirable. The question then becomes one of whether it is considered essential and, if so, how sophisticated the experiment should be. This can only be answered, albeit with great difficulty, by weighing the cost against the risks and values involved. It should not of course be forgotten that, although we may not know fully how to make predictions from material tests, for many products experience will have shown what level of material properties will be satisfactory. It would probably be fair to say that in the past the tendency has been to be somewhat frugal with product tests. There now seems to be a trend towards more product tests being specified in standards. Generally, more people want to see evidence of fitness for purpose and CEN, for example, have a policy of producing performance rather than construction/material standards.\nOn first reaction, this would seem to be wholly good in that logically performance tests on the product should give the greatest certainty that it will be satisfactory in service. However, it is extremely difficult and expensive in most cases to devise adequate simulation rigs. The pressures of standardisation are to demand that they are produced quickly and almost inevitably without any obvious source of funding. The most expedient route often has to be taken and rarely are there the resources to properly evaluate and refine the methods decided on.",
            "The result can be methods which do not adequately fulfill their objectives in properly simulating service or are unnecessarily complex and unworkable within reasonable cost. Reproducability of rigs can be very bad. There is a world of difference between a rig for development purposes in one laboratory and multi laboratory product certification. If new methods are introduced which are ambiguously written or without full interlaboratory comparisons then problems and disputes are likely to follow. It can be concluded that it would be better to rely on material properties than on inadequate or ill-defined product tests but a well designed product test provides the best proof of fitness for purpose.\n1. BS 903 Part 2,1997. Guide to application of statistics to rubber testing. 2. Hill A, Buchholz H-V and Wenzel K. ACS Rubber Division 147*\u0302 Spring Meeting,\nPhiladelphia, May 2-5, 1995, Paper 56. 3. ISO 5725, in 6 parts, 1994, 1998. Accuracy (trueness and precision) of measurement\nmethods and results. 4. ISO TR 9272, 2005. Rubber and Rubber Products - Evaluating precision for test methods. 5. ASTM D4483, 2003. Standard practice for evaluating precision for test method standards\nin the rubber and carbon black industries. 6. Guide to the expression of uncertainty in measurement (GUM),\nBIPM/IEC/IFCC/ISO/IUPAC/IUPAP/OIML, corrected and reprinted 1995. 7. ISO/TS 21748, 2004. Guidance for the use of repeatability, reproducibility and trueness\nestimates in measurement uncertainty estimation. 8. BS PD 6461-4,2004. Practical guide to measurement of uncertainty. 9. ISO 19004, 2004. Evaluation of the sensitivity of test methods. 10. ASTM D6600, 2000. Standard practice for evaluating test sensitivity for rubber test\nmethods. 11. ISO 9001, 2000. Quality management systems - Requirements. 12. ISO/IEC 17025, 2000. General requirements for the competence of testing and calibration\nlaboratories. 13. ISO 10012, 2003. Measurement management systems - Requirements for measurement\nprocesses and measuring equipment. 14. ISO 18899,2004. Rubber- Guide to the calibration of test equipment. 15. Veith A G. Polym. Test., 7,4, 1987. 16. White 1. Eur. Rubb. J., 175, No. 2, 1993, p 10. 17. Spetz G. Polym. Test., 12,4, 1993. 18. Spetz G. Polym. Test., 13, 3, 1994. 19. Veith A G. Polym. Test., 12, 2, 1993. 20. Brown R P, Soekamein A. Polym. Test., 10,2, 1991. 21. Leete J L. ACS Rubber Division 155 '\u0302' Spring Meeting, Chicago, Paper 9, 1999. 22. Koopmann R K. ACS Rubber Division 143 Spring Meeting, Denver, Paper 44, 1993."
        ]
    },
    {
        "image_filename": "designv10_4_0003059_ias.1997.643036-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003059_ias.1997.643036-Figure15-1.png",
        "caption": "Fig. 15 Flux distribution due to excitation ofphase a in case of 25% eccentric rotor I ~ O the right.",
        "texts": [
            " The flux linkages and inductances of a given system of current loops can be found using this magnetic field. In the winding function method, the iron materials is assumed to be linear and infinitely permeable, whereas in the finite element analysis linear as well as non-linear iron materials can be considered. Fig. 14 reveals the magnetic flux distribution caused by the excitation of phase a only in case of non-eccentric rotor. It is clear that the magnetic forces on both sides of the machine are identical and this results in a balanced magnetic pull in all directions. On the other hand, Fig. 15 shows that the magnetic flux distribution on both sides of the machine cross section are not identical. This results in an Unbalanced Magnetic Pull (UMP) in a radial direction towards the right hand side. It is more convenient and the problem will be much more simplified if coupled magnetic circuits approach rather than magnetic fields approach for modeling of the synchronous machine is used. In the coupled magnetic circuit approach, the rotating magnetic fields will still be considered when writing the flux linkages of the rotating coupled circuits"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.8-1.png",
        "caption": "Figure 2.8. Tooth thickness and space width at radius R.",
        "texts": [
            " The tooth thickness ts at the standard 42 Tooth Profile of an Involute Gear pitch circle is described simply as \"the tooth thickness\", in the same way that the circular pitch at the standard pitch circle is called the circular pitch. The gap between the teeth, measured around the circle of radius R, is called the space width at radius R, and like the tooth thickness, the space width is generally measured on the standard pi tch circle. Since the tooth thickness, the space width and the circular pitch are all defined as arc lengths, as shown in Figure 2.8, it is clear that the sum of the tooth thickness and the space width at any radius R is equal to the circular pi tch at radius R. A gear tooth is shown in Figure 2.9, with points B, As and A on the tooth profile at radii Rb , Rs and R. We will derive an expression for the tooth thickness tR at radius R, assuming the tooth thickness ts is known, and we start by finding the polar coordinate 9R of point A, angle xCA angle xCAs + angle AsCB - angle ACB Tooth Thickness 43 The angle ACB is given by the involute function inv 'R' as we showed in Equation (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000039_j.addma.2020.101437-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000039_j.addma.2020.101437-Figure5-1.png",
        "caption": "Figure 5 \u2013 Visualization of both build jobs within this work",
        "texts": [
            " The corresponding surface normal azimuthal angle \ud835\udf09 will be 45\u00b0, 135\u00b0, 225\u00b0 and 315\u00b0 respectively. In the second build job the surface laser relation angle \ud835\udf01 will be defined as the constant parameter with a value of 120\u00b0 at each surface, similar to the specimen in the middle of the platform. Therefore, the parts will be tilted towards the laser according the position dependent laser incidence polar angle \ud835\udf13 and equation (2.6). The part geometry itself will not be affected by this procedure except the support structure beneath for wire EDM. Both build jobs are visualized in Figure 5. The twelve specimens on both build jobs shown partially transparent in Figure 5 were built for higher statistical accuracy if required. These measurements were not needed in this work and therefore the results of these specimens will be interpolated in the visualizations in section 3. Additionally the variation of the position dependent parameters \ud835\udf13 and \ud835\udf01 over one surface will be neglected in this work. Instead the areal center of gravity will be used in calculations. The resulting maximal error of this approximation is smaller than 1\u00b0. The orientation of the surfaces will be hereinafter abbreviated with F for front, B for back, L for left and R for right"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure3-1.png",
        "caption": "Fig. 3 Coordinate systems between the cutter head and imaginary generating gear",
        "texts": [
            " Equations for the Imaginary Generating Gear The concept of an imaginary generating gear is commonly used o explain the generating cutting process of bevel gears. This maginary generating gear is a virtual gear whose teeth are formed y the locus of the cutter blades, although its tooth number is not ecessarily an integer. In addition, while its rotation axis coincides ith the rotation axis of the machine cradle, rotation angles of the radle and work gear are timed relative in the generating process ut not in the nongenerating motion. Figure 3 shows the coordinate systems between the cutter heads nd generating gear. Coordinate systems St xt ,yt ,zt and d xd ,yd ,zd are rigidly connected to the cutter head and the maginary generating gear, respectively. Point Q is the pivot point f the cutter tilt mechanism on the machine plane. Sa, Sb, and Sc re auxiliary coordinate systems that describe the cutter tilt and he relative position between the cutter head and generating gear. s shown in Fig. 3, the axial distance measured from the tilt enter Q to the pitch plane of the cutter head is defined as tilt istance hd, which is a machine constant on the cutting machine. t should be noted, however, that Q is not necessarily in the cutter ead pitch plane. In the Gleason face milling process, because tilt enter Q is normally at the intersection point between the cutter ead axis and cutter blade tip plane. Point oA is a projection of the otation center oA of the outer head on the machine plane for imulating the dual head cutter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000409_j.addma.2020.101800-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000409_j.addma.2020.101800-Figure1-1.png",
        "caption": "Fig. 1. Illustration of additive manufacturing process: (a) building direction and sample geometry, and (b) scanning strategy.",
        "texts": [
            " Lastly, detailed discussions on the relationship between the phase velocity and the experimentally obtained parameters are given. 316L SS powder manufactured by nitrogen-gas atomization was purchased from Carpenter Powder Products. Prior to fabrication, the asreceived powder was sieved to 15\u201344 \u00b5m for good flowability. All samples in this study were printed using a Concept Laser Mlab 100 R Cusing\u2122 machine, equipped with Yb: YAG fiber laser with a wavelength of 1070 nm, a focus diameter of 50 \u00b5m, and maximum power of 100 W. The scan strategy, build direction (BD), and sample geometry are illustrated in Fig. 1. An island scanning strategy was used with checkerboard patterns of 5 \u00d7 5 mm squares. In each square, the scan direction was perpendicular to the adjacent island. To study the effects of defect density and defect mode on ultrasonic response, the hatch spacing was varied from 50 \u00b5m to 150 \u00b5m. Other printing parameters were kept C. Kim et al. Additive Manufacturing 38 (2021) 101800 constant, with laser power of 90 W, scanning speed of 600 mm/s, and layer thickness of 25 \u00b5m. Different hatch spacings resulted not only in varying defect densities, but also changed the defect formation mechanism, with lack-of-fusion porosity for small energy density (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001006_j.oceaneng.2020.108480-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001006_j.oceaneng.2020.108480-Figure2-1.png",
        "caption": "Fig. 2. Coordinate frames for the AIAUV (Credit: Arnt Erik Stene and Marianna Wrzos-Kaminska).",
        "texts": [
            " In this section, we provide the model and the mathematical definition of the tracking control problem for the AIAUV, Fig. 1. The AIAUV consists of n links connected by n \u2212 1 motorized joints. Each joint is treated as a one-dimensional Euclidean joint. To follow the convention used in the robotics community, the first link is referred to as the base of the manipulator. The base link is link 1, and the front link, where the end-effector is positioned, is link n. A visual representation of the relevant frames is given in Fig. 2. In the right corner of Fig. 2 the link frames (blue coordinate-systems) have been visualized for a completely outstretched robot. Note that link frame 1 corresponds to the base frame. The joints are numbered from i = 1 to n \u2212 1 such that link i and link i+ 1 are connected by joint i. Furthermore, the AIAUV is equipped with m thrusters, including one or more thrusters acting along the body of the AIAUV to provide forward thrust and tunnel thrusters acting through the links to provide stationkeeping capability. The AIAUV is considered to be a floating base manipulator operating in an underwater environment subject to added mass forces, dissipative drag forces, and gravity and buoyancy forces, which allows us to model the AIAUV as an underwater vehiclemanipulator system (UVMS), with dynamic equations given in matrix form by (Antonelli, 2014), (From et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000247_pime_proc_1950_163_020_02-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000247_pime_proc_1950_163_020_02-Figure1-1.png",
        "caption": "Fig. 1. Highest Position of \u2018Single-pair Tooth Contact",
        "texts": [
            " The phase in which the bending moment on a tooth is a maximum is that in which the whole transmitted force is applied to that tooth at the greatest distance from the root. This is not (usually) the phase of tip contact, because there the load is divided between two pairs of teeth, but it is the phase at which contact is about to begin (or has just ceased, according to the direction of rotation) at the root of an adjacent tooth in the same gear. Contact on the loaded tooth is then as far from the root as it can be for single-pair contact (Fig. 1). The ratio between tooth-load per unit-width and maximum bending stress is determined by the form and dimensions of the tooth, and in British Standard practice is equal to the quotient of the %rength factor\u201d Y and the diametral pitch P. Calculation of the strength factor ignores the so-called \u201cstress concentration\u201d associated with the fillet at the root of the tooth. I t also assumes that the simple theory of bending evolved for a beam of uniform cross-section is sufficientlv accurate when The stress concentration factor depends on the ratio of filletradius to root-thickness, and photo-elastic analysis shows that for British Standard tooth-form in a gear with about twenty teeth, the actual maximum bending stress is about 50 per cent higher than the British Standard formula suggests"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure1-1.png",
        "caption": "Fig. 1. Parallel Cartesian robotic manipulator: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " We grouped the various formulas in an initial Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s criterion and extensions of this criterion proposed by Voinea and Atanasiu and by Manafu. We focus on a brief presentation and a critical analysis of these criteria. We apply these criteria to determine the degree of mobility of a recent fully-parallel manipulator with elementary legs, the parallel Cartesian robotic manipulator CPM (Kim and Tsai, 2002; Kong and Gosselin, 2002; Carricato and Parenti-Castelli, 2002) presented in Fig. 1, which only contains revolute (R) and prismatic (P) joints. A serial kinematic chain is associated with each elementary leg linking the mobile platform to the fixed base. The mechanism has n = 10 kinematic elements (links), p0 = 3 prismatic joints adjacent to the fixed element, pn = 9 revolute joints non-adjacent to the fixed element and q = 2 independent closed loops. Each loop contains the same number and the same type of joints. The three legs are identical from a structural point of view. In each leg the direction of the prismatic joint and the axes of the revolute joints are parallel (P||R||R||R)",
            " (3) can give different results depending of the choice of independent closed loops. To overcome this flaw Manolescu and Manafu (1963) proposed to take into consideration only the maximum value of mobility given for the same mechanism by Eq. (3). Dudit\u0327a\u0306 and Diaconescu (1987) indicated that passive mobilities of common joints must not be taken into consideration in the calculation of Mc . Agrawal and Rao (1987) introduced some additional terms in Eq. (3) to take into consideration the existence of multiple joints in the multi-loop mechanism. From Fig. 1 we can simply determine by inspection the values of the structural parameters necessary to calculate the mobility of the parallel robot CPM. This mechanism has p = 12 joints (3 prismatic and 9 revolute joints) and q = 2 independent loops. Each joint has one degree of mobility (fi = 1). Passive mobilities do not exist in the joints of this mechanism. The two independent loops have the same motion parameter b = b1 = b2 = 5. Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s mobility criterion, defined by Eqs. (1)\u2013(3) or by any other derived formula proposed by different authors mentioned in this section, gives M = 2",
            " It is therefore very difficult to make the difference between a real zero and a very small numerical value close to zero in the calculation of the determinants. This drawback is specific to all methods for mobility calculation based on rank calculation of constraint equations in a given position of the mechanism with joint location defined numerically. Symbolic calculation of the rank could overcome these limits if the constraint equations are defined symbolically in a generic position, as it will be presented in this section. The basic kinematic structure of the parallel Cartesian robotic manipulator presented in Fig. 1 is obtained by concatenating three legs denoted by A (0 \u2261 1A-2A-3A-4A-5A), B (0 \u2261 1B -2B -3B -4B -5B) and C (0 \u2261 1C -2C -3C -4C -5C). The first link 0 \u2261 1X of each leg is the fixed platform and the final link is the moving platform 5 \u2261 5X (X = A,B,C). The first joint of each leg is actuated. We denote by d1X and d\u03071X (X = A,B,C) the finite displacements and the velocities of the actuated prismatic joints and by \u03d5iX and \u03d5\u0307iX (i = 2,3,4 and X = A,B,C) the finite displacements and the angular velocities of the passive joints. We note that all revolute joints are passive joints. The closure equations of the parallel Cartesian robotic manipulator presented in Fig. 1 can be established by the condition that the linear (0vH ) and angular (0\u03c9H ) velocity of point H situated on the mobile platform (expressed in the reference system O0x0y0z0 \u2013 see Fig. 2) must be the same in the three legs (H \u2261 HA \u2261 HB \u2261 HC):[ 0vHA 0\u03c9HA ] = [ 0vHB 0\u03c9HB ] = [ 0vHC 0\u03c9HC ] , (7) or [ 0vHA 0\u03c9HA ] \u2212 [ 0vHB 0\u03c9HB ] = [0] (8) and [ 0vHA 0\u03c9HA ] \u2212 [ 0vHC 0\u03c9HC ] = [0]. (9) Eqs. (8) and (9) represents the closure equations of the closed loops 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b7 -2B -1B \u2261 0 and 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 -2C -1C \u2261 0. These loops can be considered as two independent closed loops of the Cartesian robotic manipulator, presented in Fig. 1. By calculating the velocity of point H in the three legs of the parallel robotic manipulator Eqs. (8) and (9) lead to the following sets of linear equations: [A ] [ d\u0307 \u03d5\u0307 \u03d5\u0307 \u03d5\u0307 d\u0307 \u03d5\u0307 \u03d5\u0307 \u03d5\u0307 ]T = [0] , (10) 1 6\u00d78 1A 2A 3A 4A 1B 2B 3B 4B 8\u00d71 [A2]6\u00d78 [ d\u03071A \u03d5\u03072A \u03d5\u03073A \u03d5\u03074A d\u03071C \u03d5\u03072C \u03d5\u03073C \u03d5\u03074C ]T = [0]8\u00d71, (11) [A]12\u00d712 [ d\u03071A \u03d5\u03072A \u03d5\u03073A \u03d5\u03074A d\u03071B \u03d5\u03072B \u03d5\u03073B \u03d5\u03074B d\u03071C \u03d5\u03072C \u03d5\u03073C \u03d5\u03074C ]T = [0]12\u00d71. (12) Fig. 2 presents the notations associated with the leg A. Similar notations are used for the legs B and C",
            " Euler\u2019s formula known in the theory of graphs and proposed by Hochman (1890) to calculate the number of independent closed loops q of a multi-loop mechanism (q = p \u2212 m + 1 = p \u2212 n) must be restricted, in the general case, to the structural independence (in the sense of the theory of graphs). Property 2. Structural independence of q closed loops in a multi-loop mechanism does not involve, in the general case, the kinematic independence of the q closed loops. By using Eq. (6) we get the right value of mobility of the parallel Cartesian robotic manipulator presented in Fig. 1 (M = 12 \u2212 9 = 3). We recall that the rank of the matrices [A1]6\u00d78, [A2]6\u00d78 and [A]12\u00d712 can be calculated numerically or symbolically. The numerical calculation gives to us the instantaneous rank in a given position of the mechanism defined by numerical values of joint variables and geometric parameters. The symbolic calculation gives us the global rank in a nondefined position of the mechanism without indicating numerical values of the joint variables and geometric parameters. We just use the symbolic definition of the matrices as presented in Appendix A",
            " , q) of the linear sets of kinematic constraint equations of the q loops if the rank of the linear set of kinematic constraint equations of (i + 1)th loop is equal to the dimension of the range of the restriction of Fi+1 to the kernel of F1-2-\u00b7\u00b7\u00b7-i ri+1 = dim(RF(i+1)/KF(1-2-\u00b7\u00b7\u00b7-i) ), i = 1,2, . . . , q \u2212 1. (29) The proof of Eqs. (26) and (27), presented in Appendix B, is obtained by recurrence on the basis of the demonstration presented by Fayet (1995) for q = 2. The proof of Eq. (28) results directly from Eq. (26) by taking into consideration that ri+1 dim(RF(i+1)/KF(1-2-\u00b7\u00b7\u00b7-i) ), i = 1,2, . . . , q \u2212 1. (30) The proof of Eq. (29) results directly from Eqs. (26), (28) and (30). As we have seen, for the parallel Cartesian robotic manipulator presented in Fig. 1, the symbolic calculation of the rank of the matrix (69) with MAPLE\u00ae gives r = rA-B-C = rank(A) = 9. This result can also be obtained by using Eq. (26): r = r1 + q\u22121\u2211 i=1 dim(RF(i+1)/KF(1-2-\u00b7\u00b7\u00b7-i) ) = r1 + dim(RF(2)/KF(1) ) = r1 + dim(KF(1)) \u2212 dim(KF(1) \u2229 KF(2)) = 5 + 7 \u2212 3 = 9, where r1 = 5 is the rank of [A1]6\u00d7N and dim(RF(2)/KF(1) ) = dim(KF(1)) \u2212 dim(KF(1) \u2229 KF(2)) = 7 \u2212 3 = 4 is the dimension of the range of the restriction of F2 to the kernel of F1. The dimension of the kernel of F1 and the dimension of the intersections of the kernels of F1 and F2 are determined by using symbolic calculation with MAPLE\u00ae ",
            " The rank of [A1]6\u00d78 gives the motion parameter b1 of the first loop (0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b7 -2B -1B \u2261 0) before the closure of the second loop. The dimension of the range of the restriction of F2 to the kernel of F1 gives the number of independent constraints associated to the second loop by taking into account the closure of the first loop. The value of dim(RF(2)/KF(1) ) = 4 is different from the rank of [A2]6\u00d78 (r2 = rank([A2]6\u00d78 = 5). The parallel Cartesian robotic manipulator presented in Fig. 1 does not obey Eq. (29). For this reason, mobility calculation considering the same motion parameter for the both loops fails. The following interpretation could be given to this result. The rank of [A2]6\u00d78 gives the motion parameter b2 = 5 of the second loop (0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 -2C -1C \u2261 0) before the closure of the first loop. In fact, we have to consider the number of independent constraints associated to the second loop by taking into account the closure of the first loop. We have to take into account the dimension of the range of the restriction of F2 to the kernel of F1 instead of motion parameter b2 = 5",
            " Only four independent motions (vx, vy, vz,\u03c9z) exists in this case between the extreme elements 1C and 0 (Fig. 5). These velocities form the base of RF(2)/KF(1) . Two other examples of parallel mechanisms with uncoupled translational motions and with decoupled Sch\u00f6nflies motions proposed by the author of this paper (Gogu, 2002) are presented to illustrate the applicability of Eq. (26). Fig. 6 presents a parallel robotic manipulator (Gogu, 2002) with three legs derived from the solution presented in Fig. 1 by eliminating the actuated prismatic joint from the leg C. In this case, leg C has just a guiding role by constraining the mobile platform to a planar motion. This mechanism has p = 11 joints (2 prismatic and 9 revolute joints) and q = 2 independent loops. Each joint has one degree of mobility (fi = 1). The two independent loops have also the same motion parameter b1 = b2 = 5 whichever set of independent loops is chosen. Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s mobility criteria give M = 11 \u2212 (5 + 5) = 1. This is an erroneous result",
            " Their i i applicability is limited to the mechanisms that have the rank (r) of the homogeneous linear set of kinematic constraint equations equal to the sum of the motion parameters (bi ) associated with the q structurally independent closed loops (i = 1,2, . . . , q) r = q\u2211 i=1 bi . (31) The mechanisms that do not obey Eqs. (29) or (31) do not fit Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s criterion for mobility calculation of multi-loop mechanisms presented in Section 2. These mechanisms have nothing \u201cenigmatic\u201d or paradoxical, as the literature considered. They just obey Eq. (26), as the parallel Cartesian robotic manipulator presented in Fig. 1. Paradoxical is the fact that Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s criterion is used inappropriately for these mechanisms. This can be explained by the lack of more appropriate formulas for quick calculation of mobility of multi-loop mechanisms with a wider applicability. We can conclude that Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s criterion for mobility calculation of multi-loop mechanisms is restricted to the mechanisms that have the rank (r) of the homogeneous linear set of kinematic constraint equations equal to the sum of the motion parameters (bi) associated with the q structurally independent loops (i = 1,2, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure6-1.png",
        "caption": "Fig. 6. CHTCs of the circumferential and axial water jackets.",
        "texts": [
            " The structured mesh and turbulent model (k-epsilon) are used in the CFD model. As shown in Fig. 5, the velocity distribution of the circumferential water jacket is uniform, which matches with Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 01:31:42 UTC from IEEE Xplore. Restrictions apply. the assumption of straight piping flow. However, for the axial water jacket, the velocity changes steeply near the elbows. The impact of the elbows on the CHTC is shown in Fig. 6. The CHTC distribution of the circumferential water jacket is more uniform than that of the axial water jacket. For the axial water jacket, as the velocity changes steeply near the elbows, the CHTC is much bigger. The average CHTCs calculated by the analytical method and CFD are given in Table I. The analytical result agrees with the CFD result perfectly for the circumferential water jacket rather than the axial water jacket. It is concluded that the analytical method is only effective for the circumferential water jacket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003160_20.620439-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003160_20.620439-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the primary coil and the secondary coil.",
        "texts": [
            " Grover [19] is an encyclopedic source of information, numerical and otherwise, for inductances of coils of various shapes, and includes some early material on mutual inductance Manuscript received May 14, 1995: revised November 12, 1996. K.-B. Kim is with the Living System R&D Center, SamSung Electronics E. Levi, 2. Zabar, and L. Birenbaum are with the Electrical Engineering Publisher Item Identifier S 0018-9464(97)04902-9. Co., Suwon-city, Korea. Department, Polytechnic University, Brooklyn, NY 11201 USA. primary coil between noncoaxial circular coils. The configuration of the coils used in this analysis is drawn in Fig. 1. The primary and secondary coils have the dimensions shown in the picture: the thickness of the secondary H s is assumed to be relatively small, that is, less than the depth of penetration 6 if it is a single-tum solenoid conductor; otherwise, if it is a multiturn coil, the wire diameter is assumed to be less than 6. The primary coils of tubular linear motors or coil guns usually have multitum windings to match the impedance level of the source [2]. Therefore, it is reasonable to assume that the current distribution in the primary coil is uniform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000359_j.ijmecsci.2020.106150-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000359_j.ijmecsci.2020.106150-Figure3-1.png",
        "caption": "Fig. 3 Bending model of soft actuator of Fig. 1(a). (a) Physical experiments under different input pressures. (b) Bending angle model of the actuator under input pressure [7]. L0 and L are the length of the inextensible layer and upper actuator respectively. \ud835\udefc and R represent the bending angle and radius of curvature, respectively. \u0394r is the distance from the endpoint O of the upper actuator to the bottom of the lower actuator.",
        "texts": [
            " Therefore, how to establish a model describing the relationship of driving variable, actuator deformation, and tip contact force of the actuator is a problem to be solved in the optimization design and control of soft robots. In the following paragraphs, we establish an analytical model that considers the properties of silicone rubber hyperelastic material, input pressure, bending angle, and tip contact force of the actuator. The geometry and material parameters used in the model are obtained by experimental measurements or calibration. 3.1. Modeling of bending angle As shown in Fig. 3(a), although the extensible upper layer of soft actuator is designed as pleated structures, gaps between adjacent chambers have slight influences on the smoothness of actuator bending deformation. The actuator can still be regarded as a constant curvature bending deformation. The soft actuator appears to have uniform deformation under input pressure. Therefore, to derive the analytical model of the soft actuators with pleated structures, we assume that the actuator chamber structure is accurate, uniform, and the effect of gravity is not considered. Therefore, the bending model shown in Fig. 3(b) can be established. According to the geometric relationship, we can get the following relationship: 0L R   (1) 0L L L  (2) where \ud835\udefc is the bending angle under input pressure, R is the radius of curvature, L0 is the length of the actuator in the inactive state, L is the axial length of the upper actuator after deformation, and \u0394L is the elongation of the upper actuator. In addition, the relationship between the axial length L of the actuator, the radius of curvature R, and the bending angle \ud835\udefc can be obtained from the arc length calculation formula:   0L R r L r      (3) From this, the relationship between the elongation \u0394L and the bending angle \u03b1 is obtained: L r   (4) After making a series of further analysis of the bending deformation of the soft actuator, it is not difficult to find that there be a certain corresponding relationship between the input pressure and the elongation \u0394L of the whole actuator",
            " Case 2: tip contact force experiments: the force gauge were pre-adjusted the direction and position according to different bending angles and fix it on the test platform, as shown in Fig. 11(d). When the actuator was bent and in contact with the force gauge, the tip contact forces were recorded under different input pressures P. The model of this case is expressed by Eq. (26). 5.1. Comparative analysis of bending angle experiments In this bending angle experiment, a measurement reference was established, as shown in Fig. 3. The reference point was O1, the intersection of the first chamber and the bottom of the actuator, and the reference line was the straight line of the actuator\u2019s bottom. By measuring the angle between the line O1A and the reference line, the angle \u03b1/2, which represents the bending angle of the actuator, can be obtained. Each actuator was pressurized three times in order to bend in free space, and the input pressure along with the corresponding bending angle was measured in the range of 0\u00b0 to 300\u00b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003859_detc2007-34210-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003859_detc2007-34210-Figure9-1.png",
        "caption": "Figure 9: Error surfaces after higher-order correction",
        "texts": [],
        "surrounding_texts": [
            "This paper describes a new method of tooth flank form error correction utilizing the universal motions and the universal generation model for spiral bevel and hypoid gears. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. In addition to the correction of up-to 2nd order surface errors, higher-order error components can be corrected by using the higher-order coefficients of the universal motions. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. The corrective universal motion process can be conducted with a computerized closed-loop manufacturing system. A numerical example of a face-mill completing process is presented. The developed new approach has been implemented with computer software. The new approach can also be analogously applied to the face-hobbing process [7]."
        ]
    },
    {
        "image_filename": "designv10_4_0003043_0954406041319545-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003043_0954406041319545-Figure1-1.png",
        "caption": "Fig. 1 Selective laser melting process",
        "texts": [
            " In the present work the influence of the peak power, the scan speed and the hatching pitch on the pore structure and on the fatigue strength of pure grade 1 titanium powder processed by a pulsed neodymium-doped yttrium aluminium (Nd:YAG) laser are investigated. The pore structure was investigated by optical and scanning electron microscopes. A torsional fatigue test was carried out in square bars with different surface conditions. Heat treatments such as annealing and hot isostatic pressing (HIP) were used to improve the fatigue strength of the specimens. Figure 1 shows a sketch of the selective laser melting equipment. An Nd:YAG laser of maximum peak power of 3 kW and maximum average power of 50W was used. The pulsed laser can deliver high peak power in a short pulse, thus using the high irradiance (W/cm2) of the pulsed laser; it is possible to have effective melting of the powder with a small heat-affected zone (HAZ) in the solidified part using proper parameters. Also, because of the better absorptivity of metals to short wavelength, Nd:YAG lasers seem to be more suitable than CO2 lasers for material processing when melting is involved [10, 11]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure2-15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure2-15-1.png",
        "caption": "Figure 2-15 Sketch of a strange attractor for a forced nonlinear oscillator: product space of the Poincare plane and the phase of the forcing excitation.",
        "texts": [
            " Consider, for example, a forced nonlinear How to Identify Chaotic Vibrations 55 oscillator with equations of motion x=y (2-5) y = F(x, y) + /Ocos(co/ + <J>0) (2-6) This system can be made to look like an autonomous one by defining z = tof 4- <t>Q + 2\u00ab7r (2-7) and x = y y = F(x, y) +/0cosz Z = <0 (2-8) (2-9) (2-10) Thus, a natural sampling time is chosen when z = 0. This system can be thought of as a cylindrical phase space where the values of z are restricted: 0 < z < 2?r. A picture of the Poincare map is then given as in Figure 2-15. 56 How to Identify Chaotic Vibrations Reduction of Dynamics to One-Dimensional Maps. In Chapter 1 we saw that simple one-dimensional maps or difference equations of the form xn+i = f ( x n ) can exhibit period-doubling bifurcations and chaos when the function f ( x ) has at least one maximum (or minimum), as in Figure 1-19. Period-doubling phenomena have been observed in so many different complex physical systems (fluids, lasers, p-n electronic junctions) that in many cases the dynamics may sometimes be modeled as a one-dimensional map"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002842_j.1460-2687.2002.00108.x-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002842_j.1460-2687.2002.00108.x-Figure2-1.png",
        "caption": "Figure 2 Foot and ball simulation models.",
        "texts": [
            " Hexahedron solid elements were used for the leg while shell elements were used for the ball. The air inside a ball was defined by the gamma law equation of state [p \u00bc \u00f0c 1\u00deqE, where p is the pressure, c the ideal gas ratio of specific heats, q the overall material density and E is the specific internal energy]. The number of elements for the kicking leg model in the digitized 3D curve kick model was 160 and for the drive kick model was 108. The geometry for the foot and ball models can be seen in Fig. 2. The foot joint of the human body has a very complex structure, which consists of bones, muscles, ligaments and so on. In this study, however, a simplified model was used which assumed that the 184 Sports Engineering (2002) 5, 183\u2013192 \u2022 2002 Blackwell Science Ltd lower leg and foot are represented by two kinds of material properties for the calf and the foot. In both models, the Young\u2019s modulus for the foot was 30 MPa (Asai et al. 1996), the Young\u2019s modulus of calf was 300 MPa and the Poisson\u2019s ratio was 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003524_j.rcim.2006.09.001-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003524_j.rcim.2006.09.001-Figure2-1.png",
        "caption": "Fig. 2. Kinematical scheme of the mechanism.",
        "texts": [
            " The proposed 3-DOF parallel mechanisms consist of three kinematical chains, including three actuated legs with identical topology and one passive leg with 3-DOF, connecting the fixed base to the moving platform (Fig. 1). The links of these legs have given sizes and masses. In this parallel mechanism, the kinematic chains associated with the three identical legs consist, from base to the platform, of an actuated revolute joint, a moving link, a Hooke joint, a moving link and a spherical joint attached to the platform. Let Ox0y0z0 be a fixed Cartesian reference (Fig. 2). To simplify the graphical image of the kinematic scheme of the mechanism, we will represent the intermediate reference systems by only two axes, the same method used in most of the robotics papers [1,9]. The zk-axis is represented for each component element Tk. It is noted that the relative rotation with jk;k 1 angle or relative translation of Tk body with lk;k 1 displacement take place about or along the zk-axis. One of the three active legs, for example A1A2A3A4, connects first an active revolute joint A1 attached to the base and a moving link A1x A 1 zA 1 (called TA 1 ) of length A1A2 \u00bc l1, mass m1 and tensor of inertia J\u03021, which has a rotation about the axis A1z A 1 characterized by the angle jA 10, angular velocity oA 10 \u00bc _jA 10 and angular acceleration A 10 \u00bc \u20acjA 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure3-1.png",
        "caption": "Fig. 3. Elementary open kinematic chain (0A \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b72B -1B) associated with the loop A-B of parallel Cartesian robotic manipulator: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " We have to take into account the dimension of the range of the restriction of F2 to the kernel of F1 instead of motion parameter b2 = 5. The motion parameters b1 and b2 are easily obtained by inspection with no need to calculate the rank of the matrices [A1]6\u00d78 and [A2]6\u00d78. The motion parameter b1 is given by the number of independent motions between the extreme elements 1B and 0 in the serial open kinematic chain 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b7 -2B -1B associated with the first loop when no other loop is closed (Fig. 3). We can observe that five independent motions (vx, vy, vz,\u03c9x,\u03c9y) exist between the extreme elements 1B and 0 (Fig. 3). These velocities form the base of RF(1). The motion parameter b2 is given by the number of independent motions between the extreme elements 1C and 0 in the serial open kinematic chain 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 -2C -1C associated with the second loop when no other loop is closed (Fig. 4). Five independent motions (vx, vy, vz,\u03c9x,\u03c9z) exist between the extreme elements 1C and 0 (Fig. 4). These velocities form the base of RF(2). The dimension of the range of the restriction of F2 to the kernel of F1 can also be obtained by inspection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure8-19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure8-19-1.png",
        "caption": "Figure 8-19. Forms of tear test piece. Solid line, original shape; broken line, shape after tearing",
        "texts": [],
        "surrounding_texts": [
            "particular tearing using a fracture mechanics approach which was described in a series of papers\u0302 ^\u0302 \"\u0302 \"\u0302*. They used the concept of'energy of tearing' which is the energy required to form unit area of new surface by tearing. This energy of tearing is a basic material characteristic and independent of test piece geometry; hence, using this concept and knowing the elastic characteristics of the material, the force needed to tear a given geometry can in theory be predicted. The concept also allows rational analysis of other failure processes in rubber, such as fatigue. Although the concept and importance of tearing energy is now well established, standard methods to date do not make use of it but report the arbitrary tearing force."
        ]
    },
    {
        "image_filename": "designv10_4_0003188_elan.1140060802-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003188_elan.1140060802-Figure1-1.png",
        "caption": "FIGURE 1. Electrode process for the electrochemical oxidation of GSH at the CoPC-modified SPES, reproduced from [I].",
        "texts": [
            " 'To whom correspondence should be addressed 618 Hart and Wring GSH For the determination of GSH (and the compounds discussed later), we mixed the electrocatalyst cobalt phthaloqanine (CoPC) in mrith the graphite (5% m/m) before the screening-printing procedure was performed. The CoPC was found to reduce the over potential for the electrooxidation of GSH by about 600 mV. therefore. greatly improving the selectivin of the measurement step. The reactions involved in the overall oxidation of GSH are shown in Figure 1. The CoPC-modified SPESs were evaluated usinp amperornett? in stirred solution; it was found that the calibration graph for GSH was linear over the range 1.48 X lo-- to 2.00 x mol dm-j. In a further study [lo]. SPESs were produced with several iron-containing electrocatalysts including substituted ferrocenes; their suitability as GSH sensors was then investigated using cyclic voltammetn and amperometry in stirred solutions. It was found that iron phthaloqanine and ferrocenecarboxaldehyde-containing electrodes could be applied to the detection of GSH, but neither was superior to CoPC in terms of seIectivit\\- and sensitivi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003997_3-540-27969-5-Figure10.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003997_3-540-27969-5-Figure10.5-1.png",
        "caption": "Fig. 10.5. (left) Extrinsic coordinates. (right) Intrinsic coordinates",
        "texts": [
            " However, in this case, answering the same questions introduced before (how devices determine their position and the IN-OUT pairs, and how data can be routed from IN to OUT devices) is more challenging. To explain the problems related to the above issues and to present our proposal to solve them, it is important to distinguish between what we call extrinsic and intrinsic coordinates. Extrinsic coordinates identify the position and orientation of devices with respect to a three-dimensional frame attached to the object (see Fig. 10.5(left)). The extrinsic coordinates of a device could be represented, for instance, by its (X,Y,Z) coordinates and by the two angles (\u03b8, \u03c9) determining its orientation. Intrinsic coordinates, instead, specify the positions of devices in the object surface. In other words, they are two-dimensional coordinates (\u03be, \u03b7) mapped on the surface and establishing a frame on the object\u2019s surface (see Fig. 10.5(right)). Extrinsic coordinates of a device are fundamentally important, in that they unambiguously determine the coefficients of the specific ray of light associated with the device, i.e., the ray of light received and blocked by an IN device, or the ray of light to be reproduced by an OUT device. Thus, an IN-OUT pair has to be established between two devices whose extrinsic coordinates identify the same straight line (i.e., the ray of light to be reproduced). Therefore, each device must know its extrinsic coordinates to establish such a pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003486_j.sna.2007.08.028-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003486_j.sna.2007.08.028-Figure1-1.png",
        "caption": "Fig. 1. (a) Club illustrated at address (t = 0) and at the end of the back swing during a putting stroke. The frame (I\u0302, J\u0302 , K\u0302) denotes a lab-fixed (inertial frame) at O which coincides with the location of the centroid f of the club face at address. At address, J\u0302 defines the target line. (i\u0302f, j\u0302f, k\u0302f) denotes a body-fixed frame at f (face f the sh f and \u03c6",
        "texts": [
            " / Sensors and Actuators A 141 (2008) 619\u2013630 621 r f w w c o M e 2 w t o t b t t t w a o p i t k ( T t t fi s k b\u239b \u239c\u239d w d t f F o t a o d rame), whereas (i\u0302s, j\u0302s, k\u0302s) denotes a body-fixed frame at s (shaft frame) within rame and the shaft frame are related by the manufactured lie and loft angles \u03b8 igid throughout the swing which is an appropriate assumption or putting as the club undergoes a slow, smooth motion that ill not lead to appreciable flexing of the shaft. More precisely, e wish to predict three angles that define the orientation of the lub head and the position and velocity of the geometric center f the face of the club head by exploiting measurements from EMS inertial sensors mounted remotely and within the grip nd of the shaft of the club. .1. Definitions of reference frames and orientation angles Consider Fig. 1 which illustrates a golf club at \u2018address\u2019, here the club is first lined up with the ball, and at the end of he back swing for a typical putting stroke. The geometric center f the face of the club is denoted by point f and the location of he sensor module within the shaft at the grip end is denoted y point s. At address, point f coincides with point O which is he origin of an inertial or lab frame (I\u0302, J\u0302 , K\u0302). In the lab frame, he unit vector K\u0302 points vertically up (gravity g = \u2212gK\u0302) and he unit vectors ( I, J\u0302) define the horizontal plane with J\u0302 aligned ith the initial target line of the clubface which is established at ddress. A body-fixed frame (i\u0302f, j\u0302f, k\u0302f) is introduced at f on the plane f the club face and with j\u0302f being the outward normal to this lane. The unit vector i\u0302f lies in the plane of the face where it s chosen to be parallel to the flat indexing surface that defines he top of the club face as shown in Fig. 1b. The unit vector \u02c6f then follows from k\u0302f = i\u0302f \u00d7 j\u0302f. A second body-fixed frame i\u0302s, j\u0302s, k\u0302s) is introduced at point s within the shaft at the grip. his frame defines the three mutually orthogonal sense axes of t t l w aft near the end of the grip. (b) Exploded club head view showing how the face . he accelerometers and the angular rate gyros located within he shaft as detailed in the following section. The two bodyxed frames differ by a rigid-body translation rs/f (position of relative to f) and a rotation that is determined apriori by the nown club geometry. The rotation matrix FRS defines this rigid ody rotation per i\u0302f j\u0302f k\u0302f \u239e \u239f\u23a0 = FRS \u00b7 \u239b \u239c\u239d i\u0302s j\u0302s k\u0302s \u239e \u239f\u23a0 (1) hich, in turn, depends upon two angles determined by the esign of the club. These two angles, referred to as the manufacured club lie \u03b8 and loft \u03c6 angles in Fig. 1b, yield the following orm for this rotation matrix RS = \u23a1 \u23a2\u23a3 cos \u03b8 sin \u03c6 sin \u03b8 \u2212cos \u03c6 sin \u03b8 0 cos \u03c6 sin \u03c6 sin \u03b8 \u2212sin \u03c6 cos \u03b8 cos \u03c6 cos \u03b8 \u23a4 \u23a5\u23a6 (2) The angles \u03b8 and \u03c6 are Euler angles and the rotation matrix f Eq. (2) is derived by first rotating by \u03b8 about the j\u0302f axis and hen by \u03c6 about the i\u0302f axis. Notice here that there is no rotation bout the third Euler axis k\u0302f. The sensor module within the shaft measures the acceleration f point s, denoted aS s (t), and the angular velocity of the club, enoted \u03c9S(t)",
            " Computed Cartesian coordinates for path of point f on the face of the utting robot. f swings. Impact tape leaves a visible mark where ball impact ccurs as seen in the images of Fig. 9. These images confirm that he club path closes at impact to the same position as at address to ithin the (visual) resolution of the tape (approximately 2 mm). The predicted path of the club head for a typical putt is llustrated in Fig. 10 which illustrates the computed Cartesian oordinates of point f on the club face relative to the lab-fixed rame; refer rL f/o in Fig. 1. The path largely lies in the (vertical, \u02c6 \u2212 K\u0302 plane) as expected. The maximum back swing position ccurs at Y \u2248 \u221232 cm where the club face has also been lifted \u2248 3 cm above its height at address. Note that the X displace- ent reaches a maximum \u224812 mm whereas it should ideally be ero provided there is perfect alignment of the sensor in the club nd perfect alignment of the club in the robot grip. While perfect lignments were not achieved, it is clear that the robot swings ig. 11. (Top) Overhead view of position data from one trial putt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003620_iros.1992.594498-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003620_iros.1992.594498-Figure5-1.png",
        "caption": "Figure 5: Virtual work space using SPIDAR",
        "texts": [
            " By pulsing the relay a range of restricting forces may be simulated. When the finger is ( 5 ) in contact with the virtual object, the movement of the finger is restricted by restricting all or some of the four lines. We can obtain the position of the pointer as (6) by solving the simultaneous equations (5). l o 2 + l , 2 - 1 2 2 - 1 , 2 {:I l o 2 - I l a + l 2 a .sa - 1 3 2 8a (6) 3.3 Construction of virtual work space = l o 2 - l l a - l 2 a + l 3 2 with SPIDAR 8a The virtual work space is constructed by combining SPIDAR and a stereo display (Fig.5). The display is a CRT monitor which is set in front of the operator(it is not head mounted). The operator is able to watch the virtual space fused with the real space through a stereoscopy filter. The 3.2 Force generating apparatus To simulate the force sensation that a finger would receive from an object, the apparatus restricts the movement of the finger. Movement of each of the four lines position of a instruction pointer attached to a finger is measured, and if contact of a finger with a virtual object is detected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000690_j.rcim.2021.102138-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000690_j.rcim.2021.102138-Figure2-1.png",
        "caption": "Fig. 2. Simplified models of workpiece (a) and robot (b).",
        "texts": [
            " However, the shapes of workpiece and robot and are often complex, which makes collision detection difficult and time-consuming. In order to deal with this problem, it is necessary to simplify the model of the workpiece and the robot. For the workpiece, its surface shape is mainly taken into consideration, and a sparse point cloud model is used to instead. For the robot, it is a good choice to use regular geometry, such as sphere, cylinder, cuboid and so on, to replace its link and joint. As shown in Fig. 2, the simplified model of the workpiece and the robot is given respectively. The details of the simplification method will not be discussed. By simplifying the model, the collision detection between the workpiece and the robot will become much simpler. Obviously, if all the points in the simplified model of the workpiece are not inside any regular geometry in the simplified model of the robot, it can be concluded that there is no collision between the robot and the workpiece; otherwise, there is a collision",
            " 8, the blue line represents the joint angular velocity of each key point on the machining path, and the red lines represent the plus or minus maximum value of the joint angular velocity. In Fig. 9, the blue line represents the KCI value of the robot at each key point on the machining path, and the red line represents the minimum value of KCI. In Fig. 10, the curves respectively represent the minimum distance between the simplified model of machining object and the regular geometry Gj, j = 1, 2,\u22ef15 in the robot simplified model. The distribution of Gj is shown in Fig. 2-b. Further, as can be seen from these figures: \u2022 the joint angles of the robot are all within the limited range; \u2022 the joint angular velocities of the robot are all within the limited range; \u2022 the KCI values of the robot are all greater than the minimum value KCImin; \u2022 dmin values of Gj, j = 1,2,\u22ef15 at all key points is greater than 0. Therefore, the constraints g1(\u22c5) to g4(\u22c5) are satisfied at the optimal BP. In other words, the kinematic performance of the robot is guaranteed. The above analysis shows the correctness of the proposed BP optimization method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000562_j.msea.2020.139695-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000562_j.msea.2020.139695-Figure2-1.png",
        "caption": "Fig. 2 The schematics of the sandwiched cylindrical specimens used for the compressive fatigue test. (a) original appearance (b) after preparation for in-situ observation",
        "texts": [
            " This unit cell is based on the traditional cuboctahedron structure. Three additional straight struts along the X, Y, and Z axes and four diagonal struts were added into the cuboctahedron structure. The dimensions of the COH-Z structure in the X, Y, and Z axes were 2 mm, 2 mm, and 1.44 mm, respectively. To investigate the effect of porosity on the compressive fatigue properties of the new cuboctahedron structure, cylindrical specimens with a sandwiched architecture were prepared, as illustrated in Fig. 2(a). The diameter and height of the cylinder were 13 mm and 25 mm, respectively. The heights of the solid top section, cellular middle section, and solid bottom section were 5 mm, 15 mm, and 5 mm, respectively. The strut width was adjusted to build Ti-6Al-4V cellular materials with three different porosities (33 vol%, 50 vol%, and 84 vol%) between the solid top and bottom sections. A spherical Ti-6Al-4V powder with a median particle size of 34 \u03bcm and a selective laser melting machine (SLM 250 HL, SLM Solutions GmbH, L\u00fcbeck, Germany) were used to produce the sandwiched specimens investigated in this study",
            " Before the fatigue test, a universal material testing machine (HT-9510, Hung Ta Instrument Co., Taiwan) was also used to analyze the yield strength under uniaxial compressive force. The loading rate was 0.125 mm/min. To capture the progress of the fatigue failure, the original cylindrical specimens were ground and polished. The polished samples were then observed using a CCD camera during the compressive fatigue test for in-situ observation. The schematics of the polished specimen for the fatigue test are shown in Fig. 2(b). Furthermore, the successive images taken from the in-situ observation were analyzed with two-dimensional DIC (Vic-2D, Correlated Solutions, Inc., USA) software to obtain the strain distributions on the observed plane as a function of fatigue cycles. The evolutions of the deformation and fracture during the fatigue test were clarified according to the results from in-situ observation and DIC. Representative results are presented in this study. 3.1 Microstructure and uniaxial compressive property The microstructures of the SLM and HIP samples are shown in Fig",
            " Bannykh, Fatigue strength of submicrocrystalline Ti and Zr-2.5% Nb alloy after equal channel angular pressing, Kovove Mater. 49 (2011) 65-73. [39] Y. Furuya, E. Takeuchi, Gigacycle fatigue properties of Ti-6Al-4V alloy under tensile mean stress, Mater. Sci. Eng. A 598 (2014) 135-140. [40] Z.B. Zhang, Y.L. Hao, S.J. Li, R. Yang, Fatigue behavior of ultrafine-grained Ti-24Nb-4Zr-8Sn multifunctional biomedical titanium alloy, Mater. Sci. Eng. A 577 (2013) 225-233. Fig. 1 The unit cell of the new cuboctahedron COH-Z structure. Fig. 2 The schematics of the sandwiched cylindrical specimens used for the compressive fatigue test. (a) original appearance (b) after preparation for in-situ observation Fig. 3 The microstructures of the Ti-6Al-4V cellular alloy. (a) SLM (b) HIP Fig. 4 The S-N curves of SLM and HIP samples with porosities of 33 vol%, 50 vol%, and 84 vol%. Fig. 5 The fatigue strengths at 106 cycles of SLM and HIP samples as a function of porosity. Fig. 6 The fatigue fracture surfaces of an SLM sample with 50% porosity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003129_a:1008106331459-Figure20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003129_a:1008106331459-Figure20-1.png",
        "caption": "Figure 20. Description of the cantilever deformation.",
        "texts": [
            " The resolution of force sensors based on piezoelectric materials is in the range of \u00b5N. 5.3.2. First Experimental Results For first measurements, metal-foil strain gauges have been chosen. Up to a certain extent, the investigations already gained within this field in the macroworld can be transferred into the microworld. Although alternative methods are being investigated successfully, the use of strain gauges seems is the most widely used approach, because of its good performance in terms of costs, speed and accuracy of measurement. For a cantilever type endeffector (Figure 20), as the one used in our prototype, the theoretical relation between force F applied at a certain point and strain \u03b5 induced in another point, is expressed by Equation (5): \u03b5 = 6Fl Ebh2 . (5) Parameters l, b, h are illustrated in Figure 20; E is the Young modulus of the material of the endeffector. If we use strain gauges to detect the strain in the material, we obtain a resistance change of the strain gauge\u2019s nominal resistance value, that is linked to the strain \u03b5 by following equation: 1R = kR\u03b5, (6) where R is the nominal resistance of the gauge, k is the gauge factor. The microgripper used for our experiments has the structure shown in Figure 21. It consists of three piezoceramic (PZT) bimorph actuators: one actuator permits up-and-down movements along the z-axis, the other two are used to perform the gripping process in the xy-plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000567_tro.2020.3000290-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000567_tro.2020.3000290-Figure1-1.png",
        "caption": "Fig. 1. A rendering of our model solution showing the CTR undergoing an elastic instability. The dynamic model in this article describes the robot\u2019s oscillations during this motion for the first time.",
        "texts": [
            " Second, since a dynamic model deals with the time history of the entire robot state, it provides a framework in which it is feasible to incorporate possible hysteresis phenomena, such as friction. Concentric tube friction is only just beginning to be studied and has so far been handled using lumped parameter approaches [22], or assuming unidirectional actuation histories [23]. In this article, we investigate a simple Coulomb plus viscous friction model, using assumptions similar to [22] but in a new dynamic context. Third, CTRs exhibit elastic instabilities in which the robot snaps from one configuration to another, rapidly releasing stored strain energy [24], [25], as illustrated in Fig. 1. While usually something to be avoided, it has been shown that snapping can be harnessed beneficially under certain conditions [26]. This event entails a highly dynamic transition between two different static states. While unstable regimes can be predicted [24], [25] and avoided by design [18], [27]\u2013[30], path planning [31], [32], and control [17], [33], the transition behavior itself has never been modeled, and quasi-static models fail to appropriately resolve the instability, as shown in Fig. 2",
            " In this article, we work out the implications of the concentric tube kinematic constraints in a dynamic context for the first time. The model accommodates any number of tubes with arbitrary precurvature functions and external loading and considers the dynamic effects of tube inertia (both linear and rotational), material damping, Coulomb and viscous friction, and the inertia of a rigid body held at the robot\u2019s tip. We validate the model with experiments measuring the dynamic behavior of the device during an elastic instability, (as illustrated graphically in Fig. 1) and also during tissue grasping. Following the Cosserat rod model in [37], a tube or rod with negligible shear and extension (i.e., a Kirchhoff rod) is governed by the following set of nonlinear, hyperbolic, partial differential equations [15] pi,s = Rie3, pi,t = Riqi Ri,s = Riu\u0302i, Ri,t = Ri\u03c9\u0302i ni,s = \u03c1iAipi,tt \u2212 f i = \u03c1iAiRi ( \u03c9\u0302iqi + qi,t )\u2212 f i mi,s = \u03c1iRi (\u03c9\u0302iJ i\u03c9i + J i\u03c9i,t)\u2212 p\u0302i,sni \u2212 li qi,s = \u2212u\u0302iqi + \u03c9\u0302ie3 \u03c9i,s = ui,t \u2212 u\u0302i\u03c9i (1) where all variables are functions of time t and reference arc length s, and additional constitutive laws are used to relate the internal forces to the kinematic variables"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure17-4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure17-4-1.png",
        "caption": "Figure 17-4. Permeability cell for volatile liquids",
        "texts": [],
        "surrounding_texts": [
            "Instead of putting the desiccant inside the dish, with a controlled humidity outside, the dish could contain water which is then transmitted out into a dry atmosphere and the amount transmitted measured by weight loss. By inverting the container, the transmission rate when the water is in contact with the test piece can also be measured. The transmission rates measured by the various alternative procedures will be different because different vapour pressure gradients across the test piece are being used and, logically, the conditions most relevant to service would be chosen. The alternative to using a dish is to form the material into a bag and this so-called pouch or sachet method is often used for plastics films. The advantages are that a larger surface area is exposed, leaks through the wax seal are eliminated, and the conditions are more similar to packaging applications. It is less attractive for rubbers because they are not often used in that sort of packaging application and an alternative to heat sealing the pouch would be necessary. The procedure whereby the water is placed in the container can be adapted for use with other volatile liquids and a standard method of this type has been published as ISO 6179^^ by TC45. The British standard is identical, pubhshed as BS EN ISO, and there is a similar method in ASTM D814^^ A suitable apparatus is shown in Figure 17.4, consisting of a lightweight aluminium container with a screw-on collar to retain the test piece. The rotating part of the collar applies pressure to the clamp ring through ball bearings so that the test piece is not distorted when the collar is tightened. The two filling valves allow the liquid to be changed during test without disturbing the test piece and this is recommended when a mixture of two or more liquids is used which are not transmitted at the same rate, so changing the properties of the liquid left in the cell. Two procedures are defined in the standard. In both cases the cells, after assembly, are inverted so that the liquid is in contact with the test piece and left for a preliminary exposure of 24 hours, which enables a check to be made for correct sealing. For procedure A, the container is then emptied and re-filled at 24 hour intervals until the weight loss per 24 hours is effectively constant. In procedure B, the weight loss is simply determined without emptying and refilling between weighings. The time periods can be varied for very fast or slow transmission rates, and plotting a graph of transmission rate against time will clearly identify when equilibrium is reached. With some liquids there will be appreciable swelling of the rubber which means that the thickness and permeability will not be constant and this will effect the time to equilibrium. The standard requires that the containers are placed with free passage of air across the surface of the test piece but a very high air velocity could Permeability 359 affect the result, whereas build up of solvent in a confined space could be unpleasant or dangerous. The various gravimetric methods for vapour permeability discussed above are all essentially simple but require great care to achieve good reproducibility, are time consuming, and are not generally sensitive enough to measure very low transmission rates. A considerable number of alternative techniques have been suggested for measuring vapour permeability of plastics, generally with the aim of making the measurement more convenient and increasing sensitivity. For water vapour transmission, carrier gas type commercial apparatus using an infrared sensor is now commonly used. This procedure is standardised in ASTM"
        ]
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure22-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure22-1.png",
        "caption": "Fig. 22. Photos of the prototype [56]. (a) Stator. (b) Rotor.",
        "texts": [
            " Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (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. BA-05 9 AIPM machine with outer flux barrier structure can achieve higher maximum torque density than the counterpart with inner flux barrier design. The AIPM machine with outer flux barrier design has been prototyped and measured as shown in Fig. 22. The static torque performance between FE-predicted and measured results are compared in Fig. 23 for verification. Based on the proposed categorization method, this paper has overviewed novel MFS techniques for torque enhancement in various asymmetric rotor pole IPM machine topologies. The relative merits and demerits of various AIPM rotor topologies have been analyzed, together with a comparison of torque capabilities of selected AIPM machines. It confirms that torque density can be enhanced by employing MFS effect and asymmetries in PM configuration and rotor core geometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure9-1.png",
        "caption": "Figure 9 The Bennett mechanism.",
        "texts": [
            " Then its kinematic screw system expressed by Pl\u00fccker coordinates is ( ) ( ) 1 2 0 0 1; 0 0 0 , 0 0 1; 0 0 0 , = = $ $ (28) Since the Pl\u00fccker coordinates of the two screws are completely identical, the two screws are linearly dependent and just equivalent to the one based on the screw theory. Therefore, the closed loop has one rotation freedom around z-axis. Because the Cardan joint consists of four identical loops, namely it contains four single-mobility pairs, the Cardan joint has four freedoms. Since the Bennett mechanism[49] is a classical puzzling loop and has the most overconstraints of all single-loop mechanisms, it is necessary to briefly review its mobility analysis[34]. The Bennett mechanism, as shown in Figure 9, is a spatial four-bar linkage. It keeps AB=DC and BC=AD. The axes of four revolute joints are in different directions and each joint is perpendicular to its conjoint two links. Suppose the diagonals AC=2l, BD=2m, and the angle between AC and BD is \u03b2. The midpoints of AC and BD are E and F, respectively. EF=n. E is chosen as the origin point, x-axis is along the vector EF and y-axis is along EA. Then the coordinates of four points, A, B, C, Huang Zhen et al. Sci China Ser E-Tech Sci | May 2009 | vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002863_978-94-011-4120-8_32-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002863_978-94-011-4120-8_32-Figure4-1.png",
        "caption": "Figure 4. Workspace Cross section Figure 5. Possible 5-axis machine tool",
        "texts": [
            " More precisely, the t-connected regions of a PKM are the regions of the Cartesian workspace which are free of singularity (and collisions) and where any continuous path is feasible. The size and shape of the maximal t-connected region is of primary importance for the global geometric performances evaluation of a machine tool. The orthoglide has been designed such that its Cartesian workspace is free of singularities and self-collisions. Thus, the maximal t-connected region of the orthoglide is its Cartesian workspace. Figure 3 shows the Cartesian workspace of the orthoglide, and figure 4 depicts a cross section. The Cartesian workspace has a fairly regular shape which is close to a cube. We have used here our general octree-based algorithm for the calculation of the workspace (Chablat 1998). If there is no obstacle to take into account, the workspace of the orthoglide can be easily calculated analytically by its boundaries. 4. Extension to 5-axis machines The orthoglide described above is dedicated to 3-axis machining applications. It can be extended to a 5-axis machine by adding a 2-axis orienting branch to the initial positioning structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003222_s0167-2789(96)00195-9-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003222_s0167-2789(96)00195-9-Figure2-1.png",
        "caption": "Fig. 2. The figure of the robot used in this study: above: Photograph of robot; bottom: schematic drawing of the robot.",
        "texts": [
            " l(a), the presence of the critical number in N may come from nonlinear bifurcation or from phase transition-like phenomena. In such a case an assembly of independent elements does not exhibit effective works (order), implying Wo(N) = 0 for all N. Therefore we insist that in both cases nonlinearity in N - W characteristics is essential for the effectiveness of collective behavior. 3. Experiment In this study, we assumed a simple interaction between each robot, and performed experiments with real robots. The shape of robot that was used in this experiment is shown in Fig. 2. Its size was 9.6 cm width x 6cm length x 15cm height. It is driven by a pair of DC motors. It has two fixed arms and mechanical K. Sugawara, M. Sano/Physica D 100 (1997) 343-354 345 switches equipped at the tip of each arm. They are used as touch sensors to avoid colliding with boundary walls and other robots. When the switch is turned on, the motor on the opposite side rotates in reverse: if the left switch touches something, the right motor rotates in reverse. The period that the motor rotates in reverse is constant and the robot turns about 60 \u00b0 for this period"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000250_tie.2018.2890494-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000250_tie.2018.2890494-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the proposed AFPMSM",
        "texts": [
            " A multi-physics model is established to calculate the vibration of the AFPMSM in Section IV, the modal, electromagnetic and vibration test are performed to validate the accuracy of the multi-physics model. In Section V, the vibration behaviors of the two types of dual-three phase winding are compared with the three-phase winding with considering the current harmonics induced by inverter. The vibration reduction mechanism of the novel detached winding is discussed. Finally, the vibration experiments are carried out to validate the theoretical results. The axial flux PMSM configuration and the prototype of this AFPMSM are shown in Fig. 1 and Fig. 2 respectively. The rotor is sandwiched by two stators to balance the dualside axial attracting force two stators created. Two stators are directly connected to the front and end cover, and the permanent magnets are embedded in the nonmagnetic rotor support. In order to increase the utilization rate of slot area and reduce the machine end winding length, fractional-slot concentrated winding (FSCW) is adopted. The main dimensions of the AFPMSM is listed in Table I. The two types of dual-three phase winding applied on the AFPMSM have been introduced in previous research [22], [23]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure5.35-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure5.35-1.png",
        "caption": "Fig. 5.35 Volume change of Radicon worm-gear reducers in 80 years",
        "texts": [
            " Reduction of machine weight can save material and energy. This is especially important for vehicles and airplanes. In fact, light weight has been a constant theme in machine design. Progress in materials makes lightweight design possible. During the several decades after Otto\u2019s invention, one main goal in engine design was to reduce the mass-power ratio, which continuously decreased from 272 kg/kW of Otto\u2019s engine in 1876 to 0.68 kg/kW of the aero-engine in the 1920s. Great progress was made in terms of lightweight. Figure 5.35 illustrates the change of size of worm gear reducers made by the famous British Radicon during the last 80 years. The trend in size reduction is obviously seen. Lightweight requirement inspired the metallurgic industry to produce materials of high strength. As can be seen from Fig. 5.34, the material properties were increased by several times during about one hundred years before the end of WWII. Market competition has been the driving force for saving material and energy, and thus for lightweight, in machine design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000979_s00170-021-07721-z-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000979_s00170-021-07721-z-Figure1-1.png",
        "caption": "Fig. 1 Principle of acoustic emission [11]",
        "texts": [
            " There are two major components in AE testing, a fault that is the cause of energy release in the material (event) and the transducers that gather data from the produced event [17, 18]. A fault generates the AE signal in the shape of high-frequency sound waves, which are recorded by instruments. Thus, the methodology is mostly founded on signal generation, data collection, data analysis, and final decision making. The general working principle of an acoustic emission system is shown in the schematic view in Fig. 1 [11, 19]. AE can be used during the manufacturing process to measure ultrasonic directed waves and compare various data in different ranges to evaluate the defects in the AM structures. Acoustic emission has been extensively used as one of the major techniques for inline condition monitoring in variety of applications such as structural health monitoring (SHM) [18, 20], tool wear monitoring [21], machinery and bearings condition monitoring [22, 23] to name a few, and for additive manufacturing process monitoring [24\u201326]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000656_j.robot.2021.103744-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000656_j.robot.2021.103744-Figure1-1.png",
        "caption": "Fig. 1. A typical kind of robotic system with 6-DOF, which is usually called industrial manipulator. The motion equations of industrial manipulator can be described as Eq. (1). The labels represent the joints and the local coordinates of industrial manipulator.",
        "texts": [
            " The equations of motion that describe the behavior of the robotic system can be formulated as M (q) q\u0308 + q\u0307TC (q) q\u0307 + g (q) = \u03c4. (1) In which, M (q) denotes the inertia matrix, C (q) denotes the Coriolis and centrifugal terms, and g (q) stands for the gravitational terms and Coulomb friction terms [22\u201324]. q\u0308 and q\u0307 are second order and first order derivatives of q with respect to time, which denote joint acceleration and joint velocity, and \u03c4 denotes the joint torque. The geometric parameters of the robot system used in this study are shown in Table 1. It is important for robotic system, like the one shown in Fig. 1 and Table 1, to plan velocity and acceleration of the predetermined motion path before executing. However, for a predetermined path, the velocity of the path is not yet clear, and the traversing time is also not clear. Thus, the derivatives of q with respect to time cannot be calculated. In order to solve this problem, the vector q can be considered as a function q (s) with the path parameter s. Then the derivatives of q with respect to time can be instead of the derivatives with respect to the path parameter s, as{ q\u0307 = q\u2032s\u0307 q\u0308 = q\u2032\u2032s\u03072 + q\u2032s\u0308 (2) where s, s\u0307, s\u0308 denote the position, velocity, and acceleration of the path, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.7-1.png",
        "caption": "Figure 7.7: Two-body planar space robot",
        "texts": [
            "30) i=l i=l where lT = (1, 1, ... , 1). Indeed, conservation of a nonzero value for this angular momentum leads to a singledifferential constraint in the form (7.23). Two-Body Robot The Pfaffian constraint (7.30) is in general nonholonomic. but it is integrable in the particular case of n = 2. In fact, in this case we haw n - k = 1. and. therefore. the accessibility distribution is always involutive, as pointed out in Section 7.4. \\\\'e shall now give a detailed derivation of this fad. Consider the structure shown in Fig. 7.7. The orientation of the i-th bod~\u00b7 with respect to the x axis of the inertial frame is denoted by B; (i = 1. 2). The two vector equations [ Tc.2 .. r ] rc2.y [ T'ct..r ] +. [ Tc.2 .. r ] 71/j 7112 r cl.y rc2.y 0 may bc solved for the two position vectors as [ T'c.l ] = [ ~:~.::.: 1 = rc2 r c2,:r Tc2,y whcrc l.:ll -1n2(f1- dt)/mt k12 -m2d2/mt k21 m1 (ft - d1)/mt !.:22 m1ddmt, with m 1 = m1 + mz. As a consequence, setting J; = hzz, the kinetic energy of the i-th body is i = 1, 2, for i = 1, 2. The kinetic energy of the system becomes where i = 1, 2, and b12(B1, 82) = (m1knk12 + m2k2,kn) cos(B2- BI)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-5-1.png",
        "caption": "Figure 5-5 Regions of chaotic and periodic motions for two-dimensional motion of a mass in a double-well potential in the forcing amplitude-frequency plane [from Moon (1980b); reprinted with permission from New Approaches to Nonlinear Problems in Dynamics, ed. by P. S. Holmes; copyright 1980 by SIAM].",
        "texts": [
            " The vertical hatched region in Figure 5-4 represents a region of steady chaotic motion, while the horizontally hatched region represents a preturbulent region in which there may be chaotic transients. This region is bounded below by a criterion based on the Empirical Criteria for Chaos 161 existence of homoclinic orbits (see next section). A period-doubling region is also shown in the dotted region. (d) Forced Vibrations of a Two-Degree-of-Freedom Oscillator in a Two-Well Potential As extension of the one-degree-of-freedom particle in a two-well potential has been studied by the author for the experiment shown in Figure 5-5. This problem can be modeled by two coupled nonlinear oscillators (3-3.7), dV x + yx + \u2014 = 0 dx 8V y + yy + T~dy (5-2.4) where V(x, y) represents the potential for the magnets and the elastic stiffness. The chaotic regime for the forcing amplitude and frequency are shown in Figure 5-5. Comparing this regime to that in either Figure 5-2 or 5-3, we see that the addition of the extra degree of freedom seems to have reduced the extent of the chaos region at least in the vicinity of the natural frequency of the mass in one of the potential wells. 162 Criteria for Chaotic Vibrations (e) Forced Motions of a Rotating Dipole in Magnetic Fields: The Pendulum Equation In this experiment, a permanent magnet rotor is excited by crossed steady and time harmonic magnetic fields (see Moon et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003262_1.1327585-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003262_1.1327585-Figure1-1.png",
        "caption": "Fig. 1 Asperities in a non-conforming contact subject to frictional heating",
        "texts": [
            " Modules are developed with the assistance of influence functions ~ICs! or frequency response functions ~FRF!, which are analytically derived from halfspace solutions using the integral forms of the known Green\u2019s functions @1,3,33# for thermoelastic and elastic problems, respectively. Each module is numerically verified and thermomechanical performances of a point contact of rough surfaces are studied. However, the solutions presented in this paper are limited to steady-state heat transfer and small Peclet numbers. A typical non-conforming contact problem ~Fig. 1! may be described by the contact between two convex bodies. The surface can be digitized from a real engineering element with the assistance of a three-dimensional surface measurement instrument. The contact may be simplified @1# into an equivalent rough halfspace with combined material properties in contact with a ball that is rigid, smooth, adiabatic, and moving with velocity, V , as shown in Fig. 1. Heat can be conducted into the fixed equivalent half- rom: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Term space. In thermomechanical contact problems the normal surface displacement induced by frictional heating will contribute to the gap between the two contacting bodies, and hence affect the behavior of the contact. The following assumptions are made in the model development. 1 Each body can be considered as an halfspace because the contact area is relatively small. 2 The strains are small and the theory of linear elasticity applies",
            " The heat source is equally divided between the two bodies if the materials are the same. All variables are independent of time. 5 The frictional shear is proportional to the normal pressure: s5m f p , where the friction coefficient, m f , is constant everywhere on the interface. Each asperity in contact has to be subjected to the contact pressure, frictional shear, and frictional heating, under which the asperity should experience three kinds of normal displacements: up, us, and ut, respectively. The total displacement, u, is the summation of them. Figure 1 presents the contact geometry and Transactions of the ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F the rough surface, and illustrates an asperity under the combined actions of the pressure, frictional shear and frictional heating. The elastic normal surface displacement caused by the contact pressure, p(x18 ,x28), is given by the Boussinesq formula @1# up~x1 ,x2!5 1 pE* E2` ` E 2` ` p~x18 ,x28!dx18dx28 A~x12x18!21~x22x28!2 . (1) Obviously, the corresponding Green\u2019s function may be expressed as Gp~x1 ,x2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.16-1.png",
        "caption": "Fig. 7.16 Mass-varying mechanical system. a Ladle, b vibrating griddle",
        "texts": [
            "4 Machine Dynamics in Modern Times 241 For regulation of non-periodic variation of speed, the centrifugal governor used by Watt in the steam engine was the earliest recorded application of automatic regulating device in history, which played a key role in the widespread application of steam engines (see Sect. 4.2). Both the German and Russian school conducted research on speed regulation with flywheels and governors. In German textbooks, this is termed as power balancing (Wittenbauer 1923). There is a kind of machines whose mass changes in the course of motion. For example, the ladles used in metal casting experience changes in total mass, mass center, and inertia moment during tilting and pouring the liquid metal into molds (Fig. 7.16a). Other examples include the paper roll in a printing machine, the spindle in a spinning machine, the vibrating griddle shown in Fig. 7.16b and the blast furnace hopper (\u0417\u0438\u043do\u0432\u044ce\u0432 and \u0411ecco\u043do\u0432 1964). The dynamics of mass varying system was put forward as early as in the middle 19th century. In 1897, a Russian scholar, I. Meschersky (\u0418\u0432a\u043d Me\u0449epc\u043a\u0438\u0439), derived the dynamic equation of the mass varying system. In 1929, A Soviet scientist, K. Tsiolkovsky (\u041ao\u043dc\u0442a\u043d\u0442\u0438\u043d \u0426\u0438op\u043ao\u0432c\u043a\u0438\u0439), proposed to use multistage rocket for space navigation, making important contribution to mass varying system dynamics. The theory of mass varying system dynamics, now, has been mature, and applied to various machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3-1.png",
        "caption": "Figure 3.'1. Unit vectors associated with the contact point.",
        "texts": [
            " We now determine what conditions must be met by the rack parameters, if the rack is to mesh correctly with the pinion. In order to check whether the Law of Gearing is satisfied, we adopt the following procedure. We find a typical position of the contact point between the pinion and the rack, and we draw the common normal through this point. We also draw the perpendicular from the pinion center to the rack reference line, and the point where this line intersects the common normal is labelled P'. The Law of Gearing is satisfied if pI coincides with the pitch point P. Figure 3.1 shows the pinion base circle, and a pair of teeth in contact. The base circle radius is given by Equation (2.20), (3.1) A Pinion Meshed With a Rack 55 and by making use of Equation (2.30), which gives the standard pitch circle radius in terms of the module, we can express the base circle radius in terms of the module and the pressure angle, ~Nm cos 4lS (3.2) Since the module m and the pressure angle 4ls are part of the specification of the pinion, the base circle radius Rb is known, and its value is constant. Any normal to the rack tooth in Figure 3.1 must be perpendicular to the tooth profile, while any normal to the pinion tooth must touch the base circle. Hence, as shown in the diagram, the common normal must be the base circle tangent which is perpendicular to the rack tooth profile, and the contact point must lie on this line. If E is the point where the common normal touches the base circle, the radius CE is parallel to the rack tooth profile, and the length CP' can therefore be found from triangle ECP' , CP' cos 4l~ (3.3) To find the position of the pitch point, we use Equation (1.15), which gives the pitch circle radius of a pinion meshed with an arbitrary rack with pitch p, The rack in Figure 3.1 has a pitch p~, so in this case the pinion pitch circle radius is as follows, Np~ 271\" (3.4) Point P' in Figure 3.1 will coincide with the pitch point if the length CP' is equal to the pitch circle radius Rp' We equate the two expressions given in Equations (3.3 and 3.4), and rearrange the terms to put the condition in the following form., p~ cos 4l~ 271\"Rb N (3.5) 56 Gears in Mesh The base pitch Pb of the pinion is given by Equation (2.22), 211'Rb N (3.6) and the base pitch Pbr of the rack, defined as the distance between adjacent teeth measured along a common normal, can be expressed in terms of the pitch and the pressure angle with the help of Figure 3.2, P~ cos ~~ (3.7) Hence, the condition given by Equation (3.5) implies that the base pi tch of the rack must be equal to that of the pinion, (3.B) When we replace CP' in Equation (3.3) by the pitch circle radius Rp' the equation takes the following form, (3.9) We have shown that if the length CP' is equal to the pitch circle radius, the base pitches of the pinion and the rack must be equal. The converse is also true, as we can prove A Pinion Meshed Wi th a Rack 57 by considering Equations (3.3 - 3.8) in the opposite order. If the base pitches are equal, then CP' is equal to Rp' and the Law of Gearing is satisfied. We have therefore proved that an involute pinion can mesh correctly with any rack whose teeth are straight-sided, provided the two base pitches are equal. The rack does not need to be the same shape as the basic rack. The meshing diagram is shown in Figure 3.3, with the common normal at the contact point passing through the pi tch point P. As always, the line in the rack which touches the pinion pitch circle is the rack pitch line, the common normal at the contact point is the line of action, and the angle between the line of action and the tangent to the pitch circle at P is the operating pressure angle 41 of the gear pair. Since the line of action is perpendicular to the rack tooth profile, it can be seen from the diagram that the operating pressure angle 41 is equal to the rack pressure angle, 41' r (3",
            "17), we obtain an expression for 8R in terms of the quantities defined at the pitch circle, ~ + inv 4lp - inv 4lR 2Rp Relation Between the Pinion and Rack positions (3.18) In order to obtain a general relation between the posi tions of the pinion and the rack, we consider them initially when the ~ontact point lies exactly at the pitch point, and we then determine a relation between the 60 Gears in Mesh displacements from this position. We proved in Chapter 1 that, at some moment during the meshing cycle, the contact point must coincide with the pitch point, and in Figure 3.4 we show the pinion and rack with the contact point in this position. As before, the x axis in the pinion and the xr axis in the rack each coincide with a tooth center-line, and the fixed ~ and ~ axes have their origin at the pitch point. The angular position of the pinion is specified by the angle fi, measured from line CP counterclockwise to the x axis, and the position of the rack is indicated by the distance ur of the xr axis above the ~ axis. The positions of the pinion and the rack in Figure 3.4 are as follows, fi -~ (3.19) 2Rp 1 (3.20) ur 2\"tpr where tp and tpr are the tooth thicknesses, measured on the pinion pitch circle and the rack pitch line. After the pinion has rotated an angle Ilfi from this position, and the rack has displaced a distance Ilu r , the new positions are given by the following two expressions, fi (3.21) position of the Contact Point 61 (3.22) The plnlon rotation ~$ and the rack displacement ~ur are of course related, and to find this relation we start from Equation (1",
            "25) Position of the Contact Point When we discussed the condition for correct meshing of a pinion and rack, at the beginning of this chapter, we showed that a typical contact point lies on the base circle tangent which is perpendicular to the rack tooth profile. Since the contact point always lies on this line, the path of contact is a segment of the same line. We can therefore specify the position of a contact point by its distance along this line from the pitch point. We introduce the length s, as shown in Figure 3.5, and it is defined in the manner of a coordinate, so that it is positive for points which lie above P, and negative for those lying below P. To derive an expression for s, we use a method which is very similar to the procedure just used when we found a relation between the pinion and rack positions. When the contact point is at the pitch point, the angular position of the pinion is given by Equation (3.19), 62 Gears in Mesh and the value of s is zero. After a pinion rotation ~~, the angular position of the pinion is given by Equation (3.21), fJ (3.26) The rack will have displaced a distance Rp~~' as we showed in Equation (3.24), and the corresponding value of s can then be read from Figure 3.5, s (3.27) We eliminate ~~ between Equations (3.26 and 3.27), and we use Equation (3.11) to replace (Rp cos~) by Rb\u2022 We then obtain an expression for s as a function of the pinion angular position ~, s Rb~ + lt cos ~ 2 P (3.28) If we use Equation (3.28) to find the values of s corresponding to any two positions of the subtract one result from the other, expression for the displacement ~s of pinion, we can then and we obtain an the contact point Sliding Velocity 63 corresponding to a rotation llfJ of the pinion",
            " Sliding Velocity The sliding velocity at the contact point is defined as the difference between the velocities of the two points in contact. If point A of the pinion touches point Ar of the rack, then the sliding velocity is defined as follows, Sliding veloc i ty (3.30) In order to derive an expression for the sliding 64 Gears in Mesh velocity, we need to make use of the set of unit vectors nt, n~ and nS in the directions of the coordinate axes, and we also introduce the two unit vectors shown in Figure 3.6, which are associated with a rack tooth profile. These vectors are nnr' in the direction of the outward-pointing normal to the tooth profile, and nTr , in the tangential direction toward the tip of the tooth. If the rack velocity is vr ' this is of course the velocity of any point in the rack, and therefore in vector form the veloc i ty of Ar can be wri tten, (3.31) To obtain the velocity of point A, we form the vector product of the pinion angular velocity and the position vector from C to A",
            " We find the position of a typical contact point, and then check to see if the common normal at the contact point cuts the line of centers at the pitch point. Any normal to the tooth profile of gear 1 must touch the base circle of gear 1, while any normal to the tooth profile of gear 2 must touch the base circle of gear 2. Hence, the common normal at the contact point must touch both base circles, which means it must coincide with the common tangent to the base circles. If the common tangent touches the base circles at E1 and E2 , as shown in Figure 3.7, then the posi tion of the tooth contact point must be somewhere on line E1E2 , and the common normal at the contact point lies along E1E2 . The point where this line intersects the line of centers is labelled P', and we must now check to see whether P' coincides with the pitch point P. The radii C1E1 and C2E2 in Figure 3.7 are each perpendicular to E1E2 , and they are therefore parallel. 66 Gears in Mesh Hence, the triangles E,C,P' and E2C2P' are similar, and we obtain the following relation between the sides of the triangles, The lengths E,C, and E2C2 are equal to the base circle radii, which we express by means of Equations (3.35 and 3.36), and the relation then takes the following form, (3.37) We proved in Chapter' that the pitch point P divides the line of centers C'C2 in the ratio N, :N2 \u2022 If point P' is to coincide with P, the right-hand side of Equation (3",
            " In practice, two gears intended to mesh together are almost always designed so that they have the same module m and the same pressure angle lP s \u2022 In other words, they are conjugate to the same basic rack. The base pitch of a gear is related to the module and the pressure angle by Equations (2.24 and 2.3'), 1rm cos I/I s (3.39) Hence, if the two gears are designed with the same module and the same pressure angle, this ensures that they have the same base pi tch, and therefore that they wi 11 mesh correctly. A Pair of Gears in Mesh 67 The meshing diagram of a pair of gears is shown in Figure 3.8, with line E1E2 cutting the line of centers at the pitch point P. The pitch circles of the two gears are the circles which pass through P, and their radii are expressed in terms of the center di stance C by Equat ions ('.24 and 1.25), (3.40) (3.41) We have proved that the common normal at the contact point lies along E,E2 , and this line is therefore the line of action. For a pair of gears, the operating pressure angle ~ is defined as the angle between the line of action and the common tangent to the pitch circles at P",
            "46) When this relation is compared with Equation (3.42), it is evident that the operating pressure angle of gear is equal to the operating pressure angle ~ of the gear pair, A Pair of Gears in Mesh 69 I/>pl (3.47) A similar argument shows that the operating pressure angle of gear 2 is also equal to 1/>, I/>P2 (3.48) and Equations (3.47 and 3.48) can of course be combined, to show that the three angles are all equal, I/>Pl I/>P2 (3.49) Equation (3.49) could have been proved more directly, simply by looking at the meshing diagram shown in Figure 3.9, where the contact point coincides with the pitch point. The common tangent to the tooth profiles at the contact point is perpendicular to the line of action, and it can be seen from the diagram that the three angles I/>pl' I/>P2 and I/> are all equal. We have shown that the operating circular pitches Ppl and Pp2 are equal, and that the operating pressure angles I/>Pl and I/>P2 are also equal. It is often convenient, whenever we 70 Gears in Mesh have proved that a particular quantity on one gear is always equal to the corresponding quantity on the other gear, to introduce a single symbol which can be used to stand for either quantity",
            " The same convention will be used throughout the remainder of the book, without further explanation. Relation Between the Gear Positions For gear 1, we have specified the angular posi tion by the angle f1 1, measured from line C1P counterclockwise to the x 1 axis. We now specify the angular position of gear 2 in the same manner, as the angle f12 measured from line C2P counterclockwise to the x2 axis. In this section we derive a relation between the angles f11 and f1 2\u2022 The two gears are shown in Figure 3.9, with the contact point coinciding with the pitch point, and in these positions the angles f11 and f12 can be written down by inspection, -~ 2Rp1 f11 (3.50) -~ 2Rp2 (3.51) After rotations ~f11 and ~f12' the angular positions of the two gears are given by the following expressions, The angular Equation (1.21), f11 -~+ 2Rp1 f12 -~+ 2Rp2 velocities ~f11 (3.52) ~f12 (3.53) and are related by (3.54) and we integrate this equation to find a relation between the gear rotations, Path of Contact and Line of Action 7' (3",
            " We have also shown that, for any position of the contact point on this line, the common normal at the contact point also lies along line E,E2 \u2022 Hence, the line of action, which is defined as the common normal at the 72 Gears in Mesh contact point, coincides with the path of contact. This is a special property of involute gears, as we will prove in Chapter 9. For non-involute gears, the path of contact is no longer straight, and the direction of the line of action varies, depending on the position of the contact point. Imaginary Rack The gear pair of Figure 3.10 is shown with a rack profile drawn between the teeth. Since the rack profile has no thickness, it is called an imaginary rack, or sometimes a phantom rack. The concept of the imaginary rack is useful, because the geometric properties of a pinion and rack can generally be proved more easily than those of a pair of gears. Very often, a result proved for a pinion and rack can be applied directly to the case of a pair of gears, with the help of the imaginary rack. If the imaginary rack is to fit between the gear teeth in the manner shown, the rack tooth profile must coincide with the common tangent to the gear teeth at their contact point, and the pressure angle 4>~ of the imaginary rack must therefore be equal to the operating pressure angle 4> of the gear pair, 4>' r (3",
            " We can therefore use Equations (3.28 and 3.29) directly, to write down the position s of the contact point, and the displacement ~s of the contact point corresponding to a rotation ~~, of gear \" s (3.59) ~s (3.60) Sliding Velocity We calculate the sliding velocity of a gear pair in the same manner that we did for the case of a rack and pinion. If point A, of gear' is in contact with point A2 of gear 2, we write down the velocities of A, and A2 , and subtract them to find the sliding velocity. In Figure 3.\" the unit vectors parallel with and perpendicular to the line of action are labelled nnr and nTr \u2022 This notation reflects the fact that, if we drew an imaginary rack between the gears, these would be the directions of the normal and the tangent to the teeth of the imaginary rack. 74 Gears in Mesh The position of the contact point is given by the coordinate s on the path of contact. The velocities of A, and A2 are then expressed in terms of s in the usual manner, When we subtract the velocity of A2 from (Rp ,w,+Rp2w2) disappears, as we showed and the sliding velocity is given expression, A, A2 v - v that of A\" the term in Equation (3.54), by the following (3.63) Center Distance C, and Standard Center Distance Cs When we proved that a pair of gears with equal base pitches can mesh correctly at a center distance C, we made no restrictions on the value of C. An involute of a base circle is a curve which starts at the base circle, and then spirals Standard Center Distance 75 around the base circle with ever-increasing radius, as shown in Figure 3.12. It is possible, in principle, to use any part of this curve as the tooth profile, and therefore a pair of gears with base circle radii Rb1 and Rb2 could theoretically be designed to operate at any center distance which is larger than the sum of the base circle radii. In practice, of course, there are a number of considerations which limit the useful range of center distance values. The most important of these practical considerations is the question of how the gears are to be cut. Let us assume that we have a cutting tool which can cut a pair of gears with N1 and N2 teeth, to mesh at a certain center distance",
            " We did not, however, give any recommended values for the tooth thickness or the addendum in a gear. The reason for this omission is that suitable values depend on the operating conditions of a gear pair, and in particular, on the center distance. We defined the addendum as and the dedendum bs as the radial distances from the tip circle and the root circle to the standard pitch circle. The addendum and dedendum can also be measured from the pitch circle, in the manner shown in Recommended Tooth proportions 77 Figure 3.13, and in this case we use the symbols ap and bp to distinguish these quantities from as and bs \u2022 For a pair of gears, the working depth of the teeth is defined as the amount by which the teeth overlap when the gears are in operation, and it is therefore equal to the sum of the addendum values, measured f rom the pi tch eire les, Working depth (3.66) The clearance at the root circle of each gear is the amount by which the dedendum of that gear exceeds the addendum of the meshing gear. Hence, the clearance values c 1 and c 2 for the two gears of a pair are given by the following expressions, (3"
        ],
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    },
    {
        "image_filename": "designv10_4_0003871_j.jmatprotec.2007.09.024-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003871_j.jmatprotec.2007.09.024-Figure6-1.png",
        "caption": "Fig. 6 \u2013 Schematic drawings showing the relative positions of the powder feed position, powder feed angle and focal er fe",
        "texts": [
            " It is evident from Table 4 that the deposition fficiency was most significantly affected by the powder feed osition, and very significantly by the powder feed angle, and ignificantly by the powder feed rate and travel speed, but not y the shielding gas type, laser pulse shape and focal position. .2. Discussion about the analysis results hen only considering the powder feed position and power feed angle, the deposition efficiency was the highest at he condition of 0 mm and 50\u25e6, respectively, while the lowest on the deposition efficiency and S/N ratio. at +4 mm and 70\u25e6. These two extreme cases are illustrated in Fig. 6, where the figures were drawn as exactly as possible on the basis of the measurements from Figs. 2 and 3. For optimum deposition efficiency the powder has to be melted by the laser beam and should not rebound away from the surface. It seems the most important for depositing that the powder has to stay in the laser beam as long as possible and not to rebound away against the surface. In Fig. 6(a), the powder feed position is just on the surface and the feed angle is small as 50\u25e6, where most powder strikes the surface at the center of a laser beam. At the moment the powder impacts the surface, the laser beam rapidly heats up the powder and simultaneously the surface. The heated powder becomes so plastic that it stays in contact with the surface for a long time, which melts the powder and deposits it without rebounding. This may explain why the deposition efficiency is high at 0 mm of the feed position and 50\u25e6 of the feed angle in Fig. 5. The high deposition efficiency /N ratio posit Table 5. Confirmation experiments were conducted to validate that the optimized results were correct. The deposition efficiency that would be obtained from the confirmation experiments position of the laser beam. (a) Powder feed angle, 50\u25e6; powd Powder feed angle, 70\u25e6; powder feed position, +4 mm; focal over 10% was obtained, for example, at the condition 12 in Table 3. In Fig. 6(b), the powder feed position is +4 mm over the surface and the feed angle is relatively large at 70\u25e6. A lot of powder passes through the powder stream without collision with other particles, and hits the surface at an inclined angle and out of the laser beam as shown in Fig. 6(b). In this case, the powder is only heated during its flight across the laser beam, not at the moment of an impact on the surface, so that it tends to rebound away from the surface without melting and depositing. It was observed that few grains of powder were deposited outside of a clad line, which supplements that the above explanation is meaningful. This may explain why the deposition efficiency was very low at +4 mm of the feed position and 70\u25e6 of the feed angle as shown in Fig. 5. At the condition 3 in Table 3, for example, the deposition efficiency was very low as 1",
            " If the travel speed is low, it causes the substrate surface to be heated up to higher temperature, and results in the increase of the deposition efficiency. The focal point of the laser beam had little effect on the deposition efficiency. When the laser beam was focused by the lens of 203 mm of the effective focal length, the diameter of the laser beam did not vary rapidly with a distance away from the focal spot as shown in Fig. 2. As the focal position varied from 0 to +4 mm, the diameters of the irradiated spots were found to change from 1.46 to 1.59 mm. As comparatively illustrated in Fig. 6(a) and (b), it is clearly seen that the focal position could not affect the deposition efficiency. ed position, 0 mm; focal position of laser beam, 0 mm. (b) ion of laser beam, +4 mm. The laser pulse shape did not affect the deposition efficiency, which means that the deposition efficiency was affected by the average laser power rather than the shape and peak power of single laser pulse shown in Fig. 4. 3.3. Derivation of the optimized cladding conditions and confirmation experiments The cladding conditions for maximizing the deposition efficiency were derived from the ANOVA results for the S/N ratio of the deposition efficiency"
        ],
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    {
        "image_filename": "designv10_4_0003832_0094-5765(88)90189-0-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003832_0094-5765(88)90189-0-Figure4-1.png",
        "caption": "Fig. 4. Mode shapes associated with the two frequencies of oscillation about the vertical equilibrium position.",
        "texts": [
            ") Assuming that 01 = Olexp(2z) = ~lexp(i09z), 02 = 0 2 e x p ( 2 z ) =-- ~2exp( ioz) , (26) eqns (24) and (25) yield [3(1 + al)--092] ~ 1 - al092~2 = 0, (27) --a209zO~ +[3( ! + a 2 ) - 0 9 z ] ~ : = 0 . (28) For nontrivial solutions 3(1 + a l ) - ~ o 2 - a l 0 9 2 I -a209 2 3(1 + a2) - \u00b092 1 = 0 i.e. (1 - ata2)o9 4 - 3(2 + al + a2)09 2 +9(1 + a l ) ( I + a2) = 0, yielding two nondimensional frequencies of oscil- Note than an amplitude ratio of I means that the two angles 0, and 02 are equal, implying that the two tethers are collinear. Thus, the first mode of oscillation corresponds to the three bodies remaining in a straight line [Fig. 4(a)] and oscillating with a frequency ~ times the orbital frequency, which is identical to that of pitch oscillation of a two-body tethered system. The second frequency of oscillation and the associated mode shape [e.g. Fig. 4(b)] depend on the end-masses and lengths of the tethers. This dependence may be better understood if one notes from eqn (22) that r t 1 al (31) 1 +r32' a2=r/(1 +r31 ) lation 0) 2 : N/ /3 [ ( I -'t- al)( l Jr a2)/(1 -- a la2)] 1/2. (29) The amplitude ratio O1/02 can now be obtained from eqn (27). For the two frequencies of oscillation, they are given respectively as (O1/02)1 = 1, (O,/O:): = - [a~( l +a:)]/[a2(1 + a~)]. (30) where r l= l : / l l , r32=m3/rn2 and r31=m3/ml . (32) Thus the second natural frequency 092 given by eqn (29) can be thought of as a function of two mass ratios r32 and r31 and the length ratio r~"
        ],
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    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.5-1.png",
        "caption": "Figure 16.5. Cutting points, shown on the developed cylinder of radius R.",
        "texts": [
            " Once the settings are chosen for the hobbing machine, the value of (wh/wg ) is established, and the number of teeth that will be cut in the gear is then given by the following expression, NhWh Integer closest to (--) Wg (16.15) 462 Gear Cutting II, Helical Gears Having found how the value of Ng depends on the hobbing machine angular velocities wh and wg ' we now consider the helix angle. If points AOg and A1g lie at radius R, the positions of these points at various times can be plotted on a developed cylinder of radius R, as shown in Figure 16.5. The times at which the hob touches points AOg and A1g are called T and T', and the diagram shows the positions of AOg at time T, and A1g at time T'. Since the feed of the hob is in the direction of the gear axis, the line in the diagram joining AOg and A1g is in the same direction. The diagram also shows the gear helices through these points, which appear as straight lines making an angle ~Rg with the gear axis, and these are labelled helix 0 and helix 1. The point on helix 0 in the transverse section through A1g is labelled Ag \u2022 The position of helix 0 at time T' is shown by the dotted line, and the positions of Aog and Ag at this time are shown as AOg and Ag \u2022 In Figure 16.5, the length AOgA1g represents the hob feed between the times T and T', and AgAg represents the arc Hobbing 463 length moved by point Ag in the same time interval. Since helix 0 and helix 1 are gear helices on adjacent teeth at the same radius, their positions at any instant are exactly one tooth pitch apart. A1g and Ag lie on the two helices in their positions at time T', so the distance between these points is equal to the transverse pitch. We therefore obtain the following expressions for the three lengths, A A' 9 9 A A' 19 9 The time interval required for the hob to rotate through one angular pitch can be expressed in terms of the hob angular velocity, T' - T We now use triangle AOgA1gAg to relate the three lengths, A A' - A A' 19 9 9 9 and when their values are substituted, we obtain the following relation between wh ' Wg and vh ' 211' vh -N-- tan l/IR hWh 9 ( 16"
        ],
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        "image_filename": "designv10_4_0003754_3527602844-Figure1-22-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure1-22-1.png",
        "caption": "Figure 1-22 (a} The locus of points for a chaotic trajectory of the Henon map (a /? = 0.3). (b) Enlargement of strange attractor showing finer fractal-like structure. 1.4,",
        "texts": [
            " If one follows a group of nearby points after many iterations of this map, the original neighboring cluster of points gets dispersed to all sectors of the rectangular area. This is tantamount to a loss of information as to where a point originally started from. Also, the original area gets mapped into a finer and finer set of points, as shown in Figure 1-21. This structure has a fractal property that is a characteristic of a chaotic attractor which has been labeled \"strange.\" This fractal property of a strange attractor is illustrated in the Henon map, Figure 1-22. Blowups of small regions of the Henon attractor reveal finer and finer structure. This self-similar structure of chaotic attractors can often be revealed by taking Poincare maps of experimental chaotic oscillators (see Chapter 4). The fractal property of self-similarity can be measured using a concept of fractal dimension, which is discussed in Chapter 6. It is believed by some mathematicians that horseshoe maps are fundamental to most chaotic differential and difference equation models of dynamic systems (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002828_00207170010010579-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002828_00207170010010579-Figure1-1.png",
        "caption": "Figure 1. The general n-trailer system.",
        "texts": [],
        "surrounding_texts": [
            "The material in this section is largely taken from standard textbooks in nonlinear control (see Isirori 1995, Nijmeijer and van der Shaft 1990) and from Abraham et al. (1983) and Bryant et al. (1991) for the basic facts about exterior systems and di\u0152erential forms. A more thorough presentation of this material in the same context of mobile robotics can also be found in Tilbury et al. (1995 a) and Pappas et al. (1998). 2.1. Underactuated drift-free non-linear systems De\u00ae nition 1: An underactuated drift-free control-af\u00ae ne non-linear control system is a collection of r di\u0152erential equations in the variables x and ui; i \u02c6 1; . . . ; r _x \u02c6 Xr i\u02c61 gi\u2026x\u2020ui \u20261\u2020 where x 2 D \u00bb R q with q > r and gi are input vector \u00ae elds gi: D ! R q. It is assumed that D contains the point x0 of R q. Expression (1) can be intended as a representation in a local cover D; x \u02c6 \u2026x1; . . . xq\u2020 \u00a1 \u00a2 of a point p leaving on an abstract manifold M. The tangent space at p 2 M is indicated with TpM and its expression in the local coordinate chart x as TxM. The tangent space TpM has the same dimension of the manifold M . De\u00ae nition 2: The distribution associated with the control system (1) is a collection of independent vector \u00ae elds gi. On each point x 2 D the distribution gives a vector subspace of TxM \u2026x\u2020 \u02c6 span g1\u2026x\u2020; . . . ; gr\u2026x\u2020f g x 2 D \u20262\u2020 Assume gi to be C1\u2026D\u2020 and x0 to be a regular point of , i.e. dim \u2026x\u2020 \u02c6 r 8x 2 D. For the particular kind of system studied in this paper, the dual point of view of the distribution is particularly interesting because, as will be shown below, it corresponds to highlighting the non-holonomic constraints of the system. If the cotangent space, dual to TpM, is called T \u00a4 p M (T\u00a4 xM in coordinates) then the following de\u00ae nition is obtained. De\u00ae nition 3: A codistribution I associated with the control system (1) is a collection of s \u02c6 q \u00a1 r smooth D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le ( A us tr al ia )] a t 1 1: 17 0 9 Se pt em be r 20 14 and linearly independent (over the ring of smooth functions) covector \u00ae elds \u00ac j that annihilate on each point x 2 D I\u2026x\u2020 \u02c6 span f\u00ac1\u2026x\u2020; . . . ; \u00acs\u2026x\u2020g j \u02c6 1; . . . ; s \u02c6 f\u00ac j\u2026x\u2020 2 T\u00a4 xM s:t: h\u00ac j\u2026x\u2020; gi\u2026x\u2020i \u02c6 0 8j \u02c6 1; . . . ; s; i \u02c6 1; . . . ; rg \u20263\u2020 The domain D is assumed to be such that the oneforms \u00ac j\u2026x\u2020 are C1 sections of the exterior algebra over T \u00a4 xM and the codistribution I is a smooth assignment (and therefore, at each point x, a vector subspace of T \u00a4 xM), both with respect to the wedge product, i.e. the alternating (normalized) tensor product. What (3) says is that, in coordinates, the one-forms \u00ac j\u2026x\u2020 can be written as a s \u00a3 r matrix such that the gi\u2026x\u2020 constitute a basis for the right null space of this matrix. Then, if one wants to be able to use the machinery of exterior di\u0152erential systems, one has to endow the codistribution I with some extra structure in order to make sure that the solution of the collection of one-forms is indeed an integrable distribution. This property correspond to the regularity assumption of a point in the distribution case. Such a special case of codistribution is called a Pfa an system. De\u00ae nition 4: The codistribution formed by the smooth and independent one-forms I \u02c6 f\u00ac1; . . . ; \u00acsg is said to be a Pfa an system if it generates an ideal I which is closed under exterior di\u0152erentiation. The ideal generated by I is I \u02c6 f\u00aci ^ \u00b3 s:t: \u00aci 2 I ; \u00b3 2 O\u2026M\u2020g where O\u2026M\u2020 is the module of smooth exterior di\u0152erential forms of all orders on M. 2.2. Local controllability for underactuated systems A fundamental (and well-studied) issue to deal with underactuated systems is controllability (see Nijmeijer and van der Shaft 1990) or, for example, the classical survey paper (Hermann and Krener 1977). In what follows only the local properties around a regular point x0 are of interest. De\u00ae nition 5: System (1) is said to be small-time locally controllable at x0 2 D if one can reach nearby points in arbitrarily small amounts of time remaining in D. It is well-known that the notion of local controllability (which coincides with local strong accessibility for drift-free systems) can be checked in geometric terms by considering the span of the commutators of the vector \u00ae elds that generate the system. This idea is strictly connected with that of involutive distribution via the Frobenius theorem that gives necessary and su cient condition for (local) complete integrability of a distribution. This is essentially equivalent to saying that the annihilator space of has to be spanned by exact differentials, at least locally. The fundamental tool to test local controllability is the Chow theorem which asserts that a system is locally controllable if and only if it is maximally non-integrable. The vector \u00ae elds of , together with their commutators, form an algebra called the control Lie algebra. In order to construct it, one has to build a \u00ae ltration, patching together the vector \u00ae elds of and all the new independent commutators produced at each level of Lie bracketing 0 \u02c6 , i \u02c6 span f i\u00a11 \u2021 i\u00a11; i\u00a11\u0160g;\u2030 such that 0 \u00bb 1 \u00bb \u00a2 \u00a2 \u00a2 \u00bb k \u20264\u2020 for some \u00ae nite k. Di\u0152erent rules for building the above \u00ae ltration are given in Laumond (1993 a, b), and Murray and Sastry (1993). In a regular point, the dimension of the \u00ae ltration (called the growth vector) stabilizes in correspondence of the control Lie algebra. Local controllability is obtained when the rank of the control Lie algebra is equal to the dimension of the tangent space. A dual characterization can be carried out for the Pfa an system corresponding to (1). In particular, dually to the \u00ae ltration (4), a descending chain of Pfa an systems can be constructed called the derivative \u00af ag I 0\u2026 \u2020 \u00bc I \u20261\u2020 \u00bc \u00a2 \u00a2 \u00a2 \u00bc I k\u2026 \u2020 \u20265\u2020 where I \u20260\u2020 \u02c6 I and I \u2026 j\u20211\u2020 \u02c6 f\u00aci \u02c62 I \u2026 j\u2020 s:t: d\u00aci \u00b2 0 mod I \u2026 j\u2020g is the derived Pfa an system of I\u2026 j\u2020. The expression d\u00aci \u00b2 0 mod I \u2026 j\u2020 is called a congruence and means that the exterior derivative of \u00aci is a linear combination of the one-forms of I \u2026 j\u2020 (over the ideal I \u2026 j\u2020), i.e. d\u00aci ^ \u00ac1j ^ \u00a2 \u00a2 \u00a2 ^ \u00acsj \u02c6 0 8\u00aclj 2 I \u2026 j\u2020. Similarly to the \u00ae ltration, the derivative \u00af ag also stops at a certain k for regular points. The maximal non-integrability condition can be stated in terms of the derivative \u00af ag, saying that local controllability is equivalent to the existence of an integer k at which the derivative \u00af ag becomes empty: I k\u2026 \u2020 \u02c6 0. To have controllability, the bottom system of the derivative \u00af ag, which is always integrable by the Frobenius theorem, has to be empty. This implies that there is no integrable subsystem of the original system, i.e. the solution trajectories of I are not constraints to lie on a leaf of a (non-trivial) foliation of M. 2.3. Singularities Regularity of x0 means that the distribution does not lose rank in the neighbourhood D of x0. A similar condition is of interest for the \u00ae ltration (4). If the D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le ( A us tr al ia )] a t 1 1: 17 0 9 Se pt em be r 20 14 dimension of the entire sequence (4) is constant in D, then x0 is regular with respect to the \u00ae ltration, in order to distinguish from the regularity with respect to only. De\u00ae nition 6: A point x0 which is not regular with respect to the \u00ae ltration is said to be singular. All the singular points of the system form the socalled singular locus of the system. The knowledge of the singular locus is important when checking controllability: in fact in correspondence of such a zero dimensional submanifold, the number of Lie bracketing operations needed to span the whole tangent space is di\u0152erent from the points which are regular with respect to the \u00ae ltration. The complexity of such a check (which is proportional to the complexity of a steering algorithm for the system) obviously increases in the singular points. 2.4. Embedding map The next concept needed is that of an embedding map of a manifold. De\u00ae nition 7: Given two smooth manifolds M1 and M2 with dim \u2026M1\u2020 \u02c6 q1 and dim \u2026M2\u2020 \u02c6 q2, q1 \u00b5 q2, the C1 map f : M1 ! M2 is called a local immersion of x 2 M1 if there exists a neighbourhood D 2 M1 of x0 such that rank f \u2026x\u2020 \u02c6 q1 8x 2 D. So a map between manifolds is an immersion if it has the same rank as the domain. Obviously the rank is independent of the local chart used. When an immersion is `well-behaved\u2019 it is called an embedding. For well-behaved we mean that it has to be an isomorphism onto its image with respect to the topology induced from the corresponding R q1 by the local chart used (Spivak 1979). De\u00ae nition 8: The C1 map f : M1 ! M2 is an embedding if it is an immersion and it is an homomorphism onto its image. Moreover, one has the following de\u00ae nition. De\u00ae nition 9: Suppose M1 \u00bb M2. M1 is a submanifold of M2 if the identity map id: M1 ! M2 is embedding. 3. Kinematic model for the general n-trailer Suppose a generalized n-trailer system is obtained with m \u2026m \u00b5 n\u2020 of the trailers not directly attached at the centre of the previous axle but at a positive distance Mi from this point. Assume that each body is composed of one single axle, this being equivalent to the case where two-axis bodies are present, modulo a state feedback (see Tilbury et al. 1995 b). The assumption of rolling without slipping of the wheels can be formulated in terms of non-holonomic kinematic constraints deciding the instantaneous direction of the velocity vector of each axle. Let \u00b3i be the orientation angle of the ith axle and vi the translational velocity of the midpoint of the ith axle, i 2 0; 1; . . . ; nf g. If xi and yi are the corresponding cartesian coordinates, then the one-forms can be expressed as \u00aci \u02c6 dxi sin \u00b3i \u00a1 dyi cos \u00b3i \u02c6 0 \u20266\u2020 If Li is the distance between the ith axle and the hitching point of the same trailer and Mi is the distance between the i th axle and the kingpin hitching point of the following trailer, we can use the (holonomic) relations between two consecutive nodes ith and i \u2021 1th (see \u00ae gure 1) xi\u20211 \u02c6 xi \u00a1 Li\u20211 cos \u00b3i\u20211 \u00a1 Mi cos \u00b3i yi\u20211 \u02c6 yi \u00a1 Li\u20211 sin \u00b3i\u20211 \u00a1 Mi sin \u00b3i 9 = ; \u20267\u2020 and the one-forms (6) to obtain a recursive equation for the orientation angle \u00b3i\u20211 as a function of \u00b3i and vi, i 2 1; . . . ; n \u00a1 1f g _\u00b3i\u20211 \u02c6 vi sin \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 Li\u20211 \u00a1 Mi cos \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 _\u00b3i Li\u20211 \u20268\u2020 Also the calculation of the velocity of the axle i \u2021 1 is slightly more complicated than in the standard n-trailer problem vi\u20211 \u02c6 vi cos \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 \u2021 Mi sin \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 _\u00b3i \u20269\u2020 This accounts for the intuitive phenomenon that, in presence of o\u0152-hitching, a trailer can have a (small) positive velocity and the following trailer a negative one, when the angle between the two trailers \u00b3i \u00a1 \u00b3i\u20211 is changing with high rate. Obviously, both equation (8) and equation (9) reduce to the well-known equations for the standard n-trailer problem when no o\u0152-hitching is present, namely when Mi \u02c6 0. The n-trailer system has two physical inputs, corresponding to translational and steering actions of the car pulling the trailers. Calling  1 7 \u00b30 \u00a1 \u00b31, at the kinematic level these two inputs can be considered to be the steering speed !0 \u02c6 _ 1 \u02c6 _\u00b30 \u00a1 _\u00b31 and the D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le ( A us tr al ia )] a t 1 1: 17 0 9 Se pt em be r 20 14 translational speed v0 of the driving cart. Alternatively, the steering input can be considered as: !0 \u02c6 _\u00b30 \u02c6 v0 sin  1 \u2021 L1 _ 1 L1 \u2021 M0 cos  1 To complete the state space model of the general ntrailer system, the cartesian coordinates of one of the middle points of the axles are needed: for the purposes of proving controllability it is convenient to choose \u2026x0; y0\u2020 of the driving cart _x0 \u02c6 v0 cos \u00b30 \u202610\u2020 _y0 \u02c6 v0 sin \u00b30 \u202611\u2020 whereas it has been shown in S\u00f9 rdalen (1993 a) for the standard n-trailer problem, that choosing the cartesian coordinates of the last trailer is particularly signi\u00ae cant when the task is to transform the system into a chained form, because it is connected to di\u0152erential \u00af atness (Fliess et al. 1995) _xn \u02c6 vn cos \u00b3n \u202612\u2020 _yn \u02c6 vn sin \u00b3n \u202613\u2020 In fact, the coordinates xn and yn correspond to the socalled \u00af at outputs for the standard n-trailer. In both cases, an ad hoc selection of the cartesian coordinates greatly simpli\u00ae es the calculations. The relation between v0 and vn will be derived in } 9."
        ]
    },
    {
        "image_filename": "designv10_4_0003443_j.jbiomech.2005.08.028-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003443_j.jbiomech.2005.08.028-Figure2-1.png",
        "caption": "Fig. 2. Intraject used for liquid injection experiments: (a) in side profile, and (b) in cross-section.",
        "texts": [
            " Full details on the B452 silicone rubber are given in the companion paper of Shergold and Fleck (2004a); this previous paper focuses on the deep penetration of silicone rubbers by solid cylindrical punches. In the current study on liquid jets, the threshold value of stagnation pressure is measured for the successful penetration of human skin and B452 silicone rubber; and the sensitivity of this penetration pressure to the diameter of liquid jet is explored. Informed consent was given by all of the subjects participating in the skin penetration experiments. The Intraject device shown in Fig. 2 was used for the liquid jet injection trials. The device is operated as follows. A sterile drug container is sealed at one end by a piston, and has an orifice at the other end through which the drug is ejected. A stopper held within a plastic sleeve seals the orifice and maintains drug sterility. Immediately prior to injection the plastic sleeve and stopper are removed to expose the orifice, and the orifice is placed in contact with the surface of the skin. On triggering the device a steel ram is accelerated by pressured nitrogen gas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.5-1.png",
        "caption": "Figure 4.5. Angles of approach and recess.",
        "texts": [
            " As we proved in Chapter 3, the path of contact is a segment of the line through the pi tch point perpendicular to the rack tooth profile, so the operating pressure angle ~ of the gear pair is equal to the rack pressure angle, Angles of Approach and Recess 89 -~ sin tfJ (4.11) (4.12 ) where apr is the addendum of the rack, measured from its pitch line. These expressions are substituted into Equation (4.5), and we obtain the contact ratio, Angles of Approach and Recess The tooth profile of the driving gear is shown in Figure 4.5 in three positions, first in the position of initial contact, secondly when the profile passes through the pi tch point, and thirdly in the posi tion of final contact. The profile in the three positions cuts the pitch circle at the three points D, P and D'. When the tooth profile intersects the pitch circle at any point between D and P, the contact point is approaching the pitch point, and arc DP is therefore known as the arc of approach. For a similar reason, arc PD' is called the arc of recess"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000696_tie.2021.3063869-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000696_tie.2021.3063869-Figure13-1.png",
        "caption": "Fig. 13. Analysis flowchart of vibration in multi-physic fields.",
        "texts": [
            " In the proposed motor, the two opposing segments of IPM rotor can compensate some unbalanced radial magnetic Authorized licensed use limited to: Carleton University. Downloaded on May 30,2021 at 01:17:14 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (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. pull caused by the unequal pole width. Comprehensive models using coupled multi-physic fields are established, and the analysis flowchart is shown in Fig. 13. The exciting force calculated in electromagnetic field and the modal information calculated in vibration force field will be imported to simulate the vibration response. In order to verify the compensation effect of radial force by the two opposing rotor segments, a IPM motor with a single segment rotor for the same Kt is added for comparison. The radial and axial unbalanced pulls of the three motors are calculated and compared in Fig.14. It can be seen that the proposed motor can benefit from the two opposing segmented rotor to reduce the radial unbalanced pull"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure9-1.png",
        "caption": "Fig. 9. An elementary three-legged platform.",
        "texts": [
            " Hence, this produces two constraints on the motion plane and gives the mobility 1. This mobility is obtained after removing two legs of the elementary four-legged platform. The removed four links and six joints on that orthogonal plane have no effect to the mobility of the elementary four-legged platform. This constitutes the theoretical basis of mechanism decomposition of the magic-ball mechanism as stated in Section 3. Similar to the analysis of the elementary four-legged platform, the mobility of the three-legged platform in Fig. 9 can be calculated as follows. Starting from leg 1, screws of three kinematic pairs are given as $11 : \u00f0 1 0 0 0 0 b1 \u00deT; $12 : \u00f0 1 0 0 0 a2 b2 \u00deT; $13 : \u00f0 1 0 0 0 a3 b3 \u00deT: The reciprocal screws are $r11 : \u00f0 0 0 0 0 0 1 \u00deT; $r12 : \u00f0 0 0 0 0 1 0 \u00deT; $r13 : \u00f0 1 0 0 0 0 0 \u00deT: There are two constraint couples and one constraint force for leg 1. For all three legs, there are six constraint couples and three constraint forces. The three constraint couples, $r11, $ r 21 and $r31 acting about z-axis, are the same and form a common constraint couple of the platform mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure3-1.png",
        "caption": "Fig. 3. Variations in O \u2013A i chain.",
        "texts": [
            " Here, the i th limb of the robot can be split to depict the variations in the design parameters in a vectorial form. The closed-loop kinematic chains with parallelogram is described by O \u2013A i \u2013B i \u2013B i j \u2013C i j \u2013 i \u2013P, i = 2 , . . . , 3 , j = 1 , 2 , and O \u2013A i \u2013B i \u2013C i \u2013P, i = 1 , for the RUU linkage. Vectors o , a i , b i , b i j , c i j , c i , p , are the Cartesian coordinates of points O, A i , B i , B i j , C i j , C i , P in the reference coordinate frame F b , respectively. According to Fig. 3 , a i \u2212 o = (R + \u03b4R i ) R z (\u03b7i + \u03b4\u03b7i ) j + \u03b4a zi k (4) where \u03b4R i and \u03b4\u03b7i are the variations in the nominal geometric parameters R and \u03b7i , respectively, and \u03b4a zi is the positioning error of A i along z-axis. According to Fig. 4 , b i \u2212 a i = (b i + \u03b4b i ) R Bi j (5) with R Bi = R z (\u03b7i + \u03b4\u03b7i )(I + [ \u03b4\u03c6i ]) R z (\u03b8i + \u03b4\u03b8i ) (6) where [ \u03b4\u03c6i ] represents the cross-product matrix (CPM) 2 of vector \u03b4\u03c6i = [ 0 \u03b4\u03c6yi \u03b4\u03c6zi ]T , and I is the 3 \u00d7 3 identity matrix. Moreover, \u03b4b i is the variation in b i , \u03b4\u03b8i is the error of input angle \u03b8i of the i th actuator and \u03b4\u03c6i represents the angular variations of manufacturing errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000138_s11837-019-03913-x-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000138_s11837-019-03913-x-Figure2-1.png",
        "caption": "Fig. 2. Depiction of material being added on top of a substrate, creating new surfaces for the convection and radiation boundary conditions in the DED process.",
        "texts": [
            " However, Gouge concludes that the effect of fixturing on the model accuracy is only significant near areas of contact and can be ignored in fixturing bodies with minimal contact area. Some researchers emphasize the fact that boundary conditions should be enforced on the entire developing boundary, as the AM process is evolving.13,60 This includes the small surface areas that are added as a new layer is being deposited. The high thermal gradients in these regions can cause a significant contribution of these small areas to the overall heat transfer. A schematic of the evolving surfaces is shown in Fig. 2, which considers the convection and radiation boundary conditions in a DED process. The majority of AM processes utilize either a laser or electron beam as the heat source for melting or sintering. The concept of heat source modeling has been extensively investigated for computational welding applications. Historically, the first analysis of moving heat sources is attributed to Rosenthal.63 This work provided an analytical solution to the problem of modeling the heat source, but it was problematic when incorporated into finite element codes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.3-1.png",
        "caption": "Figure 7.3. Regions of maximum stress.",
        "texts": [
            " During this period, only a certain part of the profile of each meshing tooth comes into contact with the tooth of the other gear. The ends of this section of the tooth profile are called the highest and lowest points of single-tooth contact. The maximum stresses in a spur gear tooth occur when the tooth force is at its largest value, or in other words, during the period of single-tooth contact. There are two types of stress which are of primary interest to the gear designer, the tensile stress in the fillet of each tooth, and the contact stress at the point of contact. A typical loaded tooth is shown in Figure 7.3, with the critical regions of fillet stress and contact stress marked on the diagram. For a 176 Miscellaneous Circles constant tooth force, the fillet stress increases as the load moves towards the tooth tip. The maximum value is reached when the load is applied at the highest point of single-tooth contact. Beyond this point the tooth force is approximately halved, as we showed earlier, and the fillet stress is therefore reduced. The contact stress also varies as the contact point moves along the tooth profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.15-1.png",
        "caption": "Figure 16.15. Normal section through a gear tooth.",
        "texts": [
            " We described a method in Chapter 13 for calculating the profile of the normal section through a helicoid. We now use this method to find the profile of the normal section through the hob thread. We calculate the distances, at the thread tip and at the top of the fillet, between this profile and its tangent at the standard pitch cylinder, as shown in Figure 16.14. The profile of a straight-sided hob would coincide with this tangent, and a hob of that type would therefore cut too deeply into the teeth of the gear, in the regions near the fillet and near the tip. Figure 16.15 shows the normal section through an Effect of a Non-Standard Shaft Angle 481 exact involute helicoid tooth, and it also shows the profile we obtain when the gear is cut by a straight-sided hob. The maximum differences between the two profiles are approximately equal to the distances described earlier, by which the normal section profile of the involute hob deviates from the straight line. As we can see in Figure 16.15, the tooth shape cut by a straight-sided hob is similar to the shape of a tooth cut with tip and root relief. The errors caused by the use of a straight-sided hob are therefore sometimes beneficial, and this is one of the reasons for the continued use of straight-sided hobs, when true involute hobs are also readily obtainable. There are times, however, when the errors caused by straight-sided hobs may be excessive. This is often the case for gears cut by multi-thread hobs, or by single-thread hobs of large module, whose helix angles are usually less than 85\u00b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure3-1.png",
        "caption": "Fig. 3. Temperature distribution of the small-scale model at a certain time step by detailed process simulation.",
        "texts": [
            " Moreover, some necessary details for the parameter calibration for printing thin-walled lattice structures through thermocouple experiment are presented in Appendix D. If necessary, many helpful details such as the thermal and mechanical boundary conditions employed for this kind of small-scale detailed process simulation can be found in Refs. [20,24]. According to the detailed small-scale process simulation, a typical temperature distribution of the small-scale model at a certain time step is shown in Fig. 3. Line numbering in Fig. 3 is exactly the same with that in Fig. 2. The simulated depositing order is 1-2-4-3 as in the practical LPBF process. The thermal history of the mid-point of the single wall (line 1 in Fig. 3) in the first layer is plotted in Fig. 4(a). As can be seen in the figure, two drastic temperature increases can be found due to repeated heating and cooling of the two-layer metal depositions. Especially for a point in the cross regions of the small-scale model, due to two perpendicular laser scanning paths, two melting events are simulated for materials over there. As a result, two temperature peeks are shown during depositing of a single layer based on the thermal history as plotted in Fig. 4(b). The plotted thermal profiles in Fig. 3 and thermal history curves in Fig. 4 look very reasonable and convincing. Therefore, the detailed small-scale process simulation is reliable for extraction of inherent strains in the walls of the thin-walled lattice structures. Regarding the choice of the small-scale model containing four walls, another necessary clarification is made hereby. According to experimental experience, the materials at the edge and corner of an AM build may have different mechanical behavior largely because of different thermal histories related to different boundary conditions",
            " Assume \u201ca larger RVE\u201d contains more lines in the small-scale model (selected representative volume). For example, a small-scale model where six lines are included is taken into consideration. In contrast to Fig. 2, there are three lines in each direction on the 2D plane and four square hollow sections are formed. The gap size between two walls is identically 1.0 mm like that shown in Fig. 2. New simulation results show that the extracted inherent strain values are nearly the same to those values shown in Fig. 3 as expected. The reason is that the heat source diameter is assumed to be 0.1mm, which is very small compared with the length of each line in the small-scale model (line length is 2.0 mm in Fig. 2, for example). In addition, the laser scanning velocity is 0.9m/s. Therefore, the temperature decreases very quickly after heat source moves away. Given a concerned material point in the line, those materials far away have limited influence to the point of interest. This finding can also be observed in Fig",
            " Theoretically, the size of the small-scale model should vary when the distance between walls of the lattice varies. For example, the small-scale model with wall gap size of 0.75mm and 0.5 mm should be used for volume density of 0.25 and 0.36, respectively. However, our thermal simulation result indicates a wall has no influence on the remaining walls except the cross regions. The heatinduced high temperature affected zone is very small compared with the gap size according to thermal history of the small-scale model at a certain time step as shown in Fig. 3. Therefore, we can assume the influence of a wall on the remaining walls is limited when distance between walls of the lattice is large enough. As a result, we can apply the extracted inherent strains from small-scale simulation for volume density of 0.19 to other cases in this paper. Nonetheless, it is noted that the above finding may not hold for a case where the wall gap size is close to or smaller than the wall thickness. For example, when the gap size decreases to 0.15mm for volume density of 0",
            "05mm as elucidated in Fig. 4(c). The directional inherent strain vectors including = \u2212 \u2212\u03b5 ( 0.010, 0.003, 0.009)1 * and = \u2212 \u2212\u03b5 ( 0.003, 0.010, 0.009)2 * are assigned to the four walls with respect to their span-wise direction accordingly as shown in Fig. 5. For the four corners, the two in-plane components in the directional inherent strain vector are averaged, and the simple inherent strain vector = \u2212 \u2212\u03b5 ( 0.0065, 0.0065, 0.009)3 * is assigned to those cross regions instead of using the calculated values in Fig. 3. This choice is consistent with some previous works [20,22,24,25], where the average of directional inherent strain vectors was used for the solid material scanned by rotational laser scanning strategy in the simulations to gain efficiency by layer lumping. The benefit is that the homogenized inherent strains can converge to certain values for solid material when volume density reaches its limit of 1 in the paper. However, when volume density of lattice structures increases and gap distance between two walls decreases, the four corners will be major areas occupied by materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003406_095440503321628125-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003406_095440503321628125-Figure2-1.png",
        "caption": "Fig. 2 Finite element mesh model",
        "texts": [
            " Since LBAM involves very rapid melting and solidi\u00aecation, the convective redistribution of heat within the molten pool is not signi\u00aecant. The convective \u00afow of heat, therefore, is neglected. ANSYS provides convenient means of numerically modelling the LBAM process. In this simulation, transient analysis is performed to \u00aet the requirements of the process. In \u00aenite element analysis formulation, the equation can be written for each element as \u2030C\u2026T\u2020\u0160f _Tg \u2021 \u2030K\u2026T\u2020\u0160fTg \u02c6 fQ\u2026T\u2020g \u20269\u2020 The meshed \u00aenite element model of the single-bead wall with a height h and thickness w is shown in Fig. 2. The model is meshed with an eight-node brick element. The size of the elements in the top layer is controlled, so a \u00aene mesh can be achieved in the layer concerned, and the further heat \u00afux boundary condition can be applied on the nodes with accurate position. A free mesh is carried onto the remainder of the wall and the substrate, and the eight-node brick element degrades to a tetrahedral element. The moving laser beam will be simulated automatically using an ANSYS parametric design language (APDL) program to provide a heat \u00afux boundary condition (absorbed laser energy) at di erent positions, times and values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure9.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure9.9-1.png",
        "caption": "Figure 9.9. Gear tooth fillet and pinion cutter.",
        "texts": [
            " Since we have now expressed Yr as a function of xr for all points on the cutter tooth profile below Ahr , we can use Equations (9.3 - 9.8) to calculate the corresponding section of the gear tooth profile. We could, of course, also express Yr as a function of xr for the tip section of the cutter tooth, but the method described earlier is generally more convenient. Fillet Shape Cut by a Pinion Cutter To find the fillet shape of a gear cut by a pinion cutter, we use a procedure which is essentially the same as the method described earlier, for the case when the gear was cut by a rack cutter. Figure 9.9 shows the pinion cutter, in position to cut a point on the tooth fillet of the gear. The circular section of the cutter tooth profile starts at point Ahc ' and ends at ATc \u2022 The radius of the section is r cT ' and its center A~ has polar coordinates (R~,8~) given by Equations (5.32 and 5.39). We consider the posi tion of the cutter when the line C A' c c makes an angle a with the line of centers. The coordinates 222 Geometry of Non-Involute Gears (E' ,1/') of point A~ are then given by the following equations, ~ , RC - R' cos a pc C (9",
            " We then solve Equation (10.8) for Pg ' obtaining the following expression, (p +s)2 c (10.10) In order to calculate the radius of curvature Pg at a point on the gear tooth profile, we use the methods described in Chapter 9 to find the coordinates (~,~) of the cutting point, corresponding to any specified point on the cutter tooth. The radius of curvature of the cutter tooth profile at this point gives the value of Pc to be used in Equation (10.10), and expressions for If> and s can be read from Figure 9.9, which shows the meshing diagram during the cutting process, tan If> s \u00a3. ~ -~ sin If> (10.11) (10.12) These values for P, If> and s are substituted into c Equation (10.10), and we obtain the radius of curvature Pg at the corresponding point on the gear tooth profile. We first use this method to find the radius of curvature at points on a gear tooth fillet, for the case when the gear is cut by a rack cutter. The cutting pitch circle radius of the rack cutter is infinite, and the cutting pitch circle of 236 Curvature of Tooth Profiles the gear coincides with its standard pitch circle, so the length RO defined by Equation (10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure5.14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure5.14-1.png",
        "caption": "Figure 5.14. Meshing diagram of a gear and pinion cutter.",
        "texts": [
            " For example, in a 20\u00b0 pressure angle rack cutter, with an addendum of 1.25m and a circular tip radius of 0.3m, the length h has the following value, h 1.0526m (5.46) 138 Gear Cutting I, Spur Gears Radius of the Fillet Circle We defined the fillet circle of a gear in Chapter 4, as the circle through point Af on the tooth profile, where the involute part of the profile ends and the fillet begins. To find the position of Af on a gear cut by a pinion cutter, we consider the meshing diagram of the gear blank and the cutter, which is shown in Figure 5.14. If the cutter is turning counter-clockwise, the cutting point moves outwards on the cutter tooth towards the tip, inwards on the gear tooth towards the root, and downwards along the path of contact. The involute part of the gear tooth profile is cut by the involute section of the cutter tooth. The lowest point Af on the gear tooth involute is therefore cut by Ahc ' the highest point on the cutter tooth involute, and this occurs when Ahc lies on the path of contact. The path followed by Ahc is a circle of radius Rhc ' and the point where this circle intersects the common tangent to the base circles is labelled Hc",
            " The involute section of the gear tooth profile is cut by the straight-sided part of the cutter tooth, and the end point Af of the gear tooth involute is therefore cut by point Ahr on the cutter. This cut is made when Ahr lies on the path of contact, which takes place at Hr , the point where the path followed by Ahr intersects the path of contact. Hence, the 140 Gear Cutting I, Spur Gears fillet circle of the gear passes through point Hr , and its radius is found as follows, R2 [ h-e ] 2 bg + Rbg tan 4J s - sin 4J s (5.48) In Figure 5.14, Hc is the end point of the straight-line path of contact, which corresponds to the involute sections of the gear and the cutter tooth profiles. If we were to find the position of the cutting point corresponding to a point on the gear tooth fillet, it would not lie on the same straight line. However, for the present we are only interested in the involute part of the tooth profiles, so we will regard point Hc as the end of the path of contact. Hc is shown in Figure 5.14, lying between the pitch point P and the interference point Eg \u2022 As we stated in the previous section, the position of Hc is determined by the intersection of the cutter circle of radius Rhc ' and the common tangent to the base circles. If point Hc lies below Eg , the following situation will occur. While the cutting point moves down the path of contact as far as point Eg , the gear tooth is cut with the correct involute profile, right down to point B on the base circle. However, when the cutting point reaches Eg , there is still part of the cutter involute near point Ahc ' which has not yet made a final cut on the gear tooth",
            " For this reason, provided there is no undercutting by point Ahc ' there is also no undercutting by the rounded section of the cutter tooth. When we check to see whether undercutting will take place, we can 142 Gear Cutting I, Spur Gears therefore treat the cutter tooth as if it ~nded at point Ahc ' We make the check, simply by determining the position of point Hc on the path of contact. For no undercutting, Hc must lie between the pitch point and the interference point E \u2022 In g other words, the length HcEc in Figure 5.14 must be less than or equal to EgEc' and the condition for no undercutting can be expressed as follows, (5.49) The same considerations on undercutting apply when a gear is cut by a rack cutter or a hob. The path of contact in Figure 5.15 must end between the pitch point and the interference point, so the length HrP must be less than EgP, and we obtain the following condition for no undercutting, Rbg tan tPs (5.50) It can be seen that, for any particular value of the cutter offset e, there is a lower limit to the base circle radius in the gear being cut, if there is to be no undercutting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003581_icar.2005.1507426-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003581_icar.2005.1507426-Figure2-1.png",
        "caption": "Figure 2 Artist\u2019s impression of a robotic vehicle for power line inspection.",
        "texts": [
            " Essentially the unmanned vehicle must reproduce the behavior associated with a manned vehicle \u2013 even if the data-link with a remote pilot fails. The current restriction that UAVs operate only within direct sight of a groundbased pilot is not compatible with the economics of power line inspection, which require missions to have a 10-15km range. A concept which has the potential to circumvent this problem consists of an electrically driven rotorcraft that draws its power from the overhead lines, as illustrated in Figure 2. The vehicle itself is a ducted fan configuration with contra-rotating rotor blades which gives increased propeller efficiency, reduces noise, eliminates the need for a tail rotor and provides a protective cowl for the blades, while also minimising the effect of wind-gusts. T 2880-7803-9177-2/05/$20.00/\u00a92005 IEEE A crucial part of the concept is picking up power from the overhead line and an active pantograph is proposed for this function. This concept has several advantages, the crucial point being that the vehicle is effectively tethered to the lines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002984_s0021-9290(99)00137-2-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002984_s0021-9290(99)00137-2-Figure7-1.png",
        "caption": "Fig. 7. The planar model for the long jump (schematic drawing with geometric parameters).",
        "texts": [
            " These can be attributed to the movement of the distal mass. In our model the body mass (m 1 ) is supposed to glide on a massless rod. The orientation of this rod is de\"ned by the position of the ball of the foot and the centre of the body mass. Similar to the simple spring}mass model, the body is coupled to the ground via a linear spring, representing the spring-like operation of the human leg (active peak). At a certain height, a second mass is \"xed to the rod by nonlinear visco-elastic elements (Fig. 7). The equations of motion are rK 1 \"a5 2r 1 ! k m 1 (r 1 !l(a))!g ) sin a (8a) aK\"! 1 m 1 r2 1 (r 2 )F s !*s )F q )! 1 r 1 (2r5 1 ) a5 #g ) cos a) (8b) *qK\"*s ) aK#r 2 ) a5 2#2*s5 ) a5 #(F q /m 2 )!g ) sin a (8c) *sK\"!r 2 ) aK#*s ) a5 2!2*q5 ) a5 #(F s /m 2 )!g ) cos a (8d) with the nonlinear visco-elastic force functions: F q (*q, *q5 )\"!(c q ) sgn(*q)#d q *q5 )*qlq (9a) F s (*s, *s5 )\"!(c s ) sgn(*s)#d s *s5 )*sls. (9b) The properties of the element's coupling in radial and tangential direction are assumed to be the same (c q \"c s \"c, d q \"d s \"d, l q \"l s \"l)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003552_02640410600874971-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003552_02640410600874971-Figure3-1.png",
        "caption": "Figure 3. Golf swing events used in this study.",
        "texts": [
            " The average of the two points was calculated for each frame and the velocity of this average point was calculated and used to indicate club head velocity. The difference between the systems was within the factory error specifications reported as+1 foot per second (+0.3 m s71). Figure 2. Golf testing set-up. D ow nl oa de d by [ U ni ve rs ity o f N ew H am ps hi re ] at 1 3: 04 0 4 O ct ob er 2 01 4 To identify eight swing events for each trial (as viewed in the vertical YZ plane; see Table I and Figure 3), the 200-Hz video camera was placed perpendicular to the line of shot. Video and force plate data were synchronized at ball contact. Ball contact for the force plate data was recorded by the microphone trigger system, while ball contact for the 200-Hz video was determined by visual inspection of the video. CPy was normalized to foot position at address following Mason et al. (1995). An overhead camera (50 Hz) was positioned to capture foot position at address relative to the force plate coordinate system for each trial"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure3-1.png",
        "caption": "Figure 3 The Orthoglide mechanism.",
        "texts": [
            " Then using the modified G-K criterion, we have ( ) 1 ( 1) 6 8 9 1 12 3 3. g i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + =\u2211 (11) Since the axes of pairs in each limb always keep parallel and the axes of the three pairs on the base are orthogonal with each other, eqs. (9) and (10) are invariable as long as we choose the same coordinate system as shown in Figure 2. Thus, the numbers of common constraints and redundant constraints always keep fixed. So the mobility is global. The Orthoglide mechanism[46] is shown in Figure 3. It has three limbs and each limb includes a four-bar paral- 1342 Huang Zhen et al. Sci China Ser E-Tech Sci | May 2009 | vol. 52 | no. 5 | 1337-1347 lelogram loop. Let us take the hinged parallelogram linkage into consideration firstly. It is shown in Figure 4 and can be regarded as having two limbs. Point A is chosen as the origin point, x\u2032-axis is along the link AD, y\u2032-axis locates on the plane ABCD and z\u2032-axis is along the direction of the revolute pair. For the first limb, the twist system is given by ( ) ( )1 1 0 0 1; 0 0 0 , 0 0 1; 0 , A B y x = = \u2212 $ $ (12) where (x1, y1, 0) denotes the coordinates of point B",
            " Therefore, the whole parallelogram loop is equivalent to a generalized translational pair. From the above analysis, it can be concluded that each limb of the Orthoglide mechanism is equivalent to a 4-DOF serial chain including four pairs, which are a prismatic pair fixed on the frame, a generalized translational pair and two revolute joints connecting the parallelogram loop at its two ends. In addition, the axes of three prismatic pairs fixed on the frame are orthogonal with each other. B1-xyz is the coordinate system, as shown in Figure 3, where x-axis is along the prismatic pair and z-axis is coaxial with the revolute joint. Then, the first limb twist system of the Orthoglide mechanism is ( ) ( ) ( ) ( ) 1 1 1 2 1 3 3 3 3 1 4 4 4 0 0 0; 1 0 0 , 0 0 1; 0 0 0 , 0 0 0; , 0 0 1; 0 . d e f d e = = = = $ $ $ $ (18) The constraint screw system is ( ) ( ) 11 12 0 0 0; 1 0 0 , 0 0 0; 0 1 0 , r r = = $ $ (19) which means the limb exerts two constraint couples upon the moving platform. The two couples are not only perpendicular with each other but also normal to the axis of revolute joint of this limb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure6.41-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure6.41-1.png",
        "caption": "Figure 6.41. (a) Aharonov-Bohm effect in quantum mechanics, showing phase difference between two electron trajectories passing through points Rl and R2, respectively. (b) Setup for holographic imaging of (c) electron phase distribution introduced by a magnetic specimen.",
        "texts": [
            " Although domain structures can be directly seen using Fresnel contrast and Lorentz microscopy, electron holography is probably the only technique which can provide quantitative information about the structure of domains and the field distribution around it (Mankos et aI., 1995; Tonomura, 1992). The mechanism of imaging magnetic domains in magnetic materials relies on the Aharonov-Bohm effect, which describes the relative phase shift of two electron waves traveling from point Q to P along routes enclosing a zone with magnetic field distribution (Fig. 6.41a): 1.\\<1> = <1>1 - <1>2 = - B . dS = - A\u00b7 dL 2n:e J 2n:e f h s h (6.100) where dS is a surface integral over the area enclosed by the two routes and the surface normal is pointing into the paper, A is the magnetic vector potential with B = V x A, and dL represents a path integral following Q-RI-P-RrQ. In fact, electron holography has provided direct experimental evidence for the existence of the Aharonov-Bohm effect (Tonomura, 1993). To illustrate how magnetic microstructure is quantitatively revealed by holographic imaging, we assume that the magnetic flux does not leak out of the specimen and that the sample is uniform in composition and thickness, such that the magnetization is uniform along the beam direction and the phase introduced by the electrostatic field of the specimen is constant across the specimen. For a simple in-plane closure domain (Fig. 6.41 b), the phase shift due to the magnetic flux lies in the plane of the two beam paths (x z plane) and the phase difference is 2n:e J J 1.\\<1> = h Bn(x, y) . dy dz (6.101) 319 ELECTRON CRYSTAL LOGRAPHY FOR STRUCTURE ANALYSIS 320 CHAPTER 6 where Bn is the component of the magnetic field normal to the plane determined by the wave vectors of the two split electron waves (Le., the x axis for the configuration in Fig. 6.41b). As more flux lines are enclosed, the phase shift increases linearly (Fig. 6.41c). A gradient of the phase difference with respect to y yields, for the specimen with uniform composition and negligible thickness variations, a~<p 2ne ay = hBn(x,y). d(x,y) (6.102) The phase gradient represents a direct measure of the local variations of the normal in plane component of the megnetic flux density Bn(x, y), averaged along the specimen thickness d(x, y). This is the basis for electron holography as a quantitative magnetometric method at high spatial resolution (Mankos et al., 1994, 1995; Hirayama et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000820_3411763.3451513-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000820_3411763.3451513-Figure3-1.png",
        "caption": "Figure 3: Exploded view of a FlowIO device with main module and small pump module.",
        "texts": [
            " The main driver PCB features a magnetic connector with 4 pins for connection to the pump module, a power button with programmable auto-of timer, and a 14-pin expansion port providing access to I2C, SPI, UART, and analog GPIO pins. A 500mAh LiPo battery is located underneath the valves and is rechargeable via the USB port. The entire main module has a mass of only 77 grams. The pump module comes in a small, medium, and large version to serve diferent pressure, fow-rate, or dimensional needs of users. The primary diference between them is the choice of pumps and batteries used. A pump module consists of 2 identical pumps, a custom driver board, and a LiPo battery, all enclosed in a 3D printed snap-ft enclosure (Figure 3). The driver board features power electronics for driving the pumps, a charging circuit with a USB port for easy battery charging, and electronics that support switching between a 3.7V battery source and an external power source up to 24V. The pump module connects to the main module via a 4-pin magnetic connector and via 2 silicone tubes. I made the design choice to have the pump and the main modules be voltage independent of each other, in order to allow virtually any kind of DC pumps to be used with FlowIO, and for users to be able to make their own pump modules using any pumps they desire operating between 3V and 24V"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure17.14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure17.14-1.png",
        "caption": "Figure 17.14. Load of intensity w acting at radius Rw'",
        "texts": [
            "24), depending on the value of the face contact ratio mF \u2022 We then use Equations (17.40 - 17.42) to find the radii of curvature Pt1 and Pt2 at the point where the contact 508 Tooth Stresses in Helical Gears stress is to be calculated. And finally, the factor kc is given by Equation (17.44 or 17.46), and we substitute into Equation (17.43) to obtain the contact stress. Fillet Stress, and the Equivalent Spur Gear Before we calculate the maximum fillet stress in the tooth of a helical gear, we first consider a more general case. Figure 17.14 shows a tooth profile, loaded by a force of intensity w at a typical point Aw' which is at radius Rw' The tooth profile shown is the profile in the normal section through Aw' so that the tooth force acts in the plane of the section, and along the normal to the profile. Since Aw does not lie on the tooth center-line, the tooth profile is not exactly symmetrical. Although it is possible to calculate the shape of the tooth profile in the normal section, by the method described in Chapter 13, the procedure is very long"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure15.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure15.4-1.png",
        "caption": "Figure 15.4. Directions of the unit vectors.",
        "texts": [
            " For this reason, crossed helical gear pairs are generally designed so that the values of C and I: are ei ther equal, or approximately equal, to Cs and I:s ' It is one of the major advantages of all involute gears that small errors or changes in the center distance do not affect the operation of a gear pair, since the value of C does not have to be equal to the standard value Cs ' Crossed helical gears have the further advantage, that small errors or changes can also be made in the shaft angle, and in spite of this, the angular velocity ratio remains constant. Relations Between the Uni t Vectors Before we discuss the meshing geometry in detail, it is necessary to define the directions of the various sets of unit vectors, and this is done in a manner which is consistent with the definitions given at the end of Chapter 14. The n~ direction is chosen perpendicular to the pitch planes of the imaginary rack, in the direction from COl towards CO2 ' The two pitch cylinders and the imaginary rack pitch planes are shown in Figure 15.4, viewed in the n~ 420 Crossed Helical Gears direction. The unit vectors n~ and nS are defined, as usual, in the directions perpendicular to and parallel with the teeth of the imaginary rack. We use points C01 and CO2 as the origins of the x,y,z coordinate system in each gear. This means, of course, that the origin of each coordinate system no longer lies in the end face of each gear, as it did when we discussed the geometry of parallel-axis gears in Chapter 14. There is a set of unit vectors nx1 ' ny1 and nz1 fixed in gear 1, and a second set nx2 ' ny2 and nz2 fixed in gear 2",
            " The reference directions, from which the gear rotations are measured, are chosen so that nz1 (0) and nz2 (0) are parallel with the gear axes. nx1 (0) and nx2 (0) are parallel to line C01 C02 ' so that they are perpendicular to the imaginary rack pitch planes, and in each case they point in the direction from the gear towards the imaginary rack. Finally, ny1 (0) and ny2 (0) complete the right-handed sets. The relations between the reference directions of the gears and the vectors fixed in the imaginary rack can be read from Figure 15.4. Once again, it is more convenient to express these relations in terms of the operating helix angles of the gears, rather than the rack helix angles. Relations Between the Uni t Vectors 421 (15.36) cos \"'p1 n1/ + sin \"'p1 nS (15.37) (15.38) (15.39) (15.40) (15.41) We will make use again of nnr and nTr , the unit vectors perpendicular and tangent to the tooth profile in a normal section through the imaginary rack. The vectors n E and n1/ can be expressed in terms of nnr and nTr by means of Equations ( 1 4 \u2022 85 and 1 4 \u2022 86) , - sin 9>np nnr - cos 9>np nTr (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003443_j.jbiomech.2005.08.028-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003443_j.jbiomech.2005.08.028-Figure1-1.png",
        "caption": "Fig. 1. (a) Penetration of a soft solid by a sharp-tipped punch, (b) crack opened to allow punch advance, (c) crack closed after punch removal.",
        "texts": [
            " The medical literature on skin injection and the mechanical engineering literature on rubber penetration each indicate that deep penetration by a sharp-tip solid penetrator involves cracking of the soft solid, followed by substantial reversible deformation after the penetrator has been removed (Stephens and Kramer, 1964; Katakura and Tsuji, 1985; Stevenson and Abmalek 1994; Shergold and Fleck, 2004a). A limited number of experimental studies reveal the sensitivity of crack geometry to the punch tip geometry and to the material properties of the penetrated solid (Stephens and Kramer, 1964; Katakura and Tsuji, 1985; Stevenson and Abmalek, 1994). Shergold and Fleck (2004a) have demonstrated that a sharp-tipped punch penetrates human skin and silicone rubber by the formation of a planar mode I crack ahead of the tip, see Fig. 1a. The crack faces are wedged open by a punch that advances at a velocity vP, see Fig. 1b. 0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.08.028 Corresponding author. Tel.: +441223 332650; fax: +441223 332622. E-mail address: nafl@eng.cam.ac.uk (N.A. Fleck). Upon punch removal the planar crack closes (Fig. 1c), and in this undeformed configuration the crack has a length of 2a. In this paper, we shall demonstrate experimentally that a high-speed liquid jet penetrates human skin and silicone rubber by the same mode I planar cracking mechanism as that observed for a sharptipped punch. Shergold and Fleck (2004b) have proposed that the deep penetration of a soft solid by a sharp-tipped punch occurs by the mechanism shown in Fig. 1. The soft solid represents mammalian skin and silicone rubbers, and is treated as an incompressible, hyper-elastic, isotropic solid as described by a one-term Ogden (Ogden, 1972) strain energy density function of the form f \u00bc 2m a2 \u00f0la1 \u00fe la2 \u00fe la3 3\u00de, (1) where f is the strain energy density per undeformed unit volume, a is a strain hardening exponent, m is the shear modulus under infinitesimal straining and li are the principal stretch ratios. The Shergold\u2013Fleck model predicts that the axial penetration pressure pS on the shank of the punch increases with diminishing punch radius R, and with increasing mode I toughness JIC, shear modulus m and strain hardening exponent a",
            " These findings are similar to the sharp-tipped punch penetration experiments of Shergold and Fleck (2005a). A comparison of the investigations reveals that a liquid jet requires double the pressure to penetrate human skin or B452 rubber compared with a sharp-tipped punch of equal diameter. Photographs of the injection site show that a liquid jet penetrates a soft solid by the formation of planar crack that opens to accommodate fluid flow. This penetration mechanism is similar to that of a soft solid by a sharptipped punch (Shergold and Fleck, 2005a), as shown in Fig. 1. Examples of cracking on the surface of human skin and B452 silicone rubber are given in Fig. 6. Sections taken perpendicular to the front face of the B452 rubber block a posteriori demonstrate that the crack extends deep into the block. Fig. 7 shows the crack geometry at depth into the B452 rubber block. Fig. 8 shows the length of the crack at different depths into the B452 rubber block following penetration by a liquid jet of diameter 0.34 and 0.50mm. In the case of the liquid jet of diameter 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-FigureC-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-FigureC-2-1.png",
        "caption": "Figure C-2 Elastica and boundary conditions for bilinear beam chaos.",
        "texts": [
            " As the motor speed is increased further, the beam will jump from one equilibrium position to the other. Under the right conditions (e.g., magnet spacing, motor speed, mass positions), which usually take about 5 minutes to search for, the beam will perform chaotic motions. To achieve a more theatrical effect, I have glued a small mirror on the beam and projected a laser beam on a wall or ceiling with spectacular effects as the motion makes the transition from periodic to chaotic motion. If the magnets are replaced by a thin metallic channel as shown in Figure C-2, one can demonstrate chaotic vibrations of a beam with nonlinear boundary conditions (see Chapter 3). If the metal end constraint is very thin, the audience can hear the nonperiodic or periodic tapping of the beam against the constraints. cantilevered beam in the field of two strong magnets can be described quite 282 Chaotic Toys adequately by a nonlinear differential equation of the Duffing type: x -f x \u2014 ax + /?x3 = /cos <o/ Successful experiments in chaotic vibration have been carried out with two different beams by shaking the beam clamp and magnets with an electromagnetic shaker as shown in Figure C-3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000072_s40192-019-00149-0-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000072_s40192-019-00149-0-Figure1-1.png",
        "caption": "Fig. 1 The AMB2018-01 bridge structure geometry shown here without the attached build plate. The strain/stress measurements were performed on parts still attached to the build plate",
        "texts": [
            " The PSD measurements were performed using a commercial dynamic image analysis system. Chemical compositions were measured using mass spectroscopy performed at two external laboratories. Chemical composition measurements follow ASTM E1019. Detailed results of the PSD and composition can be found on the NIST AM-Bench website, at www.nist.gov/amben ch/ amb20 18-01-descr iptio n. The AMB2018-01 tests consist of AM LPBF 3D metal alloy builds of a bridge structure geometry with 12 legs of varying size, as shown in Fig.\u00a01. The bridge-shaped structures were additively produced from virgin IN625 powder using an EOS M2701 system with modifications for in\u00a0situ measurements. The 12 legs consist of 4 replications of a section described in the green box in Fig.\u00a01. Each section consists of 3 distinct leg sizes: 5\u00a0mm, 0.5\u00a0mm, and 2.5\u00a0mm. The AM parts were built on build plates of nominally the same alloy (IN625) as shown in Fig.\u00a02. The build plates were 100\u00a0mm squares with 12.7\u00a0mm thickness, mounted to the middle of the build area of the LPBF machine. The bridge-shaped structures were built using the nominal parameter set for IN625. The contour laser power and scan speed were 100\u00a0W and 900\u00a0mm/s, respectively, and the infill laser power and scan speed were 195\u00a0W and 800\u00a0mm/s, respectively, with a hatch distance spacing of 100\u00a0\u00b5m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003244_02640410152006135-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003244_02640410152006135-Figure5-1.png",
        "caption": "Fig. 5. Anthropometric model of a shot-putter at the instant of release.",
        "texts": [
            " A more illuminating method is to derive the \u00ae tted mathematical expressions from physical models, with h(h) and n(h) being used to evaluate the models. In this study, the expression for h(h) was derived from an anthropometric model of the athlete at the instant of release and the D ow nl oa de d by [ T em pl e U ni ve rs ity L ib ra ri es ] at 0 5: 53 2 1 N ov em be r 20 14 expression for n(h) was derived from a model of the forces acting on the shot during the delivery phase. These two models are described in the following sub-sections. At the instant of release, the athlete is assumed to be standing upright, as shown in Fig. 5. The athlete has the throwing shoulder raised so that the line of the shoulders is aligned with the throwing arm, and the angle of the throwing arm to the horizontal is the same as the release angle (Susanka and Stepanek, 1988). The expression for the height of the shot at the instant of release (i.e. the release height) is: hrelease = hshoulder + larm sin h (3) where hshoulder is the height of the athlete\u2019 s shoulders when standing upright and larm is the length of the athlete\u2019 s outstretched throwing arm and shoulder",
            " Unfortunately, Maheras (1995) did not report how the release distance varied with release angle for the athletes in his study. Susanka and Stepanek (1988) reported release distances ranging from +20 cm to -4 cm for competition performances by elite male shot-putters, a negative value indicating that the shot was behind the stop board at the instant of release. The release distance is determined by how close the athlete\u2019 s body is to the stop board during the delivery phase and by the angle of the athlete\u2019 s throwing arm at the instant of release. Using the model shown in Fig. 5, the relation between release distance and release angle is of the form drelease = dshoulder + larm cos h (12) where dshoulder is the distance from the stop board to the midpoint of the athlete\u2019 s shoulders at the instant of release. For an athlete 1.80 m tall, the length of the outstretched arm and shoulder is about 1.02 m (Winter, 1990). If dshoulder is -0.70 m, then the release distance will range from about -70 cm for a vertical release angle to about +30 cm for a horizontal release angle, with a value of about +15 cm at the optimum release angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002776_s1474-6670(17)35187-x-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002776_s1474-6670(17)35187-x-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the controlled variables.",
        "texts": [
            " This can be seen as an alternative to traditional integral feedback. The paper is organized as follows. In Section 2, the aircraft model to be used is presented. In Section 3, the control objectives are defined and the controller architecture is presented. The actual control design is performed in Section 4 and simulation results are shown in Section 5. Finally, Section 6 contains some concluding remarks. In this contribution, the controlled variables are the angle of attack, 0:, the sideslip angle, f3, and the roll rate about the stability x-axis, Ps, see Fig. 1. The equations of motion describing the aircraft dynamics in terms of these variables are (Boiffier, 1998), (Stevens and Lewis, 1992): Q = q - (p cos 0: + r sin 0:) tan f3 + V 1 f3(-L-FT sino:+mg1 ) m TCOS /:J = P sin 0: - r cos 0: + ~V (Y - FTcoso:sinf3 + mg2) mT M= Iw+w x Iw (la) (lb) (lc) Here, m is the aircraft mass, I is the inertial matrix, and VT is the total velocity. Land Y are the lift and side forces respectively, FT is the engine thrust force, and g1 = g( cos 0: cos B cos \u00abt> + sin 0: sin B) g2 = g( cos f3 cos B sin \u00abt> + sin f3 cos 0: sin B - sin 0: sin f3 cosB cos \u00abt\u00bb represent the force contributions due to gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000032_j.rcim.2020.101959-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000032_j.rcim.2020.101959-Figure8-1.png",
        "caption": "Fig. 8. Special solution in point constraint calibration without a limited range.",
        "texts": [
            " = \u23a1 \u23a3 \u23a2 \u23a2 \u23a2 \u23a2\u22ee \u23a4 \u23a6 \u23a5 \u23a5 \u23a5 \u23a5 J JP P P P \u0394\u00b7 \u0394 \u0394 \u0394 pcx pcy pcx C 1 1 2 (8) \u0394JP in Eq. (8) can be solved by Levenberg-Marquardt algorithm [20] or QR decomposition method. During the solution process, \u0394JP converges to a special solution when parameter identification based on point-constrained measurement data with fixed focal length is used. The length parameters of the joints in this special solution are close to zero, i.e., the origin of the camera coordinate system and the sphere center all converge on the origin of the robot basal coordinate system, as shown in Fig. 8. Therefore, it is necessary to limit the solution range. While the calibration method based on a point constraint would only lead to large errors of the 5th and 7th joint parameters due to high coupling among parameters, the sphere center coordinates calculated using the forward solution based on identified joint parameters are very close to the preset coordinates, but the deviation of camera pose is large. Using a variable focal length in the measurement process will constrain the optical axis and improve the identification results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000513_j.addma.2020.101531-Figure18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000513_j.addma.2020.101531-Figure18-1.png",
        "caption": "Fig. 18. Sunata prediction Fig. 19. Amphyon prediction Fig. 20. Simufact prediction",
        "texts": [
            " Though there was significant delamination, the part did not result in build failure. The part started showing delamination a few layers above the supports and hence did not interfere with recoating. The compensation for this deformation and the supports suggested by each software tool was examined subsequently. na l P epr oo f Fig. 21A and 21B. Netfabb part deformation and support failure Fig. 22A and 22B. Additive Print part deformation & support failure prediction. prediction. As shown in simulation result Fig. 18, Sunata partly predicted the part deformation print result shown in Fig. 24A but does not have the capability to show support deformation. Others predicted both the part and support failure as seen in Figs. 19-22. Printability of supports and compensated geometry To assess the printability of the supports generated by each software, test geometry 1E was used. For all other test geometries in this study, supports were generated using Materialise Magics. The printability of the supports generated by the software tools was poor, as seen in Figs 23A and 23B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003427_978-94-017-0657-5_48-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003427_978-94-017-0657-5_48-Figure1-1.png",
        "caption": "Figure 1. A TPM.",
        "texts": [
            "eywords: Translational parallel manipulator, 1-0 decoupled manipulator, Type synthesis, Forward kinematics of a moving platform and a base connected by three legs in parallel (Fig. 1). Under the action of the total constraints of its three legs, the moving platform can only translate with respect to the base. TPMs have a wide range of applications such as assembly and machin ing. Several types of TPMs have been proposed, e.g., in (Appleberry, 1992; Clavel, 1990; Di Gregorio and Parenti-Castelli, 1998; Herve and Sparacino, 1991; Herve, 1995; Tsai, 1999a; Tsai, 1999b; Zhao and Huang, 2000). Several systematic approaches have also been proposed for the 453 1. Lenarcic and F. Thomas (eds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000959_j.apm.2021.03.051-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000959_j.apm.2021.03.051-Figure2-1.png",
        "caption": "Fig. 2. Singular meshing points of standard (up) and high contact ratio (down) spur gears.",
        "texts": [
            " To describe the contact position, the contact point parameter \u03be will be used [ 60\u201362] : \u03be = z 1 2 \u03c0 \u221a r 2 c1 r 2 b1 \u2212 1 (1) in which z is the number of teeth, r c is the radius of the contact point at the involute profile, r b is the base radius, and subscript 1 denotes the input gear (subscript 2 will denote the output gear). The contact point parameter is equal to the rolling angle of the input gear contact point divided by the angular pitch. \u03be is also a linear coordinate along the pressure line, with \u03be = 0 at the tangency point of the input-gear base-circumference, and \u03be = ( z 1 + z 2 )tan \u03b1\u2032 t /2 \u03c0 at the tangency point of the output-gear base-circumference, \u03b1\u2032 t being the operating transverse pressure angle. As seen in Fig. 2 , the \u03be parameters corresponding to different tooth pairs in simultaneous contact are related by: \u03be( i + j ) = \u03be( i ) + j (2) while the difference between the \u03be parameters corresponding to the theoretical inner and outer points of contact, \u03be inn and \u03be o respectively, is equal to the theoretical contact ratio, \u03b5\u03b1: \u03beo = \u03beinn + \u03b5 \u03b1 (3) Accordingly, the theoretical contact interval is described by \u03be inn \u2264 \u03be \u2264 \u03be o . But the teeth deflections under load induces an earlier start of contact and a delayed end of contact, resulting in a slightly longer effective contact interval -also named extended contact interval-, in which three different sub-intervals can be distinguished: premature contact ( \u03bemin \u2264 \u03be \u2264 \u03be inn ), theoretical contact ( \u03be inn \u2264 \u03be \u2264 \u03be o ), and delayed contact ( \u03be o \u2264 \u03be \u2264 \u03bemax )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003520_j.chaos.2004.09.028-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003520_j.chaos.2004.09.028-Figure3-1.png",
        "caption": "Fig. 3. Switching sections and basic mappings in phase plane.",
        "texts": [
            " (1), two switching sections (or sets) are: R1 \u00bc f\u00f0ti; xi;yi\u00dejxi \u00bc E1; _xi \u00bc yig; R2 \u00bc f\u00f0ti; xi;yi\u00dejxi \u00bc E2; _xi \u00bc yig: \u00f010\u00de The two sets are decomposed as R1 \u00bc R21 [ R12 [ fti;E1; 0g; R2 \u00bc R23 [ R32 [ fti; E2; 0g; \u00f011\u00de where four subsets are defined as R21 \u00bc f\u00f0ti; xi; yi\u00dejxi \u00bc E1; _xi \u00bc yi > 0g; R12 \u00bc f\u00f0ti; xi; yi\u00dejxi \u00bc E1; _xi \u00bc yi < 0g; \u00f012\u00de R32 \u00bc f\u00f0ti; xi; yi\u00dejxi \u00bc E; _xi \u00bc yi > 0g; R23 \u00bc f\u00f0ti; xi; yi\u00dejxi \u00bc E; _xi \u00bc yi < 0g: \u00f013\u00de The points {ti,E1,0} and {ti, E2,0} are both static equilibrium points of the sliding motion and the tangential points for the flows on the both sides of the separation boundary. From four subsets, six basic mappings are: P 1 : R21 ! R12; P 2 : R12 ! R21; P 3 : R12 ! R23; P 4 : R23 ! R32; P 5 : R32 ! R23; P 6 : R32 ! R21: \u00f014\u00de The switching planes and basic mappings are sketched in Fig. 3. Consider the initial and final states \u00f0t; x; _x\u00deinitial \u00bc \u00f0ti; xi; yi\u00de and \u00f0t; x; _x\u00definal \u00bc \u00f0ti\u00fe1; xi\u00fe1; yi\u00fe1\u00de in the three sub-domains Xj (j = 1,2,3), respectively. The displacement and velocity equations in Appendix A with the initial conditions gives the governing equation for the mapping Pk (k = 1,2, . . ., 6), i.e., Pk : f \u00f0k\u00de 1 \u00f0xi; yi; ti; xi\u00fe1; yi\u00fe1; ti\u00fe1\u00de \u00bc 0; f \u00f0k\u00de 2 \u00f0xi; yi; ti; xi\u00fe1; yi\u00fe1; ti\u00fe1\u00de \u00bc 0; ( \u00f015\u00de where {xi,xi+1} 2 {E1, E2}. Due to impacts at two boundaries, the impact relations are y\u00fei \u00bc l21y i ; on R21; y\u00fei \u00bc l23y i ; on R23; \u00f016\u00de where y i yi\u00fe1 for mappings P3 and P6 before impact, and y\u00fei yi for mappings P1 and P4 after impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002996_s0022-0728(00)00114-5-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002996_s0022-0728(00)00114-5-Figure3-1.png",
        "caption": "Fig. 3. Cyclic voltammograms of a CoHCF/GC electrode in phosphate buffer solution (pH 7.0) containing 0.1 mol dm\u22123 (a) KNO3, (b) NaNO3 and (c) LiNO3 as supporting electrolyte at a scan rate of 50 mV s\u22121.",
        "texts": [
            " The voltammetric responses of a CoHCF/GC electrode were also affected by the concentrations of supporting electrolyte. Fig. 2 shows the cyclic voltammograms of a CoHCF/GC electrode in three different concentrations of KNO3 (pH 7.0). With a decrease of the concentration of electrolyte, the redox peak potentials shifted in the negative direction. The dependence of the peak potential (Ep), the separation of the peaks potential (DEp) and the formal potential (E\u00b0%) on the concentration of supporting electrolyte are shown in Table 1. Fig. 3 shows the effects of alkali metal cations on the voltammetric behaviour of a CoHCF/GC electrode. From the cyclic voltammograms, one can find that the CoHCF/GC electrode showed well-defined redox peaks in K+-containing supporting electrolyte solution. In Na+-containing supporting electrolyte, only one pair of broad redox peaks was observed, the peak currents decreased drastically, and in Li+-containing supporting Table 1 Dependence of Ep/mV, DEp/mV and E\u00b0%/mV on the concentration of supporting electrolyte (pH 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003137_1097-4563(200102)18:2<55::aid-rob1005>3.0.co;2-o-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003137_1097-4563(200102)18:2<55::aid-rob1005>3.0.co;2-o-Figure1-1.png",
        "caption": "Figure 1. Photograph and schematic model of the IMI two-link manipulator.",
        "texts": [
            "j , k j , maxn j ,k2 1 where A and are the decimal valuesj, k 10 j, k 10 of the binary integers A and . The bounds onj, k j, k the decision variables are, therefore, implicitly included in the decoding step, so that the resulting problem is unconstrained in the binary string X. The GA has been implemented in a MATLAB package developed by the authors and is available on request. The effectiveness of the method is validated by experimental tests for the dynamic calibration of the SCARA two-link planar manipulator, which is produced by IMI and is shown in Figure 1. The considered manipulator has two revolute joints equipped \u017d .with brushless direct-drive motors produced by \u017d .NSK Nippon Seiko K. K., Tokyo, Japan , incorporating resolvers for position measurements. The control unit of the robot is constituted by a Pentium-90 PC with a TMS320C30 Digital Signal Processing \u017d .DSP board, and the control algorithms are implemented in C. The joint coordinates are defined according to Denavit Hartenberg notation and colTlected in vector q q q , where q represents1 2 i the angular position of joint i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000408_j.cja.2020.11.009-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000408_j.cja.2020.11.009-Figure3-1.png",
        "caption": "Fig. 3 Shape parameters of HMV.",
        "texts": [
            " In the third section, the IGCM method was designed in glide phase by adaptive dynamic surface back-stepping method. The fourth section showed the test results of IGCM method focusing on the analysis of effectiveness and robustness. Some issues were discussed in fifth section. Finally, the conclusion section gave a brief summary and critique of the findings. 2. Motion models of HMV 2.1. Shape and parameters of HMV The research object under discussion was within the scope of HMV with variable spans. The outline was showed in and morphing modes was showed in Fig. 2.33 As showed in Fig. 3, the HMV consisted of three parts, a rotational symmetrical slender body, two variable span wings and four invariant tails. From left to right in Fig. 3, the wings\u2019 span changed from minimum to maximum. The variable span of the wing was synchronously varied on both sides of the wings without differential varying. The definitions and values of parameters labeled in Fig. 3 were showed in Table 1. The morphing rate n of the variable span was defined as33 n \u00bc b b1 b2 b1 \u00f01\u00de 2.2. HMV dynamics models 2.2.1. Centroid dynamic models To establish the centroid dynamics models for HMV, the factors of the earth\u2019s rotation and the earth ellipsoid must be considered because the flight range and time were quiet long in glide phase. Then the centroid dynamics models were established in the ballistic coordinate system with spin ellipsoid earth model as _V \u00bc m 1 FgV \u00fe FxeV \u00fe FkV FsV \u00fe FeV \u00feD _h \u00bc mV\u00f0 \u00de 1 Fgh \u00fe Fxeh \u00fe Fkh Fsh \u00fe Feh \u00fe LcoscV NsincV _r \u00bc mVcosh\u00f0 \u00de 1 Fgr \u00fe Fxer \u00fe Fkr Fsr \u00fe Fer LsincV NcoscV 8>< >: \u00f02\u00de In Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure6-1.png",
        "caption": "Fig. 6. Force analysis of substructure 3.",
        "texts": [
            " (12) leads to \u03c1w, 4 = W T 4 $ w, 4 (13) where $ w, 4 = $ w,E + $ w,G E + $ w,G 5 + $ w,G 4 , $ w,G 4 = \u2212m 4 g [ \u02dc z ( r 5 + R 5 r 5 G 4 ) \u00d7\u02dc z ] , \u03c1w, 4 = [ \u03c1w, 4 , f \u03c1w, 4 ,\u03c4 ] , W 4 = [ R 4 \u02c6 r4 R 4 0 R 4 ] , r 4 = r 5 + R 5 r 5 4 , $ w, 4 is the resultant externally applied wrench imposed at point O E for joint 4, $ w, G 4 is the equivalent gravitational wrench of link 4 applying on point O E , \u03c1w, 4 is the reaction force at joint 4, \u02c6 r4 is the skew-matrix of the position vector r 4 . As shown in Fig. 6 , for substructure 3, the static equilibrium equation at point O E can be written as \u23a7 \u23aa \u23a8 \u23aa \u23a9 f E \u2212 m E g \u0303 z \u2212 m 5 g \u0303 z \u2212 m 4 g \u0303 z \u2212 m 3 g \u0303 z = R 3 \u03c1w, 3 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z \u2212 m 5 g ( R E r E 6 + R 6 r 6 G 5 ) \u00d7\u02dc z \u2212 m 4 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 G 4 ) \u00d7\u02dc z \u2212m 3 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 G 3 ) \u00d7\u02dc z = ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 + R 4 r 4 3 ) \u00d7 ( R 3 \u03c1w, 3 , f )+ R 3 \u03c1w, 3 ,\u03c4 (14) where \u03c1w, 3 , f = [ \u03c1w, 3 , f x \u03c1w, 3 , f y \u03c1w, 3 , f z ] T , \u03c1w, 3 ,\u03c4 = [ \u03c1w, 3 ,\u03c4x \u03c1w, 3 ,\u03c4y \u03c1w, 3 ,\u03c4 z ] T , \u03c1w, 3 , f and \u03c1w, 3 ,\u03c4 are the reaction force and torque of joint 3 acting at point O 3 , m 3 is the mass of link 3, G 3 is the mass center of link 3, r 4 G 3 is the position vector from point O 4 to point G 3 evaluated in { O 4 }, and r 4 3 is the position vector from point O 4 to point O 3 evaluated in { O 4 }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003920_3.20230-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003920_3.20230-Figure2-1.png",
        "caption": "Fig. 2 DRAPER I tetrahedral truss structure.",
        "texts": [
            "054 Table 2 Modal natural frequencies for the first 17 nonzero modes of the DRAPER II model Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 rad/s 0.7161 0.9231 0.9399 1.1009 2.8616 3.5019 3.7459 3.8627 3.9982 4.0315 5.1216 5.1281 5.1741 5.7532 6.1075 7.2806 9.7457 Frequency Hz 0.1140 0.1469 0.1496 0.1752 0.4554 0.5573 0.5962 0.6148 0.6363 0.6416 0.8151 0.8162 0.8235 0.9156 0.9720 1.1587 1.5512 The DRAPER I model14 is a tetrahedral truss connected to the ground by three right-angled bipods as shown in Fig. 2. These bipods take on the duties of rate sensors and force actuators, all in the direction of the members, giving the colocation necessary for a positive real model. The model has 12 dynamic degrees of freedom and thus a maximum of 12 modes. The natural frequencies for the model, as found by a NASTRAN analysis, are given in Table 1. The DRAPER II model15 is a model of a space telescope consisting of two subsystems as shown in Fig. 3. The optical support structure contains the four optical surfaces that are assumed to be rigid and kinematically mounted onto the structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000690_j.rcim.2021.102138-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000690_j.rcim.2021.102138-Figure12-1.png",
        "caption": "Fig. 12. The distribution of frames.",
        "texts": [
            "5 \u00d7 1.0m. Meanwhile, its upper surface is substantially parallel to the XY plane of the robot base frame {BP} and is symmetrical about the y-axis of its frame {T}. 4) A flat vise, which is used to clamp the workpiece, 5) Multiple workpiece with dimensions of 100 \u00d7 100 \u00d7 40mm, Q. Fan et al. Robotics and Computer-Integrated Manufacturing 70 (2021) 102138 6) A coordinate measuring machine (CMM, and its model number is HEXAGON, Explorer-05.07.05), which is used for the evaluation of machining quality. Fig. 12 shows the distribution of the frames of the main components in the robot milling station. Among them, the x, y and z directions of the robot base frame {BP}, the T-shaped workbench\u2019s frame {T} and the workpiece frame {WP} are always the same. At the same time, the position coordinates of the frame {T} and {WP} w.r.t frame {BP} are BP T P = \u23a1 \u23a3 1.160 0.000 0.581 \u23a4 \u23a6m, BP WPP = \u23a1 \u23a2 \u23a2 \u23a3 BP WPx BP WPy BP WPz \u23a4 \u23a5 \u23a5 \u23a6m (31) where the ranges of BP WPx, BP WPy and BP WPz are respectively \u23a7 \u23aa \u23aa\u23a8 \u23aa \u23aa\u23a9 1.160\u2264BP WPx \u2264 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure15.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure15.9-1.png",
        "caption": "Figure 15.9. Path of contact, viewed in the direction of the line of centers.",
        "texts": [
            " By using the relations developed in Chapter 13 between the various angles, we can express the position vector from Co 1 to the contact point in yet another form, Path of Contact 431 (15.78) Once again, the terms in the square brackets represent a unit vector. Since the coefficient of n x1 {O) is sin ~np' the path of contact must make an angle (7r/2-~np) with the n x1 {O) direction. The coefficients of nz1 {O) and ny1 {O) are in the ratio of (- tan lPp1 ) : 1, so when the path of contact is viewed in the nx1 {O) direction, as shown in Figure 15.9, it appears to make an angle lPP1 with the ny1 {O) direction. We obtain the corresponding set of results for gear 2 if we express the direction of the path of contact in terms of nx2{O), ny2{O) and nz2{O). Since the equations are exactly analogous, they will not be repeated here. The only equation which we will write out is the one corresponding to Equation (15. 75), giving the relation between s2 and the radi us R2 of the contact point, (15.79) 432 Crossed Helical Gears By substituting these expressions for sl and s2 into Equation (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure23-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure23-1.png",
        "caption": "Fig. 23. Residual deformation comparison of the bracket with support structures after cutting process through (a) simulation (vertical displacement) and (b) experimental measurement (surface normal deformation).",
        "texts": [
            " 22 before and after the cutting process. Apparent vertical deformation can be found by observing the gap along the solid-support interface. Similar to those cantilever beams Section 5.1, the residual deformation of the L-PBF bracket was measured using the Faro Arm laser scanning device. Postprocessing for the obtained cloud data including the build reconstruction and alignment to the CAD file is identical to the procedure presented in the previous example. A comparison of the simulation and experimental results is shown in Fig. 23. The vertical deformation obtained by the inherent strain based simulation is plotted in Fig. 23(a). Regarding the experimental measurement, only surficial normal deformation can be computed in Geomagics software. As seen in Fig. 23(b), the color of red/yellow indicates expansion deformation along the surface normal, while color of blue indicates shrinkage of the surface. The irregularly large negative or positive displacements denoted by dark blue and red color along the edges and sharp corners are not real. This irregular issue has been explained in Section 5.1. Especially in this example, we found it is very difficult to capture the sharp edges and corners of the bracket precisely by the Faro Arm laser scanner. One reason is the metal surfaces for LPBF solid materials are very shiny and it results in multiple reflections of the detecting laser rays especially when the sharp corners are scanned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000615_j.optlastec.2020.106872-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000615_j.optlastec.2020.106872-Figure3-1.png",
        "caption": "Fig. 3. The geometry of the tensile specimen.",
        "texts": [
            " The standard metallographic specimens were prepared by metallographic inlay machine (XQ-2B, China). After the cross-sections of samples were grinded by sandpapers from 200 to 2000 and polished by the rotary polisher. The polished samples were etched by a mixture of 4 mL HF, 4 mL HNO3, and 92 mL C2H5OH. The microstructure of the samples was observed by Ultra-depth microscope and a scanning electron microscope (JEOL JSM6490, Tokyo, Japan). Then tensile specimens were prepared according to the standard of ISO 6892 1:2009 whose geometry and sizes are shown in Fig. 3. The mechanical properties of the tensile specimens were tested by a tensile test machine (Instron, Boston, MA, USA). The measured values of three tensile specimens under the same processing parameters were averaged. The tensile fracture surface morphologies were observed by the scanning electron microscope (SEM). The forming process of SLM consists of two procedures. A plurality of single-tracks was overlapped to form a scanning plane and then multiple planes were stacked up to fabricate apart",
            " Increasing the scanning speed within an appropriate range can increase the degree of supercooling in the SLM process, which can inhibit the growth of crystal grains and reduce the columnar crystals contained in the sample. Besides, the degree of subcooling was inversely proportional to the layer thickness. Therefore, compared with the small layer thickness, both the size of the crystal grains and the ratio of the columnar crystals were increased with thicker layers. The tensile specimens shown in the Fig. 3 were formed on the substrate at 0\u25e6 and 90\u25e6 by selecting parameters with a density of more than 99.9%. The tensile strength, yield strength and elongation were tested by using a tensile test machine under the same conditions. Table. 4 shows the processing parameters of heat treatment. The processing parameters of all tensile specimens were line scanning speed of 200 mm/s and exposure time of 120 \u03bcs. Due to the scanning strategy of 67\u25e6 rotation between layers can eliminate the obvious directionality during grain growth, and no significant anisotropy of tensile properties was observed in the experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002935_iros.1993.583168-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002935_iros.1993.583168-Figure3-1.png",
        "caption": "Fig. 3 Link structure of WL-12RV",
        "texts": [
            "00 (C) 1993 IEEE Therefore, the objective of this study was to develop a biped walking robot which has an ability to compensate for the three-axis moment by trunk motion, to work out a control method of dynamic biped walking for the robot and to realize faster walking than before. 2.1 Machhe Model The biped walking robot WL-12RV (Waseda Leg-12 Refined v) is shown in Fig. 1. The total weight is 103.5 kg and the height is about 1.8 m. An assembly drawing and a link srructure of this robot are shown in Fig. 2 and Fig. 3. The assignment of DOF (Degrees Of Freedom) is shown in Fig. 3. As this diagram indicates, the lower-limbs have s ix rotational DOF on pitch-axis and the trunk has three rotational DOF on pitch-axis. roll-axis and yaw-axis. The total DOF is nine. . . . _ 2-2 Trunk M e d \" The trunk of this machine model is able to generate the three-axis moment by using three DOF link mechanisms. The weight of the trunk is 30.0 kg. A link smcture of the trunk is shown in Fig. 4. This trunk generates the three-axis moment as follows: The yaw-axis moment is generated by swinging two balance weights around the yaw-axis by a yaw-axis actuator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003460_robot.2006.1642231-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003460_robot.2006.1642231-Figure1-1.png",
        "caption": "Fig. 1 Illustration of STAR (Skin by Touch Area Receptor). It is soft, stretchable, and capable of covering a large area easily.",
        "texts": [
            " We propose a new tactile sensor skin (\u201cSkin by Touch Area Receptor\u201d or STAR) which is based on a new tactile sensing method to solve the problem that is mentioned above. In our method, a sensor element dares to have a large sensing area (several square centimeters) unlike the other elements in the literature, and it acquires not only a contact force but also a contact area . Owing to the additional sensing parameter, i.e. the contact area, a robot skin which detects minute shape features of object surfaces is easily realized by arraying the elements in low density. In consequence, we can cover a whole surface of a robot with a small number of the elements (Fig. 1). The above proposition is inspired by the characteristics of the human tactile sensation. While Two Point Discrimination Thresholds (TPDT) of humans are as large as several centimeters except on especially sensitive parts, faces and hands , humans can discriminate sensitively sharpness of objects even on such large TPDT parts. Although we still don't know exactly why and how the human skins perform like that, from these facts, we consider that sharpness is one of key components to produce general human tactile sensation [14], and suppose that sensitivity to sharpness is a high priority for human-like sensor skins"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000766_j.surfcoat.2021.126884-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000766_j.surfcoat.2021.126884-Figure2-1.png",
        "caption": "Fig. 2. (a) Schematic diagram, and (b) photo of directed energy deposition system.",
        "texts": [
            " The chemical compositions (in wt%) of CLF-1 are 0.088% C, 8.54% Cr, 1.34% W, 0.62% Mn, 0.29% V, 0.14% Ta, 0.021% N, 0.0058% Ni, 0.0011% S and balance Fe; and the chemical compositions (in wt%) of 45 # carbon steel are 0.43% C, 0.66% Mn, 0.014% S, 0.002% P, 0.23% Si and balance Fe. The pure tungsten powders used in this study were polygonal particles (as shown in Fig. 1a) with a size between 20 and 150 \u03bcm (indicated in Fig. 1b). An LDM-8060 DED system (Raycham, China) was used for LAM of pure tungsten. The system is shown in Fig. 2, which includes laser (Laserline LDF 10000\u2013100, Germany), three-axis numerical control working table, and a powder feeder. The experiment was carried out in an argon vacuumed chamber atmosphere (oxygen content <50 ppm). The distance between the coaxial laser head and the substrate was 15 mm. Based on our preliminary results, the carrier gas flow rate and powder feeding rate were set at 10 L/min, and 29.3 g/min, respectively. The laser processing parameters for single- and multiple-track samples are listed in Tables 1 and 2, respectively",
            " Accompanied by the increases of laser power to 3500 W, the temperature of the molten pool also increases, which leads to the decrease of the dynamic viscosity (\u03bc) of the composite melt. A lower dynamic viscosity increases the convection of molten pool, and allows more tungsten particles to enter the molten pool and form high tungsten content. On the other hand, to some extent, with the increasing laser energy input, the molten pool becomes wider, causing more tungsten powders to enter the molten pool; however, if the size of molten pool is lager than that of powder flow (as shown in Fig. 2a), the percentage of tungsten will decline. Therefore, as the laser power further increases to 4000 W, the percentage of tungsten in the deposited layer reduces. This phenomenon should be attributed to the higher dilution rate during DED. As shown in Fig. 5a, with the increase of laser power, the size of the molten pool (and HAZ) increases; however, with a constant and limited power feeding rate, the same amount of tungsten will be diluted more. Thus, at a given powder feeding rate, after reaching a threshold laser power, the tungsten content will decrease with a further increase of laser power"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000079_j.rcim.2019.101916-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000079_j.rcim.2019.101916-Figure1-1.png",
        "caption": "Fig. 1. WAAM fabricated parts or structures with overhanging structure.",
        "texts": [
            " In order to reduce or avoid the use of supporting structure, researchers have explored to despite parts along multi-directions by integrating rotary positioner into the AM system [7,8]. The additional Degrees of Freedom provides more flexibility for the fabrication of the components with complex geometries. However, this is not applicable to all situations. For example, WAAM is commonly used to fabricate parts with medium to large scale, it is challenging and costly to rotate such a large part in practice, as shown in Fig. 1 (a) [9]. For some cases, the structures are fixed in the service position, as shown in Fig. 1 (b) [10], a team from Netherlands built a steel bridge using multi-directional WAAM. In addition, WAAM has been used for in-situ repair of large components which cannot be placed on a rotation table. Thus, if the layers can be deposited in multiple directions [11,12], as demonstrated in Fig. 1(c), the process planning becomes less complicated and the resultant fabrication process becomes more economical. https://doi.org/10.1016/j.rcim.2019.101916 Received 27 July 2019; Received in revised form 7 November 2019; Accepted 24 November 2019 \u204e Corresponding author. E-mail address: zengxi@uow.edu.au (Z. Pan). Robotics and Computer Integrated Manufacturing 63 (2020) 101916 0736-5845/ \u00a9 2019 Elsevier Ltd. All rights reserved. T Kazanas et al. [13] reported, that for multi-directional layer deposition, the Cold Metal Transfer (CMT) variant of GMAW is an ideal process to be used due to its relatively low heat input",
            " As shown in the graph, with the aid of the gravitational force, the maximum TS increases while \u03b8 increases, the welding parameters should be chosen from the left upper parts of the humping map. The humping map approach can be used to provide a database for parameter and welding position selection. If necessary, the database can be more accurate when more tests are conducted between the boundaries of humping and no humping region. Secondly, a good understanding of humping formation provides guidelines for path planning. For example, four path planning schemes are list in Fig. 20(b) for depositing a horizontal rectangular section (yellow) parts of the workpiece in Fig. 1. The overhanging part can be fabricated by depositing horizontally (strategy A), vertical-up (strategy B), vertical-down (strategy C), or along a contoured path (strategy D). As previously analysed, taking advantages of gravity, the use of vertical-down position allows a higher welding speed than both vertical-up and flat position. From a practical WAAM perspective, some recommendations for path planning are provided as i) in the path planning stage, it is recommended to deposit overhanging parts in a vertical-down position, as strategy C in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003043_0954406041319545-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003043_0954406041319545-Figure2-1.png",
        "caption": "Fig. 2 Scanning strategy",
        "texts": [
            " The substrate is attached to a piston which goes downward by one layer thickness of 0.1mm (z direction). The process is carried out in a closed chamber and argon is flushed continuously in order to minimize oxygen and nitrogen pick-up. The material used was spherical grade 1 titanium powder (TILOP 45) supplied by Sumitomo Sitix Inc. The chemical analysis of the powder can be seen in Table 1. The powder had a very low amount of interstitial elements. The particle size was under 45 mm and the average particle size was 25 mm. Figure 2 shows the \u2018x and y\u2019 scanning strategy for building the three-dimensional models. At first, the outline of the cross-section is scanned. The odd layers (layers 1, 3, 5, . . . ) are also scanned in the x and y directions alternatively. The even layers (layers 2, 4, 6, . . . ) are scanned only on its outline. Therefore a scanning cycle consists of a scanning outline and x direction (layer 1), scanning-only outline (layer 2), scanning outline and y direction (layer 3) and scanning-only outline (layer 4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003384_rspa.2004.1371-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003384_rspa.2004.1371-Figure1-1.png",
        "caption": "Figure 1. Components of the forces Nij , Qij and moments mij along the oriented sections defined by the coordinate curves \u03b12 = const. and \u03b11 = const.",
        "texts": [
            " as t2 and the normal to the surface as n, i.e. (\u2202\u03b1i = \u2202/\u2202\u03b1i): t1 = \u2202\u03b11r g 1/2 11 , t2 = \u2202\u03b12r g 1/2 22 , n = t1 \u00d7 t2. (2.2) Here \u03b12 = const. and \u03b11 = const. define a local orthogonal coordinate system. Consider the force per unit length at a cross-section defined by the curvilinear coordinate \u03b12 = const. Since the normal to the cross-section lies along t2, we denote the force F2, following the convention introduced by Reissner (1941). This force can be resolved into its orthogonal components (see figure 1) F2 = N21t1 + N22t2 + Q2n. (2.3) Proc. R. Soc. A (2005) Similarly, the force per unit length at a cross-section defined by the coordinate \u03b11 = const. is F1 = N11t1 + N12t2 + Q1n. (2.4) Here N11, N22 are the in-plane tensile stress resultants, while N12, N21 are the inplane shear resultants, and Q1, Q2 are the out-of-plane stress resultants. In general, N12 = N21 since they correspond to forces on different elemental areas. If in addition, we denote the force per unit area as K, the equations of force equilibrium deduced from figure 2 lead to \u2212 F2 ds1|(\u03b11,\u03b12) + F2 ds1|(\u03b11,\u03b12+d\u03b12) \u2212 F1 ds2|(\u03b11,\u03b12) + F1 ds2|(\u03b11+d\u03b11,\u03b12) + K|(\u03b11,\u03b12) dA = 0. (2.5) Here ds1 = A1 d\u03b11 is the arc length in the t1-direction and A1 = g 1/2 11 . Similarly, ds2 = A2 d\u03b12, where A2 = g 1/2 22 , and dA is the element of area: dA = (det g)1/2 d\u03b11 d\u03b12 = A1A2 d\u03b11 d\u03b12. Next, we define M2 as the couple per unit of length of the middle surface parametrized by the coordinate \u03b12 = const. Since it is generated by a variation of the stress in the n-direction, it may be written as (see figure 1) M2 = n \u00d7 (m21t1 + m22t2). (2.6) Here m11, m22 are the bending torque resultants, while m12, m21 are the twisting torque resultants. Similarly, we define M1 as the couple per unit of length of the middle surface parametrized by the coordinate \u03b11 = const. Resolving it into components, Proc. R. Soc. A (2005) we write M1 = n \u00d7 (m11t1 + m12t2). (2.7) The balance of torques may then be deduced from figure 2 and leads to \u2212 M2 ds1|(\u03b11,\u03b12) + M2 ds1|(\u03b11,\u03b12+d\u03b12) \u2212 M1 ds2|(\u03b11,\u03b12) + M1 ds2|(\u03b11+d\u03b11,\u03b12)ds2t2 \u00d7 F2 ds1|(\u03b11,\u03b12+d\u03b12) + ds1t1 \u00d7 F1 ds2|(\u03b11+d\u03b11,\u03b12) = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure3-1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure3-1-1.png",
        "caption": "Figure 3-1 (a) Sketch of thermofluid convection rolls, (b) Three unstable singular points in phase space for the Lorenz equations (3-2.3).",
        "texts": [
            " Readers with access to a small computer can observe chaotic solutions of many of these models by using a Runge-Kutta numerical integration scheme. Sample problems with suggested parameters for a few of these models are given in Appendix B. Perhaps the most famous model to date is the Lorenz equations which attempt to model atmospheric dynamics. In this model, one imagines a fluid Mathematical Models of Chaotic Physical Systems 69 layer, under gravity, which is heated from below so that a temperature difference is maintained across the layer (Figure 3-1). When this temperature difference becomes large enough, circulatory, vortex-like motion of the fluid results in which the warm air rises and the cool air falls. The tops of parallel rows of convection rolls can sometimes be seen when flying above a cloud layer. The two-dimensional convective flow is assumed to be governed by the classic Navier-Stokes equations (1-1.3). These equations are expanded in the two spatial directions in Fourier modes with fixed boundary conditions on the top and bottom of the fluid layer",
            " They have been carried out in helium, water, and mercury for a wide range of nondimensional Prandtl numbers and Rayleigh numbers. These experiments emerged in the late 1970s. For example, Libchaber and Maurer (1978) observed period-doubling convection oscillation in helium. A number of experimental papers have emerged from a group at the French National Laboratory at Saclay, France, associated with Berge and coworkers (1980, 1982, 1985) See also Dubois et al. (1982). The experiment is similar to that pictured in Figure 3-1 with a fluid of silicone oil in a rectangular cell with dimensions 2 cm X 2.4 cm X 4 cm. They have observed both the quasiperiodic route to chaos (Newhouse et al., 1978) and intermittent chaos. In the former, they observe the following sequence of Physical Experiments in Chaotic Systems 113 dynamic events as the temperature gradient is increased: steady state ~ monofrequency motion biperiodic or quasiperiodic motion chaotic * motion - thermal gradient The frequency range observed in their experiments is very low, for example, 9-30 X 10 ~3 Hz",
            " Because the chaotic map in Figure 4-8 has an infinite set of gaps, its dimension is between one and two \u2014thus the word fractal dimension. In general, the set of Poincare points in a strange attractor does not cover an integer-dimensional subspace (in Figure 4-8 this subspace is a plane). Another use for the fractal dimension calculation is to determine the lowest order phase space for which the motion can be described. For example, in the case of some preturbulent convective flows in a Rayleigh-Benard cell (see Figure 3-1), the fractal dimension of the chaotic attractor can be calculated from some measure of the motion ( x ( t n ) = xn} (see Malraison et al., 1983). From {*\u201e}, pseudo-phase-spaces of different dimension can be constructed (see Section 4.4). Using a computer algorithm, the fractal dimension d was found to reach an asymptotic d = 3.5 when the dimension of the pseudo-phase-space was four or larger. This suggests that a low-order approximation of the Navier-Stokes equation may be used to model this motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure5-1.png",
        "caption": "Figure 5 The Star manipulator.",
        "texts": [
            " Based on the modified G-K criterion, the mobility of the mechanism is ( ) 1 ( 1) 6 11 12 1 12 3 3. g i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + = \u2211 (20) Evidently, eqs. (18) and (19) are invariable at any possible configuration of this mechanism in the same coordinate system as B1-xyz, so it is not difficult to conclude that the common constraints and redundant con- Huang Zhen et al. Sci China Ser E-Tech Sci | May 2009 | vol. 52 | no. 5 | 1337-1347 1343 straints are unaltered. The mobility is not instantaneous. The Star mechanism[47], as shown in Figure 5, comprises three identical limbs. For each limb, the first pair which locates in the frame is a revolute joint, the second is a helical pair H, and the last one is also a revolute joint connecting the moving platform. The axes of the three pairs are parallel, with the first two being coaxial. In addition, the last revolute pair and the helical pair connect a hinged parallelogram loop together. Similar to the analysis of the Orthoglide mechanism, the hinged parallelogram can be replaced by a generalized prismatic pair Pa, which lies on the parallelogram plane. Thus each limb is equivalent to a RHPaR chain. Besides, the axes of three helical pairs are coplanar and the angle between any two axes is 120\u00b0. The coordinate system is established as Figure 5 shows. The origin is the center of the first revolute joint, x-axis is coaxial with the revolute joint and z-axis lies on the parallelogram plane. Then the twist system of the first limb is given by ( ) ( ) ( ) ( ) 1 1 1 2 2 1 3 3 3 1 4 4 1 0 0; 0 0 0 , 1 0 0; 0 0 , 0 0 0; 0 , 1 0 0; 0 0 . d d f e = = = = $ $ $ $ (21) The constraint screw system is ( ) ( ) 11 12 0 0 0; 0 1 0 , 0 0 0; 0 0 1 , r r = = $ $ (22) which denotes two couples and restricts two rotations. The axes of the two couples are both normal to the axis of the first revolute joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000696_tie.2021.3063869-Figure19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000696_tie.2021.3063869-Figure19-1.png",
        "caption": "Fig. 19. Stator and rotor structure of (a) Motor with skewing slots. (b) The proposed motor.",
        "texts": [
            " The acceleration response of the proposed motor is in the same level as that of the motor with skewing slots. V. PROTOTYPE AND EXPERIMENTAL TEST A 8-pole/48-slot prototype with the proposed method based on the main geometric parameters given in Table I and Table II is built and tested to verify the previous analysis. For fair comparison, a prototype with skewing slots with the same machine dimensions is also made and tested. The appearance of stator and rotor of the two prototypes are shown in Fig. 19, while the silicon sheets of the conventional rotor and the proposed rotor configuration are given in Fig. 20. For the proposed rotor, two keybars are needed to facilitate assembling of the two staggered 180\u00b0 rotor segments. A commercial bench with integrated torque sensor and induction motor is used to test the prototypes, as shown in Fig. 21. The measured three-phase line back-EMF of the proposed motor at the rated speed 3000 rpm is shown in Fig. 22. Fig. 23 shows the measured three-phase current of the proposed motor under the rated load 32N\ua78fm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003581_icar.2005.1507426-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003581_icar.2005.1507426-Figure6-1.png",
        "caption": "Figure 6 Ducted-fan rotorcraft with half the duct removed to show the twin motors, counter-rotating propellers and internal construction.",
        "texts": [
            " The next stage of the research programme involves constructing a small rotorcraft to act as a technology demonstrator for the concept, so it was decided use this design as the basis for the dynamic model to be incorporated into the test rig. Intended only for laboratory use, the experimental rotorcraft must be simple to construct and operate. A ducted-fan design was selected, based on the \u2018flying platform\u2019 principle [6], where the Centre of Gravity (CG) is deliberately placed above the aircraft centre (AC) to give dynamic stability in hover [7]. Early construction is shown in Figure 6. The payload (not shown) is mounted above the duct and attitude control is accomplished by moving a mass to change the position of the CG. Lift and yaw control are achieved by changing the propeller speeds collectively or differentially. Overall, the design is quite similar to that described by Sherman et al [8]. Ando [9] has derived a simple 3 degree of freedom dynamic model for this configuration which suggests that placing the CG within a very small range of locations above the AC gives both static and dynamic stability",
            " Note that this introduces a non-minimum phase characteristic into the response, because the reaction force as the mass is accelerated to the right causes the initial duct rotation to be counter-clockwise. The aerodynamic force (HA) and torque (MAC) on the duct are given by [9]: )( gA A A A xx x HH && & + \u2202 \u2202 \u2212= (2) )( gA A ACAC AC xx x MMM && & & & + \u2202 \u2202 \u2212 \u2202 \u2202 = \u03b8 \u03b8 (3) where is the wind velocity. Using the approximate relationships in [9], tentative values for the aerodynamic derivatives in (2) and (3) were estimated according to the dimensions, mass and thrust of the rotorcraft in Figure 6. This predicts that placing the CG within a 9mm long region, located just above the duct lip, will yield a stable system. gx& Finally, the position demand to the control mass servosystem is the error between the rotorcraft\u2019s lateral position relative to the overhead lines (to be measured by the vision system) and its demanded position (above the centre line). The dynamic characteristics of (1), (2) and (3) restricts quite severely how much gain can be placed in the position feedback loop. As shown in Figure 8, the response to a demanded lateral displacement is very slow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000735_j.jmapro.2021.04.016-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000735_j.jmapro.2021.04.016-Figure8-1.png",
        "caption": "Fig. 8. Simulation distribution of temperature field under Laser power (1200 W), scanning speed (10 mm/s) and air cooling.",
        "texts": [
            " The center of the virtual square in cell B is the vertex when the virtual square in cell A is the largest, which is expressed by coordinates as: { xB = xA + \u0305\u0305\u0305 2 \u221a fscos\u03b8 yB = yA + \u0305\u0305\u0305 2 \u221a fssin\u03b8 (26) The surrounding cells are captured in turn and the state will be changed. When there are no liquid cells in the Neumann neighbor of the interface cell, the interface cell will change into a solid cell until the solidification is completed. H. Lv et al. Journal of Manufacturing Processes 67 (2021) 63\u201376 The above finite element model is solved nonlinearly, and the simulation results are shown in Fig. 8. The upper part of the figure is the temperature field distribution in the laser cladding process, and the isothermal surface of the temperature field is elliptical. The temperature value was set to 1260 \u25e6C of the IN718 alloy solidus, and the temperature field of the molten pool was obtained, as shown in the left side of the part below. The temperature field of the molten pool was locally enlarged. It was found from the observation of the molten pool that the molten pool was elliptically distributed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001012_j.triboint.2021.106927-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001012_j.triboint.2021.106927-Figure3-1.png",
        "caption": "Fig. 3. Electrical model of a rolling contact according to Jablonka et al. [15].",
        "texts": [
            " The capacity of this area CR is calculated via the electric field, which depends on the distance between the surfaces hR and is integrated over the surface AR [15]: CR = \u222b\u222b AR \u03b50\u03b5r hR(x, y) dx  dy. (3) The reciprocal distance between the undeflected bodies hR(x, y) is integrated over the surface in the two spatial directions x and y. Thus, the entire capacity of a loaded rolling contact CC is the sum of the parallel connected capacities CHz and CR. The resulting extended electrical model of the rolling contact is shown in Fig. 3. The surface area AR takes an annular shape and is the projection of the undeflected ball onto the raceway minus the hertzian contact area AHz. The surface is shown in Fig. 4 schematically. The representation of the undeflected contact area however inflicts a contradiction to the current state of research. According to equations (1) and (2), the calculation of the impedance of rolling bearings is based on the assumption that solely rolling elements with a Hertzian contact contribute to the total capacitance. Consequently rolling elements outside the load zone shouldn\u2019t add to it. In contrast, the undeflected area around the Hertzian zone increases the capacity by the factor kR as described, which implies that an unloaded rolling element should add to the total capacity of the bearing. Jablonka et al. [16] measured the capacity of a single rolling element over one revolution in the bearing and compared the result with a calculation based on the model shown in Fig. 3. Here the influence of the undeflected area of a loaded rolling element is described with equation (3). The expected capacity increase is observable as the rolling element passes the load zone, but also outside the load zone a capacity of the rolling element is measured. Previous work has examined axial loaded rolling bearings [5,17,19] in which all rolling elements are loaded. The electrical properties of the loaded single contact have also been investigated [15,18,20]. In addition to an absolute measured value, such as the lubricant film thickness, the friction regime was investigated [7,21], where unloaded rolling elements can be neglected",
            " (8) The position-dependent clearance \u03b4\u03d5, in turn, depends on the bearing clearance Pd and the radial sift \u03b4r between the bearing rings due to the radial load. \u03b4\u03d5 = \u03b4r cos \u03d5 \u2212 0.5Pd. (9) Instead of taking the Hertzian area as lower limit for the surface integral it is now integrated for the entire surface. The size of the surface AU is the area corresponding to the projection of the ball onto the raceway. It is comparable to the area AR in Fig. 4, the difference is that the Hertzian area is not present here. The distance between the undeflected as well as unloaded bodies hu(x, y) is integrated over the whole surface in x and y directions, shown in Fig. 3. The capacity of an unloaded contacts CU is calculated similar to equation (3) as follows: Fig. 5. Electrical model of a rolling bearing [2]. Fig. 6. Load zone in rolling bearing under radial load according to Ref. [25]. T. Schirra et al. Tribology International 158 (2021) 106927 CU = \u222b\u222b AU \u03b50\u03b5r hU(x, y) dx dy. (10) Fig. 7 shows the presented consideration of unloaded rolling elements and the calculation of the capacity of the peripheral area (UR) and the state of research for factors kR according to Barz [12], kR = 3",
            " Taking both into account could reduce the deviation between measurement and calculation even further. Both influences considered by Schneider et al. [22] with the factor kvh. This factor describes the ratio between the capacity of the flat plate capacitor, shown in Fig. 2 and equation (1), and the numerically calculated capacitance of the Hertzian contact. On the one hand, the difference between minimum and central lubricant film thickness decreases small lubricant film thicknesses, and for large lubricant film thicknesses, the influence of the undeflected capacitor, see Fig. 3, is large. This suggests that the influence of the minimum lubricant film thickness is negligible. On the other hand, Mann has demonstrated the influence of the minimum lubricant film thickness in the two-disc test rig. For this reason, a calculation has been carried out in Fig. 16 in which it was assumed that hmin is the lubricant film thickness in the entire rolling contact. Comparison shows the influence of hmin increases with increasing load. The actual influence has to be between the two calculations and probably closer to the initial calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003520_j.chaos.2004.09.028-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003520_j.chaos.2004.09.028-Figure4-1.png",
        "caption": "Fig. 4. A mapping structure for a periodic motion.",
        "texts": [
            "nk \u00f0Pn1 Pn2 Pnk \u00de \u00f0Pn1 Pn2 Pnk \u00de|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} m sets : \u00f018\u00de To extend this concept to the local mapping, define P \u00f0m\u00de 12 \u00f0P 1 P 2\u00de \u00f0P 1 P 2\u00de|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} m sets ; P \u00f0m\u00de 45 \u00f0P 4 P 5\u00de \u00f0P 4 P 5\u00de|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} m sets : \u00f019\u00de Introduce a mapping structure for global and local mappings, Pn1n2 ...\u00f0ninj\u00dem...nk Pn1 Pn2 P \u00f0m\u00de ninj Pnk : \u00f020\u00de As in Luo [21,22], consider a periodic motion with following mapping structure in Fig. 4, given by P 6\u00f045\u00dek2 43\u00f012\u00dek1 1 P 6 P \u00f0k2\u00de 45 P 4 P 3 P \u00f0k1\u00de 12 P 1: \u00f021\u00de Note that for k2 = k1 = 0, the foregoing mapping structure becomes the simplest structure, i.e., P 6431 P 6 P 4 P 3 P 1: \u00f022\u00de On the other hand, a generalized mapping structure is P 6\u00f045\u00dek2n 43\u00f012\u00dek1n 1...6\u00f045\u00dek2m 43\u00f012\u00dek1m 1...6\u00f045\u00dek21 43\u00f012\u00dek11 1 P 6\u00f045\u00dek2n 43\u00f012\u00dek1n 1 P 6\u00f045\u00dek2m 43\u00f012\u00dek1m 1 P 6\u00f045\u00dek21 43\u00f012\u00dek11 1: \u00f023\u00de From mapping structures of periodic motions, the switching sets for a specific regular motion can be determined through solving a set of nonlinear equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure7-1.png",
        "caption": "Figure 7 The Cardan joint.",
        "texts": [
            " g p i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + = \u2211 (26) But for the whole Carricato mechanism, the mobility is the sum of those of the parallel one and the serial one, i.e., the mobility of Carricato mechanism is four. In addition, the mobility can be directly calculated by the modified G-K criterion as well ( ) 1 ( 1) 6 15 17 1 19 3 4. g i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + = \u2211 (27) Similar to the former examples, the numbers of common constraints and parallel-redundant-constraints are invariable at any possible configuration of this mechanism. The mobility is global. The Cardan joint, as shown in Figure 7, is one of the most famous counter-examples besides the Bennett and Goldberg mechanisms pointed out by Merlet[30]. It is a chain which consists of four closed loops connected by five links in series. If each closed loop including two links and two joints is regarded as a generalized pair, the serial chain contains four generalized pairs and five links. We take one closed loop into consideration. As shown in Figure 8, the origin point locates on the center of one joint, and z-axis is along its axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003584_we.173-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003584_we.173-Figure12-1.png",
        "caption": "Figure 12. High-speed parallel gear stage",
        "texts": [
            " Finally, subsection three describes two models of the complete drive train: a purely torsional and a rigid multibody model. The high-speed stage of the gearbox is a helical gear pair. For this stage the three presented modelling techniques are implemented. First a torsional model is built, only taking into account the gear mesh stiffness. Then a rigid multibody model is implemented by adding the bearing stiffnesses. Finally, this model is extended to a flexible multibody model which integrates the components\u2019 flexibilities. In all three models, both the gear and the pinion are free to rotate in their bearings. Figure 12 shows these three models and Table III shows a comparison of the calculated eigenfrequencies. The eigenfrequency 1479 Hz calculated with the torsional model drops to 702 Hz in the rigid multibody model, indicating again the impact of the bearing flexibilities on the torque dynamics. Furthermore, other additional modes are found and are given with the main component of their corresponding mode shape. By adding the components\u2019 flexibilities in the flexible multibody model, the eigenfrequencies decrease further"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002891_63.286816-FigureI-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002891_63.286816-FigureI-1.png",
        "caption": "Fig. I. Simple RM drive model, 2 poles.",
        "texts": [],
        "surrounding_texts": [
            "I. INTRODUCTION\nOBUST drives can be achieved by using novel control R algorithms of ac machines (e.g., [l]). For certain applications (exact speed information, field-weakening capability), reluctance machines (RM) may be preferred (e.g., [2]). When the RM has no damper winding in the rotor, a closed-loop control is necessary. The rotor-position information is usually obtained from a position encoder which reduces robustness considerably. However, in this paper a novel position calculator based on current measurements is presented and applied to a drive without any mechanical sensor.\n11. NOMENCLATURE\nA. Symbols\n1\nr V , i , X U, a, X t 7\nW\nY j N ( m , f f2 ) p.u. value of inductance or reactance, respectively. p.u. value of ohmic resistance. P.U. value of voltage, current, magnetic flux. Corresponding space phasors. p.u. value of torque. p.u. value of time. p.u. value of angular velocity. Rotor angular position. Unit of imaginaries. Normally distributed random variable with mean m and variance 0'.\nManuscript received March 24, 1994; revised November 29, 1993. M. Schroedl is with the Transportation Technology Division, ELIN Vienna,\nP. Weinmeier is with the Institute of Electrical Machines and Drives, Vienna\nIEEE Log Number 9400095.\nA-I 141 Vienna, Austria.\nUniversity of Technology, A-1040 Vienna, Austria.\nB. Indexes\nS diff i m L I , 11 a , b d, 4 U, v, w Stator. Differential. Intemal. Mechanical. Load. INFORM measurement intervals. Stator-oriented reference frame. Rotor-oriented reference frame. Phase windings.\n111. MATHEMATICAL DESCRIPTION OF THE RELUCTANCE MACHINE\nA powerful method for describing the transient behavior of the machine is the space phasor theory [3]. The distributed electromagnetical quantities in the machine are represented by complex phasors. However, since the reactances in the direct (d- ) and quadrature (4- ) axes of the machine are different (Fig. l) , the equations containing these reactances are split into d- and q-components. All quantities are used in p.u. form as defined in [4].\nIn a three-phase system, the stator current space phasor is is derived from phase quantities, i s ~ , isv-, isw in the following way:\ni s ( . r ) = $ ( Z S U ( T ) + ~ S V ( T ) exp ( j 27r/3)\n(1)\nSpace phasors for voltages and flux linkages are defined in the same manner. The stator voltage equation in a reference frame rotating at W K is\n(2) dX v, = rs . a , + - + j ' W K .A,. dr\nNeglecting cross-coupling effects, the flux linkage equations in d- and q-components are\n+ Z S W ( T ) exp ( j 47r/3)).\nASd = l d ( i S d ) i S d (3) Asp = 1, is,. (4)\n0885-8993/94$04.00 0 1994 IEEE",
            "226 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 9, NO. 2. MARCH 1994\nThe d-axis reactance depends considerably on the current component i S d , whereas the q-axis reactance can be assumed constant due to the large air-gap. Fig. 2 gives measurement results of the tested 4-pole l-kW motor.\nThe mechanical system is described by the following equation:\nd w d r rm ' - = t; + t L\nat which the produced torque roduced torque\nThe indirect flux detection by on-line reactance measurement (INFORM) method was introduced by one of the authors in 1988 [5] and has been applied to different machine types [6]. The basic idea is to measure the behavior of the current space phasor due to a test voltage space phasor in real time. Because of saturation effects (permanent magnet synchronous motor with surface-mounted magnets, induction motor) or geometric facts (reluctance motor), the change of the current space phasor relative to the respective voltage space phasor depends on the angular position of the voltage space phasor relative to the flux (permanent magnet motor, induction motor) or the rotor, respectively (reluctance motor).\nA. Machine at Standstill In the first step, assume the rotor angular velocity to be zero. In Fig. 4 the space phasor relations are given for an RM(ld = 21q). Measuring the currents and knowing the direction of the test voltage space phasor (in a stator-oriented reference frame a, b), the angle a in Fig. 4 can be determined. On the other hand, a is a function of double the rotor position, a = a (27). Hence, 2 7 can be calculated from given a. For the special cases y = k n/2 ( k = 0,1 , . . .), cy is zero, i.e., voltage and current change are in phase.\nLinearizing in the magnetic set-point defined by i sdo and isyo, we obtain from (2)-(4) in a d, q -reference frame (rotating at w ) In order to achieve maximum torque production at a given current space phasor modulus lis[, an optimum zSq/ iSd ratio can be determined. In case of no saturation (constant reactances), the optimum i S q / i S d value is 1; in the real motor the curves shown in Fig. 3 have been obtained (parameter is / is[) .\nmust be known in order to impress the demanded d- and qcomponents of the stator current. Usually, this information is obtained from a position encoder. However, in the following\nrotor position without any mechanical sensor.\n(7)\n(8)\nd isd V S d iSdOTs + ld,diff . -d 7 - wisqo\nFor control purposes, the angular position of the rotor d isq V S q iSqOTs + - + w i s d o d r\nwhere\na mathematical model is presented yielding an estimate of the (9)"
        ]
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure3-1.png",
        "caption": "Fig. 3. A singular con\u00aeguration of class (RO, II).",
        "texts": [
            " (4) Condition (vii) is applied. (vii) is equivalent to the singularity of at least one of the matrices [ SBSCSD] or [ SCSGSF]. The solution of each of these equations (combined with the loop equations) is a 1-dimensional submanifold of the 2-dimensional con\u00aeguration space. The \u00aerst manifold has four connected components, and the second one has three components. All elements of the union of these manifolds, except the eight elements of {2} found in Step 2, are of the (RO, II) class. One such singularity is shown in Fig. 3. The corresponding connected component is obtained by moving the linkage while keeping the joint angle at G constant. (5) The condition (viii) is applied. (viii) is equivalent to the singularity of at least one of the matrices [ SASBSC], [ SGSCSD] or [ SESGSF]. The solution for each of these equations (combined with the loop equations) is a 1-dimensional submanifold of the 2-dimensional con\u00aeguration space. The \u00aerst and third manifolds have each two connected components, while the second one has four"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002886_s0921-5093(03)00435-0-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002886_s0921-5093(03)00435-0-Figure3-1.png",
        "caption": "Fig. 3. The definition of powder injection point and direction of scanning velocity. (a) V /0 and Dx /0; (b) V /0 and Dx /0 (c) V B/0 and Dx /0.",
        "texts": [
            " Therefore, the amount of the powder forming a clad was mainly determined by the amount of the powder injected into the melt pool. Then the influence of processing parameters on the height of single cladding layer was equivalent to their influence on the amount of the powder injected into the melt pool. Fig. 2 shows the variation of the height of single cladding layer, H , with nickel-base alloy under different conditions and will be discussed in detail as follow. Before discussion, we had to make some definitions referring to Fig. 3. First, we defined three points as follows: . Point O, the center of the laser spot on the substrate surface. . Point A, the intersection point of the axis of powder stream and substrate surface. . Point B, the intersection point of the axis of powder stream and laser beam. Then Dx was defined to be the distance between point O and A. Dx was defined to be positive when point B was beneath point O, otherwise it was negative. The direction of scanning velocity is defined as positive when powder delivery nozzle and clad are in different sides of the laser beam, otherwise it is negative",
            " This was due to the amount of the powder injected into the melt pool varied with Dx , referring to Fig. 4. In Fig. 4, the shadow area, which represented the overlap between the laser spot and the powder stream, illustrated the amount of the powder injected into the melt pool approximately. From Fig. 2(a), it can also be found that the value of Dx corresponding to the maximum H was /2 mm. When the scanning velocity was positive and Dx ]/0, most of the powder was injected into the head part of the melt pool (see Fig. 3a, b). Since the shape of the melt pool is not axisymmetrical along the longitudinal section, in other words, if we take the center of laser spot as the origin point, the area of the head part of the melt pool is smaller than that of the tail part due to the heat flux. Therefore, the amount of the powder injected into the melt pool with Dx ]/0 was less than that with Dx B/0 (referring to Fig. 4). When the scanning velocity was negative and Dx ]/0, although most powder was injected into the tail part of the melt pool, the amount was still less than that with Dx B/0. It can be found from Fig. 3(c) that, the surface of the substrate was lifted due to the clad, which changed the relative position of laser beam, powder nozzle and substrate. When Dx ]/0, part of powders hit the surface of the solidified clad instead of being injected into the melt pool and was rebounded. When Dx B/0, this part of powders was injected into the melt pool which increased the total amount of the injected powders. Therefore, the value of Dx corresponding to the maximum H was still negative. Fig. 2(a) also shows that the height of single layer H varied with the direction of scanning velocity",
            " Therefore, the powder adhering on the surface was mainly those that were not injected into the pool, the more the diverging powder, the worse the adhesion. For the effectively limited powder stream, the powder adhesion was mainly determined by the position of the interaction area of the powder stream and melt pool. When the interaction area was focused on the head part of the melt pool, the powder which was not injected into the pool hit the solid substrate ahead the pool and rebounded, referring to Fig. 3(a). Even if some powders adhered on the surface of substrate, they would be melted when the laser beam scanned over the surface. Therefore, the surface was quite smooth. However, since a part of powder was not injected into melt pool and was rebounded, the height of single cladding layer was small. While when the interaction area was focused on the tail part of the melt pool, the powder which was not injected into the pool first heated by laser irradiation and then hit the solidified metal, which made it easy to adhere and led to powder adhesion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003571_bf01212271-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003571_bf01212271-Figure1-1.png",
        "caption": "Fig. 1. The rolling hoop.",
        "texts": [
            " b~+~,a~ +' b~+2,\"z+') \\ , ~ i Otherwise stated, BL = 0 with B r 0. Thus the rank of L, which is equal to the rank of L (the pullback by q~ is one to one), is not maximal. Hence dim I z = s - 2 . 9 We illustrate various aspects of Theorems 7 and 10 on four examples. Example 1 (The Rolling Hoop). A circular hoop of radius a rolls without slipping on a fixed horizontal plane. The configuration of the hoop is defined by the projections x, y of its center C on the plane, and by the Euler angles ~, 0, ~o (see Fig. 1). The conditions that the velocity of slip is zero are cos ~ + 3~ sin ~k + a(~ cos 0 + ~b) = 0, - 2 sin ~ + 3~ cos ~ + a0 sin 0 = 0. These constraints describe a Pfaffian system of dimension 2 in five variables, I := {cos ~ dx + sin ~b dy + a cos 0 dO + a do, - s i n ~ dx + cos ~ dy + a sin 0 dO}, which is linearizable (dim 11 = 1 and dim 12 = 0). Alternatively, we could consider this Pfaffian as a driftless system with three inputs and five states (for instance, by choosing three velocities as the inputs)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002984_s0021-9290(99)00137-2-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002984_s0021-9290(99)00137-2-Figure2-1.png",
        "caption": "Fig. 2. Di!erent leg lengths at touch-down and take-o! can be described by the leg lengthening r ` . The actual shortening of the leg is *r, l(a) denotes the length of the relaxed leg which increases with a.",
        "texts": [
            " Therefore, we introduce the leg lengthening parameter r ` as the di!erence between both leg lengths: r ` \"r E !r 0 . (1) The actual length of the relaxed leg l(a) during the contact phase is then de\"ned in a linear approach by (Blickhan et al., 1995): l(a)\"r 0 #r ` (a!a 0 )/(a E !a 0 ) \"r 0 #e(a!a 0 ) (2) with e constant, leg angle a at touch-down a 0 , at take-o! a E , initial leg length r 0 , change in r by r ` during contact. Leg shortening *r(t)\"l(a(t))!r(t) is zero at the instances of touch-down and take-o! (Fig. 2). The force exerted by the leg is related by the sti!ness to the shortening of the leg *r. The leg sti!ness is de\"ned by the ratio of the ground reaction force to the leg shortening *r at maximum leg shortening: k\"F G, MAX /*r MAX . (3) We generalise the instantaneous ratio in Eq. (3) as the dynamic leg sti!ness: k $:/ (t)\"F G (t)/*r(t). (4) This de\"nition is equal to Eq. (3) for the instant of maximum shortening of the leg and corresponds to the understanding in the literature (Farley and GonzaH lez, 1996)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000871_j.ymssp.2021.107970-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000871_j.ymssp.2021.107970-Figure3-1.png",
        "caption": "Fig. 3. The motion diagram of rolling bearing.",
        "texts": [
            " This paper makes the following assumptions for rolling bearing: (1) The inner ring of rolling bearing is connected with the spindle shaft through interference fit, and the outer ring is rigidly connected with the foundation. (2) The ball is evenly distributed in the bearing raceway, of which motion is pure rolling. The whole bearing is installed normally without fault. (3) The gyroscopic torque and centrifugal force of the ball and the lubrication of the raceway have negligible effects on the dynamics of the spindle system. The motion diagram of rolling bearing is shown in Fig. 3. The rotating speed of the cage xc is as follows xc \u00bc xdi do \u00fe di \u00f01\u00de where x is the angular speed of spindle; di is the diameter of inner race; do is the diameter of outer race. As can be seen from Fig. 3, the location angle of rolling bearing ball uj is as follows uj \u00bc 2p j 1\u00f0 \u00de Z \u00fexct; j \u00bc 1;2; :::; Z \u00f02\u00de where Z is the number of rolling bearing ball; t is time variable. If x and y are the displacement of the inner ring of the bearing relative to outer ring, the deformation of the jth ball in the radial direction is as follows [41] dj \u00bc xcosuj \u00fe ysinuj c0 \u00f03\u00de where 2c0 is initial radial clearance of rolling bearing. Assuming that the contact behavior between the ball and the raceway satisfies the Hertz contact condition, then according to the Hertz contact theory, the contact force of the jth ball in the radial direction is as follows [42] f j \u00bc kb xcosuj \u00fe ysinuj c0 n xcosuj \u00fe ysinuj > c0 0 xcosuj \u00fe ysinuj c0 8< : \u00f04\u00de where kb is the Hertz contact stiffness, related to the material property and geometry of rolling bearing, and its expression is shown in formula (5) [43,44]; n is the contact index, which is 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.8-1.png",
        "caption": "Figure 14.8. Transverse section showing the backlash.",
        "texts": [
            "7 that the normal backlash is equal to the width of the gap between the teeth of the imaginary racks, measured normal to the tooth profiles in the pitch plane. Relations Between the Different Types of Backlash The relation between the normal backlash Bn and the circular backlash B can be seen immediately from Figure 14.7, B cos I/tp (14.72) In order to find a relation between the backlash B' along the common normal and the circular backlash, we first consider a typical transverse section through the gear pair, as shown in Figure 14.8. The two interior common tangents to the base cylinders are labelled E1E2 and E;Ei. The contact point in this section lies on line E1E2 , while line E;Ei cuts the non-contacting tooth profiles at points A; and Ai. Figure 14.9 shows the plane through E; and Ei, which is tangent to both base cylinders. We proved in Chapter 13 that any plane which is tangent to the base cylinder of a helical gear intersects the tooth surface along a generator, and we 392 Helical Gears in Mesh showed that all the generators of a gear make the same angle \"'b with the ",
            "9 is tangent to both base cylinders, and it therefore intersects the tooth surfaces along two parallel straight lines, which pass through A; and Ai. We will show, later in this chapter, that the normals to the tooth surfaces at A; and Ai lie in this plane, and that they are perpendicular to the generators. Hence, the backlash B' along the common normal, which is defined as the shortest distance between the tooth surfaces, is equal to the perpendicular distance between the two generators in Figure 14.9. If as is the distance between points Ai and Ai in the transverse section shown in Figure 14.8, then in Figure 14.9, as is the vertical distance between the two generators. We can therefore express the backlash along the common normal in terms of as, B' as cos \"'b (14.73) We now consider holding one gear fixed, and rotating the other to close the gap between Ai and Ai. The relation between the displacement as and the corresponding rotation ap was given by Equation (3.60), Position and Orientation of the Contact Line 393 (14.74) We use Equation (14.31) to express the base cylinder radius of the moveable gear in terms of its pitch cylinder radius, (14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000072_s40192-019-00149-0-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000072_s40192-019-00149-0-Figure6-1.png",
        "caption": "Fig. 6 Energy-dispersive X-ray diffraction measurement setup for the Z, X, and 45\u00b0 directions. The diffracted beam is 9.18\u00b0 away from the incident beam. The Q-vector points approximately 4\u00b0 along the direction of the strain component measured",
        "texts": [
            "25\u00a0mm cross section by a pair of incident beam slits, made out of a high-density tungsten-based alloy HD17 [15]. The beam penetrated the sample and diffracted through two sets of receiver slits with a fixed angle (2\u03b8) of 9.18\u00b0 to a germanium, single element Canberra GL-0055 energy-resolved detector. The multiple slit geometry results in a \u201crhomboidal\u201d-shaped diffraction volume of 0.25\u00a0mm \u00d7 1.5\u00a0mm \u00d7 0.25\u00a0mm, where the extended dimension is approximately along the Y direction of the sample (inset in Fig.\u00a06). The sample was positioned in a four-circle goniometer with built-in translation stages. Individual diffraction patterns were collected from the X\u2013Z cross section at Y = 2.5\u00a0mm (mid-plane of the sample). The setup enabled the automated positioning and rotation of the sample to collect data for the orthogonal strain components along X and Z, as well as the strain component of the 45\u00b0 off Z direction. It should be mentioned that it was not possible to determine the Y-strain component because the necessary sample orientation results in an X-ray path length of 75\u00a0mm. The X-ray absorption through 75\u00a0mm of IN625 made it impossible to measure the residual strain for the Y component. Figure\u00a06 shows the energy-dispersive X-ray diffraction setup for measurements along the X, Z, and 45\u00b0 off Z directions. The measurement locations for the lattice strains are illustrated in Fig.\u00a07. The measurements were conducted 0.25\u00a0mm from the edges of the sample. However, on the regions close to the \u201ctaper\u201d side of the sample the measurements were performed 0.75\u00a0mm from the edge of the chevron. The measurement grid spacing is divided into two parts: the large solid section with a spacing of 1\u00a0mm and the leg sections with a spacing of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003396_robot.1990.126123-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003396_robot.1990.126123-Figure1-1.png",
        "caption": "Figure 1: NASA Labomtory Telerobotic Manipulator",
        "texts": [
            " [l] developed an efficient implementation of the gradient projection scheme for manipulators with one degree of redundancy. This paper presents an efficient gradient projection optimization scheme for manipulators with multiple degrees of redundancy. This is an extension of the schcme dcveloped by Dubey et al. [l] for manipulators with one degree of \u20184dundancy.This scheme does not require the computation of the generalized inverse of the Jacobian, and it results in an efficient formulation for determining the joint velocities. The seven-degre-f-freedom NASA Laboratory Telerobotic Manipulator (LTM) [7] shown in Fig. 1 is used to demonstrate the implementation of the control scheme. Only the end-effector position (not the orientation) of the LTM is controlled which only requires three joints. Since the last joint of the LTM is a roll joint which does not affect the end-effector position; the remaining six joints allow three degrees of redundancy for controlling the position. A 3-D solid model of the LTM was developed on the SiliconGraphics IRIS workstation. Several simulations were performed to demonstrate the feasibility and effectiveness of the optimization scheme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure8.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure8.6-1.png",
        "caption": "Figure 8.6. Measurement over pins.",
        "texts": [
            "25) The right-hand side of this equation is evaluated, and N' is chosen as the integer closest to this value. The corresponding span S is then given by Equation (8.18). When the tooth thickness inspection of a gear is to be carried out by means of a span measurement, the values of N' and S are included in the specification of the gear. Measurement Over Pins A third method by which the tooth thickness can be measured is called the measurement over pins. Two cylindrical Measurement Over Pins 201 pins of known diameter are inserted into opposite tooth spaces of the gear, as shown in Figure 8.6, and we measure the distance M between the outer points of the pins. We will now show how the measured value of M can be used to calculate the tooth thickness ts of the gear. Figure 8.7 shows one tooth of a gear, with the pin positioned so that it is touching the tooth profile at A, and its center A' is lying on the center-line of the adjacent tooth space. The radius of the pin is r, and the distance between A' and the gear center C is shown as R'. We first need to find a relation between R' and the tooth thickness ts' The tooth profile involute meets the base circle at B",
            "35), ts 2R + inv tPs - inv tPR s The corresponding angle 9b of point B, the end point of the involute, is found by setting the profile angle tPR equal to zero, (8.26) If the polar angle of the line through B' is 9b, its value can be found by adding the angle BCB' to 9b , 9' b t 2: + inv tPs + ..L s Rb (8.27) The angle between CB' and CA' is equal to (inv tPR')' and the angle between the center-lines of the tooth and the tooth space is (~/N). These two angles are together equal to 9b, so we obtain the following relation between the various angles, . ~ lnv tPR' + N (8.28) Measurement Over Pins 203 Figure 8.6 shows the measurement over pins for a gear with an even number of teeth. The relation between the length M and the radius R' can be read from the diagram, M 2R' + 2r (8.29) To find the tooth thickness of a gear, we measure the length M, and R' is calculated from Equation (8.29). The corresponding profile angle 9>R' is given by Equation (2.18), cos 9>R' (8.30) and Equation (8.28) is then used to calculate the tooth thickness ts. The order of the calculations is reversed when the tooth thickness is specified, and we want to find the corresponding value of M for inspection purposes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure1-1.png",
        "caption": "Fig. 1. The thin-walled lattice support structures for overhang features in the Inconel 718 component.",
        "texts": [
            " Excessive residual deformation could cause difficulty in post-machining the components to size, and thus prohibit wider practical applications of the L-PBF technologies. Therefore, it is very meaningful to predict residual deformation and evaluate the geometrical uncertainty through efficient numerical simulation before building a large part. However, it is quite challenging to predict residual deformation through thermomechanical simulation when considering realistic laser scanning paths and process parameters. Especially, when lattice support structures such as the thin-walled hollow blocks in the L-PBF process (Fig. 1) are used to assist in building components with overhanging structures [12\u201315], it becomes more difficult to simulate the L-PBF https://doi.org/10.1016/j.addma.2020.101091 Received 1 October 2019; Received in revised form 17 January 2020; Accepted 23 January 2020 \u204e Corresponding author. E-mail address: albertto@pitt.edu (A.C. To). Additive Manufacturing 32 (2020) 101091 Available online 01 February 2020 2214-8604/ \u00a9 2020 Elsevier B.V. All rights reserved. T process because lattice support structures have lots of fine features which make mesh generation extremely difficult",
            " Typical elastic and plastic strain time history figures of a typical material point of interest have been reported in our previous work [24]. A key finding is that the depositing process of the third layer has limited influence on mechanical strain evolution of the first layer. As a result, the extracted inherent strain values have insignificant difference compared to those values extracted from the two-layer small-scale simulation. Therefore, the choice of a two-layer model in the small-scale simulation in this paper is reasonable. Given the periodicity of the features in the thin-walled lattice support structures (see Fig. 1), a small model containing four lines as shown in Fig. 2(a) is sufficiently representative. The parallel line scanning strategy is simulated as the basic scanning pattern and only single-track laser beam is employed for printing the support structures as shown in Fig. 2(b) in the L-PBF process. Due to the single-track laser scanning pattern, the wall thickness of the support structures is constant at 0.1mm, which equals the laser beam diameter. The distance between the center lines of two adjacent parallel walls is varied to control the relative volume density of the lattice support structures to satisfy different printing demands"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001012_j.triboint.2021.106927-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001012_j.triboint.2021.106927-Figure10-1.png",
        "caption": "Fig. 10. Schematic cross section of the mechanical setup and its insulation concept.",
        "texts": [
            " This hypothesis is strengthened by the fact that the effect occurs more clearly at elevated speeds and low temperatures. The estimation of radial shift does not take the lubricant film thickness into account and thus the observed effect of increasing impedance occurs more strongly. In order to investigate the electric impedance of rolling bearings, bearings of the type 6205 C3 are investigated using the test rig shown in Fig. 9. The hydraulic cylinders 1 and 2 are used to load the setup with axial, radial and combined loads to the bearings. The experimental setup of the shaft with its four bearings is shown in Fig. 10. The radial load is applied via the two middle rolling bearings and supported by the outer rolling bearings. The electric motor 3 in Fig. 9 sets the angular velocity for the shaft. The outer ring temperature of each of the four rolling bearings in the test rig is measured individually with the thermocouples 4. Besides the temperatures, the shaft velocity and the loads are used for closed-loop control of the test bench. The slip ring 5 contacts the shaft to create a voltage difference between the inner and outer ring of the rolling bearing. The contact pin 6 enables an electrical contact of the outer ring to close the electrical circuit including the rolling bearing under investigation, see Fig. 10. The test rig is equipped with a circulating oil lubrication so the bearing is completely flooded by the lubricant. Fig. 10 shows the schematic cross section of the test rig with the electrical test setup. Except for the test bearings, the bearings in between are electrically insulated to ensure the uniqueness of electrical measurement circuit. With the electrical circuit for measuring the electrical impedance, a voltage is applied to the shaft via the slip ring using an AC source operated at a signal frequency of fm = 5 MHz and a peak to peak? voltage amplitude of US = 1V. These parameters were chosen du to the effect that the current probe used does not operate below 3 MHz and skin effects were observed in different test rigs above 7 MHz [29]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure1-1.png",
        "caption": "Fig. 1. Configurations of water jackets.",
        "texts": [
            " In this article, the optimizations of thermal field in a watercooling PMSIWM are studied, including the analytical design of the water jacket, the impact of the water jacket configuration parameters, the impact of the water jacket shape, the thermal parameters of impregnation materials, the impregnation process, the optimizations of the slot shapes, and the emulational and experimental verification. In the limited space, the designers expect that the water takes away the heat from the motors causing temperature difference between the water and water jacket wall as low as possible. In terms of the manufacturing process, the circumferential and axial water jackets are widely used in the water-cooled motors. Fig. 1 shows the configurations of the circumferential and axial water jackets, where a and b are the section width and height of the water jackets, respectively. In the design process, the volume flow rate is firstly calculated. Then, an analytical method is used to obtain the CHTC. The analytical calculation is based on the assumption of straight piping flow. The velocity is supposed to be uniform along the pipe direction. Finally, the temperature difference between the water and water jacket wall is calculated",
            " In addition, when lt is beyond the inflection point, the temperature difference gradually reduces. As the increase of lt reduces lsb, the slots with short slot bottom have advantages on the slot heat dissipation. A water-cooled PMSIWM is designed based on the aforementioned optimization methods. According to the optimization methods, the final scheme is obtained. Fig. 11 shows the motor, including the axial water jacket, vacuum impregnation with epoxy, slender slots. The structure of the axial water is shown in Fig. 1. The main parameters of the water-cooled PMSIWM are shown in Table II. As stated in Section II, the water jacket designers should avoid the size of the inflection point first. Then, the impact of water jacket shapes should be considered. For the PMSIWM, the water jackets are designed based on the method in Section II. In order to avoid the inflection point in Fig. 3, the final section width and height are 40 and 16 mm, respectively. The impact of water jacket shapes on the thermal field of the PMSIWM is mainly studied in this section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002890_j.wear.2004.10.012-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002890_j.wear.2004.10.012-Figure2-1.png",
        "caption": "Fig. 2. Locations of metallographic investigations: longitudinal and transverse.",
        "texts": [
            " The discs were manufactured from two gear steel grades: EN36 and SAE 8620H, which are widely used for gear manufacturing. The chemical compositions of the two steels are g h p 8 a b i m f w t s f a m l i a p eeping constant the sum of their outer diameters. Tests were interrupted after N= n\u00d7 1.8 \u00d7 105 cycles here n= 1\u20134 and the surface condition was investigated sing light microscopy and optical profilometry. Metalloraphic investigations were carried out after the tests were topped on cross-sections obtained by sectioning the disc in ongitudinal and transverse direction as shown in Fig. 2. In addition, after each testing stage, the weight and the adii of curvature of the disc samples were measured. The esults presented here refer to the driven disc. .2. Design of experiments (DOE) One difficulty with factorial designs is that the number f combinations increases dramatically with the number of iven in Table 3. The samples were subjected to standard gear eat treatment procedures (carburising, quenching and temering), EN36 samples at David Brown Eng. Ltd. and SAE 620 samples at Bodycote Heat Treatment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000040_j.addma.2020.101442-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000040_j.addma.2020.101442-Figure4-1.png",
        "caption": "Fig. 4. (a) location of samples extracted for microstructural studies using EBSD and SEM and (b) location of residual stress measurements on the fatigue specimens.",
        "texts": [
            " Surface topography of the fatigue specimens after polishing and shot peening operations were characterised using Taylor Hobson CCI white light interferometer fitted with a 20x objective lens and with an approximate field of view of 830 by 830 \u03bcm. Raw data was processed using a Robust Gaussian filter with cut-off length of 800 \u03bcm. Filtering procedure and computation of topography parameters were performed using Talymap Gold software which is compliant to ISO25178 and ASME B46.1. Rectangular specimens for microstructural characterisation were extracted from fatigue specimens using electric discharge machining, see Fig. 4a. These specimens were mounted in an epoxy resin before being ground and polished using emery paper with progressively finer grit size and diamond suspensions. Microstructural imaging was carried out using a field emission scanning electron microscope (FESEM), JEOL JSM7600 F equipped with Oxford Instruments NordlysNano EBSD detector. Electro-chemical polishing was applied to the specimens used for electron back-scatter diffraction (EBSD) experiments. Crystallographic orientation mapping was acquired from the near surface region as shown in Fig. 4. Grain size analysis was carried out to determine the average grain diameter from the acquired EBSD map region. The averaged grain diameter was computed from all grains detected, excluding those which are found at the border (i.e. cut-off). FESEM images were used for observation of secondary phases in the alloy. Porosities of specimens H and H + HIP were characterised at the gauge section (where fatigue failures are expected to occur) using micro X-ray computed tomography (\u03bcXCT), Nikon XTH 225 ST",
            " Ten measurements were completed in the bulk material for each of the H and H + HIP conditions. Residual stress characterisation was carried out using centre-hole drilling (CHD) technique, SINT Technology Restan MTS-3000. CHD is a strain relieving technique which correlates the amount of strain being relieved on the surface with residual stresses at depth increments using algorithm described in ASTM E837-13 for non-uniform stress analysis. TML FRS-2-11-1LT (Type A) strain gauge rosette was affixed to the specimen\u2019s surface (location as shown in Fig. 4b) using Z70 cyanacrylate adhesive prior to drilling. Incremental depth drilling was carried out at increasing intervals from 10 \u03bcm in the first 100 \u03bcm then 25 \u03bcm for the next 400 \u03bcm and finally 50 \u03bcm for the next 700 \u03bcm resulting in a total hole depth of 1200 \u03bcm for determination of residual stresses at up to 0.975 mm depth. Young\u2019s modulus and Poisson ratio of 207.6 GPa and 0.29 respectively were utilised for the computation of residual stresses with the assumption that changes in these properties after shot peening were negligible",
            " Uniaxial force-controlled fatigue tests were carried out using an MTS Landmark servo-hydraulic with 250 kN load capacity. All tests were carried out in ambient temperature at a frequency of 20 Hz and an R-ratio of 0.1 (i.e. no compression). Appropriate stress levels were selected to develop a peak stress vs cycle-to-failure (S-N) plot between 104 and 106 cycles based on typical applications of the alloys. Cylindrical threaded-end plain (Kt = 1.0) fatigue specimens with continuously varying cross-section (see Fig. 3a) were machined out of the near net-shape AM parts, see Fig. 4b. The cross-section area of the specimen at its gauge section is approximately 92.5 mm2. The fatigue specimen design was selected to allow for application of strain gauge for CHD residual stress characterisation. The specimens were handpolished to achieve very low surface roughness after machining and prior to shot peening. Fractured surfaces were examined using a scanning electron microscope fitted with secondary electron for imaging. Two types of surface topography were characterised following polishing operations (H and H + HIP) and shot peening (H + SP and H + HIP + SP)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.11-1.png",
        "caption": "Figure 14.11. Directions of the unit vectors.",
        "texts": [
            " The vectors n x ' ny and n z are fixed in the pinion, with n z along the gear axis, and nx in the direction of the x coordinate axis, which coincides with a tooth center-line in the transverse section z=O, as shown in Figure 14.10. The vectors n~, nT/ and nS are fixed in the rack, with n~ perpendicular to the rack pitch plane, in the direction from the pinion towards the rack. The vectors nT/ and nS form a plane parallel to the pitch plane, and their directions are perpendicular to and parallel wi th the rack teeth, as shown in Figure 14.11. We define a new set of fixed unit vectors, nx(O), ny(O) and nz(O), as the directions of n x ' ny and n z when the pinion is in the reference position, from which the angle ~ is measured. For a spur gear, the angular position ~ was defined as the angle between the line CP and the x axis. In order to remain consistent with that definition, we now Position and Orientation of the Contact Line 395 choose the direction of nx(O) perpendicular to the rack pitch plane, so that it coincides with n~. The set of vectors nx(O), n (0) and n (0) is shown in Figure 14.11, and we can now write y z down the relations between these vectors and the set n~, n~ and nS' We have proved in Equation (14.19) that the rack helix angle ~~ is equal to the operating helix angle ~p of the pinion, and in relating the various sets of unit vectors, it will be convenient to describe all the angles in terms of those defined on the pinion. We therefore obtain the following relations from Figure 14.11, pinion at plane z=O, when the pinion has rotated through an angle p. The vectors n x ' ny and n z are expressed in terms of their reference directions by the following set of relations, 396 Helical Gears in Mesh (14.82) (14.83) (14.84) We now introduce another pair of unit vectors fixed in the rack. A normal section through the rack tooth is shown in Figure 14.13, and the vectors nnr and nTr are defined in the direction normal to the tooth surface, and in the direction of the tangent pointing towards the tooth tip"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002828_00207170010010579-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002828_00207170010010579-Figure2-1.png",
        "caption": "Figure 2. The virtual steering wheel.",
        "texts": [],
        "surrounding_texts": [
            "The basic idea is that the n-trailer system with m o\u0152hitching joints can be converted into an n \u2021 m-trailer system with m \u2021 1 steering axles, adding a steerable wheel at each of the aforementioned joints not directly hitched on the preceding axle. These m virtual steering wheels are passive, in the sense that their steering angles are (uniquely) determined by the con\u00ae guration and by the dynamic equations of the system. This is equivalent to saying that their inputs are obtained by means of feedback from the con\u00ae guration of the system and only the driving unit has exogenous input. First it is proven that a passive steering wheel is indeed admissible by the system and then, in } 6, it is shown that these virtual steering wheels provide physical insight into the extra singularities of the system due to the kingpin hitching. Proposition 1: Consider the two-trailer oV-hitching connection between the trailers i and i \u2021 1. This subsystem is equivalent to a standard three-trailer system with a steering wheel in the middle ( \u00ae gure 2). If \u00b3\u00aei is the orientation angle of the steering wheel and its steering angle is de\u00ae ned as \u00aei 7 \u00b3\u00aei \u00a1 \u00b3i\u20211, then it must be: \u00aei \u02c6 \u00b3i \u00a1 \u00b3i\u20211 \u2021 arctan \u00a1 Mi vi _\u00b3i \u00b3 \u00b4 \u202614\u2020 Proof: Consider the sketch in \u00ae gure 2. If such a virtual wheel exists, then, due to the rigidity of the connection between Mi and Li, the dynamic equation for the ith orientation angle \u00b3i, obtained in general from equation (8), must also be expressible as a function of the angle \u00aci (representing the steering angle of the virtual wheel with respect to the preceding trailer) _\u00b3i \u02c6 \u00a1 vi Mi tan \u00aci where the minus sign re\u00af ects the fact that the wheel is following and not preceding the axle. At the same time, the steering angle of the virtual wheel with respect to the following trailer i \u2021 1, \u00aei, must be such that _\u00b3i\u20211 \u02c6 vi\u20211 Li\u20211 tan \u00aei \u202615\u2020 Therefore, a physical solution exists (i.e. the wheel is admissible) i\u0152 \u00aei \u02c6 \u00b3i \u00a1 \u00b3i\u20211 \u2021 \u00aci Substituting into equation (8), we get vi\u20211 tan \u00aei Li\u20211 \u02c6 vi\u20211 tan \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 Li\u20211 \u2021 Mivi tan \u00aci MiLi\u20211 cos \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 using equation (9) vi cos\u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 \u2021 Mi sin\u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 \u00a1 vi Mi tan \u00aci \u00b3 \u00b4\u00b5 \u00b6 \u00a3 tan \u00aei \u00a1 tan \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020\u2026 \u2020 \u02c6 vi tan \u00aci cos \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 i.e. tan \u00aei \u02c6 tan \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 \u2021 tan \u00aci 1 \u00a1 tan \u2026\u00b3i \u00a1 \u00b3i\u20211\u2020 tan \u00aci \u02c6 tan \u2026\u00b3i \u00a1 \u00b3i\u20211 \u2021 \u00aci\u2020 & D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le ( A us tr al ia )] a t 1 1: 17 0 9 Se pt em be r 20 14 5. Comparison between standard and general n-trailer systems In what follows it is convenient to use the following notation: call n1; . . . ; nm, nj <nj\u20211, nm <n the indices of the axles having non-null o\u0152-hitching (Mnj 6\u02c6 0). One can group together the axles between two consecutive steering wheels: f0; 1; . . . ; n1g; . . . ; fnj\u00a11 \u2021 1; . . . ; nj \u00a1 1; njg; . . . ; fnm \u2021 1; . . . ; n \u00a1 1; ng. Each of the groups of axles, together with the steering wheel in front of it, will constitute a steering train. In case of two consecutive axles having o\u0152-hitching, then a steering train is reduced to a single axle. This is called a degenerate steering train. This notation can be rewritten as the dynamic equations of the orientation angles of the general n-trailer problem _\u00b3nj \u20211 \u02c6 vnj\u20211 tan \u2026\u00b3nj \u00a1 \u00b3nj \u20211\u2020 Lnj\u20211 \u00a1 Mnj _\u00b3nj Lnj\u20211 cos \u2026\u00b3nj \u00a1 \u00b3nj \u20211\u2020 \u202616\u2020 vnj \u20211 \u02c6 vnj cos \u2026\u00b3nj \u00a1 \u00b3nj\u20211\u2020 \u2021 Mnj sin \u2026\u00b3nj \u00a1 \u00b3nj \u20211\u2020 _\u00b3nj j 2 1; . . . ; mf g \u202617\u2020 _\u00b3nj \u00a1i \u02c6 vnj\u00a1i tan \u2026\u00b3nj\u00a1i\u00a11 \u00a1 \u00b3nj\u00a1i\u2020 Lnj\u00a1i \u202618\u2020 vnj \u00a1i \u02c6 vnj\u00a1i\u00a11 cos \u2026\u00b3nj \u00a1i\u00a11 \u00a1 \u00b3nj \u00a1i\u2020 \u202619\u2020 with j 2 1; . . . ; m \u2021 1f g, i 2 0; 1; . . . ; nj \u00a1 nj\u00a11 \u00a1 2 \u00a9 \u00aa and nm\u20211 \u02c6 n . It is assumed, in what follows, that the steering trains are not degenerate. In order to highlight the similarities of the dynamic equations (16)\u00b1 (19) with those of the standard n-trailer it is convenient to rewrite them in terms of the relative orientation angles  i 7 \u00b3i\u00a11 \u00a1 \u00b3i, i 2 1; . . . ; nf g, expressing all vi as functions of v0 and using the cartesian coordinates \u2026x0; y0\u2020. The system becomes _x0 \u02c6 v0 cos \u00b30 \u202620\u2020 _y0 \u02c6 v0 sin \u00b30 \u202621\u2020 _\u00b30 \u02c6 !0 \u202622\u2020 _ 1 \u02c6 \u00a1 v0 sin  1 L1 \u2021 !0 \u202623\u2020 _ nj \u20211 \u02c6 v0 Ynj k\u02c61 cos  k \u00c1 ! Yj\u00a11 k\u02c61 1 \u2021 Mnk Lnk tan  nk tan  nk\u20211 \u00b3 \u00b4 \u00a3 tan  nj Lnj \u00a1 sin  nj \u20211 Lnj\u20211 \u2021 Mnj Lnj Lnj \u20211 tan  nj cos  nj \u20211 \u00c1 ! \u202624\u2020 _ nj \u00a1i \u02c6 v0 Ynj \u00a1i\u00a11 k\u02c61 cos  k \u00c1 ! Yj\u00a11 k\u02c61 1 \u2021 Mnk Lnk tan  nk tan  nk\u20211 \u00b3 \u00b4 \u00a3 tan  nj \u00a1i\u00a11 Lnj \u00a1i\u00a11 \u00a1 sin  nj\u00a1i Lnj \u00a1i \u00c1 ! \u202625\u2020 j 2 f1; . . . ; mg, i 2 f0; 1; . . . ; nj \u00a1 nj\u00a11 \u00a1 2g. Notice that equations (20)\u00b1 (25) are everywhere well de\u00ae ned. Clearly, each of the components due to the kingpin hitching enters linearly into the system as an extra term added to the basic dynamic equations of the standard ntrailer, which are reobtained choosing Mnj \u02c6 0 _x0 \u02c6 v0 cos \u00b30 \u202626\u2020 _y0 \u02c6 v0 sin \u00b30 \u202627\u2020 _\u00b30 \u02c6 !0 \u202628\u2020 _ 1 \u02c6 \u00a1 v0 sin  1 L1 \u2021 !0 \u202629\u2020 _ i\u20211 \u02c6 v0 Yi k\u02c61 cos  k \u00c1 ! tan  i Li \u00a1 sin  i\u20211 Li\u20211 \u00b3 \u00b4 \u202630\u2020 i 2 1; . . . ; n \u00a1 1f g. In the rest of the paper the coordinate system in the absolute angles \u00b3i, i \u02c6 1; . . . ; n, and the other one in the relative orientation angles  i, i \u02c6 1; . . . ; n, are used indi\u0152erently according to convenience. The Pfa an system associated with (16)\u00b1 (19) is simply the collection of one-forms (6) plus the equations between pairs of cartesian coordinates of two adjacent nodes (7). So the irregularities enter only into the holonomic relations linking two consecutive one-forms via a kingpin hitch and propagate to their exterior derivatives dxnj \u02c6 dxnj\u20211 \u00a1 Lnj \u20211 sin \u00b3nj\u20211 d\u00b3nj\u20211 \u00a1 Mnj sin \u00b3nj d\u00b3nj dynj \u02c6 dynj\u20211 \u2021 Lnj \u20211 cos \u00b3nj\u20211 d\u00b3nj \u20211 \u2021 Mnj cos \u00b3nj d\u00b3nj j 2 1; . . . ; mf g. When o\u0152-hitching is missing instead we have dxnj \u00a1i\u00a11 \u02c6 dxnj \u00a1i \u00a1 Lnj\u00a1i sin \u00b3nj \u00a1i d\u00b3nj \u00a1i dynj \u00a1i\u00a11 \u02c6 dynj \u00a1i \u2021 Lnj\u00a1i cos \u00b3nj \u00a1i d\u00b3nj\u00a1i j 2 1; . . . ; m \u2021 1f g, i 2 0; 1; . . . ; nj \u00a1 nj\u00a11 \u00a1 2 \u00a9 \u00aa . In order to recover the original con\u00ae guration space dimension, we have to substitute into (7) the cartesian coordinates as functions of one single axle. In a proper domain of de\u00ae nition (see below) one can rewrite the one-forms (6) in terms of congruences: dyi \u00b2 tan \u00b3i dxi mod \u00aci i 2 0; 1; . . . ; nf g \u202631\u2020 meaning with this expression that the congruence is satis\u00ae ed up to an element of the ideal generated by \u00aci, D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le ( A us tr al ia )] a t 1 1: 17 0 9 Se pt em be r 20 14 i.e. dyi \u02c6 tan \u00b3i dxi \u2021 \u00ae ^ \u00aci for some \u00ae 2 O\u2026M\u2020 also satis\u00ae es it. In Pappas et al. (1998) it is shown how to use the congruence to obtain a relation between the exterior derivatives of the cartesian coordinates of two adjacent standard trailers. This is basically what is needed in order to eliminate the holonomic constraints on the Pfa an system. With the same notation convention used above, in the standard case see \u00ae gure 3(a), at the node nj \u00a1 i the congruence between the exterior derivatives of the orientation angle \u00b3nj \u00a1i and that of the corresponding cartesian coordinate xnj\u00a1i is modulo the two one-forms \u00acnj\u00a1i\u00a11 and \u00acnj\u00a1i. In the case Mnj \u00a1i\u00a12 \u02c6 Mnj\u00a1i\u00a11 \u02c6 0 one obtains d\u00b3nj \u00a1i \u00b2 tan \u2026\u00b3nj \u00a1i\u00a11 \u00a1 \u00b3nj\u00a1i\u2020 Lnj \u00a1i cos \u00b3nj \u00a1i dxnj\u00a1i mod \u00acnj \u00a1i\u00a11; \u00acnj\u00a1i \u202632\u2020 which gives the recursive relation dxnj \u00a1i\u00a11 \u00b2 \u20261 \u00a1 tan \u00b3nj \u00a1i tan \u2026\u00b3nj \u00a1i\u00a11 \u00a1 \u00b3nj \u00a1i\u2020\u2020 dxnj \u00a1i mod \u00acnj \u00a1i\u00a11; \u00acnj\u00a1i When, instead, a joint with kingpin hitch is involved, \u00ae gure 3(b), the formulae for the congruences gets more complicated d\u00b3nj \u20211 \u00b2 tan \u2026\u00b3nj \u00a1 \u00b3nj\u20211\u2020 \u00a1 \u2026Mnj =Lnj \u2020 tan \u2026\u00b3nj \u00a11 \u00a1 \u00b3nj \u2020 Lnj \u20211 cos \u00b3nj\u20211\u20261 \u2021 \u2026Mnj =Lnj \u2020 tan \u2026\u00b3nj\u00a11 \u00a1 \u00b3nj \u2020 \u00a3 tan \u2026\u00b3nj \u00a1 \u00b3nj \u20211\u2020\u2020 dxnj \u20211 mod \u00acnj\u00a11; \u00acnj ; \u00acnj \u20211 \u202633\u2020 which says that the congruence following a kingpin hitch involves three (instead of two) consecutive one- forms. This also appears in the recursive calculation of the dxi: dxnj \u00b2 1 \u00a1 tan \u00b3nj \u20211 tan \u2026\u00b3nj \u00a1 \u00b3nj\u20211\u2020 \u2021 \u2026Mnj =Lnj \u2020 \u00a3 tan \u2026\u00b3nj\u00a11 \u00a1 \u00b3nj \u2020\u2026tan \u2026\u00b3nj \u00a1 \u00b3nj\u20211 \u00a1 tan \u00b3nj \u20211\u2020 \u20261 \u2021 \u2026Mnj =Lnj \u2020 tan \u00b3nj tan \u2026\u00b3nj \u00a1 \u00b3nj \u20211\u2020\u2020 \u20261 \u2021 \u2026Mnj =Lnj \u2020 tan \u2026\u00b3nj \u00a11 \u00a1 \u00b3nj \u2020 tan \u2026\u00b3nj \u00a1 \u00b3nj\u20211\u2020\u2020 dxnj \u20211 mod \u00acnj\u00a11; \u00acnj ; \u00acnj \u20211 \u202634\u2020 What these complicated formulae express, as well as their vector \u00ae eld counterpart (24) and (25), is the (intuitively clear) fact that the presence of o\u0152-hitching implies that a motion with non-null steering propagates more i\u0300n depth\u2019 in the chain of trailers than in the standard con\u00ae guration, i.e. the change of the orientation angle in the trailer that follows the o\u0152-axle hitch is in\u00af uenced not only by the orientation angle of the trailer in front of it as in the standard case, but also by the one of the second trailer ahead. When the system has degenerate steering trains (i.e. it has two or more consecutive axles with kingpin hitching), the number of one-forms involved into a relation like (34) is higher than three. It will be seen in } 7 that this argument, in particular its formulation on the dual system, can help in understanding the local controllability property of the general n-trailer. Putting together all equations for adjacent axles it is obtained that the following proposition still holds true also for the general n-trailer. Proposition 2 (Pappas et al. 1998, Lemma 42): The exterior derivatives of any of the x variables are congruent modulo the Pfa an system I dxi \u00b2 fxi; j dxj mod I nq q n j j q n j - 1 +1 n q q n j q n j j-i-2 -i-1 -i (a) standard hitching: (b) o\u0152-axle hitching: Mnj \u00a1i\u00a12 \u02c6 Mnj \u00a1o\u00a11 \u02c6 0 Mnj \u00a11 \u02c6 0; Mnj 6\u02c6 0 Figure 3. The two di\u0152erent kinds of hitching. D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le ( A us tr al ia )] a t 1 1: 17 0 9 Se pt em be r 20 14 All the above reasoning has value only locally, in a (usually large enough) interval containing the origin. The set of points in which the model formulation is unde\u00ae ned is larger in the general n-trailer than in the standard n-trailer. Its physical meaning is explained in the next section."
        ]
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure6.48-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure6.48-1.png",
        "caption": "Figure 6.48. Ewald sphere construction of on Bragg (dashed lines) and off-Bragg (solid lines) diffracting conditions, where Sg is the excitation error.",
        "texts": [
            "110) This is actually a set of coupled equations for different g's and is generally written in matrix form. If the wave vector k of the Bloch wave is related to the incident beam wave vector K by k=K+vz (6.111) where z is a unit vector along the z-axis, we have [K2 - (k + gil = 2KSg - 2(K + g) . BV - v2 (6.112) where the excitation errors Sg are defined as (6.113) Sg is the distance from a reciprocal lattice point g to the intersection point of a line, drawn from g parallel to K, with the Ewald sphere (Fig. 6.48). The Bragg condition is defined by Sg = 0, which means the Bragg beam is just located on the surface of the Ewald sphere. 327 ELECTRON CRYSTAL LOGRAPHY FOR STRUCTURE ANALYSIS 328 CHAPTER 6 By neglecting the v2 tenn for high-energy transmission electron diffraction, substituting Eq. (6.112) into (6.110) yields (6.114) This is the fundamental equation of Bloch wave theory. If only the beams falling in the ZOLZ are important to the calculation, one can assume gz = O. Equation (6.114) becomes an eigenvalue equation that can be solved numerically by matrix diagonalization techniques",
            " Since the LACBED technique combines the real and reciprocal space information, the dislocation \"image\" can be seen in the pattern, which can be applied to determine the direction and magnitude of the Burgers vector using a single LACBED pattern (Cherns and Preston, 1989). To show the basis of Burgers vector determination using LACBED, we first examine the kinematical scattering intensity from a defect site. From the first Born approximation, the intensity scattered to reciprocal space vector u [Eq. (6.2)] is em Joo \"'(u) = --h2 dr exp(-2rciu\u00b7 r)V(r) 2rc -00 (6.119) If u is near a Bragg reflection h, it can be rewritten as u = h + Sh (Fig. 6.48). Using the potential function given by Eq. (6.28), the diffraction amplitude is em Joo \"'(u) = - 2 h2 dr exp[-2rci(h + Sh)' rn:= Vg exp{2rci[g\u00b7 r + g. R(r)]} (6.120) rc -00 g The column approximation is assumed to simplify this equation. Figure 6.51 illustrates the column approximation. A dislocation is situated at D inside the foil. An electron wave is incident on the top surface. The dislocation line causes a displacement of an atom in the column along AB from its true position by an amount R which depends on its distance z from the upper surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000701_acsami.1c05082-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000701_acsami.1c05082-Figure3-1.png",
        "caption": "Figure 3. 3D-printed \u201cjellyfish\u201d actuators. (a) Schematic of the actuator setup and operation principle. (b) Photos of the printed PVC gel jellyfish actuator upon an applied voltage of 1000 V. We have added fluorescent dye rhodamine B into the ink for visualization. Photos are taken in a dark environment and under 365 nm UV light. Scale bar: 10 mm. (c) Bending angle of a gel beam (thickness = 1 mm) as a function of the applied voltage. The definition of the bending angle is shown in the inset. (d) Bending angle as a function of time. The voltage is applied as a step function with the magnitude of 1000 V. The bending angle of a gel beam can reach \u223c130\u00b0 in \u223c5 s and recover back to 0\u00b0 in \u223c3 s after the voltage is removed.",
        "texts": [
            "32 For a PVC gel actuator, due to its unique actuation https://doi.org/10.1021/acsami.1c05082 ACS Appl. Mater. Interfaces 2021, 13, 24164\u221224172 24167 mechanism, bending can be directly achieved through its creeping deformation with the application of voltage. To demonstrate the bending actuation of 3D-printed PVC gels, we print a soft \u201cjellyfish\u201d that can deform under an electric field. To make the gel fluorescent under UV light (Figure S2), we add fluorescent dye (rhodamine B, RhB) into the ink. As shown in Figure 3a, a gel jellyfish with six arms is sandwiched between two electrodes (3D-printed PLA parts covered by copper tape). When an electric field is applied, the gel creeps to the positively charged electrode on top, thus causing the arms (with a thickness of 1 mm) to bend upward, as shown in Figure 3b and Movie S1. Once the voltage is removed, the arms recover to their original positions due to the elasticity of the gel. To quantitatively evaluate its actuation behavior, we define a bending angle of the arm as the angle between its initial state and deformed state. Figure 3c shows the maximal bending angle as a function of voltage. A larger bending angle is reached at a higher voltage. When the voltage is increased to 1000 V, the bending angle reaches its maximum of around 170\u00b0. The response time is characterized by measuring the bending angle as a function of time with an applied step voltage of 1000 V, as shown in Figure 3d. The time needed for the arms to bend over 90\u00b0 is less than 2 s, and they can recover from 130 to 0\u00b0 in 3 s after the voltage is removed. We also print three rectangular sheets with different thicknesses using PVC_9 to investigate the relationship between the sample thickness and bending angle. As Figure S3 shows, under the same applied voltage, the bending angle decreases when the thickness increases, which is mainly because larger sheet thickness leads to higher bending stiffness. A gel sheet printed from PVC_9 ink can maintain a bending angle of around 30\u00b0 for at least 10 h with a voltage of 500 V being applied (Figure S4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002876_s0022-460x(02)01213-0-Figure20-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002876_s0022-460x(02)01213-0-Figure20-1.png",
        "caption": "Fig. 20. Periodic shaft.",
        "texts": [],
        "surrounding_texts": [
            "A periodic shaft was fabricated to integrate with a spur gear system (see Figs. 19 and 20). The University of Maryland Transmission Test Rig (see Fig. 21) was used to evaluate the performance of the periodic shaft. The spur gear pair had a 1:1 gear ratio and 50 teeth per gear. There was a 5 in pitch diameter and a contact ratio of 1.75. Any reduction of transmitted vibrations generated by gear tooth contact would be measured at the bearing supports. The test instrumentation for the transmission rig tests are shown in Figs. 21\u201323."
        ]
    },
    {
        "image_filename": "designv10_4_0000249_admt.201800692-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000249_admt.201800692-Figure8-1.png",
        "caption": "Figure 8. a) Various coil designs showing (left to right) arbitrary (star) shaped wire profile, single loop, single layer solenoid, flat coil, multilayer solenoid, and flat cable coil. b) Optical image of the 2D inductor pattern prior to rolling (left) with four metal strips and RF ground pads and feed-lines (upper image). SEM image (right) of the four metal strips tube inductor with 15 coiled turns, after the metal strip is self-rolled along the indicated direction together with the strained SiNx membrane via unidirectional rolling (lower image). Adapted with permission.[115] Copyright 2015, the Authors, published by Springer Nature. c) Self-assembled microcoil structures that include inductors and their mutually coupled configurations\u2014transformers. Adapted with permission.[14] Copyright 2018, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. (right) Size comparison of self-assembled 3D coils and transformers with a commercial DC\u2013DC converter, the dimensions of which are determined by the scale of the passive components.",
        "texts": [
            " Another benefit of the tubular geometry is its mechanical stability that maintains the helical shape even when physically manipulated, regardless of whether the antenna is encapsulated or not, and much like the aforementioned cuboid variant, shares the ability to be produced cost efficiently by large scale fabrication processes. The cylindrical geometry is beneficial for another important passive component of the electronic circuit, namely the electromagnetic inductor. Ideally, inductors should minimize active losses (e.g., own wire resistance and magnetic core losses) and possess high inductance values. It is known that the inductance primarily depends on the geometry of the device itself,[112] therefore by reshaping the conductor into a loop profile (Figure 8a), an inductor can be created where its circular profile allows for the maximum contribution of each wire element to the magnetic flux. In fact, an effective coil design should generate the highest possible magnetic flux for a given piece of wire (GPW) by carrying an electrical current with the lowest possible losses. When a GPW is wound into several mutually coupled loops, the inductance grows proportionally with the number of windings, but fabrication of closely packed loops that are 100% mutually coupled with each other is not possible and leads to variations in inductor designs that are (Figure 8a) optimized for some particular application. Among the various coil designs, the multilayer solenoid inductor possesses optimal tradeoffs as it requires the least GPW while possessing the smallest dimensions with the highest quality factor.[112,113] While solenoids of just a few layers are simple in terms of fabrication and thermal considerations, in general, concerns associated with heat dissipation and self-capacitance of the windings require additional spacing among wires, increasing the size and lowering the efficiency of the final device. Additionally, resistive losses in the conductor depend on the material and total length, so the wire should ideally be kept short to reduce heat buildup and maintain a high quality factor, thereby leading to flat cable coil inductor designs (Figure 8a). The solenoid is also prone to generating strong fringe fields that may lead to unwanted interferences, leading to toroidal inductors being preferred in some Adv. Mater. Technol. 2019, 1800692 www.advancedsciencenews.com \u00a9 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim1800692 (9 of 29) www.advmattechnol.de application as they do not produce external fields, even though the design typically requires twice as much conductor for a given inductance value. The addition of a high permeability core further enhances the inductance of the solenoid, though the coreless design remains preferable owing to its simpler fabrication and reduced costs, core magnetic losses that limits the quality factor, and the low response resulting in a reduced bandwidth of the inductor",
            " Making solenoid inductors is difficult, however, because the standard microfabrication process implements planar inductor designs which results in a large occupied area and low efficiency. To address this issue, massive, parallel self-assembly of 3D coiled inductors was envisioned[114] to reduce fabrication efforts and footprint area of the devices, and several attempts to create self-assembled mesoscopic scale inductors were recently shown.[14,115,116] Yu et al. experimentally demonstrated a 3D tubular shaped inductor (Figure 8b) with an outer diameter of 15 \u00b5m and an inner diameter of 10 \u00b5m, and a tube length of 200 \u00b5m. These inductors exhibited high frequency performance independent of substrate conductivity with inductance values of about 5 nH at 20 GHz and a quality factor of about 5. However, while the achieved inductance density approached hundreds of nH mm\u22122 in the GHz range, it sharply dropped to zero at lower frequencies, limiting the use of these devices to high frequency RF applications.[115] Recently, we demonstrated the fabrication of self-assembled solenoids in a large scale, parallel lithographic process[14] possessing high inductance values at frequencies below 100 MHz (Figure 8c). Applying different planar layouts of various \u220f shaped loops, we harnessed the self-assembly process to form two 300 \u00b5m diameter flat cable-like solenoid inductors, and demonstrated that the inductance of the microscale (effective coil length of only 2 \u00d7 100 \u00b5m) selfassembled tubular device can be as high as 138 nH at MHz frequencies, revealing an industry standard areal inductance density[8] of more than 1000 nH mm\u22122 while employing a coreless design applicable to small scale energy conversion circuits or modules (Figure 8c, right). It is worth noting that the wafer scale self-assembly approach allows for the dramatic reduction in footprint area by more than 50 times, enhancing the performance when compared to the initially planar inductors. The close proximity among the single inductors enables mutual coupling of these devices and therefore renders the Adv. Mater. Technol. 2019, 1800692 www.advancedsciencenews.com \u00a9 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim1800692 (10 of 29) www.advmattechnol.de rolled-up self-assembly technology suitable for on-chip 3D transformers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003030_1.1767815-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003030_1.1767815-Figure4-1.png",
        "caption": "Fig. 4 Geometrical parameters on gear\u00d5disk faces",
        "texts": [
            " Similarly, the coefficient g is obtained by comparing the performances of two gears of the same diameter and module but different face widths etc. Once the complete set of coefficients has been evaluated, the validity of ~5! is finally verified for all the gears and the disk. The corresponding numerical values for a,b,g,d and c are given in Table 3. Following Dawson @8#, the power loss is divided into the windage loss at the front and rear faces of the gear ~or disk!, and the windage loss at the teeth ~or side of the disk!. 4.1 Front\u00d5Rear Faces. The friction force on any elemental annulus ~Fig. 4! can be expressed as: dF5 1 2 Cxrv2r2ds5pCxrv2r3dr (6) with: r: fluid density (kg/m3) Cx5n/(rvr2/m)m , according to @9,10# ~see Table 4!, where n and m are 2 coefficients depending on the nature of the flow. The dimensionless moment coefficient C f is deduced by integrating the elemental moments over the total surface (S) as: C f5 M 1 2 rv2R5 5 2p R5 n S rv m D m E (S) r422mdr (7) Table 3 Constants in Eq. \u201e5\u2026 a b g d c 60 20.25 0.8 20.4 0.56 rom: http://mechanicaldesign.asmedigitalcollection.asme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003450_s0389-4304(03)00035-3-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003450_s0389-4304(03)00035-3-Figure9-1.png",
        "caption": "Fig. 9. Rolling contact fatigue test using hydrogen-charged specimens.",
        "texts": [
            " Rolling contact fatigue life tests and observations of the subsurface microstructure were then made to clarify the relationship between the hydrogen content in the steel and the change in failure mode from the A-type to the B-type. This was done using test specimens precharged with a specified quantity of hydrogen by means of the cathodic charging method. The test specimens were made of carbonitrided SCM420 and measured 60 mm in diameter by 5mm in thickness. Fatigue life evaluations were made using a thrust-type rolling contact fatigue tester (Fig. 9) and oil #1 under conditions of an oil temperature of 120 C or 150 C (oil bath) and Pmax of 5.2 GPa. The results are shown in Fig. 10. At both oil temperatures of 120 and 150 C, flaking life tended to decrease as the quantity of charged hydrogen increased. Around hydrogen content of 1 ppm (= critical value, Hc) as a borderline, the failure mode changed from the A-type to the B-type, and flaking life also declined sharply. This suggests that the B-type of short-life flaking is one form of hydrogen embrittlement-induced flaking that occurs when the hydrogen content in the steel exceeds the critical value, Hc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003997_3-540-27969-5-Figure9.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003997_3-540-27969-5-Figure9.13-1.png",
        "caption": "Fig. 9.13. A single module composing the modular robot. In our research we focus on simple module having just two docking points and two IR network links one for each side (front and back) of the module.",
        "texts": [
            " The main subject of our research has been the chain-type modular robot (although we later report also about an experiment with a \u201clegged\u201d robot). In our experiments, we assumed that the robot is composed of very simple equal modules (i.e., joint actuators). Each module has a \u201cfront\u201d side and a \u201cback\u201d side. On each side there are two docking points and an infrared (IR) network link. The two docking points enable a module to physically connect with other ones. This is of course fundamental to actually building the chain constituting the modular robot. The IR link enables communication between connected modules (see Fig. 9.13). Each module runs the TOTA middleware and an agent in charge of driving the module joint. In a chain-type modular robot, modules connect by their IR links in a chain-type network, resembling the robot topology. An agent, installed on a module, looking at the active IR links, is able to infer whether it is the \u201chead,\u201d the \u201ctail,\u201d or a part of the \u201cbody\u201d of the robot. Specifically, the \u201chead\u201d agent is the one with only the back IR link active, the \u201ctail\u201d agent is the one with only the front IR link active, a \u201cbody\u201d agent is one having both the IR links active"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure4-3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure4-3-1.png",
        "caption": "Figure 4-3 Examples of geometric nonlinearities in elastic structures.",
        "texts": [
            ") 126 Experimental Methods in Chaotic Vibrations (d) Geometric Nonlinearities Geometric nonlinearities in mechanics involve materials with linear stress-strain behavior but the geometry changes with deformation. One example is shown in Figure 4-2 where the constraint on the tip displacement of the cantilever depends on the displacement. Another classic example is the contact of two smooth elastic bodies (called a Hertz contact). The force-displacement law for curved surfaces follows a nonlinear power law where 8 is the relative approach of the two bodies. Another classic example of a geometric nonlinearity is the elastica shown in Figure 4-3. In this problem, the material is linearly elastic but the large deformations produce a nonlinear force-displacement or moment-angle relation of the form where M is the bending moment, K is the curvature of the neutral axis of the beam, and u(x) is the transverse displacement of the beam. This Experimental Controls 127 problem is an interesting one for study of chaotic vibrations since the elastica can exhibit multiple equilibrium solutions (see Chapter 2). Cylindrical and spherical shells also exhibit geometric elastic nonlinearities (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure4-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure4-2-1.png",
        "caption": "Figure 4-2 Examples of mechanical systems with geometric nonlinearities.",
        "texts": [
            " (c) Nonlinear Body Forces Electromagnetic forces are represented as follows: Currents F = a/x/2 or f$IB Magnetization F = M \u2022 V B Moving media F = q\\ X B (Here / is current, B is the magnetic field, M is the magnetization, q represents charge, and v is the velocity of a moving charge.) 126 Experimental Methods in Chaotic Vibrations (d) Geometric Nonlinearities Geometric nonlinearities in mechanics involve materials with linear stress-strain behavior but the geometry changes with deformation. One example is shown in Figure 4-2 where the constraint on the tip displacement of the cantilever depends on the displacement. Another classic example is the contact of two smooth elastic bodies (called a Hertz contact). The force-displacement law for curved surfaces follows a nonlinear power law where 8 is the relative approach of the two bodies. Another classic example of a geometric nonlinearity is the elastica shown in Figure 4-3. In this problem, the material is linearly elastic but the large deformations produce a nonlinear force-displacement or moment-angle relation of the form where M is the bending moment, K is the curvature of the neutral axis of the beam, and u(x) is the transverse displacement of the beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure13-1.png",
        "caption": "Fig. 13. Thermal fields of the PMSIWM (a) With circumferential water jacket. (b) With axial water jacket.",
        "texts": [
            " The impact of water jacket shapes on the thermal field of the PMSIWM is mainly studied in this section. Once the motor has large size, the simulation with CFD is very time-consuming. For the purpose of saving computation time, CFD as well as finite-element analysis (FEA) is employed to predict the thermal field in this paper. The CHTC is firstly obtained by CFD. Then, the CHTC is added to the FEA model and regarded as a boundary condition. According to the periodicity, only one-eighth of the PMSIWM, shown in Fig. 12, is modeled in FEA. Fig. 13 shows the thermal fields of the PMSIWM with circumferential and axial water jackets. The winding temperature of the PMSIWM with axial water jacket is a little lower than that of the PMSIWM with circumferential water jacket. Although the Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 01:31:42 UTC from IEEE Xplore. Restrictions apply. circumferential water jacket has been optimized to improve the heat transfer from the water jacket to water, its heat dissipation performance is weaker than the axial water jacket\u2019s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001012_j.triboint.2021.106927-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001012_j.triboint.2021.106927-Figure8-1.png",
        "caption": "Fig. 8. Representation of the load zone of a rolling bearing at different radial loads.",
        "texts": [
            " 7 in accordance with equation (1) The bearing impedance also decreases with increasing temperature due to the decrease of the lubricant film thickness according to equations (1) and (6) and increases with increasing velocity due to the resulting increase of the lubricant film thickness according to equations (1) and (6). In Fig. 7 it can be observed especially the impedance of the URmin model increases with increasing radial load up to 1.5 kN, which does not correspond to the literature. This effect originates from the increasing number of rolling elements in the load zone from three to five in the estimation, assuming the rolling element positions in Fig. 8. As described in section 2 equation (8), the distance between the unloaded rolling elements and raceways depends on the position-dependent clearance \u03b4\u03d5. This in turn depends on the radial shift \u03b4r between the bearing rings, equation (9). In the calculations, however, the influence of the lubricant film thickness is not taken into account. At the transition T. Schirra et al. Tribology International 158 (2021) 106927 from the load zone to the unloaded area, there is a region where the clearance \u03b4\u03d5 is calculated to be smaller than the existing lubricant film thickness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000083_j.addma.2019.100935-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000083_j.addma.2019.100935-Figure15-1.png",
        "caption": "Fig. 15. Dimensional description of the test model.",
        "texts": [
            " The final regression model was obtained as follows: = \u2212 + + \u2212 \u00d7W W T W Tlayer 0.2476 1.2415 FS 0.0147 1.5032 10 FS-3 (9) The corresponding 2D layer width plot is shown in Fig. 14, it can be seen that the adaptive WFS can maintain a target layer width under different interlayer temperature and, therefore, keep a constant layer height. This prediction model will be used to adjust the WFS and TS at the PV node to ensure the uniform layer dimensions. 5. Experimental verification The proposed planning technique is verified by fabricating a largescale model. Fig. 15 shows the dimensions of the typical model, it is featured by the continuously changing diameter from the bottom up, and the wall thickness is set at 6 mm. As shown in Fig. 16, a rotary table helps to keep the building direction oriented vertically and rotated during deposition. Thus, the welding torch only needs to lift when a layer is finished. The process parameters generated for the first 100 layers were listed in Table 5. Starting from the 3th layer, the interlayer temperature was predicted according to the actually measured temperature at the TM node of the former two layers using the Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure11.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure11.2-1.png",
        "caption": "Figure 11.2. Tooth prof ile radi i of curvature.",
        "texts": [
            " The radi i of these cylinders are equal to the radi i of curvature P1 and P2 of the tooth profiles at the contact point. The maximum contact stress Gc is then given by the following expression, P +p Cp v[w( p\\P22 )] (11. 5) The quantity w in this expression is the load intensity, and Contact Stress 245 Cp is an elastic coefficient, defined as follows, '/1\"( 1-v 2 ) '/1\"( 1-v22) .J.... v[ 1 + ] Cp E1 E2 (11.6) where E1,v 1 and E2 ,v 2 are Young's modulus and Poisson's ratio for the material of each gear. The meshing diagram for a gear pair is shown in Figure 11.2, with the contact point in position s on the path of contact. We proved in Equation (10.1) that the radius of curvature P1 of the tooth profile of gear 1 at point A1 is equal to the length E1A1, while the corresponding radius of curvature P2 in gear 2 is equal to A2E2\u2022 Hence, the sum (P 1+P 2 ) is equal to E1E2 , which can be expressed in terms of the center distance C and the gear pair operating pressure angle t/>, C sin t/> (11.7) This relation is used to simplify the expression for the contact stress, 246 Tooth Stresses in Spur Gears (11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000175_j.matdes.2020.109185-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000175_j.matdes.2020.109185-Figure3-1.png",
        "caption": "Fig. 3. Schematic of the q",
        "texts": [
            " T t0\u00f0 \u00de \u00bc T t1\u00f0 \u00de \u00fe T t2\u00f0 \u00de\u2212T t1\u00f0 \u00de t2\u2212t1 t0\u2212t1\u00f0 \u00de \u00f05\u00de The time step size in the FEM model, \u0394t', is different from the data output time interval of the CFD model, \u0394t. To fully exploit the CFD temperature profiles output, \u0394t' is smaller than \u0394t to allow a temperature interpolation between any two time-adjacent CFD temperature profiles. TheQEM remedies the shortcomings of the inactive elementmethod in simulating the evolution of themolten pool and the remelting of previous tracks. The idea of the QEM is to assign null material properties to non-deposited elements whose presence should not affect the deposited elements, as Fig. 3 shows. In the QEM, the material properties of the elements should changewith the corresponding state, i.e., air, liquid or solid. As illustrated in Fig. 4, the elements' material states transfer to the liquid state from the solid state where the powders or the previous tracks and substrate are melted; elements transfer from the liquid state to the solid state due to solidification. Besides,with themolten pool evolution, the elementsmaterial statesmay transfer from liquid state to the air state when the liquid flows away, or from the air state to the liquid state when it flows in"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003493_1.339185-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003493_1.339185-Figure5-1.png",
        "caption": "FIG. 5. Temperature dependence of the saturation magnetization and the coercive field for Th-FeCo alloys.",
        "texts": [
            "208 On: Sun, 07 Dec 2014 22:48:40 sublattice. g; ,S; ,Hi (T) and B s, (Zi ) are the g factor, the spin momentum, the mean field, and the Brillouin function at site i, respectively. N is the total number of atoms per unit vol ume, I\" B is the Bohr magnetron, and k is the Boltzmann constant. The temperature dependence of M.. and He for GdTb-Fe films are shown in Figs. 4(a) and 4(b) for four compositions of (Gd, Tb) 1 _ x Fe\", exhibiting a variation i.n x of the order of 0.03. Ms andHc for Tb-FeCo films are shown in Fig. 5. The curve for \"film\" G has been calculated based on the data of film F but with a slightly higher Th content. The coercivity data have been obtained from Faraday hys- 219 J. Appl. Phys., Vol. 62, No.1, 1 July 1987 teresis loop measurements. The Curie temperature and thus the M., in the high temperature range can be raised with increasing Co content. The magnitude of the coercive energy can be controlled via the Tb content. From the sublattice magnetizations, the temperature dependence of the uniaxial anisotropy constant K u , the an isotropy field H\" = 2Ku/M\" the exchange constantA, the wall energy U w = 4~AK\", and the waH thickness 8w = 1T~A 1Ku ,can be calculated using the relations 1 Ku = - L Cik\u00b7'WjMk , 2 i7'-k 1 A =- r AikM;Mk \u2022 2 I'i\"k (Ila) ( l1b) The coefficients Gik = Cki have been determined from an isotropy measurements at fixed temperatures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002834_02783649922066628-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002834_02783649922066628-Figure1-1.png",
        "caption": "Fig. 1. Example of link splitting. A mechanism with a high branching factor (a) is converted to one with a lower branching factor (b) by treating the central link as a rigid subassembly.",
        "texts": [
            " Furthermore, to meet the claimed efficiency of O(log(NB)) execution time on O(NB) processors, the depth must not exceed O(log(NB)). 2. The lower part should be designed to minimize the total operations count and to distribute the work load as evenly as possible over the available processors. One obvious solution is to use a balanced binary tree, so let us proceed on the assumption that the assembly tree should be designed to be balanced, and let us explore the obstacles to this strategy. Consider the problem of constructing an assembly tree for the mechanism shown in Figure 1(a). Every joint in this mechanism has the property that there are eight bodies on one side and only one body on the other, so every possible assembly tree is maximally unbalanced. This is an unacceptable situation, because the DCA relies on the depth of an assembly tree being logarithmic in the number of bodies. The problem is caused by the large branching factor at the central body, and the only possible solution is to treat the central body itself as a subassembly. Figure 1(b) illustrates the general idea. In this figure, the central body has been split into four pieces, which are held together by three rigid connections. For the purpose of constructing an assembly tree, these connections get treated exactly like real joints, so it may be helpful to think of them as zero-DoF joints. A mechanism that has been modified in this way is kinematically and dynamically indistinguishable from the original, because a rigid assembly of rigid bodies behaves in a manner that is indistinguishable from a single rigid body",
            " For dynamical equivalence, the sum of the inertias of the pieces at BROWN UNIVERSITY on December 16, 2012ijr.sagepub.comDownloaded from must equal the inertia of the original body. The simplest (and probably safest) choice is to split the inertia evenly between the pieces, but there is scope for clever optimizations here. In general, more than one body may need to be divided up in this way, and the number of pieces it is split into will depend on how many joints are attached to it. Two joints per piece is a good rule of thumb, and reconnecting the pieces in a serial chain, as shown in Figure 1(b), is a good general solution, but other possibilities do exist and may occasionally be more efficient. I shall refer to this technique as link splitting. It is a preprocessing step: done once per mechanism, not once per dynamics calculation. Its purpose is to reduce the execution time of the DCA by reducing the depth of the assembly tree. Bear in mind that link splitting does increase the mechanism\u2019s body count and hence also the total number of computations performed by the algorithm, so it is possible to increase the execution time by doing too much link splitting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.9-1.png",
        "caption": "Figure 16.9. Left-handed hob and spur gear.",
        "texts": [],
        "surrounding_texts": [
            "The most commonly used method for cutting helical gears is by hobbing. As always in generating cutting, one gear is used to cut another. A typical hob is shown in Figure 16.3, and it can be seen that, apart from the gashes forming the cutting faces, the hob is simply a helical gear, in which each tooth is referred to as a thread. A hob. 458 Gear Cutting II, Helical Gears Since the hob is similar in shape to a screw, its helix angle \"'sh is always large, particularly when there is only one thread. It is cust~mary to specify the shape of a hob by means of its lead angle, rather than its helix angle. For a right-handed hob, the lead angle Ash is defined as the complement of the helix angle, (16.13) where Ash and \"'sh are measured in degrees. For a left-handed hob, whose helix angle is negative, the lead angle can be def ined as follows, - 90 0 - '\" sh ( 16.14) so that we obtain a negative lead angle for a left-handed hob. In practice, it is generally the magnitude of the lead angle which is given in the specification, together with a statement to indicate whether the hob is right or left-handed. It is clear that the lead angle can be determined from the helix angle, and vice versa. In describing the geometry of the hobbing process, we will specify the shape of the hob by means of its helix angle, since the symbols will then agree with the notation used in Chapter 15, where we described the geometry of crossed helical gears. Figure 16.4 shows a hob in position to cut a gear blank, and since their axes are not parallel, it is clear that they form a crossed helical gear pair. During the cutting process, the hob and the gear blank are rotated about their axes with angular veloci ties wh and wg ' I n order to cut the teeth of the gear across the entire face-width, the hob is moved slowly in the direction of the gear axis, and the velocity of the hob center is called the feed velocity vh . The values required for the three variables wh ' Wg and vh are achieved by means of change gears or stepping motors in the hobbing machine. There are two additional settings which must be made when the hobbing machine is being set up. These are the shaft angle ~, which is the angle between the axes of the hob and the gear blank, and the cutting center Hobbing 459 distance CC, which is the distance between the two axes. In the remainder of this section, we will determine the values required for the machine parameters wh ' wg ' vh ' E and CC, if the hob is to cut a gear with Ng teeth, normal module mn , normal pressure angle ~ns' helix angle ~sg' and normal tooth thickness t nsg Before we discuss the details of the cutting process, we will first prove that, as usual, the gear will have the same normal module and normal pressure angle as those of the hob. We showed in Chapter 15 that the minimum condition for correct meshing of two crossed helical gears is that their normal base pitches should be equal. The corresponding result, when we consider a gear being cut by a hob, is that the normal base pitch of the gear will always be equal to that of the hob. Since the normal base pitch of the hob is equal to that of the basic rack, we can conclude that the normal base pitches of the gear and the basic rack are equal, and the gear can therefore mesh correctly with the basic rack. As always, the standard pitch cylinder of the gear is defined as its pitch cylinder when it is meshed with the basic rack. The normal pitch Pns and the normal pressure angle ~ns of the gear must 460 Gear Cutting II, Helical Gears then be equal to those of the basic rack, and hence equal to those of the hob. This result remains true, whether or not the cutting pitch cylinders of the gear and the hob coincide with the i r standard pi tch cylinders. In order to cut the gear described earlier, we must therefore use a hob with the same normal module and normal pressure angle as those specified for the gear. We consider next how to cut the required number of teeth, and the correct helix angle. When a rack cutter is used to cut a gear, the helix angle of the gear depends on the angle at which the cutter is set, so it might be expected that the helix angle of a gear being hobbed would be determined by the value of the shaft angle ~. This is not the case, however, and we will now show that the number of teeth cut in the gear blank, and the helix angle at which they are cut, depend only on the values chosen for wh ' Wg and vh \u2022 In Chapter 5, we defined the cutting point as the point where the cutter makes a cut on the final tooth surface, and we showed that this point corresponds to the contact point when the gear blank and the cutter are regarded as a pair of meshing gears. The situation is no different when the cutter is a hob. We described in Chapter 15 how to find the position of the contact point in a crossed helical gear pair, and this point becomes the cutting point when we consider a hob cutting a gear. As in any metal-cutting process, the shape of each tooth cut in a gear blank is the envelope of positions through which the hob moves, relative to the gear blank. For the purpose of determining this shape, it is helpful to neglect the gashes in the hob thread, so that the threads are regarded as continuous, and we can imagine that the teeth are formed in the gear blank by grinding, rather than by cutting. If the hob and the gear blank were a pair of crossed helical gears, there would always be at least one thread of the hob making contact with the gear. Hence, for the hob and the gear blank, there is always at least one thread which is in contact with the final tooth surface of the gear. We label the points in contact AOh on the hob, and AOg on the gear. After the hob turns through exactly one angular pitch, the position of the thread containing point AOh is occupied by the Hobbing 461 next thread, and the corresponding point Alh on this thread will now be the cutting point, touching a point A1g on the gear tooth adjacent to the tooth containing AOg. As the hob rotates, we can identify a sequence of points such as AOh and Alh on the hob threads, and AOg and A1g on the gear teeth. The points on the hob lie in the same transverse section and are evenly spaced, at angular intervals equal to the angular pitch. Of course, if the hob has only one thread, the angular pitch is 360 0 , and the points all coincide. On the other hand, the gear points do not lie in one transverse section, due to the feed of the hob in the direction of the gear axis, and each point is displaced axially a small amount relative to the next point. We now consider the position on the gear of point ANg , the cutting point when the hob has turned through Ng angular pitches. Since the gear is to have Ng teeth, points AOg and ANg must be on the same tooth. Hence, if the gear is a spur gear, ANg must lie on the axial line through AOg' while if the gear is a helical gear, ANg must lie on the gear helix through AOg. The distance through which the hob is fed during one revolution of the gear blank is called the feed rate f. Since the magnitude of f is small compared with the tooth dimensions, point ANg always lies close to the axial line through AOg. The gear blank must therefore turn through approximately one revolution while the hob turns through Ng angular pitches, which is a rotation equal to (Ng/Nh ) revolutions. In order to meet this requirement, the angular velocity ratio (wh/wg ) must be approximately equal to (Ng/Nh ), or exactly equal, when a spur gear is being cut. In the case of a helical gear, the small difference between the two ratios is one of the factors which determine the helix angle of the gear, as we will show later in this section. Once the settings are chosen for the hobbing machine, the value of (wh/wg ) is established, and the number of teeth that will be cut in the gear is then given by the following expression, NhWh Integer closest to (--) Wg (16.15) 462 Gear Cutting II, Helical Gears Having found how the value of Ng depends on the hobbing machine angular velocities wh and wg ' we now consider the helix angle. If points AOg and A1g lie at radius R, the positions of these points at various times can be plotted on a developed cylinder of radius R, as shown in Figure 16.5. The times at which the hob touches points AOg and A1g are called T and T', and the diagram shows the positions of AOg at time T, and A1g at time T'. Since the feed of the hob is in the direction of the gear axis, the line in the diagram joining AOg and A1g is in the same direction. The diagram also shows the gear helices through these points, which appear as straight lines making an angle ~Rg with the gear axis, and these are labelled helix 0 and helix 1. The point on helix 0 in the transverse section through A1g is labelled Ag \u2022 The position of helix 0 at time T' is shown by the dotted line, and the positions of Aog and Ag at this time are shown as AOg and Ag \u2022 In Figure 16.5, the length AOgA1g represents the hob feed between the times T and T', and AgAg represents the arc Hobbing 463 length moved by point Ag in the same time interval. Since helix 0 and helix 1 are gear helices on adjacent teeth at the same radius, their positions at any instant are exactly one tooth pitch apart. A1g and Ag lie on the two helices in their positions at time T', so the distance between these points is equal to the transverse pitch. We therefore obtain the following expressions for the three lengths, A A' 9 9 A A' 19 9 The time interval required for the hob to rotate through one angular pitch can be expressed in terms of the hob angular velocity, T' - T We now use triangle AOgA1gAg to relate the three lengths, A A' - A A' 19 9 9 9 and when their values are substituted, we obtain the following relation between wh ' Wg and vh ' 211' vh -N-- tan l/IR hWh 9 ( 16.16) The feed rate f of the hob was defined earlier as the distance moved by the hob during one revolution of the gear blank. It is customary to express the feed velocity vh in terms of f, _f_ (211') Wg (16.17) and with this substitution, Equation (16.16) takes the following form, tan l/IRg 211'R ( 16.18) 464 Gear Cutting II, Helical Gears The helix angle of the gear at radius R is expressed in terms of the lead Lg by Equation (13.31), tan IPRg and Equation (16.18) then becomes a relation giving the lead that will be cut in the gear, l(NhWh ) f - Ng Wg ( 16.19) The quantity (Ng/Lg) is equal to the reciprocal of the axial pitch, as we showed in Equation (13.36), and this can be expressed in terms of the helix angle IPsg by means of Equation (13.42), _1_ Pzg sin IPSg Pns (16.20) Hence, Equation (16.19) can be put into two alternative forms, giving either the axial pitch or the helix angle of the gear, _1_ Pzg l(NhWh ) f - Ng Wg (16.21 ) (16.22) It is an interesting result that, as we pointed out earlier, the helix angle cut in a gear is not affected by the shaft angle ~ of the hobbing machine. This angle is generally set equal to the standard shaft angle ~s' or in other words, equal to the sum of the helix angles of the gear and the hob, ~s (16.23) We showed in Chapter 15 that a pair of crossed helical gears can mesh correctly, even when the shaft angle is not equal to the standard shaft angle. It therefore follows that a hob can cut an accurate involute gear, even when ~ is not exactly equal to ~s. However, for the remainder of this section, we will assume that the shaft angle is set equal to ~s' and in a Hobbing 465 later section of the chapter we will discuss the consequences of a small change in this value. The last setting of the hobbing machine to be considered is the cutting center distance CC , and its effect on the tooth thickness of the gear. As we discussed earlier, the cutting process can be considered as equivalent to meshing with zero backlash. An expression for the normal backlash in a crossed helical gear pair was given in Equation (15.96), The length ~Cp Equation (15.47), in this expression (16.24) was defined by (16.25) and all the other quanti ties are defined on the pitch cylinders, as indicated by the notation. We are considering, at present, a hob cutting a gear blank when the shaft angle ~ is set equal to the standard value ~s. In this case the cutting pitch cylinders coincide with the standard pitch cylinders, as we proved in Chapter 15. If we replace RP1 and Rp2 in Equation (16.25) by Rsg and Rsh ' and set the backlash in Equation (16.24) equal to zero, these two equations give an expression for the normal tooth thickness cut in the gear, (16.26) The expression in brackets in this relation represents the hob offset. When the normal tooth thickness t h of the hob is ns equal to O.5Pns' Equation (16.26) has exactly the same form as Equation (16.12), which gave the normal tooth thickness of a gear cut by a rack cutter. If the normal tooth thickness of the hob is greater than O.5Pns' the normal tooth thickness of the gear is reduced by the same amount. Whatever the value of t nsh ' the effect of a change in the hob offset on the tooth thickness of the gear is identical to the corresponding effect caused by a change in the offset of a rack cutter. In Chapter 5, we stated that the tooth thickness of a gear cut by 466 Gear Cutting II, Helical Gears a hob is generally calculated as if the gear were cut by a rac k cutter. We have now shown that thi s procedure is essentially correct, prpvided the hobbing machine is set with its shaft angle ~ equal to the standard value ~s' There is a second manner in which the cutting action of a hob resembles that of a rack cutter. In the discussion following Equations (15.74 and 15.77), we showed that the path of contact in a crossed helical gear pair touches each base cylinder, and makes an angle (~- 'tp1) with the line of centers, when viewed in the direction of the axis of gear 1. Hence, in the case of a hob cutting a gear, the path followed by the cutting point touches the base cylinders of the gear and the hob, and makes an angle (~- 'tpg) with the line of centers, when viewed in the direction of the gear axis. If the shaft angle is set at the standard value, this angle becomes (1[2 - 't ), as shown in Figure 16.6, and the path of the sg . cutting point then appears identical with the corresponding path when the gear is cut by a rack cutter. It is for this reason that, when we check for undercutting in a gear, we can regard the hob as equivalent to a rack cutter. We check that Swivel Angle 467 there would be no undercutting if the gear was cut by the rack cutter, and this implies that there will also be no undercutting when in fact the hob is used. Swi vel Angle Earlier in this chapter, we stated that it is common practice to specify the lead angle of a hob, instead of its helix angle. It is also customary to specify the angular setting of the hobbing machine by means of the swivel angle, rather than by the shaft angle. Since a hob is shaped like a screw, its helix angle is always large, particularly in the case of a single-thread hob, for which the helix angle is typically about 85\u00b0. The helix angle of the gear being cut may of course have any value, but in the majority of gears, the magnitude of the helix angle is between 0\u00b0 and 30\u00b0. In general, right-handed hobs are used to cut right-handed gears, and left-handed hobs are used for left-handed gears. In most cases, therefore, the shaft angle is approximately equal to a right angle, and the swivel angle is defined as the amount by which the shaft angle differs from a right angle. For example, if the axis of the gear is vertical during the cutting process, the swivel angle a is defined as the angle which the hob axis makes with the 468 Gear Cutting II, Helical Gears horizontal. The standard shaft angle was defined by Equation (16.23), as the sum of the gear and the hob helix angles. We express the helix angle of the hob in terms of its lead angle, by means of Equation (16.13 or 16.14), and we obtain the following expression for the standard shaft angle, ,f, + 90\u00b0 - A \"'sg - sh (16.27) where the plus and minus signs refer to a right or Hobbing Machine Gear Train Layout 469 left-handed hob. We now define the standard swivel angle os' so that it differs by a right angle from the standard shaft angle, (16.28) As discussed earlier, the hobbing machine is generally set so that the shaft angle is equal to the standard shaft angle, and it then follows that the swivel angle is equal to the standard swivel angle. Figures 16.7 and 16.8 show the relations between the shaft angles and the swivel angles when a right-handed hob is used to cut a spur gear or a right-handed helical gear, while Figures 16.9 and 16.10 show the corresponding relations when a left-handed hob is used to cut a spur gear or a left-handed helical gear. Hobbing Machine Gear Train Layout We showed in Equations (16.15 and 16.22) that the number of teeth and the helix angle cut in a gear depend on the feed rate f and the angular velocity ratio (wh/wg ) in the hobbing machine, NhWh Integer closest to (----) Wg (16.29) 470 Gear Cutting II, Helical Gears sin I/I sg l(NhWh ) f - Ng Wg (16.30) It is helpful to examine how the gear trains in some typical hobbing machines are arranged, in order to achieve the values of Ng and I/I sg required in the gear. One type of hobbing machine is shown schematically in Figure 16.11. The rectangular boxes in the diagram represent gear pairs or gear trains, with the output-input ratio in each case given by the constant k. The symbol ki stands for the ratio of the index change gears, kf is the ratio of the feed change gears, and the other k values represent the gear trains built into the machine, whose ratios cannot be altered by the user. The values of wh and wg , and of the hob feed velocity vh ' can be read from the diagram in terms of the input angular velocity w 1 ' (16.31) (16.32) Hobbing Machine Gear Train Layout 471 (16.33) The feed rate f was given by Equation (16.17), in terms of Wg and vh ' and when these are expressed by means of Equations (16.32 and 16.33), we obtain a relation between the feed rate and some of the gear ratios in the hobbing machine, f The terms in brackets are combined into a single constant, known as the machine feed constant Cf , whose value is provided by the manufacturer of the hobbing machine. The feed rate is then expressed solely as a function of the ratio kf of the feed change gears, f (16.34) To obtain the ratio (wh/wg ) in terms of the hobbing machine gear ratios, we express wh and Wg by means of Equations (16.31 and 16.32), As before, the terms in brackets are combined into another constant, the machine index constant Ci , whose value is also provided by the manufacturer, and the angular velocity ratio is then given by the following expression, C\u00b7 1 k.\" 1 (16.35) We substitute this expression into Equations (16.29 and 16.30), and we obtain the number of teeth that will be cut in the gear, and its helix angle, in terms of the hobbing machine gear ratios, NhC. Integer closest to ( __ l) k i (16.36) {16.37l We now determine how the machine ratios should be 472 Gear Cutting I I, Helical Gears chosen, in order to cut a gear with the number of teeth and helix angle required. The feed rate f and the hob angular velocity wh are chosen to obtain good metal-cutting characteristics. The values depend on the size of the hob, the hardness of the material being cut, and the surface finish required. For more details, the reader should consult references such as the Gear Handbook [2]. Once a value for f is. chosen, the required ratio kf for the feed change gears is found from Equation (16.34), f Cf (16.38) The value chosen for wh is obtained by setting the input speed change, shown in Figure 16.11, to a suitable value. With the feed change gear ratio already selected, the index change gear ratio is used to determine both the number of teeth cut in the gear, and its helix angle. We choose the ratio ki so that it satisfies Equation (16.37), in order to obtain the required helix angle, NhCi ki f sin ~Sg (16.39) (1rm + N ) n g When this value for ki is substituted into Equation (16.36), we find that we also obtain the correct number of teeth, because the magnitude of the term (f sin ~Sg/1rmn) in the expression for ki is always very much less than 0.5. It is sometimes difficult to find change gears which provide exactly the value of ki given by Equation (16.39). Once the change gears have been chosen, their actual ratio ki should be calculated, and this value is substituted into Equation (16.37), to give the helix angle that will in fact be cut in the gear. Use of a Differential in the Hobbing Machine There is one major problem associated with hobbing machines, when they are designed in the manner shown in Figure 16.11. If a second cut is required, as is often the case, it is necessary to disconnect the feed drive, in order Use of a Differential in the Hobbing Machine 473 to return the hob quickly to its starting position. It is then very difficult to reset the machine, with the work table and the hob in exactly the correct positions. This problem can be overcome if a differential is incorporated into the hobbing machine. In order to determine the relation that must be maintained between the hob feed, the work table rotation and the hob rotation, we once again consider Equation (16.30), We use Equation (16.17) to express the hob feed rate f in terms of the feed velocity vh ' and we obtain the relation which must be maintained throughout the cutting process between the hob feed velocity, the table angular velocity, and the hob angular veloci ty, (16.40) A gear train with one degree of freedom can always be represented by a linear equation relating the angular velocities of the input and the output shafts. A differential is a gear train with two degrees of freedom, and it has three shafts, either two input and one output, or one input and two output. The angular velocities of the three shafts are always related by a single linear equation. Hence, as we can see from Equation (16.40), if the hob feed, the work table drive and the hob drive were all connected to the three shafts of a suitable differential, they would then always maintain the correct relative positions. The differential may be a simple planetary gear train, or one which is constructed of bevel gears. In either case, the output angular velocity w3 is a linear combination of the input angular velocities w1 and w2 ' and can therefore be represented by the following equation, (16.41) The constants k7 and ka of the differential depend on the design of the gear train, and need not concern us here. 474 Gear Cutting II, Helical Gears The complete layout of the hobbing machine is shown in Figure 16.12, where the differential is represented as a simple planetary gear train. The hob drive is connected to the sun gear of the differential, the table drive is connected to the planet carrier, and the feed is connected to the internal gear. As before, the index change gears and the feed change gears are represented by symbols ki and kf , and now there is a third set of change gears, the differential change gears, represented by the symbol kd \u2022 The constants k1 to k6 are the fixed ratios of the gear trains in the hobbing machine. The constant k6 represents the ratio of a worm and gear, connecting the differential change gears to the internal gear of the differential. This ratio is shown with a minus sign, since the hand of the helix in the worm is chosen so that a positive angular velocity in the worm produces a negative angular veloci ty in the gear. We pointed out earlier that the number of teeth and the helix angle cut in the gear depend on the feed rate f and the Use of a Differential in the Hobbing Machine 475 angular velocity ratio (wh/wg ). We therefore need to express these two quantities in terms of the hobbing machine gear ratios. We start by writing down a number of relations between the angular velocities, Wh k1w1 (16.42) Wg k2ki k3w3 (16.43) vh k2kik4kfw3 (16.44) w 2 k2kik4kfkd(-k6)w3 (16.45) The feed rate f, which was given by Equation (16.17), can now be expressed in terms of the gear ratios, f As before, the terms in brackets are combined into a single quantity, the machine feed constant Cf , and the feed rate is then given simply in terms of the feed change gear ratio, f (16.46) When Equations (16.42 and 16.43) are used to express wh and wg ' the angular velocity ratio takes the following form, wh k1w1 Wg k2k3kiw3 and the relation between w 1 and w3 is found from Equations (16.41 and 16.45), The last two equations are combined to give the angular velocity ratio in terms of the gear ratios, and we use Equation (16.46) to express the ratio kf in terms of the feed rate f, (16.47) 476 Gear Cutting II, Helical Gears We now define the machine index constant Ci and the machine di fferent ial constant Cd as follows, C. 1 k1 k2 k3k7 k3 k7Cf k1k4 k6kS As usual, the values of the machine constants Cf ' Ci and Cd are all provided by the manufacturer of the hobbing machine. Ci is a ratio, but Cf and Cd are lengths, since they are defined in terms of the feed rate f, which is the distance moved by the hob during one revolution of the work table. When the constants are substituted into Equation (16.47), we obtain the final expression for the angular velocity ratio, (16.4S) This expression is substituted into Equations (16.29 and 16.30), and we obtain the number of teeth and the helix angle that will be cut in the gear, corresponding to the feed rate f and the change gear ratios ki and kd in the hobbing machine, C\u00b7 fkd Integer closest to [Nh(k: + c)] 1 d (16.49) (16.50) Once again, we must determine how the change gear ratios kf , k i and kd should be chosen, in order to cut a gear with Ng teeth and helix angle ~sg' As before, we choose the feed rate f from metal-cutting considerations, and the ratio kf is then given by Equation (16.46), (16.51) If we are cutting a spur gear, or in other words a gear with zero helix angle, we can satisfy Equation (16.50) by setting the value of kd equal to zero, and choosing the value of ki as follows, Use of a Differential in the Hobbing Machine k. 1 477 (16.52) The conventional method for cutting a helical gear is to use the same value for ki , and to choose kd in a manner which then satisfies Equation (16.50), Cd sin IPsg Nh '/I'mn (16.53) An alternative expression for the required differential change gear ratio is found by combining Equations (16.20 and 16.53), (16.54) When we compare the last two equations, it is clear that it is much easier to select suitable change gears, giving the correct value for kd , if we design the gear so that its axial pitch Pzg is a round number, rather than its helix angle IPsg. There are times when it is difficult, or even impossible, to find change gears which provide the exact values for ki and kd , given by Equations (16.52 and 16.53). For example, when the value required for Ng is a large prime number, we cannot obtain the exact value for ki , since most sets of change gears do not contain gears with more than 120 teeth. Also, when the helix angle ~sg is very small, it may be difficult to obtain a sufficiently accurate value for kd \u2022 When these situations occur, we can choose the index gears so that their ratio ki differs slightly from the value given by Equation (16.52), and the differential change gears are then used to ensure that Equation (16.50) is still satisfied with sufficient accuracy. Since the index change gear ratio is close to the value given by Equation (16.52), it can be represented by an expression with the following form, k. 1 (16.55) where the quantity ~ may be either positive or negative. This expression for ki is substituted into Equation (16.50), and we obtain the corresponding value of the differential change gear ratio required to cut the correct helix angle, 478 Gear Cutting II, Helical Gears (16.56) We have determined the values of ki and kd in a manner that satisfies Equation (16.50), so we know that the correct helix angle will be cut. It is now necessary to substitute the values of ki and kd into Equation (16.49), in order to confirm that the gear will also be cut with the correct number of teeth. The expressions for ki and kd given by Equations (16.55 and 16.56) are substituted into the right-hand side of Equation (16.49), with the following result, (16.57) As we pointed earlier, the magni tude of the term (f sin ~sg/wmn) is always less than 0.5, so with these values of ki and kd , the number of teeth cut in the gear will indeed be equal to the number required. The change gear ratios given be Equations (16.55 and 16.56) can be used for cutting either helical or spur gears, whenever it is difficult to obtain the values given by Equations (16.52 and 16.53). It is interesting that the quantity a has cancelled out from the expression in Equation (16.57). This means that there is no theoretical limit to the value of a which can be used, and the ratio ki may therefore differ considerably from the value given by Equation (16.52). In practice, however, it is usually easier to select the differential change gears to obtain an accurate value for kd , if the index gears are chosen so that their ratio is close to the value given by Equation (16.52), and the magnitude of a is therefore small compared wi th 1. It is evident that a differential is useful in the design of a hobbing machine, since it facilitates the selection of the necessary change gears. However, the original purpose for which the differential was introduced, as we discussed earlier in the chapter, was to maintain the correct relation between the hob feed, the work table rotation and the hob rotation, during a rapid return of the hob to its starting position. Figure 16.13 shows how this purpose is achieved. The drive is disconnected, by means of a dog clutch, between the feed change gears and the feed drive. An auxiliary motor, Theoretically Correct Shape for the Hob Thread 479 known as the hob rapid traverse motor, is then used to drive the hob feed. The drive passes through the di fferent ial, causing the work table to turn at exactly the correct speed, so that the helical teeth in the gear mesh continuously with the threads of the hob. During the entire return motion of the hob, only a very small rotation of the table is required, compared with the many revolutions that take place while the gear is being cut. Hence, the return of the hob can be carried out quite quickly, without damage to the gearing driving the work table. Theoretically Correct Shape for the Hob Thread We stated in Chapter 5 that a hob whose thread profile is straight-s;ded in the normal section will not cut exact involute tooth profiles. We are now in a position to estimate the amount of error, and to determine the correct normal 480 Gear Cutting II, Helical Gears profile in the hob thread. In Chapter 15, we proved that two involute helical gears can mesh with crossed axes, and maintain a constant angular velocity ratio. The hobbing process is essentially the same as the meshing of a pair of crossed helical gears. It therefore follows that, in order to cut correct involute profiles in the gear, the thread of the hob must also have the shape of an involute helicoid. In other words, the thread has an involute profile in the transverse section. The corresponding profile in the normal section is a convex curve, and not a straight line. However, because the helix angle of a hob is so large, the profile in the normal section is extremely close to the straight line. Hence, when a straight-sided hob is used to cut gears, the resulting error in the gear tooth profiles is generally small. We can estimate this error in the following manner. We described a method in Chapter 13 for calculating the profile of the normal section through a helicoid. We now use this method to find the profile of the normal section through the hob thread. We calculate the distances, at the thread tip and at the top of the fillet, between this profile and its tangent at the standard pitch cylinder, as shown in Figure 16.14. The profile of a straight-sided hob would coincide with this tangent, and a hob of that type would therefore cut too deeply into the teeth of the gear, in the regions near the fillet and near the tip. Figure 16.15 shows the normal section through an Effect of a Non-Standard Shaft Angle 481 exact involute helicoid tooth, and it also shows the profile we obtain when the gear is cut by a straight-sided hob. The maximum differences between the two profiles are approximately equal to the distances described earlier, by which the normal section profile of the involute hob deviates from the straight line. As we can see in Figure 16.15, the tooth shape cut by a straight-sided hob is similar to the shape of a tooth cut with tip and root relief. The errors caused by the use of a straight-sided hob are therefore sometimes beneficial, and this is one of the reasons for the continued use of straight-sided hobs, when true involute hobs are also readily obtainable. There are times, however, when the errors caused by straight-sided hobs may be excessive. This is often the case for gears cut by multi-thread hobs, or by single-thread hobs of large module, whose helix angles are usually less than 85\u00b0. Whenever there is a possibility that a straight-sided hob may cut too much tip and root relief in a gear, the procedure just described can be used to determine whether a true involute hob should be used. Effect of a Non-Standard Shaft Angle In an earlier section of this chapter, we described how to calculate the tooth thickness cut in a gear, when the shaft angle ~ of the hobbing machine is set equal to the standard value ~s. We stated at that time that we would still obtain a 482 Gear Cutting II, Helical Gears correct involute profile in the gear tooth, even if the values of E and Es wer~ not the same. The only effect of the altered shaft angle is a change in the tooth thickness, and we will now discuss briefly how the new tooth thickness can be found. Since it is not generally necessary to make this calculation, we will simply outline the steps, without presenting all the equations. When the shaft angle is not equal to its standard value, the cutting pitch cylinders of the gear and the hob do not coincide with their standard pitch cylinders. The first step is therefore to calculate the cutting pitch cylinder radii R~g and R~h. Knowing the normal thread thickness t nsh of the hob at its standard pitch cylinder, we then calculate its normal thread thickness t nph at the cutting pitch cylinder. To find the normal tooth thickness cut in the gear, we regard the hobbing process as the meshing of a crossed helical gear pair with zero backlash. An expression was given in Equation (15.96) for the normal backlash in a crossed helical gear pair, The length ~cp in this equation was defined by Equation (15.47), as the difference between the center distance and the sum of the pitch cylinder radii. For the situation of a hob cutting a gear, ~cp would represent the difference between the cutting center distance and the sum of the cutting pitch cylinder radii, We combine these equations, and set the backlash Bn equal to zero, to obtain the normal tooth thickness t npg cut in the gear. The final step is to calculate the corresponding normal tooth thickness t nsg of the gear at its standard pi tch cylinder. If we carry out this calculation, we will find that the normal tooth thickness t nsg cut in the gear is almost independent of the shaft angle E. In other words, the tooth thickness is hardly affected by a small change in the shaft Geometric Design of a Helical Gear Pair 483 angle, provided of course that the cutting center distance is left unchanged. However, the radii of the cutting pitch cylinders are very sensitive to the shaft angle value. In particular, a small change in the value of ~ can move the cutting pitch cylinder of the hob right off the surface of the hob thread. In the absence of experimental evidence, it is not certain what effect this may have on the tooth surface quality. Therefore, although the shaft angle need not theoretically be set equal to its standard value, it is nevertheless recommended that in practice this value should continue to be used. Geometric Design of a Helical Gear Pair In the final section of this chapter, we outline a procedure by which we can choose the helix angle, the profile shift values and the gear blank diameters, for a pair of helical gears intended to mesh on parallel shafts at an arbi trary center di stance C. Since the standard center distance depends on the helix angle, (16.58) it would appear that we can always choose the helix angle so that the standard center distance Cs is equal to the center distance C. In this case, the pitch cylinder of each gear would coincide with its standard pitch cylinder. However, as we will show, it is not always practical to choose the helix angle in this manner, and there is no particular advantage in doing so. When the gears are cut by a pinion cutter, the helix angle of each gear is equal to that of the cutter, so the choice of ~s is limited by the cutters that are available. When a rack cutter is used to cut the gears, the cutter veloci ty v r and the gear blank angular veloci ty must be related by Equation (16.11), 484 Gear Cutting II, Helical Gears This equation must be satisfied exactly, because an incorrect value for vr would result in uneven spacing of the teeth on the gear. However, when ~s is chosen so that Cs is equal to C, it may be impossible to find change gears giving the exact relation between vr and wg \u2022 In general, it is probably easiest to obtain the required helix angle when the gear is cut by a hob, and the differential change gear ratio is given by either Equation (16.53) or Equation (16.56). Even in this case, it may be difficult to find a set of change gears giving a sufficiently small error. The effort required is seldom justified, because a gear pair can be designed quite satisfactorily, assuming only that Cs is approximately equal to C. The procedure is essentially the same as the one described in Chapter 6, for the design of a spur gear pair. For the reasons just outlined, it is generally best to choose the helix angle ~s so that the gears can be cut wi thout difficulty, and at the same time the standard center distance Cs is slightly less than the center distance C. The value of Cs should lie within the range given by Equation (6.14), C (16.59) The design procedure now consists in the choice of suitable profile shift values, and the gear blank diameters, in order to obtain the backlash required, and adaquate values for the working depth and the clearances at each root cylinder. We consider the meshing geometry in a transverse plane, and the design steps are then identical to those used in the design of a spur gear pair. For a helical gear pair, it is customary to specify the normal backlash Bn' rather than the circular backlash B. It is therefore necessary to calculate a number of the gear parameters in the transverse plane, before we can consider the transverse plane geometry. The values of mt' Rs1 ' ~ts' Rb1 , Rp1 ' ~p' ~tP' Ptp' and Bare found from Equations (13.148, 13.150, 13.151, 13.152, 14.28, 14.7, 14.8, 14. 10 and 14.72). (16.60) (16.61) Geometric Design of a Helical Gear Pair B tan tl>ns cos \"'s Rp1 tan \"'s Rs1 Rb1 Rp1 21TC 485 (16.62) (16.63) (16.64) (16.65) (16.66) (16.67) (16.68) The design of a helical gear pair with parameters mn and tl>ns' and normal backlash Bn' has now been effectively replaced by the design of a spur gear pair with parameters mt and tl>ts' and circular backlash B. We use the method described in Chapter 6, and in particular Equations (6.45 - 6.53), to carry out the necessary steps. Since the procedure was explained in Chapter 6, the equations will be presented here with very little explanation. We start by writing down the transverse tooth thicknesses at the pi tch cylinders, 1 2\"(Ptp-B) + tlttp (16.69) 1 2\"(Ptp -B) - tlttp (16.70) where tlttp is a quantity chosen by the designer, to increase the tooth thickness in one gear, and reduce it in the other. The next four equations are given for gear 1 only, since the corresponding equations for gear 2 are found by interchanging the subscripts 1 and 2. t ttsl R [.:..!E..!. + 2(inv tP tp - invtl>ts\u00bb) (16.71) s 1 Rpl 1 tI> (tts11 (16.72) e 1 2 tan 2\"1Tmt ) ts bs1 a r - e 1 (16.73) 486 Gear Cutting II, Helical Gears b + R - R sl p1 sl (16.74) The addendum values ap1 and ap2 are chosen to give a working depth of 2.0mn , and equal clearances at each root cylinder, mn - ~(bp1 - bp2 ) 1 mn + 2(bp1 - bp2 ) (16.75) (16.76) And finally, we obtain the diameters of the two gear blanks, (16.77) (16.78) Once the dimensions of the gear pair are all chosen, the designer should of course check, as in the design of a spur gear pair, that there is no interference or undercutting, and that the contact ratio, the root cylinder clearances, and the tip cylinder tooth thicknesses are all adaquate. Gear Cutting II, Helical Gears 487 Numerical Examples Example 16. 1 A 55-tooth helical gear with normal module 4 mm, normal pressure angle 20 0 and helix angle 30 0, is to be cut with a normal tooth thickness of 6.915 mm. Calculate the cutting center distance, and the radius of the root cylinder in the gear, if it is cut by a 32-tooth pinion cutter with a normal tooth thickness of 6.40 mm, and a tip cylinder diameter of 158.12mm. mn=4, ~ns=200, ~s=300, Ng=55, t nsg=6.915 Nc =32, t nsc =6.40, RTc =79.06 Example 16.2 Rsg = 127.017 mm ~ts 22.796 0 Rbg = 117.096 ttsg = 7.985 73.901 68. 129 7.390 inv ~~p = 0.024565 ~~p = 23.471 0 201.932 mm 122.872 mm (13.113) (13.113) (16.6) (2.16,2.17) (16.7) (16.8) A hobbing machine has an index constant C. of 24, and a 1 differential constant Cd of 25 mm. Calculate the change gear ratios required to cut a 49-tooth gear with a normal module of 5 mm and a l)elix angle of 23 0, using a 2-thread hob. C.=24, Cd=25, N =49, Nh=2, m =5, ~ =23 0 1 g n s 488 Gear Cutting II, Helical Gears k. = (48/49) 1 kd = 0.3109340 40.201 mm (16.52) (16.53) (16.20) The index change ratio can obviously be provided by a single gear pair. The differential ratio can be achieved with good accuracy by two gear pairs, having ratios of (24/66) and (59/69). It is not always easy, however, to find change gears which give the required ratio. In the case described in this example, it would have been simpler if the gear pair had been designed with an axial pitch of 40 mm, in which case the required differential change gear ratio would have been exactly (25/80). Example 16.3 When lead screws and other transfer mechanisms are converted from inches to mms, it is sometimes necessary to introduce a factor of 25.4 into their drives. This factor requires a gear with 127 teeth, which is difficult to cut using conventional change gear ratios, because 127 is a prime number, and most sets of change gears do not contain gears with more than 120 teeth. Use Equations (16.55 and 16.56) to choose the ratios to cut a 127-tooth spur gear wi th a single-thread hob, when the hobbing machine has a feed rate of 0.020 inches, and the machine constants Ci and Cd are 24 and 0.5 inches. Required ki = 0.1889764 (16.52) Choose index change gears with ratios (24/41) and (31/96). (24/41) x (31/96) - (1/31) 0.8064516 (16.55) (16.56) The differential ratio can be provided by a single gear pair with a ratio of (25/31). Chapter 17 Tooth Stresses in Helical Gears Introduction The calculation of the tooth stresses in a helical gear is considerably more complicated than the corresponding calculat ion for a spur gear. The contact stress and the fillet stress in each tooth depend on the intensity of the load, and on its position. Since the load intensity varies, as the position of the contact line moves up or down the tooth face, it is not easy to decide when the maximum stresses will occur. As we pointed out in Chapter 11, we consider in this book only the static stresses that would occur if the gears were not rotating. The actual stresses that exist in normal operation are found by multiplying the static stresses by various factors, to account for dynamic effects, type of loading, and so on. Values for these factors are given in the AGMA Standard referred to in Chapter 11 [6]. The method described in this chapter for calculating the static stresses is based on the AGMA method, but differs from it in certain respects. A summary of the differences will be presented at the end of the chapter. Tooth Contact Force In a helical gear pair, there are generally several tooth pairs which are simultaneously in contact. The contact in each tooth pair takes place along a straight line, which coincides with one of the generators in each tooth. In order to calculate the tooth stresses, we assume that the load intensity w is constant along all the contact lines. The value 490 Tooth Stresses in Helical Gears of w at any instant is then equal to the total contact force W, divid.d by the total contact length Lc' w (17.1) In this section of the chapter, we determine the value of W, corresponding to any specified value of the applied torque. And in the following section, we will describe how to calculate the contact length Lc. The direction n~ of the normal to the tooth surface at A, when A is a point on the contact line, was given by Equation (14.94), n~ = cos \"'b [sin t/ltp nx(O) + cos t/ltp ny(O)] - sin \"'b nz(O) (17.2) In the absence of friction, the contact force acts in the direction opposite to n~, and its component parallel to the gear axis is therefore (w sin \"'b). Hence, the component perpendicular to the gear axis, which is the useful component, is equal to (W cos \"'b) \u2022 The base cylinder of gear 1 is shown in Figure 17.1, with Contact Length 491 the plane of action of the contact force touching the base cylinder. The diagram also shows the component of the contact force perpendicular to the gear axis. We take moments about the axis, to obtain a relation between the applied torque M1 and the contact force W, (17.3) and we use the same method to find the corresponding relation between the contact force and the torque M2 appl ied to gear 2, (17.4) The contact force is found from either of these equations. By combining the two equations, we obtain a relation between M1 and M2 , which is the same as Equation (11.3), the corresponding relation between the torques applied to a pair of spur gears. (17.5) Contact Length As we stated earlier, there generally several tooth pairs in contact at any instant, and the contact length Lc is the sum of the contact lengths on each of these tooth pairs. In this section, we will derive a general expression for Lc' It turns out that we do not often need to make use of the general expression, since the cases required for the stress analysis are always special, and therefore simpler. However, it is a matter of interest to have the general result, and it also helps to determine when the maximum and minimum values of Lc occur. A transverse section through the gear pair is shown in Figure 17.2, with the plane of action touching the two base cylinders. As usual, the ends T1 and T2 of the path of contact are the points where the tip cylinders intersect the plane of action. Figure 17.3 shows the plane of action, with the axial lines through T1 and T2 meeting the transverse plane z=O at T10 and T20 , and meeting the transverse plane z=F at T1F and T2F \u2022 The region of contact is the rectangle T10T20T2FT1F. We stated in Chapter 14 that the lines of contact on the different contacting tooth pairs can be represented by a set of diagonal lines in the region of contact, each making an angle \"'b with the gear axis, and with a vertical spacing equal to the transverse base pi tch Ptb. To find the length of the contact lines in the rectangle, it is helpful to construct two additional triangles T'T 10T1F and T10T\"T20 , as shown in Figure 17.3. The value of Lc is then found as the length of the diagonal lines in triangle T' T\"T 2F' minus the lengths in triangles T'T 10T1F and T10T\"T20 \u2022 We proved in Chapter 14 that the lengths T' T 1 F and T 1 F T 2F are equal to mFPtb and mpptb' where mF and mp are the face contact ratio and the profile contact ratio, given by Equations (14.68 and 14.64), _1_ Ptb F tan \"'b (17.6) Contact Length 493 The plane of action. In addition, the length T'T2F is equal to mcptb' where mc is the total contact ratio, equal to the sum of mF and mp , (17.8) In order to find the value of Lc' we first consider a general triangle of height mPtb' where m can represent any of the contact ratios me' mF or mp. This triangle is shown in Figure 17.4, and the upper contact line is shown in a typical position, lying a vertical distance ePtb below the top corner of the triangle, where e is any number between 0 and 1. The number of contact lines in the triangle is equal to 494 Tooth Stresses in Hel ical Gears (n +1), where n represents the integral part of the number e e (m-e). If e is greater than m, there are no contact lines in the triangle, and the value required for ne is -1. We therefore define a function, n int(f) (17.9) where f is any number, and n is the largest integer which is less than or equal to f. If, for example, f has the values 2.2, 1.0 and -0.3, the corresponding values of n are 2, 1 and -1. The val ue of n e can then be expressed by the funct ion, n e int(m-e) (17.10) In the triangle shown in Figure 17.4, the upper contact line has a length (m-w)ptb/sin ~b' The next contact line is shorter than the first by Ptb/sin ~b' and so on. The total contact length Le can therefore be expressed as an arithmetic series, whose sum is given by the following expression, (17.11) We now apply this result to the three triangles in If we use this method to calculate the contact length Lc for various values of e, we will find the following results. Minimum and Maximum Values for Lc 495 The value of L is always a minimum when e is zero, and a c contact line passes through the upper corner T10 of the region of contact. And the value of L is a maximum when e is equal to c [mF - int(mF)], and a contact line passes through the other upper corner T1F of the contact region. Minimum and Maximum Values of Lc For the purpose of the stress analysis, we would expect to be most interested in the minimum value of Lc' since this corresponds to the maximum load intensity. Now that we know that the contact length is a minimum when a contact line passes through T10 , it is possible to find simpler expressions for the value Lcmin \u2022 We can simplify the expressions further, if we consider only gear pairs in which every transverse section has either one or two contact points. This condition means that the profile contact ratio lies between the following limits, < 2 (17.16) and this range includes all gear pairs of normal design. In the transverse section shown in Figure 17.2, there are two points Q and Q' marked on the plane of action. Point Q lies a distance Ptb below T l' and Q' lies a distance Ptb above T2\u2022 If the diagram represented a spur gear pair, Q and Q' would be the points on the path of contact corresponding to the ends of the period of single-tooth contact. In a helical gear pair, there is generally no period of single-tooth contact, because the total contact ratio mc is usually larger than 2. However, Q and Q' would represent the ends of the period of single-tooth contact in any particular transverse section, and it is therefore still customary to refer to these points as the end points of single-tooth contact. The region of contact is shown again in Figure 17.5, with the axial lines through Q and Q' cutting the transverse plane z=O a~ QO and QQ' and cutting the transverse plane z=F at QF and Qp.. We have stated that the value of Lc is a minimum when a contact line passes through point T 10. There must simultaneously be a second contact line through QO' since the distance between T10 and QO is equal to the transverse base pitch Ptb' Due to the symmetry of the rectangle, we can also argue that Lc is again a minimum when there are contact lines through T 2F and QF' We now consider a particular gear pair, with the contact lines shown in Figure 17.5. One contact line passes through point T10 , while a second line starts at QO' and intersects the plane z=F at point AF , somewhere between QF and QF' For this situation to be possible, the length mFPtb must be less than (2-mp)ptb' as we can see from the diagram. Such a gear pair is therefore defined by the condition, (17.17) and will be referred to as a very low face contact ratio (VLFCR) gear pair. A spur gear pair, in which the face contact ratio is zero, would fit into this category. The condition given by Equation (17.17) is equivalent to the statement that the total contact ratio mc is less than 2. This means that there are periods of the meshing cycle when only one tooth pair is in contact, which is the situation shown in Figure 17.5. The contact length Lcmin for this case can be read directly from the diagram, L . cmln F cos \"'b (17.18) Minimum and Maximum Values for Lc 497 The same region of contact is shown in Figure 17.6, but the contact line has moved up, so that it now passes through point Qp., and a new contact line is about to enter the region at T2F \u2022 During the period when the contact line moves between the positions of Figures 17.5 and 17.6, there is only one tooth pair in contact, and the contact length Lc remains constant, with the value equal to Lcmin given by Equation (17.18). The region of contact for a second gear pair is shown in Figure 17.7. The contact line which starts at QO now intersects the plane z=F at a point between QF and T1F \u2022 The face contact ratio must lie wi thin the following range, 498 Tooth Stresses in Helical Gears < (17.19) and this type of gear pair will be described as a low face contact ratio (LFCR) gear pair. We know that the contact length is at its minimum value, since one contact line passes through T10 \u2022 To calculate the value of Lcmin ' we take the length of the contact line through QO' and we add the length of the short contact line near T2F , L . cmln F cos 1/Ib + Ptb (m +m -2) sin 1/Ib F P The expression is simplified if we use Equation (17.6) to express Ptb in terms of F, L . cmln (17.20) Lastly, we consider gear pairs in which the face contact ratio is greater than 1, > (17.21) Gear pairs that fall within this category are known as normal helical gear pairs, since most helical gear pairs are designed with a face contact ratio larger than 1. The region of contact for a gear pair of this type is shown in Figure 17.8, with the contact lines in the positions Minimum and Maximum Values for Lc 499 corresponding to the minimum contact length. Starting from the left, there is one contact line passing through QQ' then there are a number of complete contact lines stretching from the bottom edge to the top edge of the region, and finally there are either one or two lines which intersect the right-hand edge. To find the value of Lcmin' we consider in turn each of the three groups of contact lines just described. We start by defining two new quantities nc and nF , as the integer parts of mc and mF , (17.22) (17.23) The number of contact lines crossing the upper edge of the region is nF , which means that the number of complete lines is (nF-1). The total number of contact lines is nc ' so the number crossing the right-hand edge is (nc-nF). Hence, the contact length Lcmin is found as follows, L . cmln Ptb \u2022\u2022 1. [1 + mp (nF-1) + (m -n ) + (m -n +l)(n -nF-1)] sIn \"'b c c c c c The result is then simplified, and expressed in terms of the face-width F, L . cmln 500 Tooth Stresses in Helical Gears We pointed out earlier that the maximum load intensity on a gear tooth corresponds to the minimum contact length, and for this reason we derived expressions for Lcmin ' However, as we will show later in this chapter, the fillet stress is often a maximum when the contact line passes through the corner T1F of the contact region, and this occurs when the load intensity is a minimum. We therefore also need expressions for Lcmax ' the maximum contact length. Minimum and Maximum Values for Lc lie in the following range, < The contact length is again the sum of the two lengths, and, as usual, we express the result in terms of F, 5{)1 (17.27) 502 Tooth Stresses in Helical Gears lower edge of the region is then equal to (nFP+2), and the total number of contact lines in the region is (nF+2). Hence, the number of complete contact lines is (nFP+1), and the number of lines crossing the left-hand edge of the region is (nF-nFP)' By considering the three groups of contact lines described earlier, we-obtain the following expression for the contact length, As before, we simplify this result, and express Lcmax in terms of F, Contact Stress In the last section of Chapter 14, we proved that when A is a contact point between a rack and a pinion, the line of contact through A and the common normal at A both, lie in the plane of action. The same is true when A is a contact point between a pair of helical gears. To prove this statement, we need only consider the imaginary rack between the gears, and make use of the result just stated, first for one gear and the imaginary rack, and then for the second gear and the imaginary rack. The plane of action for a gear pair is shown in Figure 17.12, with the contact line GA making an angle..pb with the n direction, as we proved in Equation (14.93). Near z point A, the tooth surfaces can be represented by two circular cylinders in contact, with their axes lying in the plane of action. Their radi i are shown as Pc 1 and Pc2' with the subscript c indicating that these are the radii of curvature when we make a section through the cylinders perpendicular to the line of contact. If we make a transverse section, as shown in the diagram, the cylinders appear as ellipses. For gear 1, the semi-minor axis of the ellipse is Pc1 ' while the semi-major axis is equal to (pc 1/cOS ..pb)' The radius of Contact Stress 503 curvature Pt 1 at point A in the transverse section through the tooth profile is then equal to the radius of curvature at the corresponding point of the ellipse, 2 Pc l (17.31) The corresponding equation for gear 2 can be written down immediately, (17.32) The maximum contact stress 0c between two cylinders of radii Pc1 and Pc2 was given by Equation (11.5),"
        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.10-1.png",
        "caption": "Figure 7.10. A pinion with severe undercut.",
        "texts": [
            " Hence, the limit circle of gear 1, which is the circle through T2 , is larger than the undercut circle. Since T2 lies outside the undercut circle, the contact on the tooth face of gear 1 ceases at a point on the tooth profile above the undercut circle. Although the profile is cut away inside the undercut circle, the meshing is not affected, because the missing part of the involute would not in any case be touched by the meshing gear. The contact ratio mc is therefore given by Equation (4.9), exactly as if there was no undercutting. The meshing diagram is shown in Figure 7.10 for the second case, when the undercut circle of gear 1 is larger than the limit circle. The point where the undercut circle intersects the path of contact is again labelled U1, and in this gear pair U1 lies between point T2 and the pitch point. In a gear pair with no undercutting, the path of contact would be the line T1T2\u2022 However, if the path of contact in Figure 7.10 were to continue below point U1, there would be contact inside the undercut circle of gear 1, which is impossible because the involute tooth profile has been cut away. In this case, therefore, the path of contact extends from Tl only to point U1. The length of this line can be read from the diagram, and we divide by the base pitch to obtain the corresponding contact ratio, (7. 15) It is interesting that the value of the contact ratio given by Equation (7.15) depends only on the geometry of gear 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003305_s0956-5663(03)00276-8-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003305_s0956-5663(03)00276-8-Figure1-1.png",
        "caption": "Fig. 1. Superoxide dismutase biosensor assembly using amperometric hydrogen peroxide electrode as transducer. (a) Electrode body; (b) Ag/AgCl/Cl\u2212 cathode; (c) Pt anode; (d) electrode plastic cap filled with buffer solution; (e) cellulose acetate membrane; (f) kappa-carrageenan membrane entrapping superoxide dismutase enzyme; (g) dialysis membrane.",
        "texts": [
            "0 ml of phosphate buffer contained in the measuring cell, and then proceeding with analysis by SOD biosensor. The biosensor we used to determine the superoxide radical was obtained by coupling a transducer (an amperometric electrode for hydrogen peroxide, with a platinum anode maintained at a constant potential of +650 mV with respect to an Ag/AgCl/Cl\u2212 cathode) and the superoxide dismutase enzyme immobilised in a gel-like kappa-carrageenan membrane. The gel containing the enzyme was sandwiched between a cellulose acetate membrane and a dialysis membrane (Fig. 1). The whole assembly was fixed to the head of the electrode by means of a rubber O-ring. The preparation of the kappa-carrageenan membrane and the immobilisation of the SOD enzyme in the gel membrane was described in detail in a previous paper (Campanella et al., 1999, 2000). The antioxidant capacity using the SOD biosensor was checked as follows: the superoxide radical is produced by the oxidation in aqueous solution of the xanthine to uric acid in the presence of the enzyme xanthine oxidase xanthine + H2O + O2 xanthine oxidase\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2192 uric acid + 2H+ + O2 \u2022\u2212 (1) the disproportion reaction of the superoxide radical, catalysed by the superoxide dismutase immobilised on the H2O2 electrode, releases oxygen and hydrogen peroxide O2 \u2022\u2212 + O2 \u2022\u2212 + 2H+ superoxide dismutase\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2192 H2O2 + O2 (2) the H2O2 is monitored by the amperometric sensor for hydrogen peroxide"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002913_s0029-8018(03)00048-9-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002913_s0029-8018(03)00048-9-Figure2-1.png",
        "caption": "Fig. 2. Definition of parameters in the guidance law.",
        "texts": [],
        "surrounding_texts": [
            "The sliding error, SE\u2217, control command, u\u2217 SE\u2217(t) (1 l)y\u0307\u2217 e (t) ly\u2217 e (t),0 l 1 (4) where the superscript \u2217 represents the normalized variables. The normalization factors,Gy, and Guare used to map the signals on to a defined domain. SE\u2217 SE Gy ;y\u2217 e (t) ye(t) Gy ;r\u2217 e (t) y\u0307\u2217 e re(t) Gy ;u\u2217(t) u(t) Gu (5)"
        ]
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure11-4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure11-4-1.png",
        "caption": "Figure 11-4. Arrangements for abrasion tests",
        "texts": [],
        "surrounding_texts": [
            "Abrasive papers and cloths are cheap and easy to use but their cutting power deteriorates rather quickly. They are also characterized by the nature of the abrasive particles and their size and sharpness. Plain textiles of defined quality have also been used for mild abrasion. Friction and wear 231 Loose abradants are usually particles of the same types of material that are used to form abrasive wheels or paper, and are characterized in the same way. Metal \"knives\" can have various geometries, including a mesh and a raised pattern on a wheel. The important characteristic is the sharpness of the edges in contact with the rubber test piece, and this can be difficult to accurately maintain. Plane smooth surfaces are usually metal and are characterized by the material and the surface roughness. The choice of abradant should be made primarily to give the best correlation with service, and the usual abrasive wheels and papers really only relate to situations where cutting abrasion predominates. Materials such as textiles and smooth metal plates may be more appropriate for other applications. In practice, the abradant is often chosen largely for reasons of convenience and surfaces such as plain steel have the disadvantage of abrading slowly and, if the conditions are accelerated, give rise to excessive heat build-up. Consequently, abrasive wheels and papers are used in situations where they are inappropriate for assessment of service performance."
        ]
    },
    {
        "image_filename": "designv10_4_0000265_j.matdes.2019.108138-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000265_j.matdes.2019.108138-Figure6-1.png",
        "caption": "Fig. 6. Schematic representation of specimen geometry, including support height and spacing, and specimen width and thickness.",
        "texts": [
            " The defining geometric features of a block support structure are: the arrangement of its ligaments, referred to as \u2018type\u2019 (Fig. 4); the vertical distance bridged by the support structure; and, the associated cross-sectional area. Cross-sectional area is a function of the hatch spacing (distance between laser scan paths) defined during support generation. Block supports are the most common and versatile of the standard support structure designs (Section 2.1) and are the focus of this research. The control factors used to define support structure geometry were support height and spacing (Fig. 6). Normal strength is a standard method of quantifying the strength of porous [26] and AM structures [11]. However, this method fails to capture a key loading condition experienced by components during SLM fabrication. Deformation of fabricated geometry can occur during SLM where it will \u2018peel\u2019 away from the build platen (Fig. 7) due to residual stresses that arise during cooling [27]. To provide a thorough characterisation of support structure mechanical response, support structures were tested under two unique loading conditions1 \u2013 normal loads, as described above, and peel loads whichwere produced by an external load with line of action coincident to the edge of the support structure (Fig. 8). The load-carrying capacity of a support structure can be quantified by the peak load (Pmax) grounded at failure. This capacity can be represented as the strength associated with either the supported area or contact area. Supported area strength (\u03c3s, Eq. (1)) is associated with the supported area (As =Wsts, Fig. 6). This measure is useful for practicing engineers who intend to specify a support strength for a given supported area. 1 Loads generated using a 5569A Instron with a 50kN load cell with cross-head velocity of 0.5 mm/min. Contact strength (\u03c3c, Eq. (2)) is associated with theminimum crosssectional area (Ac) of the support structure. This measure provides insight into the fundamental mechanical response of the proposed support structures and more accurately describes true structural strength. Contact area was measured from \u03bcCT data of as-manufactured geometry, and due to the presence of teeth, occurs in the region of the solid material-support structure interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001008_j.engfailanal.2021.105260-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001008_j.engfailanal.2021.105260-Figure4-1.png",
        "caption": "Fig. 4. 3D CAD designs of some gears used in this study.",
        "texts": [
            " As the backup ratio increases, the tooth\u2019s body part grows, and the gear becomes heavier. Fig. 1. Effect of pressure angle variation on the gear tooth profile. Fig. 2. Definition of backup ratio. O. Dog\u0306an et al. When the rim ratio decreases, the body becomes too thin, and the gear\u2019s strength is reduced. Therefore, when determining the rim thickness, the optimum rim thickness should be determined by evaluating strength, durability, and weight. A total of 16 different CAD geometries were created in CATIA. The 3D CAD designs of some gears used in this study is shown in Fig. 4. In this study, involute spur gears with 28 tooth numbers and 3.175 mm module were used. The DSPA and the backup ratio were defined as variable parameters. AISI 9310 steel, which is frequently used in aviation vehicles, was used as gear material. The basic properties for AISI 9310 steel and the Paris law coefficients to be used in fatigue crack propagation analysis are given in Table 1. O. Dog\u0306an et al. Engineering Failure Analysis 122 (2021) 105260 In order to determine the crack starting point in the crack propagation analysis, static structural analyses were performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.15-1.png",
        "caption": "Figure 4.15. Backlash along the common normal.",
        "texts": [
            "36) 104 Contact Ratio, Interference and Backlash This equation proves the statement made earlier, that the circular backlash can be interpreted as the length of the maximum arc through which a point on the pitch circle of one gear can move, when the other gear is held fixed. Backlash Along the Common Normal The second manner in which the backlash is commonly defined is the backlash along the common normal. When we first introduced the topic of backlash, we pointed out that the tooth thicknesses of a gear pair are chosen so that, for each tooth in the meshing zone, there is contact on one face only, leaving a small gap at the opposite face. The backlash B' along the common normal is defined as the shortest distance across this gap. A gear pair is shown in Figure 4.15, and the contact point lies as usual on line E1E2 , which is one of the common tangents to the base circles. The diagram also shows EiEi, the other interior common tangent to the base circles, and this line cuts the profiles of two adjacent teeth at Ai and Ai. Since these profiles are both involutes, line A;E; is normal to the tooth profile of gear 1, and AiEi is normal to the tooth profile of gear 2. Hence, line EiEi is normal to both Backlash 105 profiles, and the length A;Ai is equal to the backlash B'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000306_tmech.2020.3034640-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000306_tmech.2020.3034640-Figure10-1.png",
        "caption": "Fig. 10. FEA bending of the PneuNets of different gap lengths at the pressure of 0.03 MPa and 0.04 MPa. At the applied pressure of 0.03 MPa: (a) 1 mm lg, (b) 2 mm lg, (c) 3 mm lg, (d) 4 mm lg. At the applied pressure of 0.04 MPa: (e) 1 mm lg, (f) 2 mm lg, (g) 3 mm lg, (h) 4 mm lg.",
        "texts": [
            " The Young\u2019s Modulus of the paper used in the inextensible layer is available material Dragon skin 30 silicone rubber (Dragon skin 30, smooth-on Inc., America) is used to make the PneuNet including bottom layer A, bottom layer B, and main body. The material Dragon skin 30 silicone rubber is based on the Yeoh model with parameters C10=0.11, C20=0.02, C30=0.02 respectively. Contact interaction is defined between adjacent chamber lateral walls of the PneuNets. The FEA simulation results are shown in Fig. 10. It can be seen from the FEA results, the bending angle of the PneuNets is almost the same when the gap length is 3 mm and 4 mm at the pressure of 0.03 MPa and 0.04 MPa. But the bending angle becomes larger when the gap length is 1 mm and 2 mm at the same pressure. The reason is that when the PneuNets have the gap length of 3 mm and 4 mm the chamber lateral wall after bending angles are the same and have nothing to do with the gap length of the PneuNets. When the gap of the PneuNets are 1 mm and 2 mm, the chamber lateral walls of the PneuNets are squeezed, which leads to the increase of the bending angle as shown in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000729_j.matdes.2021.109659-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000729_j.matdes.2021.109659-Figure3-1.png",
        "caption": "Fig. 3. The geometry of a twin-cantilever beam (all dimension",
        "texts": [
            " An atmosphere of N2 gas was applied to reduce the oxygen content in the build chamber to less than 0.8%, hence reducing the oxidation during themelting process. Scanning of layers was conducted using a continuous laser mode according to a stripe hatching pattern alternating 67\u00b0 between two successive layers, as illustrated in Fig. 2. For the build with preheating, the preheating temperature was selected to be 200 \u00b0C based on [24] to avoid cracking. Schematic illustration of the cantilever geometry is provided in Fig. 3. As observed, twin cantilevers are printed with supports in the overhang area. Due to its geometry, the twin cantilever is highly sensitive to distortion, and therefore, can be adopted to investigate themagnitude of deflections and residual stresses in the additively manufactures components. The LPBF fabricated cantilevers were marked at 11 different points (5 on each side) after the printing process along the middle axis of each beam with a spacing of 5 mm between every two adjacent points. In order to visualize andmeasure the amount of deflection caused by the thermally induced residual stresses, the LPBF fabricated twin cantilevers were separated from the supports by wire electrical discharge machining",
            " Total strain \u03b5total is the sum of elastic strain \u03b5elastic, plastic strain \u03b5plastic and thermal strain\u03b5thermal. \u03b1 is the temperature-dependent coefficient of thermal expansion (CTE), and\u0394T denotes the change in temperature. When f yield=0, yielding occurs and then generates plastic strains. Fig. 6. Illustration of the twin-cantilever beam ABAQUS software was utilized to carry out the modeling. The part geometry for simulation of the deflections and residual stresses is a simple twin-cantilever structure of dimensions 50mm, 10mm, and 10mm in length, width, and height, respectively (Fig. 3). For each build process, 12 parts were built on the same substrate. However, as spacing is sufficient between parts such that the build of an adjacent part has a negligible effect on the thermal history of the current part, the model is reduced to a single part, saving on computation time. Nevertheless, it is important to consider the entire build layout when calculating the cooling time between layers (120 s), as this will have a first-order impact on the thermal history of the part and consequently the residual strain field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000249_admt.201800692-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000249_admt.201800692-Figure9-1.png",
        "caption": "Figure 9. a) Model showing the measurement configuration of the off-diagonal giant magnetoimpendance (OD-GMI) device. b) Glass-coated amorphous ferromagnetic metallic microwire used in conventional GMI. Adapted with permission.[126] Copyright 2002, Elsevier Science B.V. These wires are fabricated with special treatments that generate the transversal anisotropy (lower figure). c) Miniature OD-GMI sensory system based on amorphous microwires. Adapted with permission.[127] Copyright 2018, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. d) Scanning electron microscopy image of rolled-up Py tubes with yields >90%. Azimuthally aligned 180\u00b0 magnetic domains in a rolled-up Ni rich Py tube achieved purely by the self-assembly process (bottom) and appropriate magnetostriction. Adapted with permission.[122] Copyright 2013, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. e) Schematics of the planar layout and the assembled OD-GMI device which acquires the desired magnetic anisotropy after the self-assembly process. The self-assembly process generates pick-up coils around the ferromagnetic tube. f) Real structure in planar and self-assembled state. e,f) Adapted under the terms of the CC BY-NC license.[11] Copyright 2015, the Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.",
        "texts": [
            " KGaA, Weinheim1800692 (10 of 29) www.advmattechnol.de rolled-up self-assembly technology suitable for on-chip 3D transformers.[14,114,117] A clever design of the planar geometry enables the integration of a magnetic core into the inductor within the self-assembled Swiss-roll architecture, further enhancing its inductance. This configuration can also be used for the sensing of ultrasmall magnetic fields, achieved by means of measuring the inductive response of the coil when the core is subjected to an alternating current (Figure 9a). Sensing of the magnetic field in this configuration relies on the off-diagonal giant magneto impedance effect (OD-GMI),[118\u2013120] and achieving a strong OD-GMI response (Figure 9b) requires that the magnetization of the core possesses a transversal anisotropy, or in other words, should be oriented along the windings of the coil (Figure 9c). The tubular shape provides the means to achieve such a magnetization, as the stress and the continuous curvature of the ferromagnetic layer integrated within the self-assembled tube alters the magnetic anisotropy of a properly tuned ferromagnetic material. These effects are readily observable in magnetic structures where static magnetization and magnetization dynamics of thin ferromagnetic tubes are affected by the curvature (Figure 9d),[121\u2013125] and this behavior in self-assembled tubular structures has been demonstrated to reveal a direct effect of the self-assembly process on the functionality of the GMI device as well.[11] By placing a thin permalloy (Ni81Fe19) layer between two patterned conducting elements, self-coiled on-chip GMI devices with integrated pick-up coils were fabricated (Figure 9e,f). The self-assembly process alters the geometry of the ferromagnetic layer, changing the inherent anisotropy into the desired azimuthal magnetization that lends itself to a strong change in the GMI effect compared to its planar counterpart. The effect was clearly observed by measuring the voltage response of the inductor generated by an axial component of the ferromagnetic material\u2019s alternating magnetic flux in response to an external axial magnetic field. Wafer scale fabrication of these devices is envisioned to manufacture arrays of ultrasensitive magnetic sensors and enable applications such as magnetic encephalography and magnetic cardiography"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001014_j.jmapro.2021.02.033-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001014_j.jmapro.2021.02.033-Figure5-1.png",
        "caption": "Fig. 5. The comparison of the distribution of different normalized data (the number of cube mesh cells that will be activated in each simulation step is 2 \u00d7 2): a temperature state data, b uncorrected deposition order state data, c preliminary corrected deposition order state data and d corrected deposition order state data (kcc = 0.6).",
        "texts": [
            " The deposition order state data can describe the AM process which contains the cooling process between layers, because the cooling process can be seen as an AM sub-process with zero speed. Sn i,j,k = { tn \u2212 Pi,j,k Mn i,j,k = 1 +\u221e Mn i,j,k = 0 (2) To obtain more detailed thermal field descriptions and prediction results, the size of the cells needs to be set smaller, which will result in more than one activated cell in some simulation steps. It can be seen from the previous introduction that all activated cells of the same simulation step have the same deposition order state value, although the temperature state value of them is different. It can be seen from Fig. 5(a) and (b) that this phenomenon is more obvious for those cells with smaller deposition order state value. To make the correlation between the deposition order state value and the temperature state value more obvious, a two-step corrected method for the deposition order state data is proposed. The deposition order state data is corrected based on the thermal field of a simulation step preliminary. The thermal field of a simulation step is defined as the thermal field induced by a moving heat source in a semi-infinite body at room temperature, where the moving mode of the heat source corresponds to the current simulation step",
            " {Tu} is the set of the temperature value of the center point of all the cells which will be activated in the current simulation step, and the corrected coefficient value set {kc} can be calculated by Eq. 3. A 3D matrix K (nx\u00d7ny\u00d7nz) is used to describe the corrected coefficient of each cell, and the value is 0 for the cells that will never be activated. Based on the corrected coefficient matrix K and the cell activation interval matrix D, Sn can be modified by Eq. 4 to obtain the Fn which describes the preliminary corrected deposition order state of all cells in the n-th simulation step. It can be seen from Fig. 5(a)\u2013(c) that, compared with the distribution of the uncorrected deposition order state data, the distribution of the preliminary corrected deposition order state data is more consistent with the distribution of the temperature state data. kc i = Tmax \u2212 Tu i Tmax \u2212 Tmin (3) Fn i,j,k = Sn i,j,k + Ki,j,kDi,j,k (4) Fig. 5(a) and (c) shows that the same difference of the preliminary corrected deposition order state value will correspond to a larger difference of the temperature state value when it occurs in the region with the smaller corrected deposition order state values. That is because the temperature state value of the cells that have a larger deposition order state value and have not undergone the reheating process will tend to converge during long cooling process. To embody this feature, the Fn is further corrected by Gn = exp( \u2212 kcc \u00d7 Fn) (5) Here, kcc is the corrected control factor, and Gn is the corrected deposition order state data of all cells in the n-th simulation step. Fig. 5 shows that the distribution of the corrected deposition order state data has the best consistency with the distribution of the temperature state data. In this work, a multi-layer deposition process thermal history dataset was built with the following steps: (1) Arbitrary 3D geometries were generated for defining to-bedeposited parts. (2) Five kinds of welding path patterns that are orthogonal between layers were selected and combined with each part model to generate the different GMAW-based AM processes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure4-1.png",
        "caption": "Fig. 4. Serial kinematic chains with specific constraint characteristics. (a) \u00f0RRR\u00dekE planar serial kinematic chain, (b) R\u0302R\u0302R\u0302 spherical serial kinematic chain and (c) PkPk codirectional serial kinematic chain.",
        "texts": [
            " Serial kinematic chains in which all the links are moving along parallel planes. In a kinematic chain of this class, the axes of all the R joints are parallel, and the directions of the P joints are perpendicular to all the axes of the R joints. The wrench system of this serial kinematic chain always includes a 1-f0\u20132-f1-system. The 1-f0\u20132-f1-system is composed of all the f0 whose axes are parallel to the axes of the R joints or perpendicular to all the directions of the P joints as well as all the f1 whose directions are perpendicular to all the axes of the R joints (Fig. 4(a)). A planar serial kinematic chain is denoted by \u00f0\u00dekE. Class 2 Spherical serial kinematic chains. Serial kinematic chains composed of two or more concurrent R joints. The characteristic of a kinematic chain of this class is that the axes of all the R joints are always concurrent. The wrench system of this serial kinematic chain always includes a 3-f0-system with its center at the intersection of all the axes of the R joints (Fig. 4(b)). Each R joint of a spherical serial kinematic chain is denoted by R\u0302. Class 3 Codirectional serial kinematic chains. Serial kinematic chains composed of two or more P joints whose directions are parallel. The characteristic of a kinematic chain of this class is that all the directions of the P joints are always parallel. The wrench system of this serial kinematic chain is always a 2-f0\u20133-f1system (Fig. 4(c)). Each P joint of a codirectional serial kinematic chain is denoted by Pk. Types of 4-DOF single-loop kinematic chains involving an SP virtual chain can be obtained by (a) constructing single-loop kinematic chains each composed of two of the three serial kinematic chains with specific characteristics and (b) by the application of 1\u2013ci inactive joints in the single-loop kinematic chains with a ci\u2013f0system obtained using the approach (a), and (c) constructing single-loop kinematic chains each composed of the SP virtual chain and six R and P joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003829_0094-114x(78)90028-9-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003829_0094-114x(78)90028-9-Figure4-1.png",
        "caption": "Figure 4. Four-bar linkage idealized with three elements.",
        "texts": [
            " (iii) These element mass and stiffness matrices are superposed systematically to develop the mass and stiffness matrices of the total structural system of the linkage. (iv) Determination of the unknown nodal displacements of the problem is made by solving a system of coupled ordinary differential equations. These equations are obtained by using the equilibrium conditions at the nodes. (v) All required numbers, such as stresses and strains, associated with the problem are computed. As an example, the 4-bar linkage of Fig. 4 is utilized in which each link is simulated by one element. The input shaft is assumed to be connected to a flywheel with high inertia, ensuring that no undue fluctuations occur in the input angular velocity. Then, the input crank is reduced to a rotating cantilever beam. It must be pointed out, however, that this assumption is made only to simplify the computational procedure. In Fig. 5, system-oriented generalized displacements are labeled to describe the structural deformation of the linkage as well as to maintain compatibility between the elements at the nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003829_0094-114x(78)90028-9-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003829_0094-114x(78)90028-9-Figure3-1.png",
        "caption": "Figure 3. Generalized displacements of beam element in element-oriented and system-oriented coordinates.",
        "texts": [
            "~) = m = pA, and EA L 12E/ o - p - 6 E / 4E/ o --L T L EA 0 0 L 12EI 6EI o - - - ~ ---~ 6EI 2EI o -fir L EA L 12EI o - - p - 6EI 4EI o - - \u00a3 r - U (25) With the help of eqns (14), the motion equations for the beam element may be readily derived a s t,~](~o(t)) + [\u00a3]{u(t)} = {Q}. (26) System Mass end Stiffness Matdces Consider the general element in Fig, 3 with two nodes, 1 and 2. The figure also shows two coordinate systems--the local (element-oriented) and the global (system-oriented) coordinate systems. The latter is defined, with its origin at a given node, parallel to the fixed (O-X-Y) reference frame. In Fig. 3, the two coordinate systems (1-~-~) and (1-X-Y) are shown at node 1; the same may be defined at node 2. The generalized coordinates are shown labeled in both MMT VoL 13, No, 6-=-D 610 systems. It may be shown that at node 1 u~ = U~ cos 0 +/32 sin 0 u2 = - U~ sin 0 + Us cos 0 U3 = U3 and at node 2 u4 = U4 cos 0 + Us sin 0 u5 = -/34 sin 0 + U~ cos 0 U6 = U 6. With X = cos 0 and/~ = sin 0, a transformation matrix [R] may be defined A ~ 0 0 0 O\" -t~ ,~ 0 0 0 0 0 0 1 0 0 0 jR] . . . . . . . . . . . "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.8-1.png",
        "caption": "Figure 13.8. Transverse sections through the basic rack.",
        "texts": [
            " We now consider two transverse sections through the gear, one at plane z=O and the other at plane z. As we showed earlier, the tooth profile in any transverse section must always be conjugate to the corresponding transverse section through the basic rack, so the tooth profiles in the two sections through the gear must each have a standard pitch circle and a base circle with radii given by Equations (13.14 and 13.15). The only difference between the two transverse sections through the basic rack, as we can see from Figure 13.8, is that the rack tooth profile at plane z is displaced upwards a distance (z tan \"'r)' compared with that at plane z=O. The gear tooth profile in the transverse section at plane z is therefore identical with the profile at plane z=O, The Tooth Surface of a Helical Gear 317 except that it is rotated through a certain angle 1),,9, in order to mesh correctly with the rack tooth profile in its displaced position at plane z. For a spur gear meshed with a rack, the rotation I),,~ of the gear corresponding to a displacement I)\"u r of the rack was given by Equation (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002955_j.automatica.2004.03.016-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002955_j.automatica.2004.03.016-Figure1-1.png",
        "caption": "Fig. 1. The UV prototype.",
        "texts": [
            " It has been shown that the resulting approximate implementation of the controller guarantees the reaching of an O(&2) boundary layer of the sliding manifold = 0 (Bartolini et al., 2001a, b). An UV prototype has been recently built at the DIEE-University of Cagliari as a preliminary test-bed of a novel water-jet-based propulsion system for underwater vehicles. The vehicle is about 150 cm long and 80 cm high. It contains a centrifugal pump feeding an hydraulic pipe and two variable-section nozzles, actuated by means of linear motor drives, located at the opposite ends of the hydraulic circuit (Fig. 1). The prototype is rigidly connected with a wheeled trolley that \u201csuspends\u201d the UV into a water channel (Fig. 2). This conMguration allows the UV to move freely along the channel under the reaction force exerted by the water Kow through the nozzles. The nozzle output sections can be adjusted by moving the corresponding spear valve, directly coupled with a linear electric drive. The spear valve proMle is similar to that in a Pelton turbine, so that the generated thrust is turbulence-free and almost-linearly dependent on the valve position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.2-1.png",
        "caption": "Figure 13.2. Directions of the unit vectors.",
        "texts": [
            " The purpos~ of these relations will become clear in the remaining chapters, where we di scuss the meshing, the cutt ing, and the tooth strength of helical gears. There were a number of sections in the first part of this book where vectors were employed to help in the explanation of some aspects of spur gear geometry. However, the use of vectors was not very widespread, because spur gear geometry is essentially two-dimensional, and vector theory is not often required. On the other hand, the geometry of a helical gear is three-dimensional, and vectors can be very helpful in clarifying the various proofs and explanations. Figure 13.2 shows a typical spur gear and rack, with two sets of unit vectors included in the drawing. One set, n x ' ny and n z ' are fixed in the spur gear, with nz in the direction of the gear axis. When the gear rotates about its axis, the direction of n z will not be affected, but the directions of nx A Note on the Use of Vectors 307 and ny will obviously change. The other set, n~, n~ and n S' are said to be fixed in space, which simply means that their directions do not change. The unit vector n~ is chosen perpendicular to the plane formed by the tips of the rack teeth, in the direction from the gear towards the rack",
            " When a spur gear is meshed with a rack, the axis of the gear is parallel with the teeth of the rack, so the two unit vectors nz and nS are parallel. It should be noted that a unit vector is used only to specify a direction. Since the rack does not rotate, it makes no difference whether we regard a unit vector as fixed in space, or as fixed in the rack. Hence, the three vectors n~, n~ and n S' which we originally described as fixed in space, can equally well be thought of as fixed in the rack. The two vectors nz and nS are shown in Figure 13.2 by counter-clockwise circular arrows, and these are used in conformi ty with the right-hand rule from the theory of vectors. According to this rule, a vector can correspond to a sense of rotation, using the following convention. The right hand is held so that the fingers point in the required sense 308 Tooth Surface of a Helical Involute Gear of rotation, and the thumb then points in the direction of the vector. The circular arrows in Figure 13.2 therefore indicate that the vectors point in the direction upwards out of the drawing. The spur gear and the rack are being viewed in the negative nS direction. A clockwise circular arrow would mean that the vector points downwards into the drawing. It will be the general pract ice, throughout Part 2 of thi s book, to include in each diagram a unit vector represented by a circular arrow, in order to specify the direction of the view being taken. The spur gear and rack of Figure 13.2 are shown again in The Basic Helical Rack 309 The Basic Helical Rack Figure 13.5 shows the basic helical rack, used to define the tooth surface of a helical gear. Just as the basic rack of a spur gear has teeth which are straight-sided, the basic rack in Figure 13.5 has teeth whose faces are flat planes. The angle between the gear axis and the direction of the rack teeth is shown as ~r' and it is called the basic rack helix angle. A plane cut through the rack perpendicular to the gear axis is known as a transverse section of the rack, and a plane cut perpendicular to the rack teeth, in other words perpendicular to n S' is called a normal section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure16.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure16.3-1.png",
        "caption": "Figure 16.3.",
        "texts": [
            " The relation between the required normal tooth thickness t nsg and the profile shift was given by Equation (13.117), }rmn + 2e tan 9'lns ( 16.12) The cutter should therefore be positioned so that its reference plane, which is the plane at which the normal tooth thickness and the normal space width are equal, lies a distance (Rsg+e) from the gear axis, and the offset e has the value given by Equation (16.12). The most commonly used method for cutting helical gears is by hobbing. As always in generating cutting, one gear is used to cut another. A typical hob is shown in Figure 16.3, and it can be seen that, apart from the gashes forming the cutting faces, the hob is simply a helical gear, in which each tooth is referred to as a thread. A hob. 458 Gear Cutting II, Helical Gears Since the hob is similar in shape to a screw, its helix angle \"'sh is always large, particularly when there is only one thread. It is cust~mary to specify the shape of a hob by means of its lead angle, rather than its helix angle. For a right-handed hob, the lead angle Ash is defined as the complement of the helix angle, (16"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003695_1.2359471-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003695_1.2359471-Figure7-1.png",
        "caption": "Fig. 7 The tooth surfaces and relative posit generating gear and \u201eb\u2026 gear and imaginary g",
        "texts": [
            "org/ on 01/28/201 According to the geometry in the above figure, the triangle OIOA OA can be determined, and eccentricity Exz and orientation angle e of the dual head cutter may be solved as follows: ExZ = OIOA 2 + OA OA 2 \u2212 2 \u00b7 OIOA \u00b7 OA OA \u00b7 cos OIOA OA 20 e = 180 \u2212 0I + OA OIOA 21 where 0I is the offset angle of the inside blade. Machine settings for the proposed mathematical model applied to this example are calculated and listed in Table 2. The tooth depth taper of the Cyclo-Palloid\u00a9 gears is a constant tooth depth with an epicycloidal flank line. Using the locus equations of the cutter blade, the equation of meshing, and the constraints of the gear blank, we can solve the work gear tooth surface. The generated surfaces for the example\u2014including pinion, gear, and imaginary generating gear\u2014are shown in Fig. 7. This figure also indicates the relative or the numerical example n Gear Concave A Convex I Concave A 90 deg 40 mm 6.065 mm mm 171.575 mm eg LH 30 deg RH 49 deg 71.3535 deg m 60 mm 20 deg 1 0.4 5 6 mm 135.397 mm 135 mm 135.461 mm \u221219 deg 19 deg \u221221 deg 0 deg 0 deg 0 deg \u22126.4296 deg 6.4486 deg 6.4265 deg \u221248 deg 0 deg 48 deg 3.872 mm 0 mm 3.311 mm 160.2875 deg 0 deg \u2212160.9009 deg 0 mm 0 mm 0 mm 50.033173 177.616 mm 31.3276 deg mm 8.331 mm athematical model applied to this example Pinion Gear I Concave A Convex I Concave A 0 deg 0 deg 20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000954_j.cpc.2021.107956-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000954_j.cpc.2021.107956-Figure11-1.png",
        "caption": "Fig. 11. Von Mises stress distribution. (a) Modified scaffold. (b) Original scaffold. The two structures are verified to have identical loading conditions and material properties.",
        "texts": [
            " Furthermore, it can be printed without support structures. n particular, this property of printing without support structures s extremely important in the 3D printing of bio-related scaffolds. To demonstrate the efficiency of the composite porous scaffold btained using the proposed method, we computed the magniude and distribution of the von Mises stress on a loading force f 150 N using the finite element method. Here, the material f the Schwarz P unit cells is assumed to be homogeneous, sotropic, and linearly elastic poly-DL-lactide. Fig. 11(a) and (b) how the magnitude and distribution of the von Mises stress on he modified and original scaffolds, respectively. The simulation esults confirm that the stresses on the modified scaffold are ore smoothly distributed than those on the original scaffold. hese results imply that the modified scaffold structure is more table than the original. 4.3. Scaffold with different porosities of TPMS For cell growth and the adhesion of biological tissue, scaffolds should have many pores. The highly porous structure should have a large surface area for cell growth and sufficient volume for blood vessel growth [43\u201345]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000099_s00170-020-05394-8-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000099_s00170-020-05394-8-Figure5-1.png",
        "caption": "Fig. 5 a Idealised CAD and (b) As-manufactured geometry of lattice strut element manufactured in Ti-6Al-4V by SLM",
        "texts": [
            "0 mm were found to be manufacturable if the angle between the strut and the build platen was greater than 35\u00b0. The downward-facing surfaces of struts were consistently found to have significantly greater surface roughness, and many geometric defects were identified at the node elements. An individual lattice structure strut is presented to demonstrate the geometric complexity of the potential imperfections of asmanufactured elements, such as a variable diameter, malformed node elements, and semi-melted powder particles attached to the surface (Fig. 5). The surface quality of as-manufactured MAM components remains a technical challenge for commercial applications, potentially necessitating post-processing, thereby increasing unit cost and lead times [23]. Surface quality has been found to be particularly important for the fatigue-life of dynamically loaded components as surface defects may cause early crack initiation and growth [20]. Surface roughness of MAM may be caused by the stairstep phenomena inherent to layer-wise MAM systems [24]. For example, the scanning electron microscope (SEM) micrograph presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000533_j.jmapro.2021.05.038-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000533_j.jmapro.2021.05.038-Figure3-1.png",
        "caption": "Fig. 3. Power consumption during the SLM process (LP = 200 W, LT = 35 \u03bcm, and SS = 700 mm/s).",
        "texts": [
            " Therefore, in this work, a power analyzer is in series with the SLM machine to obtain real-time power with a 1 Hz sampling rate, which is in conjunction with a MATLAB platform. The MATLAB software is used to transform the time domain power signal to the electrical energy consumption through integral transformation. The orientation and sizes of the printed parts are shown in Fig. 2. Three parts with the same size are printed under the same combination of process parameters in each experiment to avoid randomness of the experimental results. As shown in Fig. 3, the power consumption of the SLM printing process can be mainly segmented into two stages: the manual processing stage and the automatic processing stage. In the manual processing stage, the first layer is selected and melted manually three times to assure that the powder has been bonded on the stainless-steel substrate completely. Besides, the shielding gas and the temperature of the building substrate are prepared to meet the requirements before the laser supply power turns on. The oxygen content in the chamber is set below 0.4% (4000 ppm), which is kept consistent in each experiment. The power energy consumption of the pre-processing stage, including preparing gas and temperature condition, is not considered since this part of the energy is steady and close to each other in all experiments [4]. It can be seen from Fig. 3 that there are some peaks during the printing process, which is mainly due to the movement of the scraper [16] or the restart of the preheating system. During the SLM processing, the preheating system works intermittently. It is also possible that the peaks are due to the low sampling rate of 1 Hz. Obviously, it can be seen that in the automatic melting stage, three parts are melted in each layer. Once one layer powder is melted by the laser beam, the building substrate is lowered one-layer thickness and the new powder is delivered by the scraper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003077_0094-114x(95)00100-d-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003077_0094-114x(95)00100-d-Figure4-1.png",
        "caption": "Fig. 4. Change of reference for velocities.",
        "texts": [],
        "surrounding_texts": [
            "The value of the elements of matrix W depend on the frame used as reference for two reasons. First of all ~ and vo must be represented by their components with respect to the chosen reference frame. Secondly the pole is the point of the body passing through the origin of the chosen reference frame. 3D kinematics and dynamics--I 579 For these reasons, if another frame is chosen matrix W changes because the pole must be the origin of the new reference and _tp and vo must be projected onto the axis of the new reference. Matrix H behaves in the same way as W. If we have two different reference frames (r) and (s) we will indicate the representation of the velocity of a body in the two frames as W(,~ and Wt,) and the acceleration as H(,) and H(s~. Since the two matrices describe the velocity of the same body in two different frames their values are strictly dependent on each other. It is possible to prove (see Appendix A) that they are tensors which transform as: W(,) = Mr.~W(~)M,~ I (8) H(r ) = M,,,H(s) MZ~. 1 , (9) where M,.~ is the position matrix of the reference frame (s) with respect to (r). In other words W(,) and W{,) are the Cartesian representation in (r) and in (s) of a tensor W. The same statement applies to H. The validity of the previous formulas can be proved by expanding the matrices into their blocks and by executing the matrix product. For example the velocity matrix in (r) obtained by applying equation (8) is: W(r ) = -(~(r) -0---0--b-- Vo r I I , ( R tp_()Rt)t . . . . . . . . . . . . . . . I _ r , s s r , s r , s o o o : o where Rr,,~(s)R~,.s is equal to ~(r), that is the angular velocity of the body in (r) and R,.sVo, is the velocity of pole O, projected onto (r). Moreover it is easy to verify that the velocity Vo, of the new pole is: Vo, = R,.,Vo, - _o(,)t,.,. This equation is just a matrix formulation of the following vector formula: L = L + ~ x ( O , - O , ) , where O, and O~ are the origins of the frames (r) and (s), respectively. 580 Giovanni Legnani et al."
        ]
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure3-1.png",
        "caption": "Fig. 3. Illustration of how the same final surface may be produced by different growth velocities. (A) All growth velocities are parallel to each other. (B) All growth velocities are normal to the growth surface",
        "texts": [
            " (27) Holding h 1 , h 2 constant, the integration of Eq. (27) with the initial conditions (26) yields the trajectory of the cell on G with coordinates h 1 , h 2 : xG i (h 1 , h 2 , t)\"x0 i (h 1 , h 2 )#P t 0 (!vg i (h 1 , h 2 , q) dq . (28) At this point, it is of interest to note that in a typical problem of producing a sequence of surfaces G, there may be various different vector growth velocities g which produce the same set of surfaces G. But these will not have the same cell tracks, as indicated in the schematic examples shown in Fig. 3A, B. In Fig. 3A, all g are parallel. In Fig. 3B, all growth vectors are normal to the initial G. If the surfaces G at different times are smooth and g is a continuous distribution, then the successive G surfaces can always be produced by a distribution of g which is always normal to the current G. This is what is usually assumed in studies of bone growth and atrophy due to stress (Cowin 1993; Huiskes et al. 1994). It should be noted that the rate at which mass is created per unit area on G is always given by m5 \"o g \u00b7 n , (29) where n is the normal to G (n is taken positive when pointing into the tissue being created) and o is the density of the new growth or that of tissue being removed, when g \u00b7 n is negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003976_j.matdes.2008.05.024-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003976_j.matdes.2008.05.024-Figure2-1.png",
        "caption": "Fig. 2. Finite element meshes.",
        "texts": [
            " The layered element solid46 allows for up to 100 different material layers with different orientations and orthotropic material properties in each layer. The element has three degrees of freedom at each node and translations in the nodal x, y, and z directions. The layers were assumed perfectly bonded with the surface of aluminum tube. An eight-node solid element, solid45, was used for the aluminum tube. The element is defined with eight nodes having three degrees of freedom at each node translations in the nodal x, y, and z directions. Fig. 2 shows the fill scale finite element mesh for the hybrid aluminum/composite drive shaft. The mapping mesh technique was used for the entire domain. In general, phenomenological strength criteria such as maximum stress and Tsai-Wu criteria are used to detect the failure status of composite laminates. Due to the complexity of failure mechanisms in the hybrid aluminum/composite drive shaft, it is difficult to define an applicable failure criterion [13]. However, it is expected that the shear failure of the hybrid aluminum/composite drive shaft is dominated by properties of carbon and glass fiber/ epoxy composite layers, and the laminate fails just after the shear strain reached maximum failure strain from experimental results in any direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.5-1.png",
        "caption": "Figure 2.5. A cable unwinding from a cylinder.",
        "texts": [
            " 1 0 ) , Rb R (2.18) and the angle between line CA and the fixed line CB is expressed by the involute function, Pressure Angle of a Gear angle ACB inv /fiR 33 (2.19) Another common description of the involute is based on the same idea as the alternative definition given earlier. We consider a cable wrapped round a fixed cylinder of radius Rb , with one end of the cable attached to the cylinder. If the other end of the cable is partly unwound, the path followed by that end will be an involute. If Figure 2.5 were to represent the cable and cylinder, then EA would be the section of cable unwound from the cylinder, and it is obvious that the length of this part of the cable is equal to the arc EB, where the cable was originally wrapped round the cylinder. Pressure Angle of a Gear The pressure angle /fI s of a gear is defined as the gear profile angle /fiR at the standard pitch circle. The profile angle at radius R was given by Equation (2.10), and the pressure angle can be found by setting R equal to Rs in this relation, (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000621_j.mechmachtheory.2021.104319-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000621_j.mechmachtheory.2021.104319-Figure12-1.png",
        "caption": "Fig. 12. FE models of the lightweight gear configuration: (a) whole gears case, (b) six tooth pairs case.",
        "texts": [
            " Nonlinear FE analyses have been performed on the lightweight gear configuration, for a contact position at 88 % of the tooth mesh cycle, from the beginning of the contact path. Simulations have been performed by using 11 different gear pair 3D drawings, one with the whole gears and the others composed of gear bodies and a different number of teeth: first, from 2 up to 22 teeth for both pinion and gear, with a step of 4 teeth; then whole pinion (25 teeth) and 26 to 38 gear teeth, with a step of 4 teeth. Fig. 12 shows the FE model used in the case of whole gears and 6 teeth for both pinion and gear. The applied torque is 200 Nm. Mesh stiffness results, obtained by using the local slope approach of the Cooley et al. method , are reported in Fig. 13 . Furthermore, the percentage difference of the results obtained by using the different configurations has been computed and represented in Fig. 14 , taking the configuration with the whole gears as a reference. The mesh stiffness results obtained by using the complete 3D drawing of the gear pair are 3 % higher, on average, than those obtained by using the simplified one, with 2 and 6 tooth pairs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003274_tcst.2003.815613-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003274_tcst.2003.815613-Figure10-1.png",
        "caption": "Fig. 10. Outline of Cybership II: Feasible thrust domains.",
        "texts": [
            " An alternative version of the QUEST algorithm [22] based on singular value decomposition instead of eigenvalues calculates the ship\u2019s attitude in unit quaternions and converts it to Euler angles, that is the roll, pitch and heading angles. Once the orientation is found, determining the position of the ship is a straightforward operation. It is reasonable to assume that the rudders are effective when applying positive thrust. We are thus allowed to find general thrust vectors inside the shaded areas in Fig. 10. At low speed a surface vessel can be reasonably described by (51) Here, is a vector of North position, East position, and compass heading, respectively. The body-fixed velocity vector contains surge, sway and yaw and is the applied thruster force. The matrix : describes the rotation between body-fixed and Earth-fixed coordinates: (52) and its time derivative can be written where is the skew-symmetric (53) contains the mass of the vehicle, that is the sum of rigid-body and hydrodynamic added mass, and describes linear damping which is assumed to dominate quadratic damping at velocities around zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure5.21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure5.21-1.png",
        "caption": "Fig. 5.21 Jaw crushers a Blake type jaw crusher b Dodge type jaw crusher (http://www.sigmaplantfinder. com/blog/how-do-jawcrushers-work/)",
        "texts": [
            "3 Machine Inventions in Second Industrial Revolution 165 166 5 Second Industrial Revolution modern process and equipment of mineral processing appeared in this period (Singer et al. 1957). Ore dressing is a process separating useful minerals from gangue. Before dressing, the ore must be crushed and ground to very fine particles. Modern crushing machines were not created until steam engines were widely applied. In 1858, an American, Eli Whitney Blake, designed and built the first jaw crusher in the world (Wilson and Fiske 1900), called Blake jaw crusher. Later, the Dodge jaw crusher was created (Fig. 5.21). Now, the latter is more widely used. Jaw crushers are considered one of the most important inventions during the industrialization of the U.S.. In 1881, a gyratory crusher (Fig. 5.22) was invented and built by an American, Philters Gates (Lynch and Rowland 2005). A gyratory crusher (cone crusher) applies continuous crushing action, therefore is more productive than jaw crushers which have intermittent crushing action. In addition, gyratory crushers can crush ore of larger size. Grinding ore with hard balls was one of the oldest techniques"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.15-1.png",
        "caption": "Figure 2.15. A typical basic rack.",
        "texts": [
            " The corresponding systems of gears therefore have the same three values for the pressure angle ~s. To illustrate the effect of the value of ~s on the tooth shape, three gears are shown in Figures 2.12-2.14, each with 36 teeth, and the pressure angles are equal to the three standard values. The pressure angle of 14.5\u00b0 is no longer recommended for new designs, because the teeth are relatively weak, and the gears are subject to a problem known as 48 Tooth Prof i Ie of an I nvolute Gear undercutting, which will be discussed in Chapter 5. A typical basic rack is shown in Figure 2.15. In order that the same basic rack can be used to define the tooth profiles for gears of any size, the dimensions of the basic rack are expressed in terms of the module. The rack pitch is then equal to ~m, and the reference line is the line along which the tooth thickness and the space width are each equal to O.5~m. The essential difference between this basic rack and the one shown in Figure 2.1 is that, in this basic rack, the tooth profiles are rounded near the tips of the teeth. For a gear which is conjugate to the basic rack, the shape of the involute part of each gear tooth is defined by the straight part of the basic rack tooth, while the shape of the gear tooth near its root is defined by the curved section at the tip of the basic rack tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000689_s42835-021-00661-4-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000689_s42835-021-00661-4-Figure3-1.png",
        "caption": "Fig. 3 Diagram of PMSM sensorless control with SMO based on sigmoid function",
        "texts": [
            " Therefore, the sigmoid function is applied to the SMO in this study. The expression of the sigmoid function is In Eq.\u00a0(8), a is a constant used for adjusting the slope of the sigmoid function, and when a is close to infinity, the sigmoid function is transformed into a sign function. According to (6) and (7), the estimated EEMF is The diagram of the estimated position can be obtained from the analysis above, as shown in Fig.\u00a02. The diagram of SMO based on the sigmoid function for sensorless PMSM control is shown in Fig.\u00a03. Phase voltage is calculated based on the voltage of the DC bus and SVPWM switching state. The measured phase currents are transformed into i , i , then i , i are placed into the SMO model with phase voltage, and the position is obtained according to (5) and (9). The key of SMO for PMSM is to ensure that the estimated values can converge to the sliding surface. When the current error is negative, its differential value is positive; when the current error is positive, its differential value is negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003584_we.173-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003584_we.173-Figure5-1.png",
        "caption": "Figure 5. The gear mesh model of two helical gears in contact",
        "texts": [
            " Occurrence of tooth separation is considered non-existent and consequently the modelling of gear backlash is not included. This implies that the spring is always under compression. 4. Coriolis accelerations of gears that are rotating and simultaneously translating (e.g. planets on their carrier) are neglected and all gyroscopic effects as described by Lin and Parker7 are excluded. These assumptions are valid for wind turbine applications, since planetary gear stages in wind turbines are only rarely used as high-speed stages. Formulation of the gear contact forces is based on the model approach shown in Figure 5. \u2022 Co-ordinate systems X\u00a21Y\u00a21Z\u00a21 and X\u00a22Y\u00a22Z\u00a22 are oriented with X\u00a2 along the centreline pointing from gear 1 to gear 2; Z\u00a2 is lying along the axis of rotation. These co-ordinate systems are fixed to the reference frames of the respective wheels (as introduced in subsection one and Figure 4). \u2022 X1Y1Z1 and X2Y2Z2 are fixed to the respective gears and in their starting position they coincide with the corresponding X\u00a2Y\u00a2Z\u00a2. \u2022 ft is the pressure angle of the gear mesh, which is an input parameter. It is defined as the angle measured from the centreline towards the normal on the contact line in the corresponding X\u00a2Y\u00a2Z\u00a2. The sign of this angle changes when the driving direction of the system changes. \u2022 y \u00a21 and y \u00a22 are the angles measured respectively from X\u00a21 to X1 and from X\u00a22 to X2 along the corresponding Z\u00a2: y1 = ft - y \u00a21 and y2 = ft - y \u00a22. \u2022 b is the helix angle, which is positive when the teeth of gear 1 are turned \u2018left\u2019 from a reference position where b = 0; b > 0 in Figure 5. The compression of the linear spring (d) can be written as a function of the vectors and as introduced in Figure 4. Since the spring works always under compression, d should be positive. (2) with d y y y y f b w y w y y y y y f b = - - + - -( ) ( ) - - + + - -( ) ( ) x x y y u u z z X X Y Y 1 1 2 2 1 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 sin sin cos cos cos sin sin cos cos sin sign sign t t q2q1 Copyright \u00a9 2005 John Wiley & Sons, Ltd. Wind Energ. 2006; 9:141\u2013161 DOI: 10.1002/we stiffness matrix and is the force working on the gear in the XYZ systemFb The stiffness value of the linear spring, kgear, is the same as defined in subsection one, namely the ratio of the contact force on a tooth over the resulting displacement of the contact point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure15-1.png",
        "caption": "Fig. 15. Thermal fields. (a) 72-slot/8-pole motor. (b) 48-slot/8-pole motor.",
        "texts": [
            " As stated in Section III-C, the size of the inflection point should be abandoned, and the slots with short slot bottom have advantages on the slot heat dissipation. According to the conclusions, we choose the 72-slot/8-pole motor with slender slots. In order to verify this conclusion, the 72-slot/8-pole motor is Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 01:31:42 UTC from IEEE Xplore. Restrictions apply. compared to the 48-slot/8-pole motor whose slot-pole combination is the same with the motor used in Toyota Prius hybrid EVs. The two motors have the same size except the slot configuration parameters. Fig. 15 shows the thermal fields of the 72-slot/8-pole and 48-slot/8-pole motors in the rated condition. The winding temperature of the 72-slot/8-pole motor is 5.7 \u00b0C lower than that of the 48-slot/8-pole motor. It is clarified that the motor with slender slots have advantages on the slot heat dissipation. The above comparisons illustrate that the final scheme which is selected according to the theoretical analysis has advantage on the improvement of the thermal behavior. An experiment was performed to further evaluate the thermal performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.4-1.png",
        "caption": "Figure 7.4. An undercut gear.",
        "texts": [
            " A comparison of these two equations shows that the fillet circle of a gear is either smaller than the form circle, or sometimes equal in size, but never larger. Undercut Ci rcle In Chapter 5, we described the conditions for no undercutting in a gear, and we pointed out that it is 1130 Miscellaneous Circles preferable, though not essential, to design gear pairs in such a manner that neither gear is undercut. There may be times, however, when some undercutting cannot be av\u00b7oided, and in such cases it is important to know what effect this will have on the contact ratio and the tooth strength. An undercut tooth profile is shown in Figure 7.4. The point where the fillet starts is labelled Au' and the circle through this point is called the undercut circle. The diagram also shows the path followed, relative to the gear, by point Ahc on the cutter, the highest point on the involute section of the cutter tooth profile. This path lies extremely close to the fillet, as we can see in the diagram, particularly near the top of the fi llet. The only methods known to the author of this book, for finding the radius Ru of the undercut circle, all involve some form of trial and error"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure3-37-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure3-37-1.png",
        "caption": "Figure 3-37 Sketch of flow between two rotating cylinders known as Taylor-Couette flow.",
        "texts": [
            " The second is based on 1500 Poincare points and shows a breakup of the toroidal attractor before chaos sets in. The techniques used to measure the motion included laser Doppler anemometry and a differential interferometric method. More recent work involving mode locking and chaos in convection problems has been done by Haucke and Ecke (1987). Taylor-Couette Flow Between Cylinders. A classic fluid mechanics system which exhibits preturbulent chaos is the flow between two rotating cylinders (called Taylor-Couette flow) shown in Figure 3-37. Much work has been done on this system (e.g., see Swinney, 1983, for a review). This flow is sensitive to the Reynolds number R = (b \u2014 a^a^LJv and the ratios b/a and fl^/fl,, where the latter is the quotient of the outer cylinder rotation rate to the inner as well as the boundary conditions on the ends. This 114 A Survey of Systems with Chaotic Vibrations system exhibits a prechaos behavior of quasiperiodic oscillations before broad-band chaotic noise sets in. Other work includes that of Brandslater et al",
            " Figure 6-15 shows the value of the slope of logC(c) versus logc as a function of c. This is characteristic of these measurements. The slope values at small c reflect instrumentation noise, while the values at large c are those for which the size of the covering sphere or hypercube reaches the scale of the attractor. Using such techniques, one can determine how the fractal dimension changes as some control parameter in the experiment is varied. For example, in the case of Taylor-Couette flow (see Figure 3-37), Swinney and coworkers have measures the change in d as a function of the Reynolds number (Figure 6-16; see Swinney, 1985). In another fluid experiment, Ciliberto and Gollub (1985) have studied chaotic excitation of surface waves in a fluid. The surface wave chaos was excited by a 16 Hz vertical amplitude frequency; 2048 points were sampled with a sampling time of 1.5 s or around 300 orbits. Using the embedding Optical Measurement of Fractal Dimension 235 space technique, they measured both the correlation dimension (dc = 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.25-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.25-1.png",
        "caption": "Figure 13.25. Tooth thickness and chordal tooth thickness in the normal section.",
        "texts": [
            " Hence, the radius of curvature, which is equal to the distance moved divided by the angle through which the tangent turns, can be expressed as follows, R (13.118) sin2~R The normal tooth thickness at any radius R is measured along a helix known as the normal helix, which is shown in Figure 13.24 as a line perpendicular to the teeth. Its helix angle is (?r/2-~R)' and its radius of curvature PnR can therefore be found from Equation (13.118), R (13.119) 354 Tooth Surface of a Helical Involute Gear The relation between the normal tooth thickness t ns at the standard pitch cylinder, and the corresponding chordal thickness t nsch ' can be read from Figure 13.25. t 2 P n s sin ( 2 pnnss ) and we use Equation (13.119) to express Pns in terms of the radius and the helix angle at the standard pi tch cylinder, 2 Rs . t ns cos ~s --:2;-- sIn ( 2R ) cos ~s s 2 (13.120) For gears with large amounts of profile shift, it may be more convenient to measure the normal tooth thickness at a radius R which is different from Rs. The chordal tooth thickness is then given by the following equation, proved in exactly the same manner as Equat ion (13.120), R t cos2~R 2 sin( nR 2R ) (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure1.24-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure1.24-1.png",
        "caption": "Figure 1.24. Hysteresis loops for hard, soft, and medium hard magnetic materials, where Mr is the remnant magnetization and He the coercive force.",
        "texts": [
            " The Curie-Weiss law elucidates the relationship between the magnetic susceptibility and the temperature as Magnetic domain is the character of ferromagnetic materials. All of the atomic magnetic moments are aligned in the same orientation within one domain, but the magnetic moment varies from domain to domain. When the spins of all domains have been oriented in parallel, saturation is reached. To achieve this state a magnetic field with some minimum field strength is required. A hysteresis curve is the typical character of ferromagnetic materials. Figure 1.24 gives three types of hysteresis curves which are the X = + M H (a ) T X = + M H T c (b ) T X = + M H T c F ig ur e 1. 23 . M ag ne ti za ti on b eh av io rs o f (a ) di am ag ne ti c an d pa ra m ag ne ti c, ( b) f er ro m ag ne ti c, a nd ( c) a nt if er ro m ag ne ti c m at er ia ls . (c ) T t:: J:j 0 u > ; g ~ ~ O ..... . C '1 :: 1 Z n ~9 :: l \"\" \"> ::0 U t tn Z m \\C u> t::: I \u2022 60 CHAPTER 1 basis of functionality of the ferromagnetic compounds. Starting from a untreated sample, an increasing magnetic field causes an increasing magnetization until saturation is reached",
            " Functional materials always use compounds with ferromagnetism or ferroelectricity because the relationship between the magnetization or the polarization and magnetic field or electric field is nonlinear and has a hysteresis loop. The memory effect makes these materials indispensable in modern technologies and development of smart materials. Computer memories require rate-independent hysteresis loop with the smallest S value. Different applications require different shapes of the hysteresis loops (Fig. 1.24). In solid materials, phase transitions with discontinuity of a physical parameter, for example magnetization, or polarization or dimension of its volume, will induce a discontinuous hysteresis effect, which occurs for instance in ferromagnetism, ferroelectricity, and solid redox reaction (Fig. 1.27a). 1.15.1.4. SELECTIVITY, SENSITIVITY, REPRODUCIBILITY, AND RECOVERABILITY. Functional materials with chemical sensitivity are mandatory for response to a specific change in its chemical environment, such as a specific type of molecules"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003426_iros.2003.1250608-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003426_iros.2003.1250608-Figure2-1.png",
        "caption": "Fig. 2. Model of the System",
        "texts": [
            " Goswami[b] proposed the FRI(Foot Rotation Indicator) where the robot will fall down if the FRI is out of the foot supporting area. For a quadruped robot to walk stably on a sloped surface, Yoneda et a1.[7] and P.B. Wieber[8] studied the stability of the walking systems. Kitagawa et al. [9] proposed the \"Enhanced ZMP\" for the d e g coordination tasks for a humanoid robot. However, there has been no research on the ZMP analysis of a humanoid robot which can take into account several cases of armileg coordination tasks as shown in Fig. 1. 111. Two ZMPs Fig. 2 shows the model of a humanoid robot used in this paper. We assume that the sole and the hand contact with the ground and the environment, respectively. ER and Ei denote the reference coordinate and the coordinate frame fixed to the i-th ( i = I , . . . ,n) link of the robot, respectively. p H j ( = [ X H ~ Y H j Z H ~ ] ' ) , p F j ( = [XFj Y F j ZFj]') ( j = l ,Z ) , and p i ( = [x i y ; 4') denote the position vector of the contact point between the j-th hand and the object, a point included in the contact surface between the j-th foot and the ground, and the origin of E;, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000376_j.commatsci.2020.109648-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000376_j.commatsci.2020.109648-Figure6-1.png",
        "caption": "Fig. 6. Simulation domain for (a) discrete element method modeling of particle spreading, and (b) heat transfer and fluid flow modeling of molten pool dynamics during laser melting.",
        "texts": [
            " The joined type particles were treated in the same manner such that the replacement particle had the same volume as the original sphere. Such volume conservation ensures that the nominal size distribution of powder with non-spherical particles would still follow that measured experimentally (Fig. 1). The powder spreading simulation was developed based on the existing DEM model of a miniature powder bed with spherical particles [24]. In the present model, the non-spherical particles, represented by multi-sphere clumps, were introduced using the two-step procedure described above. Fig. 6(a) shows the spreading process where the particles were dispensed from the powder reservoir onto the build platform by a miniature roller. The input parameters (e.g., friction coefficients between particles) were taken from those used previously [24]. Yade, an open source discrete element method code, was used for such simulation [36]. L-PBF experiments in single track configuration were performed on a Mlab cusing AM machine produced by GE CONCEPT LASER which was equipped with a YLR-100 ytterbium fiber laser with a maximum output power of 100 W",
            " The 3-D, transient molten pool dynamics calculation was performed using the existing heat transfer and free surface flow model reported in [37]. The model numerically solved the governing conservation equations of mass, momentum and energy, and the free surface profile was tracked in an Eulerian grid (i.e., fixed mesh) using the volume of fluid (VOF) method. A detailed description of these questions is available in the literature [1,37]. The computation domain for the molten pool calculation is shown in Fig. 6(b), where the packed structure of powder particles (mixture of spherical and non-spherical particles) was obtained via initialization of the VOF field by importing the information calculated from the DEM model discussed in Section 2.3. The heat input and loss arisen from the laser-particle interaction was described using the following thermal boundary condition: \u2212 \u2202 \u2202 = \u2212 \u2212 \u2212\u03bb T n q q q qin cov rad evp (6) where \u03bb is the thermal conductivity and n is the local surface normal. qin is the laser heat flux given in the form of a Gaussian distribution, and qcov, qrad, and qevp are the heat loss by convection, radiation and evaporation, respectively; definitions of these terms can be found elsewhere [38]",
            " Although there were some experimental measurements reported in the literature [41,42], the absorptivity value is strongly dependent on the type of powder and the laser processing parameters [1]. In this study, the absorptivity was calibrated by matching the calculated track height and penetration depth on the transverse cross section to the experimentally measured values. The calibrated absorptivity was equal to 0.8, a value expected in the presence of keyhole [42]. The computational domain shown in Fig. 6(b) had dimensions of 1000 \u03bcm \u00d7 500 \u03bcm \u00d7 270 \u03bcm, and it contained 731,000 elements or cells for the case where the smallest mesh size used was 4 \u03bcm. To simulate one 750-\u03bcm-long laser melting track that involved 1.25 ms laser time and 1.25 ms cooling, it took about 12 h of CPU clock time in a workstation with 16-core AMD Ryzen Threadripper 1950X processor and 32 GB RAM. For mesh convergence test, a comparable simulation case with the minimum mesh size of 2 \u03bcm was conducted, and the CPU clock time used to complete the single track simulation jumped to 50 h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003123_s0094-114x(03)00065-x-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003123_s0094-114x(03)00065-x-Figure3-1.png",
        "caption": "Fig. 3. 3-PRPS hybrid manipulator.",
        "texts": [
            " In this case the legvectors are given by ere onwards, the subscript i is used to denote the ith leg. Si \u00bc t\u00fe qi bi; \u00f04\u00de where t \u00bc OO0, bi \u00bc OBi, and qi \u00bc O0Pi is the vector from the origin O0 of the platform frame to the platform connection-point (Pi) expressed in global reference frame, given by qi \u00bc Rpi; \u00f05\u00de where pi \u00bc O0Pi (in local frame) and R is the rotation matrix given by R \u00bc cos h sin h sin h cos h : \u00f06\u00de If R \u00bc \u00bd Fx Fy M T denotes the output forces and moment with respect to the frame at O0, the force-transformation matrix is given by H \u00bc s1 s2 s3 q1 s1 q2 s2 q3 s3 : \u00f07\u00de Fig. 3 shows a 3-PRPS hybrid manipulator. This manipulator has two prismatic actuations in each leg. Denoting the fixed axis direction in a leg by ki, the leg-vector is given by Si \u00bc t\u00fe qi bi Diki; \u00f08\u00de where the displacement of prismatic joint at the base of the leg Di is given by Di \u00bc \u00f0t\u00fe qi bi\u00de ki: \u00f09\u00de The platform-connection-points are transformed according to Eq. (5), where the rotation matrix R is given in terms of roll-pitch-yaw angles as R \u00bc RPY \u00f0hz; hy; hx\u00de \u00bc Rot\u00f0z; hz\u00deRot\u00f0y; hy\u00deRot\u00f0x; hx\u00de: \u00f010\u00de The force-transformation matrix for R \u00bc \u00bd Fx Fy Fz Mx My Mz T is given by H \u00bc k1 k2 k3 s1 s2 s3 q1 k1 q2 k2 q3 k3 q1 s1 q2 s2 q3 s3 : \u00f011\u00de Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003503_s0022-460x(03)00127-5-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003503_s0022-460x(03)00127-5-Figure3-1.png",
        "caption": "Fig. 3. Ball loading at arbitrary azimuth angle, cj :",
        "texts": [
            " In the case of the outer-race rotating type of ball bearing, the outer race has translational and angular motion and the inner race is stationary during the rotation of the ball bearing. Similar expressions can be derived to determine the distance between the position vectors of the groove radius center of the inner and outer race. Applying the Pythagorean theorem to Fig. 2, the following equations can be obtained [7,9]: Dzj Xzj 2\u00fe Drj Xrj 2 lij \u00fe dij 2\u00bc 0; X 2 zj \u00fe X 2 rj loj \u00fe doj 2\u00bc 0; \u00f011\u00de where dij and doj are the elastic deformation of the contact point between the ball and each race. Fig. 3 shows the free-body diagram of the ball acted by the contact forces of the inner and outer race, fij and foj and the centrifugal force and gyroscopic moment of a ball, Fcj and MGj: In Fig. 3, D and z are the ball diameter and the angle between the spinning axis of the ball and the bearing centerline, and lij and loj are the constants determined by the race control theory [9]. Force equilibrium of a ball can result in the following equations [7,9]: fij sin aij foj sin aoj lijMGj D cos aij \u00fe lojMGj D cos aoj \u00bc 0; fij cos aij foj cos aoj \u00fe lijMGj D sin aij lojMGj D sin aoj \u00fe Fcj \u00bc 0: \u00f012\u00de The contact force between the ball and race are expressed by using the Hertzian contact theory as follows: fij \u00bc Kijd 1:5 ij ; foj \u00bc Kojd 1:5 oj ; \u00f013\u00de where Kij ; Koj ; dij; and doj are the load\u2013deflection constants and deflections of the contact point between the ball and each race"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure1-1.png",
        "caption": "Fig. 1. Mechanical structure and body-fixed coordinate systems of the Kuka KR 500 industrial robot.",
        "texts": [
            " Section 5 shows the procedures that realize the stiffness model, and the deflections affected by different factors are separated. Section 6 identifies the compliance parameters of links with their FEA models. Section 7 gives several numerical examples to show the application of the model. The experimental validation is presented in Section 8 to confirm the correctness of the proposed model. Finally, the conclusion is drawn in Section 9 . In this study, a Kuka KR 500 industrial robot equipped with a milling spindle illustrated in Fig. 1 is taken as an example. It is a heavy-duty industrial robot with a rated payload of 500 kg. To equalize the load moment about joint 2, a hydropneumatic gravity compensator is adopted. To facilitate the analysis, a series of body-fixed coordinate systems are attached to the links and the end-effector. The origin and directions are determined by joint axes and link centerlines, which are represented as { O 1 } ~ { O 6 } and { O E } as illustrated in Fig. 1 . The orientation matrices of { O 2 }~{ O 6 } and { O E } with respect to { O 1 } can be expressed as R 2 = R 1 Rot ( Z 1 , \u03b81 ) , R 3 = R 2 Rot ( Y 2 , \u03b82 ) , R 4 = R 3 Rot ( Y 3 , \u03b83 ) R 5 = R 4 Rot ( X 4 , \u03b84 ) , R 6 = R 5 Rot ( Y 5 , \u03b85 ) , R E = R 6 Rot ( X 6 , \u03b86 ) (1) where \u03b8 i represents the rotation angle of joint i ( i = 1, \u2026, 6), Rot represents a rotation matrix around the corresponding axis with \u03b8 i , R 1 is an identity matrix, R i is the orientation matrix of { O i } with respect to { O 1 }, and R E is the orientation matrix of { O } with respect to { O }",
            " As Kuka KR 500 is widely used in robotic machining, many models have been proposed to identify the joint compliance parameters of this type robot [18 , 20 , 41 , 42] , and the values of the identified joint compliance parameters are different. The joint compliance parameters used in this study are listed in Table 1 , which were identified by Gu\u00e9rin et al. [41] based on the conventional stiffness model. The link compliances were identified on the basis of CAD models and FEA methods. For each link, a local frame is established with the origin and directions as shown in Fig. 1 . FEA-based virtual experiments are conducted in the software ABAQUS to identify the compliance parameters of each link with respect to their local frames [43 \u201345] . Data for FEA is extracted from product specifications and typical materials properties. The compliance matrices of all six links are identified as listed in Table 2 . Link 1 is taken as an example to illustrate the way to obtain the compliance matrix. After fixing the link at joint 1, a unit force is exerted at joint 2 along the X 1 -axis",
            " According to the defined body-fixed coordinate systems, it has C 1 ( 6 , 6 ) = C J 1 + C L 1 ( 6 , 6 ) , C 2 ( 5 , 5 ) = C J 2 + C L 2 ( 5 , 5 ) , C 3 ( 5 , 5 ) = C J 3 + C L 3 ( 5 , 5 ) C 4 ( 4 , 4 ) = C J 4 + C L 4 ( 4 , 4 ) , C 5 ( 5 , 5 ) = C J 5 + C L 5 ( 5 , 5 ) , C 6 ( 4 , 4 ) = C J 6 + C L 6 ( 4 , 4 ) (32) In this section, the deflections of the Kuka KR 500 industrial robot caused by the external force, link weights, and gravity compensator are numerically investigated using the developed stiffness model. The dimensional parameters of the robotic manipulator are shown in Table 3 . The mass of each link is given in Table 4 , and the locations of the corresponding mass centers are given in Table 5 . Table 6 lists the parameters of the gravity compensator. The configuration shown in Fig. 1 is defined as the initial configuration where the movements of all joints are zero. All the data are extracted or estimated from the product specifications or the 3D model. According to Eq. (21) , the balancing force generated by the gravity compensator is plotted in Fig. 10 . The force is exerted by the piston rod on link 2. It shows that force varies with \u03b82 (-40 \u00b0 \u2264 \u03b82 \u2264 110 \u00b0), and the minimum balancing force appears when \u03b82 is zero. The force can be adjusted by modifying the pre-charging pressure ( P 0 ) of the accumulator with nitrogen gas at the initial configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002771_s0924-0136(00)00850-5-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002771_s0924-0136(00)00850-5-Figure5-1.png",
        "caption": "Fig. 5. Design of: (a) the injected part; (b) the injection mold.",
        "texts": [
            " 4 shows the fabricated part using the third operation parameters. The ripple effect at the outer surface still existed, but it was much lesser than that of the second operation parameters. The ripple edge can be even further improved if the machining operation is applied for every clad and the layer thickness is further reduced. A mold fabricated by the hybrid processes of SLC and milling was used in a metal powder injection machine. The injected part and the associated mold were designed as shown in Fig. 5. The thickness of the injected part was 4 mm with a sloping surface. The dimensions of the injected part were 72 mm length and 13 mm width. The base of the core was a rectangular solid with dimensions of 112 mm 40 mm 13:5 mm. The injected part of the mold was fabricated using the hybrid processes of SLC and milling. The runner of the mold was designed and fabricated and is also shown in Fig. 5. In order to reduce the building time of the mold, the layer thickness of the fabrication parameters was set at 0.5 mm, and then the layer pro\u00aele of the cladding path was calculated according to the design of the mold. The layer pro\u00aele of the cladding path is presented in Fig. 6. As shown in this \u00aegure, the middle part of the \u00aerst four layers was in the shape of the injected part, but the dimensions of the pro\u00aele were increased. Both the runner and the cavity of the mold were fabricated together in the last four layers",
            " The dimensions of the mold cavity were measured at eight different positions. The average error of the mold cavity was about 0.15 mm. The objective of the mold modi\u00aecation is to investigate the feasibility of the mold modi\u00aecation and repair using the hybrid processes of SLC and milling. An original mold was designed and machined using CNC from raw material in mild steel with 17.5 mm height, 112 mm length, and 40 mm width. The geometry of this original mold was the same as that of the mold used in Section 4 as shown in Fig. 5. The shape of the machined mold was similar to the hybridprocessed mold as shown in Fig. 7. The new modi\u00aeed mold as shown in Fig. 8 was to lay down four clad layers to make another rectangular island at the middle of the original machined mold. Only the SLC process was applied to build up the island, because the milling head was too big to approach the mold cavity. Because the milling operation was not used to smooth the top surface of the modi\u00aeed mold, the shape of the island was not as sharp as that of the mold"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003347_anie.199105161-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003347_anie.199105161-Figure4-1.png",
        "caption": "Fig. 4. Construction of a film sensor (Kodak), which works on the zero point potentiometry principle.",
        "texts": [
            "[481 These too offer the advantages of miniaturized sensors which can be economically mass-produced. One commercially available 501 is based on the principle of zero-point potentiometry. In this one-shot disposable sensor, the measuring and reference systems are identical, and as the pair are made under identical conditions from the same materials the potential difference with the relevant membranes in contact with the same solution is zero. If one now deposits on one of the sensor surfaces a reference solution of known concentra- tion, and on the other the solution to be tested (see Fig. 4), according to the Nernst equation the observed potential difference gives a direct measure of the concentration difference between the two solutions for the relevant measured ion species (concentration meter design). The errors that are pos sible in difference methods of this sort (where no transport of samples is involved) are very small, as the problems with conventional reference electrodes (variations in potential due to diffusion), ageing effects, and electrode poisoning effects are avoided",
            " Figure 14 shows an example of an amperometric catheter electrode for measuring 0, partial ISFETs have proved successful mainly in medical technology. Up to now pH-ISFETs have become commercially available and are used for determining acidity in blood and serum (whose normal pH value is 7.41) and other body fluids. Another technological application is in the photographic industry; here ISFETs are used in process control, to maintain important parameters such as the concentrations of H@ and Ag@ ions at constant levels.[102] The Ektachem film electrodes mentioned earlier (cf. Fig. 4) can be used as one-shot disposable sensors in medical applications. The Kodak Ektachem DT 60 is a commercially available 50 . and can be used for the determination of KO, NaO, Cle and other substances. Figure 15 shows a film sensor of this type for potassium. Potentiometric sensors can be used for environmental protection both in laboratory investigations and on-line applications. One task that they can perform is the continuous monitoring of NO: and NHT concentrations in groundwater and drinking water"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000509_j.ijimpeng.2020.103671-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000509_j.ijimpeng.2020.103671-Figure4-1.png",
        "caption": "Fig. 4. EBSD images for the constituent material with specimens extracted from the (a) top, (b) front and (d) side surface of the (c) additively manufactured block. Long and slender grains are observed along the printing direction, with an average grain size of about 20\u03bcm and at least one order of magnitude of spread in the grain size.",
        "texts": [
            " A photograph of a fabricated specimen is given in Fig. 3b. Due to limitations in the manufacturing process, all shell-lattice specimens are built along the [1 1 0] direction (diagonal on specimen surface). Consequently, the uniaxial compression tests conducted on the lattice's cubic surfaces compare to testing on 45\u00b0 and 90\u00b0, with respect to the building direction. Electron Back Scatter Diffraction (EBSD) images of the polycrystalline microstructure are obtained from three orthonormal surfaces of the parallel sheet structure (Fig. 4c). The extracted samples are processed by mechanical grinding with silicon carbide paper followed by final polishing using a 60 nm alumina colloid. EBSD acquisitions are then conducted on an FEI Scios dual beam SEM at an accelerating voltage of 20 kV. A typical scan area of 500 \u00d7 500 \u00b5m is sought with a step size of 1\u00b5m. The corresponding inverse pole figures (IPF) are shown in Fig. 4. The grains feature irregular shapes and large variations in size compared to conventional cold-rolled 316L (e.g. [28]), ranging from less than 10\u00b5m to more than 100\u00b5m. A morphological anisotropy originating in a heterogeneous pattern of the martensitic grain boundaries is clearly visible. The majority of the grains are inclined towards the printing direction, exhibiting aspect ratios of up to 17:1. These observations are in line with the work of others (e.g. Thijs et al. [38], Riemer et al. [29], Wang et al [39], Suryawanshi et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003004_1.1585087-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003004_1.1585087-Figure2-1.png",
        "caption": "FIG. 2. The proposed geometrical characteristics.",
        "texts": [
            ", I0 5(2/prl 2) Pl is intensity scale factor (W/m2, Pl is the laser average power ~W!, and I is the laser beam intensity profile (W/m2). When laser beam pulse is on d51 and when laser beam pulse is off d50 as discussed by Frewin et al.14 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: 194.47.65.106 On: Mon, 20 Oct 2014 07:47:09 \u2022 Power attenuation is considered using the method developed by Picasso et al.7 with some minor modifications. Figure 2 shows the proposed geometrical characteristics in the process zone which is used in the development of the following equations. Based on their work Pw5PlSbw~u!S12 Pat Pl D1hpbp Pat Pl 3H11@12bw~u!#S12 Pat Pl DJD, ~8! 5bPl , 5bE G IdG, where Pat Pl 55 m\u0307 2rcrlrpvp cos~ujet! if rjet,rl m\u0307 2rcr jetrpvp cos~ujet! if rjet>rl. ~9! In these equations, m\u0307 is powder feedrate ~kg/s!, rc is powder density ~kg/m3), rl is radius of the laser beam on the substrate ~m!, rp is radius of powder particles ~m!, vp is powder particles velocity ~m/s!, u jet is the angle between powder jet and substrate ~deg!, r jet is radius of powder spray jet ~m!, bw(u) is workpiece absorption factor, bp is particle absorption factor, hp is powder efficiency, and b is the modified absorption factor. If we assume, the absorption of a flat plane inclined to a circular laser beam depends linearly on the angle of inclina- tion u as shown in Fig. 2 and bw(0) is the workpiece absorption of a flat surface, bw(u) can be calculated from bw~u!5bw~0 !~11awu!, ~10! where u is the angle shown in Fig. 2 and aw is a constant coefficient obtained experimentally for each material.15,7 The powder efficiency hp can be considered as the ratio between the melt pool surface and the powder stream\u2019s area ~Fig. 2! as hp5 Ajet liq A jet , ~11! where A jet liq is the intersection between the melt pool area on the workpiece and powder stream, and A jet is the cross section area of the powder stream on the workpiece. \u2022 The temperature dependency of density, thermal conductivity, specific heat, emissivity, and absorption coefficient are considered in the modeling. \u2022 In order to reduce the computational time and have a good estimation of hc , a combined heat transfer coefficient for the radiative and convective boundary conditions is calculated based on the relationship given by Goldak16 and Yang17 hc524"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000245_ijvd.2019.109873-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000245_ijvd.2019.109873-Figure8-1.png",
        "caption": "Figure 8 Step-cone pulley design (see online version for colours)",
        "texts": [
            ", 2019a), spotted hyena optimiser (SHO) (Dhiman and Kumar, 2017), RankiMDDE, TLBO, ABC, mine blast algorithm (MBA) (Sadollah et al., 2013), WCA, and GA (Gupta et al., 2007). The results of the reported methods are summarised in Table 10. It is clear that the proposed method and MFO algorithm can obtain the best results compared with other optimisers in terms of best (\u201385546.801669). Moreover, NAMDE is the best algorithm for this problem based on the lowest values for the mean, worst and standard deviation of \u201385546.801669, \u201385546.801669, and 6.5705E-11, respectively. The four step-cone pulley problem, Figure 8, must be designed for minimum weight (Rao et al., 2011). The problem include five variables, the diameters of each step di (i = 1, ..., 4) and the width of the pulley w. A total of eleven constraints are considered, of which three are equality constraints and eight are inequality constraints. The step pulley transmitted at least 0.75 hp, with an input speed of 350 rpm and output speeds of 750, 450, 250 and 150 rpm. For this problem NAMDE is compared with MFO, ALO, GWO, WOA, TLBO and ABC, the comparison results are given in Table 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000250_tie.2018.2890494-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000250_tie.2018.2890494-Figure2-1.png",
        "caption": "Fig. 2. Prototype of the proposed AFPMSM",
        "texts": [
            " A multi-physics model is established to calculate the vibration of the AFPMSM in Section IV, the modal, electromagnetic and vibration test are performed to validate the accuracy of the multi-physics model. In Section V, the vibration behaviors of the two types of dual-three phase winding are compared with the three-phase winding with considering the current harmonics induced by inverter. The vibration reduction mechanism of the novel detached winding is discussed. Finally, the vibration experiments are carried out to validate the theoretical results. The axial flux PMSM configuration and the prototype of this AFPMSM are shown in Fig. 1 and Fig. 2 respectively. The rotor is sandwiched by two stators to balance the dualside axial attracting force two stators created. Two stators are directly connected to the front and end cover, and the permanent magnets are embedded in the nonmagnetic rotor support. In order to increase the utilization rate of slot area and reduce the machine end winding length, fractional-slot concentrated winding (FSCW) is adopted. The main dimensions of the AFPMSM is listed in Table I. The two types of dual-three phase winding applied on the AFPMSM have been introduced in previous research [22], [23]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000589_j.matdes.2021.109751-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000589_j.matdes.2021.109751-Figure1-1.png",
        "caption": "Fig. 1. Build geometry, (a) printed walls, (b) tool path showing a continuous bead and the walls with 34 layers, and (c) location of thermocouples. Build plates and the table were instrumented with thermocouples to validate the thermal model of printing.",
        "texts": [
            " The ORNL and Dassault Systemes [30] created and tested models to predict and manage temperature, distortion, and residual stresses in MBAAM parts. In addition, we used the High Flux Isotope Reactor (HFIR) neutron diffraction facility to measure the residual stresses and compare the measurements to predicted results. The high-resolution neutron diffraction residual stress measurements agreed very well to the simulation results. The developed models can be used on typical desktop computers and can provide predictions of distortion and residual stresses that are sufficiently accurate for practical applications. The two parallel walls in Fig. 1 were designed to easily fit into the neutron imaging workspace without the need for major repositioning. Each wall had approximate dimensions of 304.8 mm (L) 13.3 mm (W) 78.5 mm (H). The printing toolpath was created using ORNL Slicer software that translates the standard Gcode output to the printing machine input command [28]. Each part was divided into layers and beads in Fig. 1(b). Each layer consists of one continuous bead resulting in two tracks 13.3 mm width, starting and stopping at the same place. The parts were printed simultaneously in a layer-by-layer fashion, growing both parts at the same time. A layer thickness is 2.31 mm, so each wall has 34 layers for 78.5 mm wall height. The material was L59 Lincoln wire (ER70S7 by AWS) [31], which is a mild steel used for common welding applications. After completion of the printing, only one wall was stress-relieved through heat treatment to provide comparison for neutron measurements",
            " Thermal radiation and surface convection are defined as a combined heat transfer coefficient to consider heat loss through the surrounding environment [39]. The equation is given below, hcomb \u00bc e 24:1 10 4 T1:61 \u00f011\u00de where T is the temperature, and e is the material emissivity. The dimensions of the wall were 304.8 mm (L) 13.3 mm (W) 78.5 mm (H). The dimensions of the base plate were 609.6 mm (L) 76.2 mm (W) 25.4 mm (H), and the dimensions of the table were 1219.2 mm (L) 914.2 mm (W) 73.0 mm (H) showed in Fig. 1. A characteristic mesh size of 2.3 mm for the wall and build plate and of 12.1 mm for the base plate were used to enhance computational efficiency. The FEM model had 292,032 hexahedral elements in the wall, build plate and base plate. Elements of type DC3D8 and C3D8 [37] were used for thermal and structural simulation, respectively. The experiment had four clamps that held the base plate to the table, two on each side. The build plate was assumed to be fully constrained to the base plate using the tie constraint as illustrated in the inset of Fig",
            " 7 compares the temperature distribution between (a) concentrated and (b) Goldak heat source models. The two heat sources created the same (or closely analogous) temperature profile in the wall region. In the present study, the concentrated heat source was used since the Goldak heat source requires more refined time and space resolution. As seen above, an iterative approach was used to match the measured and simulated temperature profiles. Fig. 8 shows the experimental thermal readings at stations T1, T2, T4 and T6 (shown in Fig. 1). Two trial simulations were compared to the temperature readings for calibration of the gap conductance value. Generally, both gap conductance values result in good agreement with the measured values. Still, since the trial 7 (v7) overpredicted the temperature by approximately 30 C at the beginning of T1 and T2, trial 5 (labeled v5) was finally chosen for the thermal simulation. The value of gap conductance for trial 5 was given in Table 1. In the experiment, the displacement in the build direction (U3) was measured at the bottom center of the base plate, along the Yaxis. A nodal path was created in the simulation to compare with the measured distortion. Since the trend was analogous in both the left and right walls (shown in Fig. 1), validation was only performed for the right wall. The upward distortion that was found at the side edges of base plate in Fig. 9(b) is consistent with the trend of the measured values. The maximum measured distortion was 1.77 mm at the left edge of base plate, while the predicted distortion was 1.52 mm at the same location. The residual stress contours were plotted after the clamp restraints were released. During the printing, the steel base plate acts as a heat sink and was included in the model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure12-1.png",
        "caption": "Fig. 12. A singular con\u00aeguration of class (RO, II).",
        "texts": [
            " An example is obtained from the con\u00aeguration in Fig. 10 by a small rotation of subchain C about SC 1 . (RPM, RI, RO, II, IO) has 12 con\u00aegurations and a representative can be obtained from Fig. 9 by a small rotation of subchain C about SC 1 . (4) RO- and II-type singularities There are 15 con\u00aegurations that are of the RO and II types but are not IIM nor RPM-singu- larities. From Equation (12), the conditions for RO-type singularity are: (a) Either Co must be in the plane ABC (Fig. 11), or (b) The point A must be in the plane of subchain B (Fig. 12), i.e. b_mB 1 . (5) RI- and IO-type singularities There are 15 con\u00aegurations which satisfy (viii) without being RPM or IIM-type. In these con\u00aegurations the subchain A is singular or one of the other two serial chains is fully extended. (6) Classi\u00aecation of {4} [ {5} The last three singularity classes are obtained as the intersection and di erences of {4} and {5}. (RI, IO) and (RO, II) have 15 con\u00aegurations, while (RI, RO, IO, II) is of dimension 4. Thus, for the mechanism considered in this example there are 13 di erent classes of singularities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0001704_jphysiol.1913.sp001601-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001704_jphysiol.1913.sp001601-Figure16-1.png",
        "caption": "Fig. 16.",
        "texts": [
            " If a current was passed from the platinum in C to that in B the nerve was excited at the lower end of the slot between C and B, the cathode being the point where the density of current in the nerve sud(denly decreased owing to the increase of the sectional area of the Ringer's solution surrounding it. In a similar way the nierve could be excited at the lower end of the slot between D and C. The method used here is essentially the same as that used for localising the excitation in the 'fluid electrodes' which I have described elsewhere2. There is no danger with this method of exciting elsewhere than close to the slot 1 This drawing may be more easily understood by comparison with Fig. 16, which is a plan of a trough differing from that of Fig. 5 only in the number and the size of the chambers. 2 This Journal, xxxvii. p. 114. 1908. See also Proc. Physiol. Soc. p. xxxii. 1913. AQ0 ACTION OF ALCOHOL ON NERVE. until the current-strength is raised to such an extent that its density in the whole chamber becomes equal to that which it previously had in the slot itself, and even then excitation will occur within the chamber B or C and not in the part of nerve which has passed out into the chamber A",
            " is more than 4-5 times that of the threshold can excite the nerve at a time earlier than the least interval for muscular summation, and consequently the earliest time at which it will produce muscular summation will be affected by the decrement which the impulse undergoes on its way to the muscle. In this experiment the strengths of stimulus chosen for these two purposes were respectively twice and eight times the threshold value for the resting nerve; their positions on the curve are shown at A and B in Fig. 9. While the Ringer's fluid continued to flow determinations were made Fig. 16 shows a trough with two chambers for the nerve. It differs in the length of the chambers from that used in the present experiments. 486 ACTION OF ALCOHOL ON NERVE. repeatedly of the threshold current-strength and the interval for muscular summation with both the strong and weak second stimulus. In describing the results obtained I shall refer to the former interval as the 'least interval for muscular summation,' since no stronger stimulus could give muscular summation at a shorter interval; the other interval I shall call the 'time of recovery' of the nerve for the chosen strenath of stimulus, since it involves no factor other than the strength of stimulus and the rate of recovery of the nerve",
            " 6, in which recovery was complete, is to be taken as evidence that the threshold is affected by the alcohol before conductivity is impaired. 494 It should be noticed that the difference observed here is one of three minutes only, and the observations of each quantity cannot be made at intervals of time less than two to four minutes in an experiment involving also observations on the rate of recovery. In order to get more evidence on this point I made a series of experiments in which the least interval for muscular summation and the threshold current-strength were the only quantities observed. The trough used (Fig. 16) had an alcohol chamber 30 mm. long, whereas that used in the experiments just described was 18-5mm. long; the greater length of the narcotised nerve would make a small decrement easier to detect. The method was otherwise identical with that of the other experiments in which a 0/0 alcohol in Ringer's solution was used. Before each experiment began the recovery curve was mapped out for the preparation in Ringer's solution (as in Fig. 9), so that the stimulus chosen for measuring the least interval for muscular summation might be of the correct strength to fall on the vertical part of the curve",
            " We measured the least interval for muscular suimmnation first with two stimuli applied to the same point on a frog's sciatic nerve, and then with the first stimulus applied at a point about 15 mm. distant from that on which the second fell. In the second case the interval for muscular summation was the longer by a time approximately equal to that taken in conduction between the two points of stimulation. For the present purpose I have modified the experiments slightly in order to avoid certain sources of error. The preparation was set up in the chamber shown in Fig. 16. The nerve passes through two constrictions A and B. A is mnade tight with vaseline, B is left open to allow the Ringer's solution or alcohol to pass. There are four platinum spirals in the chamber, connected as shown to the wires CD E F. If the current passes from C to D it stimulates at the point Proc. Roy. Soc. B. LXXXv. p. 510. 1912. 2 Arch. f. (Anat. u.) Physiol. p. 255. 1893. 3 This Journal, XLII. p. 495. 1911. 499 of exit of the nerve from B; if it passes from E to F it stimulates at the point of exit from A",
            " The arrangement of the circuit is shown in Fig. 17 where CDEF are the platinum spirals in the chambers, S and P are the secondary and primarv coils, and K1 K2 the keys of the pendulum. S,A is uised for getting the first stimulus at A; when this is required 500 K. LUCAS. ACTION OF ALCOHOL ON NERVE. the right hand way is plugged at a. S1B gives the first stimulus at B when the left hand way is plugged at b. S2 always gives the second stimulus at A. A third precaution is that there must be two separate platinum coils (as at D and E in Fig. 16) for leading the current into the central chamber. If the coils S1A and S1B are connected to a common platinum coil in the central chamber the coil SIB always stimulates at A as well as at B owing to shunting of its current round S1A. In my early attempts to use the method I neglected this precaution, and found the interval for muscular summation always the same whether S1A or S1B was nominally in action. It should be noticed that in this method the chamber in which the muscle lies always contains Ringer's solution, and the alcohol is applied only to the part of the nerve above A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003004_1.1585087-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003004_1.1585087-Figure3-1.png",
        "caption": "FIG. 3. Sequence of calculation in the proposed numerical model.",
        "texts": [
            " The new deposited layer creates a new tiny object on the previous domain which is limited to the intersection of powder stream and melt pool and its height is given by Dh5 m\u0307Dt prjet 2 rc , ~13! where Dh is the thickness of deposited layer ~m! and Dt is the elapsed time ~s!. The temperature profile of the added layer is assumed to be the same as the temperature of underneath layer for numerical convergence, which will be discussed in the end of this section. The new temperature profile of the combined workpiece and the layer of powder is then obtained by repeating step 1. Figure 3 shows the sequence of the proposed numerical modeling. In the left side of the figure, a moving laser beam is shown while in the right side the deposition of coating material ~step 2! is presented. The numerical solution is carried out in two different time steps. The first one is the time between two deposition steps and the second one is the time step for calculating the melt pool area. After performing step 2 and before repeating the first step, the following corrections are applied. \u2022 All thermophysical properties and absorption factor b(0) are updated based on the new temperature distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003941_tmag.2006.870936-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003941_tmag.2006.870936-Figure1-1.png",
        "caption": "Fig. 1. Two-dimensional transverse cross section of the studied motor.",
        "texts": [
            " In order to check out the validity of the model a comparative study with Flux-2D software has been Digital Object Identifier 10.1109/TMAG.2006.870936 done; in the end, some simulation results are shown to validate the proposed model. The studied motor is a permanent magnet synchronous one for which the classical positioning of the stator and the rotor are inverted, i.e., \u201creversed structure.\u201d This machine is available at the L2ES laboratory and it is integrated in a bicycle wheel \u201cengine-wheel.\u201d Fig. 1 shows the transverse cross section of one of the six pairs of poles of the motor. For reasons of symmetry and by neglecting the extremity effects, one pole pair of the geometry is sufficient to model the entire machine. The proposed permeance network which replaces the studied motor is a three-phase equivalent circuit. The main permeances are computed along the main flux paths and the leakage permeances are computed along the leakage flux paths. The latter have 0018-9464/$20.00 \u00a9 2006 IEEE either their own equivalent permeances or can be modeled by a common equivalent permeance in the three phase equivalent circuit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003675_0022-0728(90)87185-m-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003675_0022-0728(90)87185-m-Figure6-1.png",
        "caption": "Fig . 6 . Cyclic voltammograms of the Au electrode modified by 2,3-didrloro-1,4naphthoquinone using cysteamine (1); of the same electrode after 5 min incubation in 0 .1 M Tris+HC1 buffer (pH 8 .0) containing 0.02 M cysteamine and rinsing with ethanol (2) ; and of the same electrode after repeated modification by 1,4-naphthoquinone and rinsing with hot ethanol (3) . 0 .01 M boric buffer, pH 9 .18, potential scan rate, 0 .167 V/s.",
        "texts": [
            " However, application of SH or S-S groups as \"anchors\" forming a very stable bond with the electrode allows the organic layer to be desorbed easily from the electrode surface and a new layer to be obtained . For this purpose, the chemically modified electrode is treated with a solution of cysteamine, which replaces the initial organic layer and forms a new layer containing free amino groups at the electrode surface. After that, treating the electrode with another naphthoquinone allows a chemically modified electrode to be obtained with changed redox properties. Figure 6 shows cyclic voltammetric curves recorded before and after the replacement of 2,3-dichloro-l,4-naphthoquinone amino derivative by a similar 1,4-naphthoquinone amino derivative at the electrode . The pure metallic surface is not regenerated when the structure of the chemically modified electrode is changed. On the contrary, the electrode surface remains covered with cysteamine, as seen from the small capacity current for the electrode obtained after desorption of the initial quinone . The kinetics of organic layer replacement from the electrode surface is different for the Pt and Au electrodes "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure16-1.png",
        "caption": "Fig. 16. Vertical residual displacements (unit: mm) for volume density of 0.19 through (a) half-size detailed modeling, (b) half-size homogenization-based modeling, and (c) experimental measurement.",
        "texts": [
            " Then the standard CAD file of a solid block beam was imported into the software as a reference. The reconstructed build model was aligned to the CAD model based on some shared features like fixed bottom surface. After the best alignment was obtained, the software could compare deviations between the aligned surfaces and provide displacement distribution as the result. Taking the case of volume density 0.19 as the example, the displacements in the build direction obtained by the detailed simulation, the homogenization-based simulation, and experimental measurement are shown in Fig. 16 for comparison. The maximum displacements in the build direction are 0.46, 0.45 and 0.43mm in the Fig. 16(a)\u223c(c), respectively. These results show that the simulation based on homogenized inherent strains and material properties is in good agreement with the detailed simulation and experiment. Uncertainty of such experimental measurement mainly comes from device measurement resolution and large gap size between walls. For thin-walled lattice structures with low volume density like 0.19 as shown in Fig. 16(c), the scanned point cloud data could be affected by the large hollow features between thin walls. It is difficult to precisely reconstruct the thin walls given that the thickness is just 0.1mm on average and scanning resolution is around 0.075mm. It was noted that the laser beam could only scan partially inside of the hollow tubes in the low-density lattice structures. This causes larger error when the reconstructed point cloud model is aligned to a solid block model to compare the deviation. As a result, the experimentally measured residual displacement field shows significant fluctuation on the top surface caused by the hollow features between thin walls. The significant negative displacement values in Fig. 16(c) are not real. Due to this issue discussed above, a local surface with much lower position was reconstructed in the software. When compared to the solid CAD model, that local surface caused an irregularly large negative displacement in that area. This irregular issue should have been avoided by re-scanning the sample to obtain raw data with better quality. Fortunately, only one irregular local area was found in the experimental results and it was not on the center line, and hence we were able to extract useful data along the center line to validate the displacement prediction",
            " 9 are employed in the layer-by-layer simulation with the accordingly updated homogenized elastic modulus for the homogenized cantilever beam model in order to compare with already presented results. The comparison shows insignificant difference between the predicted residual deformations with and without considering uncertainty. A likely reason is that small fluctuation in inherent strain vector does not cause much change in residual stress level when a nearly ideal elasto-plastic material model is used as the homogenized model. Both Fig. 16(a) and (b) show results obtained from layer-by-layer simulation. The difference between the two figures is that Fig. 16(a) is based on half-scale simulation with local features like thin walls modeled explicitly, while Fig. 16(b) is based on the homogenized model. Simulation result gives very smooth distribution of residual displacement as seen in Fig. 16(a) and 16(b). However, in experimental measurement, the metal build was 3D-scanned that resulted in some point cloud data. The build was then reconstructed based on the obtained points given relative distance between each other. For thin-walled lattice structures with low volume density of 0.19 as shown in Fig. 16(c), the scanned point cloud data could be affected by the large hollow features between thin walls. It is difficult to precisely scan and reconstruct the thin walls given that the thickness is just 0.1mm on average. This uncertainty issue has been mentioned above. As a result, the experimentally measured residual displacement field shows significant fluctuation on top surface caused by those hollow features between thin walls as shown in Fig. 16(c). This explains why the residual displacement field of the experimental measurement in Fig. 16(c) is somewhat different from Fig. 16(a) and (b). The same explanation holds for Fig. 17, especially between Fig. 17(a) and (d). As volume density increases, this issue in experimental measurement is alleviated a little due to the smaller gap size between thin walls, as seen in Fig. 17(e) and (f). In addition, the vertical deflections along the center line of the top surface of the cantilever beam in all the above cases are illustrated in Fig. 18. Due to the considerable space between those thin walls especially for the cases with lower volume density such as 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000413_j.mechmachtheory.2021.104311-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000413_j.mechmachtheory.2021.104311-Figure8-1.png",
        "caption": "Fig. 8. Variations in B i \u2013C i chain in RU U linkage.",
        "texts": [
            " B 9 pi ] , \u03b4q pi = [ \u03b4\u03b8i \u03b4R \u03b4\u03b7i \u03b4a zi \u03b4\u03c6zi \u03b4\u03c6yi \u03b4\u03c8 zi \u03b4b \u03b4l si \u03b4r i ]T (16b) and B 1 pi = b(w iz cos \u03b8i + w iy cos \u03b7i sin \u03b8i + w ix sin \u03b7i sin \u03b8i ) , B 2 pi = w iy cos \u03b7i \u2212 w ix sin \u03b7i (17a) B 3 pi = \u2212R (w iy sin \u03b7i \u2212 w ix cos \u03b7i ) \u2212 b(w ix cos \u03b7i cos \u03b8i + w iy sin \u03b7i cos \u03b8i ) , B 4 pi = w iz sin \u03b8i (17b) B 5 pi = \u2212b(w iy sin \u03b7i cos \u03b8i + w ix cos \u03b7i cos \u03b8i ) , B 6 pi = b(w iy sin \u03b7i sin \u03b8i + w ix cos \u03b7i sin \u03b8i ) (17c) B 7 pi = w iy cos \u03b7i cos \u03b8i + w iz sin \u03b8i \u2212 w ix cos \u03b8i sin \u03b7i , B 8 pi = 1 , B 9 pi = w ix sin \u03b7i \u2212 w iy cos \u03b7i (17d) where \u03b4l si = (\u03b4l i 1 + \u03b4l i 2 ) / 2 is the mean of relative length error of links B i 1 C i 1 and B i 2 C i 2 . Compared to the RR R linkage, the RU U linkage does not consider the parameters related to the parallelogram structure, but introducing the idle terms around the axes of the revolute joints in the passive U joints, as depicted in Fig. 8 . The linearized positioning error equation is expressed as \u03b4p = h \u03b8 i \u03b4\u03b8i + h Ri \u03b4R i + h \u03b7i \u03b4\u03b7i + k \u03b4a zi + h \u03c6zi \u03b4\u03c6zi + h \u03c6yi \u03b4\u03c6yi + h bi \u03b4b i + w i \u03b4l i + \u03b4w i l i + h ri \u03b4r i + h \u03c7 i \u03b4\u03c7i + h \u03b1i \u03b4\u03b1 + h \u03b2i \u03b4\u03b2 + h \u03b3 i \u03b4\u03b3 (18) Dot-multiplying to the foregoing equation on both sides with w i leads to the relationship between the positioning errors and geometric/joint variations of the first limb, with the same expression as Eq. (15) . Based on the concept of Screw theory, the orientation error of the end-effector in the RU U linkage can be written as \u03b4\u03c9 = \u03b4\u03b7i k + \u03b4\u03c6zi k + \u03b4\u03c6yi R z (\u03b7i ) j + \u03b4\u03b8i R z (\u03b7i ) i + \u03b4\u03d1 yi R z (\u03b7i ) i + \u03b4\u03d1 zi t i \u2212 (\u03b4\u03b6zi + \u03b4\u03bei ) k \u2212 \u03b4\u03b6yi R z (\u03b7i ) j (19) where \u03b4\u03d1 zi can be written as \u03b4\u03d1 zi = \u03b4c i \u03b4w i /l i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure9-4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure9-4-1.png",
        "caption": "Figure 9-4. Hysteresis loop",
        "texts": [],
        "surrounding_texts": [
            "Considering Figure 9.3, the vector moduli in shear are defined by: G* = G' + iG\" where G* = complex (resultant) modulus, G' = in-phase or storage modulus, and G\" = out-of-phase or loss modulus. It can also be shown that: T Tn G' = \u2014 = \u2014^cos(5 = G* cos j^ To To \\G'\\ = (G''+G'''Y' tan S (the loss factor or loss tangent) = G' Dynamic stress and strain properties 177 [G*] is the absolute value of the complex modulus but in practical dynamic testing is often written as G*. In Figure 9.2, the in-phase modulus G' = b/a and this is the modulus G assumed to be measured in a static test. The out-of-phase modulus G\" = c/a. The magnitude of the complex modulus is: IG*| = ^ = . ^b'^c'^ V ^ y The loss tangent, tan 5 = c/b. Similarly, in tension or compression: Young's modulus, |^*| = (E'^ + E\"^ ) ^ ^\u0302 ^ If, in a dynamic test with forced sinusoidal oscillation, force is plotted against deflection a hysteresis loop is obtained as shown in Figure 9.4."
        ]
    },
    {
        "image_filename": "designv10_4_0003493_1.339185-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003493_1.339185-Figure3-1.png",
        "caption": "FIG. 3. Normalized temperature T(O,t)ll'oc, at r = 0 vs time in the mag neto-optic film (MOl for different layer combinations. \"Air\" represents a medium with thermal constants like that of air,",
        "texts": [
            " 0 r, - exp - ------- ~ + 4K()(t - to) \" ~ + 4KoCt - to), + Too U>B ~~) + 58 ~~)) . (9) The first term describes the reduction of temperature due to the heat flow in the film, and the second term describes the heat flow into mediums 1 and 2. Neglecting the contribu tions 8e ~), a very simple approximation of the temperature profile is obtained from Eqs. (6) and (9) for t < to and t> to, respectively. The time dependence of the temperature at the spot center To(O,f), normalized to Too is shown in Fig. 3 for different layer combinations. In the case when the magneto optical film is coated with materials of low heat conductiv ity, very high temperatures are reached. For a laser power of 5 m W, a pulse length of 50-ns, and 50-nm-thick film, Too \"\"\" 6 K, leading to maximal temperatures T;)(O,t) between 500 and 1800 K. In the case when one side is coated with a metal film with high heat conductivity, a pronounced temperature reduction occurs due to the rapid heat flow into this film. Since the approximation given in Eqs. (6) and (9) is based on an infinite thickness of the media on both sides of the magneto-optical film, the calculated temperatures ToCO,!} are too low. Finite aluminum layers are expected to induce temperatures between curves 2 and 3 in Fig. 3, which are comparable to those obtained from numerical calcula tions.s.9 However, the temperature profile with respect to time and radial dependence based on a reasonable peak tem perature can be used in good approximation to investigate the magnetic properties relevant for the switching process. It should be pointed out that the strong difference in the peak temperature for a magneto-optical film coated with and 218 J. Appl. Phys., Vol. 62, No.1, 1 July 1987 without a metal film indicates the importance of the individ ual1ayer structure and, in particular, the thicknesses of the films with high thermal conductivity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003743_j.ymssp.2006.05.010-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003743_j.ymssp.2006.05.010-Figure1-1.png",
        "caption": "Fig. 1. UH-60A gear train schematic.",
        "texts": [],
        "surrounding_texts": [
            "The transmission of the UH-60A helicopter, shown in Figs. 1 and 2, has an epicyclic, or planetary, gear train in the final stage of the main rotor gearbox. This arrangement is similar to many other helicopter transmissions. Torque is transmitted from the central sun gear through the planets to the planet carrier and from the planet carrier to the main rotor shaft. It is important to have tools to assess the condition of these components as they form a non-redundant critical part of the drive to the main rotor. One such tool is vibration analysis. However, the vibration of epicyclic gear trains is difficult to analyse. Not only are there multiple planet gears producing similar vibrations, but there are also multiple and time-varying transmission paths from the gear mesh points to the transducers, which are typically mounted on the gearbox housing. These factors combine to reduce the effectiveness of conventional fault detection algorithms when they are applied to epicyclic gear trains. In 2002, fatigue cracks were found in the planet carriers of two US Army UH-60A Black Hawk helicopter main transmissions (2400 Series). These are shown in Figs. 3 and 4. The 250mm hub-to-rim crack in the first carrier was found as a result of an inspection for the cause of repeated low transmission oil pressure warnings. e front matter Crown Copyright r 2006 Published by Elsevier Ltd. All rights reserved. ssp.2006.05.010 ing author. Tel.: +61396267577; fax: +61396267083. esses: david.blunt@dsto.defence.gov.au (D.M. Blunt), jonathan.a.keller@us.army.mil (J.A. Keller). ARTICLE IN PRESS D.M. Blunt, J.A. Keller / Mechanical Systems and Signal Processing 20 (2006) 2095\u201321112096 The 82mm crack in the second carrier was found as a result of an inspection. Both cracks initiated in the planet post-to-plate radius. Discovery of the cracks resulted in flight restrictions on a significant number of US Army UH-60A helicopters, and the search for a simple, cost-effective test capable of diagnosing this type of fault. The US Army conducted a vibration test program on the transmission with the 82mm crack. It was run in a test cell at torque settings ranging from 20% to 100% of the rated torque. This exact same transmission (gears, carrier, and main module case) was also installed in a helicopter and ground-run at torque settings of 20% and 30%. Vibration data were acquired from four other undamaged transmissions: one in the test cell, and three in UH-60A helicopters. These data sets were initially analysed by Keller and Grabill [1] using several standard diagnostic parameters that were modified for the special case of an epicyclic gearbox and applied to the time synchronous averages of the planet carrier vibration. The analysis found that two of the parameters consistently detected the presence of the fault under test-cell conditions. These were the epicyclic Sideband Index (SIe) and the epicyclic Sideband Level Factor (SLFe), which were both based on the first-order sidebands of the fundamental dominant meshing component (230 shaft-orders). However, neither of these parameters was able to detect the crack under the low-torque on-aircraft conditions. The analysis concluded that the fault was \u2018\u2018detectable in controlled test-cell conditions, but noise from other rotating components and differences in the vibration levels from aircraft-to-aircraft may overshadow the effect of a cracked planetary carrier\u2019\u2019, and that \u2018\u2018it is also possible that the low torque values of the on-aircraft testing were not sufficient to expose the fault.\u2019\u2019 The same data were also analysed by Dong et al. [2] using wavelet analysis techniques combined with Markov modelling. The analysis found success in distinguishing the faulted component data from the unfaulted component data, although the method required training data sets. ARTICLE IN PRESS D.M. Blunt, J.A. Keller / Mechanical Systems and Signal Processing 20 (2006) 2095\u20132111 2097 Wu et al. [3\u20135] reported that the crack could be detected using frequency and wavelet domain analyses of the raw vibration data, but the results depended on the sensor location and frequency band. The best results were obtained for the 5th harmonic (5 ) of the epicyclic mesh frequency for one sensor (3 in Fig. 2), and the 10th harmonic (10 ) for another sensor (5 in Fig. 2), although the reasons for this were not clear. The test-cell vibration data were also analysed by McInerny et al [6]. Like Keller and Grabill\u2019s analysis, a number of different metrics for the detection of faults in fixed-axis gears were modified and applied to the time synchronous averages of the planet carrier vibration. However, some statistics for the raw (non-averaged) vibration data were also presented, and a new metric measuring the ratio of the energy in the planet carrier average at multiples of the planet-pass frequency with the remainder of the energy in the average was ARTICLE IN PRESS D.M. Blunt, J.A. Keller / Mechanical Systems and Signal Processing 20 (2006) 2095\u201321112098 developed. It was reported that the crack was detectable, but the results depended on the accelerometer position and metric used, and none of the metrics were applied to the on-aircraft data. Based on the outcome of this earlier work, and in an effort to better understand the characteristics of this type of fault, this paper presents a new analysis of the UH-60A vibration data that is focussed on the modulation of the fundamental epicyclic gear mesh vibration. Two new vibration diagnostic methods are developed to detect the crack in the planet carrier from changes to the modulation. These methods are tested using the UH-60A vibration data sets, and compared with Keller and Gabrill\u2019s earlier results."
        ]
    },
    {
        "image_filename": "designv10_4_0001012_j.triboint.2021.106927-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001012_j.triboint.2021.106927-Figure4-1.png",
        "caption": "Fig. 4. Schematic representation of the undeflected area AR of the rolling element, which has an influence on the electrical impedance.",
        "texts": [
            " (3) The reciprocal distance between the undeflected bodies hR(x, y) is integrated over the surface in the two spatial directions x and y. Thus, the entire capacity of a loaded rolling contact CC is the sum of the parallel connected capacities CHz and CR. The resulting extended electrical model of the rolling contact is shown in Fig. 3. The surface area AR takes an annular shape and is the projection of the undeflected ball onto the raceway minus the hertzian contact area AHz. The surface is shown in Fig. 4 schematically. The representation of the undeflected contact area however inflicts a contradiction to the current state of research. According to equations (1) and (2), the calculation of the impedance of rolling bearings is based on the assumption that solely rolling elements with a Hertzian contact contribute to the total capacitance. Consequently rolling elements outside the load zone shouldn\u2019t add to it. In contrast, the undeflected area around the Hertzian zone increases the capacity by the factor kR as described, which implies that an unloaded rolling element should add to the total capacity of the bearing",
            " At the inner race, the distance between the race and the rolling element hUi is therefore given by the difference between the position-dependent clearance \u03b4\u03d5 and the lubricant film thickness of the rolling element at the outer race. hUi = \u03b4\u03d5 \u2212 hUo. (8) The position-dependent clearance \u03b4\u03d5, in turn, depends on the bearing clearance Pd and the radial sift \u03b4r between the bearing rings due to the radial load. \u03b4\u03d5 = \u03b4r cos \u03d5 \u2212 0.5Pd. (9) Instead of taking the Hertzian area as lower limit for the surface integral it is now integrated for the entire surface. The size of the surface AU is the area corresponding to the projection of the ball onto the raceway. It is comparable to the area AR in Fig. 4, the difference is that the Hertzian area is not present here. The distance between the undeflected as well as unloaded bodies hu(x, y) is integrated over the whole surface in x and y directions, shown in Fig. 3. The capacity of an unloaded contacts CU is calculated similar to equation (3) as follows: Fig. 5. Electrical model of a rolling bearing [2]. Fig. 6. Load zone in rolling bearing under radial load according to Ref. [25]. T. Schirra et al. Tribology International 158 (2021) 106927 CU = \u222b\u222b AU \u03b50\u03b5r hU(x, y) dx dy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003966_j.clinbiomech.2006.09.009-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003966_j.clinbiomech.2006.09.009-Figure1-1.png",
        "caption": "Fig. 1. The computer models of the foot of Virtual Chinese Human \u2018\u2018female No. 1\u2019\u2019: (a) 3D anatomical models of skeleton and skin of Left foot; (b) and (c) Musculoskeletal FE models of the second ray of MPLA and the fifth ray of LPLA during balanced standing. (b) The second ray: 1 cortical bone (8); 2 trabecular bone (9); 3 fat pad (6); 4 plantar fascia; 5 flexor digitorum brevis; 6 quadratus plantae; 7 spring lig.; 8 long plantar lig.; 9 tendon of tibialis posterior; 10 tendon of peroneus longus; 11 oblique head (adductor hallucis); 12 tendon of flexor digitorum longus; 13 tendon of flexor digitorum brevis; 14 plantar interossei; 15 dorsal interossei; 16 lumbricals; 17 tendon of extensor digitorum brevis; 18 tendon of extensor digitorum longus; 19 sagittal plane joints (7); 20 the second toe; 21 the second metatarsal; 22 intermediate cuneiform; 23 navicular; 24 talus; 25 calcaneus (medial); 26 dorsal lig. of joints (6); 27 plantar lig. of joints (6); 28 cuboid; 29 cervical lig.; 30 interosseous talocalcanean lig. (2); 31 tarsal canal lig.; 32 cartilage (8); 33 posterior talocalcaneal lig.; 34 Achilles tendon. (c) The fifth ray: 1 cortical bone (7); 2 trabecular bone (7); 3 fat pad (5); 4 plantar fascia; 5 abductor digiti minimi; 6 lateral muscle; 7 long plantar lig.; 8 tendon of peroneus longus; 9 short plantar lig.; 10 lateral tendon of abductor digiti minimi; 11 tendon of peroneus brevis; 12 tendon of peroneus tertius; 13 plantar interossei; 14 dorsal interossei; 15 tendon of flexor digitorum longus; 16 flexor digiti minimi brevis; 17 tendon of extensor digitorum longus; 18 medial tendon of abductor digiti minimi; 19 sagittal plane joints (6); 20 the fifth toe; 21 the fifth metatarsal; 22 cuboid; 23 calcaneus (lateral); 24 lateral process of talus; 25 dorsal lig. of joints (5); 26 plantar lig. of joints (4); 27 cartilage (7); 28 bifurcated lig.; 29 lateral talocalcanean lig.; 30 posterior talocalcaneal lig.; 31 Achilles tendon.",
        "texts": [
            ", 2000), were selected as three validation criteria for the FE simulations. These experimental results are in good agreement with predictions of current nonlinear FE models. Besides, clinical observations also complied with the current predictions of internal stress/strain changes in the foot, as shown in the following chapters. 3.1. FE models of plantar longitudinal arches of VCH \u2018\u2018female No. 1\u2019\u2019 A geometrical accurate 3D model of skeleton\u2013skin complex of left foot of Virtual Chinese Human \u2018\u2018female No. 1\u2019\u2019 was developed (Fig. 1(a)). An anatomically detailed FE model of the second ray of MPLA was established (Fig. 1(b)), involving 8 tissues, 3267 elements, 7330 nodes. Another anatomically detailed FE model of the fifth ray of LPLA was developed (Fig. 1(c)), involving 8 tissues, 2689 elements, 5938 nodes. All anatomic components of two models were marked in detail while load configurations of models were shown in Fig. 1. The predicted peak von Mises stresses/strains in specific tissues of the second ray of MPLA and the fifth ray of LPLA under seven biomechanical conditions were tabulated in Tables 2 and 3. During balanced standing, high-peak stresses of bony structures were predicted at the cortex of talus neck, calcaneal sulcus, and metatarsal body; meanwhile, relatively strong peak stresses of soft tissues were predicted at the flexor tendon in forefoot and plantar fascia (Fig. 2(a) and (b)). Simulating plantar fasciotomy resulted in an increase of peak stresses in bony structures, and two maximum stresses were predicted to shift to the body of the second metatarsal and the long plantar liga- ment attachment area of the cuboid crest (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003821_robot.2005.1570405-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003821_robot.2005.1570405-Figure2-1.png",
        "caption": "Fig. 2. The gait motion pattern in the sagittal plane. The black dot represents the COM and the triangles on the bottom represent the support feet. The external perturbation is applied during single support phase, when the COM is at Point A. The positions of the COM when the following double support, single support, and double support phase start are defined here by Point B, C, and C\u2019, as well. The angular momentum generated by the external perturbation is compensated mainly between Point B and C\u2019.",
        "texts": [
            " Then, the ground force vector can be written as Fx = mx\u0308 = m(a \u2212 ac) ( C1e \u2212( \u221a a\u2212ac)t + C2e ( \u221a a\u2212ac)t ) Fz = mg where m is the mass of the system. The rotational moment r around the y-axis can be calculated by r = m(1 \u2212 c)(aH \u2212 g) ( C1e \u2212( \u221a a\u2212ac)t + C2e ( \u221a a\u2212ac)t ) + mg( b a ) and the angular momentum \u03c9t1,t2 generated by the rotational momentum between times t = t1, t2 can be obtained as \u03c9t1,t2 = [ m(1 \u2212 c)(aH \u2212 g)\u221a a \u2212 ac ( \u2212C1e \u2212( \u221a a\u2212ac)t + C2e ( \u221a a\u2212ac)t ) +mgt( b a )]t2t1 + \u03c91 (3) where \u03c91 is the angular momentum at t = t1. Suppose the motion of the humanoid in sagittal plane is defined as shown in Figure 2. To clarify the concept of our approach, let us assume here that no angular momentum around the COM is generated in the original feedforward motion. That means the ground force vector always passes through the COM. Let us assume the humanoid is first in single support phase, and external perturbation was applied to the humanoid body causing sudden increase in the linear and angular momentum when the COM is at Point A. The increased linear momentum can be reduced by using existing approaches of 3DLIPM",
            " In order to reduce the increased linear and angular momentum to zero, the motion after the perturbation will be re-planned. The following strategies are used to counteract the increased momentum: \u2022 the position the swing leg lands onto the ground will be modified \u2022 rotational momentum will be applied to the body during the double support phase to counteract the angular momentum induced by the external perturbation. For the motion during double support phase, the following two assumptions are made: (1) the coordinate values of Point B and C in Figure 2, which are the points of COM when the double support phase begins and ends, as well, will be the same as those in the original gait motion, and (2) The motion of the COM and the trajectory of the angular momentum will follow the rules of AMPM. The ground force vector will be parallel to the vector connecting the ZMP and COM at Point C. The acceleration of the COM will be uncontinuous at Point B, as the ground force vector will be adjusted so that the angular momentum will be reduced to zero when the COM arrives to C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-31-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-31-1.png",
        "caption": "Figure 5-31 Baker's transformation.",
        "texts": [
            "23) After n iterations of the map, the local shape of the initial hypersphere depends on [/\u201e] = [vFfxJHvFCx,.,)] \u2022\u2022\u2022 [VF(X1)] (5-4.24) In general, one can find the eigenvalues of /\u201e which one orders according to 202 Criteria for Chaotic Vibrations J\\(n) >j2(n) > - \u2022 >jN(n), where the jK(n) are the absolute values of the eigenvalues. The Lyapunov exponents are then defined by 1 ,= lim -l H-\u00bbOO n (5-4.25) Farmer et al. illustrate the use of this definition for a two-dimensional map called a baker's transformation (Figure 5-31, named for its analogy to rolling and cutting pie dough. It is similar to the horseshoe map described in Chapter 1. The equations for this map are (5-4.26) System Henon Xn + l - 1 - aXl + Yn Yn + l = bXn Rossler chaos X= -(Y + Z) 7= X+ aY Z = b + Z(X- c) Lorenz X= a(Y- X) Y= X(R - Z) - Y Z = XY- bZ Rossler hyperchaos X= -(Y+ Z) 7* X+ aY+ W Z = b + XZ W= cW - dZ Parameter Values / f l = 1.4 \\ b = 0.3 a = 0.15 b = 0.20 c = 10.0 o = 16.0 R = 45.92 6 = 4.0 a = 0.25 6 = 3.0 c = 0.05 J = 0.5 Lyapunov Spectrum (bits/s) \\"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000180_j.matdes.2020.109410-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000180_j.matdes.2020.109410-Figure16-1.png",
        "caption": "Fig. 16. Two representative shapes for grains within the overlap region between two consecutive tracks: (a) grain shaped like a \u201cV\u201d, (b) grain shaped like a \u201c\u2207\u201d.",
        "texts": [
            "29625 mm, where the overlap region is outlined by the two intersecting curved white dashed lines. As shown in the closeup of Fig. 15(b), the grain in blue epitaxially grows from the existing grain from Track 1, while the grain in red originates from an out-of-plane location. Driven by the change in direction of the thermal gradient caused by Track 2, existing grains on the sides of Track 1 epitaxially grow to the adjacent melt pool, resulting in the broadening of grains often in either \u201cV\u201d or \u201c\u2207\u201d shapes, depending on the local grain structure. Fig. 16 shows two representative grains from the overlap region. The right part of the V-shape grain in Fig. 16(a) and the \u2207-shape grain in Fig. 16(b) are formed in the previous track, while the rest of these grains are formed during the deposition of Track 2, and are located in the overlap region (see Supplementary Movie 1 for an animation of this process). It should be noted that the columnar grains along the centerline of the melt pool are not affected by the deposition of Track 2. In addition, the grain morphology and distribution for Track 2 except for the overlap region repeat that revealed in Section 3.1. Fig. 15(c1) and 15(c2) show the longitudinal cross-sections at y = 376"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure11-1.png",
        "caption": "Fig. 11. A horn grown from an expanding surface G by growth velocities at various angles to G to produce logarithmic spiral cell tracks as shown. The centerline is a segment of a circle",
        "texts": [
            " This may be accomplished by the use of logarithmic spirals which are extensively discussed by D\u2019arcy Thompson (1942) in connection with the forms of shells, horns and other biological forms. Logarithmic spirals are plane curves (Fig. 10) described by r\"beh #05 a , (54) where r, h are polar coordinates and b and a are constants. The angle between the tangent to the spiral and the radius vector r is the constant angle a. This property is suggested in the alternate name of equiangular spiral. If a is (90\u00b0, then r increases with h. If a is '90\u00b0, then r decreases with h, i.e. the curve spirals inwards rather than outwards. When a\"90\u00b0, r is constant and the spiral becomes a circle. In Fig. 11, a close approximation to the boundaries shown in Fig. 9 are illustrated for a specific case. Fig. 11 is a cross-section of a horn with the following logarithmic spirals as the cell tracks. The problem to be solved is to find the growth velocity g that produces this horn. From Table 1 it can be seen that the center-line curve C 0 is a circle. The curves C 1 and C 2 are logarithmic spirals which spiral outwards. The curves C 3 and C 4 are logarithmic curves spiraling inwards. The constants in Table 1 have been adjusted so that all curves meet at the point (50, 0) so C 0 is a quarter of a circle. The cross-section shown in Fig. 11 is the curved counterpart of Fig. 8 in the sense that along any radius in Fig. 11 the angle between tangents to the curves C 0 , C 1 , C 2 , C 3 , C 4 are constants independent of h. The same is true for the cell tracks in Fig. 8, for any line drawn parallel to the x 1 axis (which is the analogue of r as rPR). To complete the description of the 3-D horn, whose section is shown in Fig. 11, we assume that G is always a circle, and that as a result, sections h 3 \"constant, are planes containing the x 3 axis. The cross-sections on such planes are then also circles. Curves on which (h2 1 #h2 2 )\"constant, are also circles in the interior on h 3 \"constant planes. The stipulation that G is always a circle, together with the two cell tracks C 1 and C 4 , completely defined the external geometry of the horn. The cell tracks in the interior in Fig. 11 are defined by requiring them to be logarithmic spirals. Cell tracks which are not in the plane shown in Fig. 11, must have some component of the growth velocity in the x 3 direction as well as in the x 1 , x 2 plane. The information given above is sufficient to develop a computer program based on Eq. (25) which generates this 3-D horn. A computer drawn 3-D view of the horn is shown in Fig. 12. Logarithmic spirals were extensively discussed by D\u2019arcy Thompson (1942), primarily with respect to shells in which the spiral angle is constant for all points of the shell. The use of inward and outward spirals for horns as in Fig. 11 was not developed. In Fig. 11, the stippled area indicates a possible cross-section of a hollow horn. The solid tip may be produced by a change of G from a circle to a ring as growth proceeds as shown schematically in Fig. 13. Example 3.7. A curvilinear horn of flatter spirals Another example of growth of a horn is illustrated in Fig. 14. In this example, no cell track is a circle, but all cell tracks are flat logarithmic spirals, similar to a long-horn steer. Here the parameters in Eq. (54) are chosen as follows. The values in Table 2 produce the curves starting at A and B in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003955_pime_proc_1979_193_019_02-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003955_pime_proc_1979_193_019_02-Figure2-1.png",
        "caption": "Fig. 2. Diagram of a rotating radially,loaded roller bearing and the corresponding electrical circuit",
        "texts": [
            " The changes in capacitance between rings that accompany changes in operating condition are therefore dominated by changes in film tluckness in the loaded sector. Consequently, the thickness of films in this sector can be deduced, by the method described for a pair of rollers, from measurements of the capacitance between rings. An electrical analogue of a radially loaded bearing, showing diagrammatically the influence of load and internal clearance on the magnitudes of the capacitances that represent the individual contacts, is shown in Fig. 2. The influence of the cage on the capacitance between rings is discussed in Appendix 2. A radial load is not shared equally between the rollers, and in consequence the films are thinnest in the centre of the loaded sector and increase very slightly in thickness with angular displacement. The total capacitance between rings is equally characteristic of the different thicknesses associated with individual rollers, and the relationship between film thickness and capacitance can be found for any place of interest in the loaded sector by inserting an appropriate value for w i n Dowson\u2019s prediction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003767_s026357470400092x-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003767_s026357470400092x-Figure3-1.png",
        "caption": "Fig. 3. Helicopter variables with fuselage coordinates.",
        "texts": [
            " We use a separated feedback system as shown in Figure 2 in order to guarantee flight safety. Even if the hovering feedback system becomes unstable, the input (attitude reference) can be limited by the attitude controller. We limit the pitch and roll angles to \u00b110 degrees. That is, the attitude controller prevents the helicopter from falling into a non-linear level. Moreover, separating attitude control from hovering control is effective for optimizing the controller, because control precision depends on attitude control precision. Figure 3 illustrates the small helicopter coordinates, and Table II shows the state parameters and their physical meanings. * The term attitude refers to the rotations of the helicopter (pitch, roll and yaw). http://journals.cambridge.org Downloaded: 11 May 2014 IP address: 164.41.102.240 Rotor time constants (main rotor tip path plane and stabilizer paddle tip path plane time constants) are very important parameters of a helicopter equipped with a bell-hiller rotor hub system. Another important parameter is the hub tilt spring constant, which influences coupling between the rotor and fuselage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003768_rob.4620050502-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003768_rob.4620050502-Figure2-1.png",
        "caption": "Figure 2.",
        "texts": [
            " As in the case of MVR, the actual value of r , depends not only on the robot configuration and the weighing matrices W, and W,, but also on the direction of the force applied by the robot end-effector. The surface (or curve for m = 2) formed by the end points of vectors r,u, for a given robot configuration can be represented by an ellipsoid with principal axes (l/[l)sl, (1/E2)82, --- (1 / [ , ) smt where sieRm is the ith column vector of S in (35). This ellipsoid will be called the manipulator-mechanical-advantage-ellipsoid (MMAE) (Fig. 2) and its shape and volume will depend on the robot configuration. This ellipsoid is equivalent to the manipulating force ellipsoid described by Yoshikawa,* if the weighting matrices Wj and W, are identity matrices. In case one or more t i are equal to zero, then the manipulator mechanical advantage in the direction(s) of si vector(s) will be infinite. Dubey and Luh: Redundant Robot Control 419 If the external force vector acting at the end-effector is in the direction($ of vector(s) si corresponding to zero t i , then the torques produced at the joints will be zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000704_j.addma.2021.102116-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000704_j.addma.2021.102116-Figure2-1.png",
        "caption": "Fig. 2. Workflow of the modified inherent strain method [45].",
        "texts": [
            " In particular, the key idea behind the modified inherent strain method is to compute the inherent strain vector from the elastic and plastic strain histories in a pre-run detailed process simulation (based on moving point heat source model) and then apply the inherent strain vector as thermal expansion coefficients on the part in a series of layer-by-layer static equilibrium analyses [44,45]. The shrinkage of the solidified material due to the complex mechanics associated with rapid heating and cooling is introduced by giving a unit temperature rise in the part-scale simulation. The modified inherent strain method avoids the expensive detailed thermomechanical analysis with fine mesh resolution and lots of time steps to yield a relatively accurate deformation profile (see Fig. 2). The basic procedures of the modified inherent strain method employed in this work to compute deformation profile are: 1) A detailed process simulation is performed on a micro-scale model to obtain the inherent strain vector which considers the inherent deformation introduced by laser melting and solidification. 2) The obtained inherent strain vector is then applied as coefficients of thermal expansion (CTE) to part-scale model for residual deformation prediction. Besides part-scale residual stress and distortion in metal AM, the modified inherent strain method has been applied to the prediction of cracking [46,47], design of support structures [16] build orientation optimization [48] and continuous scanning path [24]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure6-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure6-2-1.png",
        "caption": "Figure 6-2. Forms of parallel plate compression test for plasticity, (a) 'Plate' test; (b) 'Disc' test. Broken lines and shading show position of upper plate and shape of test piece after compression.",
        "texts": [],
        "surrounding_texts": [
            "(c) The flow produced by compression is extremely complex, the shear rate is not uniform throughout the test piece and changes during the course of the test. Consequently, it is virtually impossible to deduce fundamental rheological parameters of the rubber. Nevertheless, compression plastimeters have been found very useful for routine testing, particularly of uncompounded rubber, where only basically similar materials are compared. There are basically two forms of parallel plate compression plastimeter; (a) with both compression plates much larger than the test piece (Figure 6.2(a), 'plate' test) and (b) with one or both plates of approximately the same diameter as the test piece (Figure 6.2(b), 'disc' test). In the plate test, the test piece area increases and, hence, the pressure decreases as the rubber spreads out, whereas in the disc test the test piece area remains effectively constant because the excess material (B in Figure 6.2(b) is outside the compression zone A. However, although the compression pressure remains constant, the shear stresses in the rubber vary as its thickness is decreased^ '\u0302 ^\u0302 . A more important advantage of the disc test is that the result is less affected by variations in test piece volume^ '\u0302 \u0302 ;\u0302 of the order of \u00b15% can be allowed in the disc method as against \u00b11% in the plate method. On the other hand, the initial test piece shape factor (ratio of height to diameter) influences the result more in the disc test than in the plate test.\u0302 ^ Consequently, there is an advantage in pre-compressing the test piece to constant thickness before commencing the test proper. Pre-compression has Test on unvulcanized rubbers 69 another advantage in that the thinner test piece can be brought to the test temperature more quickly and this is the basis of the various 'rapid' plastimeters. The basic compression plastimeter principle can be modified by measuring the force required to compress the test piece to a given thickness in a given time. This was the principle adopted in, for example, the Defometer and it has the advantage that this force is proportional to the effective viscosity of the rubber under the conditions of test, although this viscosity is an average for the range of shear rates throughout the rubber. ISO 2007^^ specifies a rapid plastimeter procedure using an instrument with one platen either 7.3, 10 or 14 mm diameter and the other platen 'of larger diameter than the first' (i.e. disc type method). The size of the first platen is chosen such that the measured plasticity is between 20 and 85. The test piece is cut with a punch which will give a constant volume of 0.40 \u00b1 0.04 cm, the thickness being approximately 3 mm and the diameter approximately 13 mm. The test piece is pre-compressed to a thickness of 1 \u00b1 0.01 mm within 2 sec and heated for 15 sec. The test load of lOON is then applied for 15 sec when the test piece thickness is measured. The usual temperature of test is 100\u00b0C and the result is expressed as the thickness of the test piece at the end of the test in units of 0.01 mm and called the 'rapid plasticity number'. The Wallace rapid plastimeter, and presumably other commercial instruments, conform to this specification but it would be sensible to check with the manufacturers. A technically identical method is given in BS 903:Part A59^l ISO 7323\u0302 \"\u0302 specifies a parallel plate test based on the Wilhams plastimeter with plates 4 cm in diameter. The test piece is 2.00 \u00b1 0.02 cm^ in volume and can conveniently be a cylinder 16 mm diameter and 10 mm thick. As discussed above, a close tolerance on volume is necessary for this type of plastimeter. The test piece is preheated for 15 min (the temperature of test is usually 70\u00b0C or 100\u00b0C) and compressed under a force of 49N. The thickness of the compressed test piece is measured in mm and this value multiplied by 100 quoted as the plasticity number. The preferred time of application of the force is 3 min. The correction to the standard in 2003 was to change the tolerance on the force from 0.05N to 0.5N. The ISO method also gives a procedure for measuring the recovery of the test piece after removal of the load. The height of the test piece is measured after Imin recovery at the test temperature. The 'recovery value' is reported as the difference between plasticity number and recovered height multiplied by 100. ASTM D926^^ gives similar methods to ISO 7323 but has two recovery procedures. In procedure A the test piece is removed from the plastimeter and allowed to recover. In procedure B the test piece is compressed, not"
        ]
    },
    {
        "image_filename": "designv10_4_0003713_j.mechmachtheory.2005.10.012-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003713_j.mechmachtheory.2005.10.012-Figure2-1.png",
        "caption": "Fig. 2. Infinitesimal screws associated with the CPS1 limb of the 4-dof parallel manipulator.",
        "texts": [
            " \u00f015\u00de The expressions derived in this Section allow to compute the forward position analysis of the parallel manipulator at hand by means of equations where the generalized coordinates and the parameters are written in a explicit way. Such a procedure is called a closed-form solution. In this Section the velocity analysis of the mechanism under study is approached using the theory of screws. The inverse velocity analysis consists in computing the joint velocity rates required to produce a desired velocity state of the moving platform w.r.t. the fixed platform. Fig. 2 shows the infinitesimal screws associated with the cylindrical + prismatic + spherical (CPS1) limb of the parallel manipulator considered in this study. The velocity state of the moving platform can be written through the CPS1 limb as follows: _q1 0$1 \u00fe 1x2 1$2 \u00fe _q2 2$3 \u00fe 3x4 3$4 \u00fe 4x5 4$5 \u00fe 5x6 5$6 \u00bc ~V O; \u00f016\u00de where the infinitesimal screws 0$1 and 1$2 represent, respectively, the screws associated with the prismatic pair and the revolute joint of the cylindrical pair of the limb CPS1. Furthermore, since the velocity of the point O in the moving platform is along the Y-axis, it is evident that ~V O \u00bc xX xY xZ 0 _q3 0 2 666666664 3 777777775 ",
            " \u00f017\u00de Thus, the joint velocity rates of the CPS1 limb can be calculated for a given velocity vector ~V O as follows: X \u00bc J 1~V O; \u00f018\u00de where the Jacobian matrix J is described by J \u00bc 0$1 1$2 2$3 3$4 4$5 5$6 ; and X is described as follows: X \u00bc _q1 1x2 _q2 3x4 4x5 5x6 2 666666664 3 777777775 . It is straightforward to demonstrate that the joint velocity rates of the remaining limbs can be calculated following a similar procedure. On the other hand the forward velocity analysis is established as follows: given a set of generalized velocities f _q1; _q2; _q3; _q4g, compute the resulting velocity state of the moving platform w.r.t. the fixed platform. Introducing a line $2 in Plu\u0308cker coordinates, whose primal part is a unit vector along the first limb, see Fig. 2, and taking into account that $2 is reciprocal to all the screws representing the kinematic pairs of the CPS1 chain, excepting the screw 2$3. Thus applying the Klein form between $2 with both sides of Eq. (16), the corresponding cancellation of terms produces _q2 \u00bc KL\u00f0$2; ~V O\u00de. \u00f019\u00de A similar procedure leads to _q4 \u00bc KL\u00f0$4; ~V O\u00de; \u00f020\u00de where $4 is a line in Plu\u0308cker coordinates whose primal part is along the HPS3 kinematic chain. In order to complete the expressions for the forward velocity analysis, consider a fictitious serial manipulator type HPS3 between the point O 0 and the spherical joint S1, as seen in Fig. 2. Introducing a line $12 in Plu\u0308cker coordinates whose primal part is along the fictitious kinematic chain and according to the procedure described above, the following expression is derived: _q12 \u00bc KL\u00f0$12; ~V O\u00de; \u00f021\u00de where _q12 \u00bc q1 _q1 \u00fe q2 _q2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2 1 \u00fe q2 2 p . Casting Eqs. (19)\u2013(21) into a single expression results in the following angular velocity of the moving platform w.r.t. the fixed reference frame: ~x \u00bc S 1 _q2 _q3s\u03022Y _q12 _q3s\u030212Y _q4 _q3s\u03024Y 2 64 3 75; \u00f022\u00de where S is a matrix composed of a special arrangement of the dual parts of the lines $2, $12 and $4 as follows: S \u00bc \u00bd~sO2 ~sO12 ~sO4 T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003662_tmag.2004.830511-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003662_tmag.2004.830511-Figure2-1.png",
        "caption": "Fig. 2. Flux plot of the blushless dc motor.",
        "texts": [
            " The rating of the prototype is 900 W at 24 V; it has 11 pole pairs, 24 stator slots, and operates at 136 rpm. The permanent magnet embedded in the motor is Nd\u2013Fe\u2013B and the power electronic switching elements used in the converter are MOSFET. The motor is driven by the control strategy of two-phase-on excitation. The eddy current in the permanent magnet is taken into account in the solution by modeling the permanent magnet as a solid conductor in the electrical property. The computed steady-state flux distribution is shown in Fig. 2. The computed and measured stator phase currents are shown in Figs. 3 and 4, respectively, when the motor is fed from a PWM voltage inverter. It can be seen that the excellent agreement between the simulated and measured results is achieved. The next example is a four-pole, 24-slot stator, three-phase, 50 Hz, Y connected PM synchronous motor. The stator winding has 138 turns per phase in series and is fed by an ac\u2013dc\u2013ac PWM inverter, as shown in Fig. 5. The three-phase reference voltages are compared with a common isosceles triangular carrier wave, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000083_j.addma.2019.100935-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000083_j.addma.2019.100935-Figure14-1.png",
        "caption": "Fig. 14. 2D layer width plot.",
        "texts": [
            " For two factors chosen with five levels, the required number of experiments is 13 according to CCRD. Using the software of design expert, the experimental samples can be designed, and then the experiment was performed using the setups presented in section 2. The detailed calculation method can be referred to our previous literature [20,31]. The final regression model was obtained as follows: = \u2212 + + \u2212 \u00d7W W T W Tlayer 0.2476 1.2415 FS 0.0147 1.5032 10 FS-3 (9) The corresponding 2D layer width plot is shown in Fig. 14, it can be seen that the adaptive WFS can maintain a target layer width under different interlayer temperature and, therefore, keep a constant layer height. This prediction model will be used to adjust the WFS and TS at the PV node to ensure the uniform layer dimensions. 5. Experimental verification The proposed planning technique is verified by fabricating a largescale model. Fig. 15 shows the dimensions of the typical model, it is featured by the continuously changing diameter from the bottom up, and the wall thickness is set at 6 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003829_0094-114x(78)90028-9-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003829_0094-114x(78)90028-9-Figure5-1.png",
        "caption": "Figure 5. Generalized displacements in system-oriented coordinate system with nodal compatibility.",
        "texts": [
            " (v) All required numbers, such as stresses and strains, associated with the problem are computed. As an example, the 4-bar linkage of Fig. 4 is utilized in which each link is simulated by one element. The input shaft is assumed to be connected to a flywheel with high inertia, ensuring that no undue fluctuations occur in the input angular velocity. Then, the input crank is reduced to a rotating cantilever beam. It must be pointed out, however, that this assumption is made only to simplify the computational procedure. In Fig. 5, system-oriented generalized displacements are labeled to describe the structural deformation of the linkage as well as to maintain compatibility between the elements at the nodes. For example, at node 2, UI and U2 are required to describe the nodal translations. Two more independent displacements, U3 and U4, are necessary at node 2 to describe the rotational deformations in each of the two elements, 1 and 2. The above displacements simulate a pin 612 joint. A rigid connection between two elements, on the other hand, will be simulated by only one rotational displacement. Construction of Total System Idatdces It may be shown that [R] -I = [R] r, therefore, from eqn (30a) {U} = [Rlr{u}. (33) With the help of eqns (10a) and (30a) where {0o} = {0 , } + { / ) } (34) { 0 } = [Rlr{~}, {0 ,} = [R]T{a,} {0\u00b0} = [Rlr{ti,}. Equations of motion (26) of the beam element is then written in the system-oriented coordinate system as where [m]{ Oo(t)} + [kl{U(t)} = {Q} (35) {0}-- [RF{O}. In Fig. 6, the elements of Fig. 5 are shown separated. Appropriate displacements are labeled on each while retaining compatibility at the nodes. The system mass and stiffness matrices of the/ th element are [m], = [R] i r [ r f i ]dR] i (36) and [k] i = [R] i r [E ] i [R ] i i = 1, 2, 3. Equations (36) is valid for an element represented by six generalized displacements. The kinetic energy for the crank may be expressed, using eqn (31), as T, = ~{Oo} , r [m] , {O=} , . (37) Further, {/)o}1 is defined as -o[ .i. {Oa}] : q . i [ [ /",
            " 6) are listed below and L2 sin (04- 02) 0,3 = - L-~CO2sin (04- 03)' L2 sin ( 0 3 - 02) ~o~ = - ~4oJ2 ~ , [-- L202 sin (04 - 02) + L2w22 cos ( 0 4 - 02) + L3w32 cos (04 - 03) - L4w42] \u00b0~3 = L3 sin (04 - 03) [- L2a2 sin (03 - 02) + L2\u00a2022 cos (03 - 02) - L4\u00a2042 cos (03 - 04) + L3\u00a2032] a 4 = L4 sin (04 - 03) (AI) (A2) (A3) ( A 4 ) where oJ~ and a~ denote the angular velocity and acceleration of the ith link, respectively, and, o~2 and a2 are the prescribed input values. With the aid of the quantities listed above, the generalized rigid-body acceleration vector, {0,}, may he determined. Thus,/),~ is derived corresponding to the generalized coordinate U~ (Fig. 5) /),l = - L2o~22 cos 02 - L2a2 sin 02. (AS) Similarly Ur2 = - L2w22 sin 02 + L2a2 cos 02 (A6) and /-),3 = a2. (A7) Others may be similarly found. Appendix 2. Forms of structural damping Rewriting the equations of motion (44) [M]{/.)} + (C]{g r} + [K]{ U} = - [M]{/),}. (44) In uncoupling eqns (44), the first step involves determining the modal frequencies and the corresponding mode shapes of the structure for \"undamped free vibrations.\" This involves the solution of the following equation for its characteristic values [KI{d,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003423_iet-cta:20050357-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003423_iet-cta:20050357-Figure1-1.png",
        "caption": "Fig. 1 Horizontal motion of marine vessels",
        "texts": [
            " M is a rigid-body inertia matrix including added mass, which is constant, non-singular and positive definite. C(n) is a skew-symmetric parameterisation of the rigidbody Coriolis and centripetal matrix including added mass. The total hydrodynamic damping matrix D(n) is symmetric and positive definite. The coordinate transformation matrix J(h) has full rank. g(h) is the vector of gravitational and buoyant forces and moments. 233 As the trajectory tracking problem for marine vessels is to find a control law that asymptotically stabilises both the positions and the orientation, shown in Fig. 1, which are mainly associated with the horizontal motions, we will restrict the six-dimensional dynamics to the horizontal plane by making the following assumptions. Assumption 1: The dynamics associated with the motion in heave, roll and pitch is negligible. This is a well known assumption used in all industrial ship control systems because the magnitude of the heave, roll and pitch variables are very small (second-order damped oscillators), and therefore their influence on the motion in horizontal plane can be neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure7.11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure7.11-1.png",
        "caption": "Fig. 7.11 Cam mechanism in a 4 cylinder gasoline engine",
        "texts": [
            " A distribution shaft (originally, the cam drum) as shown in Fig. 7.10, was the soul of the machine. The inventor, C. Spencer, called it the \u201cbrain wheel\u201d (Rolt 1965). With the rotation of the distribution shaft, cams on which commanded the components to move according to the prescribed motion. In general, the speed of cams in automatic lathes was not very high. A more important application of cam mechanisms was in internal combustion engine 232 7 Birth and Development of Modern Mechanical Engineering Discipline (Fig. 7.11), and later in various automatic machines in the light industry. Since the 20th century, the continuous increasing of speed of the internal combustion engine and automatic machines have been the direct driving force for the study on dynamics and design of cams. Following the development of the internal combustion engine, force analysis of the cam mechanisms appeared at the end of 19th century. The purpose was two-fold. First, the surface contact force and the force applied on the follower system need to be determined for the purpose of strength calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure1.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure1.3-1.png",
        "caption": "Figure 1.3. A gear pair.",
        "texts": [
            " Much of the geometric theory of gears applies equally to both external and internal gears. However, for the sake of clarity, this book is restricted to the subject of external gears, except for a single chapter. The exception is Chapter 12, where we will show which parts of the theory of external gears are valid for internal gears, and we will discuss the special features that apply only to internal gears. The Requirement for a Constant Angular Veloci ty Ratio When two gears rotate together, as shown in Figure 1.3, the teeth of each gear pass in and out of mesh with those of the other gear, and this occurs in an area that lies somewhere between the gear centers C1 and C2 . The teeth from the two gears pass through the meshing area alternately, first one from gear 1, then one from gear 2, and so on. Hence, if the gears have N1 and N2 teeth, and during a certain time interval T the number of teeth from each gear passing through the meshing area is n, then the gears will make respectively (n/N 1) and (n/N2) revolutions",
            " The new requirement for the angular veloci ties can be expressed by the equation, ( 1 .4) The purpose of this chapter is to determine the condition that must be satisfied by the meshing tooth prof i les, if the gears are to have the constant angular velocity ratio given in Equation (1.4). However, before looking at the case of two gears meshing together, we will consider that of a gear meshing with a rack. Rack and Pinion Rack and Pinion 13 A rack is a segment of a gear whose radius is infinite. I f the number of teeth N2 of gear 2 in Figure 1.3 were extremely large, the radius of the gear would also be large, relative to the tooth size, and the teeth near the meshing area would lie almost on a straight line. In the limit, as N2 becomes infinite, the teeth would lie exactly on a straight line, as shown in Figure 1.4. When two gears mesh, the smaller of the two is called the pinion, and the larger is usually referred to as the gear. Any gear meshed with a rack is considered smaller than the rack, since the rack is part of a gear with an infinite number of teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.4-1.png",
        "caption": "Figure 2.4.",
        "texts": [
            " The point in Figure 2.3 where the involute curve meets the base circle is labelled B. This is the point where the end A of the bar would meet the base circle, if the bar rolled to the position where A was the contact point. Due to the fact that the bar rolls without slipping, we can say that the length of arc EB on the base circle must be equal to the length EA on the bar. In symbolic form, this can be written, arc EB EA (2.8) We now need to define a number of new symbols, and to derive the relations between them. Figure 2.4 shows the base Profile angle and roll angle. The Involute Function 31 circle, and an involute curve starting at point B, with a typical point A at radius R. The normal to the involute at A touches the base circle at E. We define an angle ~R' called the profile angle at radius R, as the angle between the radius through A and the involute tangent at A. The radius CE is perpendicular to EA, since EA touches the base circle, and CE is therefore parallel to the involute tangent at A. Hence, the angle ECA is equal to the profile angle, angle ECA (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.1-1.png",
        "caption": "Figure 4.1. The ends of the path of contact.",
        "texts": [
            " In order to measure the amount of overlap, we introduce a quantity called the contact ratio, defined in the following manner. If a~c is the angle through which a gear rotates during one meshing cycle, and aop is the angle subtended at the gear center by one tooth, the contact ratio mc is defined as follows, ( 4 \u2022 1 ) The angle aop is known as the angular pitch of the gear, and its value in radians is equal to 2~ divided by the number of teeth, 2~ N (4.2) The rotation a~c is called the angle of contact, and in order to find its value, we need to describe the meshing process in some detail. Figure 4.1 shows a pair of meshing gears, and we will assume that gear is driving and is 84 Contact Ratio, Interference and Backlash turning counter-clockwise, so that gear 2 is being driven and is turning clockwise. When the gears rotate, the first contact between a pair of teeth occurs at T2 , the point where the tip circle of the driven gear cuts the common tangent to the base circles. This is because the contact point must lie on that line, as we showed in Chapter 3, and the teeth of gear 2 are not long enough to make contact at points on that line below T2\u2022 At the initial contact, therefore, the tip of the tooth on the driven gear is in contact with the tooth of the driving gear, at a point on its profile somewhere below the pitch circle. After the initial contact, the gears continue to rotate, and the contact point in Figure 4.1 moves upwards along the path of contact. On the driving gear, the contact point moves outwards towards the tooth tip, while on the driven gear it moves inwards. Contact ceases when the contact point reaches the tooth tip of the driving gear. The position where this occurs is at point T1, where the tip circle of the driving gear crosses the common tangent to the base circles. Contact Ratio 85 The displacement as of the contact point along the path of contact was related to the gear rotation a~ by Equation (3",
            "3) Hence, if as is the contact point displacement between the c beginning and the end of the meshing cycle, the corresponding gear rotation a~c can be expressed as follows, asc Rb (4.4) We now combine Equations (4.1, 4.2 and 4.4), to obtain an expression for the contact ratio, asc 211'Rb (-N-) and since the denominator is equal to the base pitch Pb' as it was defined in Equation (2.22), the expression for the contact ratio can be simplified to the following form, (4.5) The initial and final points of contact are shown in Figure 4.1 as T2 and T1, and the length asc is equal to the distance between these points. The line segment from T2 to T1 is the path of contact, and asc is therefore equal to the length of the path of contact. From the manner in which the contact ratio was defined in Equation (4.1), it might appear that two meshing gears could have contact ratios of different values, but it is now clear from Equation (4.5) that the two values must be the same, since the base pitches of the two gears are equal. Expressions for the positions sT1 and sT2 of the end points of the path of contact can be derived with the help of Figure 4.2, which shows the essential features of Figure 4.1 in greater detail. It should be remembered that s is defined like a coordinate, so that its value is positive for points above P, and negative for those below. The positions of the end points of the path of contact are then as follows, 86 Contact Ratio, Interference and Backlash 2 2 - Rb1 tan t/I + v'(RT1 -Rb1 ) (4.6) In these equations, circles, Rb1 and Rb2 operating pressure Equation (3.44), 2 2 Rb2 tan t/I - v'(RT2 -Rb2 ) (4. ?) RT1 and RT2 are the radii of the are the base circle radii, and t/I is angle of the gear pair, given tip the by cos t/I (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002886_s0921-5093(03)00435-0-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002886_s0921-5093(03)00435-0-Figure4-1.png",
        "caption": "Fig. 4. Overlaps between laser spot and powder stream under V /0 and (a) Dx /0; (b) Dx /0; (c) Dx B/0.",
        "texts": [
            " Then Dx was defined to be the distance between point O and A. Dx was defined to be positive when point B was beneath point O, otherwise it was negative. The direction of scanning velocity is defined as positive when powder delivery nozzle and clad are in different sides of the laser beam, otherwise it is negative. From Fig. 2(a) it can be found that the height of single cladding layer H varied with the change of Dx considerably. This was due to the amount of the powder injected into the melt pool varied with Dx , referring to Fig. 4. In Fig. 4, the shadow area, which represented the overlap between the laser spot and the powder stream, illustrated the amount of the powder injected into the melt pool approximately. From Fig. 2(a), it can also be found that the value of Dx corresponding to the maximum H was /2 mm. When the scanning velocity was positive and Dx ]/0, most of the powder was injected into the head part of the melt pool (see Fig. 3a, b). Since the shape of the melt pool is not axisymmetrical along the longitudinal section, in other words, if we take the center of laser spot as the origin point, the area of the head part of the melt pool is smaller than that of the tail part due to the heat flux. Therefore, the amount of the powder injected into the melt pool with Dx ]/0 was less than that with Dx B/0 (referring to Fig. 4). When the scanning velocity was negative and Dx ]/0, although most powder was injected into the tail part of the melt pool, the amount was still less than that with Dx B/0. It can be found from Fig. 3(c) that, the surface of the substrate was lifted due to the clad, which changed the relative position of laser beam, powder nozzle and substrate. When Dx ]/0, part of powders hit the surface of the solidified clad instead of being injected into the melt pool and was rebounded. When Dx B/0, this part of powders was injected into the melt pool which increased the total amount of the injected powders"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003800_j.mechmachtheory.2006.01.004-Figure5-1.png",
        "caption": "Fig. 5. Four-DOF single-loop kinematic chains involving an SP virtual chain. (a) R\u0302R\u0302R\u0302PkV, (b) R\u0302R\u0302R\u0302\u00f0RR\u00dekEV, (c) R\u0302R\u0302\u00f0RRR\u00dekEV, (d) R\u0302R\u0302R\u0302\u00f0PR\u00dekEV, (e) R\u0302R\u0302\u00f0RRP\u00dekEV, (f) R\u0302R\u0302R\u0302\u00f0PP\u00dekEV, (g) R\u0302R\u0302\u00f0RPP\u00dekEV, (h) R\u0302R\u0302R\u0302IPkV and (i) R\u0302R\u0302R\u0302IPkV.",
        "texts": [
            " In representing of an SP-equivalent parallel kinematic chain, SP-equivalent parallel mechanism and one of their legs, the planes of relative motion of the planar chains associated with \u00f0\u00dekE as well as the directions of the P joints denoted by Pk are all parallel to a common line. Table Four-D ci 2 1 0 ci \u00bc 2 By constructing single-loop kinematic chains each composed of one Codirectional serial kinematic chain and one spherical serial kinematic chain, we obtain one type of 4-DOF single-loop kinematic chains involving an SP virtual chain (see row 2 of Table 2 and Fig. 5(a)). ci \u00bc 1 By constructing single-loop kinematic chains each composed of one planar serial kinematic chain and one spherical serial kinematic chain, we obtain several types of 4-DOF single-loop kinematic chains involving an SP virtual chain, which are listed in row 3 of Table 2 and shown in Fig. 5(b)\u2013(g). In addition to the above types, one can obtain the types of 4-DOF single-loop kinematic chains involving an SP virtual chain with ci = 1 by inserting one inactive R or P joint in 4-DOF single-loop kinematic chains 2 OF single-loop kinematic chains with an SP virtual chain Number of inactive joints Type 0 R\u0302R\u0302R\u0302PkV 0 R\u0302R\u0302R\u0302\u00f0RR\u00dekEV R\u0302R\u0302\u00f0RRR\u00dekEV R\u0302R\u0302R\u0302\u00f0RP\u00dekEV R\u0302R\u0302R\u0302\u00f0PR\u00dekEV R\u0302R\u0302\u00f0RRP\u00dekEV R\u0302R\u0302\u00f0RPR\u00dekEV R\u0302R\u0302\u00f0PRR\u00dekEV R\u0302R\u0302R\u0302\u00f0PP\u00dekEV R\u0302R\u0302\u00f0RPP\u00dekEV R\u0302R\u0302\u00f0PRP\u00dekEV R\u0302R\u0302\u00f0PPR\u00dekEV 1 R\u0302R\u0302R\u0302PkIV 2 R\u0302R\u0302R\u0302PkIIV 1 R\u0302R\u0302R\u0302\u00f0RR\u00dekEIV R\u0302R\u0302\u00f0RRR\u00dekEIV R\u0302R\u0302R\u0302\u00f0RP\u00dekEIV R\u0302R\u0302R\u0302\u00f0PR\u00dekEIV R\u0302R\u0302\u00f0RRP\u00dekEIV R\u0302R\u0302\u00f0RPR\u00dekEIV R\u0302R\u0302\u00f0PRR\u00dekEIV R\u0302R\u0302R\u0302\u00f0PP\u00dekEIV R\u0302R\u0302\u00f0RPP\u00dekEIV R\u0302R\u0302\u00f0PRP\u00dekEIV R\u0302R\u0302\u00f0PPR\u00dekEIV 0 Omitted involving an SP virtual chain with ci = 2. The results obtained are listed in row 4 of Table 2 and shown in Fig. 5(h) and (i). Note that an inactive joint can be placed anywhere within a single-loop kinematic chain. Hence, we just list some types, from which all the types can be readily obtained by changing the topological position of the inactive joint. ci \u00bc 0 By constructing single-loop kinematic chains each composed of the SP virtual chain and six R and P joints, many types of single-loop kinematic chains can be obtained. Among these types, those types with simple structure, such as UPSV, PUSV and RUSV, are of practical interest. Moreover, some types of single-loop kinematic chains can be obtained by the application of ci, where ci > 0, inactive joints in the single-loop kinematic chains with a ci\u2013f0-system obtained above. The types that were obtained are listed in rows 5 and 6 of Table 2. For a better understanding of the notation used, several single-loop kinematic chains involving an SP virtual chain are shown in Fig. 5. In Fig. 5, the SP virtual chain is drawn with dashed lines. By removing the virtual chain in a 4-DOF single-loop kinematic chain involving an virtual chain, one leg for SP-equivalent parallel mechanisms can be obtained. For example, by removing the virtual chain in an R\u0302R\u0302R\u0302\u00f0RR\u00dekEV kinematic chain (Fig. 5(b)), an R\u0302R\u0302R\u0302\u00f0RR\u00dekE leg (Fig. 6(b)) can be obtained.2 Such a leg has a 1-f0-system. The f0 passes through the common point of the axes of three R\u0302 joints and is parallel to the axes of the R joints within \u00f0RR\u00dekE. In this way, all the legs for SP-equivalent parallel mechanisms have been obtained and are listed in Table 3. Based on the results obtained in steps 1 and 2, we can construct types of SP-equivalent parallel kinematic chains using the following three sub-steps. Step 3a: Take one combination of leg-wrench systems from Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure9.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure9.5-1.png",
        "caption": "Figure 9.5. Gear tooth fillet and rack cutter.",
        "texts": [
            " Fillet Shape Cut by a Rack Cutter The general theory just described, which gives the shape of tooth profiles conjugate to an arbitrary basic rack, can also be used to find the shape of gear tooth profiles, when they are cut by a rack cutter with curved teeth. In particular, when we consider involute gears, we will use the Fillet Shape Cut by a Rac k Cutter 213 method to find the shape of the tooth fillet, which is cut by the circular section at the tooth tip of the rack cutter. The tooth profile of the rack cutter is shown in Figure 9.5. The circular section of the profile extends from point Ahr to point ATr \u2022 The radius of this section is rrT' and its center is at point A~, whose coordinates (x~,y~) are given by Equations (5.43 and 5.44). In the general theory described in the previous section, we chose a point Ar of the cutter tooth profile, and determined the position ur of the cutter, at which Ar would be the cutting point. For the special case when the cut ter tooth profi Ie is circular, it is sl ightly more convenient to reverse this order. We choose the position of the cutter, and we then determine which point Ar of the circular profile is the cutting point. We therefore consider the cutter in the position shown in Figure 9.5, with an offset e and with the x axis lying a r distance (-ur ) below line CPo In this position of the cutter, the center A~ of the tooth profile circular section has coordinates (~' ,~'), which are given by the following equations, ~ I e + x' r (9.10) 214 Geometry of Non-Involute Gears 1/' (9.11) If the line from the pitch point to A~ intersects the tooth profile at Ar' and Ar is a point on the circular part of the profile, then the normal to the profile at Ar passes through P, and Ar must be the cutting point. The line ArP is the line of action, when the cutter is in the position shown in Figure 9.5. We now reintroduce the coordinate s, measured from the pitch point along the line of action, with points above P being positive. The positions s' and s of points A' r and Ar on the line of action can be expressed as follows, s' s s' - r rT (9.12) (9.13) and we then write down the position of the cutting point Ar' (9.14) ( ...\u00a7...) ., \u2022 s' 'f (9.15) It is evident that the negative signs of s\u00b7 and s cancel out, and it would have been simpler to have used positive values. However, we will make use of these equations again in Chapter 10, when we discuss the fillet curvature, and for that purpose it is important to retain the correct sign fors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003129_a:1008106331459-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003129_a:1008106331459-Figure9-1.png",
        "caption": "Figure 9. Robot motion during transportation.",
        "texts": [
            " When performing a micromanipulation task, the manipulator tip must stay under the microscope objective. In this case, the center of rotation of the robot is the point A or B, correspondingly, on the endeffector tip (Figures 10 (a) and 10 (b)). However, both the linear and the rotational motion phase are performed sequentially by using both these methods so that the whole operation time of the robot is generally not optimal. When performing a navigation task by the third method, the center of rotation is point OA (Figure 9 (c)). In this case, the route length between points OA and OB is minimized. When performing a micromanipulation task, the center of rotation is the tip of its manipulator (in the initial state \u2013 point A, Figure 10 (c)). In the latter case, the route length between points A and B is minimized to keep the endeffector tip under the microscope objective. An advantage of the third method is the possibility to move along an optimal trajectory in minimal time. However, as the actual direction of the linear robot motion is determined by its current orientation, the motion direction must be continuously corrected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.9-1.png",
        "caption": "Figure 3.9. Meshing diagram, with contact at the pitch point.",
        "texts": [
            "46) When this relation is compared with Equation (3.42), it is evident that the operating pressure angle of gear is equal to the operating pressure angle ~ of the gear pair, A Pair of Gears in Mesh 69 I/>pl (3.47) A similar argument shows that the operating pressure angle of gear 2 is also equal to 1/>, I/>P2 (3.48) and Equations (3.47 and 3.48) can of course be combined, to show that the three angles are all equal, I/>Pl I/>P2 (3.49) Equation (3.49) could have been proved more directly, simply by looking at the meshing diagram shown in Figure 3.9, where the contact point coincides with the pitch point. The common tangent to the tooth profiles at the contact point is perpendicular to the line of action, and it can be seen from the diagram that the three angles I/>pl' I/>P2 and I/> are all equal. We have shown that the operating circular pitches Ppl and Pp2 are equal, and that the operating pressure angles I/>Pl and I/>P2 are also equal. It is often convenient, whenever we 70 Gears in Mesh have proved that a particular quantity on one gear is always equal to the corresponding quantity on the other gear, to introduce a single symbol which can be used to stand for either quantity",
            " The same convention will be used throughout the remainder of the book, without further explanation. Relation Between the Gear Positions For gear 1, we have specified the angular posi tion by the angle f1 1, measured from line C1P counterclockwise to the x 1 axis. We now specify the angular position of gear 2 in the same manner, as the angle f12 measured from line C2P counterclockwise to the x2 axis. In this section we derive a relation between the angles f11 and f1 2\u2022 The two gears are shown in Figure 3.9, with the contact point coinciding with the pitch point, and in these positions the angles f11 and f12 can be written down by inspection, -~ 2Rp1 f11 (3.50) -~ 2Rp2 (3.51) After rotations ~f11 and ~f12' the angular positions of the two gears are given by the following expressions, The angular Equation (1.21), f11 -~+ 2Rp1 f12 -~+ 2Rp2 velocities ~f11 (3.52) ~f12 (3.53) and are related by (3.54) and we integrate this equation to find a relation between the gear rotations, Path of Contact and Line of Action 7' (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.8-1.png",
        "caption": "Figure 3.8. Meshing diagram of a gear pair.",
        "texts": [
            " In practice, two gears intended to mesh together are almost always designed so that they have the same module m and the same pressure angle lP s \u2022 In other words, they are conjugate to the same basic rack. The base pitch of a gear is related to the module and the pressure angle by Equations (2.24 and 2.3'), 1rm cos I/I s (3.39) Hence, if the two gears are designed with the same module and the same pressure angle, this ensures that they have the same base pi tch, and therefore that they wi 11 mesh correctly. A Pair of Gears in Mesh 67 The meshing diagram of a pair of gears is shown in Figure 3.8, with line E1E2 cutting the line of centers at the pitch point P. The pitch circles of the two gears are the circles which pass through P, and their radii are expressed in terms of the center di stance C by Equat ions ('.24 and 1.25), (3.40) (3.41) We have proved that the common normal at the contact point lies along E,E2 , and this line is therefore the line of action. For a pair of gears, the operating pressure angle ~ is defined as the angle between the line of action and the common tangent to the pitch circles at P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002777_s0021-9290(98)00043-8-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002777_s0021-9290(98)00043-8-Figure1-1.png",
        "caption": "Fig. 1. Drawing of the experimental setup. The radius and ulna of the specimen were attached to a Plexiglas plate. The wrist was fixed in a neutral position by passing a fiberglass rod through the intramedullary canal of the third finger, into the carpal bones of the wrist and into the radius. Moment arms for each joint were measured separately. The two joints not to be tested were fixed in a neutral position using K-wires. The 3-Space tracker was used to measure joint excursion. One sensor from the 3-Space tracker was attached to the distal bone of the joint to be tested. The potentiometers were used to measure tendon excursion. The Plexiglas guides were used to ensure that the joint motion was only in the desired plane.",
        "texts": [
            " Abduction and adduction motions of the thumb away from and toward the palm, respectively (Smith and Butterbaugh, 1994). The neutral position of the IP and MP joints are defined to be when the long axes of the distal and proximal phalangeals and when the long axes of the proximal phalangeal and the metacarpal are parallel, respectively. The neutral position of the CMC joint is the mid-point of CMC flexion/extension and CMC adduction/abduction (bent index finger with the thumb sitting on the radial side of DIP of the index finger). Moment arms for each of the joints were measured separately in the setup (Fig. 1). One sensor from the 3-Space tracker was attached to the distal bone of the joint to be tested. The source was attached to the Plexiglas test fixture 30 cm from the sensor. The two joints that were not to be tested were fixed in a neutral position using K-wires which were confirmed not to affect the accuracy of 3-Space measurements. A second sensor was used to digitize points on the bones distal and proximal to the joint for establishing the coordinate system for defining joint rotation. The joint was then passively moved using a fiberglass rod that was inserted into the distal phalanx along two Plexiglas guides to ensure the motion in the desired plane (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000154_j.addma.2020.101091-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000154_j.addma.2020.101091-Figure14-1.png",
        "caption": "Fig. 14. The full-scale model of the lattice structure block with 1.0 mm lattice unit size.",
        "texts": [
            " To give a thorough investigation, the full-scale block with all the detailed lattice features is also simulated. However, only the case of the lowest volume density 0.19 with 1.0 mm center-wall-towall distance is studied because the computational cost is not affordable for the remaining cases with denser lattice structures. The full-scale thin-walled lattice support structures containing 1,125 (75 in length \u00d7 15 in width) hollow tubes on the solid base are created and meshed finely in ANSYS as shown in Fig. 14. The 10.5mm-high model is divided into 30 equivalent layers, five layers of which are for the 3mmthick solid base. Activation layer thickness has a significant influence on the distortion prediction results through the layer-by-layer simulation. This topic was carefully studied in our previous paper [25]. In this section, an activation layer thickness of 0.6 mm is used since there are 5 equivalent layers in the 3-mm thick solid base under the lattice structures. Given the physical layer thickness is 0",
            " As a result, the homogenized model can now be represented effectively by a homogeneous block of the same size. The solid material below the thin-walled lattice structures is modeled as an isotropic material, while the homogenized lattice structures are modeled as an anisotropic material. As a result, the elasticity tensor C given in Eq. (2) is isotropic for the solid base and is anisotropic for material in homogenized model for thin-walled lattice structures. The total element number in the homogenized model is 109,375, which saves nearly 80 % in the number of elements compared to the full model (see Fig. 14). There are 30 equivalent layers defined in the homogenized model and different inherent strain vectors will be used for the five layers in the solid base and the remaining layers in the lattice support structures. Element killing is also adopted to simulate the stress release phenomenon after the AM process is completed. Moreover, the same mechanical boundary condition employed in the full-scale simulation is also used in this simulation. It took nearly one hour to finish the simulation based on the homogenized model on the same desktop computer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000442_j.surfcoat.2020.125706-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000442_j.surfcoat.2020.125706-Figure3-1.png",
        "caption": "Fig. 3. The profile of the laser cladding.",
        "texts": [
            " In order to balance the influence of laser cladding process parameters on the results of research, a single track orthogonal experiment is conducted, In addition, the degree of tilt angle in the orthogonal experiment has an increment of 20\u00b0 with the range of 0\u201360\u00b0 (total 4 levels). The experimental scheme of design is given in Table 1. Through orthogonal experiment, geometric characteristics of single track laser cladding can be studied. According to geometric characteristics of the laser cladding, profile of the cladding is displayed in Fig. 3. There are eight major geometric parameters defined. They are the molten pool depth h\u2032, the layer cladding height h, the layer cladding width W, the peak shift u, the elevation side width we, the reduction side width wr, the elevation side depth de, and the reduction side depth dr, as shown in Fig. 3(b). But the peak shift u almost disappears when the tilt angle is approaching to 0\u00b0, as shown in Fig. 3(a). Then, the results of orthogonal experiment are analyzed. The results of the orthogonal experiment with the same tilt angle calculate the mean, as shown in Fig. 4(b). And it is made to obtain Fig. 4(a) that the difference between the maximum and the minimum of the means under different tilted angles. As can be seen from Fig. 4(a), tilt angle mainly affects the layer cladding width, elevation side width, layer cladding height, reduction side width, and the peak shift. The degree of influence is sequentially lowered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003129_a:1008106331459-Figure19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003129_a:1008106331459-Figure19-1.png",
        "caption": "Figure 19. Schematic drawing of the microrobot\u2019s design.",
        "texts": [
            " Sensor Design and Physical Principle Without taking a closer look at the design of the microrobots, it is obvious that the following requirements have to be met when developing force sensors for micromanipulation tasks: small dimensions, low weight, high resolution, high linearity, high accuracy, and suitability for the use in a scanning electron microscope (SEM), see Section 7. More requirements on the force sensors ensue from the design of the microrobots developed at the IPR. They consist of three main units: a positioning unit, an integrated micromanipulation unit and a gripper (Figure 19). The interface between the manipulation unit and the gripper is formed by a steel ball which can be positioned with three rotational degrees of freedom by piezoceramic tubes (see [21, 22, 25] for more detail about the microrobots\u2019 design and actuation principle). There are no mechanical joints between these two units. Hence, it is not possible to integrate force/torque sensors, which are well known from conventional macrorobots, between gripper and manipulation unit. So the use of laser-based force sensors might be taken into consideration, often used in scanning force microscopes to measure forces by beam deflections with very high resolutions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003745_70.54745-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003745_70.54745-Figure1-1.png",
        "caption": "Fig. 1 . Manipulation with two planar arms",
        "texts": [
            " l , j is a measure of the isotropy of the force ellipsoid. C . A Planar Dual Arm Manipulation System-An Example As an example. we consider two planar robot manipulators, where each has two revolute joints. We model the gripped object as a small cylinder (the radius is small compared with the link lengths). and the interaction between the hvo arms is modeled as a revolute joint. In these circumstances, the system may be modeled as a closed fivebar chain (with five revolute joints) and four actuators. as is shown in Fig. 1. The mobility of the linkage is cqual to two. and the task space i s the 2D translational space. Since the number of control inputs (actuators) is four, the system is redundant. Let (x, y ) be the coordinates of thc ob.ject and 8, be the joint variables. Further, let c , , s,. c , , , and s , , denote cos 8,. sin 0 , . IEEE TRANSACTIONS ON ROBOI'ICS .AY[) AV1'O!dAIION. VOI. 6. N O 2 . APRII. 1990 27 1 cos(8, + 0 ) ) . and sin(8, + 0,). respectively. The rate kinematics equations are where and Inverting the Jacobians analytically"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003783_38.55154-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003783_38.55154-Figure5-1.png",
        "caption": "Figure 5. The physical effects of approaching a singularity. The achievable velocity of the hand becomes restricted to the nonsingular direction. However, because of the duality of the static force and velocity relationships defined by the Jacobian, the singularity also results in the ability to balance large forces in the singular direction.",
        "texts": [
            " A A Singularities and pseudoinverse solutions The above discussion shows that the minimum singular value is important in determining the conditioning of the Jacobian and therefore in obtaining usable solutions to Equation 1. Since the conditioning of Equation 1 becomes worse as omin decreases, we should consider the worst case-what happens when omin is equal to zero. Then J is referred to as singular, and an exact solution to Equation 1 will not exist for an arbitrary desired hand velocity. To examine the physical significance of this situation, consider the configuration of the arm shown in Figure 5. The arm is approaching the singular configuration of being completely stretched out. Joint rotations about each of the three joints result i n approximately the same motion at the hand; in mathematical terms the joints are becoming linearly dependent. Note that it becomes increasingly easier to move in the direction of ul, while velocities along u2 become increasingly more difficult. At the actual singularity there is no combination of joint velocities that can result in a hand velocity along u2",
            "2~4~7~\u201d~14~17\u201918 However, using true pseudoinverse solutions for any equations describing the motion of articulated figures still has fundamental drawbacks. Such equations are not isolated mathematical formulas, but represent how the physical system evolves over time. As such, we are repeatedly solving sets of equations slightly perturbed from the previous set of equations. Physically, their solut ions must have continuity, and here the pseudoinverse solutions fail. As an example, consider the singular value decomposition of the Jacobian for the arm in Figure 5, where the diagonal matrix of singular values is given by Equation 6 . While CT, remains nonzero, the pseudoinverse of D will be given by r l 0 1 101 I D+=ll However, when the arm moves into the singular configuration and CT, becomes zero, the pseudoinverse becomes The difficulty therefore is not at the singularity, where the pseudoinverse provides a perfectly reasonable solution, it is the discontinuous transition between singular and nonsingular configurations. Unfortunately, at this transition the equations are also most ill conditioned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003160_20.620439-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003160_20.620439-Figure2-1.png",
        "caption": "Fig 2. Configuration of mesh matnx",
        "texts": [
            " Therefore, it is reasonable to assume that the current distribution in the primary coil is uniform. In this analysis, the number of turns in the primary coil is Np, and that in the secondary coil is N,, the current in the primary winding is Ip , and the off-center distance is y. 11. CALCULATION WITH COMPLETE ELLIPTIC INTEGRALS AND MESH-MATRIX METHOD In order to account for the finite dimensions of the coils, the primary and secondary are considered to be subdivided into meshes of filamentary coils as shown in Fig. 2 [6], [20], [22]. In this figure, the cross-sectional area of the primary coil is divided into (2M + 1) by (2N + 1) cells, and that of the secondary coil into (2m + 1) by (an + 1) cells. These cells need not correspond to the actual turns of the coils. If the cross section of the coils is not rectangular, e.g., circular, the current densities in nonexisting elements can be regarded as zero when the calculation is performed. Each cell in the primary coil contains one filament, and the current density in the coil cross section is assumed to be uniform, so that the filament currents are all equal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002750_s0043-1648(00)00384-7-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002750_s0043-1648(00)00384-7-Figure6-1.png",
        "caption": "Fig. 6. Relation between two adjacent points at the beginning of the mesh cycle, and as they pass through the contact. The points are depicted at three different angular positions of the gear wheels. s and s are the slid distances for point one and two, respectively.1 2",
        "texts": [
            " The model is not restrained as Hertz\u2019 model and can handle non-smooth surfaces. The model is, however, more tedious to use in calculations, especially if the springs are coupled. The gain in precision is also too small to be of significance in these simulations. The single point observation method has been thoroughly described in previous papers by the authors and w xwas first used by Andersson and Eriksson 10 . The method is also used in this paper where the wear depth is calculated at discrete points as they pass through the contact \u017d .see Fig. 6 . In every time step, the sliding speed between two adjacent points in contact is calculated and the sliding distance s for that particular time step and point can be calculated as: s s\u00d5 D t 5\u017d .p p ,slide Relevant properties such as pressure, position and sliding speed are calculated for every point that is in the contact zone. The sliding speed for a point is the difference between the components of \u00d5 and \u00d5 and that are perpen-1 2 \u017d .dicular to the line of action see Fig. 6a . Since a point on the pinion will rarely be exactly adjacent to a point on the gear when in mesh, virtual points are created on the gear \u017d .flank in every time-step see Fig. 7 . Sliding speed and pressures on the pinion\u2019s points are then calculated relative to the imaginary points. The wear depths at the true points on the gear are interpolated from the virtual points. Many wear models have been proposed over the years, both empirical and phenomenological. The authors have previously investigated some phenomenological models w x1\u20133 that dealt with oxidation as well as with adhered lubricant molecules"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000273_j.addma.2020.101088-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000273_j.addma.2020.101088-Figure5-1.png",
        "caption": "Figure 5 Distribution of von Mises stress in (a) conventional design and (b) optimized design under the same tension loading. The von Mises stress reached yield strength (880 MPa) for both designs.",
        "texts": [
            " It should be noted that manufacturing constraints for conventional manufacturing techniques are not considered in the optimization of this study since we want to utilize the capability of EBM process in printing structures with complex geometry. However, the minimum thickness is set to 1 mm which is slightly above the printing limit of the EBM A2X machine. Detailed design on the result of topology optimization is performed to produce a clean-up, finalized design. Figure 4 shows the conventional and optimized designs, and Figure 5 shows the distribution of von Mises stress in the two designs under tension loading condition, in which both designs reach yielding condition at the same load. It can also be seen in Figure 5 (b) that the maximum stresses of the optimized design occur at the left and right bottom corners of the hole-areas. As shown in Figure 4, the hole-area of the optimized design at the bottom plate (90 \u00d7 77 mm) is larger than that of the conventional design (53 \u00d7 54 mm). The minimum thickness of the optimized design is 1.8 mm, which is also thinner than that of the conventional design (4 mm). Some of the mass reduced in the bottom plate of the conventional design is redistributed to the top plate in optimized design, which increases the bending strength of the wishbone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003347_anie.199105161-Figure17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003347_anie.199105161-Figure17-1.png",
        "caption": "Fig. 17. Hydrogen sensor produced by thick-film technology[ll3] (see Text).",
        "texts": [],
        "surrounding_texts": [
            "The essential principle of a chemo- or biosensor is described in terms of three basic components (Fig. 1). The most important component is the receptor (the recognition system), where in general an energetic interaction specific to the substance in question (the analyte) enables it to be recognized. The development of new recognition principles, or the improvement of known processes for this purpose, is a task for the chemist or physical chemist. Campared with this challenge the next stage is less difficult; the function of this second component of any chemo- or biosensor is to \"relay\" the substance-specific signal, in other words to transform an energy quantity into an electrical signal proportional to it. Karl Cammann, born in i939 in Diisseldorf, studied Chemistry at the Technical University of Munich after obtaining a degree in chemical engineering and working in industry (Beckman Instruments) for several years. His scientific advisor for the Diplom thesis was H. Gerischer; his Ph.D. advisor was G. Ertl (University of Munich). After postdoctoral positions with G. A. Rechnitz (State University of New York at Buffalo) and S. Mazur (University of Chicago) he accepted an assistant professorship for Analytical Chemistry at the University of Ulm. In 1986 he became an Associate Professor of Analytical Chemistry at the Technical University of Munich and shortly thereafter (i987) Full Professor of Analytical Chemistry at the Westfiilische Wilhelms University of Miinster (chair of Prof. E: Umland). His research interests lie in the field of selective chemical detectors and monitors. In 1987 he received two awards for the development of a new plasma-emission-spectroscopic GC-detector (OcP van der Grinten Pollution Control Award: Technology Transfer Award of the German Ministry for Education and Science). Angew. Chem. Inr. Ed. Engl. 30 (1991) 516-539 517 Receptor Transducer (recognition sys tem) e.g. semiconductor surface. ion-selective membrane. biomolecule. reagent layer Electronics Output e.g. e.g. change in electrode. potential,current, omplifier, photodiode -light guide/ l ight in,ensity, A-D converteretc. n pen recorder, data-processing system This task is usually performed by one of a wide choice of familiar physical transducers. Often a third component, consisting of a further electronic unit (a preamplifier, impedance converter, multiplexer, analogue-to-digital converter, etc.) is placed directly after the transducer, to suppress as far as possible external influences caused by interfering electric or magnetic fields, or to feed the separate signals from several recognition systems simultaneously to the data processing unit through a single electrical connection. Chemo- and biosensors can be classified according to the type of sensor element used for molecular recognition, or according to the type of transducer. If the emphasis is on analytical selectivity, the most important component is the recognition system. If on the other hand the limit of detectability or the signal-to-noise ratio is crucial, the critical component may be the physical or electronic transducer (see Table 2). All chemo- and biosensors can be used directly for analyzing gases and liquids (the latter also includes suspensions or pastes) for specific ions or molecules, in concentrations varying from the ppb range to the percent range. As the sample preparation required for chemo- or biosensors of adequate selectivity is minimal, and the sensors are available at low cost, high rates of growth are forecast by all the market studies that have been carried out. For sensors that are less selective, it is still possible in many cases to design a comparatively inexpensive measuring instrument, by incorporating automatic sample preparation based on a chemical reaction which is selective, or on separation techniques. Flow injection analysis is especially valuable in this respect.[241 2. Chemosensors 2.1. Electrochemical Sensors 2.1.1. Ion-Selective Electrodes Till a few years ago ion-selective electrodes (including the glass pH electrode) were the most important class of chemosensors in economic terms, since at that time the \u201clambdaprobe\u201d for controlling three-way catalytic converters for automobiles was not yet produced in today\u2019s numbers because of the absence of legal requirements. In ion-selective potentiometry the data are processed using an extension of the Nernst equation derived empirically by N i ~ o l s k y . ~ ~ ~ ] This extended equation (a) relates the activity of the ion species to be determined and the measured voltage when an ISE halfcell is connected to a common reference electrode, taking into account the effects of all interfering components. RT U = U o +7 In [ a M + x K M - -MF I Li = potential of the cell R = universal gas constant T = absolute temperature F = Faraday constant Uo = standard potential of the cell aM = activity of the ion being measured zM = charge of the ion being measured (with appropriate sign) KM-, = selectivity coefficient (measured ion vs. interfering ion) a, = activity of the interfering ion z , = charge of the interfering ion (with appropriate sign) The selectivity is described by the selectivity coefficient K M - , , which unfortunately is not a constant, since it depends on the method used for the determination and on the concentrations of all the interfering species and the ion to be measured. For good ISEs it is of the order of which means that a 104-fold excess of the interfering ion would change the reading by a factor of 2 (i.e. an error of 100%). A new theoretical model of the mechanism for the selectivity in the potential generated at the phase boundary between the ionselective membrane and the measured medium has been developed in the last few years.[26-301 This is based on the studies of Koryta13 l1 and others on electrochemical phenomena at the interface between two immiscible electrolytes, and also on results from studies on corrosion involving competing electrode reactions. The basic principle of ion-selective potentiometry is the observation of an ion-selective change in the potential at the phase boundary. This in turn depends on the ion-selective change (or shift) of charge (or charge distribution) at this boundary, i.e., a significant transfer between the phases occurs only for the ion species in question. This requires that 518 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 certain energetic and geometrical variables be optimally matched. If an uncharged ion-selective membrane electrode which satisfies the electrical neutrality condition is immersed in an electrolyte solution, a transfer of charge carriers occurs between the phases. The direction of this (membrane + solution or the reverse) is determined by the gradient of the chemical potential. When only one species of ion can selectively cross the boundary (this selectivity results, for example, from specific complex formation in liquid or PVC membranes, or from the dimensions of lattice sites in polycrystalline or semicrystalline materials), this selective transfer of charge carriers leads to a redistribution and an accumulation of charge at the phase boundary. This generates an electric field, thus counteracting the ion transfer which was at first energetically favored, so that eventually, under the combined influence of the electrostatic repulsion between similarly charged particles and the attractive forces due to the oppositely charged carriers left behind, the transfer of charge carriers ceases and the reverse reaction is favored. In the equilibrium state the microscopic ion currents passing in both directions through the phase boundary are equal, and the ion-selective potential difference that is thereby established is constant and can be measured. Externally the condition is one of zero current (a requirement for potentiometric measurement). In terms of electrochemical kinetics the transport of charge carriers (measured ions) across the phase boundary between the electrode or ion-selective membrane and the solution corresponds to a directed electric current i'or i(depending on whether the direction is from membrane to solution or the reverse). In the equilibrium state i'= i= i,. The current density j , (= &/A, A = area) is called the exchange current density (see Fig. 2). The two opposing current densities :and Jmaintain the ion-selective charge distribution at the phase boundary at a constant value. Furthermore, these microscopic ion-currents actually make it possible to measure the charge distribution at this interface, since in practice one cannot avoid drawing a current of lo-'' to A in i [ pAlcmZ] Fig. 2. Schematic representation of the forward and reverse currents iand i passing through the phase boundary; the selectivity is given by the ratio of the (equilibrium) charges qH and q, for the measured and interfering ions respectively (see text). the measuring circuit, depending on the amplifier used, which corresponds to a net flow of lo9 to lo5 elementary charges per second. The ion-selective electrical potential generated at the phase boundary of such an ion sensor by selective charge separation is, of course, dependent on the concentration of the ionic species which can cross the boundary. The relationship between ion concentration and interfacial potential was derived theoretically by Nernst as long ago as 1889, in the brilliant work leading to the equation named after him. From the ion-exchange current density j,, which can be determined experimentally, the recent theory predicts the selectivity of a potentiometric sensor. The potential in each case is determined by the ionic species that has the greatest exchange current density. Other reactions may take place at the phase boundary in parallel with the process described (because real solutions usually contain interfering ions in addition to those being measured). The thermodynamic equilibrium potentials for the individual electrode reactions (in this case, the parallel processes in which the measured and interfering ions cross the phase boundary between two ionic conductors), as in the case of corroding metal electrodes, may not be fully achieved. This results in deviations from the theoretical Nernst behavior. In order to achieve a high ion-exchange current density and thereby obtain the desired selectivity, appropriate changes can be made in the thermodynamic and kinetic variables. For example, introducing into the membrane an ionophore for a particular ion species causes an increase in the exchange current density, and therefore in the selectivity for that ion. The selectivity obtained in this way is probably due to a long-range ion-dipole interaction between this particular ion species in the solution and the ionophore in the membrane surface. It is conceivable that, specifically for the potential-determining ion species, an overlap of the energy barriers involved (desolvation and decomplexation activation-energy profiles) occurs, which results in the lowering of the effective activation energy for ion transfer over the entire phase boundary. This activation energy can also be expressed in electrochemical terms as an ion-transfer resistance. This in turn is inversely proportional to the exchange current density, and can be obtained, for instance, from impedance spectra.r32* 331 The selectivity of all types of ion-selective membranes, the rapid establishment of the potential, even for thick membranes, and the abnormally large graph slopes in the U vs. log a diagram that are occasionally found (steeper than predicted by the Nernst factor preceding the logarithm of the activity of the measured ion, see Eq. (a)), can all be satisfactorily explained by this novel theoretical approach which also considers kinetic parameters. Numerous fundamental studies have been carried out in our research group since 1975 to determine the conditions that must be fulfilled for a particular ion to be potential-determining (and therefore able to be measured selectively). For every type of electrode the critical factor was the ratio of the exchange current density for the measured ion to that for the relevant interfering ion. In every case this ratio was equal to the potentiometrically measured selectivity coeficient in the extended form of the Nernst equation [Eq. (a)]. A comparison of good ion-selective electrodes reveals several common features. Firstly, they have a rather high poten- Angew. Chem. Ini. Ed. Engl. 30 (1991) 516-539 519 tial-determining exchange current density for the measured ion at the phase boundary between the ion-selective membrane and the solution. Secondly, for solid membranes, there is a preferential ionic conductivity in regions near the surface (e.g., Ag,S is a good conductor for Ag@ ions, and LaF, doped with EuZ0 is a good conductor for F' ions). In PVC membranes with selective ionic charge carriers the preferred method is to use only iondipole interactions, as is evident from a glance at the list of so-called electroactive compounds that are available.[341 Apparently the course of the activation energy threshold for the transfer of ions from the membrane phase to the solution, together with the course of activation energy for the desolvation process, determines the intersection point (i.e., the effective energy of activation for the phase transition of the relevant ion). The existence of a purely kinetic effect in favor of the ion being measured is a necessary, but not a sufficient, condition for a selective Nernst sensor which performs well and above all is stable over long periods. In addition there must be a certain degree of nonpolarizability. This quantity, as electrochemists use it, is, in simple terms, a measure of the ability of an electrochemical half-cell to maintain a constant potential regardless of the instantaneous current density at the interface. Good ion-selective electrodes, like good reference electrodes, have a relatively steep characteristic curve in the current vs. voltage diagram (C-V curve) for the ion being measured. Viewed from this standpoint, the interfering ions have characteristic C-V curves that are less steep than that for the ion being measured. If these ions are present in a solution together with the measured ions, according to our present state of knowledge a mixed potential is established, as is the case for corroding metal electrodes. This is determined predominantly by the equilibrium potential for that electrode reaction (transfer of ions between phases) which has the steepest C-V characteristic. To obtain a favorable C-V characteristic over as large a range of overpotential as possible, it is also necessary to take concentration polarization effects into account. Here higher concentrations of the measured ions in the membrane phase turn out to be beneficial; their diffusion from there into the solution, which has an unfavorable effect on the limits of detection, is hindered by complexation and by the charges of appropriately chosen counterions. This also has the advantage of increasing the buffer capacity for the chemical potential of the measured ions in the membrane phase. A detailed treatment of these aspects has been Ion-selective electrodes can be used as electrochemical half-cells in combination with suitable constant-potential reference electrodes for the quantitative determination of a wide range of substances (see Table 1). They can be classified according to the type of membrane, viz., glass, solid, liquid, or PVC membrane electrodes.[36q 371 Glass and solid membrane electrodes are robust and have a typical lifetime of several years, much longer than liquid or PVC membrane electrodes, which only remain effective for about six months, depending on the application, unless one is prepared to accept large sacrifices in sensitivity and selectivity. However, for the latter types of electrodes some manufacturers have introduced a modular design which allows the easy and rapid renewal of sensitive electrode elements. The most important types of ionophores required to make one's own selective PVC membranes are available commercially,[381 and are supplied complete with instructions; these were developed mainly by Simon's research group in Zurich. 2.1.2 Ion-Selective Field Effect Transistors (ISFETs) It was believed for a long time that in ion-selective field effect transistors, first described by Bergveldt3'* 401 in 1970, we at last had a new generation of sensors which met all the requirements of miniaturizability, compatibility with microelectronics, and the capability for being mass-produced, with attendant cost savings. The now familiar production techniques of microelectronics seemed to offer prospects for developing chemosensors in the form of disposable mass-produced articles. Since then the initial euphoria has given way to a more realistic assessment, since these sensors still pose difficulties with regard to long-term stability and integration with miniaturized reference electrodes. Nevertheless, it is of interest to examine this class of sensors in a little more detail in the following discussion, since they bring together the disciplines of chemistry, electronics, and thin film technology, and they provide the basis for biochips. An ISFET can be generally regarded as a very miniaturized version of an ion-selective half-cell with an in-built impedance converter. It can be used to determine the activity of not only individual ion species, for which ion-selective macro-electrodes are also available, but also-in the form of an enzyme-coated ISFET (b iochip ta wide variety of substrates. The transistors that are used can in most cases be made as very small devices, allowing the accommodation of several sensitive surfaces for detecting different ions or substrates on a single chip with an area of only a few mm2. The entire electronic control circuit, including temperature compensation, can also be fitted on the same chip. The basic building block of all ISFETs is a field effect transistor (FET), in which the metallic gate of a conventional transistor is replaced by an insulating layer, above which is an ion-selective layer. The value at any instant of the gating potential, which controls the current between the source and the drain, is determined by the activity of the ion species being measured, through the presence of the ion-selective surface film. Figure 3 shows the basic construction of an ISFET in a form which has certain advantages. Often, however, instead of measuring the variation of the source-todrain current as a function of the activity of the measured ion 520 Angew. Chem. Int. Ed. EngI. 30 (1991) 516-539 species, one measures the control voltage that must be applied via a reference electrode to hold this current at a constant value; this makes it possible to maintain an optimal working point, chosen to reduce temperature effects. In an ISFET the ion-selective PVC membrane, which is applied to the gate surface mainly by spin-coating, forms the sensor element, which recognizes specific substances. By using known electroactive compounds, all types of ion-selective PVC membrane electrodes can also be incorporated into ISFETs. However, problems with the adhesion of the plastic membrane to the gate surface result in contact difficulties, since the membrane which gives the selectivity becomes detached, usually after a few weeks. In a pH-ISFET[41-44] protons produce a field, whose intensity depends on the H@ concentration, at a thin film of SiO,, Si,N,, A1,0, or Ta,O, . A serious disadvantage of these materials is that in many cases they still have some sensitivity to light and redox systems. Also, the diffusion of impurities into the lower layers of the semiconductor, which are known to be sensitive to this, usually results in a slow drift of the measuring signal, of the order of a few mV per day. The disadvantages mentioned, together with the fundamental problem of leakage-path formation in the insulation of the remaining transistor surfaces, which again causes drift in the readings before the device finally ceases to function, has so far prevented ISFETs from achieving a larger commercial success. However, recent developments in the area of electrolytic glazing offer some hope of improvements.[451 In the development of ISFETs work is already in progress on multisensor arrays146. 471 in which several different ion-selective sensor elements controlling separate gates are integrated on a single chip. Here, however, one is approaching the limits of miniaturization technology. The spin-coating technique cannot lay down closely spaced regions of different selectivity less than 1 mm2 in area. Experiments in which a common plasticized PVC membrane is laid down to cover all the gates before local regions above individual gate surfaces are doped with different electroactive compounds have also encountered problems, because diffusion of ionic carriers within the membrane smears out the ion selectivities. It is also necessary to integrate into the ISFET a miniaturized reference electrode with long-term stability, in order to exploit fully the advantages of the device as a miniaturized chemosensor. If the dimensions of the salt-bridge elements are too small, resulting in only short-term resistance of the integrated reference electrode to invasion by potentialfalsifying substances, it will only be possible to make disposable sensors. Here, however, it is important to investigate the possibility of using a conventional thick-film design for the electrodes, which might also be cheaper. In this connection an interesting alternative to ISFETs are film electrodes produced using planar technology.[481 These too offer the advantages of miniaturized sensors which can be economically mass-produced. One commercially available 501 is based on the principle of zero-point potentiometry. In this one-shot disposable sensor, the measuring and reference systems are identical, and as the pair are made under identical conditions from the same materials the potential difference with the relevant membranes in contact with the same solution is zero. If one now deposits on one of the sensor surfaces a reference solution of known concentra- tion, and on the other the solution to be tested (see Fig. 4), according to the Nernst equation the observed potential difference gives a direct measure of the concentration difference between the two solutions for the relevant measured ion species (concentration meter design). The errors that are pos sible in difference methods of this sort (where no transport of samples is involved) are very small, as the problems with conventional reference electrodes (variations in potential due to diffusion), ageing effects, and electrode poisoning effects are avoided. However, continuous measurements are not possible with this device. 2.1.3. Ion-Conducting Solid Electrolyte Sensors The lambda-probe, which has become familiar because of the three-way catalytic converter, is currently the most widely used of all electrochemical sensors. It enables the measurement of the residual oxygen content in the exhaust from internal combustion engines, making use of the selective ionic conductivity of the 02@ ion in yttrium-doped ZrO, at temperatures above 400\u00b0C. A potentiometer device for measuring 0, concentrations can be designed as a concentration cell, which allows the gaseous oxygen to be in equilibrium with the lattice oxygen in the solid electrolyte [reaction (l)]. If there is a higher oxygen concentration on one side of the ZrO, membrane than on the other (i.e. on one side an oxygen partial pressure p r f , for example, of the outside atmosphere or of a reference gas, and on the other side a partial pressure pgImPle, for example, of the exhaust gas or other medium being analyzed), according to the Nernst equation a potential difference proportional to the logarithm of the ratio of the two oxygen pressures is set up [Eq. (b)]. RT pgf U=-ln4 F pgTPle The selectivity of this sensor results from the fact that in ZrO, there is a selective conductivity for OZe ions (similar to that for Fe ions in single crystals of LaF,), which also determines the surface reaction. Figure 5 shows schematically the construction of a lambda-probe working on the potentio- Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 521 metric prin~iple.[~\u2019~ With regard to the other analytical properties of the device, the same arguments as for ion-selective membrane electrodes apply here. The range of concentrations that can be measured is enormous ( > 10 decades), provided that the current in the measuring circuit is considerably less than the exchange current for the redox reaction (a) at the platinum contact electrodes. The precision in this case also is limited to 0.1 mV, and at constant temperature this gives a relative precision of about 2 YO in the measured concentration. This accuracy is sufficient for the typical use in a three-way catalyst for automobiles; due to the logarithmic dependence of the signal according to the Nernst equation an immense potential difference results. LaF, , which has an appreciable ionic conductivity even at room temperature, has been found to be a suitable solid electrolyte for the determination of 0, at room temperature.[\u201d] In this material a change in potential is produced by OHe and HOF ions formed as intermediates, and this allows an indirect measurement of the 0, High temperature solid electrolytes with Oze conductivity can also be used at a constant oxygen concentration for detecting oxidizable substances, by making use of a second reaction that takes place at the electrodes. An example where this occurs is in the catalytic oxidation of NH, and the determination of chromium in molten steel,[5s1 by reaction (2) . 3OZe(SIC) + 2Cr(metal) --t Cr,03(2nd phase) + be-(metal) (SIC = solid ionic conductor) (2) Here the OZe ions moving in the solid electrolyte oxidize the chromium with the release of electrons, which can be measured as a change in potential. It has also been shown that silicon can be determined by a similar method when ZrSiO, is the solid ionic A very compact sensor suitable for applications at these high temperatures (above 1600\u00b0C) has recently been developed; this can be used for up to 10 h in molten Special sensors have also been developed for determining oxygen in liquid sodium, which is used in fast breeder reactor^.^^^*^^^ In addition to withstanding high temperatures and mechanical loading, these sensors must also be resistant to radiation and corrosion by sodium. Solid electrolyte sensors that have been developed for determining substances other than oxygen include especially those for SO,/SO, and C0,.[601 These consist for example, of Li,SO, + Ag,S0,[57~6*-641 and have a working temperature of about 400 \u201cC. The sensitivity of such sensors is in the range of 3 to lo4 ppm of SO,, and they are currently being tested for use in monitoring exhaust gases. The measurement of CI, is also possible with surface-modified solid electrolytes, e.g. the ionic conductor LiAICI, with its surface covered by a thin film of LiCl or AlCl,. The cell voltage is determined by the partial pressure of chlorine, and obeys the Nernst equation.t65* 2.1.4. Amperometric Sensors To avoid the requirements for temperature constancy in the lambda-probe, and obtain a linear instead of a logarithmic relationship between signal and concentration with higher accuracy, which is essential in engines working with I > 1 .O, the sensor can alternatively be designed as a limiting current probe.t67. 681 This configuration, which can also be operated at temperatures below 400\u00b0C, differs from the potentiometric form of a lambda-probe in that a current flows through the 0, concentration cell as a result of an externally applied voltage (\u201cpumping voltage\u201d), thereby transporting oxygen from one side of the ZrO, membrane to the other (an \u201coxygen pump\u201d). In front of the cathode there is a diffusion barrier (e.g. a porous ceramic layer), which the oxygen must traverse before being reduced and transported through the ZrO, to the anode (Fig. 6). If the applied voltage is chosen so that each oxygen molecule that arrives is immediately reduced at the cathode, a voltage-independent limiting current region is obtained, as in polarography. The current then flowing is directly proportional to the 0, concentration to be measured, and the temperature coefficient is no longer given by the Nernst factor, but is determined by the properties of the diffusion barrier.t691 The amperometric measuring principle has largely been used to advantage in industrial chemosensors for gases. The classic example of this is the Clark oxygen The oxygen whose concentration is to be measured diffuses through a gas-permeable membrane 10 to 50pm thick, which is made of polytetrafluoroethylene (Teflon) or a fluorinated ethylene-propylene copolymer (FEP) with a very high permeability to oxygen. Behind this membrane is an electrolyte solution containing chloride ions, in which are immersed a platinum or gold cathode as the working electrode 522 Angew. Chem. In!. Ed. Engl. 30 (199!) 516-539 and an anode of Ag/AgCl as the constant potential counterelectrode (cf. Fig. 14). The reduction of the oxygen takes place at a working electrode potential of approximately - 0.8 V relative to the Ag/AgCl electrode. The rate-limiting step is the diffusion of the oxygen through the gas-permeable membrane, and the rate of this depends on the gradient of the 0, partial pressure across the membrane. The current is therefore determined primarily by the 0, partial pressure. As the membrane is impermeable to liquids and electrolytes, the sensor can also be used to determine dissolved oxygen in liquids; in this case the dependence on the partial pressure must be noted. The sensor gives the same reading for air and for a liquid that is saturated with air! To obtain a reading which indicates the dissolved oxygen in mgL-' it is necessary to calibrate the sensor. A disadvantage of most 0, sensors based on this principle is that oxygen is consumed. When they are used in stationary liquids there may not be a sufficient flow of oxygen to the electrode (resulting in an oxygen-deficient layer in the liquid whose growth follows a I/i law), which gives readings that are too low. The solution being measured must therefore be stirred, but this leads to some extent to a dependence of the observed signal on the convection flow. The effects of this disadvantage (especially in biomedical applications) can be minimized by reducing the area of the working electrode, which in turn causes difficulties because the current then becomes very small. Efforts are now in progress to overcome this problem by using an array of ultramicroelectrodes (Fig. 7). The use individual electrodes as small as 1 pm in diameter, has led to such low reaction rates that the Brownian motion of the molecules together with the radial diffusion sphere ensures a sufficient oxygen supply. However, sensor technologies of this sort can only be put into effect with the most modern microelectronics manufacturing processes. Amperometric oxygen electrodes are widely used as transducers for many types of biosensors (see Table 7). Many gas sensors for SO,, CO and NO function on a similar principle. The measurement is based on the electro- chemical oxidation of the relevant gas in the space separated off by the gas-permeable membrane. The selectivity of amperometric sensors can be tailored to suit particular needs. Up to now the main technological use for amperometric chemosensors has been for measurements on gases, even though amperometry is also suitable for analyzing liquids, because of their limited selectivity. In the most commonly used aqueous electrolytic media, the usable voltage range extends over about 2 V. All substances that can be altered electrochemically, i.e. those that can be oxidized or reduced, which number many tens of thousands, are converted at voltages within this range. In the ideal case one can expect to distinguish ten substances at best in a voltammetric diagram by virtue of their different half-wave potential^.^'^] The separation capacity achieved by the proper choice of a working electrode potential within the limiting current region for the substance to be determined is in general inadequate for the analysis of unknown liquids. However, if a gas-permeable membrane is interposed, the interfering substances are limited to gases that can permeate the membrane equally well, and also undergo electrochemical reactions under these conditions. In the case of the Clark 0, sensor, for example, these are chlorine and some haloforms (CHX,). These interferences can be even further reduced by a careful choice of the membrane material and the electrolyte. Occasionally a difference in electrochemical reversibility coupled with pulse techniques is also exploited to increase selectivity. The limit of detectability for amperometric gas sensors is determined by the noise level of the background current. Nevertheless, chemosensors for environmental applications (measurement of NO,, SO, etc.) can be employed in the low ppm region without special signal-processing techniques. 2.1.5. Galvanic Sensors Amperometric measurements are also possible without an external current source, if a galvanic circuit is formed. The Angew. Chem. Int. Ed. Engl. 30 (199f) 516-539 523 best known example is the so-called internal electrolysis, in which Cu2@ ions are reductively deposited on a platinum wire mesh when this is connected to a zinc rod immersed in a zinc sulfate solution which is separated by a diaphragm from the solution containing the copper ions. Here again the driving force for the current which arises when zinc dissolves and copper ions are deposited on the platinum surface is the difference between the chemical potentials, or the energy difference between the two redox reactions in the electrochemical series. If in this example one connects a galvanometer externally between the zinc electrode and the platinum mesh, the current vs. time diagram obtained during the electrolysis has an exponential shape. The quantitative deposition of the Cu2@ ions on the platinum mesh is complete when the current has fallen to about 0.1 YO of its initial value. In this case, instead of using the gravimetric method, the amount of copper deposited can be calculated by Faraday\u2019s law from the total charge that has flowed (the integral of the current vs. time curve) as long as interference from side-reactions is absent. This coulometric procedure is one of the most precise absolute determination methods available, and requires no calibration. Coulometry is still an elegant method with exciting new possibilities for the development of intelligent sensors, and regrettably is too little used. Over 25 years ago a coulometric measurement cell for SO, was proposed.[\u201d] Subsequent advances in miniature electrochemical cells based on thin-film and thick-film technologies allow the easy application of such a cell as a chemosensor (Fig. 8). If the reaction is quantitative, a current of the order of 1 PA, which is easily measurable, corresponds to an analyte reaction rate of only lo-\u2019\u2019 mols-\u2019 ! Here the selectivity is achieved by a preceding chemical reaction or membrane separation stage, either of which can nowadays easily be realized by means of a suitable layered structure. An \u201canalytical fuel cell\u201d of this kind has recently also appeared on the market in the form of an alcohol meter (for analysis of breath samples). As well as using the catalytic activity of noble metal electrodes, it is also possible, of course, to use enzymes to give increased selectivity. The H,O,, which is then often produced in quantities proportional to the amount of analyte, can also be easily determined coulometrically. A galvanic measuring cell for the determination of oxygen in solutions has been well-known since the rnid-1960~.[\u2019~1 In contrast to the Clark sensor, the Mackereth oxygen sensor uses lead instead of silver as the anode material, and silver instead of platinum as the cathode material. This has the important advantage that a calibration in a blank solution (such as a saturated sulfide solution) is no longer necessary, since the electrodes produce no current in the absence of oxygen. For the internal electrolyte either sodium hydroxide or potassium hydrogen carbonate can be used. 2.2. Semiconductor Gas Sensors Sensors based on semiconductors are often used in gas alarm devices. The underlying principle here depends on a transfer of electrons between a semiconductor surface and adsorbed gas molecules. This charge transfer results in an increase or decrease in the number of free charge carriers at the semiconductor surface, causing a change in conductivity which can be measured and is proportional to the number of reacting gas molecules present. Oxidizable gases such as hydrogen, hydrogen sulfide, carbon monoxide, and alkanes of low molecular mass reduce the surface conductivity of certain n-type semiconductors (SnO,, ZnO etc.), which are used at temperatures between 100 and 600\u00b0C. Reducible gases such as chlorine, oxygen, or ozone have an analogous effect on p-type semiconductors (NiO, CuO etc.). The mechanism of the electron transfer is still under intensive study and one possible model shown in Figure 9. When a gas molecule of the analyte approaches the surface of the semiconductor it first undergoes a weak physisorption. In the following step it can be either desorbed or chemisorbed with the transfer of an electron. The latter process causes a distortion of the valence 524 Angew. Chem. I n f . Ed. Engl. 30 (1991) 516-539 and conduction bands, and alters the electronic work function. Depending on the composition and the structure of the surface and on the interactions between the molecules and the surface, certain types of molecules can act preferentially. The selectivity of simple sensors of this kind, which can be easily and cheaply produced with thick film techniques (see Fig. lo), can be altered within certain limits using existing knowledge of heterogeneous catalysis. To obtain improved sensitivities and selectivities for particular applications, however, mechanistic studies of the kind used in heterogeneous catalysis research, requiring sophisticated and expensive equipment, are necessary, rather than the time-consuming trial-and-error methods of nonspecialists. Often the semiconductor surface is modified by introducing metals such as palladium, silver, or platinum, whose purpose is to weaken the 0, double bond. The selectivity can be further increased to a certain extent by choosing the best operating temperature (Fig. 11) . Nevertheless, the selectivities of these types of b) a) aK[%] 6ol A K [%] 6ol 4017p 20 , . ::p+ '\\ 200 400 600 800 T[\"C] 200 400 600 800 T[\"C] Fig. 11. Effects of temperature and of the presence of platinum on the selectivity of an SnO, gas sensor. a) Pure SnO, sensor, b) SnO, sensor with 1 % platinum. sensors based on semiconductors are often insufficient.[731 The surface composition, density of charge carriers, Fermi energy level, number of reactive centers at the surface, and even the extent of distortion of the bands, can be affected by the presence of other species (interfering molecules such as water, catalyst poisons etc.). This can cause changes in selectivity. These effects must be taken into account during calibration. A change in the selectivity, sensitivity (signal per unit concentration in the analyte) or zero point of the calibration line between carrying out the calibration and the analysis is inadmissable. As it is a simple matter to modify the sensitivity, experiments are now in progress to use a sensor array in which each miniaturized individual sensor has a different sensitivity profile. Samples which contain interfering substances cause each individual sensor to give a different signal. By carrying out calibration measurements with different concentrations of the various interfering components, it should be possible, by a pattern recognition analysis, to use a special algorithm for the calculation of the true sample content. A simultaneous analysis on a mixture using such a sensor array should in principle enable the determination of every substance which has an effect on the signal, if more sensors than components to be analyzed are used. This has in fact been achieved for simple and well-defined Nevertheless, the analytical chemist with experience of industrial practice will harbour doubts about the feasibility of this method for real samples whose composition is generally unknown and continually changing. Taking the simplest form of an analytical function (c) is it possible to keep the parameters a and e constant between the calibration and the measurement? How can the algorithm take into account situations where interfering substances poison the sensors to differentor cause different drift phenomena? What are the consequences of \"matrix effects\" which cause the sensitivity e to vary from sample to sample? Table 3. Materials for selective chemosensor elements. Sensor Examples Species Refs. materials detected ~~ ~ glasses Li,O-BaO-SO, H@ (5.61 synthetic PVC, silicone and PMMA mem- e.g. K\", Na@, [14-16, suitable carriers NHF, NO? PTFE membranes for gas sensors NH,, CO,, SO, [37] solid LaF, F e (371 Na,O-AI,O,-SO, Na@ [71 polymers branes[a] with plasticizers and Gaze, Mg'\", 34.36-381 0, [53,541 ZrO, (lambda probe) 0, [5l. 521 Cr (551 TiO,, Nb,O, 0, Nasicon [b] Na [651 Na@ [661 ZrSiO, Si ~561 Na,SO, + Ag,SO, SO,/SO, [57,60-641 semi-con- Si, GaAs, Sic, SnO,, ZnO, CuO Oxidizing or [73.109- 1 1 11 ductors reducing gases metal oxide AI,O,, Si,N,, SO,, TiO, as HO, H,, 0, [73,109-1111 or nitride insulators, electronic conductors films and electroactive materials [a] Polylmethylmethacrylate. [b] Na, ..Zr,Si,P,.,O,,. 2.3. Fiber-optic Sensors (Optodes) Chemical information can also be translated into measurable signals through the interaction of electromagnetic radiation with the analyte. Spectroscopic analysis, spectrophoto- Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 525 metry, fluorimetry, and luminescence measurements are well-established and proven techniques. Their adaptation for performing in situ analyses with miniaturized probes that can be employed in the same way as chemosensors has come about through the application of modern light-guide technology. For use in conjunction with fiber optics a new class of sensors was developed, known as optodes (also as opt r o d e ~ ) . [ ~ ~ - ~ ~ ] These optical sensors make use of changes in fluorescence, absorption, chemiluminescence, light scattering, polarization, Raman scattering, refractive index, or reflection, which at present are still detected by conventional optical or spectroscopic instruments. The light input is fed into the sample by a light-guide. The return path for the fluorescence emission or reflected light from the sample to the detector can be through the same light-guide or through a second branch (in a Y-branched light-guide). Figure 12 shows as an example the layout of a fiber-optic analytical system as commonly used for fluorescence measurements. The AC signal produced by a chopper is amplified frequency- and phase-selectively by a lock-in amplifier. This procedure makes it possible to measure delayed fluorescence as well (by the phase shift). Fluorescence and luminescence measurements give high sensitivity compared with other optical measurement methods and are therefore preferable for trace analysis. , 1 Fig. 12. Fiber-optic system for analysis by fluorescence measurements; the excitation unit (2) contains the light source (xenon or halogen lamp or laser) producing a beam which is passed through a monochromator (3), a chopper (4). and an optical coupler (5) into the light guide (6). The fluorescence radiation passes through a second light guide branch, coupler (7). and monochromator (8) to the detector (9), which consists of a photodiode or photomultiplier. (1) is the base plate. Chemiluminescence measurements have an additional advantage, as they do not require an external light source. However, because chemiluminescence is a comparatively rare phenomenon, the method is mainly limited to systems such as H,O,/luminol. The great advantage of fiber-optic sensors is that the measurements do not require a reference system, apart from comparison of the light intensities in the beam before and after it passes through the sample compartment (i.e. measuring Zo/l), or the use of a dual beam arrangement to compensate for fluctuations in the intensity of the light source. With the electrochemical sensors described earlier a second electrode giving a constant potential is always needed. Optodes can easily be miniaturized, as light-guides of suitably small diameter (e.g. 0.1 mm) are commercially available, although increasing miniaturization makes good coupling of the input radiation more difficult. Optodes can also be used in complex media such as blood. They are less susceptible to disturbance by electromagnetic fields and temperature changes than are potentiometric electrodes and semiconductor sensors. On the other hand, problems can arise from scattered and background light falling on optodes. In many cases these sensors can only be used within a small range of concentrations, like the spectroscopic analytical cuvette techniques on which they are usually based, and their selectivity is similar to that of those techniques. The detection limit also leaves room for future improvements, as it is restricted at present by the thinness of the optical films generally used for the measurements (see Table 4). Despite all this, fiber-optic sensors are expected to emerge from their present status as research devices and find a place in industrial use in future; the flow-through cuvettes will probably be abandoned first. The types most studied are pH-optodes. The technique is based on the immobilization of an indicator dye at the end of the light-guide, which allows pH values to be determined by measuring fluorescence or absorption. Indicators that have been used include 8-hydroxypyrene-I ,3,6-trisulfonate (HPTS) as well as conventional dyes such as eosin or phenyl orange.1791 Such pH-optodes also form the basis for a range of gas sensors. For example, CO, and NH, optodes contain a pH optode immersed in a suitable internal solution behind a gas-permeable membrane, as in the analogous potentiometric sensors. The acidity or basicity of the above gases alters the pH of the internal solution by an amount related to the gas concentration to be measured. Such sensors are of particular interest for in vivo applications (blood, body fluids, etc.), since unlike electrochemical sensors they do not have electrical connections to voltage-carrying components. The fields of application are similar for 0, optodes, which work on the principle of direct fluorescence quenching. The mathematical basis of this type of sensor is given by the Stern-Volmer equation.[\"] The fluorescence of an indicator such as decacyclene or perylene, which is immobilized on the tip of the light-guide, is partially quenched by oxygen. This effect can be used, after calibration, for the determination of Some new developments are based on applying knowledge of the selectivity mechanism of ion-selective electrodes to fiber-optic systems. For example, valinomycin as a selective K@ carrier can be immobilized in a suitable matrix, together with a pH-sensitive indicator in its protonated form, so as to produce a membrane which can be attached to the tip of a light-guide. If this sensor is immersed in a solution containing K@ ions, these ions will preferentially enter the membrane phase, with the formation of a potassium-valinomycin complex. To maintain electrical neutrality H@ ions (as the most readily mobile ion species) move out of the membrane phase, causing a change in the absorption or fluorescence of the pH indicator in the membrane, which can easily be measured.Is l ] In conclusion it should be noted that at present there are only a few manufacturers of optodes, and it will certainly take several more years before such fiber-optic analytical systems become as widely used as electrochemical sensors. 0 2 . 2.4. Mass-Sensitive Transducers Chemosensors based on mass-sensitive transducers have been less thoroughly investigated, and their use has so far been restricted to special applications. The measuring prin- 526 Angew. Chem. Int. Ed. Engl. 30 (1991) S16-S39 ciple depends on the shift Af in the characteristic frequency of a quartz oscillator due to a mass change Am, which occurs when a layer of foreign material is deposited on its surface. The oscillation frequency is usually in the 9 to 14 MHz range, and the selectivity is obtained by coating the surface with an appropriate adsorbent. By using phthalocyanine, for example, planar-conjugated molecules and higher alcohols can be determined; in this case mass changes as small as g can be d e t e ~ t e d . ~ ~ ~ * * ~ ] When working in vacuum the relationship between A f and Am is linear for small values of Am and is given by the Sauerbrey equation [Eq. (d)].[s41 f, = resonance frequency in the unloaded condition m = mass of the quartz crystal in the unloaded condition The suitability of quartz oscillators for gas analysis has been demonstrated beyond doubt. Difficulties arise, however, in the search for selective ab- or adsorbents for particular analytes, and in compensation for the effects of moisture and other interfering deposits. Also it must be noted that the surface adsorption or film absorption are not usually reversible. Transducers of this type are potentially important for biosensors for gas phase use. At present, however, their high cost inhibits the development of practicable oneshot disposable sensors. When quartz oscillator detectors are used directly in liqu i d ~ [ ~ \u2019 * 861 without a drying stage before the mass-change measurement, the damping of the oscillations must also be taken into account [Eq. (e)]. q = viscosity of the liquid p = density of the liquid pQ = shear modulus of the quartz pQ = density of the quartz The latest st~dies,\u2019~\u2019] which are based on an exact coulometric calibration, show that a 0.41m thick layer of the surrounding liquid moves with the quartz crystal surface during its oscillation. This makes exacting demands on the constancy of all the effects that shift the frequency. The layer of liquid that moves with the surface reduces the mass resolution (i.e. the ability to measure very small mass changes). It should also be mentioned here that a similar device is marketed for determining the densities of liquids ; density changes of the order of a few parts per million can be detected. Surface acoustic wave (SAW) detectors are devices in which acoustic waves are produced at the surface of a suitable material, by setting up appropriate resonance conditions between two surfaces. The resonance frequency is typically a few hundred MHz, and according to the Sauerbrey equation (d) this should result in greater sensitivity. However, this cannot be fully exploited, as it is only possible to measure the change in mass within a very thin layer between the two specially shaped electrodes. The selectivity is governed by the same considerations as above. 2.5. Applications of Chemosensors The use of chemosensors in technology has grown enormously during the past decade. R & D in the field of chemosensors is being energetically pursued worldwide, but especially in Japan. The range of uses of conventional chemosensors extends from chemical process control technology through applications in clinical chemistry to municipal services. A field of special importance for chemosensors is environmental protection, where increased public awareness and ever stricter legislation make it increasingly necessary to set up on-line monitoring systems for environmentally significant gases such as NO, SO,, NH,, CO, or C0,.t88-931 The wide variety of chemosensors that have so far been developed means that in many cases the most suitable one for a particular application can be chosen from a number of alternative constructions. As an example Table 4 lists the various methods of measurement available for determining a single substance, in this case oxygen. The largest market for chemosensors at present is the automobile industry, which even in 1987 required over ten million oxygen sensors (lambda-probes) throughout the world for controlling the operating conditions of the threeway catalytic converter. A similarly large market exists for semiconductor sensors based on SnO, for detecting oxidizable gases such as CO, NO, and CH,, which are used mainly in monitoring instruments (alarm devices) in underground garages, tunnels, and coal mines, and for measuring emissions in industry. Here the poor selectivity is not a serious disadvantage; on the contrary it gives extra safety. Conventional electrochemical sensors too are widely used in measurement and control technology, especially glass pH electrodes, of which about a million are produced every year throughout the The largest areas of use for conventional potentiometric sensors are in medicine and environmental technology. In clinical chemistry, for example, ion-selective sensors have many uses for measurements in biological media.[95 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 527 They have been used successfully for some years to measure concentrations of individual ion species such as NaO, KO, CaZO, and Mg20 in blood. Unlike other methods of analysis such as atomic absorption spectroscopy (AAS), which always measure the total concentration of the ion species (both free and bound ions), ion-selective sensors allow a direct measurement of the activity of the free ion, which is the effective concentration and the only component that is relevant for medical diagnostic purposes.r1001 Fluoride in urine and blood can be determined by, for example, a LaF, single crystal electrode, which gives an extremely high selectivity for Fe. A knowledge of the fluoride concentration is important in the chemotherapeutic treatment of osteoporosis and kidney disease, and in the determination of the Fe content of the blood after the use of narcotic^.^^'] The detection of traces of cyanide in blood is necessary during treatment of hypertonia with sodium pentacyanonitrosylferrate(i1) (sodium nitroprusside), and this too can be carried out with an ion-selective electrode. Iodide- and bromide-selective sensors are of interest in clinical toxicology, in connection with radioimmunological investigations into the functioning of the thyroid gland (using the iodine-I31 isotope) and the administration of the bromine-containing sleeping drugs, ureides. Use of the latter often causes toxic effects due to metabolic dehalogenation and a dangerous build-up of Bre ions. In treating manic-depressive patients a control of the lithium content is of particular importance; this can be determined using ion-selective membrane electrodes which consist of PVC and a lithium ionophore such as ETH 1810 (N, N-dicyclohexyl-N', Nf-diisobutyl-cis-cyclohexane-1,2-dicarboxamide). The non-invasive measurement of the transcutaneous blood CO, partial pressure is a technique that can be used to advantage in operations, in amputational surgery and in sport related medical practice. Here the sensor works on a principle analogous to that of other potentiometric gas sensors such as NH, or SO, detectors. It is essentially a pH probe consisting of a glass electrode and an Ag/AgCl reference electrode. The gas diffuses through a semipermeable membrane into an intermediate electrolyte, whose pH changes according to the gas partial pressure and is measured by the pH electrode. Figure 13 shows a sketch of the sensor. The sensors that have been described are still used mainly for in vitro measurements, but the main research objective is to develop catheter needle electrodes for in vivo measure- cover glass electrode housing electrolyte rese electrolyte gas membrane Fig. 13. Gas sensor for measuring CO, partial pressures in medical applications[95]; the sensor allows transcutaneous measurement of C0,. ments. Figure 14 shows an example of an amperometric catheter electrode for measuring 0, partial ISFETs have proved successful mainly in medical technology. Up to now pH-ISFETs have become commercially available and are used for determining acidity in blood and serum (whose normal pH value is 7.41) and other body fluids. Another technological application is in the photographic industry; here ISFETs are used in process control, to maintain important parameters such as the concentrations of H@ and Ag@ ions at constant levels.[102] The Ektachem film electrodes mentioned earlier (cf. Fig. 4) can be used as one-shot disposable sensors in medical applications. The Kodak Ektachem DT 60 is a commercially available 50 . and can be used for the determination of KO, NaO, Cle and other substances. Figure 15 shows a film sensor of this type for potassium. Potentiometric sensors can be used for environmental protection both in laboratory investigations and on-line applications. One task that they can perform is the continuous monitoring of NO: and NHT concentrations in groundwater and drinking water. This gives early warning of excessive concentrations in the water, allowing the necessary corrective measures to be applied quickly. Figure 16 is an example of a recorder trace obtained with a sensor used to monitor nitrate in drinking water. The trace shows immediately if the maximum legally permitted nitrate concentration of 50 mg L-' (50 ppm) is exceeded. Here the technique of flow injection analysis (FIA) can be used, since the selectivity of the sensor makes a preliminary chromatographic separation unnecessary.\" 041 528 Angew. Chem. Inr. Ed. Engl. 30 (1991) 516-539 100 Table 6. Summary of commercially available sensors - - A 3 min Fig. 16. Recorder trace obtained during the FIA monitoring ofNO? in drinking water; carrier electrolyte: 50 ppm NO? in 0.01 M NaH,PO, ' H,O; flow rate: 3.0 mLmin-'; sample quantity: 0.3 mL in 0.01 M NaH,PO, H,O. The numbers represent the concentration of nitrate in mgL- ' ; A: doubly distilled water: B: drinking water. In process engineering, ion-selective sensors for Ca2@, Na@, NHF, or CIo can monitor the purity of boiler feed water in steam with a glass electrode for Na@, ppb concentrations are detectable. Monitoring these concentrations is critically important in relation to boiler scale formation and turbine corrosion. Table 5 lists important characteristics of the various types of sensors described here, such as the range of measurement, useful life and detection limits. ISEs that do not incorporate PVC membranes can also be used to a limited extent in nonaqueous media. For example, it is well known in the oil industry that impurities in crude oil feedstocks can adversely affect the refining process, and it is therefore essential to carry out continuous anaIyses.[lo6] Table 6 gives a summary of some commercially available sensors.\" \"1 2.6. Development Trends One should not overlook the fact that the majority of development work on sensors proceeds by methods that are still more or less empirical. Recently the most up-to-date research techniques, e.g., electrochemical impedance spec- Supplier detector Species Range Applications detected AEG NO, monitor NO, 0-600 ppm vehicle exhausts. flue gases gas analyzing CO 0- 1500 ppm NO 0-1000 ppm 0- IS00 ppm flue gases 0-200 ppm I MSI (Drager) 0, 0-20.9% computer so, NO, Unitronic (Figaro) CH, gas monitor C,H, C4HlO CO NH3 H,S H 2 0 Transducer NO2 Research, Inc. H2S gas monitor CO 500- 10.000 ppm 50- 1000 p p i 30-300 ppm tunnels) 5 - 100 ppm 0-100 ppm humidity gas alarms (garages, gas alarms I 10ppb-50ppm 0-1000 ppm Bran & Liibbe Na@ 0-20 ppb Ionometer S'O troscopy,[' OS1 tracer methods, and surface analytical techniques[\"'- '\"1 such as secondary ion mass spectrometry (SIMS), Auger electron spectroscopy (AES), or X-ray photoelectron spectroscopy (XPS, also known as ESCA), have been applied to optimize performance parameters such as selectivity, stability, dynamic behavior, reproducibility and sensitivity. These methods will at the same time provide a deeper insight into the mechanisms of functioning of the selective sensor elements. A changing trend can now be seen in the technology of chemosensors, away from the hitherto conventional sensor design principle based on electrode-like structures, towards miniaturization with recognition systems and signal processing integrated in a single device.\" 12, ' l31 These developments can benefit from the existing technology of microelectronics. Besides savings in materials, this technology can also lead to considerable cost reductions through mass production, and may sometimes even result in sensors with improved proper- ties. Physical sensors for a wide variety of variables are produced by these methods and are already well-known, while chemical sensors made in this way are just appearing on the market. Thick-film technology offers an alternative way of integrating sensor recognition systems and subsequent signal processing on a single chip, and is within the financial budgets of medium-sized industrial concerns. A potentiometric hydrogen sensor based on thick-film technology and developed by the Battelle Institute is shown in Figure 37. The sensitive material is Nasicon (Na, +xZr,Si,P,-,O,,), a solid ionic conductor which responds to hydrogen at elevated temperatures, but is a good Na@ sensor at room temperature and in solutions. This sensor based on Nasicon is at present one of only a few commercially available sensors made by thick-film technology. 3. Biosensors A biosensor combines in a single sensor element the sensitivity of a chemosensor with the selectivity of a biological recognition mechanism. The great promise offered by such a combination has been the subject of increasing research efforts in the last few years, as is evident from the rapid growth in the number ofpublications in this area and the appearance of the first monographs on the A number of different biosensors with biological or biochemical recognition systems coupled to various types of chemosensors have been demonstrated. Although to date biosensors have commercial importance only in medical technology, their use in future in other fields such as environmental monitoring and process engineering is likely. For this reason some relevant developments are described below. Biosensors functioning on enzymic principles belong to the oldest generation of sensors in this category; they employ selective chemical reactions catalyzed by selected enzymes. The most effective method is to immobilize the relevant enzymes in or on the sensor element, which allows the device to be used repeatedly. Unfortunately the stability of enzymes immobilized in this way is at present rather limited, and consequently the lifetime at room temperature under working conditions varies between only a few days and several months, depending on the enzyme used and the immobilizing technique. However, if it is refrigerated and freeze-dried, an immobilized enzyme retains its activity almost indefinitely. Another class of biosensors are immunosensors. These operate on a different principle, namely the selective association between antigens and antibodies. This specific biocomplex formation can be exploited in a number of ways as a means of analysis for one of the two partners. The methods that are of importance for the development of these sensors differ from those involved in radio immuno-assay (RIA), and are based either on enzymic immuno-assay (EIA) in combination with various detection methods (photometry, amperometry, or surface plasmon resonance), or on direct potentiometry . Some of the systems under development function without isolation of biomolecules. In other words, these are enzymic biosensors in which biological materials such as intact cell cultures, tissue sections or microorganisms are used directly without purification; for immunosensors one uses intact receptors, receptor structures or reconstituted units. As the development of biosensors follows on that of transducers or chemosensors, biosensors are not yet at such an advanced stage, and only a few types are commercially available at present. Nevertheless, some important advances have been achieved in each class of biosensors. 3.1. Monoenzyme Sensors Monoenzyme sensors were the first biosensors to be developed, and are the best known. Here an enzyme is coupled to an optical or electrochemical chemosensor, which selectively detects one of the reaction partners of the substrate, or a reaction product. As early as the 1960s with the first enzyme electrodes, immobilization of the enzyme was a development goal. Although the immobilization technique is crucial to the behavior of the biosensor, it will not be considered in detail here. The situation is basically similar to that in bioreactors, where the aim is to achieve a high surface activity combined with a high durability; accordingly, the immobilization techniques used in biosensors are similar to those for bioreactors.[116-'201 However, it must be said that many of the techniques are still far from giving reproducible results. Many preparative procedures evolved by trial and error, and if a breakthrough could be achieved in immobilization without loss of activity, many of the present disadvantages of biosensors would be overcome. The modification of the coenzyme nicotinamide adenine dinucleotide (NAD@) can also be regarded as a type of immobilization.t121. 1221 If the effective molecular mass of NAD@ is increased by reaction with polyethylene glycol (PEG) to give PEG-NAD@, the coenzyme can be immobilized behind a dialysis membrane, so that it can be used repeatedly after a recycling procedure. Chemically preactivated membrane filters for simple and rapid immobilization of enzymes have recently become commercially available (Immunodyne, Gelman Sciences). The simplification of the procedure brought about by them could lead to a breakthrough in extending the storage life of biosensors. If a filter membrane freshly coated with the enzyme could be fitted to the sensor shortly before making a measurement, the cost of the biomaterial would be worthwhile in view of the great advantages of a rapid but selective measurement. 3.1 .I . Electrochemical Biosensors In the past the development of monoenzyme biosensors with different transducers was mainly limited to electro- 530 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 chemical sensors. This situation has now changed to some extent through the development of new optodes and of the technique of surface plasmon resonance. Biosensors with electrochemical transducers are still essentially restricted, owing to the nature of the products from enzymic reactions, to two methods of measurement, namely amperometry and potentiometry . Amperometric Biosensors: The majority of biosensors used in research are of the amperometric type. Table7 gives a short summary, which is by no means exhaustive, of the many different types of biosensors using conventional amperometry. Table 7. Amperometric biosensors. Substrate Enzyme Product(s) Range Refs. detected deh ydrogenase choline oxydase alcohol oxidase alcohol malate formiate choline ethanol formaldehyde formaldehyde dehydrogenase glucose glucose oxidase glutamine glutaminase, glutamate oxidase glycerol glycerol dehydrogenase hypoxanthine xanthine oxidase lactate lactate oxidase oligosaccharides glycoamylase, glucose oxidase phenol polyphenol oxidase inorganic nucleoside phosphorus phosphorylase 10-150mmolL-' NADH ( 5 - 1 0 0 ) ~ 1 0 - ~ m o l L - ' [121,124] H,O, 500 mmolL-' [a] [125] NADH mol L-' [a] [126] H,O, 10 mgL-' [a] I1 141 H,02 0-7gL-I [127-1351 H,O, 0-25 mmolL-' ~1361 NADH, O2 11371 H20, 4 - 1 8 0 ~ 1 0 ~ ~ m o l L - ' [138,139] H,O, 0.1-2.5mmolL-' [140] H20, 1-4011Un0lL-' 11141 quinone - 11251 [a] Only the upper limit is known In amperometric transducers, reaction partners or products of the enzymic reaction are directly reduced or oxidized at the working electrode, and the resulting current is measured. From this, on the basis of the stoichiometry, the quantity of the substrate that has reacted can be determined. As is evident from Table 7, the most commonly used transducers are based on the oxygen/hydrogen peroxide electrodes described in Section 2.1.4, since many enzymic reactions (e.g. those of the oxygenases) involve the consumption or production of oxygen. This consumption of 0, or production of H,O, is measured by an 0, electrode. In this area of development considerable time has been invested in the glucose sensor, which is based on reaction ( 3 ) (3) GOD B-D-glucose + 0, -+ H,O -gluconic acid + H,O, catalyzed by the enzyme glucose oxidase (GOD). In this selective reaction three concentration changes can be and have been used to determine the amount of material reacted: 1) the reduction in concentration of the cosubstrate (reduction in O,), 2) the increase in H,O, concentration, or 3) the concentration of the He ions generated by the disso- ciation of the gluconic acid. Greater progress has been made in the area of in-vitro glucose measurements than in any other, which is not surprising in view of the large amount of research effort on this topic (about half of all the papers on biosensors are concerned with glucose measurements). Despite this, however, an implantable glucose sensor, which would be desirable in medical technology, is still not within sight. Implants need to have a lifetime of several years, because if it is shorter the added trauma for the patient as a result of more frequent operations is unacceptable. Up to now the lifetime of the enzyme GOD in synthetic glucose solutions has been at best about 100 days.['231 Among the problems which hinder applications are those arising from the nature of the cosubstrate (the quantity of 0, available for reaction ( 3 ) limit the measurement range), from product inhibition, from the possibility of the enzyme being attacked by proteases, and from diffusion difficulties caused by encapsulation of the implant. Other types of amperometric biosensors are those based on the detection of a coenzyme. Well over 100 enzymic reactions are known in which nicotinamide adenine dinucleotide (NAD@) functions as a coenzyme. The direct electrochemical reduction of NAD@ or oxidation of the reduced form NADH have both been successfully demonstrated,['42' 1431 but owing to the very large overvoltage that must be applied (+ 0.7 to + 1.0 V vs. Ag/AgCl), the determination of both species is instead carried out with electron carriers (mediators), which work on the principle shown in Figure 18.[144-1471 A similar situation exists for the coenzyme N A D P ~ . The compounds used as mediators are reversible redox systems with high exchange current densities, often redox dyes such as methylene blue or thionine, or sometimes modified ferrocenes or hexacyanoferrates. The advantages of such a mediator are well-known: it reacts with the coenzyme NAD@ in a homogeneous solution without significant inhibition by kinetic factors, the mediator itself is electrochemically reversible, and it reacts at the electrode at a significantly lower potential than NAD@. Because of the lower working potential fewer interfering effects from other electrolyzable substances in the sample are expected. Ferrocenes have also been used to effect the direct transfer of electrons between the enzyme and the electrode. A modified ferrocene serves as mediator between immobilized glucose oxidase and a graphite e l e c t r ~ d e . ~ ' ~ ~ ~ This glucose sensor, developed at the Cranfield Institute of Technology (UK), is unaffected by O,, as the ferrocene replaces oxygen as the cosubstrate. The sensor can therefore also be used in anaerobic media (e.g. in fermenters). In general the immobi- Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 531 lization of mediators presents difficulties. An immobilization effective enough to prevent loss of the mediator from the transducer with time is usually accompanied by severe deactivation of that mediator. Potentiometric Biosensors: Biosensors with potentiometric transducers can be used in any situation where protons are either generated or removed in the course of the enzymic reaction. Most types are based on a pH electrode, as can be seen from Table 8, which gives a short summary of potentiometric biosensors. A pH measurement is an alternative way of following the glucose conversion reaction (eq. (3)) already described under amperometric biosensors. In this case the change in pH caused by the formation of gluconic acid is measured. Fats may be determined by measuring the change in pH caused by the formation of fatty acids, as listed in Table 8. Though still at the development this method seems to offer great promise, especially in view of the numerous potential applications in food technology. Recently stable lipases which even allow the determination of fats in organic solutions have been isolated. The performance of all biosensors that work by means of a pH measurement is greatly affected by the buffer capacity of the sample solution. A lipophilic layer or membrane between the reaction zone and the buffer system decreases this dependence. Whereas with amperometric sensors, which consume some of the substance being determined during the course of the measurement, deposits of proteins formed on their surface attenuate the signal, with potentiometric sensors only the response time and not the magnitude of the signal is affected, since here the measurement does not consume the substance. This can be a crucial factor in the case of implants. The conversion of aspartam by the enzyme L-aspartase is of interest in connection with the production and use of artificial sweeteners. The NH, generated in the reaction can be determined by the well-known NH, gas electrode. This type of electrode has also been used successfully for some time to determine urea in urine by means of the enzyme urease. The enzymic hydrolysis of urea [reaction (4)], like the oxidation of glucose, allows the use of various chemosensors as transducer. CO(NH,), + 2 H,O 2 NHY + C0:O (4) In aqueous solution the reaction products give the pHdependent equilibria (5) and (6), which provide further spe- NHF + OHe ZII? NH,+H,O (5) C O i e + H @ ZII? HCOF z=? C O , + H , O (6) He -Ha cies for which transducers are available. Potentiometric ISEs are available for two of the reaction products, the ammonium and carbonate ions. Furthermore, the gases NH, and CO, which may be produced depending on the pH in the reaction zone can be detected by means of the appropriate gas electrodes mentioned above.[1601 A urea sensor as described here can be made in the form of a simple triple-membrane configuration as shown in Figure 19. Conductometry is another electrochemical transducer principle which can be applied to biosensors, since the progress of an enzymic reaction can also be measured by the change in the resistivity of the solution. However, as well as lacking selectivity, this method suffers from the fundamental difficulty that only the total resistivity can be measured and the change in resistivity is caused not only by the reaction, but also by the introduction of an ion-containing medium. A difference method has been proposed by Wut~on.['~'' Con- 532 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 ductometric biosensors for urea and for D-amino acids are described by Rechnitz et a1.['621 3.1.2. Biochips The new microelectronic transducers are becoming increasingly important, as they make it possible to produce one-shot disposable biosensors. This offers a possible solution to the ever-present problems of poor storage properties and short lifetimes of biosensors. Even the problem of sterilization could be solved by sterile sensor elements which are introduced immediately before the measurement. Special mention must be made here of ion-selective field effect transistors (ISFETs), whose small size, particularly, warrants their application as transducers in biosensors, as this factor is of great importance for catheter sensors in medical technology. Enzyme-modified ISFETs, known as ENFETs, consist in many cases of pH-sensitive ISFETs with an enzyme immobilized on their surface; this catalyzes the reaction of a substrate which generates or removes protons. Examples of the use of ENFETs are the determination of glucose)'52* 1631 urea, and penicillins,\" 5 8 * 1651 in which the appropriate enzymes were immobilized on the pH-sensitive surface of the ISFET with glutaraldehyde and bovine serum albumin, or in membranes. To compensate for errors caused by temperature fluctuations or by pH changes from effects other than the enzymic reaction, a differential measurement can be performed with two pH-ISFETs, one coated with the enzyme and one bare, as described in the first German patent for a b i o ~ h i p . [ ' ~ ~ ] The determination of triglycerides has also been performed by a differential measurement, with lipase immobilized in a polyvinylpyrrolidone membrane on the pH-sensitive surface of a pH-ISFET.['661 Table 9 gives a summary of the ENFETs that have been reported. 3.1.3. Optical Transducers In addition to the well-proven electrochemical transducers, optical sensors have recently been exploited to an increasing extent for substrate recognition by enzymic reactions, since fiber-optic spectrophotometers and fluorimeters are now commercially available. The way in which these optical biosensors function will be described here with the help of a few examples. Wolfbeis and T r e f f n ~ k \" ~ ~ ~ have developed a biosensor for glucose determination using the reaction described in Eq. ( 3 ) ; this sensor contains as its transducer an oxygen optode which has already been described in Section 2.3. The glucose oxidase was bound to a nylon membrane by activated carboxyl groups (Immunodyne) and the membrane was attached to the surface of the optode. Another approach of Wolfbeis et al.['68] is based on the intrinsic fluorescence of the enzyme concerned. Enzymes with FAD (flavine adenine dinucleotide) as prosthetic group change their fluorescence properties during the reaction with the substrate, because flavoproteins have different properties in their oxidized and reduced states. This change can be measured with optical fibers that have the enzyme held at their ends by a dialysis membrane. Experiments have been carried out on this system with glucose oxidase, lactate monooxygenase and cholesterol oxidase as enzymes. An optical biosensor has been developed for controlling the biotechnological manufacture of penicillin. This sensor monitors the change in pH caused by the enzymic conversion of penicillin to penicillic acid; the measurement can be performed either electrochemically or optically.['691 For the latter the enzyme penicillinase was immobilized in a polymer together with a pH-indicator, as described in Section 2.3 for pH-optodes. Urea can be determined by an analogous meth- These examples of optical sensors, which are summarized in Table 10, clearly illustrate that, like electrochemical biosensors, nearly all optical sensors depend on just a few basic principles, such as 1 ) the measurement of oxygen concentration by the fluorescence quenching of a dye (transducer: 0, optodes), 2 ) pH-measurements (transducers: pH optodes), and 3) the determination of NADH fluorescence using a bifurcated light-guide. Combining these measurement principles with different enzymes results in biosensors similar to those based on electrochemical transducers. There are no great differences in performance between them. Figure 20 shows the basic design features of an optical biosensor. od.\" 701 3.1.4. Mass-Sensitive Transducers A class of biosensors that have hitherto not been widely used are those based on piezoelectric crystals or surface acoustic wave (SAW) These provide a simple means of detecting changes in mass through the alteration in the resonance frequency of a crystal. If such a transducer is covered with a selectively adsorbing surface or absorbing film, the concentration of the ab- or adsorbed substance can be determined from the change in resonance frequency. Using a 9 MHz piezoelectric quartz crystal, for example, it is theoretically possible to measure mass changes as small as lo-' g. Guilbault et al. describe sensors based on piezoelectric crystals coated with enzymes. The selectivity is provided by the formation of an enzyme-substrate complex, and the sensitivity is given by the stoichiometric mass increase given by the equation of the reaction. With immobilized formaldehyde dehydrogenase,[' \"1 atmospheric formaldehyde concentrations in the range from 1 to 100 ppm can be detected, with choline esterase,\" 731 pesticides in the ppb range. Measurements in liquid media cause greater problems and are controversial. To maintain the theoretical sensitivity described in Equation (d), piezoelectric sensors should be subjected to a reproducible drying step in air before use. 3.2. Multienzyme Sensors The repeated use of expensive coenzymes is possible if they are regenerated by a second enzyme. The recycling method described by Schepers et al.\" 7 4 1 could be applied to many analytes. The fluorescence of the reduced coenzyme nicotinamide adenine dinucleotide (NADH) is measured in a flow-through cell using a fiber-optic device. The molecular mass of the NAD@ is increased by binding it onto polyethyleneglycol in order to trap it within the cell, together with an enzyme such as alcohol dehydrogenase, behind a dialysis membrane. When a second enzyme, e.g. lactate dehydrogenase, is also included behind this membrane, it becomes possible to regenerate the NADH by adding pyruvate. However, the need to add this reagent means that the device is no longer a sensor in the narrow sense, because a sensor should work without addition of reagents. Several enzymes, or even a whole enzyme series, could be necessary in cases where a single enzymic reaction step does not yield a substance which can be detected by a transducer.[' 14, 3.3. Biosensors Based on Tissue Sections or Cell Cultures Not only isolated enzymes but also entire groups of intact cells can be used as the basis for biosensors. Compared with the isolated enzymes, these often have the advantage of being active for longer periods, as the enzymes are kept in their natural environment. In this case an additional immobilization step for the coenzymes or cofactors is not necessary. However, such cell groups are often less selective, as they contain mixtures of enzymes. Arnold and R e ~ h n i t z \" ~ ~ ] published a table listing biosensors based on tissues and related materials. NH, or 0, chemosensors are often used as transducers. The principle of these devices will be explained by taking as an example a biosensor for hydrogen peroxide. As bovine liver contains relatively high concentrations of the enzyme catalase, a section of fresh tissue only 0.1 mm thick is immobilized with nylon mesh on the surface of a membrane-covered 0, electrode. The hydrogen peroxide whose concentration is to be determined undergoes enzymic decomposition to oxygen and water, and the oxygen thus produced is measured amperometrically. This sensor is less sensitive to fluctuations in temperature and pH, and has a longer lifetime than a biosensor containing an isolated enzyme.['76] Another device of this kind which is frequently cited is the \"bananatrode\" which has been described by Rechnitz et al.['77] Here a thin slice of banana in front of an 0, sensor is used as a detector for dopamine, which undergoes oxidation by the enzyme polyphenol oxidase present in bananas. The consumption of oxygen is then measured. 3.4. Microbial Biosensors The majority of biosensors based on immobilized microorganisms function with amperometric oxygen sensors as transducers.[' 'I Biosensors for the determination of phosphate, nitrate, nitrite, sulfite, methane, and phenol have recently been described, but none has yet achieved a commercial breakthrough. The determination of phosphate was performed with a sensor based on the microorganism Chlorella vulgaris in immobilized form. An 0, optrode was used to measure the increase in the photocurrent on introducing phosphate. The photocurrent was found to be a function of the phosphate concentration in the range from 8 to 70 mmol L- .I1 791 Karube, Kitagawa et al.\" have developed a microbiological sensor for alcohol using a pH ISFET as a transducer. For this the acetic acid bacterium Gluconobacter suboxydans was immobilized on the ISFET behind a gas-permeable membrane. Ethanol which diffuses in through the membrane is converted to acetic acid by the bacteria. This biosensor can be used for the determination of ethanol in the range from 3 to 70 mmol L-I. 3.5. Immunosensors Antibodies (Ab) and antigens (Ag) (or haptenes) bind specifically and strongly to each other. Techniques for following such reactions in order to determine one of the reac- 534 Angew. Chem. Int. Ed. Engl. 30 (1991) 516-539 tion partners have up to now relied mainly on labeling one of the immunoreactands. This is the principle used in immunoassays, which are now indispensable in biochemical analysis. Immune reactions are subject to the limitations imposed by the law of mass action. In the equilibrium reaction between the free antigen (Ag) and the antibody (Ab) to form the antigen-antibody complex, the equilibrium ratio between the concentrations of the complex and of the free reaction partners is determined by the affinity constant K [Eq. (f)l. In immunoassays quantitative determinations can be carried out by means of competitive binding tests or sandwich tests. In competitive tests labeled antigens are used. If radioactive labeling is used, the procedure is called a radioimmunoassay (RIA). If instead, an enzyme is covalently bound to the antigen (horseradish peroxidase or alkaline phosphatase are often used), the procedure is called enzyme immunoassay (EIA). The labeled antigen and the antigen to be assayed compete for the binding of the immobilized antibody, and the concentration of the antigen can be determined by comparison with a reaction of a known concentration of the pure antigen. Sandwich tests are carried out with labeled antibodies. When radioactive labeling is used the measurement is described as an immunoradiometric assay (IRMA), whereas if the antibody is attached to an enzyme it is called an enzyme-linked immunosorption assay (ELISA). The antigen which is to be determined binds to an antibody which is immobilized on a support, and is quantitatively determined by means of a second labeled antibody. Both systems have important disadvantages. Purified antibodies and antigens are required. The calibration curves are only linear over a small concentration range. With radioactive labeling there are problems of waste management. Although an immunoassay is simple to perform, it involves a succession of stages, and often a separation step, requiring several hours of work. In the last few years several immunosensors have been developed in which the immunological reaction is measured directly. These sensors use electrochemical, optical, or piezoelectric transducers or capacitance bridges. It should eventually be possible to perform the most important types of immunochemical analysis with disposable sensors.[' ' I Enzyme immunoelectrodes comprise the transducer (electrode), the immune reaction system, and an enzyme indicator and are based on the usual EIA phnciples, except that the product of the enzyme-catalyzed reaction (often H,O,) is detected electrochemically and not by photometry.[182, 1831 Ion-selective membrane electrodes have also been used for the determination of antibodies. The method is described by Rechniiz et al./1841 in which the corresponding antigen is covalently bound to an ionophore of the benzo-crown-ether group and immobilized in a PVC membrane to give an electrode sensitive to alkali metal ions. The change in the potential of the electrode which occurs on adding the appropriate antibody is caused by the alteration of the properties of the ionophore when the antibody binds to the antigen-ionophore complex. Another type of immunosensor is based on the antigen-induced change in the potential of a chemically modified semiconductor surface (TiO,), the mechanism of which is still not understood.t1851 Based on early fundamental studies on potentiometric immunosensors during the period 1978 - 89, the interdisciplinary research center for chemoand biosensors at the Westfaelische Wilhelms University (FRG) has just elucidated the general mechanism of immunologically-induced changes in electrode potential.\" 86* 1871 There are in principle many different antibodies for a particular antigen or haptene, so that a large variety of organic molecules can be selectively determined. If the remaining problems of standardization and storage life can be solved, this analytical technique should revolutionize at least molecular analysis, since a potentiometric immunoassay is fast, sensitive, and extremely economic. Immunosensors based on mass-sensitive transducers (piezoelectric crystals and SAW devices) exploit the mass increase which results from the immune reaction.\" 881 Here again measurements in liquids present problems. Immune reactions at surfaces also alter certain optical properties, on which optical sensors are based. One optical effect that can be used to determine antigens with immobilized antibodies is the change the resonance angle in surface plasmon resonance (SPR) spectroscopy[' 891 when immunocomplexation forms a film on a silicon or metal oxide base layer. Others are the change in light scattering from a coated glass surface when an immunocomplex is formed,\"901 and changes in the reflection and absorption of a light beam (evanescent wave te~hnique).['~'] A strict definition classifies immunosensors not as true sensors, but as dosimeters, because the immune reactions are not reversible. Under suitable conditions (e.g. by altering the pH) it is possible to break down the biocomplex to recover the antibody and the antigen, allowing a quasi-continuous measurement sequence.['86, l E 7 1 A continuously operating type of immunosensor based on competitive reactions has been developed ; here the analyte and a heterobifunctional complex compete for binding sites on an immobilized antibody!'921 Nonspecific binding is a difficulty which limits the sensitivity of immunosensors in many applications. This problem has been investigated in detail by Cullen and L ~ w e . ~ ' ~ ~ ] 3.6. Biosensors Based on Receptors A very promising approach is the development of biosensors in which individual receptors or receptor structures from living organisms are immobilized on transducers.\" 94] The advantages of receptors over enzymes, for example, lie in very high sensitivities and short response times. It is known, for example, that some marine species can recognize substances at concentrations as low as mol L-' , However, the problems of isolating receptor molecules and of their instability when immobilized are still so great, that this idea must be regarded at present as an interesting approach with potential for future developments. A sensor for the determination of glucose which is based on a receptor protein has been developed by Schultz and Meadows.\"951 This makes use of the competition between glucose and a glucose analogue, a dextran labeled with fluorescein isothiocyanate (FITC-dextran), for binding sites on Angew. Chem. Int . Ed. Engl. 30 (1991) 514-539 535 the glucose receptor protein concanavalin A labeled with rhodamine (Rh-Con A). FITC-dextran and Rh-Con A are sealed in a length of dialysis tube at the end of a bifurcated light guide with a diameter of 100 pm (Fig. 21). Light of a suitable wavelength excites FITC, which fluoresces. If the FITC is connected via the dextran to the Rh-Con A, the energy absorbed by the FITC is transmitted to the rhodamine, which then also fluoresces. If glucose diffuses through the dialysis membrane into the measuring cell, the dextran is partly displaced from its binding sites by the glucose and the measured FITC fluorescence increases, because less energy is transferred from FITC to rhodamine. From increase in fluorescence intensity the glucose concentration can be determined. 3.7. Applications of Biosensors An important technological application of biosensors is the control of fermentation processes. Here it is desirable to measure continuously as far as possible, to ensure optimization of the fermentation process and to minimize the consumption of expensive nutrients. It is particularly important to monitor glucose, ethanol, lactate, cephalosphorins and penicillins. Another area in which biosensors are used, is food technology and food testing. Of interest is the glucose content of wine and fruit drinks,[1961 lactate production during milk processing,[1971 and the freshness of fish, which is measured with a hypoxanthin sensor.[19s1 An area of growing importance is monitoring the quality of water and effluents. Most of the sensors developed so far are based on the combination of microorganisms and transducers. Some sensors serve to determine individual constituents of water, such as phosphate, nitrite, and nitrate,\" '] while others measure composite parameters through their inhibiting effects on microorganisms or enzymes. However, the latter are more like simple early warning systems (screening) than true sensors, as an alarm indication needs to be followed by a more precise analysis. Moreover, these systems work irreversibly. Such warning systems are used in particular to monitor pesticide contents or concentrations of heavy metal ions and the inhibition of the microorganisms is mea- sured by the reduction in CO, production.['991 To obtain a quantity which can be related to the biological oxygen demand (BOD), changes in the respiratory rate of E-ichosporon cutaneum are measured with an oxygen electrode.[z00] A sensor of this type is already in routine operation in Japan. A final example of a field in which biosensors are finding application is medical technology. The most frequently performed analyses are of glucose and lactate, and it is therefore in this area that the most intensive research is being undertaken. The desirability of in-vivo measurements, for example, to control an insulin pump, is giving impetus to the development of miniaturized biosensors. Here of utmost importance is the requirement that the reagents are biocompatible and physiologically harmless. Already a few biosensors, based on electrochemical or optical transducers or on piezoelectric crystal measurements in the gas phase, are commercially available. Analytical instruments have been developed to avoid some problems of biosensors. Here pretreatment of the samples can prolong the life of the sensor. The early commercially available analytical instruments for medical technology are usually based on an oxygen or hydrogen peroxide electrode as a transducer, with an oxidase as the biochemical component. They permit analyses on whole blood for glucose content in the range from 0 to 30 mmolL-' or lactate content from 0 to 15 mmol L-l. A BOD-measuring instrument based on the BOD sensor described earlier is now also available. A list of commercially available analytical instruments based on biosensors can be found in the article by Owen.[201] 4. Outlook This article aimed to give a concise overview of the present state of development of chemical sensors that are already or might become important for chemical, medical, and environmental applications. However it does not claim to be exhaustive. In the field of biosensors alone there are, according to recent CAS on-line searches, over 3000 publications and over 300 patents, although there are at present barely a dozen types of commercially available sensors, of which more than a half are for glucose. One of the main reasons for this striking imbalance with regard to marketing success may be found in the low degree of interdisciplinary cooperation among scientists. Many of the publications go no further than demonstrating a reproducible effect observed for a single chemical substance. Often there is no investigation into the effects of interfering substances, nor an answer to the central analytical question: how accurately and reliably does the sensor measure the substance for which one is analyzing? Reports which only give information on reproducibility, measured on pure synthetic samples containing no interfering constituents, should be avoided in view of the present wealth of knowledge about sources of systematic errors. To an analytical chemist a report on the development of a new analytical method which tells one nothing about matrix effects, and therefore about its absolute accuracy (defined as coincidence with the true content in the sample) is like a report on a synthetic method for a new compound which was identified by elemental analysis alone (i.e. without 536 Angew. Chem. in[ . Ed. Engl. 30 (1991) 516-539 Confirmation by universally recognized and indeed prescribed methods of modern structural analysis). In the field of chemosensor development, as in that of ultra-trace analysis, there is a growing tendency to play down the importance of interfering effects. The disproportionately large amount of research effort devoted to the microelectronic aspects of modern transducers is pointless if not accompanied by a deeper understanding of the mechanisms by which substances are specifically recognized. The fundamental mechanisms of the molecular interactions taking place in these devices cannot be planned and optimized on purely engineering considerations; they depend on natural laws that one can use but cannot alter! In summary it may be concluded that the development of sensors will advances further simply because there is a strong demand for it. The more research effort concentrated on the central problem of a selective molecular recognition, the quicker such advances will be achieved. Our present knowledge of mechanisms indicates that it is necessary to involve chemists from a wide variety of disciplines: theoretical, inorganic, organic, biochemical, analytical, and physico-chemical. The development of new sensors can only progress by an interdisciplinary approach, which must also include the collaboration of biologists, physicists, and medical scientists. At this stage improvement in the transducer properties has a lower priority than improvement in the selectivity of chemosensors and the lifetime of biosensors. The transducers now available have adequate stability and sensitivity, and their full exploitation is prevented only by the laws of physicalchemistry or by shortcomings in the properties of the sensor elements. The basic ideas ofthe novel approach to the theory of ion-selective electrodes described here were developed in 1975 by K. Cammann in his Ph.D. thesis. He would like to thank his academic teachers, Prof. Dr. G. Ertl and Prof. Dr. H . Gerischer, for many discussions and helpful suggestions. During a Humboldt-Fellowship, for which the Alexander von Humboldt Foundation is sincerely thanked, Prof. Dr. S. L. Xie could verifv this far-reaching theory completely by means of the most modern experimental equipment. The basic research in this field during recent years was generously funded by the Deutsche Forschungsgemeinschaft (DFG) and the Fonds der Chemischen Industrie, which we have much appreciated. Grateful acknowledgement is also given to the Bundesministerium fur Forschung und Technologie (BMFT) for its generous financial help to research in the field of biosensors at Miinster. Last but not least, we owe a debt of gratitude to the State of Nordrhein- Westfalen, which is establishing a research institute for chemical sensors and biosensors (attached to the University of Miinster) in cooperation with the FraunhoferManagement-Gesellschaft (FhM) . 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        ]
    },
    {
        "image_filename": "designv10_4_0001008_j.engfailanal.2021.105260-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0001008_j.engfailanal.2021.105260-Figure5-1.png",
        "caption": "Fig. 5. Finite element mesh structure for the stress analysis.",
        "texts": [
            " In this study, the hexahedral mesh structure was preferred for static stress analysis. Since the geometry was extensive, the mesh size is selected more frequently in the critical regions for analysis, and a large mesh size was preferred for the less critical parts for the analysis. The mesh structure approximately consists of 38,300 elements and 156,000 nodes. Since the geometry may change slightly for different pressure angles and rim thickness, the number of elements and nodes will also differ. An example of a mesh structure created in this study was shown in Fig. 5. A mesh convergence study was performed to show the reliability of the mesh structure. Five different mesh sizes were used for the FEA, and the maximum bending stress results were obtained for each analysis. The result of the mesh independency study for 14000, 17000, 24000, 38300, and 53,500 elements, as shown in Fig. 6. Up to 38,300 elements, the stress was continually decreasing. It is seen that the stress changes very little in 53,500 elements. For this reason, the number of elements of the analysis was determined as 38,300 elements to avoid creating unnecessary data in the computer area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000079_j.rcim.2019.101916-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000079_j.rcim.2019.101916-Figure6-1.png",
        "caption": "Fig. 6. The experimental setup.",
        "texts": [
            " In downhand welding, it is obvious that the gravitational force helps to suppress the accumulation of weld metal [39]. However, the effect of gravitational force is different in the positional deposition, instead of driving the molten metal to backfill the gouging area, the metal flow trends downward as shown in Fig. 5. The momentum of the backward stream of molten weld metal has been increased greatly by the influence of gravity, resulting in a poor positional capability of multi-directional WAAM. Fig. 6 presents the setup of the robotic WAAM system for the investigation of humping issue in a positional deposition. Its main components include a 6-axis ABB industrial robot with a positioner, a Fronius TPS 4000 CMT Advanced welding unit, a personal computer, two CCD cameras, an infrared pyrometer, and a laser scanner. In this study, the ABB IRB 2600 industrial robot with six Degrees of Freedom (DoF) was used to hold the welding torch. A two-DoF workpiece positioner was employed to keep base plate vertical for the positional deposition",
            " Two CCD cameras were mounted on the welding torch to capture the molten pool formation behaviour. A structured light laser scanner was integrated into the robotic welding system to measure the height of the multi-layer thin-walled structure for updating the robot path. In addition, an infrared pyrometer was used to monitor the inter- pass temperature. A data acquisition unit and a personal computer serve as the master control for the welding machine, robot, positioner, camera, and laser scanner. As shown in Fig. 6, the vision system includes two CCD cameras mounted on the robotic arm to capture the side-view and the top-view of the weld bead separately. In addition, Fig. 7 demonstrates the basic concept of CMT process, the detailed metal transfer process can be divided into three steps; 1) the metal melting phase Fig. 7(a), 2) the background current phase/wait phase Fig. 7(b), and 3) the short-circuiting phase Fig. 7(c) [52]. In the metal melting phase, it is hard to observe the profile of the molten pool due to the illumination of the arc core when electrical arc forms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003832_0094-5765(88)90189-0-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003832_0094-5765(88)90189-0-Figure1-1.png",
        "caption": "Fig. 1. (a) Geometry of the system (Liu [2]). (b) Geometry of the system (Lorenzini et al. [3]).",
        "texts": [],
        "surrounding_texts": [
            "The tethered system under consideration consists of three bodies having masses rn~, m2 and rn 3 as shown in Fig. 2. The dimensions of the bodies are much smaller compared to the lengths of the tethers and hence, the bodies can be approximated as point 1059 masses. The mass of the tether(s) is assumed to be negligible. The instantaneous centre of mass C is assumed to follow a circular orbit. The orbital coordinate axes x, y, z located at C are such that z-axis is directed towards the centre of the Earth and x-axis is in the direction of flight. The length of the tether between one end-mass mt and the middle mass m 3 is denoted by l~. Similarly, 12 denotes the length of the tether joining the middle mass to the other end-mass. Two possible situations are considered here: (i) l~ and /2 are independent of each other, as in the case of a tethered constellation; (ii) Ii and l 2 add up to a constant, i.e. It +12 = It (total tether length). The latter corresponds to the case of mass transportation from one end to the other. The formulation for case (i) is considered first; that for case (ii) is slightly different due to the constraint equation and is considered later. 2.1. Equations o f motion when l I and 12 are independent The motion is assumed to be confined to the orbital plane; thus only the co-ordinates x~ and zi, i = 1, 2, 3, are nonzero. Furthermore, since C is the centre of mass of the system, 3 3 E m i x i = O, E mizi = 0 . ( 1 ) i = 1 i = 1 Because of the two constraint eqns (1), the motion can be described by four independent generalized co-ordinates; here they are chosen as ll, 12, 01 and 0 z as shown in Fig. 2, 01 and 02 being the angles of inclination of the two tethers to the local vertical. From geometry, Xl = It sin 01 + x3, Zl = 11 cos 01 + z3 (2a) x2 = - (l: sin 02 - x3), z2 = - (lz cos 02 - z3). (2b) Substituting eqns (2a) and (2b) into eqns (1) one obtains {-,} ,.':\" sir\" O, x: = [A] ) j : , X3 {zl} ,lcoso, , z, = [A] ( t , cos 0. 3 Z (3a) (3b) where 1 --/~j M2 ] [ A ] = [ - P l - 1 + # 2 , L P2 d (3c) Pl, P2 being the mass ratios given by p l=rn l /m , i t2=m2/m, (3d) while m = rn I + m 2 + m3. The kinetic energy of the system is given by 3 T = \u00bd ~ mi[(Rc + r,)\"(Rc + l',)] 3 3 = \u00bd rn ~'c\" Rc + Rc\" Z rn,#, + \u00bd Z m,r,. t,, (4) i = 1 i = 1 where I~ c is the position vector of C with respect to the centre of the Earth and \u00a2; is the position vector of the ith mass relative to C. The first term in the above expression is the orbital kinetic energy; the second term vanishes since C is the centre of mass while ii is given by i, = .~;i + L k + ( - t ) j ) x (x;i + z ,k) = (x, - flz;)i + (-~ + f~x,)k, (5) where i, j, k are the unit vectors along x, y, z-axes, respectively. Substituting eqn (5) into eqn (4), using eqns (3) and carrying out some algebra, one obtains r = To, b + \u00bdm [#, (1 -- #1 )[/.jz + li(0, -- f~)2] + # 2 0 - #2) [/'i + l~(02 - t'l) 2] + 2 # , # 2 \u00d7 {[/.1 i2 + l, 6(0, - f ~ ) ( O 2 - ~ ) ] c o s ( 0 , - 02) + f f l l 2 (O 2 - n ) - 11/.2 x (0, - ~)]sin(0, - 02)}], (6) where Tomb is the orbital kinetic energy, while the rest is the kinetic energy associated with the attitude dynamics. The potential energy of the system is given by L GM~mi V = - ;=1 I(Rc + r,)i 3 = - ~ G M ~ m ; [ ( - R c k + r , ) i = 1 x ( - Rc k + r,)]- 1/2 (7) where GM\u00a2 is the product of the universal gravitational constant and the mass of the Earth. Expanding the right-hand side of eqn (7) in a binomial series and retaining terms up to 0(l /R3), one obtains V = - ( G M e m / R c ) - (GMelRZc)k where q;-- 01, 02, ll and 12. They are as follows: m#, ( I - # , ) I~ [0., + 2(i, 1 1 1 ) ( o , - ~) + 3 ~ sin 01 cos 01] + m#l #2ll 12 x { c o s ( 0 1 - 02)[0\"2 + 2 ( i 2 1 1 2 ) ( 0 2 - n)] + 3f~ 2 sin 01 cos 02 + [(0 2 - ~)2 _f~2 _ ('l~/12)] sin(01 - 02)} = Qol, (10) m#2(l - la2)1210.2 + 2(/.2/12)(02 - ~) + 3f~ 2 sin 02 cos 02 ] + m#l #2 l112 x {cos (02 - 01) [0\" 1 + 2(/\" 1/1~ ) (01 - f~)] + 3fF sin 02c0s 01 + [(0j - f~)2 - f~2 - ( ' l l / l l ) ] s in (OE-Ol ) }=Qo2 , ( l l ) my, ( i - # , ){l] - [(01 - f l )2 +[12(3 cos 2 01 - 1)]/l } + re#l#2 x {COS(0~ -- 02)1~ + 2(02 -- [2) sin(01 -- 02)/.2 + [O~sin (01 -- 02) -- 3f~ 2 cos 01 cos 02 + d2(zta - d2)cos(01 - 02112} = Q, , , (12) m#2( 1 - #z){]~ - [(02 - ft) 2 + f F ( 3 cos 2 02 - 1)]12} + mPl #2 x {cos (02 - 01 )'l I + 2(0~ - f~)sin (02 - 01 )/.l + [0.1 sin(02 - 01) - 3~ 2 cos 01 cos 02 + 0~(2f~ - 01)cos(02 - 0~]ll} = Qa. (13) The generalized forces Qm etc. can be obtained using the principle of virtual work and are given by Qol=Qo2=O, Q n = - T J , Q t z = - l \" 2 , (14) where T1 and T 2 are the tension in the two tethers. Note that when one of the lengths is put to zero [say /2 = 0 in eqns (10) and (12)], equations for the two-body system are recovered. 3 3 \u2022 ~ re, r, + (GMdR3)~ m,[ r i . r , - 3(k.r,)2]. i=1 i=1 In the above expression, the first term corresponds to the potential energy associated with orbital motion, while the second term vanishes since C is the centre of mass. Using the co-ordinates of the masses given by eqns (3) and noting that GMe/R 3 = f~2, the potential energy becomes V = Vo,b + \u00bdmfl2{#1(1 -- #1)12~ (1 -- 3 cos 2 0,) +#2(1 -- #z)l~(1 -- 3 COS 2 02) +2#1#21112[c0s(01 -- 02) - - 3 COS 01 COS 02] }. (8 ) The equations of motion can now be obtained from d pOZl - + = (9)"
        ]
    },
    {
        "image_filename": "designv10_4_0003000_s002850050081-Figure27-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003000_s002850050081-Figure27-1.png",
        "caption": "Fig. 27. Schematic illustration of origin of possible residual stresses due to surface growth. (A) Uniform growth without residual stresses up to time t\"t 1 . (B) Incompatible growth due to non-uniform surface growth, assuming no residual stresses. (C) Resulting shape if residual stresses are assumed to maintain compatibility of the growing structure",
        "texts": [
            " Suppose that after some time, the growth velocity changes so that for a period from t 1 to t 2 the growth velocity is g\"v 0A1#b cos nr 2aB i 3 , (66) where r is the cylindrical coordinate and b is a constant. After time t 2 , it is assumed the growth velocity g reverts to Eq. (30). Since the growth velocity g given by Eq. (66) is not compatible with rigid body motion, residual stresses will be required to maintain the continuity of the horn and skull. The problem to be solved to find the residual stresses is illustrated in Fig. 27. The uniform growth up to time t 1 is shown in Fig. 27A. For a time t during the interval t 1 (t(t 2 , the uninhibited growth assumed (Eq. (66)) would produce the incompatible parts shown in Fig. 27B. Residual stresses are required to maintain continuity of the horn and skull as shown in Fig. 27C. In the problem posed in Fig. 27, residual stresses are required beginning at t\"t 1 and they will be changing with time thereafter due to the continued incompatible growth. In the above discussion, it is assumed that the cells producing growth are capable of producing the assumed growth velocity g , Eq. (66) against the influence of the residual stresses that such incompatible growth produces. In real life it may be expected that such residual stresses will influence the rate of growth and tend to force it into a compatible mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure6-8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure6-8-1.png",
        "caption": "Figure 6-8. Oscillating disc rheometer trace.",
        "texts": [],
        "surrounding_texts": [
            "The apparatus is described in fairly general terms, for example the dies should be made of a non-deforming material and have a pattern of grooves to prevent slippage but the precise geometry of the dies and the grooves is not specified. Similarly, there are recommendations for die closure, frequency and amplitude of oscillation, and temperature control. Although not mentioned in the standard, a sealed cavity in a moving die instrument is more difficult from an engineering point of view but can be advantageous in retaining a positive pressure. ASTM D 5289\u0302 ^\u0302 for rotorless curemeters, although rather more specific, is overall very similar to ISO 6502 in technical requirements. The British standard* \u0302 ^ is identical to ISO 6502. Norman*'\u0302 gave a valuable discussion of the problems with curemeters, pointing out that there is no one level of cure which gives optimum values for all physical properties and no satisfactory procedure for dealing with a \"marching modulus\". He also listed problems such as non-uniform temperature distribution, possible slip of the test piece over rotor or cavity and porosity. Test on unvulcanized rubbers 87 In a practical instrument, there must be some time lag to reach thermal equilibrium When the oscillating disc curemeter superceded the reciprocating paddle type it brought one disadvantage in that it had a larger unheated mass in the disc and, hence, had greater thermal lag. Hands and Horsfall\u0302 \"\u0302\u0302 used an isothermal apparatus to obtain basic cure rate data and developed a mathematical cure model for predicting cure distributions in non-isothermal conditions, as in industrial processes. The rotorless curemeter is shown, for example by Hands et al*^^ to more approximate isothermal conditions than both other types because of the absence of an unheated rotor and a thin test piece, hence giving more accurate predictions for fast curing materials. It is essentially this factor which resulted in the rotorless type of instrument rapidly becoming the most popular. Rosco and Vergnaud^^^ determined the limitations of moving die curemeters under isothermal conditions by considering the temperature and degree of cure profiles through EPDM samples. Clearly, cure meters will not always agree due to their differing thermal characteristics. Because the Mooney is often used to measure scorch, it is worth noting a comparison between Mooney and curemeter scorch made by Bristow^^^ in which he found poor correlation for higher curing temperatures. Hands et al^'^ Sezna '\u0302\u0302 and Ahmad and Soo\u0302 ^\u0302 give comparisons between different curemeters and indicate how older instruments differ from more recent ones. The effects of thermal parameters is briefly considered in an annex to ISO 6502. The oscillating die cure meters are a type of dynamic test and the use of sophisticated forms of the apparatus offers the possibility of alternative measures of cure parameters. Dick and Pawlowski\u0302 ^^ demonstrate the subtle changes detectable by such instruments and consider alternative measures of scorch and cure characteristics which can be used. It has been suggested that the maximum cure rate may sometimes have advantage over the more usual cure parameters*^^ and consideration given to curemeter testing for cure of thick sections^^ .\u0302 Curemeters are usually run under isothermal conditions to determine cure parameters at the temperature(s) of interest. Rosea and Vergnaud^^^ investigated the use of a temperature ramp as being a more efficient way of obtaining kinetic parameters. The sophisticated oscillating die instruments can continue the measurement of dynamic properties after full cure has been reached. ASTM D660l'^'^ covers measurements both during and after cure. A sealed cavity instrument is specified with amplitude \u00b1 0.2^ during cure and \u00b1 1 to \u00b1 100% strain after cure. In addition to the usual cure parameters, the in and out of phase moduli and tan 5 are reported."
        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.21-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.21-1.png",
        "caption": "Figure 13.21. Normals to the tooth surfaces at points A and A I.",
        "texts": [
            " We then showed that the base pitch is equal to the distance between adjacent tooth profiles, measured along a common normal. The normal base pitch of a helical gear was defined earlier in this chapter, as the distance between corresponding points of adjacent teeth, measured on the developed base cylinder in a direction perpendicular to the lines of the teeth. We will now show that the normal base pitch, defined in this manner, is also equal to the distance between adjacent tooth surfaces, measured along a common normal. Figure 13.21 shows the base cylinder of a gear, with the base helices of two adjacent teeth. We consider two points, A on one tooth and A' on the other, with generators starting at points G and G', and we will determine what conditions must be satisfied if there is to be a common normal at A and A'. A first condition, necessary for the existence of a common normal, is that the normals to the tooth surfaces at A and A' should be parallel. This condition can be written as follows, (13.107) and when we use Equation (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.6-1.png",
        "caption": "Figure 7.6: An n-body planar space structure (satellite+manipulator)",
        "texts": [
            " Moreover, he has pointed out that a more convenient model format is obtained by choosing (x, y) as the position coordinates of the last trailer rather than of the tow ing vehicle. It has been shown [42] that the maximum degree of nonholonomy (i.e., its maximum value for q E IRn) for this modified robot is FN+ 3 , where Fk indicates the k-th Fibonacci number. By analogy, we conjecture that the maximum degree of nonholonomy for our model (7.28) should be FN+4\u00b7 Consider an n-body planar open kinematic chain which floats freely, as shown in Fig. 7.6. One of the bodies (say, the first) may represent the bulk of the space structure ( a satellite), and the other n- 1 bodies are the manipulator links. An interesting con trol problern arises when no gas jets are used for controlling the satellite attitude, while the only available control inputs for reconfiguring the space structure are the manipu lator joint torques, which are internal generalized forces. In fact, it may be convenient to refrain from using the satellite actuators, so to minimize fuel consumption",
            " By computing the Liebrackets cos () 0 - sin () sin () 0 cos () [g1, f] = 0 [g2,f] = 1 ' [g2, [f, [g1, flll = 0 0 0 0 0 0 0 it is apparent that the dynamical model of the unicycle satisfies both the accessibility and the small-time controllability conditions. In fact, the vector fields span a space of dimension five at each ~' and satisfy the conditions of Theorem 3. n-Body Robot Derrote by T E mn-1 the vector of torques at the n - 1 joints. As shown in [27]' the dynamical model (7.40)-(7.41) for the n-body space robot of Fig. 7.6 takes the form B(B)B+n(B,B) = prT lrB(B)B = 0, with the elements of B(B) and P respectively given by eqs. (7.31) and (7.32), and n(B, B) computed as n(B, B) = B(B)B- ~ ( :B (er B(B)e)) r The reduced state-space model consists of 2n - 1 first-order differential equations, namely, where rP = iJ = M(rjJ) m(r/J, v) V lTB(rjJ)S lT\u00df(rjJ)l V M-1(1;) [-m(r/J, v) + T], PB(rjJ)PT Af(rjJ)v- ~:1; (vTM(rjJ)v). It can be proven that this system satisfies the conditions for accessibility and small time local controllability (see [27])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003599_acc.2006.1657333-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003599_acc.2006.1657333-Figure4-1.png",
        "caption": "Fig. 4. Embedded mini rotor aircraft",
        "texts": [],
        "surrounding_texts": [
            "The on-board computer we use is the Rabbit RCM3400 which runs at 29.4 MHz, with 512K flash memory, including 5 serial ports, 8 channels of programmable gain, 12-bit analog input, two 10-bit timers and 4 programmable PWMs and it is optimized for floating-point calculations. It is programmed using the Dynamic C compilator. It is worth mentioning that this feature allowed us to generate C code based on the RTW embedded coder of Simulink/Matlab. 1) Radio control system: We use a commercial 6 channel FM radio control system FUTABA, whose main signal is obtained and treated in such a way that it allows the user to have either manual and/or automatic operation. The radio can be used for trimming small offset deviations. The radio signal is sent to the flying object every 20 ms."
        ]
    },
    {
        "image_filename": "designv10_4_0002876_s0022-460x(02)01213-0-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002876_s0022-460x(02)01213-0-Figure14-1.png",
        "caption": "Fig. 14. (a) Primary and (b) inverted configurations.",
        "texts": [
            " Waves are assumed to propagate through the gear elements as if they were part of the same material as the shaft. The element material properties and geometry were made to reflect those of the steel gears available in the lab. The actual configuration for the transverse vibration testing is shown in Fig. 12. The model must also consider the added inertia of the bearings at either end of the shaft in order to accurately predict the propagation parameter. The analysis considers the bearings to be effectively pinned boundary conditions (see Fig. 13). The shaft was tested in two orientations (see Fig. 14). The propagation parameter for the periodic shaft in both configurations are shown in Figs. 15 and 16. Note that there are attenuation regions at lower frequencies for the periodic shaft including the bearing and gear inertias than for the shaft without their inclusion (see Fig. 17). The propagation parameter of a uniform shaft with the mass of the gear added is shown in Fig. 18. Note that although the shaft alone has no attenuation regions, that with the addition of the gear inertia introduces attenuation regions, albeit very small",
            " The drive motor of the test rig was run at several operating speeds, thus generating a variety of mesh excitation frequencies. The periodic shaft was tested in both orientations as well as a uniform shaft for comparison purposes (see Table 1 for a comparison of the shafts). Table 2 shows the operating speeds and torque loads that were used to evaluate the performance of the periodic shaft. The attenuation properties in bending of the shaft are indicated in Fig. 24 (the primary configuration) and Fig. 25 (the inverted configuration). These two configurations are defined in Fig. 14. Notice that strong attenuation is achieved in the frequency range from 600 to 1200 Hz and 1250 to 2000 Hz for both configurations, though the inverted configuration should exhibit stronger attenuation and slightly larger attenuation zones. Experimental results for testing the periodic shaft were obtained at a variety of rotation rates. Representative results are presented for the 450 r:p:m: case. The acceleration at each bearing for a given shaft are compared as well as comparisons of the uniform and periodic shafts at a given bearing in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003205_978-3-7091-4362-9_7-Figure7.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003205_978-3-7091-4362-9_7-Figure7.1-1.png",
        "caption": "Figure 7.1: Generalized coordinates of a rolling disk",
        "texts": [
            " Correspondingly, the number of degrees of freedom is reduced to n - 1, but the number of generalized coordinates cannot be reduced. This conclusion is gelleral: for a mechallical system with n gelleralized Coordi nates and k llonholollomic collstraillts, although the gelleralized velocities at each point are confined to an ( n- k )-dimensional subspace, accessibility o f the whole configuration space is preserved. The following is a classical instance cif nonholonomic system. Example. Consider a disk that rolls without slipping Oll a plane, as shown in Fig. 7.1, while keeping its midplane vertical. Its configuration is completely described by four variables: the position coordinates (x, y) of the poillt of contact with the ground in a fixed frame, the angle () characterizing the disk orientatioll with respect to the x axis, and the angle <P between a chosen radial axis Oll the disk and the vertical axis. Due to the no-slipping constraint, the system generalized velocities cannot assume arbitrary values. In particular, denoting by p the disk radius, they must satisfy the constraints x- pcose~ iJ- psin e ~ 0 0, (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003203_28.740849-Figure15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003203_28.740849-Figure15-1.png",
        "caption": "Fig. 15. Flux distribution due to excitation of phase a in the case of 25% eccentric rotor to the right.",
        "texts": [
            " The results are close enough to those found by the winding function method because linear simulation has been performed for both cases. The difference in the stator magnetizing inductances from both methods are presented in Figs. 12 and 13. Fig. 14 reveals the magnetic flux distribution caused by the excitation of phase only in the case of the noneccentric rotor. It is clear that the magnetic forces on both sides of the machine are identical, and this results in a balanced magnetic pull in all directions. On the other hand, Fig. 15 shows that the magnetic flux distribution on both sides of the machine cross section are not identical. This results in an unbalanced magnetic pull (UMP) in a radial direction toward the right-hand side. It is more convenient and the problem will be much more simplified if the coupled magnetic circuits approach rather than the magnetic fields approach for modeling of the synchronous machine is used. In the coupled magnetic circuit approach, the rotating magnetic fields will still be considered when writing the flux linkages of the rotating coupled circuits"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.11-1.png",
        "caption": "Figure 13.11. Developed cylinder of radius R and length L.",
        "texts": [
            "16) in terms of the transverse module, For many gears, the specification contains the value of the normal module, but not that of the transverse module, so it is convenient to combine Equations (13.16 and 13.29), in order to express the standard pitch cylinder radius in terms of the normal module, (13.30) An alternative expression for tan \"'R can be found by combining Equations (13.23 and 13.27), tan \"'R (13.31) If we develop a cylinder of radius R and length equal to the gear lead L, we obtain a rectangle with sides 2~R and L, as shown in Figure 13.11. It can be seen from Equation (13.31) that the diagonal of this rectangle makes an angle \"'R wi th the z axis. We have also shown that gear helices become straight lines in the developed cylinder, making the same angle \"'R with the z axis. Hence, all gear helices, such as intersections between the cylinder and the tooth surfaces, will appear in the developed cylinder of length L as lines parallel with the diagonal of the rectangle. Tooth Surface of a Helical Involute Gear 323 Base Cylinder We showed in Figure 13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000496_j.ymssp.2020.106747-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000496_j.ymssp.2020.106747-Figure1-1.png",
        "caption": "Fig. 1. Two degree-of-freedom of robotic manipulators.",
        "texts": [
            " Lagrange-Euler method is commonly used to represent the dynamic of the robotic manipulators as in [52] which is briefly explained in this section. A nonlinear dynamic model of robotic manipulators can be represented by s \u00bc M q\u00f0 \u00de\u20acq\u00fe H q; _q\u00f0 \u00de \u00fe G q\u00f0 \u00de \u00f01\u00de where q, _q and \u20acq 2 Rn are the angular position, velocity, and acceleration of each joint in n-DOF robotic manipulators. M q\u00f0 \u00de 2 Rn n denotes the symmetric positive definite inertia matrix, H q; _q\u00f0 \u00de 2 Rn represents the vector of the Coriolis and centripetal forces, G q\u00f0 \u00de 2 Rn is the vector of gravitational terms and s 2 Rn denotes the applied torques. Fig. 1 illustrates a free-body-diagram of 2-DOF robotic manipulators. For 2-DOF robotic manipulators, (1) can be rearranged in a canonical form as \u20acq \u00bc M 1 q\u00f0 \u00de H q; _q\u00f0 \u00de G q\u00f0 \u00de\u00bd \u00feM 1 q\u00f0 \u00des \u00f02\u00de _x \u00bc _q M q\u00f0 \u00de 1 H q; _q\u00f0 \u00de G q\u00f0 \u00de\u00bd \u00feM q\u00f0 \u00de 1 0 I u \u00f03\u00de where x \u00bc q1 q2 _q1 _q2\u00bd T and u \u00bc s1 s2\u00bd T . In this study, the derived nonlinear model of 2-DOF robotic manipulators was used to validate the proposed controller. By using the Lagrange-Euler method [52], nonlinear dynamic equations of 2-DOF robotic manipulators can be described as m1l1 2 3 \u00fem2l1 2 \u00fem2l2 2 3 \u00fem2l1l2 cos q2 \" # \u20acq1 \u00fe m2l2 2 3 \u00fem2l1l2 2 cos q2 \" # \u20acq2 m2l1l2 sin q2\u00bd _q1 _q2 m2l1l2 sinq2 2 _q2 2 \u00fe m1 2 \u00fem2 gl1 cos q1 \u00fe m2gl2 2 cos q1 \u00fe q2\u00f0 \u00de \u00bc s1 \u00f04\u00de m2l2 2 3 \u00fem2l1l2 cos q2 2 \" # \u20acq1 \u00fe m2l2 2 3 \" # \u20acq2 \u00fe m2l1l2 sin q2 2 _q1 2 \u00fem2gl2 cos q1 \u00fe q2\u00f0 \u00de 2 \u00bc s2 \u00f05\u00de By referring to (4) and (5), the matrices in (1) can be expressed as M q\u00f0 \u00de \u00bc m1 l1 2 3 \u00fem2l1 2 \u00fe m2 l2 2 3 \u00fem2l1l2 cos q2 m2 l2 2 3 \u00fe m2 l1 l2 2 cosq2 m2 l2 2 3 \u00fe m2 l1 l2 2 cos q2 m2 l2 2 3 \" # , H q; _q\u00f0 \u00de \u00bc m2l1l2 sin q2\u00bd _q1 _q2 m2 l1 l2 sinq2 2 h i _q2 2 m2 l1 l2 sin q2 2 h i _q1 2 2 4 3 5 and G q\u00f0 \u00de \u00bc m1 2 \u00fem2 gl1 cos q1 \u00fe m2gl2 2 cos q1 \u00fe q2\u00f0 \u00de m2gl2 2 cos q1 \u00fe q2\u00f0 \u00de #\" \u00f06\u00de Based on the derived equations of motion in (4) and (5), the robotic manipulators are highly nonlinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003581_icar.2005.1507426-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003581_icar.2005.1507426-Figure7-1.png",
        "caption": "Figure 7 Co-ordinate reference frames, forces and moments for the ductedfan model.; {W} = world, {A} = aircraft, {P} = control mass.",
        "texts": [
            " Lift and yaw control are achieved by changing the propeller speeds collectively or differentially. Overall, the design is quite similar to that described by Sherman et al [8]. Ando [9] has derived a simple 3 degree of freedom dynamic model for this configuration which suggests that placing the CG within a very small range of locations above the AC gives both static and dynamic stability. In practice, it is anticipated that active (gyro) stabilization will be necessary but starting with a system which is near passive stability is attractive. Ando\u2019s model is extended, as shown in Figure 7, to include a servo-controlled mass (mp) on a prismatic joint with origin at a distance l above AC. Moving this mass to the right causes the duct to \u2018topple\u2019 clockwise and the horizontal thrust component thus produced accelerates it to the right. Assuming that for a hover condition the thrust TA is adjusted to give a null component along the zA axis, a linearised model for the accelerations of the control mass, the duct (at AC) and the pitch angle is given by: \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 \u2206++ ++ + \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1 \u2212 \u2212 \u2212\u2212\u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b ++ = \u23a5 \u23a5 \u23a5 \u23a6 \u23a4 \u23a2 \u23a2 \u23a2 \u23a3 \u23a1\u2206 xgmgmM gmmH gmF II mm ImmmI x x ppAC apA pxp aa apa A \u03b8 \u03b8 \u03b8 \u03b8 ll ll && && && )( 10 011 1112 (1) where I is the sum of the individual moments of inertia of mp and mA about yp and yA respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003584_we.173-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003584_we.173-Figure8-1.png",
        "caption": "Figure 8. Natural mode shapes for the helical gear pair (wireframe, undeformed; solid, deformed)",
        "texts": [
            " These values match almost perfectly with the results calculated by Kahraman,5 which proves the validity of the model implementation in the frictionless case. Figure 7(a) shows how the eigenfrequencies change with changing b. Only w2, w4, w8 and w12 are influenced and the largest relative change is observed for w2, which is only 6% for b = 20\u00b0 (Table I). Thus the influence of the helix angle is rather small; as a result, a simplification of a parallel helical gear system to a spur gear pair can be justified when calculating only the eigenfrequencies. The effect of the helix angle on the corresponding mode shapes is shown in Figure 8 for w2, w4, w8 and w12. Influence of the Bearing Stiffness Values (kbax, kbrad, kbtilt). The fourth mode shape in Figure 8 (for b = 0\u00b0) corresponds to the eigenmode that was calculated with a torsional multibody model in Figure 2 and which has the biggest impact on the torque. Remarkable is the drop in frequency (2955 \u00c6 1566 Hz) for this mode as a result of adding realistic bearing flexibilities in the rigid multibody model, which were lacking in the torsional model. Users of torsional models are aware of this limitation in their models and therefore often use gear mesh stiffness reduction factors based on their experience"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure11.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure11.5-1.png",
        "caption": "Figure 11.5. Contact at the highest point of single-tooth contact on gear 1.",
        "texts": [
            "30) So far, we have shown how to calculate the fillet stress when the load is applied at an arbitrary radius Rw' The tooth load moves along the tooth face during the meshing cycle, and the fillet stress depends on the position of the load. We now consider the load position which causes the fillet stress to reach its max imum value. I n general, the fi llet stress increases as the load moves towards the tip of the tooth. However, when the contact point is near the tooth tip, the total tooth force is shared between two pairs of teeth, provided the gears are accurately cut. The maximum fillet stress is therefore reached when the load is applied at the highest point of single-tooth contact. Figure 11.5 shows the meshing diagram for a typical gear pair. The length of the path of contact T1T2 can be expressed as mcPb' where mc is the contact ratio, given by Equation (4.9). On gear 1, the load is at the highest point of single-tooth contact when the contact point is at Q', a distance Pb above T2 \u2022 Hence, the maximum Fillet Stress 253 fillet stress occurs when the load is applied at a radius Rw' given by the following expression, (11.31) When the gears are not cut with sufficient accuracy to ensure load-sharing, we have to allow for the possibility of the total tooth force continuing to act on one tooth, right up to the tip"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003726_036354658601400509-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003726_036354658601400509-Figure3-1.png",
        "caption": "Figure 3. At the start of the acceleration phase, the club is held horizontally.",
        "texts": [
            " The activity of each swing was then quantified from 20 ms segments of the digitized records of each muscle, and the activity of each muscle expressed as a percentage of the MMT figure. Zero to 15 was considered minimal activity, 15 to 30 low level, 30 to 60 moderate, and greater than 60, marked activity. RESULTS AND DISCUSSION Each swing was divided into four segments: 1. Takeaway (Fig. 1): from the beginning of motion in the address position to the end of the backswing. 2. Forward swing (Fig. 2): from the end of the backswing until the club again becomes horizontal. 3. Acceleration (Fig. 3): from the point at which the club is horizontal until ball contact. 4. Follow-through (Fig. 4): from ball contact until the end of motion. On the left side, during the takeaway phase there was minimal to low level activity in all muscles recorded except the subscapularis, which was showing marked activity (Fig. 5). During left forward swing subscapularis and latissimus dorsi activity were both moderate (Fig. 6). The pectoralis major, latissimus dorsi, and subscapularis fired at a high level during the acceleration phase, immediately prior to ball contact (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000094_j.jmapro.2020.03.018-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000094_j.jmapro.2020.03.018-Figure1-1.png",
        "caption": "Fig. 1. A part with overhangs (in red) and its support for conventional verticalup deposition (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).",
        "texts": [
            " [2] explains that Wire Arc Additive Manufacturing (WAAM), a direct energy deposition technology, is particularly suitable for fabricating medium to large scale metallic components due to its high deposition rates and relatively low cost. For conventional AM, a 3D CAD model is sliced into a set of 2.5D layers along the deposition direction, and the slicing direction is elaborately selected to enable each layer to be deposited in the downhand position. However, Jiang, et al. [3] points out that in order to fabricate complex components using the WAAM, extra support is usually unavoidable to deposit \u2018overhang\u2019 structures. As shown in Fig. 1, to produce a part with an \u2018overhang\u2019 structure (in red), a temporary support structure (in yellow) would be required if being deposited in the fixed vertical up direction, resulting in the deposition of extra material, and the additional cost of a post-machining process to remove it. Multi-directional Additive Manufacturing, or Multi-orientational Additive Manufacturing, has the potential to build up overhangs without extra support to improve the efficiency of the AM process. Yang, et al. [4] describes in the multi-directional additive manufacturing system, a deposition nozzle is mounted on a multi-axis actuator, such as the Computer Numerical Control (CNC) machine or the industrial robot, to deposit materials in multiple directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000854_j.triboint.2021.106881-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000854_j.triboint.2021.106881-Figure3-1.png",
        "caption": "Fig. 3. The cross-sectional view of the spindle after the steady-state condition at 5000 rpm.",
        "texts": [
            " The internal heat includes that generated in the four front and two rear bearings, the stator, and rotor of the embedded motor. The coefficients of heat dissipation considered heat convection of the balls hb and inner rings in the lubricant hi, and heat convection of the spindle shaft hs. In particular, the heat convection coefficients hh for the front, middle, and rear parts of the housing were calculated by measuring the temperature rises on the housing relative to the room temperature. Therefore, the housing convection coefficients vary in the mentioned parts of the housing. Fig. 3 shows the results of the spindle temperature distribution with the boundary conditions corresponding to the speed of 5000 rpm. The highest temperature is on the bearing balls and inner rings, and the temperature of the rear part of the housing is lower than that of the front part. The results of the steady-state thermal model are loaded into the static structural model for obtaining the changes in the nodal coordinates of points on the ball surface, before fitting for the ball radius. The updated radius of the ball is then employed to calculate the heat generation in the bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003993_05698190600614874-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003993_05698190600614874-Figure8-1.png",
        "caption": "Fig. 8\u2014Bearing force projections in the normal and tangential directions.",
        "texts": [
            " It is to be noted that the forces within the bearings are internal and do not appear in the equilibrium equations. Consequently, the measurement by the force transducers of the loads transmitted to the mounts via the bearings allows the total instantaneous friction force between the mating teeth to be determined by projections perpendicular to the base D ow nl oa de d by [ D al ho us ie U ni ve rs ity ] at 1 8: 15 0 1 A ug us t 2 01 3 Fig. 9\u2014Total friction forces at the mesh for various friction laws\u2014Cr = 1570 mN; \u03c9e = 200 rpm; spur gears; hydrostatic bearings. plane (Fig. 8). One fundamental limitation comes from the high frequencies generated by the meshing combined with the rather narrow bandwidth of the load cells. In this context, only low-speed measurements were used, which corresponded to the hydrostatic bearing arrangement and the spur gear set. The resisting torque was 1570 Nm and the pinion rotational speed was set at 200, 400, and 600 rpm, respectively. Figures 9 and 10 show the corresponding measured and simulated global friction forces. Simulations were performed under the following conditions: (a) no friction, (b) a constant friction coefficient of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003699_095440604322787009-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003699_095440604322787009-Figure6-1.png",
        "caption": "Fig. 6 Km, s is expressed as the disc stiffness KB and the nominal stiffness K m in series connection",
        "texts": [],
        "surrounding_texts": [
            "In most cases, gear body stiffness is a major component of the total torsional stiffness of a gear. According to the analysis here, the gear body stiffness is 2 to 4 times higher in magnitude than a single tooth on its own. In general, the gear body stiffness will not remain constant, especially when the change occurs from the single to double pair of teeth in contact or vice versa. The constraint on the gear body (circular disc) from rotation within one tooth space to two teeth spaces resulted in the torsional stiffness increasing by 8.6 per cent (calculated). This shows that the torsional stiffness variations of the gear body in the double zone (or in the single zone) are believed to be smaller than 8.6 per cent. An assumption can now be made by assuming the torsional stiffness of the gear body to have a constant value KB in the double zone (KB is calculated to be 755 709.74N m/rad). The nominal tooth stiffness can then be calculated in the single-tooth pair mesh cycle. The nominal tooth stiffness can be de ned as a partial tooth stiffness, which is connected with the gear body stiffness in the manner of a series spring in the singletooth mesh zone. The individual nominal tooth stiffness can be calculated with the results in Fig. 3. It can also be calculated as the combined nominal tooth stiffness with the results in Fig. 4. The procedure will be simpli ed if the nominal combined tooth mesh stiffness K m, where the combined nominal tooth stiffness is expressed as in F ig. 6, is calculated as K m \u02c6 KBKm,s KB \u00a1 2Km,s \u20265\u2020 where Km,s represents the combined torsional mesh stiffness of the single-tooth gear model in a single-tooth pair mesh cycle and KB represents the stiffness of the gear body. Km,s can also be the stiffness derived from the model of the single-tooth gear in contact with the rigid line. It should be noted calculation of K m does not need to separate the meshing teeth from the gear body. The advantage of using the nominal tooth mesh stiffness is that it can be used in calculation of the combined torsional mesh stiffness over a complete mesh cycle, especially for the calculation of the double contact zone, where the stiffness is counted as a parallel spring Proc. Instn Mech. Engrs Vol. 218 Part C: J. Mechanical Engineering Science C14902 # IMechE 2004 at UNIV OF PITTSBURGH on November 27, 2014pic.sagepub.comDownloaded from connection for the meshing teeth in series with both gear bodies as shown in Fig. 7. As shown above, the combined torsional mesh stiffness for the double pair contact zone can be written as Km \u02c6 KB6K A,B m KB \u2021 2K A,B m \u20266\u2020 where K A,B m is calculated as a parallel spring and K A m and K B m are calculated in the mesh positions A and B, which denote the contact point of each tooth pair along the path of contact of the double-tooth pair contact zone. Km is plotted in F ig. 8. The result of this calculation shows better agreement with the result obtained from modelling the complete gears with exible contact(s) and adaptive meshing, discussed in section 5. The basic stiffness sharing inside the meshing gears has been proven and it can be considered as one of the quick methods to evaluate the basic gear stiffness property via simple calculations. However, the closed form is unable to produce results with the in uence of load to show the details in the changeover region(s)."
        ]
    },
    {
        "image_filename": "designv10_4_0003077_0094-114x(95)00100-d-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003077_0094-114x(95)00100-d-Figure3-1.png",
        "caption": "Fig. 3. Velocity and acceleration of a body.",
        "texts": [],
        "surrounding_texts": [
            "The value of the elements of matrix W depend on the frame used as reference for two reasons. First of all ~ and vo must be represented by their components with respect to the chosen reference frame. Secondly the pole is the point of the body passing through the origin of the chosen reference frame. 3D kinematics and dynamics--I 579 For these reasons, if another frame is chosen matrix W changes because the pole must be the origin of the new reference and _tp and vo must be projected onto the axis of the new reference. Matrix H behaves in the same way as W. If we have two different reference frames (r) and (s) we will indicate the representation of the velocity of a body in the two frames as W(,~ and Wt,) and the acceleration as H(,) and H(s~. Since the two matrices describe the velocity of the same body in two different frames their values are strictly dependent on each other. It is possible to prove (see Appendix A) that they are tensors which transform as: W(,) = Mr.~W(~)M,~ I (8) H(r ) = M,,,H(s) MZ~. 1 , (9) where M,.~ is the position matrix of the reference frame (s) with respect to (r). In other words W(,) and W{,) are the Cartesian representation in (r) and in (s) of a tensor W. The same statement applies to H. The validity of the previous formulas can be proved by expanding the matrices into their blocks and by executing the matrix product. For example the velocity matrix in (r) obtained by applying equation (8) is: W(r ) = -(~(r) -0---0--b-- Vo r I I , ( R tp_()Rt)t . . . . . . . . . . . . . . . I _ r , s s r , s r , s o o o : o where Rr,,~(s)R~,.s is equal to ~(r), that is the angular velocity of the body in (r) and R,.sVo, is the velocity of pole O, projected onto (r). Moreover it is easy to verify that the velocity Vo, of the new pole is: Vo, = R,.,Vo, - _o(,)t,.,. This equation is just a matrix formulation of the following vector formula: L = L + ~ x ( O , - O , ) , where O, and O~ are the origins of the frames (r) and (s), respectively. 580 Giovanni Legnani et al."
        ]
    },
    {
        "image_filename": "designv10_4_0000348_j.actamat.2020.07.049-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000348_j.actamat.2020.07.049-Figure1-1.png",
        "caption": "Fig. 1. Schematic of specimen orientations, respective crack planes, and crack propagation directions.",
        "texts": [
            " The XZY orientation results in a crack lane and crack propagation direction that is parallel to the build ayers (YX and + X , respectively). The ZXY and YXZ orientations ave crack planes that are perpendicular to the build layers (ZY nd YZ, respectively), and exhibit crack propagation directions that re either parallel (-Z) or perpendicular (-Y) to the build direction, espectively. From here on, the XZY, ZXY and YXZ orientations are eferred to as Edge, Vertical and Flat orientation, respectively, as hown in Fig. 1 . After fabrication, the specimens were wire cut-off the base late. Stress-relief (SR) heat treatments were conducted on half of he specimens using a 5 kW Gallenkamp muffle furnace (Type 2) ith an inbuilt temperature controller. A type-K thermocouple was nserted into the furnace for a more accurate temperature reading ear the specimens. SR was conducted at 480 \u00b0C for eight hours, ollowed by a furnace cool. This temperature was selected to minmise any microstructural changes while still reducing the residual tress, as suggested by Ter Haar and Becker [27] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003195_tmag.2004.824127-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003195_tmag.2004.824127-Figure1-1.png",
        "caption": "Fig. 1. Transformer.",
        "texts": [
            " 2) For the \u2013 problem, if there is only one solid conductor, the turn no. (here, we define that one turn is equal to two conductors). This is different with the stranded windings. However, for the \u2013 problem, if there is only one solid conductor, the turn no. . This is the same as for the stranded windings. 3) Usually the two solid conductors on each side of the same turn cannot be set up as one conductor winding. They should be connected together in the external circuit. The turn no. of each conductor . For example, Fig. 1 shows a transformer. Its primary winding (on the left side) is stranded winding and can be set up as one winding. Its seconding winding (on the right side) has only one short-circuit turn and it contains two solid conductors as shown in Fig. 2(a). The currents in the two solid conductors should be the same, that is, . However, if they are set up as one winding as in Fig. 2(b), the currents in the two solid conductors may be different, . This is not a practical situation. 4) Periodic boundary conditions can be applied to reduce the computing time substantially"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003243_978-94-011-4120-8_45-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003243_978-94-011-4120-8_45-Figure2-1.png",
        "caption": "Figure 2. The three types of admissible legs for translating mechanisms",
        "texts": [
            " If a parallel mechanism, composed by a mobile platform connected to the ground by several serial kinematic chains (further called legs), trans lates, it m\\!st move according to 73. In fact the wrench system W3, recip rocal to 73, constrains the mobile platform to perform only translational movements. Since 73 is a self-reciprocal screw system, it is W3 = 73. So, W3 is composed of three linearly independent wrenches of infinite pitch too and it represents the set of torques, exerted by the legs on the platform, to avoid its rotations. Legs, which allow a translational movement (T-Iegs), will be classified by their number of DOF (see figure 2). The trivial case of six DOF legs will not be considered. A single T-Ieg, that prevents any rotation, must be composed by at least three linearly independent prismatic joints. It can exert any reaction torque and will be called a type 3 leg. Analogously a T-Ieg composed by four linearly independent joints, will be called a type 4 leg. It is reciprocal to two wrenches of infinite pitch, and so it can exert only reaction torques that lie in a plane. Finally a T-Ieg, composed by five linearly independent joints will be called a type 5 leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003056_s0094-114x(03)00003-x-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003056_s0094-114x(03)00003-x-Figure10-1.png",
        "caption": "Fig. 10. Projection of distances, angles and forces on the XY plane in the contact Cis\u2013Cei.",
        "texts": [
            " 8B): The distance between the centres of curvature will be A2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0XCis1 XCei2\u00de2 \u00fe \u00f0YCis1 YCei2\u00de2 \u00fe \u00f0ZCis1 ZCei2\u00de2 q \u00f059\u00de The relative displacement between the two centres of curvature will be equal to D2 \u00bc A2 A0 \u00f060\u00de The contact angle will be a2 \u00bc arcsin \u00f0Zcis1 ZCei2\u00de A2 \u00f061\u00de The reaction in the ball bearing will be q2 \u00bc KDn 2 \u00f062\u00de As for the previous contact, it is now also interesting to observe the relationship of the angles in the contact (Fig. 10). A2 cos a2 is the projection on the XY plane of the distance between centres of curvature Cis and Cei: cos b2 \u00bc XCis2 XCei2 A2 cos a2 \u00f063\u00de sin b2 \u00bc YCis2 YCei2 A2 cos a2 \u00f064\u00de The x; y; z components of the reaction will be q2x \u00bc q2 cos a2 cos b2 \u00f065\u00de q2y \u00bc q2 cos a2 sinb2 \u00f066\u00de q2z \u00bc q2 sin a2 \u00f067\u00de Substituting (63) in (65) and (64) in (66), the following is obtained: q2x \u00bc q2 XCis2 XCei2 A2 \u00f068\u00de q2y \u00bc q2 YCis2 YCei2 A2 \u00f069\u00de The vector position of the point of application of the reaction shows the following x; y; z components: R2x \u00bc XCis2 \u00fe \u00f0d A2\u00de 2 cos a2 cos b2 \u00f070\u00de R2y \u00bc YCis2 \u00fe \u00f0d A2\u00de 2 cos a2 sin b2 \u00f071\u00de R2z \u00bc ZCis2 \u00fe \u00f0d A2\u00de 2 sin a2 \u00f072\u00de where d \u00bc diameter of the ball bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure10-1.png",
        "caption": "Fig. 10. The decomposed planar loop-chain on the xy plane.",
        "texts": [
            " The four-legged elementary platforms constitute the equatorial circular loop-chain that is the core of the ball mechanism after mechanism decomposing into one equatorial circular loop-chain and supplementary chains. From the above analysis, the mobility of the four-legged platform does not change after the removal of two scissors typed legs that contain four links and six joints. Thus, in order to simplify the calculation of the mobility of the magic ball mechanism, all two scissorstyped legs perpendicular to the loop-chain in Fig. 10 of all four-legged elementary platforms are removed. The remaining mechanism forms a circular loop-chain in Fig. 10. It is a kinematic chain joined by parallelograms and planar two-legged platform on the x\u2013y plane. The mobility of the loop chain does not change. In this kinematic loop-chain, the symmetrical mechanism is composed of basic units each of which consisting of a planar two-legged platform and two parallelogram mechanisms as in Fig. 11a. Fig. 11b is the corresponding topological graph [22]. From the similar analysis in Fig. 8 and the constraints mentioned in Section 4, the mobility of the basic unit is one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000225_s40684-020-00221-7-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000225_s40684-020-00221-7-Figure3-1.png",
        "caption": "Fig. 3 DED paths and overlapping efficiency",
        "texts": [
            " A chiller with power of 16 kW from DONGSHIN FINETEK was installed to cool the equipment. The 3-axis (x, y, z) stage system has dimensions of 800 mm \u00d7 780 mm \u00d7 1290 mm. The dust collector was connected to the table for DED. The controller for 3-axis control was a UMAC controller with UMAC base S/W. Through experiments on various parameters, the DED conditions were selected with reference to prior literature to determine conditions under which AM can be successful for this device. Table\u00a01 lists the DED conditions for depositing the Ti-6Al-4V powder [18, 19]. Figure\u00a03 shows the DED paths according to deposition method and overlapping efficiency. The Ti-6Al-4V powder is deposited in one 1 3 direction (single track deposition) and zig\u2013zag (multi-layer deposition) for specific distances. In addition, the DED path for the multi-layer deposition is designed to have a constant overlapping section according to the deposition width [20]. In order to analyze the deposition characteristics according to the laser power, laser feed rate, argon gas flow rate and powder feed rate, single track deposition was performed using the powder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000733_jsyst.2020.3006059-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000733_jsyst.2020.3006059-Figure2-1.png",
        "caption": "Fig. 2. Schematic configuration.",
        "texts": [
            " The inputs to these models are the altitude, UAV velocity, wind direction, and direction cosine matrix, where the output is the gust velocity in the body frame. In the case of external disturbances, an effective dynamic model of the system is needed to design an adaptive, effective, and robust controller to capture the nonlinearities of UAV flight dynamics. In this article, an X-configuration-based 6-DOF underactuated UAV is considered. Six degrees of freedom includes three translational motion in three rotational motion around three axes. The schematic configuration of the UAV is shown in Fig. 2, in which four propellers are divided into two pairs, clockwise (CW) and counterclockwise (CCW), that are mounted on four motors at two orthogonal directions to compensate for the effect of reactive torques. The front F1 and rear F3 propellers rotate CCW, while the lateral propellers (F2 and F4) rotate in the CW direction to generate the lift force and to balance the yaw torque as needed. The roll rotation is performed by adjusting the propeller\u2019s speed of motors F2 and F4. The pitch rotation is realized by adjusting the speed of F1 and F4 motors of the Authorized licensed use limited to: University of Cape Town",
            " Assumption 2: The designs of the quadrotor and propeller have a rigid body with six degrees of freedom that can be derived by using Newton\u2013Euler equations. Assumption 3: The thrust and drag are equal to the size of the propeller\u2019s square. 1) Reference Frames and Transformation: The mathematical model of the UAV is derived by using (1)\u2013(3) assumptions. Let E = {Oe, Xe, Ye, Ze} denote an inertial-fixed frame and B = {Ob, Xb, Yb, Zb} denote a body-fixed frame, whose origin O is at the center of mass of the UAV, as shown in Fig. 2. RBE \u2208 SO(3) is the orthogonal rotation matrix with its determinant det(RBE) = 1; therefore, (RBE) \u22121 = (RBE) T , and it can be expressed as (7), shown at the bottom of this page, where \u03c6, \u03b8, and \u03c8 represent roll, pitch, and yaw angles, respectively. The position of the UAV in the inertial or earth-fixed frame is indicated by \u03be = [x, y, z]T , and by successive rotations of the yaw \u03c8, pitch \u03b8, and roll \u03c6 attitude or by obtaining Euler angles \u03b7 = [\u03c6, \u03b8, \u03c8]T . The translational velocities are expressed by\u03c5 = [\u03c5x, \u03c5y, \u03c5z] T in thex, y, and z directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003309_095440605x32075-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003309_095440605x32075-Figure1-1.png",
        "caption": "Fig. 1 The schematic diagram of the Stewart platform manipulator",
        "texts": [
            "eywords: Stewart platformmanipulator, kinematics analysis, dynamic formulation, Newton\u2013 Euler method, Lagrange formulation The Stewart platform manipulator, as shown in Fig. 1, is a parallel kinematic link system with six controlled degrees of freedom (d.o.f.) that is obtained from generalization of the mechanism proposed by Stewart [1] as a flight simulator. This kind of manipulators have higher stiffness, accuracy, and payloadweight ratio due to the parallel linkage distributing the payload and averaging out the positioning error instead of accumulating. These make this kind of parallel manipulators attractive for certain applications, such as the flight simulators, the machine tools, and the force\u2013torque sensors",
            " Then rotating the resulted frame over an angle u around the intermediate Y0-axis. Accordingly, the Z-axis rotates to Z0-axis, and the X0-axis to X1-axis. 3. Finally rotating over an angle f around the X1axis. Accordingly, the Y0-axis rotates to Y1-axis, and the Z0-axis to Z1-axis. Then the frame X1 Y1 Z1 is obtained. Therefore, the fully parameterized rotation matrix is R \u00bc cc cu cc su sf sc cf sc cu cc cf\u00fe sc su sf su cu sf 2 64 sc sf\u00fe cc su cf sc su cf cc sf cu cf 3 75 (1) where s(.) \u00bc sin(.), c(.) \u00bc cos(.). The Stewart platform, as shown in Fig. 1, consists of the moving platform and the base platform that are connected by six extensible legs, each of which has a spherical joint at the upper end, a universal joint at the lower end, and a prismatic joint in between. There are two different frames chosen to describe the motion of the moving platform, i.e. a reference frame {B, X , Y , Z} is fixed to the base and a platform frame {P, X1, Y1, Z1} is attached to the platform (including the payload) whose centre of gravity (c.o.g.) is coincident with the origin of platform frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure4-1.png",
        "caption": "Figure 4 The hinged parallelogram loop.",
        "texts": [
            " (9) and (10) are invariable as long as we choose the same coordinate system as shown in Figure 2. Thus, the numbers of common constraints and redundant constraints always keep fixed. So the mobility is global. The Orthoglide mechanism[46] is shown in Figure 3. It has three limbs and each limb includes a four-bar paral- 1342 Huang Zhen et al. Sci China Ser E-Tech Sci | May 2009 | vol. 52 | no. 5 | 1337-1347 lelogram loop. Let us take the hinged parallelogram linkage into consideration firstly. It is shown in Figure 4 and can be regarded as having two limbs. Point A is chosen as the origin point, x\u2032-axis is along the link AD, y\u2032-axis locates on the plane ABCD and z\u2032-axis is along the direction of the revolute pair. For the first limb, the twist system is given by ( ) ( )1 1 0 0 1; 0 0 0 , 0 0 1; 0 , A B y x = = \u2212 $ $ (12) where (x1, y1, 0) denotes the coordinates of point B. The constraint screw system of this limb is ( ) ( ) ( ) ( ) 11 12 13 14 1 1 0 0 0; 1 0 0 , 0 0 0; 0 1 0 , 0 0 1; 0 0 0 , 0; 0 0 0 . r r r r x y = = = = $ $ $ $ (13) For the second limb, the twist system is ( ) ( ) 1 10 0 1; ( ) 0 , 0 0 1; 0 0 , C D y x l l = \u2212 + = \u2212 $ $ (14) where l denotes the length of the link AD"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003056_s0094-114x(03)00003-x-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003056_s0094-114x(03)00003-x-Figure5-1.png",
        "caption": "Fig. 5. Clearance between races and ball bearing.",
        "texts": [
            " Assuming that the radii of curvature of the raceways are equal, the initial coordinates (represented by 1) of the four centres of curvature, without taking the axial clearance into account, are: XCii1 \u00bc dm 2 \u00fe h cosw \u00f08\u00de YCii1 \u00bc dm 2 \u00fe h sinw \u00f09\u00de ZCii1 \u00bc a \u00f010\u00de XCis1 \u00bc dm 2 \u00fe h cosw \u00f011\u00de YCis1 \u00bc dm 2 \u00fe h sinw \u00f012\u00de ZCis1 \u00bc a \u00f013\u00de XCei1 \u00bc dm 2 h cosw \u00f014\u00de YCei1 \u00bc dm 2 h sinw \u00f015\u00de ZCei1 \u00bc a \u00f016\u00de XCes1 \u00bc dm 2 h cosw \u00f017\u00de YCes1 \u00bc dm 2 h sinw \u00f018\u00de ZCes1 \u00bc a \u00f019\u00de The initial distance (Fig. 3) between diagonally opposed centres of curvature is equal to A \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0a2 \u00fe h2\u00de p \u00f020\u00de However, the existing clearance modifies some of the coordinates of the centres of curvature of the Z axis. If Pr is defined as being the existing radial clearance, rc as the radius of curvature and d as the diameter of the ball bearing, we have the following relation (Fig. 5): 2\u00f0rc Pr\u00de A \u00bc d \u00f021\u00de Taking the inner ring as a reference, the outer ring will move down by an amount j, equal to the axial clearance, until contact exists between the sphere and the raceways. Fig. 6 shows the positions of the centres of curvature in the initial position, taking into account the axial clearance j. The following relationship may be deduced from Fig. 6: A02 \u00bc \u00f02h\u00de2 \u00fe \u00f02a\u00fe j\u00de2 \u00f022\u00de From expression (21), as in the contact Pr \u00bc 0, it can be deduced that 2rc A0 \u00bc d \u00f023\u00de From the expressions (21) and (23) it can be deduced that A0 \u00bc 2Pr \u00fe A \u00f024\u00de Finding j from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure12-1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure12-1-1.png",
        "caption": "Figure 12-1. Types of flexing test, (a) De Mattia; (b) \"flipper\" machine; (c) Du Pont; (d) Ross. In (a), (b) and (d) the flexed form is shown by broken Hnes.",
        "texts": [],
        "surrounding_texts": [
            "specialised tests for particular products which may have characteristics of both types. For example, tyres fail by fatigue in which heat build-up is important and also suffer from groove and sidewall cracking, so that, logically, a realistic test would simulate both."
        ]
    },
    {
        "image_filename": "designv10_4_0003213_0094-114x(95)00089-h-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003213_0094-114x(95)00089-h-Figure4-1.png",
        "caption": "Fig. 4. Vectors associated with the computation of Jv~'.",
        "texts": [
            " m - l d -- T \"~--\" -~ \"JI- q ) ~ - T ( r ) ' 3 L T (mqm ) =rn_lhrnm-lf.om-}-m-l(.om x mqm =m_lOOm(m_lhmm-Is_m-~ m- lsm x m q m ). (12) Further, = h 'n - l sm+' -~sm mqm, (13) rn-Is~ m-I m - \u00d7 where m- Isbn is the moment part of the screw representing the helical pair joining links m - I and m, with respect to an arbitrary coordinate system whose origin is located at O. Hence 450 Jos~ Maria Rico Martinez and Joseph Duffy Proposition 5. The velocity of a point O fixed in body m of the serial chain shown in Fig. 4, with respect to the reference frame m, is given by Ju__~=jOJj+lJSJo+l'jf-j+l(-Oj+2J+lsJ+2\"~-''''JP m_2(-Om_lm-2~-l'JI-m_lO)mm-Is ~ . ( 1 5 ) Proof: The initial step of the induction proof is already given by (14). Then, by the induction hypothesis, J + Iu__0n = j + I ( O j + 2 j + IS__J+2 -[- ' ' \" JI- m - 2 (-/~m- 1 m - 2S_~n- 1 \"JI- m - I O)m m - IS~n \" (16) Further, from Fig. 4, \u2022 Jd Jd (jr_.J+l.Jl_J+lqm) Jd (jrJ+l) Yd lqm). Jv__'~ = dt (jl?-m) = ~ = ~ - + ~ ( j+ However, using proposition 3, Jd J+ td dt (j+lq,,,) =_..~_ (j+lqm)+j~j+l X j+lq,, =j+lVg,+jogj+l X j+lqm. Thus J~__~ = jh j+ l J ~ +1 ,Ji-J~__ j+ l x J+ lqm ..~ J+ l~_~ = j(z)j+ lOh j+ lJS_ j+ l \"I- is j+ l x J+ lqm) j l - j+ l f)~. (17) It is easy to recognize that JS__Jo + ' = j h j + l JS__ J+ ' .Jr-is_ j+ l X j+ Iqm. ( 1 8 ) Thus, by substituting the induction hypothesis, (16), as well as (18), into (17) J1)~=j("
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000480_j.automatica.2021.109708-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000480_j.automatica.2021.109708-Figure2-1.png",
        "caption": "Fig. 2. Vision-based measurement.",
        "texts": [
            " Automatica 130 (2021) 109708 w 3. Vision-based finite-time control for target tracking 3.1. Vision-based measurement The vision-based measurement is mostly based on the approach given in Dobrokhodov et al. (2006), Meir et al. (2008) and Stepanyan and Hovakimyan (2008). It is supposed that the target information is provided by a monocular camera. The monocular camera is mounted on a gimbal fixed to the follower, and the camera\u2019s optical axis is parallel to the follower\u2019s xB axis of its body-frame FB, as shown in Fig. 2. In accordance with (Stepanyan & Hovakimyan, 2008), the visionbased measurement model is given as follows. The bottom-level control law of the UAV is not a part of our concern, so we assume that the inner-loop attitude control of UAV have been designed and perfectly implemented according to Choi and Kim (2014) and Zhu et al. (2016, 2017). The bearing angle \u03b3 and elevation angle \u03b8 of the target with respect to the follower are represented as \u03b3 = tan\u22121 ( yI ) , f \u03b8 = tan\u22121 \u239b\u239d zI\u221a f 2 + y2I \u239e\u23a0 , (15) where f denotes the focal length, and (yI , zI) is the target\u2019s geometric center in the image plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003754_3527602844-Figure5-18-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003754_3527602844-Figure5-18-1.png",
        "caption": "Figure 5-18 The development of a folded horseshoe-type map for points in the vicinity of a homoclinic orbit.",
        "texts": [
            " As we saw in Chapter 1, horseshoe-type maps lead to unpredictability and unpredictability or sensitivity to initial conditions is a hallmark of chaos. To see why homoclinic orbits lead to horseshoe maps, we recall that for a dissipative system areas get mapped into smaller areas. However, near the unstable manifold, the areas are also stretched. Since the total area must decrease, the area must also contract more than it stretches. Areas near the homoclinic points also get folded, as shown in Figure 5-18. A dynamic process can be thought of as a transformation of phase space; that is, a volume of points representing different possible initial conditions is transformed into a distorted volume at a later time. Regular flow results when the transformed volume has a conventional shaped volume. Chaotic flows result when the volume is stretched, contracted, and folded as in the baker's transformation or horseshoe map. The Melnikov Method. The Melnikov function is used to measure the distance between unstable and stable manifolds when that distance is small [see Guckenheimer and Holmes (1983) for a mathematical discussion of the Melnikov method]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure1.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure1.8-1.png",
        "caption": "Figure 1.8.",
        "texts": [
            " When the pinion and rack are in motion, the velocity of any point on the pinion pitch circle is equal to RpW, and the velocity of any point on the rack pitch line is equal to vr ' Since these velocities are equal, as we can see from Equation (1.16), the motion of a rack and pinion is identical to the motion that would be obtained if the rack pitch line and the pinio~ pitch circle were to make rolling contact with no slipping. Ci rcular pi tch The circular pitch of the pinion teeth at any radius R is defined as the distance between corresponding points of adjacent teeth, measured around the circumference of the circle of radius R. Thus, the circular pitch PR at radius R, which is shown in Figure 1.8, is given by the following expression, 211'R N (1.17) In the case when the circular pitch is measured on the pitch Circular pitch. Law of Gearing for Two Gears circle, we use the symbol Pp' and its value can substituting Rp in place of R in Equation (1.17). 211'Rp Pp N 19 be found by (1.18) When we replace the pitch circle radius Rp in this equation by the expression given in Equation (1.15), it is clear that the circular pitch of the gear at its pitch circle is equal to the pitch p of the rack, p (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000053_j.matchar.2019.01.018-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000053_j.matchar.2019.01.018-Figure2-1.png",
        "caption": "Fig. 2. Schematic representation of specimen orientation in build chamber. Black arrow indicates the building direction. Individual layers are along the XYplane. Note: All specimens were built in one build.",
        "texts": [
            " In the standard theme, the hatch was melted first by \u2018snaking\u2019 strategy and then the two contours were melted as continuous lines. The specimens were provided by an industrial partner and the detailed information about the parameters such as laser power, beam velocity, laser spot size, etc., are treated as IP and hence cannot be revealed. Fig. 1 shows the definition of contour and hatch region for the two processes. The specimen building direction with respective to the build chamber of the machines is presented in Fig. 2. The specimens are built along the Z-axis of the machine while the individual layers are along the XY-plane. After the printing process, the powder was recovered to be reused as per the recommended protocols by the equipment manufacturers. The specimens were cut off from the base plate using a band saw in the case of EBM and a wire cut electro-discharge machine in the case of SLM. Furthermore, no stress relieving treatment was performed before cutting off the specimens from the base plate. Half the number of specimens manufactured by each of the processes were HIP:ed in a Quintus QIH21 HIP furnace at 1200 \u00b0C and 120MPa for 4 h followed by uniform rapid quenching (URQ)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003708_j.jsv.2004.06.010-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003708_j.jsv.2004.06.010-Figure1-1.png",
        "caption": "Fig. 1. Dynamic model of the physical system.",
        "texts": [
            " Nomenclature b half of clearance (backlash) c damping coefficient e gear motion transmission error f external force g discontinuous displacement function HBM Harmonic Balance Method I polar mass moment of inertia J Jacobian matrix k gear mesh stiffness M Monodromy matrix m mass n mesh frequency ratio (n \u00bc Z2=Z3) NI numerical integration p relative gear mesh displacement Q number of discrete time points q discrete time interval R number of harmonic components considered in the solution r radius S matrix form of non-linear algebraic equation set T torque t time u displacement harmonic amplitude U displacement vector v describing function Z number of gear teeth d Kronecker delta L dimensionless frequency k dimensionless mesh stiffness l\u0302 control parameter y rotational displacement o characteristic frequency O nominal rigid-body angular velocity z damping ratio Subscripts a alternating component c characteristic quantity eq equivalent i gear index m mean component ni ith natural mode Superscripts \u2018 gear mesh index (\u2018 \u00bc 1; 2) rms root-mean-square value T matrix transpose frequency gear mesh harmonic orders must be balanced at the bearing supports and are eventually transmitted to the housing to act as the main excitations for gear related noise. In addition, cyclic dynamic loading experienced by the gear teeth impacts the fatigue life of the gear systems directly. Therefore, a better understanding of the gear system dynamics is viewed as crucial to designing products at acceptable noise levels and fatigue lives. One such common gear system, a multi-mesh gear train that is formed by three shafts and two gear pairs whose dynamic model is shown in Fig. 1, is considered in this study. The shaft in the middle holds two separate gears, each forming a mesh with another gear held by another shaft. This system finds its applications in automotive, aerospace, marine and industrial products. For instance, in automotive applications, this gear set arrangement is used commonly as the final drive unit of transverse, front-wheel-drive automatic transmissions, manual transmissions, and continuously-variable transmission final drive units. The main focus of this study is on the nonlinear dynamic behavior of such gear systems",
            " gear backlash nonlinearity and timevarying mesh stiffness: (1) linear, time-invariant (LTI) models that neglected both tooth separations caused by gear backlash and variations in gear mesh stiffness, (2) linear, time-varying (LTV) models that included only a time-varying mesh stiffness, (3) nonlinear time-invariant (NTI) models that considered gear backlash, but not time-varying parameters, and (4) nonlinear time-varying (NTV) models having both effects included. Published experimental data [4,5] states that the resultant dynamic behavior of a spur gear pair can only be described by a NTV model. In view of the same classification, published dynamic models for the multi-mesh system considered in this study (Fig. 1) fall mostly under LTI [6\u201314] or LTV [15\u201318] models. As the LTI models employed a standard eigen value solution combined with the modal summation technique yields both free and forced vibration characteristics of the gear system, a large number of degrees of freedom were allowed in these models. Therefore, they were able to include several effects that existed in the actual system such as coupledtransverse-torsional-axial motions of the helical gear systems, and detailed shaft and bearing formulations",
            " Lim and Li [8] developed a multimesh counter-shaft geared rotor model with six-degree-of-freedom (sdof) motion for each rigid gear wheel. The linearized equations of motion applied to double mesh geared rotors. The damping coefficients were defined in terms of the modal coefficients. The effects of the angles between the power transmission lines on the overall dynamic response were shown. A general shaft finite element formulation was applied to the same system to study coupled shaft, bearing and gear vibrations [14]. The linear, time-varying investigations of the physical system of Fig. 1 focused primarily on the stability of the parametrically excited system. As one of the earlier LTV gear system models, Benton and Seireg [16] used the phase plane method to solve for a time-varying gear mesh coupling. Sinusoidal and rectangular functions were considered as extreme cases of mesh stiffness variations. It was predicted that gear systems could exhibit primary and sub-harmonic resonances resulting in regions of unstable motions. The stability and solution was analyzed for extreme cases of mesh excitations mentioned earlier",
            " Experimental studies demonstrate that, as vibration amplitudes increase significantly, the tooth separations (loss of contact) occur resulting in a softening type behavior with bounded stable motions instead of unstable ones [4,5,13,19]. In addition, many other experimentally observed nonlinear phenomena exhibited by this type of systems [13,20] are yet to be fully described. Accordingly, the main objective of this study is to develop a multi-degree-of-freedom NTV model of the physical systems as shown in Fig. 1 to investigate the influence of nonlinear and time-varying parameters on the dynamic response. The analytical solutions for the steady-state response of the system will be obtained by using a multiterm HBM formulation. Harmonic balance solutions will be verified by comparing them to those of numerical simulation. Detailed parametric studies will be performed to investigate the sensitivity of the nonlinear dynamic behavior to each key system parameter including alternating mesh stiffness amplitude, mesh damping, mean load transmitted, and the ratio of mesh frequencies",
            " Since the focus is on the nonlinear behavior, a minimum number of degrees of freedom will be utilized in the model in the form of torsional displacements. Accordingly, shaft and bearing flexibilities will be ignored. Also only period-1 motions will be considered in this study while the sub-harmonic motions are investigated in a companion paper [21]. The stability of the steady-state period-1 solutions will be determined by using the Floquet theory. Behavior of the dynamic model of the physical system shown in Fig. 1 is the main focus of this study. The system consists of two separate gear meshes. Four gears mounted on three shafts form this gear train. It consists of two gear pairs mounted on rigid bearings and shafts. The following assumptions are employed in this model: (1) The shafts are assumed to be rigid such that no deflection in any direction is possible. (2) Gears are connected to the shafts rigidly. (3) Gear blanks (rims) are assumed to be rigid, only gear flexibility is possible at the gear mesh via representative mesh stiffness",
            " (4) Bearings are considered to be rigid so that, together with the rigid shafts, shaft\u2013gear interfaces and gear blanks, they allow the gears to rotate only in torsional direction about their axes of rotation. (5) Gear mesh damping values are assumed to be constant (time-invariant) and not subject to gear backlash non-linearity. (6) Gears are assumed to be precise with no tooth-to-tooth variations and gear blank errors so that the motion transmission error excitation can be described by the gear mesh (tooth pass) frequency and its higher harmonics. This assumption also ensures that the gear backlash magnitudes remain constant. In Fig. 1, each gear of polar mass moment of inertia Ii and base radius ri is allowed to vibrate in torsional direction by y\u0304i; (i \u00bc 124). Here, y\u0304i represents the vibrations of gear i about its nominal rigid-body rotation Oi t\u0304; where Oi is the rotational speed in radians per second and t\u0304 is real time in seconds. An over bar denotes that this parameter is dimensional. Gear mesh stiffnesses k1\u00f0t\u0304\u00de and k2\u00f0t\u0304\u00de represent gear mesh flexibilities of the first and second gear meshes. The gear mesh damping values are denoted by c1 and c2. These stiffness and damping elements were applied at respective gear meshes in the direction of the gear mesh line of action and displacement excitations e1\u00f0t\u0304\u00de and e2\u00f0t\u0304\u00de are connected in series to the stiffness and damping elements as shown in Fig. 1. Similar to the sdof model presented earlier, gear backlash non-linearities are introduced here as piecewise linear \u2018\u2018dead-zone\u2019\u2019 type clearance functions g\u03041 and g\u03042 of amounts 2b\u03041 and 2b\u03042; respectively. Since the shafts are assumed rigid both torsionally and in bending, the rotational displacements of gears 2 and 3 are equal, y\u03042\u00f0t\u0304\u00de \u00bc y\u03043\u00f0t\u0304\u00de: Accordingly, the model shown in Fig. 1 can be represented by three degrees of freedom with coordinates y\u03041\u00f0t\u0304\u00de; y\u03042\u00f0t\u0304\u00de and y\u03043\u00f0t\u0304\u00de; and the polar mass moment of inertia associated with y\u03042\u00f0t\u0304\u00de becomes I23 \u00bc I2 \u00fe I3: Equations of motion of this system can be obtained as I1 \u20ac\u0304y1\u00f0t\u0304\u00de \u00fe r1c1 r1 _\u0304y1\u00f0t\u0304\u00de \u00fe r2 _\u0304y2\u00f0t\u0304\u00de \u00fe _\u0304e1\u00f0t\u0304\u00de h i \u00fe r1k1\u00f0t\u0304\u00deg1\u00f0t\u0304\u00de \u00bc T1\u00f0t\u0304\u00de; (1a) I23 \u20ac\u0304y2\u00f0t\u0304\u00de \u00fe r2c1 r1 _\u0304y1\u00f0t\u0304\u00de \u00fe r2 _\u0304y2\u00f0t\u0304\u00de \u00fe _\u0304e1\u00f0t\u0304\u00de h i \u00fe r2k1\u00f0t\u0304\u00deg\u03041\u00f0t\u0304\u00de \u00fe r3c2 r3 _\u0304y2\u00f0t\u0304\u00de \u00fe r4 _\u0304y4\u00f0t\u0304\u00de \u00fe _\u0304e2\u00f0t\u0304\u00de h i \u00fe r3k2\u00f0t\u0304\u00deg\u03042\u00f0t\u0304\u00de \u00bc 0; \u00f01b\u00de I4 \u20ac\u0304y4\u00f0t\u0304\u00de \u00fe r4c2 r3 _\u0304y2\u00f0t\u0304\u00de \u00fe r4 _\u0304y4\u00f0t\u0304\u00de \u00fe _\u0304e2\u00f0t\u0304\u00de h i \u00fe r4k2\u00f0t\u0304\u00deg\u03042\u00f0t\u0304\u00de \u00bc T4\u00f0t\u0304\u00de; (1c) where g\u03041 and g\u03042 are non-linear type clearance functions defined mathematically as g\u03041 \u00bc \u00bdr1y\u03041\u00f0t\u0304\u00de \u00fe r2y\u03042\u00f0t\u0304\u00de \u00fe e\u03041\u00f0t\u0304\u00de b\u03041; \u00bdr1y\u03041\u00f0t\u0304\u00de \u00fe r2y\u03042\u00f0t\u0304\u00de \u00fe e\u03041\u00f0t\u0304\u00de 4b\u03041; 0; r1y\u03041\u00f0t\u0304\u00de \u00fe r2y\u03042\u00f0t\u0304\u00de \u00fe e\u03041\u00f0t\u0304\u00de pb\u03041; \u00bdr1y\u03041\u00f0t\u0304\u00de \u00fe r2y\u03042\u00f0t\u0304\u00de \u00fe e\u03041\u00f0t\u0304\u00de \u00fe b\u03041; \u00bdr1y\u03041\u00f0t\u0304\u00de \u00fe r2y\u03042\u00f0t\u0304\u00de \u00fe e\u03041\u00f0t\u0304\u00de o b\u03041; 8>< >: (2a) g\u03042 \u00bc \u00bdr3y\u03042\u00f0t\u0304\u00de \u00fe r4y\u03044\u00f0t\u0304\u00de \u00fe e\u03042\u00f0t\u0304\u00de b\u03042; \u00bdr3y\u03042\u00f0t\u0304\u00de \u00fe r4y\u03044\u00f0t\u0304\u00de \u00fe e\u03042\u00f0t\u0304\u00de 4b\u03042; 0; r3y\u03042\u00f0t\u0304\u00de \u00fe r4y\u03044\u00f0t\u0304\u00de \u00fe e\u03042\u00f0t\u0304\u00de pb\u03042; \u00bdr3y\u03042\u00f0t\u0304\u00de \u00fe r4y\u03044\u00f0t\u0304\u00de \u00fe e\u03042\u00f0t\u0304\u00de \u00fe b\u03042; \u00bdr3y\u03042\u00f0t\u0304\u00de \u00fe r4y\u03044\u00f0t\u0304\u00de \u00fe e\u03042\u00f0t\u0304\u00de o b\u03042: 8>< >: (2b) Since the system is semi-definite with a rigid-body mode at zero natural frequency, the number of equations of motion can be reduced to two by defining the following two new coordinates: p\u03041\u00f0t\u0304\u00de \u00bc r1y\u03041\u00f0t\u0304\u00de \u00fe r2y\u03042\u00f0t\u0304\u00de \u00fe e\u03041\u00f0t\u0304\u00de; p\u03042\u00f0t\u0304\u00de \u00bc r3y\u03042\u00f0t\u0304\u00de \u00fe r4y\u03044\u00f0t\u0304\u00de \u00fe e\u03042\u00f0t\u0304\u00de: (3a,b) These new coordinates have physical significance since they represent the relative gear mesh displacements",
            " Following a multi-term harmonic balance procedure that was applied to sdof nonlinear time-varying systems successfully [4,5,22], one writes ki\u00f0t\u00de and f i\u00f0t\u00de in Fourier series form as k1\u00f0t\u00de \u00bc 1\u00fe XK h\u00bc1 k\u00f01\u00de2h cos\u00f0hLt\u00de \u00fe k\u00f01\u00de2h\u00fe1 sin\u00f0hLt\u00de h i ; (7a) k2\u00f0t\u00de \u00bc 1\u00fe XK h\u00bc1 k\u00f02\u00de2h cos\u00f0hnLt\u00de \u00fe k\u00f02\u00de2h\u00fe1 sin\u00f0hnLt\u00de h i ; (7b) f 1\u00f0t\u00de \u00bc f \u00f01\u00de 1 \u00fe XL \u2018\u00bc1 f \u00f01\u00de 2\u2018 cos\u00f0\u2018Lt\u00de \u00fe f \u00f01\u00de 2\u2018\u00fe1 sin\u00f0\u2018Lt\u00de h i ; (8a) f 2\u00f0t\u00de \u00bc f \u00f02\u00de 1 \u00fe XL \u2018\u00bc1 f \u00f02\u00de 2\u2018 cos\u00f0\u2018Lt\u00de \u00fe f \u00f02\u00de 2\u2018\u00fe1 sin\u00f0\u2018Lt\u00de h i : (8b) Here, L1 \u00bc L and L2 \u00bc nL are the fundamental frequencies of the stiffness of the first and second gear meshes, respectively, where L \u00bc O1=oc is the dimensionless gear mesh frequency, and the multiplier n can be any real number as it defines the ratio of the number of teeth of gears 2 and 3 in Fig. 1, n \u00bc Z2=Z3: Given the periodic excitations of Eqs. (7) and (8), the harmonic balance procedure requires that the steady-state response be periodic as well. Accordingly, one can describe p1\u00f0t\u00de and p2\u00f0t\u00de in Fourier series form as p1\u00f0t\u00de \u00bc u \u00f01\u00de 1 \u00fe XR r\u00bc1 u \u00f01\u00de 2r cos\u00f0rLt\u00de \u00fe u \u00f01\u00de 2r\u00fe1 sin\u00f0rLt\u00de h i ; (9a) p2\u00f0t\u00de \u00bc u \u00f02\u00de 1 \u00fe XR r\u00bc1 u \u00f02\u00de 2r cos\u00f0rnLt\u00de \u00fe u \u00f02\u00de 2r\u00fe1 sin\u00f0rnLt\u00de h i ; (9b) where u \u00f01\u00de 1 ; u\u00f01\u00de2r ; u \u00f01\u00de 2r\u00fe1; u \u00f02\u00de 1 ; u\u00f02\u00de 2r ; u \u00f02\u00de 2r\u00fe1 (r \u00bc 12R) are unknown coefficients of the assumed solution [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003955_pime_proc_1979_193_019_02-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003955_pime_proc_1979_193_019_02-Figure3-1.png",
        "caption": "Fig. 3. Cross-sectional diagrams of the bearings. The electrically insulating components are shown cross-hatched",
        "texts": [
            " These were measured with thermocouples, those fitted to the inner ring passing along the bore of the hollow shaft to a multi-channel slip ring unit. The estimation of film thickness by measurements of capacitance required the latter to be unaffected by any close approach between the ends of the rollers and the roller retaining flanges. This requirement was met by inserting an insulating membrane under the central flange of the spherical roller bearing and by replacing all other flanges with identical components made from an insulating material. Cross-sectional diagrams of the two bearings showing these modifications are shown in Fig. 3. *A correction for the effect of shear heating on the viscosity of an oil in the inlet to a rolling contact has been applied to all predictions of oil fdm thicknea reported in thn paper. To indicate the magnitude of these corrections, which were determined by experiment, those applicable to the base oil contained in the grease used in this investigation are given in Fig. 1. F\u2019roc lnstn Mech Engrs Vol 193 2.3 Dielectric constant of the lubricants It was essential that the lubricant used in determining the relationship between capacitance and film thickness for the two bearings should have a dielectric constant matching 0 IMechE 1979 by guest on December 8, 2015pme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000584_lra.2021.3067279-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000584_lra.2021.3067279-Figure5-1.png",
        "caption": "Fig. 5. The experimental platform consists of an FBG shape sensing system, an optical tracking system, and a robotic-assisted colonoscope system with a multi-core fiber.",
        "texts": [
            " RMSEs of our method using LEMAF are all more than four times better than the ones of the conventional method. It is also worth noticing that, the results using 6-core signals are slightly better than those using 3 cores. As for LEMAF, it can improve approximately two times of performance regarding the RMSE metric, which qualitatively concludes its effectiveness for 3D shape estimation in our model. To evaluate the improvement of our algorithm, we compared with the same conventional method used in Section IV. 1) Platform Overview: We built up an experimental platform as shown in Fig. 5, where we implemented the algorithms and recorded the sensing results in a Python software. To validate the sensing performance for flexible surgical instruments, we embedded a multi-core FBG fiber into a self-developed roboticassisted colonoscope system, in which a dual-wheel friction Authorized licensed use limited to: East Carolina University. Downloaded on June 20,2021 at 11:23:27 UTC from IEEE Xplore. Restrictions apply. module and a dial drive module are accordingly designed to control the insertion/retraction and deflection motions of an Olympus CF-30 L colonoscope whose working length is 167"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000854_j.triboint.2021.106881-Figure19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000854_j.triboint.2021.106881-Figure19-1.png",
        "caption": "Fig. 19. Mode shapes. The (a) first, (b) second, and (c) third modes at room temperature.",
        "texts": [
            " 18(a) shows significant decreases in the third natural resonance, while there are smaller changes in the first and the second modes. The reason for this is that the first two modes reflected the shaft and its connection to the other parts of the spindle D.S. Truong et al. Tribology International 157 (2021) 106881 system, especially in relation to the housing. On the other hand, the shifts in the third mode are mainly caused by the decreased bearing stiffness. This phenomenon is also included in the FEM of the mode shapes and their corresponding frequencies, as shown in Fig. 19. Fig. 19 reveals that, for all three modes, the biggest deformations are evident in the spindle shaft. However, the housing-associated mode shapes are dominant in the first and second modes. The deformations of the spindle shaft in the first and second modes are similar; meanwhile, differences in deformation can be seen in the housing for the modes two and three. Similar changes in vibration modes also occurred in the experimental results, as shown in Fig. 18(b). Another outstanding characteristic can be seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002873_s0925-2312(02)00626-4-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002873_s0925-2312(02)00626-4-Figure2-1.png",
        "caption": "Fig. 2. Diagram of a two-link robot manipulator.",
        "texts": [
            " (22), which has the superiority of simple structure, can guarantee the convergence of tracking error. However, the guaranteed convergence of tracking error to be zero does not imply convergence of the estimated value of the uncertain term bound to its optimal value. The persistent excitation condition [3,19] should be satisLed for the estimated value to converge to its optimal value. The e4ectiveness of the proposed SMNN control system can be veriLed by the following simulation results. For simplicity, a two rigid-link robot manipulator shown in Fig. 2 is utilized in this study to verify the e4ectiveness of the proposed control scheme. The dynamic model of the adopted robot system can be described in the form of Eq. (1) as [21] M(q) = [ l22m2 + l21(m1 + m2) + 2l1l2m2 cos (q2) l22m2 + l1l2m2 cos (q2) l22m2 + l1l2m2 cos (q2) l22m2 ] ; Vm(q; q\u0307)q\u0307 = [ \u22122l1l2m2 sin(q2)(q\u03071q\u03072 + 0:5q\u030722) m2l1l2 sin(q2)q\u030721 ] ; G(q) = [ (m1 + m2)l1g cos(q1) + l2m2 cos(q1 + q2) m2l2g cos(q1 + q2) ] ; (29) where q1 and q2 are the angle of joints 1 and 2; m1 and m2 are the mass of links 1 and 2; l1 and l2 are the length of links 1 and 2; g is the gravity acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003222_s0167-2789(96)00195-9-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003222_s0167-2789(96)00195-9-Figure3-1.png",
        "caption": "Fig. 3. Example of movement. A robot which meets a puck radiates light for a short period. After that, it moves to home which radiates IR. Another robot which has no puck reacts to the light.",
        "texts": [
            " Other robots which have no puck react to this light and turn their directions toward the light by using a pair of photo sensors. Thus the robot follows the gradient of light field. After the interaction period, the robot which has a puck turns offits light and changes its mode to homing mode. In homing mode, the robot moves toward the IR-LED array at the center of the field using their two IR sensors. When it knows that it has arrived home by using the photo reflector, it changes the direction randomly, and again searches for pucks. Fig. 3 shows an example of their movement. The field for this experiment was 190 x 190cm and its surface was black. The boundary had a wall. There was a white square and IR-LED array at the center of the field. We will call this square \"Home\". The total amount of pucks used in this experiment was 32. The size of a puck was 4 x 4 x 4 cm. Various kinds of distribution are possible. We chose two types of distribution in this experiment: the homogeneous field and the localized field (Fig. 4). The interaction periods were 0 s (no interaction) and 30 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003129_a:1008106331459-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003129_a:1008106331459-Figure7-1.png",
        "caption": "Figure 7. Piezoceramic tube actuator (left) and \u201cmaking a step\u201d with a piezo leg (right).",
        "texts": [
            " The sensor information gathered is passed on to the parallel computer system, where it is used as the set point for the control loop. Each of the station\u2019s robots has a mobile platform, which is driven by three tubeshaped piezoceramic legs. The legs are 13 mm long and have an outer diameter of 2.2 mm and an inner diameter of 1 mm. Each leg is covered by an inner and an outer metal electrode, which force the ceramic to change its length when a voltage is applied. In order to be able to bend a leg, the outer electrode is divided into four segments, axially arranged every 90\u25e6 (Figure 7, left). By applying different voltages to the electrodes, a leg can be bent into any direction due to volume changes of the piezoceramic material between the electrodes. This method of supplying energy makes it possible to control the motion of a robot\u2019s leg exactly, just by varying the strength and direction of the electric field [22]. The legs are bonded to metal mountings, which are screwed to a platform. Small ruby spheres with a diameter of 1 mm, which serve as feet and guarantee precise motions and a constant friction on the glass base, are glued to the legs. Glass as base material was chosen due to its smooth and flat surface, which is required for the implemented slip-stick actuation principle. The process of walking is based on inertia forces. A slip-stick actuation principle has been implemented (Figure 7, right). A small movement is achieved by bending all three legs slowly in the same desired direction. Then, the polarity of the voltage is abruptly changed making the legs bend in the opposite direction. Because of the inertia, the legs slip on the ground without moving the platform. Finally, the voltage is slowly decreased to relax the legs, causing another small movement. By repeating these three steps, the robot can move over long distances. The maximum stroke of a leg at an applied voltage of \u00b1150 V is about \u00b13\u00b5m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.13-1.png",
        "caption": "Figure 2.13. Tooth profile, N=36, ~s=20\u00b0.",
        "texts": [],
        "surrounding_texts": [
            "Of all the many types of machine elements which exist today, gears are among the most commonly used. The basic idea of a wheel with teeth is extremely simple, and dates back several thousand years. It is obvious to any observer that one gear drives another by means of the meshing teeth, and to the person who has never studied gears, it might seem that no further explanation is required. It may therefore come as a surprise to discover the large quantity of geometric theory that exists on the subject of gears, and to find that there is probably no branch of mechanical engineering where theory and practice are more closely linked. Enormous improvements have been made in the performance of gears during the last two hundred years or so, and this has been due principally to the careful attention given to the shape of the teeth. The theoretical shape of the tooth profile used in most modern gears is an involute. When precision gears are cut by modern gear-cutting machines, the accuracy with which the actual teeth conform to their theoretical shape is quite remarkable, and far exceeds the accuracy which is attained in the manufacture of most other types of machine elements. The first part of this book deals with spur gears, which are gears with teeth that are parallel to the gear axis. The second part describes helical gears, whose teeth form helices about the gear axis. The book is primarily about involute gears, since this type of gear is by far the most commonly used. However, the first chapter introduces the Law of Gearing, which must be satisfied by any pair of gears, and the statements made apply not only to involute gears, but are also true for non-involute types of gear. There is one other chapter of the book which also deals with non-involute gears. Chapter 9 is on the general theory of gear tooth geometry, and 2 Introduction is included in the book simply because the tooth profiles of involute gears contain sections which are not involute. In particular, the part of each tooth near its root, known as the fillet, is not an involute, but its shape can be found from the general theory of gears. And in some gears, small alterations from the involute shape, known as profile modifications, are made in the teeth, and again the final shape of the teeth can be found by means of the general theory. In helical gears, the angle between the helix tangent and the gear axis is known as the helix angle. Spur gears can be regarded as helical gears, in which the helix angle is zero. Since a spur gear is therefore simply a special case of a helical gear, it might be asked why the two types should be dealt with separately. However, the geometry of spur gears is considerably simpler than that of helical gears, and it is therefore convenient to describe it first. The cross-section of a helical gear perpendicular to its axis, known as its transverse section, is the same as the cross-section of a spur gear, so a knowledge of spur gear geometry makes a good starting point for the study of helical gears. The treatment of spur gear theory in this book is fairly conventional, except in one respect. No distinction is made between a gear pair meshed at the standard center distance, and one at extended centers. The terminology and the notation are the same for both cases. In conformity with this principle, the name \"pitch circle\" is always used for the circle of a gear which passes through the pitch point, and its radius is always represented by the symbol Rp' whatever its value. It is important to make a clear distinction between the pitch circle when a gear is in operation, and the pitch circle when it is meshed with its basic rack, which is used as a reference circle. For this reason, the pitch circle when the gear is meshed with its basic rack is called the standard pitch circle, and its radius is labelled Rs' where the subscript s is used to indicate the word \"standard\". Apart from this change, the definitions and notation in this book have been chosen to conform as closely as possible with those used in current North American practice. However, a few additional alterations have been made, in cases where Introduction 3 the existing terminology is confusing. For example, the phrase \"pre'ssure angle\" is used at present for several different angles. Its original meaning is the angle between the line of action and the common tangent to the pitch circles, but it is used also for the angle between the tooth profile and the tooth center-line of a rack, and the angle between the radius and the profile tangent of a gear tooth at either the standard pitch circle or the pitch circle. In addi t ion, the angle between the radi us and the prof i Ie tangent at a typical radius R of the tooth profile is also commonly known as the pressure angle. In current usage, all these angles are called either the pressure angle or the operating pressure angle, and they are all represented by the symbol ~ when they are equal to the pressure angle of the basic rack, and ~' when they are not. Over the years, several attempts have been made to rename some of these angles, but the proposed alternative names have not been widely accepted, so in this book the name \"pressure angle\" has generally been retained, while the notation has been altered to help identify the particular angle that is referred to. The angle between the radius and the profile tangent at a typical point of the gear tooth profile is referred to as the profile angle at radius R, and it is represented by the symbol ~R' The profile angles of a gear at the standard pitch circle and the pitch circle are called the pressure angle and the operating pressure angle of the gear, with the symbols ~s and ~P' and the pressure angle of the basic rack is represented by the symbol ~r' Finally, the angle between the line of action and the common tangent to the pitch circles is called the operating pressure angle of the gear pair, and this is the only angle for which the customary symbol ~ is still used. The symbols for the different pressure angles are distinguished by their subscripts, and the same convention is used for all quantities, such as the circular pitch and the tooth thickness, whose values are functions of the radius. The subscripts R, s, p, or b are used whenever a quantity is measured on a gear tooth at a general radius R, at the standard pitch circle, at the pitch circle, or at the base circle, and the subscript r applies to the corresponding quantity measured on a rack tooth. 4 Introduction The second part of the book deals with the geometry of helical gears, and the treatment differs substantially from the traditional approach. The sUbject is essentially three-dimensional, and in the past the geometr ic theorems have usually been proved with the help of projective geometry. In other fields of mechanics, projective geometry has been largely superseded by vector methods, and in the author's opinion, most of the theorems relating to helical gears can be proved far more easily using vector algebra than using projective geometry. The entire description of helical gears in this book is therefore given with the help of vector theory. I t is believed that most younger engineers, and today's engineering grounding in vector students, receive a more thorough theory than they do in projective geometry, and should therefore find thi s new approach to helical gear geometry easier to understand. The word \"pitch\" is used in this book in a manner which differs slightly from the customary North American usage, and is in fact based on current European practice. In North America, the phrase \"circular pitch\" describes a particular length on a spur gear, while \"diametral pitch\" is a quantity used to indicate the tooth size, defined as the number of teeth divided by the diameter of the standard pitch circle. The original meaning of the word \"pitch\" is the distance between similar objects that are repeated at regular intervals. In this book, the word is only used in a manner which conforms with the original meaning. The of a spur gear is defined in the usual circular pi tch way, and the corresponding lengths in a helical gear are called the transverse pitch, the normal pitch, and the axial pitch. In general, the diametral pitch is not referred to in this book, since it is not a pitch in the sense described above. In order to specify the tooth size of a gear we use the module, which is the method used throughout Europe and Japan. However, since the diametral pitch is still in common use in North America, the relation between the module and the diametral pitch is described in the text, and the diametral pitch is used in some of the examples at the end of each chapter. A list of references is provided, and this consists of a number of books and articles which the author has found Introduction 5 particularly helpful in his own study of gear geometry. In addition, several articles are listed because they describe, in considerable detail, certain topics which are only outlined in this book. The list is not intended to include all possible references, and no attempt has been made in the text to identify a source for each idea or theorem. In some cases, it would probably be very di ff icult to di scover where a particular idea originated. When any reference is quoted in the text, it is identified by a number in square brackets, which refers to the number in the list of references at the end of the book. In the diagrams throughout the book, the gear tooth profiles were drawn by a computer-driven plotter. The remaining parts of the diagrams were drawn by Mr. Hiroshi Yokota, of the University of Alberta. The author would like to thank him for his excellent work. The author also wishes to express his appreciation to the University of Alberta, and to the Natural Sciences and Engineering Research Council of Canada, both of whom provided support for the project. This book is about the theoretical geometry of involute gears, and is not intended to replace the many books and manuals that exist on the design of gears. However, the full potential of the involute as a tooth profile can only be used by a designer who has a good understanding of its fundamental geometric properties. It is hoped that the book will contribute to that understanding. PART 1 SPUR GEARS Chapter 1 The Law of Gearing External and Internal Gears A spur gear is a gear cut from a cylindrical blank, with teeth which are parallel to the gear axis, as shown in Figure 1.1. If the teeth face outwards, the gear is called an external gear, and if they face inwards, like those of the gear shown in Figure 1.2, the gear is known as an internal gear. Much of the geometric theory of gears applies equally to both external and internal gears. However, for the sake of clarity, this book is restricted to the subject of external gears, except for a single chapter. The exception is Chapter 12, where we will show which parts of the theory of external gears are valid for internal gears, and we will discuss the special features that apply only to internal gears. The Requirement for a Constant Angular Veloci ty Ratio When two gears rotate together, as shown in Figure 1.3, the teeth of each gear pass in and out of mesh with those of the other gear, and this occurs in an area that lies somewhere between the gear centers C1 and C2 . The teeth from the two gears pass through the meshing area alternately, first one from gear 1, then one from gear 2, and so on. Hence, if the gears have N1 and N2 teeth, and during a certain time interval T the number of teeth from each gear passing through the meshing area is n, then the gears will make respectively (n/N 1) and (n/N2) revolutions. By expressing the number of '0 The Law of Gearing Figure'. ,. An external gear. revolutions in radians and dividing by the time taken, we obtain average- values for the gear angular velocities w, and w2 , (w, ) average (w2 )average (...!l.)211' N, T _ (...!l.) 211' N2 T Figure '.2. An internal gear. ( 1.1) (1. 2) Constant Angular Veloci ty Ratio 11 where the minus sign indicates that the direction of rotation for gear 2 must be opposite to that of gear 1. From Equations (1.1 and 1.2), we can immediately obtain a relation between the average angular veloc i ties, - N (w ) 2 2 average ( 1. 3) Equation (1.3) is true for all gears, whatever the shape of the teeth. However, if the tooth shape is arbitrary, the gears will not run smoothly. Suppose gear 1 is driving, and turns at a constant angular velocity. In general, the angular veloci ty of gear 2 wi 11 not be constant, but wi 11 be a periodic function, repeating itself as each pair of teeth are meshed, with an average value given by Equation (1.3). The variation in angular veloci ty of gear 2 leads to vibrations in the gear train, and will generally cause fatigue cracks to form in the teeth, resulting in early failure of the gears. Theoretical studies of gear tooth profiles date back to the 16th Century, but for many years the craftsmen who cut gears made no use of the knowledge that was available. Most machinery was quite slow-moving, and vibration was not considered important. Toward the end of the 18th Century, 12 The Law of Gearing machine designers began to make greater demands on the gears in the machines they bui It. The gears turned faster than before, and were more heavily loaded. Tooth breakage then developed into a serious problem, and it became necessary to choose tooth profiles which would allow the driven gear to maintain a constant angular velocity, whenever the driving gear angular velocity was constant. To achieve this end, the angular velocity ratio (w 1/w2 ) must remain constant at all times, and not simply on average, as described by Equation (1.3). The new requirement for the angular veloci ties can be expressed by the equation, ( 1 .4) The purpose of this chapter is to determine the condition that must be satisfied by the meshing tooth prof i les, if the gears are to have the constant angular velocity ratio given in Equation (1.4). However, before looking at the case of two gears meshing together, we will consider that of a gear meshing with a rack. Rack and Pinion Rack and Pinion 13 A rack is a segment of a gear whose radius is infinite. I f the number of teeth N2 of gear 2 in Figure 1.3 were extremely large, the radius of the gear would also be large, relative to the tooth size, and the teeth near the meshing area would lie almost on a straight line. In the limit, as N2 becomes infinite, the teeth would lie exactly on a straight line, as shown in Figure 1.4. When two gears mesh, the smaller of the two is called the pinion, and the larger is usually referred to as the gear. Any gear meshed with a rack is considered smaller than the rack, since the rack is part of a gear with an infinite number of teeth. Hence, it is common to speak of a rack and pinion. Whereas a gear pair is used to transmit rotary motion between shafts, a rack and pinion are used to convert rotary motion into linear, or vice-versa. One well-known application is the rack and pinion steering of many automobiles. Part of a rack is shown in Figure 1.5. The pitch p is the distance between corresponding points of adjacent teeth. If we draw any line along the rack parallel to the line of teeth, 14 The Law of Gearing the intersection of this line with the tooth profiles will determine the tooth thickness and the space width, measured along that particular line. We define the rack reference line as the line along which the tooth thickness and the space width are equal, and since their sum is equal to the pitch p, the tooth thickness and the space width measured along the rack reference line must each be equal to (p/2). We now introduce coordinates xr and Yr fixed in the rack, with their origin on the rack reference line. The xr axis lies along a tooth center-line, and the Yr axis coincides with the rack reference line, as shown in Figure 1.5. A typical point of the rack tooth profile is labelled Ar' and the tangent to the tooth profile at this point makes an angle ~Ar with the x axis. The angle ~Ar is called the rack profile angle a~ point Ar \u2022 In relating the rack velocity to the pinion angular velocity, the reasoning is identical to that used earlier for two gears. During any time interval T, the number n of rack teeth passing through the meshing area is equal to the number of pinion teeth which pass through. Thus, average values for the rack velocity vr and the pinion angular velocity ware given by the following expressions, (W)average !!E T ( 1. 5) ( 1. 6) where vr is defined as positive in the upward direction, and W is defined as positive when the angular velocity is counter-clockwise. The relation we require is obtained by eliminating (niT) from Equations (1.5 and 1.6). N 21r(w)average ( 1. 7) Equation (1.7) is exactly analogous to Equation (1.3). As with a pair of gears, the satisfactory operation of a rack and pinion requires that the relation between vr and w should remain constant. Hence, the tooth shapes must be such that vr and w satisfy the following equation, . Ar Ar - 51n IP n - cos IP n t ~ ( 1. 9) Since Ar is the contact point, the unit vector nnr lies in the direction of the common normal. The velocity of Ar' and its component along the common normal, are given by the following two equations, 16 The Law of Gearing A - cos ~ r v r (1.10) (1.11) where the dot indicates the scalar product between two vectors. If the vector from the pinion center C to point A is (xnE+Yn~), then the velocity of point A and its component along the common normal can be expressed as follows, VA wnS x (xnE+Yn~) - wYne + wxn~ (1.12) A nnr vA . Ar Ar (1.13) vn wY Sln ~ - wX cos ~ where the symbol x in Equation (1.12) indicates the vector product. We now equate the normal velocity components of Ar and A, given by Equations (1.11 and 1.13), and use Equation (1.8) to express the relation we require between vr and w. We then obtain the following equation that must be satisfied by X and Y, the coordinates of the contact point. Rack and Pinion y (x - ~) 211\" A cot 1/1 r 17 (1.14) Equation (1.14) can be interpreted in the following manner. There is a fixed point P, at a distance (Np/211\") from C on the line through C perpendicular to the rack reference line, such that the slope of line PA is equal to cot I/IAr \u2022 This means that line PA makes an angle (11\"/2 _I/iAq with the n~ direction, and it is therefore the common normal at the contact point A, since the common tangent makes an angle I/IA r with the n~ direction. The position of point P is shown in Figure 1.7. The result just proved is known as the Law of Gearing, as it relates to a rack and pinion. It may be stated in the following way. The condition that must be satisfied by the tooth profiles of a rack and pinion, in order that the relation between rack velocity and pinion angular velocity should remain constant, is that the common normal at the contact point should at all times pass through a fixed point P. The position of P is at a distance (Np/211\") from the pinion center C, on the perpendicular from C towards the rack reference line. The point P is called the pitch point. The circle passing through P whose center is at C is called the pinion pitch circle, and its radius Rp is equal to the length CP, (1.15) In Equation (1.8), we gave the relation that we require between the rack velocity and the pinion angular velocity. We used that relation to prove the Law of Gearing, which lead us to define the pitch point and the pinion pitch circle. Having now derived an expression in Equation (1.15) for the pitch circle radius, we can combine Equations (1.8 and 1.15), and we obtain a simpler form for the relation between the rack velocity and the pinion angular velocity, (1.16) The line in the rack which touches the pinion pitch circle at P, as shown in Figure 1.7, is known as the rack 18 The Law of Gearing pitch line. When the pinion and rack are in motion, the velocity of any point on the pinion pitch circle is equal to RpW, and the velocity of any point on the rack pitch line is equal to vr ' Since these velocities are equal, as we can see from Equation (1.16), the motion of a rack and pinion is identical to the motion that would be obtained if the rack pitch line and the pinio~ pitch circle were to make rolling contact with no slipping. Ci rcular pi tch The circular pitch of the pinion teeth at any radius R is defined as the distance between corresponding points of adjacent teeth, measured around the circumference of the circle of radius R. Thus, the circular pitch PR at radius R, which is shown in Figure 1.8, is given by the following expression, 211'R N (1.17) In the case when the circular pitch is measured on the pitch Circular pitch. Law of Gearing for Two Gears circle, we use the symbol Pp' and its value can substituting Rp in place of R in Equation (1.17). 211'Rp Pp N 19 be found by (1.18) When we replace the pitch circle radius Rp in this equation by the expression given in Equation (1.15), it is clear that the circular pitch of the gear at its pitch circle is equal to the pitch p of the rack, p (1.19) This result can be used to provide an alternative definition of the pitch circle of a pinion, when it is meshed with a rack. The pitch circle can be defined as the circle on which the pinion circular pitch is equal to the rack pitch p. Law of Gearing for Two Gears It was shown in the previous section that a rack and pinion behave in the same manner as if the rack pitch line and the pinion pitch circle were to make rolling contact with no 20 The Law of Gearing slipping. We now investigate whether the same idea can be used for two gears. First, we find two pitch circles which, if they made rolling contact with each other, would provide the same angular velocity ratio as the gears. And then we will establish that the Law of Gearing also applies for a pair of gears, or in other words, that the common normal at the tooth contact point always passes through a fixed point. Figure 1.9 shows two gears, with point Al of gear 1 in contact with point A2 of gear 2. The distance C between the gear centers is called the center distance. Parts of the pitch circles have been drawn in, and their radii are shown as RPl and Rp2 . The point where they touch is the pitch point P. If the pitch circles are to make rolling contact with no slipping, their radii must satisfy the following equations, C (1.20) (1.21) The angular velocity ratio that we require was given in Equation (1.4), (1.22) Equations (1.21 and 1.22) imply that the ratio of the pitch circle radii is equal to the ratio of the tooth numbers, ( 1. 23) We now solve Equations (1.20 and 1.23), to obtain the radii of the pi tch ci rc les, ( 1 .24 ) (1.25) The pitch point P, which is the point where the pitch circles touch, therefore lies on the line of centers and divides C1C2 in the ratio N1:N2 . We use this point as the origin of a fixed system of coordinates E, ~ and S, with axes Law of Gearing for Two Gears 21 in the directions shown in Figure 1.9. The position of the contact point relative to the pitch point is then given by the coordinates ~ and 1/. As we did in the case of the rack and pinion, we write down the velocities of points Al and A2 , and then equate their components along the common normal. The direction nn of the common normal, which is unknown at present, can be written in the following form, where s~ and s1/ are the components of nn in directions. Then the velocities of Al and components in the normal direction, are following four equations. Al v = w 1nS x [(Rpl+~)n~+1/n1/] A2 v (1.26) the coordinate A2 , and their given by the ( 1. 29) ( 1 .30) A A Equating the expressions for vn 1 and vn 2 , we obtain a relation which must be satisfied by the vector components s~ and s1/' o (1.31) The expression between the square brackets is zero, as we can see from Equation (1.21). The angular velocities w1 and w2 can never be equal, because for a pair of external gears the angular velocities must be of opposite sign, and for a pinion meshed with an internal gear, the pinion angular velocity must be greater than that of the internal gear. Hence, the term (w 1-w2 ) cannot be zero, and it follows that the remaining term is zero. The condition given by Equation (1.31) therefore reduces to the following form, 22 The Law of Gearing ( 1. 32) Equation (1.32) can be interpreted as showing that the unit vector nn along the common normal is parallel to line PA 1. In other words, the common normal at the contact point must always pass through the pitch point, which is the point that divides the line of centers C1C2 in the ratio N1 :N2 \u2022 This is the statement of the Law of Gearing, as it applies to a pair of gears. We proved in Equation (1.19) that when a pinion is meshed with a rack, the circular pitch of the pinion at its pitch circle is equal to the pitch of the rack. A similar result is also true for a pair of gears. The circular pitch of each gear at its pitch circle is given by Equation (1.18), Pp1 211'Rp1 N1 ( 1. 33) Pp2 211'Rp2 N2 (1.34) When we use Equations (1.24 and 1.25) to express the pitch circle radii RP1 and Rp2 ' it is immediately clear that the circular pitches of the two gears must be equal, (1.35) Path of Contact The locus of successive contact points between a pair of teeth is called the path of contact. One consequence of the Law of Gearing is that the path of contact must pass through the pitch point. To prove this statement, we need only consider the situation if it were not true. If the path of contact were to cross the line of centers at any point P' which is not the pitch point, then when the contact point was at P', the common normal at the contact point would not pass through the pitch point, and the gear pair would not satisfy the Law of Gearing. The Basic Rack 23 Conjugate Profiles and the Basic Rack Any pair of tooth profiles that satisfy the Law of Gearing are said to be conjugate. If the tooth profile of one gear is chosen arbitrarily, it is possible to find a tooth profile for the other gear, such that the two profiles are conjugate. In particular, we can specify a rack tooth profile, and then define a system of gears as having tooth profiles which are conjugate to the chosen rack. This is the method generally used by various organisations, such as the American Gear Manufacturers Association (AGMA) and the International Organisation for Standardization (ISO), to define the tooth profiles for a system of gears. The rack tooth profile is then known as the basic rack for the system of gears. In the next chapter, we will consider a particular basic rack, which is the one used to define the tooth profile of an involute gear, and we will then describe the geometry of the gear teeth. Chapter 2 Tooth Profile of an Involute Gear Basic Involute Rack In general, the tooth profile of a rack may be curved, and the profile angle ~Ar would then vary from one point of the tooth to another. We now consider a particular rack, in which the teeth are straight-sided. This is the basic rack which we use to define the tooth shape of an involute gear. The profile angle for this rack is constant, and the value of the constant will be represented by the symbol ~r' which is called the pressure angle of the basic rack. Thus, for the basic rack used to define involute tooth profiles, constant (2.1) In some cases the profile angle ~Ar may vary near the tips and the roots of the basic rack teeth. For example, the teeth may be rounded at the tips. The rack is still called an involute rack, provided a substantial part of its tooth profile is straight-sided. For the purpose of finding the shape of the gear tooth, we will start by assuming that the basic rack has teeth which are entirely straight-sided, as shown in Figure 2.1. The pressure angle is ~r' and we use the symbol Pr to represent the pitch of the basic rack. Base Pi tch of the Basic Rack The dimensions of the basic rack are determined by the values of Pr and ~r' In addition, there is a third quantity shown in Figure 2.1 called the rack base pitch, which is Standard pitch Circle 25 defined as the distance between adjacent teeth, measured along a common normal. The reason why this particular length on a rack is called the base pitch will be made clear later in this chapter. For the moment, we will simply use Figure 2.1 to express the base pitch Pbr of the basic rack in terms of its pi tch and pressure angle, (2.2) The three quantities Pr' Pbr and 4J r are the parameters used to describe the basic rack. Since they are related by Equation (2.2), it is clear that only two of the quantities are independent. We can choose any two, and then use Equation (2.2) to find the third. Standard Pi~ch Circle For any tooth profile, there are a number of quantities whose values are functions of the radius R. These include the circular pitch PR' which was introduced in Chapter 1, and the profile angle and the tooth thickness, which will be 26 Tooth Profile of an Involute Gear discussed later in this chapter. As part of the description of a gear, it is necessary to provide the values of each of these quantities at some specified radius. An obvious choice for this radius is the pitch circle radius of the gear when it is meshed with its basic rack. In Chapter 1 we defined the pitch circle of a gear as the circle through the pi tch point, and we used the symbol Rp to represent its radius. We showed there that the value of Rp depends on the pitch of the rack, when the gear is meshed with a rack, and on the center distance when the gear is meshed with another gear. In order, therefore, to identify the particular pitch circle of a gear when it is meshed with its basic rack, we will call it the standard pitch circle, and we will represent its radius by the symbol Rs' In Equations (1.15 and 1.18), we gave expressions for the pitch circle radius of a gear when it is meshed with an arbitrary rack, and for the circular pitch measured at the pitch circle, We also showed, in Equation (1.19), that the circular pitch at the pitch circle is equal to the pitch p of the rack, When we replace the rack pitch p in these equations by Pr' the pitch of the basic rack, the first two equations give the standard pitch circle radius Rs of a gear, and its circular pi tch p at the standard pi tch ci rcle, while. the thi rd s equation shows that the circular pitch of the gear at its standard pitch circle is equal to the pitch of the basic rack, RS NPr (2.3) 21r Ps 211'Rs N (2.4) Ps Pr (2.5) Tooth Profile of an Involute Gear 27 The Involute Tooth Profile We will now determine the shape of gear tooth profiles which are conjugate to the basic rack in Figure 2.1. The word conjugate means, as we defined it in Chapter 1, that the gear teeth are shaped in such a manner that the Law of Gearing is satisfied, when the gear is meshed with the basic rack. In Figure 2.2, a pinion is shown meshing with the basic rack. The plnlon pitch circle radius is Rs' given by Equation (2.3), and the pitch line is the line in the basic rack which touches the pinion pitch circle at the pitch point P. The Law of Gearing states that the common normal at the contact point must pass through P. For any particular position of the rack, there is only one point Ar of the rack tooth profile whose normal passes through P, and this point must be the contact point. The pinion tooth must therefore be shaped so that its profile touches the rack tooth at Ar \u2022 28 Tooth Profile of an Involute Gear The point of the pinion tooth profile in Figure 2.2 which coincides with Ar is labelled A. The line joining the contadt point to the pitch point is called the line of action, since it coincides with the common normal at the contact point, and therefore in the absence of friction the contact force must act along this line. The angle between the line of action and the tangent to the pinion pitch circle at P is called the operating pressure angle ~ of the gear pair. Since the line of action is perpendicular to the tooth profile of the basic rack, it can be seen from the diagram that, when a gear is meshed with its basic rack, the operating pressure angle of the gear pair is equal to the pressure angle of the basic rack, (2.6) If we were to consider the basic rack in a new position, the description of the meshing geometry would be essentially a repetition of the last paragraph. The new contact point would again lie on the line which passes through the pitch point in a direction perpendicular to the tooth profile of the basic rack. This result is true for any position of the basic rack. Hence, the path of contact, which is the locus of all contact points, is a segment of the same straight line. And since the line of action is always the line joining the pitch point to the contact point, the direction of the line of action is fixed, and the line of action coincides with the line containing the path of contact. We now construct the perpendicular from the pinion center C to the line of action, and the foot of this perpendicular is labelled E, as shown in Figure 2.2. The pinion circle with center C and radius equal to CE is known as the base circle, and its radius is represented by the symbol Rb \u2022 Since the rack tooth profile and line CE are both perpendicular to the line of action, they must be parallel, and the angle ECP is equal to ~r' We can then use triangle ECP to express the base circle radius in terms of the standard pitch circle radius, (2.7) Alternative Definition of the Involute 29 The shape of the pinion tooth must be such that the normal to the tooth profile at point A passes through P. This is a direct statement of the Law of Gearing. using the base circle just defined, we can restate the property of the tooth shape a little differently. The shape of the tooth profile must be such that the normal at the contact point touches the base circle. As the pinion rotates, the contact point moves along the pinion tooth, and therefore at each point of the profile the normal to the profile must touch the base circle. A curve with this property is known as an involute of the base circle, and this is the origin of the name \"involute gear\". Alternative Definition of the Involute There is another manner in which the involute can be defined. If the base circle is fixed, and a rigid bar AD rolls without slipping on the base circle, as shown in Figure 2.3, then the path followed by point A is an involute. It is easy to prove that the two definitions are equivalent. If point E is the contact point between the base circle and bar, then E is also the instantaneous center of the bar as it rolls. The 30 Tooth Profile of an Involute Gear velocity of point A is therefore perpendicular to EA. This means that the tangent to the involute at A is perpendicular to EA, and therefore the normal is along EA, which is the property by which the involute was originally defined. The Involute Function The alternative definition is useful in helping to derive some of the fundamental geometric equations of the involute. The point in Figure 2.3 where the involute curve meets the base circle is labelled B. This is the point where the end A of the bar would meet the base circle, if the bar rolled to the position where A was the contact point. Due to the fact that the bar rolls without slipping, we can say that the length of arc EB on the base circle must be equal to the length EA on the bar. In symbolic form, this can be written, arc EB EA (2.8) We now need to define a number of new symbols, and to derive the relations between them. Figure 2.4 shows the base Profile angle and roll angle. The Involute Function 31 circle, and an involute curve starting at point B, with a typical point A at radius R. The normal to the involute at A touches the base circle at E. We define an angle ~R' called the profile angle at radius R, as the angle between the radius through A and the involute tangent at A. The radius CE is perpendicular to EA, since EA touches the base circle, and CE is therefore parallel to the involute tangent at A. Hence, the angle ECA is equal to the profile angle, angle ECA (2.9) Referring to triangle ECA, we obtain two immediate results, (2.10) EA (2.11) Next, we define an angle ER, called the roll angle at radius R, as the angle between the radius through B and the involute tangent at A. Since CE is parallel to the involute tangent at A, the angle ECB is equal to the roll angle, angle ECB (2.12) and the length of arc EB is therefore given by the following equation, arc EB (2.13) where ER must of course be expressed in radians. We now combine Equations (2.8, 2.11 and 2.13), in order to obtain a relation between ER and ~R' (2.14 ) The angle between the radii CA and CB is clearly a function of ~R' and the name inv ~R (short for involute function of ~R) has been chosen for this function. We express the angle ACB as the difference between angles ECB and ECA, and since angle ECB is given by Equation (2.14) in radians, 32 Tooth Prof i Ie of an I nvol ute Gear the angles in the following equation are all expressed in radians. inv I/>R angle ACB (2.15) The function inv I/>R is used throughout the geometry of involute gears. Since, as we have shown, it represents an angle measured in radians, it is generally convenient to express other angles also in radians. For this reason, the following convention will be used in this book. Unless it is explicitly stated that an angle is given in degrees, it will be understood that the value is expressed in radians. For example, the polar coordinate 9R of a point on the tooth profile is given by Equation (2.35). The units are not given, so it is understood that the equation gives the value of 9R in radians. When I/>R is known, the value of inv I/>R is given by Equation (2.15). It is also sometimes necessary to find I/>R' when the value of inv I/>R is known, and this can be carried out by means of the following two steps, q (inv If> ) 2/3 R 1.0 + 1.04004q + 0.32451q2 - 0.00321q3 - 0.00894q4 + 0.00319q5 - 0.00048q6 (2.16) (2.17) The maximum error given by the procedure is 0.0001\u00b0, for values of I/>R between 0\u00b0 and 65\u00b0, and this range of I/>R values is sufficient for most practical purposes. The coefficients in Equation (2.17) are a simplified version of a set of ceofficients developed by Polder [9]. For the purpose of describing the geometry of a tooth, we generally use the radius R to specify any point A on the tooth profile. The profile angle at A is then given by Equa t i on (2. 1 0 ) , Rb R (2.18) and the angle between line CA and the fixed line CB is expressed by the involute function, Pressure Angle of a Gear angle ACB inv /fiR 33 (2.19) Another common description of the involute is based on the same idea as the alternative definition given earlier. We consider a cable wrapped round a fixed cylinder of radius Rb , with one end of the cable attached to the cylinder. If the other end of the cable is partly unwound, the path followed by that end will be an involute. If Figure 2.5 were to represent the cable and cylinder, then EA would be the section of cable unwound from the cylinder, and it is obvious that the length of this part of the cable is equal to the arc EB, where the cable was originally wrapped round the cylinder. Pressure Angle of a Gear The pressure angle /fI s of a gear is defined as the gear profile angle /fiR at the standard pitch circle. The profile angle at radius R was given by Equation (2.10), and the pressure angle can be found by setting R equal to Rs in this relation, (2.20) 34 Tooth Profile of an Involute Gear When Equation (2.20) is compared with Equation (2.7), it is clear that the pressure angle of the gear is equal to that of the basic rack, \"'r (2.21) There is a more direct proof that the two pressure angles are equal. Figure 2.6 shows the gear meshed with its basic rack, in positions such that the contact point coincides with the pitch point. If As is the point on the gear tooth profile at radius Rs' the pressure angle of the gear is defined as the angle between the radius CAs and the tooth profile tangent at As. Since As is also the contact point, when the gear and the basic rack are in the positions shown, the tangent to the gear tooth profile lies along the rack tooth profile, and the pressure angle \"'s of the gear is therefore equal to the basic rack pressure angle \"'r. It is evident that the name \"pressure angle\" is used for several angles, each defined in a different manner. The pressure angle \"'r of the basic rack is the angle between the Base pi tch 35 tooth profile and the tooth center-line, while the pressure angle ~ of a gear is the profile angle at its standard pitch s circle. Each of these two angles is a constant quantity associated with a particular gear, and in principle it can be measured on the gear. On the other hand, the operating pressure angle ~ of a gear pair only exists when the two gears are meshed. For a rack and pinion, it is defined as the angle between the line of action and the tangent to the pinion pitch circle at P, while for a pair of gears it is the angle between the line of action and the common tangent to the two pitch circles. We have shown, in Equations (2.6 and 2.21), that for a pinion meshed with its basic rack, the three pressure angles are all equal in value. In Chapter 3 we will show that, in general, the operating pressure angle ~ of a gear pair may differ from the other two pressure angles. However, even when the values are equal, it is important to know which angle is referred to when the name \"pressure angle\" is used, and for this reason the symbols ~r' ~s and ~ will be used throughout this book to distinguish the three angles. Base pitch The circular pitch at radius R was defined in Chapter 1 as the distance between corresponding points of adjacent teeth, measured around the circle of radius R. An expression for the circular pitch at radius R was given by Equation (1.17), 211\"R N The base pitch Pb of a gear is defined in a similar manner, as the distance between corresponding points of adjacent teeth, measured around the base circle. In other words, the base pitch is the circular pitch at the base circle, 211\"Rb N (2.22) In Equation (2.10), we gave an expression for the base circle radius in terms of a typical radius R and the corresponding 36 Tooth Profile of an Involute Gear profile angle /fiR' We combine the last three equations to derive a relation between the base pitch and the circular pitch at radius R, (2.23) and as a special case of this equation, we set R equal to Rs' and we obtain the corresponding relation between the base pitch and the circular pitch at the standard pitch circle, (2.24) There is a property of involute curves which we will make use of in the chapters that follow. The normal to a tooth profile at any point A is also normal to any other involute of the base circle, and if it cuts the next tooth profile at point A', the length AA' is equal to the base pitch Pb' Thus, the distance between adjacent tooth profiles, measured along a common normal, is equal to Pb' These results can be proved Gear Parameters 37 with the help of Figure 2.7. The normal to the involute at A must touch the base circle at some point E, since this is the defining property of the involute. If line EA cuts the next tooth profile at A', the normal to the second tooth profile at A' must also touch the base circle, and therefore coincides with line EAA'. Hence, a line which is normal to one involute is also normal to other involutes of the same base circle. To prove that the length AA' is equal to the base pitch, we make use of Equation (2.8), which states that EA is equal to arc EB. Referring again to Figure 2.7, we have the following relations, AA' EA' - EA arc EB' - arc EB arc BB' Since the involutes shown in Figure 2.7 are the profiles of adjacent teeth, arc BB' is by definition equal to the base pitch, and the equation can be written, AA' (2.25) We have therefore proved the statement made earlier, that the distance between adjacent tooth profiles, measured along a common normal, is equal to the base pitch. The definition of the base pitch given in Equation (2.22) would not apply in the case of a rack, because both the base circle radius and the number of teeth are infinite. However, earlier in the chapter we gave a definition for the base pitch of a rack, as the distance between adjacent tooth prof i les, measured along a common normal. In view of the result given by Equation (2.25), it is now possible to see that there is no essential difference between the two definitions. Relations Between the Gear Parameters and Those of the Basic Rack We pointed out earlier that the parameters Pr' Pbr and 'r can be used to describe the basic rack, and for gears we introduced three corresponding quantities, the circular 38 Tooth Profile of an Involute Gear pitch Ps at the standard pitch circle, the base pitch Pb' and the pressure angle 41 s \u2022 We have already shown in Equations (2.5 and 2.21) that the two pi tches and the two pressure angles are equal, The two base pitches were expressed in terms of the remaining quantities by means of Equations (2.2 and 2.24), When we compare these equations, bearing in mind that the pitches and pressure angles are equal, it is clear that the two base pi tches are also equal, = (2.26) We stated in Chapter 1 that we can define a system of gears, simply by specifying the shape of the teeth in the basic rack. The teeth of each gear in the system must be shaped so that they are conjugate to the basic rack. We have now shown that, for any gear in an involute system, the circular pitch at the standard pitch circle, the base pitch and the pressure angle must each be equal to the corresponding quantity in the basic rack. When the geometry of a gear is described, it is necessary to refer repeatedly to the circular pitch at the standard pitch circle. Since this phrase is so cumbersome, it is common practice to describe Ps simply as the \"circular pitch\". There is no danger of confusion, provided the circular pitch at any other radius is clearly identified, and therefore from now on in the book we will adopt this convention. The same convention will be used for the names of several other gear tooth quantities, whose values depend on the radius, and these will be pointed out as they occur. Tooth Profile of an Involute Gear 39 Module and Diametral pitch When we introduced the standard pitch circle of a gear, we stated that a number of the gear parameters are defined on the standard pitch circle. As part of the specification of a gear, we must therefore give the radius of the standard pitch circle, or alternatively some quantity from which the radius can be calculated. The standard pitch circle radius Rs was given originally by Equation (2.3) in terms of the basic rack pitch Pr' NPr \"\"\"21r (2.27) and since the pitch of the basic rack is equal to the circular pitch of the gear, the radius of the standard pitch circle can be expressed directly in terms of the circular pi tch, (2.28) For a system of gears conjugate to a particular basic rack, it would therefore be necessary to specify only the value of the circular pitch Ps' which is the same for every gear in the system, and we would then use Equation (2.28) to calculate the standard pitch circle radius of each gear. This method of specification was in fact used in the past, and gears in which the circular pi tch is specified as a convenient length are known as \"circular pitch gears\". However, they are seldom made today, as they have one slight disadvantage. If the value of the circular pitch is chosen as a round number, the standard pitch circle radius is always an inconvenient size, due to the presence of the factor w in Equation (2.28). It has been found more practical to design gears in which the standard pitch circle radius is a round number. With this consideration in mind, we introduce a quantity called the module m, defined in terms of the basic rack pitch, m (2.29) We now combine Equations (2.27 and 2.29), in order to express the standard pitch circle radius in terms of the module, 40 Tooth Profile of an Involute Gear (2.30) and, since once again the circular pitch of the gear is equal to the basic rack pitch, a relation between the circular pitch and the module can be found immediately from Equation (2.29), (2.31) The module, which we have shown is proportional to the circular pitch, is used not only in the calculation of the standard pitch circle radius, but also as a measure of the tooth size. When two gears are meshed together, they must clearly have teeth of approximately the same size, and in prac t ice they are des i gned with the same module m and the same pressure angle ~s. In other words, the two gears are both conjugate to the same basic rack. We will show in Chapter 3 that these conditions ensure correct meshing of the gears. The module can be measured in either mms or inches. In practice, it is most commonly measured in mms, since the module is generally used in countries which have adopted the metric system. In North America, the quantity used at present to specify the tooth size of a gear is known as the diametral pitch Pd. This is defined as the number of teeth in the gear, divided by the diameter of the standard pitch circle, N 2Rs (2.32) A relation between the diametral pitch and the circular pitch can be found from Equations (2.28 and 2.32), ..JL Ps (2.33) and when we use Equation (2.31) to express the circular pitch in terms of the module, it is clear that the diametral pitch is equal to the rec iprocal of the module, 1 m (2.34) Since the diametral pitch is expressed in teeth per inch, Equation (2.34) requires that the module be given in inches. Tooth Thickness 41 It seems probable that the use of the diametral pitch will eventually be abandoned in favour of the module. The gear geometry in this book is therefore described in terms of the module, and the module is also used in most of the examples at the end of each chapter. However, since the diametral pi tch is still widely used in North America, a number of examples are also included in which the tooth size is specified by means of the diametral pitch. For these problems, the module will first be found, using Equation (2.34), and the remaining calculations will then be carried out in terms of the module. Tooth Thickness The tooth thickness at radius R is defined as the arc length between opposite faces of a tooth, measured around the circumference of the circle of radius R. We will show in this section that when we know the tooth thickness at one radius, we can calculate it at any other. Thus, it is only necessary to specify the tooth thickness at one particular radius, and for this purpose we generally choose the standard pitch circle. The symbol ts is used to designate the tooth thickness at the standard pitch circle, and tR is used for the tooth thickness at radius R. The tooth thickness ts at the standard 42 Tooth Profile of an Involute Gear pitch circle is described simply as \"the tooth thickness\", in the same way that the circular pitch at the standard pitch circle is called the circular pitch. The gap between the teeth, measured around the circle of radius R, is called the space width at radius R, and like the tooth thickness, the space width is generally measured on the standard pi tch circle. Since the tooth thickness, the space width and the circular pitch are all defined as arc lengths, as shown in Figure 2.8, it is clear that the sum of the tooth thickness and the space width at any radius R is equal to the circular pi tch at radius R. A gear tooth is shown in Figure 2.9, with points B, As and A on the tooth profile at radii Rb , Rs and R. We will derive an expression for the tooth thickness tR at radius R, assuming the tooth thickness ts is known, and we start by finding the polar coordinate 9R of point A, angle xCA angle xCAs + angle AsCB - angle ACB Tooth Thickness 43 The angle ACB is given by the involute function inv 'R' as we showed in Equation (2.19), and since the profile angle at the standard pitch circle is equal to the pressure angle 's' the angle AsCB is equal to inv,s. Hence, the expression for 8R can be written, = (2.35) Having found the polar coordinate 8R of point A, we can immediately write down an expression for the tooth thickness at radius R, In order to find a relation between the thicknesses at any two radii R1 and R2, we use Equation twice to write down the tooth thicknesses tR and tR ' h 1 \" b h ,1 2 t en e lmlnate ts etween t e two expressIons, tR tR = R2[r + 2(inv 'R - inv'R )] 2 1 1 2 (2.36) tooth (2.36) and we (2.37) where 'R and /fiR are the prof ile angles at the two radi i. 1 2 44 Tooth Profi Ie of an I nvol ute Gear There is another quantity which will be useful in the description of a gear tooth profile, in particular in Chapter 11, where we discuss the tooth strength of a gear. We define an angle YR, as shown in Figure 2.10, as the angle between the profile tangent at point A and the tooth center-line, which coincides with the x axis. Since line CE in Figure 2.10 is parallel to the profile tangen~ at A, the angle between CE and the x axis is equal to YR' and we can therefore express YR as follows, (2.38) We replace 8R by the expression given in Equation (2.35), and the equation for YR then takes the following form, Standard Basic Rack Forms 45 and bs between these circles and the standard pi tch circle are called the addendum and the dedendum, and for this reason the tip and root circles are also called the addendum and dedendum circles. The sum of the addendum and the dedendum is known as the whole depth of the gear teeth. Finally, we use Figure 2.11 to express the addendum and the dedendum in terms of RT, Rs and Rroot ' Standard Basic Rack Forms R - R T s (2.40) (2.41) Although it is possible to choose arbitrary values for the module m and the pressure angle ~r of a basic rack, there are a number of standard values which are most frequently used. As we have shown, the module and pressure angle ~s of a gear are equal to the module and pressure angle ~r of its 46 Tooth Profile of an Involute Gear basic rack, so by choosing standard values for the basic rack parameters, we are also choosing the same values for the parameters of the gear. These standard values are recommended by organisations such as the ISO and the AGMA, first because they have been found in practice to give satisfactory results, and secondly for economic reasons. The tools used for cutting gears have dimensions which depend on the module and the pressure angle of the gear to be cut. A gear manufacturer will normally keep in stock the tools necessary for cutting gears with standard values of module and pressure angle, but when di fferent values are required, the cutting tool must be made specially, and the cost of the gear is therefore increased. Preferred values for the module, measured in mms, are as follows, 1, 1.25, 1.5, 8, 10, 12, 2, 2.5, 3, 16, 20, 25, 4, 5, 6, 32, 40, 50, and the preferred values for the diametral pitch, measured in Standard Basic Rack Forms 47 teeth per inch, are given below."
        ]
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure6.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure6.4-1.png",
        "caption": "Figure 6.4. A gear pair with partial recess action.",
        "texts": [],
        "surrounding_texts": [
            "There are several reasons why the initial design just described may need to be improved. For instance, there may be interference, or one of the gears may be undercut. For the moment we will simply describe how the design can be altered, and in the later sections of this chapter we will discuss some of the reasons for making the changes. In the initial design, we chose to make the tooth thicknesses tP1 and tP2 equal to each other. We now increase one of the tooth thicknesses by an amount ~tp' and in order to retain the same backlash in the gear pair, we must reduce the other tooth thickness by the same amount. Hence the tooth thicknesses, which in the initial design were given by Equation (6.25), are now as follows, l(p -B) + ~t 2 P P (6.45) = l(p -B) - ~t 2 P p (6.46) 160 Profile Shift The rest of the design follows exactly the procedure described earlier. In the original description, the equations used to calculate the gear blank diameters were interspersed with other equations, which were necessary to explain the reasons for each step in the procedure. For the sake of clarity, we will now repeat the equations that are specifically required for the calculation of the gear blank diameters. Whenever the equations for the two gears are identical, apart from the interchange of subscripts, the equation for gear 1 only will be given. tsl ~ 2(inv q,p - inv q,s)] (6.47) Rsl [R + pl 41 (t sl - 17Tm) (6.48) e l 2 tan 2 s bsl a -r e l (6.49) bPl bsl + RPl - Rsl (6.50) apl m - 1 '2(bpl - bp2 ) (6.51) ap2 m + 1 '2(bp1 - bp2 ) (6.52) DT1 2RT1 2(Rp1 +ap1 ) (6.53) Equations (6.45 - 6.53) form a design algorithm, which can of course be programmed for a micro-computer. The value of ~tp is chosen by the designer, and it may be either positive or negative. Whatever value is chosen, we obtain a gear pair in which the working depth is equal to 2.0m, and the clearances at the two root circles are equal to each other. For the case when the center distance C is equal to the standard center distance Cs ' the initial design procedure gives a gear pair in which the tooth thicknesses tsl and ts2 are equal, and the addendum as in each gear is equal to 1.0m. If a non-zero value is then chosen for ~tp' the addendum in one gear is increased, while that in the other gear is reduced by the same amount. This type of design is known as the \"long and short addendum system\". The name is not appropriate for gear pairs with non-standard center distances, because the Geometric Design of a Spur Gear Pair 161 addendum values are unequal in both the initial and the final designs. Dedendum Values of Gears Cut by a Pinion Cutter In the design procedure just described, the dedendum bsl of gear 1 was given by Equation (6.49), for the case when the gears are cut by a rack cutter. If the gears are cut by a pinion cutter, the dedendum of each gear is still equal to the cutter addendum minus the cutter offset, but for a pinion cutter the offset is no longer equal to the profile shift of the gear. A method for finding the offset of a pinion cutter, corresponding to a tooth thickness tsg in the gear, was described in Chapter 5. The relevant equations will be repeated here, with no further explanation. The pressure angle ~~ of the gear and the cutter at their cutting pitch circles can be found from Equation (5.18), . c lnv ~p (6.54) Once the value of (inv ~~) is known, we use Equations (2.16 and 2.17) to calculate the corresponding value of ~~. The cutting pressure angle, the cutting center distance, and the cutter offset are then given by Equations (5.19, 5.20 and 6.2), ~c P (6.55) Rbg+Rbc cos ~c (6.56) CC _ CC s (6.57) We use these equations to find the cutter offset ~C~l' required to cut the gear tooth thickness tsl given by Equation (6.47). The dedendum in gear 1 is then given by the following expression, a - ~Cc sc sl (6.58) 162 Profile Shift where a sc is the addendum of the pinion cutter. This equation replaces Equation (6.49) in the design procedure, and the dedendum of gear 2 is of course found in the same manner. Avoidance of Undercutting, Interference and Pointed Teeth If the initial design produces a gear pair in which one of the gears is undercut, the tooth thickness in that gear should be increased until the undercutting disappears, while the tooth thickness in the meshing gear is correspondingly reduced. If there is interference, it generally occurs at the tooth fillets of the pinion, and in this case the pinion tooth thickness should be increased until the interference ceases. Finally, if the teeth of either gear are too close to being pointed, or in other words, the tooth thickness at the tip circle is less than O.25m, then the tooth thickness of that gear should be reduced. The design procedure will automatically reduce the addendum, and the tooth thickness at the tip circle will be increased. In every case, the best value for ~tp can be found most simply by trial and error. When a micro-computer is used, the program can carry out the checks to determine whether there is undercutting or interference, and whether the teeth are too pointed. The designer can increase or decrease ~tp until a satisfactory gear pair is found, or alternatively, until it becomes clear that the requirements cannot all be met. Balanced Strength Design The subject of tooth strength, and the calculation of the tooth stresses, will be discussed in Chapter 11. At this stage it is sufficient to state that the tooth strength of a gear depends not only on the module, the pressure angle and the tooth thickness, but also on the number of teeth in the gear. If two meshing gears have equal tooth thicknesses ts1 and t s2 ' the teeth of the pinion are weaker than those of the gear. When a gear pair is designed, the initial choice of zero Recess Action Gears 163 for Atp often produces a gear pair which satisfies all the geometric requirements. However, if the tooth strengths of the two gears are significantly different, the design can be improved by increasing the tooth thickness of the pinion, and reducing that of the gear. If Atp is chosen so that the tooth strengths are equal, the design is known as a \"balanced strength design\". Recess Action Gears I n Chapter 4, we defined the angles of approach and recess as the angles through which the driving gear turns, during the periods when the contact point is approaching towards, and receding from, the pitch point. It is found in practice that the performance of a gear pair is smoother during the recess part of the meshing cycle than during the approach. We proved in Chapter 3 that the sliding velocity 164 Profile Shift between the meshing teeth changes sign as the contact point passes through the pitch point. The change in the direction of the sliding velocity causes the friction force to change direction, and this is responsible for the smoother operation of the gear pair during the recess phase of the meshing cycle. When one gear is always the driver, and the other is always driven, it is possible to design a gear pair to take advantage of the smoother recess action. The gear pair is designed so that most, or even all, of the path of contact lies on the recess side of the pitch point. This can be done by increasing the tooth thickness of the driving gear, and reducing that of the driven. If the recess side of the contact path is significantly longer than the approach side, the gear pair is said to have partial recess action. If the entire contact path lies on the recess side, the gear pair has recess action only. An example of each type of gear pair is shown in Figures 6.4 and 6.5. Profile Shift 165 Contact Ratio and Root Circle Clearance In the three previous sections, we showed how the design of a gear pair can often be improved by the use of unequal tooth thickness design. There are, however, two aspects of gear pair design which cannot be improved by this type of modi fication. When gear pairs are designed according to the procedure described earlier, it is very unusual for the contact ratio to be less than the recommended minimum of 1.4. This is because the gear pairs always have a working depth of 2.0m, and this generally ensures an adaquate contact ratio. In the rare cases where the contact ratio in the initial design is too low, it is possible to increase its value by reducing the tooth thickness of the pinion and increasing that of the gear. However, this solution to the problem is normally impractical, since it involves weakening the teeth of the pinion, which are already weaker than those of the gear. A better solution is to try a completely different design, in which the module is reduced and the number of teeth in each gear is increased. In some designs, the clearances at the root circles may be inadaquate. It will be found that, for gears cut by a rack cutter or a hob, the value of atp has absolutely no effect on the size of the clearances, so if they are too small in the ini tial design, they will not be improved by any choice of ~tp. A rack cutter with an addendum of 1.25m would give clearances of O.25m in a gear pair meshing with zero backlash at the standard center distance Cs \u2022 When the gear pair is designed with a normal amount of backlash, the teeth of each gear are cut slightly deeper, and the clearances are of course increased. If the same cutter is used to cut a gear pair for a center distance C which is greater than the standard center distance, and the tooth thicknesses are chosen so that the backlash is unchanged, the clearances become smaller for larger values of C. Hence, inadaquate clearances are an indication that the the value of (C-Cs ) is too large. This is the reason why there is a lower limit for the value of Cs ' and in the next section we will show how the expression given in Equation (6.14) was derived. 166 Profile Shift"
        ]
    },
    {
        "image_filename": "designv10_4_0003997_3-540-27969-5-Figure8.8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003997_3-540-27969-5-Figure8.8-1.png",
        "caption": "Fig. 8.8. (a) Original MANET; (b) Planarized MANET; (c) Right-hand routing",
        "texts": [
            " These dead ends happen in those situations in which a tuple arrives at a node, but then does not find any neighbor closer to the intended destination. In such cases, the tuple should stop acting greedily, travel a bit backward (thus getting farther from the destination) and look for alternative paths (see Fig. 8.7). To overcome this problem, the solution mainly adopted [18, 75, 81] is to move past the local minima by applying a graph traversing algorithm, to the planar graph [42] obtained by locally pruning links in the network. The idea is the one depicted, in more detail, in Fig. 8.8 and described in the following: 1. Tuples start propagating following plain Euclidean considerations. However, when a tuple finds itself at a minimum of the coordinate system, it switches to a, let us call it, \u201ccircumnavigate\u201d propagation mode. 2. Since most graph traversing algorithms works only in planar graphs, the first thing a tuple has to do is to prune (i.e., avoid using) some of the network links in the host node neighborhood. This can be easily done by enforcing a planarization algorithm as proposed in [18, 75]. This locally transform the MANET in a planar network, and logically divides the network into a set of adjacent \u201cfaces.\u201d 3. Suppose now that the tuple wants to travel from a vertex s to a vertex t of the network in Fig. 8.8(c). First it needs to calculate the line segment st joining s to t. Then it navigates across the face crossed by st. The tuple can navigate across a face, provided with only local information, by always choosing the leftmost link from the direction from which it comes (right-hand rule [18, 75, 81]). 8.3 TOTA Implementation Details 171 4. The above step is repeated either until no other faces, crossing st, can be found or until the tuple can revert to the Euclidean routing propagation (this propagation mode is only intended for escape from a dead end). 5. In the end, once the tuple reaches the last face (F3 in Fig. 8.8), it routes to the node of that face closest to t. Further details on this algorithm are in [18, 75, 81]. It is worth noting that, in this implementation, the route to the destination is computed dynamically as the tuple travels across the network. In fact, the route derives actually from the hop-by-hop execution of the tuples\u2019 propagation algorithm. This implies that if, during propagation, the underlying coordinate system changes, then the tuple takes into account such a new coordinate system on the fly (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003785_s11431-008-0219-1-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003785_s11431-008-0219-1-Figure6-1.png",
        "caption": "Figure 6 The Carricato mechanism.",
        "texts": [
            " The whole mechanism can be considered as having twelve kinematic joints and eleven links including the frame, i.e., n=11 and g=12. Using the modified G-K criterion, we have ( ) 1 ( 1) 6 11 12 1 12 3 3. g i i M d n g f \u03bd = = \u2212 \u2212 + + = \u2212 \u2212 + + = \u2211 (23) Since eqs. (21) and (22) are invariable at any possible displacement in the coordinate system O-xyz, the numbers of the common constraints and redundant constraints are invariable as well. Therefore, the mobility is not instantaneous. The Carricato mechanism[48] is shown in Figure 6. Its moving platform is linked to the frame by three identical PRPR limbs and a 6-DOF UPUR leg. The complex mechanism is the combination of a serial chain and a parallel mechanism. The parallel one has four limbs as mentioned above. The serial one is a single-pair chain with a revolute pair connecting the end-effector. The three axes of frame O-xyz are parallel to three slideways in the base, respectively. The limb, where the axis of the uppermost revolute pair is coincident with x-axis, is taken to analyze firstly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003700_rnc.1397-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003700_rnc.1397-Figure3-1.png",
        "caption": "Figure 3. Regularization of three-sliding quasi-continuous car control: (a) car; (b) car trajectory; (c) steering-angle derivative; and (d) steering angle.",
        "texts": [
            " After the integration step was changed to 10\u22126, the accuracy of the nested controller changed to | | 2\u00d710\u221215, |\u0307| 4\u00d710\u221210, |\u0308| 1\u00d710\u22124, which corresponds to the classical 3-sliding accuracy. The parametric adjustment is demonstrated for the quasi-continuous controller (Figure 2). It is seen that with =0.5 the transient is two times longer, whereas with =2 it is two times shorter. In the latter case, with respect to (14); hence, was changed to the value 23\u00d75=40. Consider the kinematical car model (Figure 3(a)) x\u0307=v cos , y\u0307=v sin , \u0307= v l tan , \u0307=u Here, x and y are Cartesian coordinates of the rear-axle middle point, is the orientation angle, v is the longitudinal velocity, l is the length between the two axles and is the steering angle, u is the control. The task is to steer the car from a given initial position to the trajectory y=g(x), while g(x) and y are measured in real time. Define = y\u2212g(x). Let v=const=10m/s, l=5m,g(x)= 10sin(0.05x)+5, x= y= = =0 at t=0. Copyright q 2008 John Wiley & Sons, Ltd",
            "5 [\u0308+2(|\u0307|+| |2/3)\u22121/2(\u0307+| |2/3sign )]/[|\u0308|+2(|\u0307|)+| |2/3)1/2] =min[1, (| |+|\u0307|+|\u0308|)2] Copyright q 2008 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2009; 19:1657\u20131672 DOI: 10.1002/rnc Only the control gain is to be chosen here and is taken as 0.5. The resulting controller is continuous, since (0)=0, but exactly keeping =0 is lost. The values of , \u0307, \u0308 were replaced by their estimations obtained by the differentiator [8], taken exactly as in [9]. The control was applied from the moment t=1. The resulting performance is shown in Figure 3. Obviously, the chattering was removed. The accuracies | | 0.21, |\u0307| 0.32, |\u0308| 0.97 were obtained. The performance did not change, when noises were introduced in the measurements of not exceeding 0.1m in the absolute value. Frequency properties of the noises did not show any significance. This paper is summarized as follows. The controller parameters can be easily adjusted providing for the desired convergence rate. The discontinuity magnitude can change with respect to the uncertainty bounds, and it can even vanish in a small vicinity of the goal mode without significant accuracy loss"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003579_s0022112007005563-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003579_s0022112007005563-Figure2-1.png",
        "caption": "Figure 2. Sketch of the soap-film tunnel.",
        "texts": [
            " In our experiments, the flow speed is always smaller than the wave traverse speed of the soap film and therefore the flow can be considered to be two-dimensional and incompressible. The experiments were conducted in a soap-film tunnel developed in our lab, which is similar to the apparatus used by Zhang et al. (2000). A detailed description of the vertical soap-film apparatus can be found in Rutgers, Wu & Daniel (2001). A sketch of the soap-film tunnel used in our experiments is illustrated in figure 2. The set-up is 2 m in height with a test section of 90 mm in width. An upper reservoir contains the soap solution maintained at a fixed pressure head. A stopcock is used to control flux. Two nylon fishing threads with diameter 1.5 mm are supported by the frame, connecting the upper reservoir and the lower one. The lower reservoir collects soap solution for recycling. A pump is used to return the solution to the upper reservoir. The soap film is driven by gravity. As the solution flows through the stopcock to the injection point at the top of the tunnel, the soap film accelerates, but soon slows down due to air resistance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure2.36-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure2.36-1.png",
        "caption": "Fig. 2.36 Antikythera mechanism. a Mechanical gear assembly constructed from the remains. b M. Wright\u2019s reconstruction (Paz et al. 2010)",
        "texts": [
            " (Pan and Wang 2005). Mechanical timers did not appear until the 14th century. Ancient humans began making astronomical instruments very early, such as the celestial globe and the armillary sphere. Some of them also had the function of timer. This book does not intend to explain the detail of all ancient astronomical instruments, which requires a fully understanding of the astronomical perspective of the time. Instead we briefly introduce several of the most representatives as a clue for further reading. Figure 2.36 shows the remains of an ancient bronze instrument, the so-called \u201cAntikythera mechanism\u201d found in a sunken wreck off the Antikythera island in Greece (Williams 2003). Research on the mechanism indicated that the instrument was made around 87 BC (according to a more recent view, in 205 BC). The discovery has inspired wide curiosity among scholars on history of science and technology. Many of them devoted great effort to study this mechanism. A paper on the journal Nature concluded that it was a solar system instrument for predicting the position of celestial bodies (Freeth et al",
            " The Arabian scholars displayed an interest in creating human-like machines for practical purposes but lacked real impetus to pursue their robotic science (Rosheim 1994). The rope drive was the earliest transmission humans ever used. It could be seen in bow drills (Fig. 2.54), spinners and water-driven blowers (Fig. 2.26). In the 1950s, archaeologists in China found an iron ratchet gear of the 3rd century BC to the 1st century AD, a bronze ratchet gear and metal gears of the 3rd century BC, and herringbone gears (Fig. 2.46) of the 1st century (Needham 1987a). The gear trains in the Antikythera mechanism (Fig. 2.36) and in the south pointing chariot (Fig. 2.31) were very complicated. The worm drive was an evolution from the screw, one of the ancient simple machines. Although It is not clear who invented the worm drive, humans noticed the unique features of worm drives very early, such as the large reduction ratio, the force amplification, and self-locking. At first, the rudder of a sailboat was driven with rope wound on a drum. Steering of the sailboat needed a few boatmen to pull 2.2 Various Ancient Machines 47 the rope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000762_j.precisioneng.2021.01.002-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000762_j.precisioneng.2021.01.002-Figure2-1.png",
        "caption": "Fig. 2. Position of replicas on the build platform (in red). The z-axis indicates the building direction, and the black arrow shows the rake movement. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)",
        "texts": [
            " From here, therefore, two series of surfaces are identified: internal and external. Internal surfaces are numbered identically to the corresponding external ones. The analysis of internal surfaces is aimed at characterising surface roughness of the cavities of the component in which sintered powder is encapsulated. The production of the artefact was performed using an Arcam A2X system and standard Ti6Al4V Grade 5 Arcam powder with the particle size that ranges from 45 to 150 \u03bcm [51]. The layer thickness was set equal to 50 \u03bcm. Fig. 2 shows the arrangement of eight replicas of the artefact on the build platform and the raking direction. The surfaces of the artefact were placed perpendicularly to the rake movement. Each replica was identified by a letter and a number that identify the row and column where the replica was positioned, respectively. The job was processed using EBM build processor 5.0 and the standard Ti6Al4V Arcam theme for A2X system. According to that, the contour of the cross-section of the part was melted adopting the MultiBeam\u2122 strategy, and the inner part using standard hatching strategy",
            " The theoretical limits of the acceptable interval at a confidence level of 95% are 5.01 and 24.74. Since both experimental values are within limits, it is possible to affirm, with a risk level of 5% that the collected data are normally distributed, and no systematic errors can be detected. A descriptive statistical analysis was adopted to verify that the position of the replica had no systematic effect on the surface roughness. Fig. 3 shows the box plot for the surface roughness values grouped according to the build position (Fig. 2). Since the variance of the roughness of the replicas overlaps each other, the produced artefacts can be considered statistically equivalent. The asterisks in Fig. 3 indicate the outliers of the measurements. Several analyses of variance (ANOVAs) were conducted to evaluate the effect of the slope, the orientation and the presence of a closed zone on surface roughness. The statistical questions were the following: \u2212 Does the sloping angle affect the surface roughness? \u2212 Is there any difference between the upskin and downskin surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure7.1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure7.1-1.png",
        "caption": "Figure 7.1. The end points of single-tooth contact.",
        "texts": [
            " Chapter 7 Miscellaneous Circles The specification of a gear includes the diameters of a number of circles, such as the standard pitch circle and the tip circle. In addition to these circles, there are several others whose sizes must be determined by the designer, in order to check that the design will perform satisfactorily. We have already discussed the limit circle and the fillet circle of a gear. In this chapter we will introduce some other circles which are frequently needed, and we will show how their radii can be calculated. Highest and Lowest Points of Single-Tooth Contact A typical meshing diagram is shown in Figure 7.1. The ends of the path of contact are labelled T1 and T2 , and these lie between the interference points E1 and E2 , as they must in any properly designed gear pair. We define two additional points Q and Q' on the path of contact, where Q lies a distance Pb below T l' and Q' lies a distance Pb above T2\u2022 We stated in Chapter 4 that, when there are two pairs of teeth simultaneously in contact, the distance between these contact points is equal to the base pitch Pb' We can see from Figure 7.1 that, whenever there is a contact point between T2 and Q, there must simultaneously be a second contact point between Q' and T1. However, when a contact point lies between Q and Q' , this is the only contact point. The total contact force must remain constant, if there is to be a uniform transmission of power. It is clear, therefore, that the contact force is roughly halved, when it is shared between two pairs of teeth in contact. Figure 7.2 Highest and Lowest Points of Single-Tooth Contact 175 shows how the contact force acting on one tooth depends on the position of the contact point, as it moves along the path of contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003307_1.2791809-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003307_1.2791809-Figure3-1.png",
        "caption": "Fig. 3 A coupled system",
        "texts": [
            ", t -= [t~ r . . . . . t,r] r and w ~- [w r . . . . . w,r] r (3) where t~ and w~, for i = 1 . . . . . n, are defined in Eq. (1). and M: the 6n x 6n matrices of generalized angular velocity and mass, respectively, namely, -= diag [ ~ , . . . . . 1~,] and M =- diag [M~ . . . . . M,,] (4) where ~ i and M~, for i = 1 . . . . . n, are given in Eq. (2). //: the n-dimensional independent vector of joint rates, i.e., O ~- [0 , . . . . . 0 , ] ~ (5) where 0~ is the displacement of the ith joint, as shown in Fig. 3. 3 Dynamic Model ing Using the DeNOC For a serial-chain mechanical system shown in Fig. l, the steps to obtain the dynamic equations of motion using the DeNOC matrices are given below: 1 Derivation of the Unconstrained Newton-Euler (NE) Equations of Motion: (a) From the free-body diagram of the ith rigid body, Fig. 2, write the Newton-Euler equations of motion as Iigo i -I- 0.) i X I io0 i = n i (6a) mi~ri : f i (6b) where ni and f~ are the resultant moment about and force applied at the mass center, C~, respectively",
            " Derivation of Kinematic Constraints: 3, can be expressed as to i = oJj + 0iei (1 la) vi = vj + ooj x rj + oJ~ x d i . (1 lb) The above six scalar equations are written in a compact form as ti = B0t j + Pi0i (12) where the 6 X 6 matrix, B~j, and the six-dimensional vector, p~, are as follows: Bu -= c o \u00d7 1 and Pi ~- e i N d i % \u00d7 1 being the cross-product tensor associated with vector c u , defined similar to tos \u00d7 1 of Eq. (2), i.e., (% \u00d7 1)x ~ % \u00d7 x, for any arbitrary three-dimensional Cartesian vector x. The vector, % , as shown in Fig. 3, is given by, % --= -d~ - rj. It is interesting to note here that the matrix, B~j, and the vector, p~, have the following interpretations: \u2022 For two rigidly connected moving bodies, #i and #j, B 0 , propagates the twist of #j to #i. Hence, matrix B u is termed here as the twist propagation matrix, which has the following properties: BuBjk=B~k, B , = 1, and B~ 1 = Bji. (14) Matrix B~j is nothing but the state transition matrix of Rodriguez (1987). \u2022 Vector, pi, on the other hand, takes into account the motion of the ith joint. Hence, p~ is termed as the joint-rate propagation vector, which is dependent on the type of joint. For example, the expression of p~ in Eq. (13) is for a revolute joint shown in Fig. 3, whereas for a prismatic joint vector p~ is given by pi--- [e0] : for a prismatic joint (15) where e~ is the unit vector parallel to the axis of linear motion. Correspondingly, 0~ of Eq. (12) would mean the linear joint rate. Other joints are not treated here because any other joint, e.g., spherical or screw, can be treated as combination of revolute or revolute and prismatic pairs, respectively. 988 / Vol. 66, DECEMBER 1999 Transactions of the ASME Downloaded From: http://appliedmechanics.asmedigitalcollection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003537_tro.2006.870649-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003537_tro.2006.870649-Figure5-1.png",
        "caption": "Fig. 5. Projection of the GZMP.",
        "texts": [
            " We first introduce a vector ~pG(= [~xG ~yG ~zG] T ), and consider the change of coordinates between pG and ~pG defined by _LGy M +xG( zG + g) (zG zE) xG=~xG( ~zG + g) (~zG zE) ~xG (16) _LGx M + yG( zG + g) (zG zE) yG=~yG( ~zG + g) (~zG zE) ~yG (17) ~zG = zG: (18) Applying the change of coordinates to (6) and (7), the position of the GZMP can be defined as follows: xE = ~xG( ~zG + g) (~zG zE) ~xG ~zG + g (19) yE = ~yG( ~zG + g) (~~zG zE) ~yG ~zG + g : (20) Note that (19) and (20) are the same as those of an inverted pendulum. The following proposition can be held for the projection of the GZMP included in a virtual plane onto the real floor (Fig. 5). Proposition 3 (Projection of GZMP): Draw a line including both ~pG(zE = zG) and the GZMP on the virtual floor. The intersection of the line and the real floor corresponds to the GZMP on the real floor. Proof: In (19) and (20), the GZMP is concentrated on a single point ~pG(zE = zG) = xG _L (M( z +g)) yG + _L (M( z +g)) zG (21) when zE = ~zG. Moreover, (19) and (20) are linear equations with respect to pE . Therefore, since all points on the line including both ~pG(zE = zG) and the GZMP on the virtual floor can be the GZMP, we confirm the theorem is correct"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000094_j.jmapro.2020.03.018-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000094_j.jmapro.2020.03.018-Figure11-1.png",
        "caption": "Fig. 11. The molten pool in the (a) vertical-down and (b) vertical-up deposition.",
        "texts": [
            " properly determined WFS does improve the surface evenness, but higher deposition rates are a prominent advantage of wire-feed additive manufacture, and because the surface appearance is of less concern if a post-machining process is used, a lower surface quality and higher deposition rate may benefit the productivity of the process. The same process parameters were used to produce thin walls in the vertical-up and vertical-down direction, with the results presented in Table 3. It reveals that the bead geometry variation is similar to a horizontal deposition, as shown in Fig. 8. However, the maximum WFS of vertical welding is reduced to 3 m/min compared to 4 m/min in the horizontal welding. As shown in Fig. 11, the molten pool can be divided into the previous molten pool and the pending molten pool for both vertical deposition directions. In the vertical-down deposition, the previous molten metal flows downward slightly on the pending molten pool during the solidification process. On the other hand, in the vertical-up deposition, the pending molten pool flows downward on the previous molten metal. In both cases, a larger surface tension force f\u03b3 is required in a vertical deposition, which results in a limited operating range of WFS in the vertical deposition compared to the horizontal deposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure3.4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure3.4-1.png",
        "caption": "Figure 3.4. Contact at the pitch point.",
        "texts": [
            "17), we obtain an expression for 8R in terms of the quantities defined at the pitch circle, ~ + inv 4lp - inv 4lR 2Rp Relation Between the Pinion and Rack positions (3.18) In order to obtain a general relation between the posi tions of the pinion and the rack, we consider them initially when the ~ontact point lies exactly at the pitch point, and we then determine a relation between the 60 Gears in Mesh displacements from this position. We proved in Chapter 1 that, at some moment during the meshing cycle, the contact point must coincide with the pitch point, and in Figure 3.4 we show the pinion and rack with the contact point in this position. As before, the x axis in the pinion and the xr axis in the rack each coincide with a tooth center-line, and the fixed ~ and ~ axes have their origin at the pitch point. The angular position of the pinion is specified by the angle fi, measured from line CP counterclockwise to the x axis, and the position of the rack is indicated by the distance ur of the xr axis above the ~ axis. The positions of the pinion and the rack in Figure 3.4 are as follows, fi -~ (3.19) 2Rp 1 (3.20) ur 2\"tpr where tp and tpr are the tooth thicknesses, measured on the pinion pitch circle and the rack pitch line. After the pinion has rotated an angle Ilfi from this position, and the rack has displaced a distance Ilu r , the new positions are given by the following two expressions, fi (3.21) position of the Contact Point 61 (3.22) The plnlon rotation ~$ and the rack displacement ~ur are of course related, and to find this relation we start from Equation (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000240_j.apm.2020.11.003-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000240_j.apm.2020.11.003-Figure3-1.png",
        "caption": "Fig. 3. Symbols used in Eq. (10) .",
        "texts": [
            " Further, for a certain gear pair i , the total elastic deformation D i can be calculated by: D i = \u03b4pi + \u03b4gi + \u03b4hi = \u03b4p ti + \u03b4p f i + \u03b4g ti + \u03b4g f i + \u03b4hi = F i (q p ti + q p f i + q g ti + q g f i + q h ) (9) where \u03b4p,gi is the elastic deformation of the pinion and gear, respectively; \u03b4p , g ti is the elastic deformation of the tooth part of the pinion and gear, respectively; \u03b4p , g fi is the elastic deformation of the gear body of the pinion and gear, respectively; \u03b4hi is the Hertzian contact deformation of the gear pair; F i is the meshing force of the gear pair; q p , g ti is the flexibility of the tooth part of the pinion and gear, respectively; q p , g fi is the local gear body-induced tooth flexibility of pinion and gear, respectively. To calculate the local gear body-induced tooth flexibility, the following analytical formula presented in [7] was used: q p,g f i = 1 E 1 b cos 2 \u03b1m [ L \u2217(\u03b5, \u03b8 f ) ( u f S f )2 + M \u2217(\u03b5, \u03b8 f ) u f S f + P \u2217(\u03b5, \u03b8 f ) \u00d7 [ 1 + Q \u2217(\u03b5, \u03b8 f ) t g 2 \u03b1m ]] (10) where \u03b5 = r f /r int (see in Fig. 3 ); L \u2217, M \u2217, P \u2217, Q \u2217 are coefficients depending on \u03b5 and \u03b8 f , and one can find more details in [7] . The deformation compatibility condition [12 , 13] is another important concept applied in the FGB model, which means the base pitches of two tooth pair that in simultaneously contact should be equal (see Fig. 4 ). According to Fig. 4 , one can establish the following equations: { P \u2032 b = P b + e p1 \u2212 e p2 + \u03b4g1 \u2212 \u03b4g2 P \u2032 b = P b \u2212 e g1 + e g2 \u2212 \u03b4p1 + \u03b4p2 (11) where e pi (i = 1, 2) is the tooth profile error of tooth pair 1 and 2 of the pinion, respectively; e gi (i = 1, 2) is the tooth profile error of tooth pair 1 and 2 of the gear, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003384_rspa.2004.1371-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003384_rspa.2004.1371-Figure11-1.png",
        "caption": "Figure 11. Schematic of set-up and geometry when the packing force is applied at a distance b from the centre of the frame.",
        "texts": [
            "58 but this solution is inadmissible because the total angular sector over which the sheet is in contact with the cylinder is (2\u03c0 \u2212 3 \u00d7 2sc) < 0. This conclusion is also qualitatively consistent with our observations. (iv) Determination of the phase and position of a fold We now consider the azimuthal location of the fold. If the sheet is pushed axisymmetrically at the centre of the frame, the position of the fold is undetermined and s0 is unknown. This symmetry is broken if the force is applied at a distance b from the centre, as shown in figure 11. Then the angle \u03b1 that the generators make with the horizontal plane must satisfy the inequality \u03b1 \u03b5(\u03b8), (4.43) where \u03b5(\u03b8) = d/ (\u03b8), with (\u03b8) = \u2212b cos \u03b8 + (R2 \u2212 b2 sin2 \u03b8)1/2 being the distance from the point of application of the force to the cylindrical frame and the angle \u03b8 as measured in figure 11. In terms of the two dimensionless parameters, \u03b5 = d/R and \u03b4 = b/R, we can write \u03b5(\u03b8) = \u03b5 \u2212\u03b4 cos \u03b8 + (1 \u2212 \u03b42 sin2 \u03b8)1/2 . (4.44) Since the relations (4.30), (4.31) remain valid in this regime, the shape of the sheet in the free region can be written as \u03b1 = A cos a(s \u2212 s0) + B cos(s \u2212 s0) + C sin a(s \u2212 s0) + D sin(s \u2212 s0). (4.45) However, the continuity conditions at the point of contact with the frame are now different from the earlier case where the sheet is pushed symmetrically. To leading order, s \u2248 \u03b8, so that continuity of the deflection \u03b1(s) and its derivative Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003644_j.euromechsol.2004.12.003-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003644_j.euromechsol.2004.12.003-Figure2-1.png",
        "caption": "Fig. 2. Elementary open kinematic chain associated with the leg A (0A \u2261 1A-2A-3A-4A-5A) of parallel Cartesian robotic manipulator and the notations used in the kinematic constraint equations: (a) kinematic chain; (b) associated graph.",
        "texts": [
            " We denote by d1X and d\u03071X (X = A,B,C) the finite displacements and the velocities of the actuated prismatic joints and by \u03d5iX and \u03d5\u0307iX (i = 2,3,4 and X = A,B,C) the finite displacements and the angular velocities of the passive joints. We note that all revolute joints are passive joints. The closure equations of the parallel Cartesian robotic manipulator presented in Fig. 1 can be established by the condition that the linear (0vH ) and angular (0\u03c9H ) velocity of point H situated on the mobile platform (expressed in the reference system O0x0y0z0 \u2013 see Fig. 2) must be the same in the three legs (H \u2261 HA \u2261 HB \u2261 HC):[ 0vHA 0\u03c9HA ] = [ 0vHB 0\u03c9HB ] = [ 0vHC 0\u03c9HC ] , (7) or [ 0vHA 0\u03c9HA ] \u2212 [ 0vHB 0\u03c9HB ] = [0] (8) and [ 0vHA 0\u03c9HA ] \u2212 [ 0vHC 0\u03c9HC ] = [0]. (9) Eqs. (8) and (9) represents the closure equations of the closed loops 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b7 -2B -1B \u2261 0 and 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 -2C -1C \u2261 0. These loops can be considered as two independent closed loops of the Cartesian robotic manipulator, presented in Fig. 1. By calculating the velocity of point H in the three legs of the parallel robotic manipulator Eqs. (8) and (9) lead to the following sets of linear equations: [A ] [ d\u0307 \u03d5\u0307 \u03d5\u0307 \u03d5\u0307 d\u0307 \u03d5\u0307 \u03d5\u0307 \u03d5\u0307 ]T = [0] , (10) 1 6\u00d78 1A 2A 3A 4A 1B 2B 3B 4B 8\u00d71 [A2]6\u00d78 [ d\u03071A \u03d5\u03072A \u03d5\u03073A \u03d5\u03074A d\u03071C \u03d5\u03072C \u03d5\u03073C \u03d5\u03074C ]T = [0]8\u00d71, (11) [A]12\u00d712 [ d\u03071A \u03d5\u03072A \u03d5\u03073A \u03d5\u03074A d\u03071B \u03d5\u03072B \u03d5\u03073B \u03d5\u03074B d\u03071C \u03d5\u03072C \u03d5\u03073C \u03d5\u03074C ]T = [0]12\u00d71. (12) Fig. 2 presents the notations associated with the leg A. Similar notations are used for the legs B and C. The expressions of the matrices [A1]6\u00d78, [A2]6\u00d78, [A]12\u00d712, are given in Appendix A. By symbolic calculation of the rank of these matrices with MAPLE\u00ae we obtain: r1 = rA\u2212B = rank(A1) = 5, r1 = rA\u2212C = rank(A2) = 5 and r = rA\u2212B\u2212C = rank(A) = 9. We can see that r = r1 + r2. This result indicates that the structurally independent closed loops 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5B - \u00b7 \u00b7 \u00b7 -2B -1B \u2261 0 and 0 \u2261 1A-2A- \u00b7 \u00b7 \u00b7 -5A \u2261 5C - \u00b7 \u00b7 \u00b7 \u2212 2C -1C \u2261 0 are not independent from a kinematic point of view"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure6.33-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure6.33-1.png",
        "caption": "Figure 6.33. (a) Young's double-slit experiment showing the effects of (b) source energy spread and (c) source size on the contrast of the interference images.",
        "texts": [
            " This assumption is a good approximation in practice because the energy spread of an electron source is no more than 1-2 e V. On the other hand, the emitted electrons have a range of energy spread and no perfect coherent source is available. Thus, significant details could be introduced by the partial coherence. We now use Young's double-slit experiment to show the effect of source coherence on lattice imaging. If the illumination source is a perfect coherent point source, the interference of the wave from the two slits is an ideal sinusoidal function (Fig. 6.33a). When the two slits are illuminated by a point source with finite energy spread, the contrast of the fringes would be reduced due to a relatively small shift in the interference pattern (Fig. 6.33b). If the source has a finite size, the slits are illuminated by a group of plane waves of different wave vectors (or incident beam directions), and the contrast of the observed interference fringes is also reduced owing to a relative shift in the fringes produced by the plane waves propagating along different directions. This simple double-slit experiment clearly illustrates the effect of source coherence on HRTEM imaging. In practice, the effect of source energy spread on imaging is negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003108_1.2893808-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003108_1.2893808-Figure4-1.png",
        "caption": "Fig. 4 The geometry of a bearing witli inner race defect",
        "texts": [
            " ZPQ M'ziOi'zj ZPr (39) (40) sin {r \u2014 m + 2)<f>, sin (r \u2014 m \u2014 2)<l>i r ~ m + 2 r \u2014 m ~ 2 (31) The frequency spectrum of the response from the outer race will have components at outer race defect frequency and its multiples, i.e., ZjOc and the ampHtude of these components will be: ' Zjw,MzjOilj \u2022 ^ 2Mi<a} X 6T{ZJ - i \u00b1 r ) (32) The response of the inner race due to the outer race defect will be much smaller in comparison to the response of the outer race and is, therefore, not considered in the present study. 4.2 Inner Race Defect. Figure 4 shows the geometry of a bearing with inner race defect. At (f> = lOct, the static deflec tion can be expressed as (Harris, 1966): S(MJ) = S^,,U - ( l /2e ) ( l - cos \u00a30,0] (33) The race deformation due to inner race defect can be ex pressed as: Si(o)J) = P cos m(cOc \u2014 (Os)t (34) Therefore, the total deformation of the race under a rolling element at angle cjj can be given by: S'{(oJ) =\u0302 Si{oJ)[l + P2 cos m(t<), - (o,)t] (35) w h e r e p2 = /S/S^ean The contact force at angle taj can be obtained as P,A(oJ) = P(io,t)[l + P2 cos m(w, - w,)f]\" (36) Substituting P{ci)j) from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003537_tro.2006.870649-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003537_tro.2006.870649-Figure3-1.png",
        "caption": "Fig. 3. Model of the system.",
        "texts": [
            " However, the research studies on manipulation by a humanoid robot are limited, except for [8] and [14]\u2013[17], though manipulation is necessary for a humanoid robot to work in a real environment. So far, there has been no research on the ZMP applicable for several types of manipulation tasks. Maintenance of Contact: Form closure and force closure are known indexes for a mechanical system to maintain a given motion without breaking contact. In robotics, both indexes have been mainly used to constrain an object grasped by a robotic hand [18]\u2013[20]. In the field of assembly, the stability of an object placed on a jig under gravity was studied [23]. Fig. 3 shows a model of the humanoid robot studied in this paper. We imposed the following assumptions: 1) we consider a humanoid robot standing/walking on a flat floor, where at least one of the hands contacts the environment; 2) the hand does not grasp, but simply touches, the environment; 3) the friction forces at all contact points of the robot are small enough. Assumption 3 is imposed because if the internal force exists under the frictional contacts, it becomes difficult to determine the internal force uniquely for a given motion of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure17.16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure17.16-1.png",
        "caption": "Figure 17.16. The ideal load curve.",
        "texts": [
            " They have therefore been recalculated [11], using essentially the original method, and they can be represented by the following expression, (17.61) The angle v must be expressed in degrees, as indicated by the notation, and the equation is valid for values of v between 0\u00b0 and 25\u00b0. In order to calculate the value of Ch required for a particular helical gear, we must choose the value of v to be used in Equation (17.61). On the helical gear, the generator inclination angle vR varies with the radius R. Hence, the load on the plate in Figure 17.15 should really lie along a curve, as shown in Figure 17.16, instead of a straight line. However, the bending-_moment intensity at A is determined primarily by the load in the immediate vicinity of point Aw' so it is sufficiently accurate to represent the load curve by a straight line at an angle v , where v is the generator w w inclination angle at point A \u2022 The value of v is given by w w Equation (13.87), in terms of the helix angle and the transverse profile angle of the helical gear at radius Rw' sin v w sin \"'w sin 9>tw (17.62) When this value of Vw is substituted into Equation (17"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000861_tia.2021.3064779-Figure11-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000861_tia.2021.3064779-Figure11-1.png",
        "caption": "Fig. 11. 72-slot/8-pole water-cooled PMSIWM. (a) Structure diagram. (b) Stator with epoxy.",
        "texts": [
            " 10(b). The inflection point causes a hottest spot. In the motor design, the optimization of slots should avoid the size of lsb = 2.2 lt. In addition, when lt is beyond the inflection point, the temperature difference gradually reduces. As the increase of lt reduces lsb, the slots with short slot bottom have advantages on the slot heat dissipation. A water-cooled PMSIWM is designed based on the aforementioned optimization methods. According to the optimization methods, the final scheme is obtained. Fig. 11 shows the motor, including the axial water jacket, vacuum impregnation with epoxy, slender slots. The structure of the axial water is shown in Fig. 1. The main parameters of the water-cooled PMSIWM are shown in Table II. As stated in Section II, the water jacket designers should avoid the size of the inflection point first. Then, the impact of water jacket shapes should be considered. For the PMSIWM, the water jackets are designed based on the method in Section II. In order to avoid the inflection point in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.15-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.15-1.png",
        "caption": "Figure 13.15. Transverse section through point A.",
        "texts": [
            "52) The third unit vector n~ of the of the orthogonal set is found simply by forming the vector product (n~ x n~) , Equations (13.50, 13.52 and 13.53) give the directions of the three unit vectors n~, n~, and n~, defined on the gear helix at a typical point A of the tooth surface. The lines through A in these three directions are known as the tangent, the principal normal and the binormal to the helix at A. Tooth Surface of a Helical Involute Gear 329 Transverse Profile Angle at Radius R The transverse profile angle of a helical gear is defined in exactly the same manner as the profile angle of a spur gear. Figure 13.15 shows the tooth profile in a transverse section, and the point where it intersects the cylinder of radius R is labelled A. The transverse profile angle at radius R is defined as the angle between CA and the profile tangent at A, as shown in Figure 13.15, and it is represented by the symbol ~tR' Since line CE is parallel to the profile tangent at A, the angle ECA is also equal to ~tR' Two relations can now be read from Figure 13.15, each of them equivalent to the corresponding relations for spur gears. cos ~tR Rb R EA Rb tan ~tR (13.54) (13.55) Since the tooth profile in the transverse section is an involute, we can make use of the involute property given by Equa t ion (2. 8) , arc EB EA (13.56) 330 Tooth Surface of a Helical Involute Gear The angle ECB can be found by combining Equations (13.55 and 13.56), angle ECB arc EB Rb tan I/l tR and angle ACB can then be read from Figure 13.15, angle ACB (13.57) (13.58) Lastly, Equation (13.54) can be combined with Equation (13.34) to give one of the fundamental equations relating the angles in a helical gear, Transverse Pressure Angle tan \"'b tan \"'R (13.59) The transverse profile angle at the standard pitch cylinder is called the transverse pressure angle I/lts of the gear. We can find its value from Equation (13.54), if we substitute Rs in place of R, (13.60) The Generator Through Point A 331 In Equation (13.15) we gave the base cylinder radius of the gear in terms of the standard pitch cylinder radius and the transverse pressure angle \"'tr of the basic rack, ( 13",
            " Coordinates of Point G For any point A of the tooth surface, there is a generator passing through the point, and this generator touches the base cylinder at some point G. Very often, we will want to find the position of G corresponding to a particular point A, and we can do this most conveniently by deriving expressions for the cylindrical coordinates (RG,eG,zG), in terms of the coordinates (R,eA,Z) of point A. Since G lies on the base cyl inder, the radi us RG is equal to the base cylinder radius Rb \u2022 And since G lies on the axial line through E, the angular coordinates of G and A differ by ~tR' as we can see from Figure 13.15. Finflly, length EA in Figure 13.18 is equal to (Rb tan ~tR)' as we stated in Equation (13.55), and the length GE is equal to EA divided by (tan ~b). Hence, the coordinates of point G are related to those of A in the following manner, eG eA - ~tR Properties of Point G Rb tan ~tR z - tan ~b ( 13.67) (13.68) (13.69) There are two important properties associated with point G, shown in Figure 13.18. First, point G lies on the Properties of Point G 335 gear helix through BO and B. And secondly, the generator GA is also the helix tangent at G",
            "70) This equation can be adapted to give the angular difference ~e between any pair of points on the same gear helix, when nei ther point lies in the plane z=O, (13.71) where ~z is the difference between the z coordinates of the two points. We now determine whether points G and B satisfy this equation. Since point E lies on the axial line through G, as shown in Figure 13.18, the difference between the e coordinates of B and G is equal to the angle between the radii through Band E. This is the angle ECB, shown in Figure 13.15, and its value is given by Equation (13.57). angle ECB tan qJtR (13.72) 336 Tooth Surface of a Helical Involute Gear Point B lies in the transverse plane z, and the axial distance between Band G can therefore be found from Equation (13.69), Rb tan 9>tR tan 1/Ib (13.73) It is evident that the coordinate differences given by Equations (13.72 and 13.73) satisfy Equation (13.71). We have therefore proved that the same helix passes through Band G, or in other words, that G lies on the gear helix through B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003821_robot.2005.1570405-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003821_robot.2005.1570405-Figure1-1.png",
        "caption": "Fig. 1. The Angular Momentum inducing inverted Pendulum Model (AMPM). The ZMP is allowed to move over the ground, and its position must be linearly dependent to that of the COM. The horizontal component of the ground force vector is allowed to change, by an amount which must be linearly dependent on the COM.",
        "texts": [
            " 1989 have applied the proposed method only to gait motion, the idea can be used for motions such as running and standing, as well. In this section, we review the Angular Momentum inducing inverted Pendulum Model (AMPM) [8]. The AMPM enhances the 3DLIPM in the following directions; (1) the ZMP is allowed to move over the ground, (2) the ground force vector is calculated to be not only parallel to the vector connecting the ZMP and the COM; its horizontal element can be linearly correlated to the ZMP-COM vector (Fig. 1). As a result, rotational moment will be generated by the ground force. Let us assume the position of the COM is (x,H), the position of the ZMP is (cx + d, 0), and the vector of the ground force is parallel to the vector (a(x \u2212 zmp) + b, g) where a, b, c, d are constant values and g is the gravity constant. As the height of the COM is assumed to have a constant value H , the relationship between the acceleration of the COM and its position can be written by: Fx : Fz = x\u0308 : (z\u0308 + g) = H g (a(x \u2212 (cx + d)) + b) : H"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003384_rspa.2004.1371-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003384_rspa.2004.1371-Figure6-1.png",
        "caption": "Figure 6. Schematic of a puckered cone. (a) An axial force at the centre of the plate makes it buckle into a conical shape with one fold. The normal forces K act along the line of contact between the cone and the cylindrical frame. (b) The angles \u03b8 and \u03b2 with respect to an Eulerian frame and the moving orthonormal trihedron {t, u, n} characterize the surface.",
        "texts": [
            " The three-dimensional analogue of packing a planar curve into a circle (or equivalently of packing a cylindrically deformed sheet into a slightly smaller cylinder as treated in the previous section) is the packing of a sheet into a sphere. However, the latter problem is far more difficult than one might first imagine owing to the strong constraints imposed by geometry and the contact conditions. Here we will consider the somewhat simpler situation of packing a sheet into an open cylindrical frame which can be achieved via a conically deformed shape much like a coffee filter paper as depicted in figure 6a, a geometry first studied nearly a century ago by Mallock (1908), who pointed out the importance of inextensible conical deformations. More recently (Cerda & Mahadevan 1998; Cerda et al . 1999) we showed that this geometry is amenable to analysis and experiment. Here, we revisit this problem and show that it is possible to reduce the fully nonlinear problem to quadratures allowing us to examine the solutions in some detail. (a) Geometry When a circular sheet of paper of radius Rp is pushed into a cylindrical frame of radius R by applying a centred transverse force directed along the axis of the cylinder, as shown in figure 6a, it responds by buckling out of the plane to form a non-axisymmetric conical surface that is only in partial contact with the frame. The effectiveness of packing is controlled by the axial distance d through which the tip is pushed into the frame, and defines a dimensionless packing parameter \u03b5 = d/R. Geometrically, the surface may be described by a family of generators originating at the centre of the sheet, with the angle \u03b2 between a generator and the vector e3 characterizing the normal to the plane of the supporting frame. When cot \u03b2c = \u03b5 (4.1) the generators are in contact with the frame and the shape of the sheet is a cone of opening angle \u03b2c.\u2020 Of course, this conical shape only describes part of the sheet, \u2020 In the following all the variables evaluated along the contact region will carry the subscript \u2018c\u2019. Proc. R. Soc. A (2005) since all the generators cannot satisfy (4.1) without violating the inextensibility condition. The non-axisymmetric conical shape shown in figure 6a is therefore a natural outcome of respecting the constraint of inextensibility almost everywhere, except in the vicinity of the tip. In addition to forming a simple system in which to study the packing problem of a sheet, this example thus affords the simplest example of stress, strain and energy localization occurring in the vicinity of a point, namely the centre of the sheet. The most general description of a conical shape is given by the parametrization r(s, r) = ru(s), (4.2) where r is the distance from the origin located at the tip, u(s) is a unit vector, and s is the arc length of the curve (see figure 6b) measured from the position of maximum elevation of the fold. The motion of u(s) describes a curve C in space. Since the total length of this curve surrounding the tip is invariant under inextensible deformations, a circular curve with initial length 2\u03c0 (at an initial radius r = 1) will not change its length. Therefore, the surface defined by the locus of the straight line ru(s) will be a developable surface. The metric tensor associated with this class of deformations has components gss = r2, gsr = 0 and grr = 1 and remains constant. To describe the surface, we use a moving orthonormal trihedron (equivalent to the repe\u0300re mobile of Cartan) t1 = t, t2 = u, n = t \u00d7 u. (4.3) Here t is the tangent vector to the curve C, and t and n are in a plane perpendicular to u. To parametrize the vectors t, u, n while emphasizing the correspondence with the packing problem treated in \u00a7 3, we use the vectors e\u03b8 and n\u03b8 = u \u00d7 e\u03b8, which span the plane containing t and n, as shown in figure 6, with \u03c6(s) being the angle between t and e\u03b8. Then t = cos \u03c6e\u03b8 + sin\u03c6n\u03b8, n = sin\u03c6e\u03b8 \u2212 cos \u03c6n\u03b8. } (4.4) Proc. R. Soc. A (2005) In terms of spherical coordinates we may write u as u(s) = sin\u03b2 cos \u03b8e1 + sin\u03b2 sin \u03b8e2 + cos \u03b2e3 = sin\u03b2e\u03c1 + cos \u03b2e3, (4.5) where e\u03c1 = cos \u03b8e1 + sin \u03b8e2 is the radius vector in the horizontal plane containing the cylindrical frame and \u03b2 = \u03b2(s) and \u03b8 = \u03b8(s). Differentiating (4.5) yields \u2202su = t = cos \u03b2\u03b2\u0307e\u03c1 + sin\u03b2\u03b8\u0307e\u03b8 \u2212 \u03b2\u0307 sin\u03b2e3 (4.6) in terms of the trihedron {e\u03c1,e\u03b8,e3}. Comparing the result with the first of relations (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000822_j.chemosphere.2021.130874-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000822_j.chemosphere.2021.130874-Figure5-1.png",
        "caption": "Figure 5. (A) Nyquist semicircle plots of various modified electrodes in the mixture of 5 mM 395 [Fe(CN)6] 3-/4-",
        "texts": [
            "1 M)/[Fe(CN)6 3\u2212/4\u2212 ] (5 mM) is used to study the electro-kinetics and the obtained 348 results are fit in best with the Randle circuit (Rs[Cdl-Rct-W]) where the solution resistance (Rs) is 349 continually connected with charge transfer resistance (Rct). The Warburg resistance (W) is 350 connected in parallel position to the double-layer capacitance (Cdl). The obtained diameter of the 351 semicircle in the Nyquist plot unravels the kinetics of charge transfer in the electrode-electrolyte 352 interface. Fig.5. (A) illustrates the EIS of bare GCE that exhibits a greater Rct value with a very 353 slow rate of electron transfer because of the low conductivity of GCE. However, after fabricating 354 the V2Se9 nanorods on GCE, the portion of Nyquist semicircle becomes smaller which might be 355 for the increase in conductivity of modified GCE that leads to an easy enhancement in the rate of 356 electron transfer and is an indication for lower impedance. Nevertheless, the bare GCE gave a Rct 357 value of 342",
            " Therefore, 364 V2Se9/rGO/GCE nanocomposite was suitable for further electrochemical experimentations and 365 the determination of 2,4,6-trichlorophenol (TCP). These results imply that the as per fabricated 366 electrode by V2Se9/rGO/GCE nanocomposite is highly conductive as it breaks the resistance 367 barrier between the oxidation probe and the GCE. 368 Jo urn al Prepro of To investigate the behavior of V2Se9/rGO on the modified GCE electrode, a different film 369 experiment is conducted for determining 2,4,6- trichlorophenol (TCP) using cyclic voltammetric 370 analysis. Fig.5. (B) illustrates the CV analysis performed in the ferricyanide solution. Briefly, the 371 conductance was measured for bare GCE and GCE modified with V2Se9, rGO, and V2Se9/rGO in 372 0.1 M of KCl, accompanied with 5mM of Fe(CN)6 3\u2212/4\u2212 , at 50 mV s -1 scan rate. The peaks 373 obtained for the different modified GCE electrodes in Fe(CN)6 3\u2212/4\u2212 are bare (Ipa: 170.3) < V2Se9 374 (Ipa: 205.6) < rGO (Ipa: 276.4) and < V2Se9/rGO nanocomposite (Ipa: 354.6). The enhancement in 375 the peak current is owed to the particle-particle interaction between V2Se9 and rGO and the 376 active surface area by an enrichment in the mechanism of the redox reaction of Fe(CN)6 3\u2212/4\u2212 . 377 Fig.5. (C) displays the scan rate attained for V2Se9/rGO/GCE nanocomposite from 0.2 V s -1 to 378 0.20 V s -1 in Fe(CN)6 3\u2212/4\u2212 environment. The corresponding plot displays the cathodic peak 379 current vs scan rate in Fig.5. (D) with linear regression assigned to Ipc & Ipa as Ipc y = 1.7852x + 380 218.73 and R 2 = 0.9918, whereas Ipa y = -2.0275x \u2013 205.29 with R 2 = 0.9909. When compared to 381 the other modified electrodes, the active surface area of V2Se9/rGO/GCE is high resulting from 382 CV analysis. The electroactive surface area (A) is calculated using the Randle-Sevcik equation: 383 Ip = 2.69 x 10 5 x ACn 3/2 D 1/2 \u03bd 1/2 ; 384 where Ip/ \u03bd 1/2 = slope of redox current versus the square root of potential scan rate, n = number of 385 electrons involved in the process, C = concentration of ferricyanide solution. Based on this 386 equation, the electroactive surface area of the nanocomposite modified GCE (V2Se9/rGO/GCE) 387 is calculated to be 0.124 cm 2 . Similarly, the active surface area for bare GCE (0.056 cm 2 ), V2Se9/ 388 GCE (0.072 cm 2 ), and rGO/GCE (0.107 cm 2 ) were calculated which were comparatively less 389 than that of V2Se9/rGO/GCE; and the results obtained were in accordance with the current peaks 390 obtained for each of the modified electrode as shown in Fig. 5(B). this variation in the calculated 391 Jo rna l P re- pro of results show the proportionality of the electrical conductance with the active surface area due to 392 more charge transfer. 393 and 0.1 M of KCl at \u00b1 5 mV amplitude with 0.01Hz-100kHz frequency range 396 (inset: Randel\u2019s equivalent circuit model). (B) CV plot of different modified electrodes in the 397 ferricyanide system companied with 5mM of Fe(CN)6 3\u2212/4\u2212 , at 50 mV s -1 scan rate. (C) The scan 398 rate of V2Se9/rGO/GCE nanocomposite from 0",
            " 588 Figure 3. TEM images of (A) rGO sheets, (B, C) V2Se9 nanorod, (D-F) V2Se9/rGO 589 nanocomposite, (G) SAED pattern, (H) EDX spectra with weight percentage of the elements in 590 the nanocomposite V2Se9/rGO, (I) pie chart representing percentage elemental composition in 591 the nanocomposite. 592 Figure 4. STEM images of (A) rGO sheets, (B) V2Se9 nanorod, (C, D) V2Se9/rGO 593 nanocomposite, (E) elemental composition (mix), (F) carbon (C), (G) oxygen (O), (H) vanadium 594 (V), and (I) selenium (Se). 595 Figure 5. (A) Nyquist semicircle plots of various modified electrodes (inset: Randel\u2019s equivalent 596 circuit model). (B) CV plot of different modified electrodes in the ferricyanide system (C) The 597 scan rate of V2Se9/rGO/GCE nanocomposite from 0.2 V s -1 to 0.20 V s -1 (D) calibration plot for 598 current vs the scan rate. 599 Jo urn al Pre- pro of Figure 6. (A) Different amounts of concentration of TCP spiked on to the V2Se9/rGO/GCE 600 electrode, (B) calibration plot for different addition of concentration vs peak current obtained, 601 (C) CV curves obtained for different scan rates to V2Se9/rGO/GCE of TCP in 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003291_pnas.94.25.13554-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003291_pnas.94.25.13554-Figure2-1.png",
        "caption": "FIG. 2. Bioelectrochemical reactor for the electrode-driven P450cam biocatalytic cycle. The reactor is modified from a 40-ml cylindrical glass vessel (6 cm high). Two tin oxide working electrodes with a total surface area of 16 cm2 were wrapped in Pt mesh (not shown) that had no electric contact and was at open circuit potential during electrolysis. At the point of minimum separation, the working electrodes were about 1 mm from the Pt grid counter electrode. The extent of Pt grid counter electrode submergence was varied to maximize electrochemical oxygen evolution without causing chlorine evolution, which is severely detrimental to activity. Details concerning operation of the reactor during electrolysis are given in the text.",
        "texts": [
            "4) and an initial protein concentration ratio of [CYPos]y[Pdxr] 5 0.1. A potential pulse was applied starting from open circuit to a final voltage 20.9 V, and absorbance at 455 nm was used to calculate kobs (see ref. 17). Comparable results were obtained from the exponential decay of the 392 nm absorbance (after subtracting the Pdx contribution at that wavelength) giving a pseudo-first order rate constant of 0.017 s21 for the conversion of CYPos to CYPrs. Bioelectrochemical Reactor Design and Operation. Fig. 2 is a schematic of the reactor used to generate the data shown in Fig. 3 corresponding to the 4.2 nmol productymin-nmol CYP101 turnover rate listed in Table 1. The bioreactor working solution volume in this design was about 20 ml and incorporated two tin oxide working electrodes (16 cm2 reaction surface). The large solution volume was needed to accommodate the combination oxygenytemperature electrode (Orion, no. 084010) used in some experiments. Other experiments were performed in a smaller reactor (1 ml solution volume), which retained the most important features of the larger reactor design: electrode surface areaysolution volume, Pt counter-electrode and Pt grid shielding of the working electrode, stir-bar mixing, solution purging, and head space gas handling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.17-1.png",
        "caption": "Figure 12.17. Displacement direction to avoid rubbing.",
        "texts": [
            " Moreover, during the cutting strokes, there may be many points of each cutter tooth profile making contact with the gear blank, instead of the single point that would be in contact once the gear reaches its final shape. In the discussion which follows, we will assume that the gear blank remains fixed, and the cutter is displaced away from the cutting zone. We will then calculate the direction required for the cutter displacement. If in fact the cutter remains fixed and the gear blank is displaced, the direction is obviously reversed. We consider first the trailing profile of one of the cutter teeth. Figure 12.17 shows the positions of the gear and the cutter, when the involute part of the cutter tooth profile is just starting to cut into the gear blank. In other words, point Ahc of the cutter tooth, the point on the trailing profile at the radius Rhc given by Equation (5.34), lies on the tip circle of the gear. The tangent to the cutter tooth at Ahc makes an angle a' with the line of centers, and the value of a' can be read f rom the diagram, Rubbing 293 a' (12.90) The cutter rotates as the tooth penetrates further into the gear blank, and the angles between the contact point tangents and the line of centers become smaller than a'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000944_j.rineng.2021.100201-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000944_j.rineng.2021.100201-Figure1-1.png",
        "caption": "Fig. 1. Rotary wing (a), Fixed wing (b), and hybrid (c) aircraft examples.",
        "texts": [
            " In Europe, unmanned aircraft systems over 150 kg are governed by the European Union Aviation Safety Agency (EASA) and they have the same certification requirements as any other manned aircraft [21]. In the UK, the Air Navigation Order (ANO) separates drones into 2 categories: (1) below 20 kg take-off mass, including batteries and fuel, and (2) between 20 and 150 kg take-off mass [20]. Legislation is more stringent on the heavier class of vehicles. In this paper we will investigate technologies and methodologies most applicable to aircraft below 20 kg take-off mass, due to their greater ubiquity for industrial inspection tasks. Fig. 1 shows the three main types of drone systems encountered. (a) Rotary wing (helicopter or multirotor) (b) fixed wing (conventional aeroplane), and (c) hybrid systems (c). Rotary wing vehicles have been adopted by industry faster than fixed wing [22,23]. The advantages of rotary wing vehicles over traditional fixed wing aircraft are that they can hover, the footprint required to operate is smaller, and the skills required to operate them are significantly reduced. On the other hand, fixed wing aircraft offer greater forward flying efficiency which translates to longer range and higher endurance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003508_robot.1995.525390-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003508_robot.1995.525390-Figure4-1.png",
        "caption": "Fig. 4 Problem of Ordinary Magnetic Wheel",
        "texts": [
            " Here we formed a magnet into an axle to which outer tires and magnetic inner wheels as shown in Fig. 2 are attached. Because we used the magnet as an axle rather than as the inner wheels, the magnet lasts much longer, and a powerful magnetic force is generated because of the closed magnetic circuit formed by the pipe. This dual magnetic wheel allows the robot to travel over bumps which are lower than half the diameter of the outer wheel as shown in Fig. 3. To be more specific, the subject of the ordinary magnetic wheel mechanisms are shown in Fig. 4. There are two suction forces at point A and B and the suction force at point A disturbes the robot to climb a sharp obstacle. It can be resolved because the inner wheel can climb even inside the locked outer tire in Fig. 3-1. Rust, which is a problem with orldinary magnetic wheels, is easily removed by wheel rotation when the outer tire moves away from the magnet. An ideal type to overcome Problem 3 is an autonomous robot that operates without an external power supply or communication cables. First, equipping the robot with a battery can eliminate the need for a power supply cable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000297_j.corsci.2020.108838-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000297_j.corsci.2020.108838-Figure2-1.png",
        "caption": "Fig. 2. Schematic illustration of one of the mounted samples for the electrochemical tests.",
        "texts": [
            " To eliminate this effect, all samples were chosen from the middle length of the bars. The backside of each mount was drilled up to the sample, and a wire was glued to establish the electrical connection required for the electrochemical test. Mounted samples were ground with SiC sandpapers, up to 1500 grit, then slightly polished with 0.05 \u03bcm alumina slurry, and washed ultrasonically with ethanol and dried using compressed air. To minimize the effect of crevice corrosion between sample and epoxy mount the circumference was coated as schematically shown in Fig. 2. The remained exposed area was 7mm in diameter. To ascertain the reproducibility of tests, eight identical samples from each group were prepared and examined. To minimize the influence of time between preparation and exposure of the sample on electrochemical measurements, all samples were kept in a desiccator for 24 h after preparation. One day after preparation, samples were immersed in a 0.5M NaCl neutral aqueous solution. A minimum of 40 cm3 of the test solution was considered for every exposing 1 cm2 area of the sample [34]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003119_rnc.4590040307-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003119_rnc.4590040307-Figure5-1.png",
        "caption": "Figure 5. (From Reference 15)",
        "texts": [
            " An extension of the results to a nonlinear system whose linearization possesses complex zeros is under investigation. APPENDIX: DYNAMICAL MODEL OF THE AIRCRAFP.~* Let the principal axes of an aircraft be the body axes (x, y , z). The orientation of the airplane body axes with respect to earth axes or inertial space, defined by rotations 4, $, 8 is shown in Figure 4. The orientation of wind axes, stability axes, and body axes and the conventions for linear velocities, angular velocities, and control surface deflections are shown in Figure 5 . The nomenclature is: stability axes body axes earth axes wind axes yaw angle, pitch angle, angle of bank (rad) angle of sideslip (rad) angle of attack (rad) aileron deflection angle (rad) rudder deflection angle (rad) 412 L. BENVENUTI, M. D. DI BENEDETTO AND J. W. GRIZZLE 6, elevator deflection angle (rad) I,, I,, Iz p , q, r u, u, w W weight of aircraft (kg) V g gravitational acceleration (m/s2) moments of inertia about principal axes (kg m2) angular velocity components along aircraft principal axes (rad/s) linear velocity components along aircraft principal axes velocity of aircraft centre of mass (m/s) The complete set of equations of motion of the rigid aircraft is given by: l5 ( W / g ) ( l i - r u + q w ) = X + T (W/g)(ir - p w + ru) = Y (W/g)(W + pu - qu) = 2 Ix$ + (I* - Iy)qr = L Iyq - ( I , - Ix)rp = M where (N, Y, 2) and (L, M, N ) are the components of force and moment due to aerodynamic and gravity effects, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.3-1.png",
        "caption": "Figure 2.3. A rigid bar rolling on a fixed cylinder.",
        "texts": [
            " The shape of the tooth profile must be such that the normal at the contact point touches the base circle. As the pinion rotates, the contact point moves along the pinion tooth, and therefore at each point of the profile the normal to the profile must touch the base circle. A curve with this property is known as an involute of the base circle, and this is the origin of the name \"involute gear\". Alternative Definition of the Involute There is another manner in which the involute can be defined. If the base circle is fixed, and a rigid bar AD rolls without slipping on the base circle, as shown in Figure 2.3, then the path followed by point A is an involute. It is easy to prove that the two definitions are equivalent. If point E is the contact point between the base circle and bar, then E is also the instantaneous center of the bar as it rolls. The 30 Tooth Profile of an Involute Gear velocity of point A is therefore perpendicular to EA. This means that the tangent to the involute at A is perpendicular to EA, and therefore the normal is along EA, which is the property by which the involute was originally defined. The Involute Function The alternative definition is useful in helping to derive some of the fundamental geometric equations of the involute. The point in Figure 2.3 where the involute curve meets the base circle is labelled B. This is the point where the end A of the bar would meet the base circle, if the bar rolled to the position where A was the contact point. Due to the fact that the bar rolls without slipping, we can say that the length of arc EB on the base circle must be equal to the length EA on the bar. In symbolic form, this can be written, arc EB EA (2.8) We now need to define a number of new symbols, and to derive the relations between them. Figure 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003077_0094-114x(95)00100-d-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003077_0094-114x(95)00100-d-Figure6-1.png",
        "caption": "Fig. 6. Screw pair.",
        "texts": [],
        "surrounding_texts": [
            "3D kinematics and dynamics--I 583\nThe potential energy Pk of the body k due to the gravitational effects is expressed by:\nPk = -- Trace (Hg(0) Jg(0)).\nKnowing the kinetic and potential energy of a body, it is quite easy to develop the dynamic equations of a system of rigid bodies using the Lagrangian approach. More details are given in Part II of this paper in relation to serial manipulators.\nany square matrix X or tensor X is defined as follows:\ns k e w [X] = X - X t.\nTensors \u2022 and F are skew-symmetric, therefore the equations (18) and (20) or vectorial equations (19) and (21) can be written as:\nq~k(0) = s k e w [Uo, k Jk(0)] (25)\nFk(O) = s k e w [W0, k Jk(0)]. (26)\nThe notation (25) and (26) stresses that each of the two expansions is equivalent to a linear system of 6 equations: in fact, both \u2022 and F have only six independent elements. For example, in the trivial case of the body rotating around a principal inertial axis, if equation (25) is expressed in matrix form with respect to a frame having the origin in the center of the mass and the axes parallel to the principal inertial axes of the body, the system will assume the well known form:\n(I~x + I.:)(by \"] ~ , = mfi\n([~x + I~,y)~: L.f: = m~\"\n5 . M A T R I X L\nThe matrix representing the instantaneous screw axis USA) of a body can be obtained from its velocity matrix W dividing it by the module of its angular velocity:\nW L ~ m ~\n0 --/dz Uy\nu. 0 -- u x\n- - Uy U x 0\n0 0 0\nb.v by b.\n0\ny\n-o- - 6 - -o- -6- 2+(.02. where Ital = x/og~ + COy If IoJI = 0, matrix L is defined as:\nW L-R--- .\nIbl\nFrom the definition of W it is possible to see that _u represents the direction (unit vector) of the ISA, b can be expressed as:\nb = - YPax + P u,\nwhere p is the pitch and P~x is a point of the axis. In other words ux, Uy, u=, b.,., by, b. are the Plucker coordinates of the screw axis. These coordinates are generally known as L, M, N, P, Q, R [39] or L, M, N, P*, Q*, R* [8]. Matrix L of this paper has a meaning similar to matrix Q defined in [34, 40] and matrix Ai presented in [41].\nFrom equation (6) if we consider an infinitesimal interval of time dt, the displacement dP of point P is:\nd P = P dt = W P dt,",
            "584 Giovanni Legnani et al.\nwhere the product W dt represents the infinitesimal displacement of the body:\nW d t =\n0 - d~b: dSy\nd(~ 0 -d~b~\n- - d~by dSx 0\n0 0 0\nd x o\ndyo dzo\n0\nI I I\nd_~ : dto I\nI\n. . . . I . . . .\no -o--6 1o\nwhere d~bx, d~by, d4~z are the infinitesimal rotations of the body and dxo, dyo, dzo is the linear displacement of the pole.\nIf the direction and the position of the ISA are constant, for example when the body is connected by a screw or revolute joint to the reference frame, matrix L is constant and we can write the following differential equation:\ndP =/~ dt = LP dq~\nor also:\ndP - - = LP.\nWhen integrated this becomesf:\nP(O~) = exp[Lq~]P(O) = Q(~b)P(O),\ntexp[A] indicates the exponential of a square matrix A which is equal to:\nA 2 A 3 A n exp[A] = I + A + ~r + ~ . + '\" \"n-~",
            "3D kinematics and dynamics--I 585\nwhere P(0) is the init ial pos i t ion o f the point , P ( $ ) is the pos i t ion o f the po in t after ro to t r ans la t ion o f tp a r o u n d the screw axis and Q(q~) is the mat r ix descr ibing the ro to t rans la t ion :\n:7 Q(~b) = exp[L~b] -- 0 0 0\nwhere mat r ix R can be expressed as:\nR = I + _uq~ + u 2 . . . - + - u ' T . , + - - .\nSince _u\" + 2 = _ u_\" (for any n) we can rewrite this equa t ion as follows:\nR = I + _ u ~ b - - ~ - . w + 5~- . . . . +-u2 . 4! I- \" \" .\nN o t i n g tha t the terms between round brackets are the series expans ions o f sine and cosine we get:\nR = I + _u sin(q~) + _u2(1 - cos(~b)).\nThe t rans la t ion t can be ca lcula ted as follows:\nt = (I - R)pax + _upq~.\nThese results p rove the contents o f Section 2.3.\n6. C O N C L U S I O N S\nThe a d o p t i o n o f the presented m e t h o d o l o g y gives rise to simple no ta t ion and easy p r o g r a m m a b l e a lgor i thms because:\n(a) bo th l inear and angu la r terms are hand led s imul taneously , (b) usual concepts like veloci ty compos i t ion , Cor io l i s ' theorem or the vir tual work principles can be easily appl ied , and (c) the prac t ica l app l ica t ions o f our theory required only the knowledge o f classic mechanics and o f the homogeneous t r ans fo rma t ion theory. M o r e o v e r this m e t h o d o l o g y connects different methodolog ies for the k inemat ics and dynamics o f r igid bodies such as homogeneous t rans format ions , screw theory, and the tensor method . Pract ical app l i ca t ions o f the present m e t h o d o l o g y are repor ted in Par t II.\nAcknowledgements--The authors thank J. Trevelyan and R. Owens (University of Western Australia) and R. Garziera (University of Parma) for the precious suggestions during the compilation of the paper. The work has been partially supported by C.N.R. grant n. 93.00896 PF67 and a MURST grant.\nR E F E R E N C E S 1. J. Denavit and R. S. Hartenberg, Trans. ASME J. Appl. Mech. 22, 215-221 (June 1955). 2. S. H. Dwivedi, Ming-Shu Hsu and Dilip Kohli, 6th IFToMM Worm Cong. (1983). 3. E. F. Fitchter, Int. J. Robot. Res. (1986). 4. K. P. Jankowski and H. A. E1Maraghy, Int. J. Robot, Res. 505 528 (1993). 5. K. Kozlowski, Robotica 11, 27-36 (1993). 6. J. Casey and V. C. Lam, Mech. Mach. Theory 21, 87-97 (1986). 7. J. E. Baker, Mech. Mach. Theory 4, (1986). 8. E. H. Bokelberg, K. H. Hunt and P. R. Ridley, Mech. Mach. Theory 27, I 15 (1992). 9. K. H. Hunt, Robotica 4, 171-179 (1986).\n10. P. R. Ridley, E. H. Bokelberg and K. H. Hunt, Mech. Mach. Theory 27, 17-35 (1992). 11. J. M. McCarthy, Int. J. Robot. Res. 5, (1986). 12. D. P. Chevallier, Mech. Mach. Theory 26, 613-627 (1991). 13. I. S. Fisher, J. Mech. Design 114, 263-268 (1992). 14. G. R. Veldkamp, Mech. Mach. Theory !1, 141-156 (1976). 15. J. Angeles, Int. J. Robot. Res. 4, (Summer 1985). 16. B. M. Bahgat and S. A. EI-Shakery, Mech. Mach. Theory 28, 407~,15 (1993). 17. P. Choiffet, Les Robots, Tome I: Modelisation et Commande. Hermes, Neully (1981). 18. C. W. Spoor and F. E. Veldpaus, 3\". Biomech. 13, 391 393 (1980). 19. J. Wittenburg, Dynamic of System of Rigid Bodies. B. G. Teubner, Stuttgardt, Vol. 33 (1977). 20. M. Vukobratovi6, Applied Dynamics o f Manipulation Robots. Springer-Verlag, Berlin (1989). 21. J. Denavit, R. S. Hartenberg, R. Razi and J. J. Uicker, J. Appl. Mech. 903 (1965)."
        ]
    },
    {
        "image_filename": "designv10_4_0000281_j.promfg.2020.04.215-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000281_j.promfg.2020.04.215-Figure10-1.png",
        "caption": "Fig. 10. (a) forged T-section, (b) forged T-section with added p-LMD structure, (c) forged T-section with added WAAM structure and (d) final machined hybrid Ti-6Al-4V part.",
        "texts": [
            " To achieve this, the starting point of each layer is shifted by 90\u00b0 and a contouring is added after each layer to ensure near-netshape and edge stability during build-up. This strategy avoids accumulation of deposited material due to delay during laser on/off and acceleration/deceleration of the axes, since the powder is continuously fed. The process parameters used to build up the specimens for the fundamental analysis are shown in Table 1. To deposit the WAAM-layers on the forged basic geometry (see Fig. 1 and Fig. 10), wire with a diameter of 1 mm was fed into the melt pool produced by an electric arc, using a six-axis FANUC robot with a welding power source TPS/i 500 by Fronius. In order to prevent oxidation, the material was deposited within a closed argon gas chamber. The applied WAAM process parameters were the following: 95A current, 13V voltage, 8 m/min wire feed rate and the layer thickness was approximately 4 mm. To investigate the influence of different heat treatments on the microstructure evolution and mechanical properties, three different conditions were applied to the p-LMD material: (1) \u201cas-built\u201d, (2) stress-relief annealing at 710\u00b0C for 6h, followed by cooling at ambient air and (3) \u03b2-annealing at 1050\u00b0C for 3h, followed by stress-relief annealing at 710\u00b0C for 6h, followed by cooling at ambient air",
            " As shown in the previous section, the p-LMD process can be used to produce components made from Ti-6Al-4V with a tensile strength and ductility almost comparable to the strength requirements of conventionally processed Ti-6Al-4V material. Hence, the developed technique was applied to the production of a hybrid bracket. In addition, wire-arc additive manufacturing was used to further accelerate the production and to manufacture the same component. As base material, a forged T-section from titanium alloy Ti-6Al-4V was used. Fig. 10 shows the forged base material and two different geometries, manufactured by the two different AM-techniques, as well as a final machined part. Applying p-LMD, various structures were deposited onto the forged T-section. The toolpath planning was carried out using the LMDCAM software developed at Fraunhofer ILT. For such a complex geometry, parameters like track-offset, distance between contour and hatch, and the build-up strategy can easily be set in the software. Machine data can be generated from the CAD file with the aid of a postprocessor (Fig",
            " Production of a hybrid part As shown in the previous section, the p-LMD process can be used to produce components made from Ti-6Al-4V with a tensile strength and ductility almost comparable to the strength requirements of conventionally processed Ti-6Al-4V material. Hence, the developed technique was applied to the production of a hybrid bracket. In addition, wire-arc additive manufacturing was used to further accelerate the production and to manufacture the same component. As base material, a forged T-section from titanium alloy Ti-6Al-4V was used. Fig. 10 shows the forged base material and two different geometries, manufactured by the two different AM-techniques, as well as a final machined part. Fig. 10. (a) forged T-section, (b) forged T-section with added p-LMD structure, (c) forged T-section with added WAAM structure and (d) final machined hybrid Ti-6Al-4V part. Applying p-LMD, various structures were deposited onto the forged T-section. The toolpath planning was carried out using the LMDCAM software developed at Fraunhofer ILT. For such a complex geometry, parameters like track-offset, distance between contour and hatch, and the build-up strategy can easily be set in the software. Machine data can be generated from the CAD file with the aid of a postprocessor (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure10.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure10.5-1.png",
        "caption": "Figure 10.5. Envelope formed by curve 01.",
        "texts": [
            " The velocity of A can be related to the velocity of P. If PA makes an angle ~ with the tangent to the pitch circles at P, the velocity of P has a component perpendicular to PA of 232 Curvature of Tooth Profiles (vp sin 1/1), and the velocity vAil can be expressed as follows, (10.4) In this expression, s is the distance from P to A. The symbol vAil is used to represent the velocity of A, to indicate that the velocity is measured relative to gear 1. We next determine the velocity of A, measured relative to gear 2. Figure 10.5 shows the system with gear 2 at rest, and gear 1 rolling on the pitch circle of gear 2 with a clockwise angular velocity w. As before, the positions of the moving gear at the two times T and T' are indicated by the unprimed and the primed symbols. Curve 02 is now the envelope of curve 01' and the two positions shown of curve 01 touch curve 02 at A and A'. The lines PA and P'A' are normal to curve 02' so the point 02 where they meet is the center of curvature, and the length 02A is the radius of curvature P2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure8-1.png",
        "caption": "Fig. 8. AIPM rotor topologies with symmetrical V-shape PMs and asymmetric rotor core. (a) Flux barriers near rotor surface and outside PMs [21]. (b) Flux barriers near rotor surface and inside PMs [36]. (c) Extra arc PMs and flux barriers outside PMs [37]. (d) Flux barriers inside PMs and between rotor surface and PMs [38]-[39]. (e) Asymmetric spoke-type flux barriers [40].",
        "texts": [
            " Moreover, as only part of the stator is utilized for PM magnetic flux, the back electromotive (EMF) and PM torque components are restricted due to stator core saturation. To deal with the issues of multiple rotor parts in HRAPM machines, the AIPM rotor topology using only one rotor with conventional symmetrical PM configuration and asymmetric rotor core geometry, i.e. employing asymmetric flux barriers to utilize MFS effect, is proposed firstly in [21]. The AIPM machine topology has symmetrical V-shape PMs and asymmetric flux barriers outside the V-shape PM cavity that is located at the right-side PM near the rotor surface in each pole as shown in Fig. 8 (a), which utilizes MFS effect by shifting the position of reluctance axes. An AIPM machine rotor topology is proposed in [36] as shown in Fig. 8 (b), but the flux barrier is located inside the V-shape PMs. Both novel AIPM machines can achieve obvious torque enhancement. Besides, it is found that the flux barrier design in Fig. 8 (b) influences both PM and reluctance torque components but flux barriers in Fig. 8 (a) show negligible effects on PM field and PM torque. [37] employs additional arc PM and asymmetric flux barriers near the right side of V-shape PMs in each pole based on [21] as shown in Fig. 8 (c). The proposed Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (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. BA-05 5 machine shows significant torque enhancement and torque ripple reduction simultaneously compared with the Toyota Prius 2004. However, more PMs are used and the thin arc PM causes concerns for potential demagnetization. Different from flux barriers near the rotor surface in [21] and [36]-[37], an AIPM machine rotor topology with V-shape PMs is proposed in [38] and analyzed in [39], which employs a flux barrier inside the PM cavity in each pole while the outer and inner ends are located near the rotor surface and near a PM, respectively, as shown in Fig. 8 (d). The comparison indicates that small torque enhancement and torque ripple reduction can be achieved by the proposed machine due to diminishing negative torque components resulted from cross magnetization effect. However, as fractional slot concentrated windings are employed in the studied machine [39], the MFS is insignificant because of small reluctance torque. Asymmetric spoke-type flux barriers whose outer and inner ends are located near the outer and inner surfaces of the rotor are employed in a V-shape AIPM machine [40], as shown in Fig. 8 (e). In this novel design, the increase of torque density can be achieved compared with the conventional V-shape IPM with the same total volume of PMs, although the improvement is not significant. However, this topology raises mechanical issue due to flux barrier structure. Asymmetric rotor geometry can also be used in spoke-type AIPM machine rotor topologies. Extra asymmetric flux barriers near rotor surface are employed in [41] as shown Fig. 9 (a), which can utilize both flux-focusing and MFS effects to enhance torque density while notably reduce cogging torque simultaneously",
            " Similar demagnetization withstand capability to the V-shape IPM benchmark is also proved for the proposed AIPM machine, with slightly complicated rib structures. In [56], an AIPM rotor topology with asymmetric V-shape PMs and extra flux barriers outside the PMs is proposed for IPM synchronous machines as shown in Fig. 15. The outer and inner ends of flux barrier are located near the rotor surface between adjacent V-shape PMs and near the bottom of asymmetric PM cavity, respectively. The proposed AIPM machine with outer flux barrier [56], Fig.15, and the AIPM machine with inner flux barrier [38]-[39], Fig. 8(d), are designed with the same stator, rotor diameter and PM usage to the conventional V-shape IPM machine for Toyota Prius 2010 and final optimal machines are compared. It confirms the proposed AIPM machine with outer flux barriers shows inherently higher torque density than the AIPM machine with inner flux barrier structure, as will be further described in Section IV.B. Compared with the IPM machine benchmark, significant torque enhancement is achieved by employing the proposed AIPM topology. Besides, the improved CPSR, efficiency and thermal performances in the AIPM machine with outer flux barriers are also revealed",
            " Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (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. BA-05 8 To illustrate the MFS effect for torque density enhancement in various AIPM machine topologies, six typical AIPM rotor topologies in four categories, including AIPM-SS [23] in Figs. 6 (a)-(c), AIPM-SA [22] in Fig. 8 (a), AIPM-AS [46]-[47] in Fig. 10 (b), as well as AIPM-AA1 [25], AIPM-AA2 [56], and AIPM-AA3 [57] that are shown in Figs. 14-15 and Fig. 16 (b) respectively, are redesigned with the same stator, rotor diameter, and PM usage to the conventional V-shape IPM machine in Toyota Prius 2010 [60]. Some key parameters of selected AIPM machines and IPM benchmark machine for Prius 2010 are given in Table II. The torque performance of these machines is calculated by using finite element (FE) analysis. The phase back electromotive forces (EMFs) of AIPM machines and the Prius 2010 benchmark are compared in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002823_s0956-5663(02)00185-9-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002823_s0956-5663(02)00185-9-Figure1-1.png",
        "caption": "Fig. 1. Sensor design (51 /16-mm). The electrodes are fabricated with screen-printing technology by Trace GmbH (Braunschweig, Germany). The working electrode (inner, 3.0-mm diameter) is made of Au or Pt ink; the other two electrodes in the entire screen-printed electrode can serve as reference (outer) and counter electrodes.",
        "texts": [
            " Cyclic voltammetry measurements were performed using an EG&G PAR 273 potentiostat /galvanostat system (Princeton, NJ) connected to a PC. Electrochemical deposition of PB onto the screen-printed electrodes and cyclic voltammetric investigations of the PB modified electrodes were performed in an electrochemical cell containing a Pt net auxiliary electrode, a saturated calomel electrode (SCE) as reference, and either the Au or the Pt screen-printed electrodes (diameter 3.0 mm, Trace GmbH, Braunschweig, Germany, see Fig. 1) were used as working electrodes. Flow-injection experiments were performed using a programmable Ismatec flow injection system (Zurich, Switzerland) with two peristaltic pumps (variable and invariable) furnished with Tygon pumping tubings and Teflon tubings of 0.7 mm I.D. A flow through electrochemical cell (no. 0014, Trace GmbH, Braunschweig, Germany) was connected to the outlet of the flowinjection system and was controlled by a LC4C potentiostat (Bioanalytical Systems Inc., West Lafayette, IN). The cell contained an Ag j AgCl reference electrode placed in a separate circular chamber situated at the backside of the working screen-printed electrode. The chamber was filled with 0.1 M KCl from an external syringe. This chamber contacted the working electrode space via four holes (0.3 mm) in the ceramic support of the electrode (Fig. 1). These four holes concentrically surrounded the working electrode at a distance of about 0.5 mm. The Au and Pt screen-printed electrodes were modified with PB and used as working electrodes in further studies. Prior to surface modification, the Au and Pt screenprinted electrodes were mechanically polished with alumina powder (Al2O3, 0.25 and 1 mm, Struers, Denmark) until a mirror finish was obtained followed by extensive rinsing with ultrapure water. Electrodeposition of the PB film was accomplished galvanostatically: the screen-printed electrode (Au or Pt) was inserted in an aqueous solution (R1) consisting of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002944_ac010657i-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002944_ac010657i-Figure5-1.png",
        "caption": "Figure 5. CVs for a 5.4 mM solution of ascorbic acid in phosphate buffer (pH 7.4): (a) unmodified composite electrode and (b) TPYmodified PFE. v ) 100 mV/s.",
        "texts": [
            " After prior deprotonation, ascorbic acid is oxidized electrochemically to a diketolactone, which is rapidly hydrated to dehydroasorbic acid. This rearranges to another ene-diol, which is further oxidized at higher potentials.53-56 Depending on the solution conditions, dehydroascorbic acid undergoes different subsequent reactions; thus, under anaerobic conditions, it degrades to furfural and carbon dioxide, but under aerobic conditions diketogluconic acid, oxalic acid, and other species are the final products.57 Figure 5 compares CVs for a solution of ascorbic acid (5.4 mM) in phosphate buffer (pH 7.4) at an unmodified (a) and a TPYmodified (b) composite electrode. At a bare composite electrode, a prominent anodic peak appears at +0.38 V with no coupled cathodic peaks. At a TPY-modified electrode, the oxidation process is significantly inhibited. Because at neutral pHs ascorbic acid is almost entirely in the form of ascorbate ions, this lack of response can be associated with the electrostatic repulsion exerted by the zeolite framework with regard to anionic ascorbate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure6-1.png",
        "caption": "Fig. 6. HRAPM machine with two-part rotor. (a) Machine topology [23], [31]-[32]. (b) SPM rotor part with shaped PMs [23]. (c) Multi-layer reluctance rotor part [23]. (d) Spoke-type IPM rotor part with ferrite PMs [32].",
        "texts": [
            " Later, HRAPM machine has been theoretically analyzed in [21], which reveals that the torque enhancement is due to utilizing MFS effect. Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (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. BA-05 4 Two-part rotor HRAPM machines are shown in Fig. 6 (a) in which SPM and reluctance rotor parts have the same axial length. In [23] and [31], HRAPM machines with SPM and multi-layer reluctance rotor parts are used and the maximum PM and reluctance torque components can be achieved at approximately the same current advancing angle. Shaped PMs shown in Fig. 6 (b) are employed in [23] to reduce the torque ripple. Moreover, IPM rotor with non-rare earth PMs can also be a candidate for the reluctance rotor part, as [32] uses the spoke-type IPM rotor with ferrite PMs shown in Fig. 6 (d) to improve efficiency and to reduce expensive rare-earth PM usage. To mitigate the issue of unbalanced axial electromagnetic force in two rotor parts HRAPM machine [33], rotor structure with three parts that uses the same rotor parts at both axial ends is proposed [33]-[35] as shown in Fig. 7, while the displacement angle between both rotor end parts and the central part is optimized to better utilize the MFS effect. The topology with the SPM rotor sandwiched by two multi-layer reluctance rotors is proposed in [33] that has higher average torque and lower torque ripple than a PM-assisted synchronous reluctance machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000874_j.isatra.2021.07.009-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000874_j.isatra.2021.07.009-Figure1-1.png",
        "caption": "Fig. 1. 2 coordinate frames of USV.",
        "texts": [
            " \u2225 \u00b7 \u2225 and (\u00b7)T denote the L2 norm and the transpose of a matrix, respectively. \u02c6(\u00b7) and \u02dc(\u00b7) are the estimate and estimate error, respectively. sig\u03b1(e) = |e|\u03b1sgn(e). We must first establish the mathematical USV model and the specific control objectives owing to the high nonlinearity of the USV. In this paper, the USV is assumed to move in a two-dimensional (2-D) space and is driven to follow a parameterized 2-D path typically used to guidance USVs, unmanned aerial vehicles, and robots. 2.1. USV model As shown in Fig. 1, the USV that we investigate has only one rudder at the front and one propeller at the rear. USVs move on the surface of the water, and have six degrees of freedom. We consider only three directions to facilitate the calculation, namely, sway, surge, and yaw. A mathematical model for ship moving was first developed by Manoeuvring Mathematical Model Group (MMG) [43]. The main feature of the model is that the hydrodynamics and torques acting on the ship are physically decomposed into the components acting on the hull, propeller, and rudder, as well as the interaction among them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure14.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure14.7-1.png",
        "caption": "Figure 14.7. Pitch plane section through the imag i nary rac ks.",
        "texts": [
            " The tooth thicknesses of the imaginary racks were chosen exactly equal to those of the two gears, measured at Backlash 389 their pitch circles. In Figure 4.14 we showed the pitch plane section through the imaginary racks, and we then proved that the circular backlash of the gear pair is equal to the distance that either imaginary rack can move, when the other is held fixed. We follow the same procedure for the case of a helical gear pair. Figure 14.6 shows a transve~se section through the gear pair, with the imaginary racks drawn in, and Figure 14.7 shows the pitch plane section through the imaginary racks. A typical pair of teeth are in contact along line ArA~, and the gaps between the teeth are represented by the narrow un shaded bands. As we proved earlier in this chapter, the transverse pi tch, normal pi tch and helix angle of the imaginary racks are equal to the corresponding quantities in the gears, measured at their pitch cylinders. The transverse tooth thicknesses of the imaginary racks are chosen equal to those of the gears, 390 Helical Gears in Mesh and it then follows that the corresponding normal tooth thicknesses are also equal. These values are therefore shown on Figure 14.7, and it is clear that the circular backlash of the gear pair, defined by Equation (14.69), is equal to the width of the gap between the teeth of the imaginary racks, measured in the transverse direction. We now introduce a third method for defining the backlash in a helical gear pair. We define the normal backlash Bn of the gear pair in a manner similar to Equation (14.69), as the difference between the normal space width of one gear and the normal tooth thickness of the other, both measured at the pi tch cylinders, p - t - t np np1 np2 (14.70) The tooth thicknesses in the normal and transverse directions are related by Equation (13.112), (14.71) Backlash 391 Hence, with the definition given in Equation (14.70), it can be seen in Figure 14.7 that the normal backlash is equal to the width of the gap between the teeth of the imaginary racks, measured normal to the tooth profiles in the pitch plane. Relations Between the Different Types of Backlash The relation between the normal backlash Bn and the circular backlash B can be seen immediately from Figure 14.7, B cos I/tp (14.72) In order to find a relation between the backlash B' along the common normal and the circular backlash, we first consider a typical transverse section through the gear pair, as shown in Figure 14.8. The two interior common tangents to the base cylinders are labelled E1E2 and E;Ei. The contact point in this section lies on line E1E2 , while line E;Ei cuts the non-contacting tooth profiles at points A; and Ai. Figure 14.9 shows the plane through E; and Ei, which is tangent to both base cylinders",
            " These positions of the two end faces determine the minimum theoretical value of the gear face-width, but the actual value should be increased slightly, to ensure that the end points of the contact locus lie at a certain distance inside each end face. Backlash The three different types of backlash in a crossed helical gear pair are defined in essentially the same manner as they were in the case of parallel-axis helical gears. However, there are some differences in the expressions used to calculate the backlash values, and in the relations between the different types of backlash. When we discussed the normal backlash of a parallel-axis gear pair, we showed in Figure 14.7 a section through the pitch plane of two imaginary racks, whose tooth thicknesses are chosen so that each imaginary rack is in contact with both faces of the teeth in the corresponding gear. As a consequence, the normal and transverse tooth thicknesses of each imaginary rack at its pitch plane are equal to the normal and transverse tooth thicknesses of the corresponding gear at its pitch cylinder. The normal backlash Bn of the gear pair was then defined as the gap width, measured in the normal direction, between the tooth profiles of the two imaginary racks in the pitch plane section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000011_jsen.2019.2918018-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000011_jsen.2019.2918018-Figure10-1.png",
        "caption": "Fig. 10. (a) Test PMSM in experiments (b) Photograph of TMR sensors mounted outside the motor stator yoke.",
        "texts": [
            " On the other hand, the four sensing positions S1, S7, S13 and S19 are 90-degree different so that Brad and Btan at these four positions are of the same phase, respectively. It can be easily found that Brad and Btan also changed corresponding to the occurrence of short-circuit fault. Thus, it is feasible to detect the inter-turn short-circuit fault in stator windings by sensing the stray magnetic field. To experimentally verify the effectiveness of the proposed short-circuit fault detection approach, a 3.3-kW 8-pole/36-slot SPMSM was installed on the testing platform as the test motor (see Fig. 10(a)). Its main specifications and parameters are given in Table I. The SPMSM was fed through space vector control using an adjustable-speed motor drive. The motor was also coupled with a high-speed flywheel and a generator to adjust the load level in experiments. During the experiments, the phase currents (i.e., ia, ib and ic) of test motor as well as the fault resistor current (iRf) were monitored by four AC current probes (Tektronix TCPA300). The three-phase parallel-connected winding configuration of the test motor is illustrated in Fig. 6 and Fig. 7. In order to simulate the inter-turn short-circuit faults in test motor, the winding a1 and a7 were alternatively shorted by the fault resistor Rf in experiments by controlling the switches S1 and S2, same as in simulation. Three electrical taps were extracted outside the motor cover to connect the switches and as fault resistors for producing the short-circuit faults (see Fig. 10(a) and Fig. 10(b)). The aluminum housed resistors (from Arcol HS series [34]) with maximum tolerance of \u00b110% were chosen as the fault resistors in the experiments. The resistance values of the fault resistors were also measured by a Keithley 2450 SourceMeter before the experiments. By directly using or series-connecting the fixed-value resistors, the resistances of the fault resistors in the experiments were in the range from 0.022 to 1.003 \u03a9. The motor cover was drilled in order to mount 24 TMR sensor units close to the stator yoke surface for measuring the stray magnetic field, as shown in Fig. 10(b). The size of holes 1558-1748 (c) 2019 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. (i.e., 10 \u00d7 20 mm) can be possibly further reduced due to the compact size of TMR sensors (i.e., 3 \u00d7 3 \u00d7 1.45 mm SOT package). The distance between the TMR sensors and stator yoke surface is approximately 2 mm. It should be noted that the installation of TMR sensors can be completed during the fabrication stage of a new PMSM",
            " The detailed parameters of two TMR sensors and the signal amplification gain are listed in Table II. Each TMR sensor utilizes a push-pull Wheatstone bridge composed of four unique TMR elements. The typical magnetic-field-sensitivities of TMR2001 sensor and TMR2503 sensor are 80 mV/V/mT and 10 mV/V/mT, respectively. Moreover, the sensitive direction of TMR2001 sensor is horizontal to the sensor package, whereas that of TMR2503 sensor is perpendicular to the surface of sensor package. As the enlarged figure in Fig. 10(b) shows, the PCB with two sensors is arranged in parallel to the surface of motor stator yoke. Hence, the TMR2001 sensor and TMR2503 sensor were used to measure the tangential (Btan) and radial (Brad) components of the stray magnetic field, respectively. The voltage outputs of TMR sensors were amplified by the differential instrumentation amplifiers (AD620) and then filtered by a low-passer filter in order to eliminate the noise interface from 1558-1748 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000379_tcyb.2020.2981090-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000379_tcyb.2020.2981090-Figure2-1.png",
        "caption": "Fig. 2. Diagram of the 2-DOF manipulator.",
        "texts": [
            " (27) Furthermore, we can adjust the radiuses of region of set tracking errors by applying \u03bai,z, \u03c6i,1, ki,1, and i, that is larger parameters \u03bai,z, \u03c6i,1, ki,1, and i can obtain smaller convergence radiuses. Two examples will be given in this section to show the effectiveness of the proposed algorithm. Example 1: Considering the networked manipulator system has three followers and two leaders. The model of the twolink manipulator is assumed for each follower [10], and its physical parameters are illustrated in Fig. 2. Fig. 3 shows the information communications among the three followers and two leaders. For each follower, the inertia matrix Mi(qi) = [Mimn] \u2208 R2\u00d72 and the centripetal matrix Ci(qi, q\u0307i) = [Cimn] \u2208 R2\u00d72 are defined as Mi(qi) = [ ai,1 + 2ai,2 cos(qi,2) ai,3 + ai,2 cos(qi,2) ai,3 + ai,2 cos(qi,2) ai,3 ] Ci(qi, q\u0307i) = [\u2212ai,2 sin(qi,2)q\u0307i,2 \u2212ai,2 sin(qi,2)(q\u0307i,1 + q\u0307i,2) ai,2 sin(qi,2)q\u0307i,1 0 ] where ai,1 = Ii,1 + mi,1L2 i,c1 + mi,2L2 i,1 + Ii,2 + mi,2L2 i,c2, ai,2 = mi,2Li,1Li,c2, ai,3 = Ii,2 +mi,2L2 i,c2, mi,1 and mi,2 are the links\u2019 masses, Ii,1 and Ii,2 are the inertia\u2019s moments, Li,1 and Li,2 are the links\u2019 lengths, and Li,c1 and Li,c2 are the links\u2019 mass centers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003768_rob.4620050502-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003768_rob.4620050502-Figure4-1.png",
        "caption": "Figure 4. A line diagram of the 3-D redundant robot.",
        "texts": [
            " In Figure 3, z i , i = 1 to 6 are the unit vectors representing axes of rotation for the corresponding rotational joints and z r is the axis of translation for the prismatic joint. The control schemes developed to improve robot\u2019s efficiency and mechanical advantage were applied to the seven-degree-of-freedom redundant robot of Figure 3. Desired end-effector motion was also obtained by locking the prismatic joint and, by using the pseudo-inverse solution. The weighting matrices W,, W o , W,, and W, were selected suitably to incorporate different units associated with the components of vectors x, d, f and 7 respectively. A line diagram of the robot, shown in Figure 4, was used to draw the robot configurations along the trajectory. The offset, upper arm and forearm are drawn as straight lines in proportion to their lengths u 2 , 1 2 , and a, respectively. The axes of rotation for the wrist joints z 3 , 2 4 , and z5 are drawn as short straight lines at the wrist. 426 Journal of Robotic Systems-1988 Simulations were performed for various straight line trajectories in the xyz space. Here we present the simulation results for a straight line trajectory AB. While moving the robot end-effector along this trajectory, the orientation of the end-effector was kept constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000225_s40684-020-00221-7-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000225_s40684-020-00221-7-Figure2-1.png",
        "caption": "Fig. 2 Experimental set-up for DED",
        "texts": [
            " The cutting depth for LAM was selected by analyzing the temperature distribution through thermal analysis for LAM of the fabricated workpiece. LAM experiments using a real-time laser power control system were performed by referring to thermal analysis results and recommended cutting conditions of the cutting tool. Compared to traditional machining without preheating, machining characteristics, including cutting force and surface roughness, were analyzed, and tensile test, hardness, surface analysis and microstructural analysis were performed. The experimental set-up for DED AM was configured as shown in Fig.\u00a02. The DED head was a 20 kW AK390TC model from Raytools. A diode laser with power of 4 kW and focal length of 210 mm from Laserline was used. The laser spot has a Gaussian energy distribution with diameter of 900 \u00b5m. A powder feeder (Metco Twin 150) with a capacity of 1.5 L (2 pcs) from Oerlikon was used. The Ti-6Al-4V powder was continuously transported through a 3-way coaxial nozzle with argon shielding gas stream. The particle size of the Ti-6Al-4V powder was 150 ~ 200 \u00b5m. Workpieces were built on Ti-6Al-4V flat substrates with thickness of 12 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000658_j.ymssp.2021.107711-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000658_j.ymssp.2021.107711-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of the passing process traveled by the rolling element: (a) entry phase, (b) impact phase, and (c) exit phase.",
        "texts": [
            " Kinematically, the speed of the rolling element changes sharply from its entry to strike on the trailing edge of the spall zone, resulting in the collision force and vibration of bearing. Based on the investigation on ball-spall interaction, formulas for the collision force can be derived. As for the bearing system, an impact process due to the collision of the rolling element with the spall area is the internal transmission of kinetic energy to a system, the REB is considered as a conservative system. In Fig. 4, assuming the mechanical energy of the rolling element is conservative during its release of deformation from the entry (see Fig. 4(a)) to impact (see Fig. 4(b)), the outer ring is assumed to be fixed and rigid, and both the cage and the inner race speeds are assumed to be unaffected by the rolling element short speed variations. Thus, it can be concluded that \u00f01 2 mballV 2 b1 \u00fe 1 2 Ib1x2 b1\u00de \u00femballg Dball cos hL 2 \u00fe 1 2 kDx2 \u00bc \u00f01 2 mballV 2 b2 \u00fe 1 2 Ib2x2 b2\u00de \u00femballg Dball cos himp 2 \u00f015\u00de where mball represents the mass of the rolling element, g is the gravitational acceleration, k and Dx are the stiffness and elastic deformation between the ball and the bearing race respectively and can be calculated using the method in [16], and Ib1 and Ib2 denote the moment of inertia of rolling element relative to the center of the rolling element and the contact edge of the spall area, respectively",
            " Hence, Ib1 and Ib2 can be expressed by Ib1 \u00bc 2mball 5 Dball 2 2 \u00f016\u00de and Ib2 \u00bc Ib1 \u00femball Dball 2 2 \u00f017\u00de where Vb and xb represent the linear velocity and angular speed of the rolling element respectively, and they can be linked together based on the theory of circling motion, that is Vb \u00bc xbR \u00f018\u00de where R corresponds to the radius of circling motion. Substituting Eqs. (16)\u2013(18) into Eq. (15) gives V2 b2 \u00bc 7 12 V2 b1 \u00fe 5 12 gDball\u00f0cos hL cos himp\u00de \u00fe 5 12 kDx2m 1 ball \u00f019\u00de in which hL denotes the entry angle (see Fig. 4(a)) of the rolling element into the spall zone, and himp refers to the impact angle as shown in Fig. 4(b). According to the geometrical relationship as illustrated in Fig. 4(a), hL can be formulated by cos hL \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 \u00f0sin hL\u00de2 q \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Lspall=Din 2q \u00f020\u00de similarly, cos himp \u00bc cos# \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 \u00f0sin#\u00de2 q \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Lspall=Dball 2q \u00f021\u00de Substituting Eqs",
            " (22) gives Vb2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 7x2 r D2 m D2 ball cos2 a 2 192D2 m \u00fe 5 12 gDball cos hL cos himp \u00fe 5 12 kDx2m 1 ball vuuut \u00f024\u00de As illustrated in Fig. 4, according to the conservative theorem of momentum of the rolling element from its entry to impact on the trailing edge in the radial direction, it can determined that F imp cos#\u00f0timp 0\u00de \u00bc mball 0 \u00f0 V imp\u00de \u00f025\u00de where V imp indicates the impact velocity and can be expressed by V imp \u00bc Vb2 cos p 2 # \u00f026\u00de where timp represents the duration time of the impact force. It can be determined from the ball-trailing edge interaction that the timp approximately equals to half of the time measured by the rolling motion of the rolling element from the midway through the spall area to exit from it [19], that is timp \u00bc Dball sin# 4V re \u00f027\u00de where V re is the relative velocity between the rolling element and the inner race, hence it can be written as follows V re \u00bc VLE Vb1 \u00f028\u00de where VLE is the linear velocity which is measured at the leading edge of the spall zone and can be formulated by VLE \u00bc 0:5xrDin"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000634_j.addma.2021.102152-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000634_j.addma.2021.102152-Figure1-1.png",
        "caption": "Fig. 1. CAD model of reference samples: (a) series R (b) series T.",
        "texts": [
            " The algorithm will be applied to understand the impact of artificial defects on the light intensity collected by an on-axis photodiode to detect the LoF pores. The image processing algorithm will then analyze the output of the software. The impact of variation in print parameters on the detection of defects will also be discussed. The results are validated through Micro-CT-Scanning datasets. Two sets of design of experiments (DoE), including cubical samples with a size of 8 \u00d7 8 \u00d7 10 (W \u00d7 L \u00d7 H) mm, were devised and labeled as R-series (Fig. 1.a) and T-series (Fig. 1.b). In the design of the R-series, the effect of LoF was mimicked by embedding artificial voids in the samples, as shown in Fig. 2. Two different void geometries of cylindrical (R2, R3, and R5) and spherical (R4) shapes with different sizes were fabricated using an EOS-M290 LPBF machine. One control sample (R1) without any artificial void was also printed. To study the pores\u2019 distribution, voids were distributed at different vertical positions with respect to the build plate and different print layers location (R5, shown in Fig",
            " This arrangement will combine artificial voids and process parameter deviation on the signal intensity and stability. The print parameters listed in Table 1 were selected according to the print parameters used to obtaining highquality Hastelloy-X [EOS Nickel Alloy HX, Krailling, Germany] parts [38]. Each sample was printed eight times at different locations of the build plate with respect to the direction of the gas flow as well as the re-coater (Fig. 3.a). In the design of each sample, vertical and horizontal grooves were added for registering the location of porosities in the CT scan datasets (Fig. 1). In T-series, the samples were designed and printed by only varying print parameters to create randomized and stochastic voids produced by LoF. The geometry of these samples was similar to R1, and the print parameters for each one are listed in Table 2. Six samples from each K. Taherkhani et al. Additive Manufacturing 46 (2021) 102152 design were labeled and arranged on the build plate (Fig. 3.b). Additionally, in all samples (R-series and T-series), the stripe scan strategy with 67\u2070 rotation after each layer was used; but, the down-skin scan strategy (process parameters are similar to the core) was used around voids embedded in samples R2-R8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure8.5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure8.5-1.png",
        "caption": "Figure 8.5. Radius of the span measurement contact points.",
        "texts": [
            "4 is held so that the lengths AE and A'E are not qui te equal, there is no change in the measured length S. Number of Teeth in the Span We have not yet considered the number N' of teeth over which the span measurement should be made. Ideally, the caliper jaws should touch the tooth faces near the middle of their profiles. This means, as we pointed out earlier, that the contact should take place at a radius of approximately (Rs+e). The value of N' must therefore be chosen with this consideration in mind. The points of contact between the gear and the caliper are shown in Figure 8.5. To simplify the analysis, we will now assume that the caliper is positioned symmetrically, so that the length AE is equal to half the span measurement S. The 5pan Measurement 199 radius R of the circle through point A is approximately equal to (Rs+e), and we therefore obtain the following equation for 5, (8.20) We express Rb in terms of Rs' and expand the expression in the square brackets as a power series in (e/Rs )' neglecting terms of second degree and higher. The equation for 5 then takes the following form, 5 5",
            "23), a number of approximations were used, and it is therefore important to know whether the resulting value of N' is always acceptab~e. The equation can be checked by the following method. For any particular gear, the expression on the right-hand side of Equation (8.23) is evaluated, and N' is 200 Measurement of Tooth Thickness chosen as the integer closest to this value. Equation (8.18) is used to calculate the span measurement S, and the radius R at which contact takes place can then be read from Figure 8.5, R (8.24) If this procedure is carried out for a large number of gears, we obtain the following results. The value of N' is always satisfactory when e is small. However, for gears with large values of e, particularly those with a small number of teeth, the value of N' given by Equation (8.23) is sometimes too large. I n these cases the contact would take place theoretically outside the tip circle of the gear. The error occurs because, when e is large and N small, the power series expansion in (e/Rs )' which was used to derive Equation (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000180_j.matdes.2020.109410-Figure10-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000180_j.matdes.2020.109410-Figure10-1.png",
        "caption": "Fig. 10.Microstructure simulation results for the single track casewith different views: (a) top view, (b) YZ cross-section view, and (c) XZ cross-section view, where thewhite dashed lines show the extent of melting (T= Tl) and the black dashed lines show the locations of the cross-sections. In the closeup of figure (b), grains (e.g., A) epitaxially grow from partially melted particles.",
        "texts": [
            " 9(b), most grains are columnar, as represented by the density of points in the region b/a < 0.4 and c/a < 0.4. The pole figures in Fig. 9(c) demonstrate that texture has developed. The (100) pole shows a peak intensity (the red area) close to the center from the scan direction (+X), which indicates a preferred orientation aligned along the build direction. The texture strength of the solidification grain structure is characterized by the texture index, which is 6.11 \u00d7 10\u22123. To probe the spatial distribution of the grains, several 2D views of the final simulation results are shown in Fig. 10, including a top view, a YZ cross-section at x = 296.25 \u03bcm, and two XZ cross-sections: one at y = 145.0 \u03bcm and the other at y = 205.0 \u03bcm. In Fig. 10(a), the top view of the deposition shows that the morphology of the solidification microstructure outlined by the white dashed lines is different from that of unmelted powders on the left side. This shows that the columnar grains from both sides of the melt track proceed in a curved shape towards the center of the melt pool with a mean angle of 78\u00b0 to the scan direction, which is attributed to the growth direction of the columnar grain following the trailing edge of themelt pool. At the center of the track, grains elongated in the direction perpendicular to this crosssection appear equiaxed. These central grains typically grow epitaxially, and tilt in the direction of the thermal gradient, in this case along the scan direction. This is demonstrated in Fig. 10(b), which shows a transverse cross-section of these same grains, and Fig. 10(c), which shows a longitudinal cross-section. The spatial inhomogeneity of the grain structure related to the melt pool geometry is demonstrated well by 2D cross-sections. From the YZ cross-section view of the final grain structure plotted in Fig. 10(b), one can find that the columnar grains epitaxially grow from the partially melted pre-existing grains and adopt a growth direction radiating from the boundaries towards the top center of the melt pool in what we will term a radial growth pattern, because of the thermal gradient distribution shown in Fig. 7(b). The grains tend to grow parallel to the local thermal gradient direction, and therefore normal to the fusion boundary indicated by the white dashed curved line. In addition, the closeup in Fig. 7(b) shows that grains growing epitaxial from partially melted powder are captured, reproducing a phenomenon also noted experimentally [4]. Fig. 10(c1) is a central longitudinal cross-section to the track, and Fig. 10(c2) is an off-center longitudinal cross-section. Both of these indicate that grains grow epitaxially from the pre-existing grains in the substrate, with their growth directions slightly tilting off vertical towards the scanning direction, aligning with the temperature gradient directions shown in Fig. 7(a). Moreover, the grains with colors close to red (representing the grain orientation [001], parallel to the build direction) overgrow other neighboring grains. This is because grains with their fastest growth direction alignedwith the temperature gradient best survive the growth competition. One difference between the two longitudinal cross-section results is that the off-center cross-section in Fig. 10(c2) exhibits finer grain structures at the top of the melted regions. These structures are columnar grains sectioned along their narrow directions and have grown from out-of-plant locations on the curved fusion zone boundary and extend across the YZ slice, as can be seen in Fig. 10(b). The high fidelity 3D numerical simulations allow these phenomena to be directly observed, providing an important tool for interpreting 2D results andmore generally understanding the development of texture during the process. The results shown in Figs. 7 and 10 are in agreement with the previously observed relationship between temperature gradient and growth direction of grains, e.g. in Fig. 3 of [4] showing the as-built prior-\u03b2 grain structure during solidification, and Fig. 12 in [32]. Five further processing conditions listed in Table 5 were analyzed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003338_s1359-6462(00)00600-x-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003338_s1359-6462(00)00600-x-Figure5-1.png",
        "caption": "Figure 5. The dislocation model for the formation of extrinsic stacking faults and twin nucleation. For the detailed explanation of the model, please refer to the main text. Circles around dislocation pairs indicate the product dislocations, i.e. Bd 1 Ad 5 dC, dC 1 DA 5 Bd, bA 1 Ad 5 bd, and bA 1 dC 5 bd/AC.",
        "texts": [
            " [8] and Hirth et. al [14] have investigated the extrinsic SFs formation in high SFE pure metals in which SFs are hard to nucleate. Their model is similar to our previous model [5] for the nucleation of twinning and intrinsic SFs. Therefore, our model will be modified here to explain extrinsic SFs and twinning nucleation considering extrinsic SFs as the precursor features for twinning will be introduced. The proposed mechanism for extrinsic stacking fault formation and twinning nucleation is illustrated in Figure 5 as follows: (a). Two partial dislocations (separated by intrinsic SFs) in Figure 5.a, one in the primary and the other one is in the conjugate {111} slip planes, form a Lomer-Cotrell lock with a 1/3 a[100] type stair rod [13]. (b). Upon application of high levels of external stress, the trailing partial approaches the leading partial since the Schmid factor for trailing partial is higher than the one for the leading partial. The core of the trailing Bd partial dissociates into a stair rod, ad, and the Shockley partial, Ba, that slips on the cross slip plane (a) as shown in Figure 5.b [7]. The partial Ba dissociates further into another stair rod, da, and a partial bd on the primary d plane. The driving force for this dissociation and gliding onto the next parallel (d) plane comes from the external stress and the pile-up stress of dislocations. (c). Because of the attraction between stair rod, ad, and the leading partial, dC, the partial dC first recombines with the stair rod ad to form aC. Then aC recombines with the stair rod da to form dC on the next d plane. Since the current configuration of partials in the next d plane (Bd is the leading and dC is the trailing partials) corresponds to the high-energy fault, it can be transformed to the lower energy extrinsic fault arrangement as shown in Figure 5.c. (d). An extrinsic SFs can be pinned at two points as suggested by Pirouz [3]. Clusters of interstitial atoms, forest dislocations or kink formation may provide the pinning points. The leading partial has a higher resolved shear stress than the trailing one in the orientations and stress states in Table I. Thus, the mobilities are different which leads to the formation of a faulted loop as envisaged in Figure 5.d. Since the leading partial, Bd, is behind the trailing one at this point, it can double cross slip to the next d plane with the same mechanism as in Figure 5.b. Succesive repetition of this cross-slip process constitutes thin layer of twins as shown in Figures 2,3 and 4. The single crystals of the present material have exhibited extrinsic faults in almost every case in which intrinsic SFs or normally twinning is not favorable. For the aforementioned dislocation model to be valid, the following conditions should be satisfied: i) The leading partial of the extrinsic fault must be faster than the trailing one. ii) The stress level on the leading partial must be sufficient to overcome the fault tension",
            "1 G in a high SFE pure metal, i.e. Ni. However, in the present cases, the low SFE and very high stress levels decrease the extrinsic SFE similar to the intrinsic one [5]. Moreover, the Mn-C couples introduce a local internal stress field that helps the formation of extrinsic SFs. Furthermore, the carbon field around partial dislocations doubles the constriction energy to start the cross slip process [16]. Thus, deformation will proceed by dissociation of dislocations on the primary plane d in the way shown in Figure 5.b instead of a regular cross slip process. The shear stress on the leading partial of the extrinsic stacking fault should overcome the fault tension to nucleate twinning. The fault tension is approximately gE/bp>150 MPa assuming gE>gi 5 23 mJ/m2 and bp 5 1.5 \u00c5 in the present material. From this, the necessary stress should be 320 MPa for the [001] orientation under tension. For this orientation a yield level of approximately 300 MPa was observed experimentally. This demonstrates that once kinematic barriers are overcome due to the aforementioned reasons, twinning is likely in the cases presented in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000374_j.engfailanal.2020.104477-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000374_j.engfailanal.2020.104477-Figure1-1.png",
        "caption": "Fig. 1. Room and high temperature fatigue specimen (A). Creep specimen (B). Surface defect (C).",
        "texts": [
            " The present work aims to integrate the number of results available focusing on the influence of surface defects and temperature on fatigue performance and creep resistance of SLM processed Ti-6Al-4V. The specimens used for the present study were manufactured by selective laser melting using a SLM Solutions (SLM 280) device. The build direction coincides with the longitudinal axis and the process details are indicated in Table 1. The two geometries produced, for fatigue and creep testing, are reported in Fig. 1(A and B) respectively. During SLM fabrication a defect was introduced in the form of a slight misalignment of the build axis in correspondence of the minimum cross section trait, as indicated in Fig. 1C. The fatigue specimens were produced to a minimum diameter of 6 mm. Four of them were being tested at room temperature with the asbuilt surface, while the rest of them had the surface lathe-machined down to a diameter of 5 mm as reported in Fig. 1A. The creep specimens where tested with the as-built surface. All the specimens were tested with the as-built microstructure consisting of acicular \u03b1\u2019 martensitic phase in elongated \u03b2 grains as shown in Fig. 2. A certain degree of porosity can be detected in the longitudinal cut as observed from Fig. 2. The fatigue testing was performed, by a hydraulic machine, in strain control applying a fully reversed displacement, that corresponds to a displacement ratio \u22121, at a strain rate of 0.1%/s with the feedback provided by an induction axial extensometer",
            " Considered the entity of the defect, a misalignment of the build axis of 75 \u00b5m, it is evident how even a small defect can have huge repercussions on the structural integrity, which is particularly of importance for the production of complicated topology-optimized geometries, the realization of which is allowed by the great flexibility of the AM technologies, where postproduction surface machining can be non-cost effective or impossible. A similar reduction of strain-controlled fatigue life is originated by an increase of ambient temperature to 600 \u00b0C. The fatigue failure at high temperature is characterized by a diffused secondary cracking originated by weakening of the grain boundary regions, as seen in Fig. 4b. The creep testing was performed on a series of 8 specimens of the geometry specified in Fig. 1b. The samples where tested applying a constant nominal stress with a drop weight machine with induction heating at temperatures of 450, 550 and 650 \u00b0C, respectively. The results are reported in Fig. 5 in terms of nominal stress vs time to failure, showing a consistent behavior for the whole range of time to failure, from 120 s to 655 h. The consistency of the behavior is evident in the summary of the results in terms of nominal stress versus Larson Miller parameter, in Fig. 6, in which all the results can be approximately described by a single power function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000030_j.jmst.2019.12.020-Figure19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000030_j.jmst.2019.12.020-Figure19-1.png",
        "caption": "Fig. 19. Schematic representation of heat gradient and heat history for th",
        "texts": [
            " [57], the transition from conduction mode o keyhole mode can be determined by the H/hs ratio, which can e calculated by Eq. (4): H hs = AP hs \u221a Dv 3 (4) here H refers to the specific enthalpy, hs to the enthalpy of meltng, A to the absorptivity, D to the thermal diffusivity and to the aser beam size. Therefore, H/hs is also proportional to the P/ \u221a v atio, which suggests that the higher laser power is more likely to ause the transition to keyhole mode. The schematic representation f heat gradient and heat history during conduction and keyhole odes is shown in Fig. 19. Compared with conduction mode, more eat under keyhole mode can be dissipated horizontally from the ide walls of MP to the prior solidified parts, which can lead to a arger angle between the columnar crystal growth direction and the eposition direction. In addition, under a keyhole mode, the already olidified parts will experience more SLM thermal cycles of remeltng and cooling, due to the greater depth of MP. This means that the rior solidified parts will be tempered more fully and completely in keyhole mode, which can make the microhardness and strength of LMed 300M steel decreased"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure9-1.png",
        "caption": "Fig. 9. AIPM machine rotor topologies with symmetrical spoke-type PMs and asymmetric rotor core. (a) Asymmetric flux barrier [41]. (b) Asymmetric rotor profile [42].",
        "texts": [
            " Asymmetric spoke-type flux barriers whose outer and inner ends are located near the outer and inner surfaces of the rotor are employed in a V-shape AIPM machine [40], as shown in Fig. 8 (e). In this novel design, the increase of torque density can be achieved compared with the conventional V-shape IPM with the same total volume of PMs, although the improvement is not significant. However, this topology raises mechanical issue due to flux barrier structure. Asymmetric rotor geometry can also be used in spoke-type AIPM machine rotor topologies. Extra asymmetric flux barriers near rotor surface are employed in [41] as shown Fig. 9 (a), which can utilize both flux-focusing and MFS effects to enhance torque density while notably reduce cogging torque simultaneously. Asymmetric rotor profile is applied in a spoke-type AIPM machine [42] (Fig. 9 (b)) to reduce magnetic field harmonics introduced by PM magnetic flux density, thereby significantly reducing both torque ripple and vibration albeit with small decrease of average torque. In summary, the AIPM machine rotor topologies discussed in Figs. 8 and 9 generally employ additional asymmetric flux barriers in conventional IPM machines to utilize MFS effect by shifting the axis of rotor saliency. Thus, rotor structures are generally simple for easy manufacturability. However, the enhancement of torque density is generally relatively small and flux barrier designs especially for topologies with thin ribs may raise mechanical stress issues"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000907_j.jallcom.2021.160044-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000907_j.jallcom.2021.160044-Figure2-1.png",
        "caption": "Fig. 2. Illustration diagram of experimental process and EPT equipment.",
        "texts": [
            " Cylindrical samples were fabricated with a dimension of 100 mm in length, 17 mm in diameter, and the axial direction of the cylinder is along the building direction. The cylinders were then annealed at 800 \u00b1 14 \u00b0C for 2 h \u00b1 10 min, followed by furnace cooling. It is necessary to clarify that the SLMTi6Al4V alloy used for EPT has been treated by stress relief treatment, because it is easier to remove the printing samples from the substrate with less possibility of bending or cracking than the asbuilt state. As illustrated in Fig. 2a, the annealed cylinder was cut into platelike samples with a dimension of 50 \u00d7 6.5 \u00d7 2.5 mm3 by wire electrical discharging machine for EPT. The EPT experiments were carried out at ambient temperature by a self-made device equipped with a capacitor bank discharge circuit (Fig. 2b), and the clamping device is shown in Fig. 2c. We chose EPT discharge voltages from 6 kV to 8.5 kV (Table 3) as experimental parameters based on the previous experiences, which efficiently promote the mechanical properties of steels [18,19]. The EPT duration was approximately 400 ns, followed by air cooling. Hereafter, the samples treated at 6 kV was referred to as EPT-6 sample and so forth. Correspondingly, the original sample without EPT was marked as EPT-0 sample. The Vickers microhardness tests were carried out by an AMH43 automatic micro-indentation hardness testing system under an application load of 200 g with dwell time of 15 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003537_tro.2006.870649-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003537_tro.2006.870649-Figure4-1.png",
        "caption": "Fig. 4. Convex-polyhedron-based method. (a) Convex hull of contact points. (b) Rotation around a segment of convex hull. (c) Plane including two edges. (d) Region of ZMP. (e) Stable region.",
        "texts": [
            " However, when the hand contacts the environment, the GZMP is different from the COP of the foot\u2013ground contact, and may exist outside of the foot-supporting area. Here, Takenaka [9] considered the ZMP during manipulation as the COP of the foot\u2013ground contact. In this section, we obtain the region of GZMP by considering both the infinitesimal displacement of the constrained convex polyhedron and the moment about the edges of it. Also, the region is defined on the floor by introducing the method for projecting the GZMP. We will explain our proposed method using the 3-D convex polyhedron shown in Fig. 4(a). Since the robot will rotate about an edge of the convex hull when falling down, we focus on the rotational motion of the convex polyhedron about the edge, including the vertices X and Y . Let prot be the position vector of an arbitrary point on the line including the vertices X and Y . Also, let qrot = [ qTrot T rot] T be the infinitesimal translational/rotational displacement vector of the convex polyhedron. Since the vertex Z may break contact with the environment but it cannot go inside it, the following inequality can be satisfied: d (XY ) j qrot 0; (j = 1; ",
            " In this subsection, we will obtain the relationship between the GZMP and the moment about an edge of the convex hull. By using the duality between the force and the infinitesimal displacement, the moment about the edge including the vertices X and Y satisfies the following equation: m (XY ) = d (XY )T k; k 0: (12) If Proposition 1 is satisfied, (12) shows that the sign of m(XY ) is same as that of . Then, to obtain the relationship between the GZMP and the moment about an edge of the convex polyhedron, we introduce a virtual plane and define the GZMP on the plane as shown in Fig. 4(b). By using the force fE and moment E at the GZMP on the virtual plane, we can also formulate the moment about the edge including the vertices X and Y as m (XY ) = pTX pTY kpX pY k (pE prot) fE + eZe T Z E (13) where eZ denotes the unit normal vector of the virtual plane. When (pX pY ) TeZ 6= 0 is satisfied in (13), E affects the moment about the edge. In this case, the direction of the moment about the edge cannot be uniquely determined by simply considering the position of the GZMP on the virtual plane",
            " When the virtual plane is expressed as z(XY ) E = z (XY ) Ed , the position of the GZMP modified in Definition 2 can be expressed as x (XY ) E y (XY ) E = fME [( pG g) D]g 1 ME pG ez (XY ) Ed ( pG g) +E _LG (14) where E = [e(XY ) x e (XY ) y ]T D = 1 0 0 0 1 0 T e = [0 0 1]T : Now, the virtual plane is divided into two regions, using the line including the edge where each region is identified by the direction of moment about the edge. However, since the direction of moment about an edge satisfying Proposition 1 is unique, the GZMP is included in one of the two regions on the virtual plane. Then, let us consider the virtual plane including two edges sharing a common vertex, as shown in Fig. 4(c). By using two lines, we divide the virtual plane into four regions. The four regions on the virtual plane can be identified by the direction of moment about two edges, as shown in Fig. 4(d). If both of the edges satisfy Proposition 1, the GZMP is included in one of the four regions. Fig. 4(c) shows the region of the GZMP corresponding to m(XY ) > 0 and m(XZ) < 0. Also, Fig. 4(d) shows the four regions on the plane defined by the vertices X; Y , and Z . Furthermore, let us consider the motion of the convex hull after the convex hull begins rotating about the edge including the verticesX and Y . Let us observe the motion of the robot from the reference coordinate system fixed to its sole. The direction of the gravity force changes due to the rotation about the edge. This change of gravity force vector affects the moment about the edge. To explain the basic mechanism as simply as possible, let us suppose that an inverted pendulum moves from the unstable equilibrium state",
            " Using Proposition 3, we project the line including the edges of the convex hull satisfying Proposition 1 onto the real floor, and the lines projected on the floor form the edge of the region of the GZMP. Here, since (21) depends on the position of the COG of the robot, the region of the GZMP also depends on the position of the COG. Now, the method for obtaining the region of the GZMP for maintaining the balance of a humanoid robot is summarized by the following theorem. Theorem 1 (Region of GZMP): Project all the edges of the convex hull satisfying Proposition 1 onto the floor using Proposition 3, as shown in Fig. 4(e). The region of the GZMP is defined by the direction of moment about an edge using (12). If Proposition 2 is satisfied, the robot might fall down when the GZMP lies on the edge of the region. Motion of the Object: Let us consider the case where a humanoid robot pushes an object placed on the floor and where the weight of the object is light. In such a case, the robot may fall down as the object moves away from the robot. To prevent the robot from falling down, the COP of the foot\u2013ground contact should be included in the 2-D convex hull of the foot-supporting area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003223_tro.2006.882956-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003223_tro.2006.882956-Figure2-1.png",
        "caption": "Fig. 2. OLT and the associated moments.",
        "texts": [
            " But this modification results in a complex dynamical model of the vehicle. This issue is solved by synthesizing an appropriate controller which takes into account these model nonlinearities. For more details on system design and technical analysis, refer to [4], [5], and [9]. Differential Propeller Speeds: Since it is possible to independently modify the speed of each propeller, then the rolling moment can be given by = l(P1 P2) (1) where l is the distance from the motors to the aerodynamic center O (see Fig. 2). P1 and P2 are the lifts generated by the two propellers. Longitudinal Tilting (LT): The yaw moment is obtained by differential LT of the rotors = l(P1 sin 1 P2 sin 2) (2) where 1 and 2 are the LT angles. Since the center of gravity G is located below the tilt axes, the sum of longitudinal components of P1 and P2 generates a pitching moment with respect to G. It can be expressed as = h(P1 sin 1 + P2 sin 2) (3) where h is the distance from G to the tilt axes. Opposed Lateral Tilting (OLT): Referring to Fig. 2, forcing propellers to precess laterally in opposite directions will create gyroscopic moments (M1 ;M2 ) [9], which are directed as shown in Fig. 2. Their total magnitude, calculated in Section III, is given by M = M1 +M2 = Ir _ (!1 + !2) cos (4) with Ir is the fan inertia moment about its spin axis. Also, a nonzero tilt angle will generate a component of the fan torques (Q1; Q2) along the lateral axisE2, creating a pitching moment on the aircraft in the same direction as M . Then, = Ir _ (!1 + !2) cos + (Q1 + Q2) sin . The key idea consists of using both LT and OLT for pitch/forward motion control. More precisely, the collective LT generates a pitching moment ( ) by directing the combined thrust vector, and the OLT creates complementary pitching moments ( ) and minimizes or eliminates the resulting adverse reaction Ma r . The complete dynamics of a helicopter is quite complex, and somewhat unmanageable for the purpose of control [10]. Therefore, we consider a helicopter model as a rigid body incorporating a force/torquesgeneration process [6]. A. Rigid-Body Dynamics The equations of motion for a rigid body subject to body force F0 2 3 and torque 2 3 applied at the center of mass and specified with respect to the body coordinate frame A = (E1; E2; E3) (see Fig. 2) are given by the Newton\u2013Euler equations inA, which can be written as m _ A + m A = F0 J _ + J = (5) where A 2 3 is the body velocity vector, 2 3 is the body angular velocity vector, m 2 specifies the mass, and J 2 3 3 is an inertia matrix.F0 combines the force of gravity and the lift vectorF generated by the propellers. The first equation in (5) can be also expressed in the inertial frame I = (Ex; Ey; Ez). By defining = (x; y; z) and I as the position and the velocity of the helicopter relative to I , we can write _ = I ; m _ I = RF mgEz J _ + J = (6) where R 2 SO(3) is the rotation matrix of the body axes relative to I , satisfying R 1 = RT and det(R) = 1. It can be obtained by using the Euler angles = ( ; ; ) which are yaw, pitch, and roll (cf. [5] and [11] for its expression). B. Force/Torques-Generation Process In the following, we express the force/torques pair (F; ) exerted on the helicopter. To develop our analysis, we use two additional coordinate frames, A1 = (A1x; A1y; A1z) and A2 = (A2x; A2y; A2z), which are associated with the rotor n 1 and rotor n 2, respectively (see Fig. 2). Therefore, the orientation of the rotors n 1 and n 2 with respect toA can be defined by the rotational matrices T1 and T2 whose expressions are given, respectively, by c s s s c 0 c s s c s c c ; c s s s c 0 c s s c s c c : (7) Force Vector: The forceF generated by the rotorcraft is the resultant force of the thrusts generated by the two propellers P A 1 = (0; 0; P1) T ; P A 2 = (0; 0; P2) T : (8) Pi is the lift that the propeller i produces by pushing air in a direction perpendicular to its plane of rotation [10]",
            "2c )s : (11) Fan Torques: As the blades rotate, they are subject to drag forces which produce torques around the aerodynamic center O. These moments act in opposite directions relative to ! Q A 1 = (0; 0; Q1) T ; Q A 2 = (0; 0; Q2) T : (12) The positive quantities Qi can be written as a function of propeller speeds Qi = Ct! 2 i ; Ct > 0. Similarly, these torques can be written in A as Q = 2 i=1 TiQ A i = (Q1s Q2s )c (Q1 +Q2)s (Q1c Q2c )c : (13) Thrust-Vectoring Moment: Denote O1 (O2) as the application point of the thrust P1 (P2). From Fig. 2, we can define O1G = (0; l; h)T and O2G = (0; l; h)T as positional vectors expressed in A. Then, the moment exerted by F on the airframe is MF = (T1P1) O1G+ (T2P2) O2G: (14) After some development, we obtain MF = l(P1c P2c )c + h(P1 P2)s h(P1s + P2s )c l(P1s P2s )c : (15) Adverse Reactionary Moment: As described in Section II, this moment appears when forcing the rotors to tilt longitudinally. It depends especially on the propeller inertia It and on tilt accelerations. This moment acts as a pitching moment, and can be expressed in A as follows [9]: Ma r = It( 1 + 2) E2: (16) The complete expression of the torque vector acting with respect to the center of mass of the helicopter and expressed in A is =M +M +Q+MF +Ma r: (17) Finally, the explicit expression of could be obtained by replacing the right-hand terms in (17) by the formulae (10)\u2013(16)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003333_s0021-9797(03)00148-6-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003333_s0021-9797(03)00148-6-Figure4-1.png",
        "caption": "Fig. 4. Sweep rate dependence of the cyclic voltammograms under finite diffusion conditions for an [Os(bpy)2(PVI)10Cl]+ film on a 3-mm glassy carbon electrode. Sweep rates (top to bottom) 40, 20, 10, and 5 mV s\u22121. Surface coverage \u0393 is 1.8 \u00d7 10\u22128 mol cm\u22122. Supporting electrolyte is aqueous 0.1 M p-toluenesulfonic acid.",
        "texts": [
            " Therefore, it is important to distinguish between specific ion effects and simple changes in E\u25e6\u2032 brought about by changing the electrolyte concentration. This objective can be achieved by varying the concentration of the ion that undergoes ion pairing in a series of solutions where the ionic strength is kept constant [29]; e.g., for the Os\u2013PVI system the tosylate concentration has been systematically varied while keeping the ionic strength fixed with HCl that does not ion pair with the metal complex [30]. As illustrated in Fig. 4, the experimental response of this [Os(bpy)2PVP10Cl]+ polymer film is well defined and is largely consistent with that expected for an ideal system [31, 32]. Although the bpy ligands can be electrochemically reduced in a nonaqueous solvent such as acetonitrile, the most analytically useful redox process is that associated with the metal-based Os2+/3+ couple. In sensing applications, the Os2+ or Os3+ acts as a mediator between a redox-active substrate in solution and the electrode to drive a mediated reduction or oxidation reaction",
            " For example, in the case of oxidases, the formal potential of the flavin redox center is low enough so that a relatively weak oxidant with a potential in the range from +30 to \u2212100 mV versus Ag/AgCl would be sufficient to efficiently mediate electron transfer to the enzyme. The advantage of a low driving potential is that interference from redox-active species such as ascorbate is substantially reduced. Metallopolymers in which a poly-4vinylpyridine or poly-N -vinylimidazole backbone contains covalently bound osmium polypyridyl complexes such as [Os(bpy)2Cl]+ or [Os(4,4\u2032-dimethoxy-2,2\u2032bipyridine)2Cl]+ have proven to be particularly useful in this regard. As shown in Fig. 4, the redox potential for the bipyridyl complex is approximately +250 mV, but it shifts to +35 mV on going to the dimethoxy derivative. These metallopolymers exist as hydrogels, thus providing an ideal microenvironment within which the enzyme can react. As discussed in Section 2.4, the rate of charge transport through these materials is often limited by either charge compensating counterion transport or the movement of the redox centers through segmental motions of the polymer backbone. These processes tend to be rather slow and freely diffusing oxygen can compete in turning over the immobilized enzyme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure12.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure12.6-1.png",
        "caption": "Fig. 12.6 Structural ceramic parts. a Various parts, b ceramic bearing, c ceramic cylinder body",
        "texts": [
            " They have found numerous applications in many industries, one of which is in internal combustion engines installed on civil and military vehicles. Ceramic components make higher operating temperature possible which means higher efficiency of the combustion of fuel. From the 1970s, many countries, including the U.S., Japan, Germany, Italy, and China, attempted to make ceramic components of internal combustion engines. The common parts which can be made with ceramics include cylinders, cams, combustors, rotors etc. some examples are shown in Fig. 12.6. 438 12 Manufacturing Technology During New Era Although these materials have superior properties, machining is still a big challenge. Thus, many companies keep the technologies of machining difficult-to-cut materials as business secret. Some countries even treat it as national critical technologies. Machining of difficult-to-cut materials has some overlap with high speed machining and ultraprecision machining. Machining of difficult-to-cut materials, as any modern technology, involves cutting tools, machines and process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000815_j.mechmachtheory.2021.104331-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000815_j.mechmachtheory.2021.104331-Figure5-1.png",
        "caption": "Fig. 5. Force analysis of substructure 4.",
        "texts": [
            " (10) results in \u03c1w, 5 = W T 5 $ w, 5 (11) where $ w, 5 = $ w,E + $ w, G E + $ w, G 5 , $ w, G 5 = \u2212m 5 g [ \u02dc z ( r 6 + R 6 r 6 G 5 ) \u00d7\u02dc z ] , \u03c1w, 5 = [ \u03c1w, 5 , f \u03c1w, 5 ,\u03c4 ] , W 5 = [ R 5 \u02c6 r5 R 5 0 R 5 ] , r 5 = r 6 + R 6 r 6 5 , $ w, 5 is the resultant externally applied wrench imposed at point O E for joint 5, $ w, G 5 is the equivalent gravitational wrench of link 5 applying on point O E , \u03c1w, 5 is the reaction force at joint 5, \u02c6 r5 is the skew-matrix of the position vector r 5 . Similarly, the equation of static equilibrium of substructure 4 shown in Fig. 5 can be formulated as \u23a7 \u23aa \u23a8 \u23aa \u23a9 f E \u2212 m E g \u0303 z \u2212 m 5 g \u0303 z \u2212 m 4 g \u0303 z = R 4 \u03c1w, 4 , f \u03c4E \u2212 m E g ( R E r E G E ) \u00d7\u02dc z \u2212 m 5 g ( R E r E 6 + R 6 r 6 G 5 ) \u00d7\u02dc z \u2212 m 4 g ( R E r E 6 + R 6 r 6 5 + R 5 r 5 G 4 ) \u00d7\u02dc z = ( R E r E 6 + R 6 r 6 5 + R 5 r 5 4 ) \u00d7 ( R 4 \u03c1w, 4 , f )+ R 4 \u03c1w, 4 ,\u03c4 (12) where \u03c1w, 4 , f = [ \u03c1w, 4 , f x \u03c1w, 4 , f y \u03c1w, 4 , f z ] T , \u03c1w, 4 ,\u03c4 = [ \u03c1w, 4 ,\u03c4x \u03c1w, 4 ,\u03c4y \u03c1w, 4 ,\u03c4 z ] T , \u03c1w, 4 , f and \u03c1w, 4 ,\u03c4 are the reaction force and torque of joint 4 acting at point O 4 , m 4 is the mass of link 4, G 4 is the mass center of link 4, r 5 G 4 is the position vector from point O 5 to point G 4 evaluated in { O 5 }, and r 5 4 is the position vector from point O 5 to point O 4 evaluated in { O 5 }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003375_1.2197850-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003375_1.2197850-Figure1-1.png",
        "caption": "Fig. 1 Contact problem definition: bodies I and II in contact, planes of principal curvatures, geometrical parameters, and applied force Q \u20207\u2021",
        "texts": [
            " All deformations occur in the elastic range; \u2022 The stress disappears at a great distance from the contact zone; \u2022 Loading is perpendicular to the surface: the effect of surface shear stresses is neglected; \u2022 Tangential stress components are zero at both surfaces within and outside the contact zone; \u2022 The stress integrated over the contact zone equals the force pushing the two bodies together; \u2022 The distance between the two bodies is zero within the contact zone but finite outside: the contact area dimensions are small compared to the local radii of curvature of the bodies under load; \u2022 In the absence of an external force, the contact zone degenerates in a point. The notations and main results commonly used in the Hertzian contact theory are going to be exposed now. 2.2 Geometrical Description of Contact. Figure 1 presents the contacting surfaces of two bodies. is the angle between planes O ,xI ,z and O ,xII ,z . The contacting surface of the two bodies ellipsoids , subscript I and II rolling elements and raceways in case of rolling bearings , is defined by their principal curvature =1/r along two perpendicular directions x and y denoted with subscript I or II according to the considered body. The resulting notations of curvature are Ix and Iy for body I and IIx and IIy of body II. Curvature is negative if the center of curvature is outside the body i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003233_jsvi.2000.3169-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003233_jsvi.2000.3169-Figure1-1.png",
        "caption": "Figure 1. Schematic view of a helical spring.",
        "texts": [
            " In fact, the Wittrick}Williams method [16] is used to determine the natural frequencies more e$ciently. Moreover, the dynamic sti!ness matrix can be used directly as an &&exact'' element in a model of a more complicated structure, for example a vehicle. The method allows an e$cient calculation to be made which accounts for the complex modal behaviour of springs at high frequency. The method is applied to a typical spring from a car suspension in section 3. For clarity, the equations of a helix are introduced \"rst and used to derive the equations of motion of a helical spring. Figure 1 shows a helical coil spring, the axis of which lies along the x-axis. The helix radius is R and the helix angle is a. The variable s is used to measure the distance along the wire and is related to the angle / by /\"s cos a/R. (1) The global (x, y, z) co-ordinates are related to / by x\"R/ tan a, y\"R cos/, z\"R sin / . (2) At any point on the helix, local co-ordinates are de\"ned as shown in Figure 2, with u( radial, w( tangential and v( binormal to the other directions. The displacements (u, v, w) in these local co-ordinates are related to those in global co-ordinates (u x , u y , u z ) by i g j g k u v w e g f g h \" 0 ",
            " Frenet formulation [17] allows all the displacements and resultant forces to be given as functions of s. The curvature i and tortuosity q of the helix are de\"ned by i\" cos 2 a R , q\" sin a cos a R . (4) The relations between these parameters and the three unit vectors [14] can be written in matrix form as L Ls i g j g k u( v( w( e g f g h \" 0 q !i !q 0 0 i 0 0 i g j g k u( v( w( e g f g h . (5) Consider the situation in which the spring is subjected to an arbitrary dynamic load F1 , as shown in Figure 1. Then at any cross-section the wire is subjected to three components of force P u , P v , P w and three moments M u , M v , M w about the u( , v( and w( directions (see Figure 2). These forces and moments result in the linear and rotational displacements of the wire and cause the coupling e!ects of motion of the spring. It will be assumed that the cross-section of the wire has two axes of symmetry which coincide with the directions u( and v( . Suppose that the components of the linear displacements d, rotations h, concentrated forces P and moments M at position s are de\"ned by i g g j g g k d h( P M e g g f g g h \" d u d v d w h u h v h w P u P v P w M u M v M w i g j g k u( v( w( e g f g h "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure6-1.png",
        "caption": "Fig. 6. Circular kinematic loop-chain on x\u2013z plane and Y-shaped unit on the 1st octant.",
        "texts": [
            " The mobility of the closed loop can hence be obtained and is the same as that of the whole mechanism. The mobility of each of the kinematic sub-chains also has the same mobility. This principle can be used to decompose the ball mechanism to facilitate the mobility analysis. Decomposing the ball into a circular kinematic loop-chain, several semi-circular kinematic chains and Y-shaped mechanism units in eight octants, the motion of the circular loop-chain remains the same as that before the decomposition. Thus, the mobility analysis can be implemented in the circular loop-chain as in Fig. 6. It can be seen that the loop-chain consists of a set of elementary four-legged platforms and the Y-shaped unit consists of an elementary three-legged platform and parallelograms. Thus the mobility of these elementary platforms is essential to the mobility analysis of the ball. The elementary four-legged platform is the basis of a circular loop-chain. It acts to connect two orthogonal circular loop-chains and to connect the loop chains to a Y-shaped unit in an octant. The platform consists of two square hubs as a platform and a radially movable base and four legs in the form of scissors structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002816_ip-cta:19951613-Figure19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002816_ip-cta:19951613-Figure19-1.png",
        "caption": "Fig. 19 BTT-CLOS guidance",
        "texts": [
            " A guidance controller is utilised at the ground station taking account of tracker information, about missile position, target position and the angular velocity and acceleration of the line of sight, to provide demanded accelerations for the missile. These can then be transmitted to the missile via a radio link. In this case it is also assumed that a bank-toturn (BTT) control strategy is utilised. The missiles ailerons are employed first, to roll the missile to the desired orientation, with the elevators then used to accelerate the missile towards the line of sight, as shown in Fig. 19. In 0,125 0.115 practice both ailerons and elevators are employed simultaneously, leading to nonlinear cross-coupling [30]. Likewise, BTT control complicates the calculation of missile position as a highly nonlinear axes transformation is now required. Applying the basic laws of aerodynamics while making assumptions such as constant mass, small attack angle a and small sideslip angle b. the nonlinear model shown in Section 9.2 can be developed [31]. This includes many of the important nonlinear aspects of BTT-CLOS guidance, such as the axes transformation and nonlinear 1EE Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000281_j.promfg.2020.04.215-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000281_j.promfg.2020.04.215-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the hybrid manufacturing process route starting from a basic forged geometry followed by AM.",
        "texts": [
            " For many applications, near-net-shape technologies such as additive manufacturing (AM) could enable a more resourceefficient production than conventional manufacturing routes [4]. However, process time and hence manufacturing costs in additive manufacturing rise rapidly with the part size [5]. Therefore, applying AM processes only partially could compensate for the lack of resource efficiency and flexibility of die-based serial production by forging. Combining AM and forging, two possible manufacturing routes can be put into practice: First, an additive manufacturing process can be used to add structural or functional elements to a forged pre-form (see Fig. 1). This hybrid manufacturing route is currently subjected to intensive research [6-8]. However, most of the existing work on titanium alloy Ti-6Al-4V focuses on additive manufacturing of features for pre-formed sheet metal components. This study investigates the use of AM for generating or modifying ribs from Ti-6Al-4V on pre-forms created by hot forging, allowing for:  simple creation of variants  complex and near-net-shape components  repair of parts  local properties The second manufacturing route can be used to generate a pre-form by AM, which then will be forged into its final shape by using only one single forging step",
            " The present study investigates the use of two different additive manufacturing processes for hybrid manufacturing of Ti-6Al-4V high-performance aerospace components: i.e. powder laser metal deposition (p-LMD) and wire-arc additive manufacturing (WAAM). Powder laser metal deposition is used to manufacture specimens for a fundamental analysis of the process as well as the behavior and properties of the specimens under different heat treatment conditions. After the basic characterization of specimens, a hybrid bracket as shown in Fig. 1, is manufactured by p-LMD and by wire-arc additive manufacturing. The WAAM process seems to be superior to other AM techniques \u2013 such as p-LMD \u2013 regarding the manufacturing time and deposition rate, power efficiency as well as investment costs [13]. The paper is structured as follows: Section 2 gives a deep overview of the manufacturing of the specimens considered in this study. Also, the procedures used for microstructural analysis and for the determination of mechanical properties are presented",
            " / Procedia Manufacturing 47 (2020) 261\u2013267 263 2 Author name / Procedia Manufacturing 00 (2019) 000\u2013000 process and low resource-efficiency, with a material yield far from 100% [2, 3]. For many applications, near-net-shape technologies such as additive manufacturing (AM) could enable a more resourceefficient production than conventional manufacturing routes [4]. However, process time and hence manufacturing costs in additive manufacturing rise rapidly with the part size [5]. Therefore, applying AM processes only partially could compensate for the lack of resource efficiency and flexibility of die-based serial production by forging. Fig. 1. Illustration of the hybrid manufacturing process route starting from a basic forged geometry followed by AM. Combining AM and forging, two possible manufacturing routes can be put into practice: First, an additive manufacturing process can be used to add structural or functional elements to a forged pre-form (see Fig. 1). This hybrid manufacturing route is currently subjected to intensive research [6-8]. However, most of the existing work on titanium alloy Ti-6Al-4V focuses on additive manufacturing of features for pre-formed sheet metal components. This study investigates the use of AM for generating or modifying ribs from Ti-6Al-4V on pre-forms created by hot forging, allowing for:  simple creation of variants  complex and near-net-shape components  repair of parts  local properties The second manufacturing route can be used to generate a pre-form by AM, which then will be forged into its final shape by using only one single forging step",
            " The present study investigates the use of two different additive manufacturing processes for hybrid manufacturing of Ti-6Al-4V high-performance aerospace components: i.e. powder laser metal deposition (p-LMD) and wire-arc additive manufacturing (WAAM). Powder laser metal deposition is used to manufacture specimens for a fundamental analysis of the process as well as the behavior and properties of the specimens under different heat treatment conditions. After the basic characterization of specimens, a hybrid bracket as shown in Fig. 1, is manufactured by p-LMD and by wire-arc additive manufacturing. The WAAM process seems to be superior to other AM techniques \u2013 such as p-LMD \u2013 regarding the manufacturing time and deposition rate, power efficiency as well as investment costs [13]. The paper is structured as follows: Section 2 gives a deep overview of the manufacturing of the specimens considered in this study. Also, the procedures used for microstructural analysis and for the determination of mechanical properties are presented",
            " To achieve this, the starting point of each layer is shifted by 90\u00b0 and a contouring is added after each layer to ensure near-netshape and edge stability during build-up. This strategy avoids accumulation of deposited material due to delay during laser on/off and acceleration/deceleration of the axes, since the powder is continuously fed. The process parameters used to build up the specimens for the fundamental analysis are shown in Table 1. To deposit the WAAM-layers on the forged basic geometry (see Fig. 1 and Fig. 10), wire with a diameter of 1 mm was fed into the melt pool produced by an electric arc, using a six-axis FANUC robot with a welding power source TPS/i 500 by Fronius. In order to prevent oxidation, the material was deposited within a closed argon gas chamber. The applied WAAM process parameters were the following: 95A current, 13V voltage, 8 m/min wire feed rate and the layer thickness was approximately 4 mm. To investigate the influence of different heat treatments on the microstructure evolution and mechanical properties, three different conditions were applied to the p-LMD material: (1) \u201cas-built\u201d, (2) stress-relief annealing at 710\u00b0C for 6h, followed by cooling at ambient air and (3) \u03b2-annealing at 1050\u00b0C for 3h, followed by stress-relief annealing at 710\u00b0C for 6h, followed by cooling at ambient air"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003387_robot.1987.1087795-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003387_robot.1987.1087795-Figure1-1.png",
        "caption": "Figure 1. Velocity Ellipsoid.",
        "texts": [
            " This is an effective means for singularity avoidance, since the volume of this ellipsoid is zero at singularities (where the achievable task velocity collapses into a lower dimension). For clarity, we will refer to this ellipsoid as the velocity ellipsoid. The velocity ellipsoid is a useful tool for visualizing the velocity transmission characteristics of a manipulator at a specific posture. The principal axes of the velocity ellipsoid coincides with the eigenvectors of (J J ')-I and the length of a principal axis is equal to the reciprocal of the square root of the corresponding eigenvalue (see Fig. 1). The optimal direction for effecting velocity is along the major axis of the ellipsoid, where the transmission ratio is at a maximum. Conversely, the velocity is most accurately controlled along the minor axis of the ellipsoid, where the transmission ratio is at a minimum. 2.2 The Force Ellipsoid Analogous to the velocity ellipsoid, we can also define a force ellipsoid for describing the force transmission characteristics of a manipulator at a given posture. Forces in joint space and task space are mapped via the same Jacobian through the relation z = J T f (3) where f is the force vector in task space and z is the joint torque vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003460_robot.2006.1642231-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003460_robot.2006.1642231-Figure3-1.png",
        "caption": "Fig. 3 Supposed surface stress distribution \u03c3(x, y).",
        "texts": [
            " There are three pieces of stretchable conductive fabric on the soft layer, between the soft and hard, and under the hard. Each piece has an area of 30\u00d730 mm2. The side length of the conductive fabric piece is comparable to the TPDT on human forearms. The insulator layers and the conductive pieces adhere to each other by soft double-faced tape, and two capacitors are formed in the layers. Supposing that a robot surface is hard, we attach the bottom of the sensor element prototype to an acrylic base. We suppose a surface stress as illustrated in Fig. 3; a uniform surface stress distribution \u03c3(x, y) [Pa] is vertically loaded to the surface of the sensor element in a contact field S, that is, ( ) ( )\u23a9 \u23a8 \u23a7 \u2209 \u2208 \u2261 S,if0 S,if/ ),( yx yxSF yx (1) Soft layer \u03bb1 is more easily compressed than hard layer \u03bb2. where F [N] is the total intensity of the contact force and S [m2] is the area of S. Now we take note of the area of S, not the shape, so we suppose that S is circular for simplicity. We also assume the following. First, the nonlinear elasticity of the insulator layers is the entropy elasticity [16] expressed as )2,1(1 3 2 =\u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u2212= n E n n n \u03bb \u03bb (2) n n n d d\u0394 \u2212\u22611\u03bb (3) where n is the layer identification; n = 1 means the upper soft layer and 2 the lower hard layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003427_978-94-017-0657-5_48-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003427_978-94-017-0657-5_48-Figure3-1.png",
        "caption": "Figure 3. Some legs for linear TPMs.",
        "texts": [
            " 2 PPRR The axis of the second P joint Parallel to the axes of R joints 3 PRPR is perpendicular to the axes of 4 PRRP the R joints 5 PRRR The axis of the P joint is not Parallel to the axes of R joints perpendicular to the axes of the R joints 6 RPPR The axes of the R joints are Perpendicular to the axes of 7 RPRP not perpendicular to the axes the two unactuated P joints 8 RRPP of all the P joints 9 RRPRR The axis of the P joint is Parallel to the axes of R joints 10 RRRPR perpendicular to the axes of 11 RRRRP the R joints 12 RRRRR Parallel to the axes of R joints 13 RPRRR The axis of the P joint is Parallel to the axes of R joints 14 RRPRR perpendicular to the axes of 15 RRRPR the R joints 16 RRRRR Parallel to the axes of R joints For a better understanding of the legs for linear TPMs, their basic types are classified into the following four classes. 1) Legs for linear TPMs with an actuated P joint and two unactuated P joints. This class of legs includes the PPP (Fig. 3(a)) leg. 2) Legs for linear TPMs with an actuated P joint and a combination of two unactuated R joints with parallel axes and one unactuated P joint whose axis is perpendicular to the axes of the unactuated R joints with parallel axes, or a combination of three unactuated R joints with parallel axes. This class of legs includes the PPRR, PRPR, PRRP and PRRR (Fig. 3(b)) legs. 3) Legs for linear TPMs with an actuated Rjoint and two unactuated P joints. This class of legs includes the RPPR, RPRP (Fig. 3( c)) and RRPP legs. 4) Legs for linear TPMs with an actuated R joint and a combina tion of two unactuated R joints with parallel axes and one un- actuated P joint whose axis is perpendicular to the axes of the unactuated R joints with parallel axes, or a combination of three unactuated R joints with parallel axes. This class of legs includes the RRPRR, RRRPR, RRMp, RRMR (Fig. 3(d)), RPRRR, RRPRR, RRRPR, and RRMR legs. It is noted that in a leg for linear TPMs with an actuated R or H joint, there must be one and only one unactuated R or H joint whose axis is parallel to the axis of the actuated R or H joint. Once the actuated R or H joint is locked, the unactuated R or H joint with parallel axis is also locked by the total constraints on the moving platform of all the legs in a linear TPM. Otherwise, the orientation of the moving platform will change. In the HPPR, HPRP, HRPP, RHPP, RPHP and RPPH legs for linear TPMs, the axes of the Hand R joints are not necessarily perpendicular to the axes of the two unactuated P joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003904_jra.1987.1087138-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003904_jra.1987.1087138-Figure1-1.png",
        "caption": "Fig. 1. Link parameters 8, d, a, and CI.",
        "texts": [
            " It involves multiplications of 4 x 4 matrices to transform coordinate frames in symbolic forms. In contrast, dual-number transformation requires multiplications of 3 X 3 matrices for the same operation, so long as the dual angle is adopted. After the coordinate transformation, constructing the dynamic and kinematic equations is also convenient using the dual-number transformation procedure. The relationship between these two transformations in robotics are as follows. Consider the standard defining relationship between coordinate frames of two adjacent links of a robot, as shown in Fig. 1, given in [lo, p.531: rotate about Z k - 1 (axis), an angle e,; translate along z k - a distance dk; translate along rotated x k - = x k (axis), a length a k ; rotate about x,, the twist angle a k . . I .. .. .. + \u20acbo in which a. = a- \u2018a = a/llall, and bo = 01 (b - The homogeneous transformation that decribes these four 618 IEEE JOURNAL OF ROBOTICS AND AUTOMATION, VOL. RA-3, NO. 6, DECEMBER 1987 where c 6 k = cos 6 k , s 6 k = sin 0 k , etc., for abbreviation. Note that the first two matrices represent a rotation about and a translation along the same axis, hence they are commutable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.19-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.19-1.png",
        "caption": "Figure 13.19. Transverse section through point A.",
        "texts": [
            " Direction of the Normal to the Tooth Surface at A The simplest method for finding the normal to the tooth surface at A is to find the directions of any two tangents through A. The two tangents define the tangent plane, and the direction of the normal must be perpendicular to both of them. One line which touches the tooth surface at A is the generator through A, since the entire generator lies within the surface, and is therefore tangent to it. Hence, the normal to the tooth surface at A is perpendicular to the generator direction nG A second tangent direction can be seen in /.I' 338 Tooth Surface of a Helical Involute Gear Figure 13.19, which shows the transverse section through A. The profile normal at A touches the base circle at E, and the profile tangent at A is therefore parallel to CEo Point G lies on the axial line through E, so in Figure 13.19, G would appear exactly behind E. The vector n~ is therefore parallel to CE, and hence is also parallel to the profile tangent at A. We introduce a unit vector n~ to indicate the direction normal to the tooth surface at A. We have shown that nA must n be perpendicular to both n: and n~, and it can therefore be expressed as follows, n: x n~ (13.78) The unit vector n~ is found from Equation (13.53), if we substitute G and Rb in place of A and R. We then obtain an expression for the unit vector normal to the tooth surface at A, Normal Section at A We define the normal section at any point A as the section through the gear perpendicular to the helix tangent at A, or in other words, perpendicular to n~",
            " Generally, we will consider the normal section through a point A which lies on the tooth surface, but the definition remains valid whether A lies on the tooth surface or not. Normal Profile Angle at Radius R Figure 13.20 shows the normal section through point A on the tooth surface at radius R. The shape of the tooth profile in a normal section is unknown at present, but we will describe later in this chapter how the shape can be calculated. If C is the centre of the transverse section through A, as shown in Figure 13.19, the line CA also lies in the normal section, since the unit vector n~ along CA is Normal Profile Angle at Radius R 339 perpendicular to n~. Earlier, we def ined the transverse profile angle ~tR as the angle between CA and the profile tangent in the transverse section. We now define the normal profile angle ~nR in a similar manner, as the angle between CA and the profile tangent in the normal section. The unit vector n~ in Figure 13.20 points in the direction of the normal to the tooth surface at A, and is therefore perpendicular to any line touching the surface at A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000225_s40684-020-00221-7-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000225_s40684-020-00221-7-Figure7-1.png",
        "caption": "Fig. 7 Workpiece fabricated by DED process",
        "texts": [
            " In the case of deposition using nitrogen, blackening (burning phenomenon) is confirmed because of low air environment blocking effect. Therefore, it is recommended to supply argon gas to powder feeder and DED device. Table 2 Final DED process conditions of the Ti-6Al-4V powder obtained in this study Laser power (W) 700 Laser feed rate (mm/s) 15 Argon gas flow (L/min) 20 Powder feed rate (g/min) 6 Fig. 4 Bead shape according to the laser power 1 3 Finally, the workpieces were fabricated for LAM, as shown in Fig.\u00a07. A hexahedral shape having the width, length and height of 100 mm, 20 mm and 10 mm was deposited in consideration of the properties test, and three workpieces (fabrication time: about 3 h per workpiece) were manufactured. The surface and inside of the deposited workpiece were measured to analyze the void and cracks, and no void and cracks occurred. An unmelted metal powder was found on the workpiece surface. However, the metal powder fused to the surface will be removed by post processing. To obtain the cutting depth for LAM, thermal analysis was performed by analyzing the temperature distribution during preheating"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure8.34-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure8.34-1.png",
        "caption": "Figure 8.34. Schematics showing electron energy filtering using (a) the n-filter and (b) the Gatan image filter in TEM, where OL = objective lens, I.L. = intermediate lens, P.L. = projection lens, CL = camera length. (After Krivanek et al., 1991, reprinted with permission from Les Editions de Physique.)",
        "texts": [
            " One method uses a Castaing-Henry filter, which consists of two 900 magnetic prisms and a retarding electric field (Castaing and Henry, 1962). The filter is located between the objective lens and the intermediate lens. The electrons are sent to a 900 electromagnetic sector, and then they are reflected by an electrostatic mirror. The electrons having different energies are dispersed. The second 900 prism deflects the electron back onto the optical axis. A slit is placed before the intermediate lens and selects the electrons with specific energy losses. This is the Q filter in Fig. 8.34a. This energy filtering can only be performed on a specially built TEM, but it has an advantage of using all of the transmitted electrons and it is most suitable for collecting the large angle scattered electrons. A detailed introduction of this energy-filtering system and its applications has been given by Reimer et al. (1990a and b). The other energy-filtering method uses a parallel-detection electron energy loss spectrometer attached to the bottom of a TEM (Shuman et al., 1986; Krivanek et al., 1991) (Fig. 8.34b). The system is composed of four components: TEM, electron energy loss spectrometer (EELS), energy-filtering system, and charge-coupled device (CCD) camera for digital data recording. The operation of the TEM is almost independent of the energy-filtering system, because the energy filtering occurs after the electron has passed through all of the lenses belonging to the TEM. The electrons are dispersed by the magnetic sectors in the EELS spectrometer, thus, electrons having different velocities (or energies) are focused on different positions in the plane of the energy-selecting slit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000076_j.ijfatigue.2019.105353-Figure14-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000076_j.ijfatigue.2019.105353-Figure14-1.png",
        "caption": "Fig. 14. Cumulative damage contour of the bogie frame made of S355J2W with weld polishing.",
        "texts": [
            " The shallower slope is 2m\u2212 1, and the endurance stress range is 5MPa near the cutoff limitation point. The material parameter m with a survival probability of 97.5% for the BM and welded joint are 0.0674 and 0.196, respectively. \u23a7 \u23a8\u23a9 = > = <\u2212 C N \u03c3 N N C N \u03c3 N N i ai m i ai m 1 D 2 2 1 D (15) The standard nominal stress framework in Section 4.1 and measured fatigue P-S-N curves are adopted for revealing the maximum fatigue cumulative damage region of the bogie welded frame with gear meshing excitation and weld toe polishing treatment, as plotted in Fig. 14. Compared with well-defined material grade based on BS 7608, it can be clearly observed that no distinct damage still takes place on the BM region of entire welded frame. However, the maximum fatigue cumulative damage (Dmax) is 0.0009 located at the journal guidance seat (as a welded region), which is considerably lower than those than original Fig. 9 (Dmax= 0.86) and improved Fig. 11 (Dmax= 0.08). Therefore, such Dmax= 0.0009 can be discounted to the total life of about 12,000 million kilometers. The safety factor of key load-carrying Fig. 12. The picture of bogie frame details and specimens. Note that the frame was actually polished around the weld and then HCF specimens were also smoothed. components of powered bogie frame can be estimated as 12000/10.8 \u2248 1111. Such a fairly high safety factor of welded frames made of S355J2W validates the applications of new steel grade and weld toe polishing technique. Nevertheless, the maximum damage region as the weld (see Fig. 14) can trigger a potential failure hazard particularly an improper welding process is adopted during the manufacturing of the powered bogie frame. Furthermore, during the routine quality inspection and actual operation maintenance, such position should also be carefully monitored to avoid a fatigue crack initiation under extremely complex fatigue loading. The synthesized action of external excitations and the novel internal excitation means the MNIEF on the fatigue life of high-speed bogie frames is investigated by a numerical model based on vehicle system dynamics and finite element simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003328_s0022-0728(96)04804-8-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003328_s0022-0728(96)04804-8-Figure7-1.png",
        "caption": "Fig. 7. Cyclic voltammograms of l mM catechol in water, (a) in the absence of, (b) and (c) in the presence of I mM 4HC at a glassy carbon electrode electrode. (d) Variation of peak current ratio /pa ~ //pc ~ ) vs. scan rate\u2022 Supporting electrolyte 0.15M CH3COONa; scan rate 100mVs-t; T = 26__ I\u00b0C.",
        "texts": [
            " However, I H NMR [26] and 13C NMR results indicate that o-quinone-3-carboxylic acid (2e) formed from the oxidation of le is selectively attacked from the C-4 position by enolate anion 2 leading to the formation of product (5c). 5c According to the voltammetric results, it seems that the chemical reaction between 4HC and o-quinone-3-carboxylic acid is fast enough and favours the progress of the subsequent reactions. The oxidation of catechol ( la) in the presence of 4HC as a nucleophile in water was studied by cyclic voltammetry. Fig. 7 (curve a) shows the cyclic voltammogram of l mM catechol in aqueous solution containing 0.15M sodium acetate. Similar to the previous cases, in the presence of 4HC, the peak current rat io Ipal/Ipcl increases proportionally to the augmentation in 4HC concentration, as well as by decreasing the potential sweep rate, and a second irreversible peak appears at 1.10 V vs. SCE (Fig. 7, curve b). Contrary to the report of Tabacovic et al. [23], this peak A 2 can be attributed to the oxidation of 4HC (see Fig. 1, curve c). Moreover, the multicyclic voltammogram of catechol in the presence of 4HC shows a new anodic peak A 0 at 0 .26V vs. SCE (Fig. 7, curve c). For this solution, the effect of increasing potential scan rate on the peak current ratio is shown in Fig. 7, curve d. Controlledpotential coulometry was performed at 0 .45V vs. SCE, and cyclic voltammetric analysis carried out during the electrolysis shows the formation of a new anodic peak A 0 at less positive potentials. All anodic and cathodic peaks decrease and disappear at a rate corresponding to the consumption of 4e ~ per molecule. The reaction mechanism is similar to that of previous cases, and according to our results it seems that the chemical reaction between 4HC and o-quinone (2d) is fast enough and favours the progress of the subsequent reactions leading to the formation of product (5d)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000458_j.jmapro.2020.07.023-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000458_j.jmapro.2020.07.023-Figure4-1.png",
        "caption": "Fig. 4. Schematic showing the mesh and co-ordinate system used in the simulation of the vertical component.",
        "texts": [
            " Vertical and horizontal model specification and mesh The model of the vertical specimen contained 135,086 elements with a typical size of \u00d7 \u00d70.30 0.30 0.26 mm3. A deposited \u2018block\u2019 height of around 1mm was used meaning the model contained 91 layers, approximately 20 times the layer thickness in the build. Each block deposited contained 4 elements through the thickness. The analysis took around 48 h to completing running on ABAQUS 6.14 on a node with 16 cores and 24GB memory on a high-performance computing facility. A schematic displaying the mesh and co-ordinate system used for the vertical specimen model is shown in Fig. 4. The model of the horizontal specimen contained 121,407 elements with a typical size of \u00d7 \u00d70.30 0.30 0.26 mm3. A deposited \u2018block\u2019 height of around 0.8 mm was used meaning the model contained 15 layers, approximately 16 times the layer thickness in the build. The analysis took around 18 h to complete running on ABAQUS 6.14 on a node with 16 cores and 24GB memory on a high performance computing facility. A schematic displaying the mesh and co-ordinate system used for the horizontal specimen model is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002842_j.1460-2687.2002.00108.x-Figure8-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002842_j.1460-2687.2002.00108.x-Figure8-1.png",
        "caption": "Figure 8 The pressure contours on the deformed shape at 4 ms after impact using the digitized 3D instep model.",
        "texts": [
            " Using 188 Sports Engineering (2002) 5, 183\u2013192 \u2022 2002 Blackwell Science Ltd the digitized 3D instep kick model and the digitized 3D infront kick model, this study then analysed the pressure distribution and the impact force at impact during the instep kick and the infront kick. Also, the shape of the infront kick model was with the ankle bent rectangularly and rotated outside 45 deg, and the offset distance was 0.02 m. The pressure contours on the deformed shape at 4 ms after the impact for the simulation result using the digitized 3D instep kick model are shown in Fig. 8. High compressive pressure is seen not only in the impact part but in the plantar as well, and tensile pressure is observed in the shin. The maximum pressure at this time was 126 KPa, while the minimum pressure was )543 KPa. The pressure contours on the deformed shape at 4 ms after the impact for the simulation result using the digitized 3D infront kick model are shown in Fig. 9. High compressive pressure is seen not only in the impact part but also in the plantar as well, and tensile pressure isobserved in thebackof theankle joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000001_j.surfcoat.2019.02.009-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000001_j.surfcoat.2019.02.009-Figure16-1.png",
        "caption": "Fig. 16. Surface measurement of tracks deposited with the large nozzle, true to scale. The right side shows cross sectional areas that are evaluated on a length of 0.6 mm. The left side shows the magnified track end as used for an approximation of the melt pool size.",
        "texts": [
            " The different standoffs change the diameter of the laser spot on the base material, leading to a varying melt pool area. The laser focuses inside the nozzle, thus a higher standoff results in a bigger laser spot size. The influence of the process parameters and heat input on the melt pool size is further analyzed by Huang et al. [25]. Sections of cladding tracks were measured with a Leica DCM 3D surface metrology microscope. Surface roughness is removed with a low-pass filter and a cut-off length of 0.35mm. The resulting wavy track surface is shown in Fig. 16 for the large nozzle and standoffs between \u22125.2 and \u22124.0mm on the right side. The cross sectional area Am of each track is evaluated numerically on a length of 0.6mm. Knowing the total powder mass flow, the mean powder catchment efficiency \u03b7c from cladding tracks and the related standard deviation for this measurement length can be calculated. As shown on the left side, the melt pool length is approximated by analyzing the shape of the track end. Multiple measurements reveal that the melt pool length lm is 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000908_tmag.2021.3076418-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000908_tmag.2021.3076418-Figure13-1.png",
        "caption": "Fig. 13. AIPM machine rotor topologies with asymmetric single-layer PMs and rotor cores. (a) Asymmetric bar-shape AIPM machine [36], [52]-[53]. (b) AIPM machine with inset PMs [54]. (c) AIPM machine with asymmetric Vshape PMs [55].",
        "texts": [
            " As illustrated in the previous sections, either asymmetric PM configuration or asymmetric rotor core geometry can adjust the axes of PM field and reluctance torque components, respectively. By employing both asymmetric PMs and rotor core the MFS effect in AIPM machines can be better utilized for torque enhancement with more freedoms of design. Various novel AIPM machine topologies with asymmetric PMs and asymmetric rotor core geometry are proposed in recent years, as overviewed below. Several AIPM machines with single layer asymmetric PMs and asymmetric rotor core are shown in Fig. 13. An AIPM machine rotor topology with asymmetric bar-shape PMs and extra flux barrier in each pole whose outer and inner ends are located near the rotor surface and right side of the PM in each pole, respectively, has been proposed and analyzed in [36], [52] and [53], as shown in Fig. 13 (a). Compared with the conventional bar-shape IPM machine benchmark, significant enhancement of torque density per magnet volume can be achieved. The AIPM machine with asymmetric inset PMs [54] as shown in Fig. 13 (b) shows the increase of torque compared with a conventional SPM machine due to fully aligned maximum PM and reluctance torque components. An AIPM machine exhibiting single layer asymmetric V-shape PMs Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 31,2021 at 23:28:03 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003751_s0263574708004748-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003751_s0263574708004748-Figure3-1.png",
        "caption": "Fig. 3. Motion of the sphere : Steps 1 and 2.",
        "texts": [
            " It can be observed that in this maneuver, only the Euler angle \u03c6 changes keeping \u03b1 and \u03b8 constant at \u03b10 and \u03b80, respectively. The control input u3 = \u03c6\u0307 is applied till the xb-axis is parallel to the XY plane on which the sphere is rolling. From (1), kI component of ib (unit vector along xb) is zero if either \u03b8 = 0 or 2\u03c0 or \u03c6 = \u00b1\u03c0 2 . If \u03b80 = 0 or 2\u03c0 , this can be achieved by changing the angle \u03c6 from \u03c60 to either \u03c0/2 or \u2212\u03c0/2 using the input u3 in this step. The contact point travels along a latitude circle of radius sin \u03b8 on the sphere surface and along a straight line on the plane as shown in Fig. 3 given by x = x0 + sin \u03b80 sin \u03b10 \u00d7 (\u03c6 \u2212 \u03c60) y = y0 \u2212 sin \u03b80 cos \u03b10 \u00d7 (\u03c6 \u2212 \u03c60). http://journals.cambridge.org Downloaded: 29 Nov 2014 IP address: 132.203.227.62 When the angle \u03c6 changes from \u03c60 to \u00b1\u03c0/2, the contact point reaches the position given by x1 = x0 + sin \u03b80 sin \u03b10 \u00d7 ( \u03c0 2 \u2212 \u03c60 ) y1 = y0 \u2212 sin \u03b80 cos \u03b10 \u00d7 ( \u03c0 2 \u2212 \u03c60 ) \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad for 0 \u2264 \u03c60 \u2264 \u03c0 x1 = x0 + sin \u03b80 sin \u03b10 \u00d7 ( \u2212\u03c0 2 \u2212\u03c60 ) y1 = y0 \u2212 sin \u03b80 cos \u03b10 \u00d7 ( \u2212\u03c0 2 \u2212\u03c60 ) \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad for \u03c0 \u2264 \u03c60 \u2264 2\u03c0. At the end of this maneuver, the configuration of the sphere is given by q1 = (x1, y1, \u03b10, \u03b80, \u00b1\u03c0 2 )",
            " Step 2: During this step since xb-axis is parallel to the XY plane, the sphere can be rolled about xb-axis using input u1 so that the zb-axis becomes vertical (perpendicular to the XY plane on which the sphere is rolling). This can be achieved by changing \u03b8 from \u03b80 to 0 or 2\u03c0 . Setting u3 = 0, u1 = 0, \u03c6 = \u00b1\u03c0/2, and \u03b1 = \u03b10 in model (8) the equations are given as x\u0307 = \u00b1(cos \u03b10)u1 y\u0307 = \u2213(sin \u03b10)u1 \u03b1\u0307 = 0 \u03b8\u0307 = \u00b1u1 \u03c6\u0307 = 0 \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad for \u03c6 = \u00b1\u03c0/2. It can be observed that the angles \u03b1 and \u03c6 do not change in this maneuver. Only the angle \u03b8 changes from \u03b80 to 0 or 2\u03c0 aligning zb-axis vertical. The contact point travels along a straight line as shown in Fig. 3 given by x = x1 + cos \u03b10 \u00d7 (\u03b8 \u2212 \u03b80) y = y1 \u2212 sin \u03b10 \u00d7 (\u03b8 \u2212 \u03b80). When \u03b8 changes from \u03b80 to 0 or 2\u03c0 , the contact point reaches the position given by x2 = x1 \u2212 cos \u03b10 \u00d7 \u03b80 y2 = y1 + sin \u03b10 \u00d7 \u03b80 } for 0 < \u03b80 \u2264 \u03c0 x2 = x1 + cos \u03b10 \u00d7 (2\u03c0 \u2212 \u03b80) y2 = y1 \u2212 sin \u03b10 \u00d7 (2\u03c0 \u2212 \u03b80) } for \u03c0 \u2264 \u03b80 < 2\u03c0. At the end of this maneuver, the configuration of the sphere is given by q2 = (x2, y2, \u03b10, 0, \u00b1\u03c0 2 ). Figure 3 shows how the sphere rolls in Steps 1 and 2. As the angle \u03c60 is in the range \u03c0 \u2264 \u03c60 \u2264 2\u03c0 , Step 1 is carried out to change the angle \u03c6 from \u03c60 to \u2212\u03c0 2 . Step 3: Let the point of contact at the end of Step 2 be P = (x2, y2). If O is the origin of the inertial frame attached to the XY plane, then the geometrical construction shown in Fig. 4 helps reconfiguration of the sphere. We construct two circles, one with center P and radius 2\u03c0n1 and another with center O and radius 2\u03c0n2; n1, n2 \u2208 Z. At the point P the zb-axis is vertical and circle centered at P and radius 2\u03c0n1 gives all possible locations where the sphere can be reconfigured with zb-axis vertical again"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003899_tcst.2005.863674-Figure16-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003899_tcst.2005.863674-Figure16-1.png",
        "caption": "Fig. 16. Possible sliding mode due to the set-valued vector field.",
        "texts": [
            " The point on reflects the origin in the state-space of (8) and is an equilibrium point of (8) (see Sections IV and V). Therefore, the discontinuity related to the friction model is not taken into account in the following. In order to understand the dynamics of (8) on , one should realize that on the vector field is set valued. The vector field is locally parallel to at and solutions may slide along . However, sliding along is only possible if the direction of lays in the convex hull of the set-valued vector field , where and (19) as illustrated in Fig. 16. Since solutions which slide along are also allowed to leave (and, consequently, ), by choosing any other direction from the convex hull of the set-valued vector field, this type of solution is not unique. Consequently, to guarantee uniqueness of solutions of (8), sliding along must be avoided. In order to study possible sliding modes along , we introduce a vector in the plane which is normal to . A condition such that sliding along is impossible is , since this assures that . Consequently, sliding along is not possible if , where "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000974_j.jmapro.2021.06.035-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000974_j.jmapro.2021.06.035-Figure5-1.png",
        "caption": "Fig. 5. Longitudinal sectioning through the fractured surfaces of a) MH and b) MV samples.",
        "texts": [
            " To prepare metallographic samples, transverse cuts (planes shown in Fig. 3a and b) were collected from the grip section of the MH and MV tensile samples. To investigate the effect of the as-built surface of the NMV on the tensile properties, the metallographic samples were prepared by longitudinally sectioning the NMV sample, Fig. 3c. Alongside the metallographic samples collected from transverse sections of the MV and MH samples, the fractured surfaces of the MH and MV samples were sectioned longitudinally (along the tensile axis) as demonstrated in Fig. 5, for crack path characterisation. All metallographic samples were etched using Kroll's reagent (3% HF + 5% HNO3 + 92% distilled water) for 50 s. Prior to etching, all samples in the polished condition were examined for porosity content via the 2D area fraction method, employing optical microscopy and image analysis software, ImageJ.1 Phase identifications of the sectioned samples were conducted with X-ray diffraction in a Rigaku MiniFlex 600 XRD machine with Cu radiation, operating at 40 kV and 15 mA, with a scan speed of 10\u25e6/min over a range of 2\u03b8 from 30\u25e6 to 80\u25e6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000273_j.addma.2020.101088-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000273_j.addma.2020.101088-Figure3-1.png",
        "caption": "Figure 3 Loading cases considered in optimization corresponding to (a) turning, (b) braking, and (c) road bump, respectively.",
        "texts": [
            " The full design domain of the wishbone is shown with blue edges in Figure 2, while the area where loading or constraints are applied is shown with black edges. The material used is Ti-6Al-4V with density being 4430 kg/m3, Young\u2019s Modulus being 113.8 GPa, Poisson ratio being 0.342 and yield strength being 880 MPa [24]. Figure 1 The lower wishbone arm (solid green part) in the car suspension system. Figure 2 Wishbone with the design domain shown with blue edges. Three loading conditions were considered in the optimization, as shown in Figure 3, which correspond to turning, braking, and road bump case, respectively. The two tubes at the back end of the wishbone are fixed. The symmetric condition is adopted to make sure the optimized shape is symmetric in the y-z plane. The objective of the optimization is weight minimization with the constraints that the optimized design and the conventional design have equal strength under the same loading conditions. To achieve this, we first determine the max admissible load of the conventional design under each loading case (here the max admissible load is the load under which the conventional wishbone starts to yield)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure13.28-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure13.28-1.png",
        "caption": "Figure 13.28. Normal section through point D.",
        "texts": [
            " The normal plane through a point D is defined as the plane through D, perpendicular to the helix tangent direction nD. jJ. The normal section profiles that we are most likely to require are the sections either through a point on the tooth profile, or through a point on the standard pitch cylinder. The method is the same in both cases, so we will deal with the most general situation, where D is an arbitrary point at any radius R', not necessarily on the tooth surface. We introduce local coordinates xn and Yn in the normal plane, as shown in Figure 13.28, and in order to determine the shape of the 360 Tooth Surface of a Helical Involute Gear normal section profile, we will show how to calculate the values of xn and Yn for points on the profile. We choose point D by specifying its cylindrical coordinates R', 9D and zD. If the gear helix through D cuts the transverse plane z=O at DO' the angular coordinate of DO is given by Equation (13.35), ( 13.135) The position vector to D and the direction of the helix tangent at D can be found from Equations (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003674_022-Figure3-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003674_022-Figure3-1.png",
        "caption": "Figure 3. Schematic illustration of boundary conditions applied to lungs and body nodes in (a) no-contact surface where internal nodes of the body and lung are attached, and (b) the contact surface model where internal nodes of the body and lung are separated and allowed to slide relative to each other (Note: the gap between lung and body in (b) is shown for clear illustration).",
        "texts": [
            " The nonlinear geometry principle is applied in the model to account for the expected large displacement effects. The lungs and body are modeled during inhale as a primary state. Using HyperMorph (HyperWorks, Altair Engineering, Troy, MI), a guided surface projection algorithm, the nodes on the inhale model are projected to the surface defined by the exhale surface of the lung. The differences in position between inhale and exhale are the boundary conditions applied on the inner surface of the body in contact with lungs and at the external surface of the body, as illustrated in figure 3. The internal nodes of body and lungs are identical when no contact surface is applied (figure 3(a)). However, these internal nodes are allowed to slide relative to each other in the contact surface model (figure 3(b)). Mechanical properties of human lung tissue have been experimentally measured by a limited number of investigators (Zeng et al 1987, Gao et al 2006). A hyperelastic material model is used in this study using the experimental test data presented by Zeng et al with a Poisson\u2019s ratio (\u03bd) of 0.43. The specimens were obtained in ex vivo from persons whose death did not affect the lungs. The specimens were tested within 48 h after death. Although lung tissues were tested in the biaxial mode, the uniaxial mode was included as a special case (Zeng et al 1987)",
            " Since material properties of the lung tissues are affected by different factors including the initial distortion of tissue (Denny and Schroter 2006), age (Lai-Fook and Hyatt 2000) and its location in the lung (lobes) (Zeng et al 1987), different values of modulus of elasticity and Poisson\u2019s ratio have been used in the literature (De Wilde et al 1981, Zhang et al 2004, Villard et al 2005). An elastic modulus of 7.8 kPa and a Poisson\u2019s ratio of 0.43 are used in this study. A modulus of elasticity of 1.5 kPa with Poisson\u2019s ratio of 0.4 is used in this study for the body. However, it has a little effect on the results of the lung, which is the focus of this investigation, because boundary conditions are applied to the lungs directly in the no-contact model and from adjacent body nodes in contact surface analysis allowing lungs nodes to slide (figure 3). This effect may be increased by including other contact parameters such as friction. In order to check the accuracy of the model deformation, anatomical points are identified on the inhale image representing the bifurcation of the vessels and bronchi. The same bifurcation points are tracked and located on the exhale images. The actual displacement measurement of these points is represented by the difference between the location of the inhale points and their exhale location. In each lung, 45 bifurcation points are selected as shown in figure 5(a)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure15-2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure15-2-1.png",
        "caption": "Figure 15-2. Temperature retraction apparatus",
        "texts": [],
        "surrounding_texts": [
            "bath at -70\u00b0C and allowing it to retract freely whilst the temperature is raised a 1\u00b0C per minute. The temperatures are noted at which the test piece has retracted by 10%, 30%, 50% and 70% of the applied elongation and these temperatures designated TRIO, TR30, etc. A suitable form of apparatus is shown in Figure 15.2. The upper test piece clamps are counterbalanced to give a small stress of between 10 and 20 kPa on the test pieces, and it is essential that the cord and pulley systems are virtually friction free. The upper clamps can also be locked in position after the test pieces are stretched and while they are cooled to the starting temperature. The standard makes no mention of any automatic heater control to raise the temperature at PC per minute but this is desirable if not essential. In its original form, the test is a trifle crude but more modern versions have been developed*\"\u0302 . At the time of writing, a revision of ISO 2921 is at an advanced stage which decreases the tolerance on the measure of recovery. This will, in principle, improve the accuracy of the method, although the Effect of temperature 293 limit in the past was more likely to be due to crudely built apparatus. Errors in using a simple scale for length measurement are much reduced when the results are taken from a graph. The identical test is also standardised as BS903:Part A29*\u0302 and a very similar procedure is in ASTM D1329^ .\u0302 With such an ad hoc method, it is essential that the details of procedure given in the standard are followed to achieve good interlaboratory agreement. The ISO and BS methods are identical and the ASTM appears to have no really significant differences, but all allow different elongations and ISO 2921/BS903 note that different elongations may not give the same results. The method does not seem to be very popular nor considered very precise in the USA and Britain but it is given rather more importance in Scandinavia."
        ]
    },
    {
        "image_filename": "designv10_4_0000615_j.optlastec.2020.106872-Figure5-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000615_j.optlastec.2020.106872-Figure5-1.png",
        "caption": "Fig. 5. The diagram of the scanning strategy.",
        "texts": [
            " The singletracks are also stable and the width of the single-tracks increases from 449 \u03bcm to 591 \u03bcm at the exposure time of 160 \u03bcs, however, small spatter can be observed on the surface. When with the further increase of the exposure time to 180 \u03bcs, the single-tracks discontinuity and overheating phenomenon occur due to the high energy input and excessive Y. Liu et al. Optics and Laser Technology 138 (2021) 106872 temperature gradient in the molten pools. According to the experimental analysis of the single-tracks, the multi-layer samples were fabricated by processing parameters shown in Table 3. The overlap rate was set based on the width of the single- tracks. Fig. 5. shows the scanning strategy used in the experiment. The scanning lines rotate 67 degrees after finishing the previous scanning plane to further melt the upper layer of un-melted powder and hole defects to avoid energy concentration and error accumulation. [29] Choosing an excellent scanning strategy can greatly improve the forming quality and mechanical properties of the part, such as rotating the scanning line to a certain angle and selecting multiple scanning strategies. In 2019, Bandar et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002812_a:1016559314798-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002812_a:1016559314798-Figure4-1.png",
        "caption": "Figure 4. A kR planar redundant manipulator.",
        "texts": [
            " From (9) and (10) the pseudoinverse is computed as follows: (i) If m < n and r(A) = m then A# = AT (AAT )\u22121. (15) (ii) If m > n and r(A) = n then A# = (AAT )\u22121AT . (16) From (11) A# = A\u22121, if m = n and r(A) = m. This section addresses the concepts associated with the generalization of classical manipulating structures in the perspective of introducing DOF to form redundant robots. A kinematically redundant manipulator is a robotic arm possessing more DOF than those required to establish an arbitrary position and orientation of the end effector (Figure 4). Redundant manipulators offer several potential advantages over nonredundant arms. In a workspace with obstacles, the extra DOF can be used to move around or between obstacles and, thereby, to manipulate in situations that otherwise would be inaccessible. When a manipulator is redundant it is anticipated that the inverse kinematics admits an infinite number of solutions. This implies that, for a given location of the manipulator\u2019s end effector, it is possible to induce a self-motion of the structure without changing the location of the gripper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003524_j.rcim.2006.09.001-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003524_j.rcim.2006.09.001-Figure1-1.png",
        "caption": "Fig. 1. CAD model of the proposed parallel mechanism with revolute actuators.",
        "texts": [
            " Furthermore, all the existing approaches are of analytical type, while the matrix recursive method, proposed in this paper, is simple and generic one. 2. Inverse geometric modelling by RMM Some iterative matrix relations for kinematic and dynamic analysis of a 3-DOF parallel mechanism with revolute actuators are established in the paper. The proposed 3-DOF parallel mechanisms consist of three kinematical chains, including three actuated legs with identical topology and one passive leg with 3-DOF, connecting the fixed base to the moving platform (Fig. 1). The links of these legs have given sizes and masses. In this parallel mechanism, the kinematic chains associated with the three identical legs consist, from base to the platform, of an actuated revolute joint, a moving link, a Hooke joint, a moving link and a spherical joint attached to the platform. Let Ox0y0z0 be a fixed Cartesian reference (Fig. 2). To simplify the graphical image of the kinematic scheme of the mechanism, we will represent the intermediate reference systems by only two axes, the same method used in most of the robotics papers [1,9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure2.6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure2.6-1.png",
        "caption": "Figure 2.6. Meshing diagram, with contact at the pitch point.",
        "texts": [
            " Pressure Angle of a Gear The pressure angle /fI s of a gear is defined as the gear profile angle /fiR at the standard pitch circle. The profile angle at radius R was given by Equation (2.10), and the pressure angle can be found by setting R equal to Rs in this relation, (2.20) 34 Tooth Profile of an Involute Gear When Equation (2.20) is compared with Equation (2.7), it is clear that the pressure angle of the gear is equal to that of the basic rack, \"'r (2.21) There is a more direct proof that the two pressure angles are equal. Figure 2.6 shows the gear meshed with its basic rack, in positions such that the contact point coincides with the pitch point. If As is the point on the gear tooth profile at radius Rs' the pressure angle of the gear is defined as the angle between the radius CAs and the tooth profile tangent at As. Since As is also the contact point, when the gear and the basic rack are in the positions shown, the tangent to the gear tooth profile lies along the rack tooth profile, and the pressure angle \"'s of the gear is therefore equal to the basic rack pressure angle \"'r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.12-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.12-1.png",
        "caption": "Figure 12.12. Meshing diagram of a gear and cutter.",
        "texts": [
            " It is preferable to use a pinion cutter whose teeth are rounded at the tips, as shown in Figure 12.11, since otherwise the tooth fillets of the internal gear will have a very small radius of curvature, and this will cause high stresses in the fillets. On the pinion cutter, the end point Ahc of the involute section of the tooth profile has polar coordinates (Rhc ,9hc )' given by Equations (5.34 and 5.35), and the center A~ of the circular section has coordinates (R~,9~), given by Equations (5.32 and 5.39) . The meshing diagram for the cutting process is shown in Figure 12.12, where the subscripts g and c refer, as usual, to the gear and the cutter. The cutting pressure angle and the radii of the cutting pitch circles can all be expressed in terms of the cutting center distance Cc , 280 Internal Gears cos q,c (12.48) (12.49) (12.50) The cutting pressure angle q,~ of the gear or the cutter is equal to q,c, and the cutting circular pitch can be found from either of the cutting pitch circle radii, ( 12.51 ) (12.52) Since the cutting process is equivalent to meshing with no backlash, the tooth thickness of the gear is equal to the space width of the cutter, both measured at the cutting pitch circles, (12",
            "55) If we want to calculate the cutting center distance to be used, in order to obtain a specified tooth thickness tsg in the gear, we start by using Equation (12.55) to find the value of inv t/l~, inv t/l~ inv t/l + _l_(p t - t ) s 2Cc s - sg sc s (12.56) We use Equations (2.16 and 2.17) to calculate the corresponding value of t/l~, and the cutting center distance is then given by Equations (12.51 and 12.48), t/lc P Rbg-Rbc cos t/lc (12.57) (12.58) Shape of the Fillet 283 The meshing diagram shown in Figure 12.12 can be used to derive an expression for the fillet circle radius of the internal gear. The involute section of the tooth profile on the internal gear is cut by the involute part of the cutter tooth, which ends at point Ahc \u2022 The path of contact is a segment of the common tangent to the base circles. The upper end of the path of contact is therefore at Hc' the point where the path followed by Ahc intersects the common tangent to the base circles. When the cutting point reaches Hc on the path of contact, point Ahc of the cutter touches point Af on the gear tooth profile, the point where the involute section of the profile meets the fillet",
            "80) Since the value of RO is generally quite large, the fillet radius of curvature r f is only slightly greater than 288 Internal Gears the cutter tooth tip radius r cT \u2022 If the cutter tooth tip has no rounded section, the value of r CT is zero, and we obtain a very small fillet radius of curvature in the gear. It is for this reason that a pinion cutter with rounded tooth tips is recommended for cutting internal gears. To consider the possibility of undercutting, we refer again to the meshing diagram of the cutting process, shown in Figure 12.12. The interference point of the internal gear is Eg , the point where the common tangent to the base circles touches the internal gear base circle. For an external gear, if the cutting point lies near the interference point, the corresponding point on the gear tooth profile is close to the fillet. However, when we consider an internal gear, this relation is reversed. A cutting point near the interference point corresponds to a point near the tip of the gear tooth. ~t the other extreme, point Af of the gear tooth profile, where the involute meets the fillet, is cut when the cutting point lies at Hc' which is the end of the path of contact furthest from the interference point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003317_tec.2003.822294-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003317_tec.2003.822294-Figure1-1.png",
        "caption": "Fig. 1. Induction machine scheme.",
        "texts": [
            " The machine electromagnetic torque can be obtained from the magnetic co-energy (9) The magnetic co-energy is the energy stored in the magnetic circuits and can be written as (10) The precise knowledge of the inductances making up the matrices in (5) and (6) is essential for the analysis and simulation of the IM. The following sections present a method for the calculation of such inductances considering radial and axial nonuniformity, due to skew and air-gap eccentricity. An IM scheme is presented in Fig. 1 to help obtain the equations that allow the inductance calculation. To make this scheme clearer, neither stator windings nor rotor end-rings are shown. There are no restrictions about skewing and winding and rotor bar distribution for the analysis. Furthermore, restrictions over the air-gap eccentricity are not assumed. Then the machine can exhibit nonuniform static or dynamic eccentricity down the axial length. The stator reference position of the closed-loop , angle , is measured at an arbitrary point along the air gap. The path stretches along the axial axis a length . Points and are located in and (both equal zero), points and are located in and . Points and are located on the stator internal surface whereas points and are located on the rotor external surface. is the rotor angle with respect to a fixed stator point. By applying the Ampere\u2019s law over the closed path , shown in Fig. 1, the following relation can be obtained: (11) where is the magnetic field intensity, is the current density, and is a surface enclosed by . Since all of the wires enclosed by the closed path carry the same current , (11) results as follows: (12) The function will be called in this paper the 2-D spatial winding distribution and represents the number of the winding turns enclosed by the path . This distribution, unlike previous proposals, depends on the geometry of the windings down the machine axial length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000275_s00170-019-04851-3-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000275_s00170-019-04851-3-Figure7-1.png",
        "caption": "Fig. 7 Description of the allotropic transformation of pure titanium [74]",
        "texts": [],
        "surrounding_texts": [
            "The scan speed refers to the laser beam\u2019s rate of change in distance along the substrate/previous layer while processing. The scan speed has an influence on the laser/material interaction time, with slower scan speeds resulting in longer interaction time leading to high temperature gradient and slow cooling [46, 47, 28]. Short interaction times may cause some material to be left unfused because of the inability of substrate or layer surfaces and powders to absorb energies enough to reach melting necessary for fusion thus increasing porosity [42]. The low amounts of powder available for melting is an issue related to high laser scan speeds as nozzles are attached to the same head with the laser beam. Melt pool shape is also highly sensitive to scan speeds, typically elongating and becoming shallower at faster scan speeds [22]."
        ]
    },
    {
        "image_filename": "designv10_4_0000284_17452759.2020.1760895-Figure7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000284_17452759.2020.1760895-Figure7-1.png",
        "caption": "Figure 7. Schematic diagram of laser beam spot size (a) and the multiple reflection the laser under different Dd: (b) negative Dd (convergent) and (c) positive Dd (divergent).",
        "texts": [
            " According to the defect types and melt pool modes, there are two situations: when the negative Dd (close to the focal point) or the focal point is adopted, it is categorised as situation I; when the positive Dd or the negative Dd (far from the focal point), it is categorised as situation II. The corresponding relationship among Dd, number of defect types, melt pool modes and situation is shown in the Table 2. The change in Dd influences the laser spot size, the internal energy intensity, and the nature of the laser beam. Figure 7(a) shows the correlation between the laser spot size changing and different Dd. With the increase of the absolute value of Dd, the laser spot size increases. The spot size diameter is the same when the absolute value of Dd is the same. The nature of negative defocusing laser beam is convergent. In contrast, the nature of positive defocusing laser beam is divergent. Moreover, the energy distribution changes with the Dd, which is indicated by the system model established in ZEMAX software. According to the simulation results, the maximum laser power density (1",
            " The flat-top distribution leads to the trough-like melt pools, whereas the Gaussian beam leads to the deep and conical-like melt pools. Under situation II when Dd> 0 mm, the laser power density decreases as the Dd increases due to the increased laser spot size. Besides, the Gaussian distribution transforms into the flat-top. At the same time, the outward-divergent laser beam leads to limited propagating depth. Afterwards, the light is reflected toward the top of the melt pool. After the third reflection, the laser was directly reflected to the outside of the melt pool (Figure 7(c)), leading to the shallow melt pool (CM, Depth < 100 \u03bcm, Width < 200 \u03bcm). In the case of focal position (Dd = 0 mm), the laser spot size is the smallest and the laser power density is the highest. Therefore, the mixture of the deep and shallow melt pools (TM) is formed in specimens fabricated under situation I when Dd= 0 mm compared with the specimens fabricated at Dd > 0 mm. As for the specimens fabricated at Dd < 0 mm, the phenomenon is completely different. After the first reflection, the inward-convergent laser beam propagates to the bottom of the melt pool (Zhang et al. 2018). As for the second reflection, the laser beam is in the depth of the melt pool, and then laser beam travels inward. But after the third reflection, the reflection point of laser is at the middle of the melt pool and the laser travels upward. Finally, the laser beam is reflected from the melt pool (Figure 7(b)). The melt pool mode transforms from TM to KM, then to CM. The melt pool transformation is attributed to the competition between Fresnel absorption and spot size. When the substrate is not far away from the focal position, the laser power density is high enough to trigger the large round pores, and the convergent laser results in strong Fresnel absorption. Hence, the laser beam propagates to the bottom of the melt pool, forming the KM (Depth > 300 \u03bcm, Width > 350 \u03bcm). KM and TM are formed under situation I when \u22123"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003426_iros.2003.1250608-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003426_iros.2003.1250608-Figure4-1.png",
        "caption": "Fig. 4. Projection of the Generalized Zero Momenr Paint",
        "texts": [
            " We first introduce a vector pG(= [fG YG icIT) and consider the change of coordinates between pG and pG defined by -LGy/%f+XG(& +g) - (ZG - Z E ) i G =fG(?G + g ) - ( i G - z E ) & (22) = YG(& + g) - (k - Z E ) k , (23) i G = ZG. (24) LGx/%f +YG(ZG + g) - (ZG - ZE)YG Applying the change of coordinates to eqs.(l2) and (13). the position of the GZMP can be defined as follows: We note that eqs.(25) and (26) are same as those of an inverted pendulum. Assume that the real floor is the XE - Y E plane when zE = 0. As shown in Fig.4, the following proposition can be hold for the projection of the GZMP included in a virtual floor above the real one: Proposition 3 (Projection of GZMP) Draw a line including bath of pG(z5 = w) and the GZMP on the vinual floor. The intersection of the line and the ground correspondr to the GZMP on the real ground Proof In eqs.(25) and (26). the GZMP is concentrated on a sigle point: ] (27) when ZE = i ~ . Moreover, eqs.(25) ond (26) are linear equations with respect to pE Therefore, since all points on the line including both &(ZE = ZG) and the GZMP on the vinualjoor con be the GZMJ"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002807_s0094-114x(97)00053-0-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002807_s0094-114x(97)00053-0-Figure4-1.png",
        "caption": "Fig. 4. A singular con\u00aeguration of class (RI, IO).",
        "texts": [
            " (5) The condition (viii) is applied. (viii) is equivalent to the singularity of at least one of the matrices [ SASBSC], [ SGSCSD] or [ SESGSF]. The solution for each of these equations (combined with the loop equations) is a 1-dimensional submanifold of the 2-dimensional con\u00aeguration space. The \u00aerst and third manifolds have each two connected components, while the second one has four. All elements of the union of these manifolds, except the eight elements of {2}, belong to the (RI, IO) class. Figure 4 provides an example. The connected component corresponding to the shown con\u00aeguration is obtained by moving the linkage while keeping the points B and C \u00aexed. (6) The intersection of the sets obtained in Steps 4 and 5 consists of 16 con\u00aegurations. Apart from the eight con\u00aegurations classi\u00aeed in Step 3.5 as (RPM & II and IO)-singularities, the others are (RI, RO, IO, II)-class singularities. The remaining con\u00aegurations obtained in Step 4/5 belong to the class (RO, II)/(RI, IO). Thus, four di erent classes of singularities are obtained for the given mechanism: eight (RPM, II, IO) singularities, Step (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure12.9-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure12.9-1.png",
        "caption": "Figure 12.9. Alternative positions for radial assembly.",
        "texts": [
            " For the remaining teeth, the point furthest from the ~ axis is the corner point of the tooth. In order to determine whether the gear pair can be assembled radially, we calculate the ~ coordinates of the labelled points on the pinion, and check that in each case they are less than the ~ coordinates of the corresponding points on the internal gear. If this condition is satisfied for each pair of points, then radial assembly can be carried out. In cases where radial assembly is not possible in the position of Figure 12.8, we can consider an alternative position, as shown in Figure 12.9. We place the gear pair so that a tooth space of the pinion is lined up with a tooth of the internal gear, and again we calculate the ~ coordinates of the various tooth points. As before, radial assembly is only possible if each point on the pinion is closer to the ~ axis than the corresponding point on the internal gear. The minimum value of (N2-N 1) for which radial assembly is possible depends primarily on the pressure angle. For 278 Internal Gears example, radial assembly of 20\u00b0 pressure angle gear pairs can generally be carried out when (N2-N 1) is 17 or larger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003584_we.173-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003584_we.173-Figure6-1.png",
        "caption": "Figure 6. Helical gear system. The two bearings supporting each of the shafts are represented by one stiffness matrix per shaft with equivalent radial (kbrad), axial (kbax) and tilt (kbtilt) stiffness values. The helix angle b is varied through the analysis and both the input and the output shaft are free at their boundaries",
        "texts": [
            " The formulation of the gear forces in matrix form yields (3) where with cb = cosb, sb = sinb, cy = cosy and sy = siny. When b \u03c0 0, it is possible to have no zero components in the matrices. At that moment, all DOFs of both gears are coupled with each other. The application of this method is given below in an example of a parallel and a planetary gear stage. The analysis of a multibody model of the parallel helical gear system introduced by Kahraman5 is described. The presented model consists of a helical gear pair mounted on two rigid shafts supported by rolling element bearings assembled in a rigid housing. Figure 6 shows this set-up with the necessary input parameters for the model. Here the helix angle b is variable and its influence on the calculated results is examined in a sensitivity analysis. Furthermore, the same gear system with b = 0\u00b0 and kb = \u2022 was used as an example of a torsional model in subsection one. As a result, conclusions concerning the advantages of the more detailed approach presented here can be drawn. This is discussed in the sensitivity analysis of the bearing stiffnesses. k ij k b y b y y b b y b b y b b y y b y b y y b y b b y b b y y b b y b y b b y b b y 11 2 2 1 2 1 1 1 2 1 1 1 2 1 2 1 1 2 2 1 1 1 1 2 1 2 1 1 = - - - - - - - c s c c s c s s c s s c s c s c s c c s c c c s c c s c s c s c c c c s s c s c 1 2 2 1 2 1 1 2 1 1 1 1 1 2 1 1 2 2 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 - - - - - - - - s s s c c s c s s c s c s s s s s s c s c s s c s c s c s c s c b b y b y b b b b y b b y y b y b y b y y b b y b b y y b b y b y s r r r r r r r r r 1 1 2 1 1 1 2 2 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 12 2 1 2 r r r r r r r r r r s c s s c c s c c s c c c s c s s c s c c s s b y y b y b b y b y b y b b b b y b b y b k b y y - - - - - \u00c8 \u00ce \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u02d8 \u02da \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 = - - - - - - - c c s c s s c s s s c s c s c s c c s c c c c s c c s c s c s c c c c c s s c s c s 2 2 2 1 1 1 2 2 1 2 1 2 1 2 2 1 2 1 1 2 1 2 1 2 2 2 b y y b b y b b y y b b y y b y b y y b y y b b y b b y y b b y y b y b b y b b y b b y b y b b b b y y b b y y b y b y y b y y b b y b b y y b b y y b - - - - - - - s s s c c s c s s s c s c s s s s s s c s c s s c s c s c s c c s c 2 2 2 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 2 2 1 1 1 1 1 2 1 1 2 1 2 r r r r r r r r r y b y y b y y b b y b y b y b b b b y b b y b k b y 1 1 2 1 2 1 2 1 2 1 1 1 2 2 1 2 2 1 1 2 1 2 1 2 21 2 1 r r r r r r r r r r s c s s c c c s c c s c c c s c s s c s c c s s - - - - \u00c8 \u00ce \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u02d8 \u02da \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 = y b y y b b y b b y y b b y y b y b y y b y y b b y b b y y b b y y b y b b y b b y 2 2 1 2 2 1 2 1 2 2 2 2 2 1 2 1 2 2 2 1 1 2 2 2 1 1 - - - - - - - c c s c s s c s s s c s c s c s c c s c c c c s c c s c s c s c c c c c s s c s c s s s s c c s c s s s c s c s s s s s s c c s s c s c s c s c c s c 2 2 1 2 1 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 1 2 1 2 2 2 b b y b y b b b b y y b b y y b y b y y b y y b b y b b y y b b y y b - - - - -r r s r r r r r r r y b y y b y y b b y b y b y b b b b y b b y b k b 2 2 2 2 1 2 2 1 2 2 2 2 2 1 2 2 1 2 2 1 2 1 2 2 22 2 2 r r r r r r r r r s c s s c c c s c c s c c c s c s s c s c c c s - - - - - \u00c8 \u00ce \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u02d8 \u02da \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 = - y b y y b b y b b y b b y y b y b y y b y b b y b b y y b b y b y b b y b b y b b 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 c c s c s s c s s c s c s c s c c s c c c s c c s c s c s c c c c s s c s c s s - - - - - - - s s c c s c s s c s c s s s s s s c s c s s c s c s c s c s c c y b y b b b b y b b y y b y b y b y y b b y b b y y b b y b y b y y 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 - - - - r r r r r r r r r r s s 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 - - - - \u00c8 \u00ce \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u00cd \u02d8 \u02da \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 \u02d9 r r r r r r r r s c c s c c s c c c s c s s c s c c b y b b y b y b y b b b b y b b y b F F F F T T T F F F F T T T X Y Z X Y Z T X Y Z X Y Z T 1 1 1 1 1 1 1 2 2 2 2 2 2 2 = [ ] = [ ] F F q q 1 2 11 12 21 22 1 2 \u00c8 \u00ce\u00cd \u02d8 \u02da\u0307 = \u00c8 \u00ce\u00cd \u02d8 \u02da\u0307 \u00c8 \u00ce\u00cd \u02d8 \u02da\u0307 k k k k kgear Copyright \u00a9 2005 John Wiley & Sons, Ltd. Wind Energ. 2006; 9:141\u2013161 DOI: 10.1002/we Influence of the Helix Angle b. Table I shows the eigenfrequencies calculated for the helical gear pair in Figure 6 for b = 0\u00b0 and 20\u00b0. These values match almost perfectly with the results calculated by Kahraman,5 which proves the validity of the model implementation in the frictionless case. Figure 7(a) shows how the eigenfrequencies change with changing b. Only w2, w4, w8 and w12 are influenced and the largest relative change is observed for w2, which is only 6% for b = 20\u00b0 (Table I). Thus the influence of the helix angle is rather small; as a result, a simplification of a parallel helical gear system to a spur gear pair can be justified when calculating only the eigenfrequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003905_robot.2005.1570171-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003905_robot.2005.1570171-Figure6-1.png",
        "caption": "Fig. 6. Size of rotary-type soft actuator used for Type II.",
        "texts": [
            " Since the other side of the bellows expands to the (a) Palm side (b) Arm side Fig. 3. Shape of appliance. axial direction by reinforcement at the only bending side, this actuator bends circumferentially when the compressed air is supplied into the actuator. The part between the bending and fixed parts of the bellows is not reinforced for releasing the palm appliance. Fig.5 shows the outlook of actuator. Depending on the reinforcement of bellows, when the compressed air is supplied to the actuator, the actuator expands to the axial direction as shown in Fig.5(b). Fig.6 shows the size of the rotary-type soft actuator used for type II. The outer and inner diameter and length of rubber tube are 16, 12, 180[mm], respectively. The outer and inner diameter of polyester bellows are 28, 22, respectively The both sides of the bellows with length 60[mm] from the end are reinforced for inhibiting axial expansion. The bending side at center part of bellows with length 60[mm] is reinforced. Fig.7 shows the fundamental characteristics of actuator. Enough bending angle \u03b4\u03b8 for assisting with human wrist can be obtained as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002935_iros.1993.583168-Figure4-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002935_iros.1993.583168-Figure4-1.png",
        "caption": "Fig. 4 Link structure of trunk",
        "texts": [
            " An assembly drawing and a link srructure of this robot are shown in Fig. 2 and Fig. 3. The assignment of DOF (Degrees Of Freedom) is shown in Fig. 3. As this diagram indicates, the lower-limbs have s ix rotational DOF on pitch-axis and the trunk has three rotational DOF on pitch-axis. roll-axis and yaw-axis. The total DOF is nine. . . . _ 2-2 Trunk M e d \" The trunk of this machine model is able to generate the three-axis moment by using three DOF link mechanisms. The weight of the trunk is 30.0 kg. A link smcture of the trunk is shown in Fig. 4. This trunk generates the three-axis moment as follows: The yaw-axis moment is generated by swinging two balance weights around the yaw-axis by a yaw-axis actuator. The balance weights are linked to the yaw-axis actuator, which is installed at the top of the m n k . The pitch-axis and the roll-axis moments are generated by swinging the yaw-axis actuator and the balance weights around a pitchaxis actuator and a roll-axis one. By installing the yaw-axis actuator at the top of the trunk and using its weight itself to compensate for the pitch-axis and the roll-axis moments, the authors were able to generate the three-axis moment by the trunk without adding to the total weight of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000575_j.mechmachtheory.2020.104156-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000575_j.mechmachtheory.2020.104156-Figure1-1.png",
        "caption": "Fig. 1. Gear macro- and micro-geometry (I \u2013 tip and root relief; II \u2013 profile angle; III \u2013 profile crowning; IV \u2013 end relief; V \u2013 lead angle; VI \u2013 lead crowning).",
        "texts": [
            " \u2022 by applying the most suitable lubricants \u2013 by improving the understanding of lubricants and lubricants themself, it is possible to reduce both the friction coefficient and wear in gear pairs. \u2022 by adjusting the gear geometry \u2013 by investing additional time and knowledge to find the most suitable gear pair ge- ometry for a given application, it is possible to ensure the better operational characteristics, which is the focus of this paper. The gear geometry can be further divided into gear macro-geometry and gear micro-geometry (see Fig. 1 ). The macrogeometry includes the basic geometric parameters - the gear module, face width, number of teeth, profile shift coefficient, pressure angle, helix angle, and type of the flank curve. The gear tooth symmetry should also be considered, even though the application of symmetrical gears is vastly exceeding their asymmetric counterparts. All the macro-geometric parameters are outcomes of basic tool geometry and the manufacturing process parameters. On the other hand, modifications of micro-geometry require changes to the basic gear tooth geometry and are achieved through additional machining operations",
            " In the literature, micro-geometry effects on the gearing performance are also studied by using FEM. Shehata et al. [73] carried out such study, observing the relationship between the gear micro-geometry and ensuing stresses. The authors considered the micro-geometry modifications, misalignment, and a combination of the two, finding that the analytical methods are more conservative when compared to FEM. Using the same method, Tesfahunegn et al. [72] have investigated the effects of the profile angle modifications (please see Fig. 1 -II) on transmission error and tooth stresses (both flank and root stress). By using the numeric model validated through experiment, Tesfahunegn et al. have concluded that profile modifications do not affect the root and flank stress, while significantly affecting the gear strength itself. However, similarly to most of the studies within the field, one specific case was observed, thus causing concerns regarding the generality of solutions. Furthermore, Korta and Mundo [74] proposed using the response surface methodology to optimise gear profile modifications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003447_j.apsusc.2005.10.025-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003447_j.apsusc.2005.10.025-Figure2-1.png",
        "caption": "Fig. 2. Sketch of the LCF substrate.",
        "texts": [
            " In this paper, laser cladding forming rebuilding of V-grooves up to 20 mm in depth on common carbon AISI 1045 steel substrates have been systematically investigated, microstructure and mechanical properties of the repaired regions have been characterized and assessed with different testing methods. The experimental system consists of a 6 kW CO2 laser source, an automatic wide-band powder feeding device, a SIEMENS numerical control system and a four-axis working plate. V-grooves with dimensions shown in Fig. 2 were premachined to a roughness of Ra12.5 mm on AISI 1045 block substrates with a size of 75 mm 150 mm 200 mm. 316L stainless steel powder (<0.03 C, 16\u201318 Cr, 12\u201314 Ni, 2\u20133 Mo, 0.68 Si and balance Fe, wt.%) was used as the rebuilding material. Before laser deposition, the 316L stainless steel powder was dried in a vacuum stove; the substrate was polished with sand paper and cleaned with acetone to remove the greasy and rust. Parameters used in the experiments are: laser power 2.25\u20133.75 kW, overlapping 27"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003599_acc.2006.1657333-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003599_acc.2006.1657333-Figure1-1.png",
        "caption": "Fig. 1. Four-rotor aircraft",
        "texts": [
            " Quad-rotors are mechanically simpler than classical helicopters, they do not have a swashplate and have constant pitch blades. A quad-rotor is controlled by varying the angular speed of each rotor. The force fi produced by motor i is proportional to the square of the angular speed, that is fi = k\u03c92 i . The front and rear motors rotate counterclockwise, while the other two motors rotate clockwise. Gyroscopic effects and aerodynamic torques tend to cancel in trimmed flight. The main thrust is the sum of the thrusts of each motor, see Figure 1. The pitch torque is a function of the difference f1 \u2212 f3, the roll torque is a function of f2 \u2212 f4, and the yaw torque is the sum \u03c4M1 + \u03c4M2 + \u03c4M3 + \u03c4M4 , where \u03c4Mi is the reaction torque of motor i due to shaft acceleration and the blade\u2019s drag. Let us denote \u0393e = { \u0131\u0302e, j\u0302e, k\u0302e } as the inertial frame, \u0393b = { \u0131\u0302b, j\u0302b, k\u0302b } as the body frame attached to the aircraft and qe = [xe ye ze \u03c8 \u03b8 \u03c6]T = [\u03be \u03b7]T as the generalized coordinates which describe the vehicle\u2019s position and orientation. \u03be \u2208 R 3, denotes the position of the vehicle\u2019s center of mass relative to the inertial frame, and \u03b7 \u2208 R 3 are the three Euler angles; the yaw, the pitch and the roll, which represent the aircraft\u2019s orientation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000245_ijvd.2019.109873-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000245_ijvd.2019.109873-Figure2-1.png",
        "caption": "Figure 2 Tension spring design (see online version for colours)",
        "texts": [
            " It can be observed from Table 4 that the results obtained by NAMDE are very competitive when compared with the used algorithms for the truss problem. Regarding the mean, worst, and Std NAMDE is better than UFA, SSBSA, WCA, MVDE and DSS-MDE. By achieving the lower value of Std Rank-iMDDE and UABC are the most robust for this case. The UFA shows superiority in terms of FEs number with smallest value of 450. The optimal design of tension/compression spring problem is to minimise the volume of the spring (Figure 2) under four non-linear constraints. There are three continuous design variables: the wire diameter, mean coil diameter and number of active coils (Arora, 1989). The problem has been solved using UFA, ideal gas molecular movement (IGMM) (Varaee and Ghasemi, 2017), multi-level cross entropy optimiser (MCEO) (MiarNaeimi et al., 2018), hybrid interior search-hill climbing (H-ISA) (Yildiz, 2017), water cycle moth flame optimisation algorithm (WCMFO) (Khalilpourazari and Khalilpourazary, 2017), SSBSA, \u03b5DE-LS, \u03b5DE-PCGA, improved accelerated particle swarm optimisation (IAPSO) (Guedria, 2016), Rank-iMDDE, UABC, COMDE, WCA, DELC, DSS-MDE, hybrid particle swarm and receptor editing (PSRE) (Yildiz, 2009), and accelerated adaptive trade-off model (AATM) based evolutionary algorithm (Wang et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003468_978-1-4612-4764-7-Figure4.2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003468_978-1-4612-4764-7-Figure4.2-1.png",
        "caption": "Figure 4.2. Essential details of Figure 4.1.",
        "texts": [
            " The line segment from T2 to T1 is the path of contact, and asc is therefore equal to the length of the path of contact. From the manner in which the contact ratio was defined in Equation (4.1), it might appear that two meshing gears could have contact ratios of different values, but it is now clear from Equation (4.5) that the two values must be the same, since the base pitches of the two gears are equal. Expressions for the positions sT1 and sT2 of the end points of the path of contact can be derived with the help of Figure 4.2, which shows the essential features of Figure 4.1 in greater detail. It should be remembered that s is defined like a coordinate, so that its value is positive for points above P, and negative for those below. The positions of the end points of the path of contact are then as follows, 86 Contact Ratio, Interference and Backlash 2 2 - Rb1 tan t/I + v'(RT1 -Rb1 ) (4.6) In these equations, circles, Rb1 and Rb2 operating pressure Equation (3.44), 2 2 Rb2 tan t/I - v'(RT2 -Rb2 ) (4. ?) RT1 and RT2 are the radii of the are the base circle radii, and t/I is angle of the gear pair, given tip the by cos t/I (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003391_978-1-4615-5367-0-Figure7.7-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003391_978-1-4615-5367-0-Figure7.7-1.png",
        "caption": "Figure 7.7. Relative rotation of lattice 2 with respect to lattice 1 to transform vector X2 into Xl' This transform is performed to find the optimal matching points in O-lattice theory.",
        "texts": [
            " The boundary rotation is fixed but the boundary plane can be freely chosen. The interpenetrating lattices with positions of the \"best fit\" represent a complete description of all the possible boundaries between two crystals of given structures and orientations. The interpenetrating lattices are constructed only for identifying the optimal matching grain boundaries. We now consider two interpenetrating translation lattices with an assumption that lattice 1 is fixed and all of the translation and rotation are performed on lattice 2 (Fig. 7.7). With the relative orientation of the two lattices being given, lattice 2 is translated in such a way that one of its points coincides with a point in lattice 1. That point is termed a lattice coincidence site. An atom located there is in an unconstrained position for both lattices. Thus, this point is also referred to as a \"point of best fit\". CSL theory starts with the 0 points, which can be understood as coincidences of internal coordinates or coincidences of points which are in equivalent positions in the two crystals. The equation which determines the O-lattice will now be derived. If an arbitrary point A with coordinates Xl in lattice 1 is chosen (Fig. 7.7), the position of the corresponding point B in lattice 2 is (7.8) where R is the rotation matrix as described in Eq. (7.6). In lattice 1, a point G with a translation t1 with respect to a point A is (7.9) If point G is coincidence with point B, the position of this point is defined as the 0 point which is Solving Eq. (7.10), one obtains (7.10) 349 STRUCTURE ANALYSIS OF FUNCTIONAL MATERIALS 350 CHAPTER 7 where I is a unit matrix. Bollmann (1970) has shown that the translation vector tl is the lattice translation vector h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003056_s0094-114x(03)00003-x-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003056_s0094-114x(03)00003-x-Figure6-1.png",
        "caption": "Fig. 6. Position of the ball when the clearance is absorbed.",
        "texts": [
            " 3) between diagonally opposed centres of curvature is equal to A \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0a2 \u00fe h2\u00de p \u00f020\u00de However, the existing clearance modifies some of the coordinates of the centres of curvature of the Z axis. If Pr is defined as being the existing radial clearance, rc as the radius of curvature and d as the diameter of the ball bearing, we have the following relation (Fig. 5): 2\u00f0rc Pr\u00de A \u00bc d \u00f021\u00de Taking the inner ring as a reference, the outer ring will move down by an amount j, equal to the axial clearance, until contact exists between the sphere and the raceways. Fig. 6 shows the positions of the centres of curvature in the initial position, taking into account the axial clearance j. The following relationship may be deduced from Fig. 6: A02 \u00bc \u00f02h\u00de2 \u00fe \u00f02a\u00fe j\u00de2 \u00f022\u00de From expression (21), as in the contact Pr \u00bc 0, it can be deduced that 2rc A0 \u00bc d \u00f023\u00de From the expressions (21) and (23) it can be deduced that A0 \u00bc 2Pr \u00fe A \u00f024\u00de Finding j from Eq. (22) and substituting Eq. (24) in this equation, the following equation is obtained for the axial clearance: j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f02Pr \u00fe A\u00de2 \u00f02h\u00de2 q 2a \u00f025\u00de Thus, taking the axial clearance into account, the initial coordinates on the Z axis of the centres of curvature Cei1 and Ces1 are modified, where ZCei1 \u00bc a j \u00f026\u00de ZCes1 \u00bc a j \u00f027\u00de Once the clearance has been overcome, the outer loads (Fr, Fz and M) are applied on the outer ring, and these cause displacements of the centres of curvature of the outer raceways, dr, dz and h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000143_j.ijheatmasstransfer.2019.119187-Figure1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000143_j.ijheatmasstransfer.2019.119187-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the FCCZ lattice channel: (a) FCCZ unit cell, (b) transparent view, and (c) frontal view.",
        "texts": [
            " In addition, the hermal fluid field, internal channel temperature, and stress disribution of the FCCZ lattice channel were analyzed. The optimal orosity of the FCCZ lattice channel was determined in terms of he performance factors. Furthermore, the variations in the conective heat transfer coefficient, pressure drop, and stress were anlyzed with respect to the inlet velocity. Finally, the performances f the FCCZ lattice channels manufactured with 17-4 PH, H13, and araging steel were compared. . FCCZ lattice channel design and experiments .1. FCCZ lattice channel As shown in Fig. 1 (a), an FCCZ lattice channel was chosen as a elf-supporting structure. The FCCZ lattice channel possesses high tructural stability; its strength is more than those of the FCC, BCC, nd BCCZ lattice structures [31] . Moreover, the FCCZ lattice channel as a shape that effectively generates a turbulent flow because the attice is designed such that its direction is perpendicular to the diection of flow. As shown in Fig. 1 (b), the FCCZ lattice channel with 0 unit cells was arranged such that its direction was the same as hat of the direction of flow to enable the inlet and turbulence efects to be considered in the flow analysis [24] . The upper part of he outer surface was selected as the working surface that receives oth the heat flux and pressure load. As shown in Fig. 1 (c), the nner channel width, inner channel height, and the distance beween the working surface and the inner channel (DSC) were set t 4 mm. The diameter of the FCCZ lattice channel was varied to nalyze the effect of porosity, whereas the other dimensions of the hannel were fixed. It must be noted that a conventional straight hannel has a porosity of 1.0. The specifications and geometric paameters of the FCCZ lattice channel are summarized in Tables 1 nd 2 , respectively. .2. Experiments Thermal fluid experiments were conducted to validate the simlation model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003947_0-387-29012-5-Figure7-1-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003947_0-387-29012-5-Figure7-1-1.png",
        "caption": "Figure 7-1. Preparation of a density column",
        "texts": [],
        "surrounding_texts": [
            "column will last a long time and it is possible to remove old samples with a wire basket. Ten minutes is suggested as the minimum time to allow test pieces to come to equilibrium but a large number of samples can be tested at one time and only a very small sample is required. A typical single column apparatus is shown in Figure 7.1. Mass, density and dimensions 99 A useful procedure for checking if test pieces lie within certain limits of density is to prepare two liquids of different but known densities; to be within the known limits a test piece must sink in one liquid and float in the other. This can be employed, for example, to rapidly sort parts made in two materials which have been mixed up. A further variation^ is titration of a heavier liquid into a lighter liquid until the test piece just floats, as given in IS0 1183-1^ Because density is often used as a quality control check on batches of rubber compound, there has been a necessity to make measurements essentially in accordance with standards such as ISO 2781 but making the determinations as rapidly as possible. Hence, various designs of 'specific gravity balance' are in existence which to varjdng degrees automate the process. In the basic forms of apparatus, the practical steps of weighing in air and water are taken but the result may then be read directly from a scale calibrated in density. Complete automation has been achieved both by using the principle of weighing a moulded test piece of known volume and by using the displacement of water principle. For thin sheet material, it will be more expedient, and perhaps more useful, to measure mass per unit area rather than density. This is achieved by weighing a uniformly shaped piece of the material with known dimensions. Obviously, the density of any uniform piece of rubber can be obtained, at least approximately, but weighing and measuring all the dimensions in a non-contact manner."
        ]
    },
    {
        "image_filename": "designv10_4_0002921_s0165-0114(03)00135-0-Figure6-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002921_s0165-0114(03)00135-0-Figure6-1.png",
        "caption": "Fig. 6. Membership functions of input e and us1 in the fuzzy supervision controller.",
        "texts": [
            " It is easy to get fuzzy control rules from the common experience, for example, IF e is PB1 (positive big); THEN us1 is PB2 (positive big); IF e is PS1 (positive small); THEN us1 is PS2 (positive small); IF e is ZR1 (zero); THEN us1 is ZR2 (zero); IF e is NS1 (negative small); THEN us1 is NS2 (negative small); IF e is NB1 (positive big); THEN us1 is NB2 (positive big): (15) Where e=d1 \u2212 d2, d1 and d2 are the distances from the ball to the left and right boundaries, respectively. The universes of discourse of e and us1 are [\u22120:07; 0:07 m] and [\u22120:03; 0:03 arc=s2], respectively. For convenience, we introduce two scaling factors Ge = 14:3 and Gus = 30, such that the normalized input and output of the fuzzy supervision controller are both varied in [\u22121; 1]. The normalized input e and output us1 both adopt triangular-shaped, full-overlapped and equally spaced membership functions as shown in Fig. 6, where NB1, NS1, ZR1, PS1, PB1 are Ive fuzzy sets for input, while NB2, NS2, ZR2, PS2, PB2 are Ive fuzzy sets for output us1. Here we still adopt the Sum\u2013Product method for fuzzy inference and the Center of Gravity method for defuzziIcation. Fuzzy planning controller should determine a desired trajectory in order to control the ball from point A through the path A \u2192 B \u2192 C \u2192 D \u2192 E \u2192 F \u2192 G to point G without hitting the obstacles and in the least time. Now we will explain how to translate the human experience into the fuzzy control rules"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0003829_0094-114x(78)90028-9-Figure2-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0003829_0094-114x(78)90028-9-Figure2-1.png",
        "caption": "Figure 2. Rigid-body and elastically deformed configurations of beam elements, generalized displacements and coordinate systems.",
        "texts": [
            " The displacement finite element method [ 1-3], on the other hand, utilizes the nodal displacements as the unknowns of the problem. The compatibility conditions in and among the elements are initially satisfied. The equations are expressed in terms of these nodal displacements utilizing the equilibrium conditions at each nodal point. The displacement finite element method formulation is in general found to be much simpler for a larger number of structural problems. For this reason, this latter method will be used here to develop the equations of motion. Elastic Beam Element in Plane A general beam element is shown in Fig. 2 in two frames of reference. These are the fixed (O-X-Y) and the rotating (0-x-y) frames, the rotating frame of reference being such that the x-axis is parallel to the beam element axis. The beam element is shown in its rigid-body position (dotted) as well as in its elastically deformed configuration, as shown by the solid lines. The elastic deformations of the beam element may be completely described[3] by the six nodal displacements, u~ through ut, illustrated in Fig. 2. These displacements, shown in their positive directions with reference to the rigid-body position of the beam element, locate the deformed positions of the nodes A and B. From Fig. 2, the following relationships may be expressed in the fixed (0-X-Y) reference frame XA, = XA + ul cos 0 - u2 sin 0 YA, = YA + U~ sin 0 + U2 COS 0 OA'=O+u3. (1) Differentiating eqns (1) with respect to time, expressions for velocity and acceleration of node A may be obtained in the fixed coordinate system. .~A, = ~'A + uJ cos 0 - ul0 sin 0 - li2 sin 0 - u20 cos 0 I;'A, = I?A + t~ sin 0 + u10 cos 0 + ti2 cos 0 - u2O sin 0 (2) 605 and J(A' = XA +//I COS 0 -- 2Ul0 sin 0 - u102 COS 0 - u,0\" sin 0 - / /2 sin 0 - 2u20 cos 0 + u202 sin 0 - u20\" cos 0 ~'A' = ~'a +/ / , sin 0 + 2u,0 cos 0 - u~02 sin 0 + u~0 cos 0 + ii2 cos 0 - 2u2# sin 0 - u202 cos 0 - u20\" sin 0 (3) = +a3",
            " #o(~, 0 2 = ~. ~ ,b,(~)\" ~bi(~) \u2022 ~\u00b0,(t) \u2022 Uoj(t) t) 2= \u2022 \u2022 \u2022 u\u00b0,(t) The kinetic energy T=Tw+T~ T=~ m(.~). ~'o(X, t)2dx + m(,~) \u2022 ~o(~, t)2dg ~Oo(X, t) = ~k2(~) \u2022 ~o2(t)+ ~b3(g) \u2022 uo3(t)+ tks(~) \u2022 Uos(t)+ ~b6(~) \u2022 ua6(t) ~o(~, t )= ~b,(~). ~o,(t)+ ~k4(~)\" ~o4(t). i , j = 2,3,5 and6 k, ! = 1 and4. (15) (16) d-'~ \\ \u00b0 l i d Ouj + Oui a e m e n ~ l Msss and Stiffness Matflces Selecting u~ (i : 1 . . . . . 6) as the generalized coordinates of the problem, the equations of motion of the elastic beam element in Fig. 2 may be described by Lagrange's equations 608 where and l L Tw =~ [o ~, ~ m(x)~k'(x)\u00a2h(x)u\"(t)ti'i(t)dX 1 L Interchanging the order of integration and summation, define an element ~0 of the generalized mass matrix [n~] as r~ii = m(X)d?i(X)$~(X) d.~ (18) and similarly ~ = fo L m(:~)4~k(X)O~(g) d\u00a3 In matrix form 1 r Tw = 5{Uai} [ ffliil{l~ai } (19) and 1 r Tv = ~{llak} [fflkl]{aak }. Superimposing Tw and T~, the total kinetic energy 1 r T = 5{uo} [,~]{ao}, o r T = ~ [{ti,} + {t~}]r [r~ ][{ti,} + {4}]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0000492_978-981-15-0833-2-Figure13.17-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0000492_978-981-15-0833-2-Figure13.17-1.png",
        "caption": "Fig. 13.17 Historical development of machine design of strength",
        "texts": [
            "5 Theories of Strength 495 A further development of the damage tolerance design method is the intelligent structure and healthy monitoring, which is based on smart materials and structural technologies (Gandhi and Thompson 1992). It contains the following main contents: (1) Monitoring the stress and strain within the material with embedded micro-sensors. (2) With advanced life prediction theory, developing structural life prediction methods which have comparable accuracy to lab tests. (3) Warning potential structural safety issues, and controlling of structural fractures, including self healing technology and other advanced automatic control technologies. Figure 13.17 gives a brief time line of the development of strength theories in mechanical design. Tribology is a science and engineering subject which studies the mechanism of friction, lubrication, and wear between interacting surfaces in relative motion. 496 13 Development of Theories in Mechanical Engineering of New Era Statistics indicated that friction consumes about 1/3 of the total primary energy in the world, and 60% of materials loss is from wear. In several industrialized countries, for example, the U"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure13-1.png",
        "original_path": "designv10-4/openalex_figure/designv10_4_0002963_j.mechmachtheory.2003.12.004-Figure13-1.png",
        "caption": "Fig. 13. Deployed shape of the quarter-circular chain.",
        "texts": [
            " The first type of supplementary chains are semi-circular chains formed by elementary fourlegged platforms. Similar to the analysis in the previous sections, the legs containing four links and six joints, which are perpendicular to the semi-circular chain, are removed from every elementary platforms in the chain. The mechanism hence left is a semi-circular chain joined by parallelogram mechanisms and planar two-legged platform mechanisms and can be illustrated in Fig. 12. Decomposing the above, a quarter-circular chain is obtained in Fig. 13. From the previous analysis, the mobility of this mechanism is one. The second type of supplementary kinematic chains consists of three-legged elementary platforms. The analysis of this type results in mobility one from the similar mobility analysis as before. Hence the ball mechanism is completely decomposed and the mobility analysis is concluded. This paper revealed the multi-loop mechanism of a complex and articulated ball, characterized the mechanism with three-legged elementary platforms and four-legged elementary platforms and developed mechanism decomposition in the mobility analysis of the ball"
        ],
        "surrounding_texts": []
    }
]